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Update most of libquadmath/math/ from glibc, automate update (PR libquadmath/68686). 

libquadmath sources are mostly based on glibc sources at present, but
derived from them by a manual editing / substitution process and with
subsequent manual merges.  The manual effort involved in merges means
they are sometimes incomplete and long-delayed.

Since libquadmath was first created, glibc's support for this format
has undergone significant changes so that it can also be used in glibc
to provide *f128 functions for the _Float128 type from TS 18661-3.
This makes it significantly easier to use it for libquadmath in a more
automated fashion, since glibc has a float128_private.h header that
redefines many identifiers as macros as needed for building *f128
functions.

Simply using float128_private.h directly in libquadmath, with
unmodified glibc sources except for changing function names in that
one header to be *q instead of *f128, would be tricky, given its
dependence on lots of other glibc-internal headers (whereas
libquadmath supports non-glibc systems), and also given how some libm
functions in glibc are built from type-generic templates using a
further set of macros rather than from separate function
implementations for each type.

So instead this patch adds a script update-quadmath.py to convert
glibc sources into libquadmath ones, and the script reads
float128_private.h to identify many of the substitutions it should
make.  quadmath-imp.h is updated with various new internal
definitions, taken from glibc as needed; this is the main place
expected to need updating manually when subsequent merges from glibc
are done using the script.  No attempt is made to make the script
output match the details of existing formatting, although the
differences are of a size that makes a rough comparison (ignoring
whitespace) possible.

Two new public interfaces are added to libquadmath, exp2q and
issignalingq, at a new QUADMATH_1.2 symbol version, since those
interfaces are used internally by some of the glibc sources being
merged into libquadmath; although there is a new symbol version, no
change however is made to the libtool version in the libtool-version
file.  Although there are various other interfaces now in glibc libm
but not in libquadmath, this patch does nothing to add such interfaces
(although adding many of them would in fact be easy to do, given the
script).

One internal file (not providing any public interfaces),
math/isinf_nsq.c, is removed, as no longer used by anything in
libquadmath after the merge.

Conditionals in individual source files on <fenv.h> availability or
features are moved into quadmath-imp.h (providing trivial macro
versions of the functions if real implementations aren't available),
to simplify the substitutions in individual source files.  Note
however that I haven't tested for any configurations lacking <fenv.h>,
so further changes could well be needed there.

Two files in libquadmath/math/ are based on glibc sources but not
updated in this patch: fmaq.c and rem_pio2q.c.  Both could be updated
after further changes to the script (and quadmath-imp.h as needed); in
the case of rem_pio2q.c, based on two separate glibc source files,
those separate files would naturally be split out into separate
libquadmath source files in the process (as done in this patch with
expq_table.h and tanq_kernel.c, where previously two glibc source
files had been merged into one libquadmath source file).  complex.c,
nanq.c and sqrtq.c are not based on glibc sources (though four of the
(trivial) functions in complex.c could readily be replaced by instead
using the four corresponding files from glibc, if desired).

libquadmath also has printf/ and strtod/ sources based on glibc, also
mostly not updated for a long time.  Again the script could no doubt
be made to generate those automatically, although that would be a
larger change (effectively some completely separate logic in the
script, not sharing much if anything with the existing code).

Bootstrapped with no regressions on x86_64-pc-linux-gnu.

	PR libquadmath/68686
	* Makefile.am: (libquadmath_la_SOURCES): Remove math/isinf_nsq.c.
	Add math/exp2q.c math/issignalingq.c math/lgammaq_neg.c
	math/lgammaq_product.c math/tanq_kernel.c math/tgammaq_product.c
	math/casinhq_kernel.c.
	* Makefile.in: Regenerate.
	* libquadmath.texi (exp2q, issignalingq): Document.
	* quadmath-imp.h: Include <errno.h>, <limits.h>, <stdbool.h> and
	<fenv.h>.
	(HIGH_ORDER_BIT_IS_SET_FOR_SNAN, FIX_FLT128_LONG_CONVERT_OVERFLOW)
	(FIX_FLT128_LLONG_CONVERT_OVERFLOW, __quadmath_kernel_tanq)
	(__quadmath_gamma_productq, __quadmath_gammaq_r)
	(__quadmath_lgamma_negq, __quadmath_lgamma_productq)
	(__quadmath_lgammaq_r, __quadmath_kernel_casinhq, mul_splitq)
	(math_check_force_underflow_complex, __glibc_likely)
	(__glibc_unlikely, struct rm_ctx, SET_RESTORE_ROUNDF128)
	(libc_feholdsetround_ctx, libc_feresetround_ctx): New.
	(feraiseexcept, fenv_t, feholdexcept, fesetround, feupdateenv)
	(fesetenv, fetestexcept, feclearexcept): Define if not supported
	through <fenv.h>.
	(__quadmath_isinf_nsq): Remove.
	* quadmath.h (exp2q, issignalingq): New.
	* quadmath.map (QUADMATH_1.2): New.
	* quadmath_weak.h (exp2q, issignalingq): New.
	* update-quadmath.py: New file.
	* math/isinf_nsq.c: Remove file.
	* math/casinhq_kernel.c, math/exp2q.c, math/expq_table.h,
	math/issignalingq.c, math/lgammaq_neg.c, math/lgammaq_product.c,
	math/tanq_kernel.c, math/tgammaq_product.c: New files.  Generated
	from glibc sources with update-quadmath.py.
	* math/acoshq.c, math/acosq.c, math/asinhq.c, math/asinq.c,
	math/atan2q.c, math/atanhq.c, math/atanq.c, math/cacoshq.c,
	math/cacosq.c, math/casinhq.c, math/casinq.c, math/catanhq.c,
	math/catanq.c, math/cbrtq.c, math/ccoshq.c, math/ceilq.c,
	math/cexpq.c, math/cimagq.c, math/clog10q.c, math/clogq.c,
	math/conjq.c, math/copysignq.c, math/coshq.c, math/cosq.c,
	math/cosq_kernel.c, math/cprojq.c, math/crealq.c, math/csinhq.c,
	math/csinq.c, math/csqrtq.c, math/ctanhq.c, math/ctanq.c,
	math/erfq.c, math/expm1q.c, math/expq.c, math/fabsq.c,
	math/fdimq.c, math/finiteq.c, math/floorq.c, math/fmaxq.c,
	math/fminq.c, math/fmodq.c, math/frexpq.c, math/hypotq.c,
	math/ilogbq.c, math/isinfq.c, math/isnanq.c, math/j0q.c,
	math/j1q.c, math/jnq.c, math/ldexpq.c, math/lgammaq.c,
	math/llrintq.c, math/llroundq.c, math/log10q.c, math/log1pq.c,
	math/log2q.c, math/logbq.c, math/logq.c, math/lrintq.c,
	math/lroundq.c, math/modfq.c, math/nearbyintq.c,
	math/nextafterq.c, math/powq.c, math/remainderq.c, math/remquoq.c,
	math/rintq.c, math/roundq.c, math/scalblnq.c, math/scalbnq.c,
	math/signbitq.c, math/sincos_table.c, math/sincosq.c,
	math/sincosq_kernel.c, math/sinhq.c, math/sinq.c,
	math/sinq_kernel.c, math/tanhq.c, math/tanq.c, math/tgammaq.c,
	math/truncq.c, math/x2y2m1q.c: Regenerate from glibc sources with
	update-quadmath.py.

From-SVN: r265822
devel/gomp-5_0-branch
Joseph Myers 2018-11-05 23:03:55 +00:00 committed by Joseph Myers
parent 0f31a75031
commit 4239f144ce
101 changed files with 4545 additions and 2844 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

56
libquadmath/ChangeLog
View File

@ -1,3 +1,59 @@
2018-11-05 Joseph Myers <joseph@codesourcery.com>
PR libquadmath/68686
* Makefile.am: (libquadmath_la_SOURCES): Remove math/isinf_nsq.c.
Add math/exp2q.c math/issignalingq.c math/lgammaq_neg.c
math/lgammaq_product.c math/tanq_kernel.c math/tgammaq_product.c
math/casinhq_kernel.c.
* Makefile.in: Regenerate.
* libquadmath.texi (exp2q, issignalingq): Document.
* quadmath-imp.h: Include <errno.h>, <limits.h>, <stdbool.h> and
<fenv.h>.
(HIGH_ORDER_BIT_IS_SET_FOR_SNAN, FIX_FLT128_LONG_CONVERT_OVERFLOW)
(FIX_FLT128_LLONG_CONVERT_OVERFLOW, __quadmath_kernel_tanq)
(__quadmath_gamma_productq, __quadmath_gammaq_r)
(__quadmath_lgamma_negq, __quadmath_lgamma_productq)
(__quadmath_lgammaq_r, __quadmath_kernel_casinhq, mul_splitq)
(math_check_force_underflow_complex, __glibc_likely)
(__glibc_unlikely, struct rm_ctx, SET_RESTORE_ROUNDF128)
(libc_feholdsetround_ctx, libc_feresetround_ctx): New.
(feraiseexcept, fenv_t, feholdexcept, fesetround, feupdateenv)
(fesetenv, fetestexcept, feclearexcept): Define if not supported
through <fenv.h>.
(__quadmath_isinf_nsq): Remove.
* quadmath.h (exp2q, issignalingq): New.
* quadmath.map (QUADMATH_1.2): New.
* quadmath_weak.h (exp2q, issignalingq): New.
* update-quadmath.py: New file.
* math/isinf_nsq.c: Remove file.
* math/casinhq_kernel.c, math/exp2q.c, math/expq_table.h,
math/issignalingq.c, math/lgammaq_neg.c, math/lgammaq_product.c,
math/tanq_kernel.c, math/tgammaq_product.c: New files. Generated
from glibc sources with update-quadmath.py.
* math/acoshq.c, math/acosq.c, math/asinhq.c, math/asinq.c,
math/atan2q.c, math/atanhq.c, math/atanq.c, math/cacoshq.c,
math/cacosq.c, math/casinhq.c, math/casinq.c, math/catanhq.c,
math/catanq.c, math/cbrtq.c, math/ccoshq.c, math/ceilq.c,
math/cexpq.c, math/cimagq.c, math/clog10q.c, math/clogq.c,
math/conjq.c, math/copysignq.c, math/coshq.c, math/cosq.c,
math/cosq_kernel.c, math/cprojq.c, math/crealq.c, math/csinhq.c,
math/csinq.c, math/csqrtq.c, math/ctanhq.c, math/ctanq.c,
math/erfq.c, math/expm1q.c, math/expq.c, math/fabsq.c,
math/fdimq.c, math/finiteq.c, math/floorq.c, math/fmaxq.c,
math/fminq.c, math/fmodq.c, math/frexpq.c, math/hypotq.c,
math/ilogbq.c, math/isinfq.c, math/isnanq.c, math/j0q.c,
math/j1q.c, math/jnq.c, math/ldexpq.c, math/lgammaq.c,
math/llrintq.c, math/llroundq.c, math/log10q.c, math/log1pq.c,
math/log2q.c, math/logbq.c, math/logq.c, math/lrintq.c,
math/lroundq.c, math/modfq.c, math/nearbyintq.c,
math/nextafterq.c, math/powq.c, math/remainderq.c, math/remquoq.c,
math/rintq.c, math/roundq.c, math/scalblnq.c, math/scalbnq.c,
math/signbitq.c, math/sincos_table.c, math/sincosq.c,
math/sincosq_kernel.c, math/sinhq.c, math/sinq.c,
math/sinq_kernel.c, math/tanhq.c, math/tanq.c, math/tgammaq.c,
math/truncq.c, math/x2y2m1q.c: Regenerate from glibc sources with
update-quadmath.py.
2018-10-31 Joseph Myers <joseph@codesourcery.com>
PR bootstrap/82856

4
libquadmath/Makefile.am
View File

@ -44,7 +44,7 @@ nodist_libsubinclude_HEADERS = quadmath.h quadmath_weak.h
libsubincludedir = $(libdir)/gcc/$(target_alias)/$(gcc_version)/include
libquadmath_la_SOURCES = \
math/x2y2m1q.c math/isinf_nsq.c math/acoshq.c math/fmodq.c \
math/x2y2m1q.c math/acoshq.c math/fmodq.c \
math/acosq.c math/frexpq.c \
math/rem_pio2q.c math/asinhq.c math/hypotq.c math/remainderq.c \
math/asinq.c math/rintq.c math/atan2q.c math/isinfq.c \
@ -58,6 +58,8 @@ libquadmath_la_SOURCES = \
math/tanhq.c math/expq.c math/modfq.c math/tanq.c math/fabsq.c \
math/nanq.c math/tgammaq.c math/finiteq.c math/nextafterq.c \
math/truncq.c math/floorq.c math/powq.c math/fmaq.c math/logbq.c \
math/exp2q.c math/issignalingq.c math/lgammaq_neg.c math/lgammaq_product.c \
math/tanq_kernel.c math/tgammaq_product.c math/casinhq_kernel.c \
math/cacoshq.c math/cacosq.c math/casinhq.c math/casinq.c \
math/catanhq.c math/catanq.c math/cimagq.c math/conjq.c math/cprojq.c \
math/crealq.c math/fdimq.c math/fmaxq.c math/fminq.c math/ilogbq.c \

125
libquadmath/Makefile.in
View File

@ -147,53 +147,58 @@ am__installdirs = "$(DESTDIR)$(toolexeclibdir)" "$(DESTDIR)$(infodir)" \
LTLIBRARIES = $(toolexeclib_LTLIBRARIES)
am__dirstamp = $(am__leading_dot)dirstamp
@BUILD_LIBQUADMATH_TRUE@am_libquadmath_la_OBJECTS = math/x2y2m1q.lo \
@BUILD_LIBQUADMATH_TRUE@ math/isinf_nsq.lo math/acoshq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/fmodq.lo math/acosq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/frexpq.lo math/rem_pio2q.lo \
@BUILD_LIBQUADMATH_TRUE@ math/asinhq.lo math/hypotq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/remainderq.lo math/asinq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/rintq.lo math/atan2q.lo \
@BUILD_LIBQUADMATH_TRUE@ math/isinfq.lo math/roundq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/atanhq.lo math/isnanq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/scalblnq.lo math/atanq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/j0q.lo math/scalbnq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/cbrtq.lo math/j1q.lo \
@BUILD_LIBQUADMATH_TRUE@ math/signbitq.lo math/ceilq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/jnq.lo math/sincos_table.lo \
@BUILD_LIBQUADMATH_TRUE@ math/complex.lo math/ldexpq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/sincosq.lo math/copysignq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/lgammaq.lo math/sincosq_kernel.lo \
@BUILD_LIBQUADMATH_TRUE@ math/coshq.lo math/llroundq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/sinhq.lo math/cosq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/log10q.lo math/sinq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/cosq_kernel.lo math/log1pq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/sinq_kernel.lo math/erfq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/logq.lo math/sqrtq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/expm1q.lo math/lroundq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/tanhq.lo math/expq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/modfq.lo math/tanq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/fabsq.lo math/nanq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/tgammaq.lo math/finiteq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/nextafterq.lo math/truncq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/floorq.lo math/powq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/fmaq.lo math/logbq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/cacoshq.lo math/cacosq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/casinhq.lo math/casinq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/catanhq.lo math/catanq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/cimagq.lo math/conjq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/cprojq.lo math/crealq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/fdimq.lo math/fmaxq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/fminq.lo math/ilogbq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/llrintq.lo math/log2q.lo \
@BUILD_LIBQUADMATH_TRUE@ math/lrintq.lo math/nearbyintq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/remquoq.lo math/ccoshq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/cexpq.lo math/clog10q.lo \
@BUILD_LIBQUADMATH_TRUE@ math/clogq.lo math/csinq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/csinhq.lo math/csqrtq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/ctanq.lo math/ctanhq.lo \
@BUILD_LIBQUADMATH_TRUE@ printf/addmul_1.lo printf/add_n.lo \
@BUILD_LIBQUADMATH_TRUE@ printf/cmp.lo printf/divrem.lo \
@BUILD_LIBQUADMATH_TRUE@ printf/flt1282mpn.lo \
@BUILD_LIBQUADMATH_TRUE@ math/acoshq.lo math/fmodq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/acosq.lo math/frexpq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/rem_pio2q.lo math/asinhq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/hypotq.lo math/remainderq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/asinq.lo math/rintq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/atan2q.lo math/isinfq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/roundq.lo math/atanhq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/isnanq.lo math/scalblnq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/atanq.lo math/j0q.lo \
@BUILD_LIBQUADMATH_TRUE@ math/scalbnq.lo math/cbrtq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/j1q.lo math/signbitq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/ceilq.lo math/jnq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/sincos_table.lo math/complex.lo \
@BUILD_LIBQUADMATH_TRUE@ math/ldexpq.lo math/sincosq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/copysignq.lo math/lgammaq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/sincosq_kernel.lo math/coshq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/llroundq.lo math/sinhq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/cosq.lo math/log10q.lo \
@BUILD_LIBQUADMATH_TRUE@ math/sinq.lo math/cosq_kernel.lo \
@BUILD_LIBQUADMATH_TRUE@ math/log1pq.lo math/sinq_kernel.lo \
@BUILD_LIBQUADMATH_TRUE@ math/erfq.lo math/logq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/sqrtq.lo math/expm1q.lo \
@BUILD_LIBQUADMATH_TRUE@ math/lroundq.lo math/tanhq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/expq.lo math/modfq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/tanq.lo math/fabsq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/nanq.lo math/tgammaq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/finiteq.lo math/nextafterq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/truncq.lo math/floorq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/powq.lo math/fmaq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/logbq.lo math/exp2q.lo \
@BUILD_LIBQUADMATH_TRUE@ math/issignalingq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/lgammaq_neg.lo \
@BUILD_LIBQUADMATH_TRUE@ math/lgammaq_product.lo \
@BUILD_LIBQUADMATH_TRUE@ math/tanq_kernel.lo \
@BUILD_LIBQUADMATH_TRUE@ math/tgammaq_product.lo \
@BUILD_LIBQUADMATH_TRUE@ math/casinhq_kernel.lo math/cacoshq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/cacosq.lo math/casinhq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/casinq.lo math/catanhq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/catanq.lo math/cimagq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/conjq.lo math/cprojq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/crealq.lo math/fdimq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/fmaxq.lo math/fminq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/ilogbq.lo math/llrintq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/log2q.lo math/lrintq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/nearbyintq.lo math/remquoq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/ccoshq.lo math/cexpq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/clog10q.lo math/clogq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/csinq.lo math/csinhq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/csqrtq.lo math/ctanq.lo \
@BUILD_LIBQUADMATH_TRUE@ math/ctanhq.lo printf/addmul_1.lo \
@BUILD_LIBQUADMATH_TRUE@ printf/add_n.lo printf/cmp.lo \
@BUILD_LIBQUADMATH_TRUE@ printf/divrem.lo printf/flt1282mpn.lo \
@BUILD_LIBQUADMATH_TRUE@ printf/fpioconst.lo printf/lshift.lo \
@BUILD_LIBQUADMATH_TRUE@ printf/mul_1.lo printf/mul_n.lo \
@BUILD_LIBQUADMATH_TRUE@ printf/mul.lo printf/printf_fphex.lo \
@ -464,7 +469,7 @@ AUTOMAKE_OPTIONS = foreign info-in-builddir
@BUILD_LIBQUADMATH_TRUE@nodist_libsubinclude_HEADERS = quadmath.h quadmath_weak.h
@BUILD_LIBQUADMATH_TRUE@libsubincludedir = $(libdir)/gcc/$(target_alias)/$(gcc_version)/include
@BUILD_LIBQUADMATH_TRUE@libquadmath_la_SOURCES = \
@BUILD_LIBQUADMATH_TRUE@ math/x2y2m1q.c math/isinf_nsq.c math/acoshq.c math/fmodq.c \
@BUILD_LIBQUADMATH_TRUE@ math/x2y2m1q.c math/acoshq.c math/fmodq.c \
@BUILD_LIBQUADMATH_TRUE@ math/acosq.c math/frexpq.c \
@BUILD_LIBQUADMATH_TRUE@ math/rem_pio2q.c math/asinhq.c math/hypotq.c math/remainderq.c \
@BUILD_LIBQUADMATH_TRUE@ math/asinq.c math/rintq.c math/atan2q.c math/isinfq.c \
@ -478,6 +483,8 @@ AUTOMAKE_OPTIONS = foreign info-in-builddir
@BUILD_LIBQUADMATH_TRUE@ math/tanhq.c math/expq.c math/modfq.c math/tanq.c math/fabsq.c \
@BUILD_LIBQUADMATH_TRUE@ math/nanq.c math/tgammaq.c math/finiteq.c math/nextafterq.c \
@BUILD_LIBQUADMATH_TRUE@ math/truncq.c math/floorq.c math/powq.c math/fmaq.c math/logbq.c \
@BUILD_LIBQUADMATH_TRUE@ math/exp2q.c math/issignalingq.c math/lgammaq_neg.c math/lgammaq_product.c \
@BUILD_LIBQUADMATH_TRUE@ math/tanq_kernel.c math/tgammaq_product.c math/casinhq_kernel.c \
@BUILD_LIBQUADMATH_TRUE@ math/cacoshq.c math/cacosq.c math/casinhq.c math/casinq.c \
@BUILD_LIBQUADMATH_TRUE@ math/catanhq.c math/catanq.c math/cimagq.c math/conjq.c math/cprojq.c \
@BUILD_LIBQUADMATH_TRUE@ math/crealq.c math/fdimq.c math/fmaxq.c math/fminq.c math/ilogbq.c \
@ -661,7 +668,6 @@ math/$(DEPDIR)/$(am__dirstamp):
@$(MKDIR_P) math/$(DEPDIR)
@: > math/$(DEPDIR)/$(am__dirstamp)
math/x2y2m1q.lo: math/$(am__dirstamp) math/$(DEPDIR)/$(am__dirstamp)
math/isinf_nsq.lo: math/$(am__dirstamp) math/$(DEPDIR)/$(am__dirstamp)
math/acoshq.lo: math/$(am__dirstamp) math/$(DEPDIR)/$(am__dirstamp)
math/fmodq.lo: math/$(am__dirstamp) math/$(DEPDIR)/$(am__dirstamp)
math/acosq.lo: math/$(am__dirstamp) math/$(DEPDIR)/$(am__dirstamp)
@ -727,6 +733,19 @@ math/floorq.lo: math/$(am__dirstamp) math/$(DEPDIR)/$(am__dirstamp)
math/powq.lo: math/$(am__dirstamp) math/$(DEPDIR)/$(am__dirstamp)
math/fmaq.lo: math/$(am__dirstamp) math/$(DEPDIR)/$(am__dirstamp)
math/logbq.lo: math/$(am__dirstamp) math/$(DEPDIR)/$(am__dirstamp)
math/exp2q.lo: math/$(am__dirstamp) math/$(DEPDIR)/$(am__dirstamp)
math/issignalingq.lo: math/$(am__dirstamp) \
math/$(DEPDIR)/$(am__dirstamp)
math/lgammaq_neg.lo: math/$(am__dirstamp) \
math/$(DEPDIR)/$(am__dirstamp)
math/lgammaq_product.lo: math/$(am__dirstamp) \
math/$(DEPDIR)/$(am__dirstamp)
math/tanq_kernel.lo: math/$(am__dirstamp) \
math/$(DEPDIR)/$(am__dirstamp)
math/tgammaq_product.lo: math/$(am__dirstamp) \
math/$(DEPDIR)/$(am__dirstamp)
math/casinhq_kernel.lo: math/$(am__dirstamp) \
math/$(DEPDIR)/$(am__dirstamp)
math/cacoshq.lo: math/$(am__dirstamp) math/$(DEPDIR)/$(am__dirstamp)
math/cacosq.lo: math/$(am__dirstamp) math/$(DEPDIR)/$(am__dirstamp)
math/casinhq.lo: math/$(am__dirstamp) math/$(DEPDIR)/$(am__dirstamp)
@ -830,6 +849,7 @@ distclean-compile:
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/cacoshq.Plo@am__quote@
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/cacosq.Plo@am__quote@
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/casinhq.Plo@am__quote@
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/casinhq_kernel.Plo@am__quote@
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/casinq.Plo@am__quote@
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/catanhq.Plo@am__quote@
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/catanq.Plo@am__quote@
@ -854,6 +874,7 @@ distclean-compile:
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/ctanhq.Plo@am__quote@
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/ctanq.Plo@am__quote@
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/erfq.Plo@am__quote@
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/exp2q.Plo@am__quote@
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/expm1q.Plo@am__quote@
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/expq.Plo@am__quote@
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/fabsq.Plo@am__quote@
@ -867,14 +888,16 @@ distclean-compile:
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/frexpq.Plo@am__quote@
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/hypotq.Plo@am__quote@
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/ilogbq.Plo@am__quote@
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/isinf_nsq.Plo@am__quote@
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/isinfq.Plo@am__quote@
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/isnanq.Plo@am__quote@
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/issignalingq.Plo@am__quote@
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/j0q.Plo@am__quote@
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/j1q.Plo@am__quote@
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/jnq.Plo@am__quote@
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/ldexpq.Plo@am__quote@
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/lgammaq.Plo@am__quote@
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/lgammaq_neg.Plo@am__quote@
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/lgammaq_product.Plo@am__quote@
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/llrintq.Plo@am__quote@
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/llroundq.Plo@am__quote@
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/log10q.Plo@am__quote@
@ -906,7 +929,9 @@ distclean-compile:
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/sqrtq.Plo@am__quote@
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/tanhq.Plo@am__quote@
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/tanq.Plo@am__quote@
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/tanq_kernel.Plo@am__quote@
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/tgammaq.Plo@am__quote@
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/tgammaq_product.Plo@am__quote@
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/truncq.Plo@am__quote@
@AMDEP_TRUE@@am__include@ @am__quote@math/$(DEPDIR)/x2y2m1q.Plo@am__quote@
@AMDEP_TRUE@@am__include@ @am__quote@printf/$(DEPDIR)/add_n.Plo@am__quote@

2
libquadmath/libquadmath.texi
View File

@ -157,6 +157,7 @@ The following mathematical functions are available:
@item @code{cosq}: cosine function
@item @code{erfq}: error function
@item @code{erfcq}: complementary error function
@item @code{exp2q}: base 2 exponential function
@item @code{expq}: exponential function
@item @code{expm1q}: exponential minus 1 function
@need 800
@ -173,6 +174,7 @@ The following mathematical functions are available:
@item @code{ilogbq}: get exponent of the value
@item @code{isinfq}: check for infinity
@item @code{isnanq}: check for not a number
@item @code{issignalingq}: check for signaling not a number
@item @code{j0q}: Bessel function of the first kind, first order
@item @code{j1q}: Bessel function of the first kind, second order
@item @code{jnq}: Bessel function of the first kind, @var{n}-th order

24
libquadmath/math/acoshq.c
View File

@ -1,4 +1,4 @@
/* acoshq.c -- __float128 version of e_acosh.c.
/* e_acoshl.c -- long double version of e_acosh.c.
* Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
@ -16,11 +16,11 @@
/* acoshq(x)
* Method :
* Based on
* acoshl(x) = logl [ x + sqrtl(x*x-1) ]
* acoshl(x) = logq [ x + sqrtq(x*x-1) ]
* we have
* acoshl(x) := logl(x)+ln2, if x is large; else
* acoshl(x) := logl(2x-1/(sqrtl(x*x-1)+x)) if x>2; else
* acoshl(x) := log1pl(t+sqrtl(2.0*t+t*t)); where t=x-1.
* acoshl(x) := logq(x)+ln2, if x is large; else
* acoshl(x) := logq(2x-1/(sqrtq(x*x-1)+x)) if x>2; else
* acoshl(x) := log1pq(t+sqrtq(2.0*t+t*t)); where t=x-1.
*
* Special cases:
* acoshl(x) is NaN with signal if x<1.
@ -30,11 +30,11 @@
#include "quadmath-imp.h"
static const __float128
one = 1.0Q,
one = 1.0,
ln2 = 0.6931471805599453094172321214581766Q;
__float128
acoshq (__float128 x)
acoshq(__float128 x)
{
__float128 t;
uint64_t lx;
@ -44,16 +44,16 @@ acoshq (__float128 x)
return (x-x)/(x-x);
} else if(hx >=0x4035000000000000LL) { /* x > 2**54 */
if(hx >=0x7fff000000000000LL) { /* x is inf of NaN */
return x+x;
return x+x;
} else
return logq(x)+ln2; /* acoshl(huge)=logl(2x) */
return logq(x)+ln2; /* acoshl(huge)=logq(2x) */
} else if(((hx-0x3fff000000000000LL)|lx)==0) {
return 0.0Q; /* acosh(1) = 0 */
return 0; /* acosh(1) = 0 */
} else if (hx > 0x4000000000000000LL) { /* 2**28 > x > 2 */
t=x*x;
return logq(2.0Q*x-one/(x+sqrtq(t-one)));
return logq(2*x-one/(x+sqrtq(t-one)));
} else { /* 1<x<2 */
t = x-one;
return log1pq(t+sqrtq(2.0Q*t+t*t));
return log1pq(t+sqrtq(2*t+t*t));
}
}

18
libquadmath/math/acosq.c
View File

@ -10,11 +10,11 @@
*/
/*
__float128 expansions are
Long double expansions are
Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
and are incorporated herein by permission of the author. The author
and are incorporated herein by permission of the author. The author
reserves the right to distribute this material elsewhere under different
copying permissions. These modifications are distributed here under
copying permissions. These modifications are distributed here under
the following terms:
This library is free software; you can redistribute it and/or
@ -28,8 +28,8 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
License along with this library; if not, see
<http://www.gnu.org/licenses/>. */
/* acosq(x)
* Method :
@ -57,7 +57,7 @@
#include "quadmath-imp.h"
static const __float128
one = 1.0Q,
one = 1,
pio2_hi = 1.5707963267948966192313216916397514420986Q,
pio2_lo = 4.3359050650618905123985220130216759843812E-35Q,
@ -272,11 +272,11 @@ acosq (__float128 x)
s = sqrtq (z);
/* Compute an extended precision square root from
the Newton iteration s -> 0.5 * (s + z / s).
The change w from s to the improved value is
The change w from s to the improved value is
w = 0.5 * (s + z / s) - s = (s^2 + z)/2s - s = (z - s^2)/2s.
Express s = f1 + f2 where f1 * f1 is exactly representable.
Express s = f1 + f2 where f1 * f1 is exactly representable.
w = (z - s^2)/2s = (z - f1^2 - 2 f1 f2 - f2^2)/2s .
s + w has extended precision. */
s + w has extended precision. */
u.value = s;
u.words32.w2 = 0;
u.words32.w3 = 0;

20
libquadmath/math/asinhq.c
View File

@ -1,4 +1,4 @@
/* asinhq.c -- __float128 version of s_asinh.c.
/* s_asinhl.c -- long double version of s_asinh.c.
* Conversion to long double by Ulrich Drepper,
* Cygnus Support, drepper@cygnus.com.
*/
@ -14,21 +14,25 @@
* ====================================================
*/
/* asinhl(x)
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: $";
#endif
/* asinhq(x)
* Method :
* Based on
* asinhl(x) = signl(x) * logl [ |x| + sqrtl(x*x+1) ]
* asinhq(x) = signl(x) * logq [ |x| + sqrtq(x*x+1) ]
* we have
* asinhl(x) := x if 1+x*x=1,
* := signl(x)*(logl(x)+ln2)) for large |x|, else
* := signl(x)*logl(2|x|+1/(|x|+sqrtl(x*x+1))) if|x|>2, else
* := signl(x)*log1pl(|x| + x^2/(1 + sqrtl(1+x^2)))
* asinhq(x) := x if 1+x*x=1,
* := signl(x)*(logq(x)+ln2)) for large |x|, else
* := signl(x)*logq(2|x|+1/(|x|+sqrtq(x*x+1))) if|x|>2, else
* := signl(x)*log1pq(|x| + x^2/(1 + sqrtq(1+x^2)))
*/
#include "quadmath-imp.h"
static const __float128
one = 1.0Q,
one = 1,
ln2 = 6.931471805599453094172321214581765681e-1Q,
huge = 1.0e+4900Q;

20
libquadmath/math/asinq.c
View File

@ -10,11 +10,11 @@
*/
/*
__float128 expansions are
Long double expansions are
Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
and are incorporated herein by permission of the author. The author
reserves the right to distribute this material elsewhere under different
copying permissions. These modifications are distributed here under the
and are incorporated herein by permission of the author. The author
reserves the right to distribute this material elsewhere under different
copying permissions. These modifications are distributed here under the
following terms:
This library is free software; you can redistribute it and/or
@ -28,10 +28,10 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
License along with this library; if not, see
<http://www.gnu.org/licenses/>. */
/* asinq(x)
/* __ieee754_asin(x)
* Method :
* Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
* we approximate asin(x) on [0,0.5] by
@ -58,11 +58,10 @@
*
*/
#include "quadmath-imp.h"
static const __float128
one = 1.0Q,
one = 1,
huge = 1.0e+4932Q,
pio2_hi = 1.5707963267948966192313216916397514420986Q,
pio2_lo = 4.3359050650618905123985220130216759843812E-35Q,
@ -129,8 +128,7 @@ static const __float128
__float128
asinq (__float128 x)
{
__float128 t = 0;
__float128 w, p, q, c, r, s;
__float128 t, w, p, q, c, r, s;
int32_t ix, sign, flag;
ieee854_float128 u;

24
libquadmath/math/atan2q.c
View File

@ -1,4 +1,4 @@
/* atan2q.c -- __float128 version of e_atan2.c.
/* e_atan2l.c -- long double version of e_atan2.c.
* Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
@ -15,9 +15,9 @@
/* atan2q(y,x)
* Method :
* 1. Reduce y to positive by atan2q(y,x)=-atan2q(-y,x).
* 1. Reduce y to positive by atan2l(y,x)=-atan2l(-y,x).
* 2. Reduce x to positive by (if x and y are unexceptional):
* ARG (x+iy) = arctan(y/x) ... if x > 0,
* ARG (x+iy) = arctan(y/x) ... if x > 0,
* ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
*
* Special cases:
@ -51,7 +51,7 @@ pi = 3.14159265358979323846264338327950280e+00Q, /* 4000921fb54442d18469898
pi_lo = 8.67181013012378102479704402604335225e-35Q; /* 3f8dcd129024e088a67cc74020bbea64 */
__float128
atan2q (__float128 y, __float128 x)
atan2q(__float128 y, __float128 x)
{
__float128 z;
int64_t k,m,hx,hy,ix,iy;
@ -64,14 +64,14 @@ atan2q (__float128 y, __float128 x)
if(((ix|((lx|-lx)>>63))>0x7fff000000000000LL)||
((iy|((ly|-ly)>>63))>0x7fff000000000000LL)) /* x or y is NaN */
return x+y;
if(((hx-0x3fff000000000000LL)|lx)==0) return atanq(y); /* x=1.0Q */
if(((hx-0x3fff000000000000LL)|lx)==0) return atanq(y); /* x=1.0L */
m = ((hy>>63)&1)|((hx>>62)&2); /* 2*sign(x)+sign(y) */
/* when y = 0 */
if((iy|ly)==0) {
switch(m) {
case 0:
case 1: return y; /* atan(+-0,+anything)=+-0 */
case 1: return y; /* atan(+-0,+anything)=+-0 */
case 2: return pi+tiny;/* atan(+0,-anything) = pi */
case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
}
@ -85,8 +85,8 @@ atan2q (__float128 y, __float128 x)
switch(m) {
case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
case 2: return 3.0Q*pi_o_4+tiny;/*atan(+INF,-INF)*/
case 3: return -3.0Q*pi_o_4-tiny;/*atan(-INF,-INF)*/
case 2: return 3*pi_o_4+tiny;/*atan(+INF,-INF)*/
case 3: return -3*pi_o_4-tiny;/*atan(-INF,-INF)*/
}
} else {
switch(m) {
@ -102,19 +102,19 @@ atan2q (__float128 y, __float128 x)
/* compute y/x */
k = (iy-ix)>>48;
if(k > 120) z=pi_o_2+0.5Q*pi_lo; /* |y/x| > 2**120 */
else if(hx<0&&k<-120) z=0.0Q; /* |y|/x < -2**120 */
if(k > 120) z=pi_o_2+0.5Q*pi_lo; /* |y/x| > 2**120 */
else if(hx<0&&k<-120) z=0; /* |y|/x < -2**120 */
else z=atanq(fabsq(y/x)); /* safe to do y/x */
switch (m) {
case 0: return z ; /* atan(+,+) */
case 1: {
uint64_t zh;
uint64_t zh;
GET_FLT128_MSW64(zh,z);
SET_FLT128_MSW64(z,zh ^ 0x8000000000000000ULL);
}
return z ; /* atan(-,+) */
case 2: return pi-(z-pi_lo);/* atan(+,-) */
default: /* case 3 */
return (z-pi_lo)-pi;/* atan(-,-) */
return (z-pi_lo)-pi;/* atan(-,-) */
}
}

15
libquadmath/math/atanhq.c
View File

@ -1,5 +1,5 @@
/* s_atanhl.c -- __float128 version of s_atan.c.
* Conversion to __float128 by Ulrich Drepper,
/* s_atanhl.c -- long double version of s_atan.c.
* Conversion to long double by Ulrich Drepper,
* Cygnus Support, drepper@cygnus.com.
*/
@ -22,8 +22,8 @@
* atanhl(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
* 2 1 - x 1 - x
*
* For x<0.5
* atanhl(x) = 0.5*log1pl(2x+2x*x/(1-x))
* For x<0.5
* atanhl(x) = 0.5*log1pq(2x+2x*x/(1-x))
*
* Special cases:
* atanhl(x) is NaN if |x| > 1 with signal;
@ -34,11 +34,12 @@
#include "quadmath-imp.h"
static const __float128 one = 1.0Q, huge = 1e4900Q;
static const __float128 zero = 0.0Q;
static const __float128 one = 1, huge = 1e4900Q;
static const __float128 zero = 0;
__float128
atanhq (__float128 x)
atanhq(__float128 x)
{
__float128 t;
uint32_t jx, ix;

13
libquadmath/math/atanq.c
View File

@ -1,15 +1,15 @@
/* s_atanl.c
*
* Inverse circular tangent for 128-bit __float128 precision
* Inverse circular tangent for 128-bit long double precision
* (arctangent)
*
*
*
* SYNOPSIS:
*
* __float128 x, y, atanl();
* long double x, y, atanq();
*
* y = atanl( x );
* y = atanq( x );
*
*
*
@ -55,9 +55,8 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
License along with this library; if not, see
<http://www.gnu.org/licenses/>. */
#include "quadmath-imp.h"
@ -228,7 +227,7 @@ atanq (__float128 x)
/* Index of nearest table element.
Roundoff to integer is asymmetrical to avoid cancellation when t < 0
(cf. fdlibm). */
k = 8.0Q * x + 0.25Q;
k = 8.0 * x + 0.25;
u = 0.125Q * k;
/* Small arctan argument. */
t = (x - u) / (1.0 + x * u);

61
libquadmath/math/cacoshq.c
View File

@ -1,5 +1,5 @@
/* Return arc hyperbole cosine for __float128 value.
Copyright (C) 1997, 1998, 2006 Free Software Foundation, Inc.
/* Return arc hyperbolic cosine for a complex type.
Copyright (C) 1997-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
@ -14,13 +14,11 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#include "quadmath-imp.h"
__complex128
cacoshq (__complex128 x)
{
@ -38,57 +36,54 @@ cacoshq (__complex128 x)
__imag__ res = nanq ("");
else
__imag__ res = copysignq ((rcls == QUADFP_INFINITE
? (__real__ x < 0.0
? M_PIq - M_PI_4q : M_PI_4q)
: M_PI_2q), __imag__ x);
? (__real__ x < 0
? M_PIq - M_PI_4q
: M_PI_4q)
: M_PI_2q), __imag__ x);
}
else if (rcls == QUADFP_INFINITE)
{
__real__ res = HUGE_VALQ;
if (icls >= QUADFP_ZERO)
__imag__ res = copysignq (signbitq (__real__ x) ? M_PIq : 0.0,
__imag__ x);
__imag__ res = copysignq (signbitq (__real__ x)
? M_PIq : 0, __imag__ x);
else
__imag__ res = nanq ("");
}
else
{
__real__ res = nanq ("");
__imag__ res = nanq ("");
if (rcls == QUADFP_ZERO)
__imag__ res = M_PI_2q;
else
__imag__ res = nanq ("");
}
}
else if (rcls == QUADFP_ZERO && icls == QUADFP_ZERO)
{
__real__ res = 0.0;
__real__ res = 0;
__imag__ res = copysignq (M_PI_2q, __imag__ x);
}
/* The factor 16 is just a guess. */
else if (16.0Q * fabsq (__imag__ x) < fabsq (__real__ x))
{
/* Kahan's formula which avoid cancellation through subtraction in
some cases. */
res = 2.0Q * clogq (csqrtq ((x + 1.0Q) / 2.0Q)
+ csqrtq ((x - 1.0Q) / 2.0Q));
if (signbitq (__real__ res))
__real__ res = 0.0Q;
}
else
{
__complex128 y;
__real__ y = (__real__ x - __imag__ x) * (__real__ x + __imag__ x) - 1.0;
__imag__ y = 2.0 * __real__ x * __imag__ x;
__real__ y = -__imag__ x;
__imag__ y = __real__ x;
y = csqrtq (y);
y = __quadmath_kernel_casinhq (y, 1);
if (signbitq (x))
y = -y;
__real__ y += __real__ x;
__imag__ y += __imag__ x;
res = clogq (y);
if (signbitq (__imag__ x))
{
__real__ res = __real__ y;
__imag__ res = -__imag__ y;
}
else
{
__real__ res = -__real__ y;
__imag__ res = __imag__ y;
}
}
return res;

33
libquadmath/math/cacosq.c
View File

@ -1,5 +1,5 @@
/* Return cosine of complex __float128 value.
Copyright (C) 1997, 1998 Free Software Foundation, Inc.
/* Return cosine of a complex type.
Copyright (C) 1997-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
@ -14,9 +14,8 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#include "quadmath-imp.h"
@ -25,11 +24,29 @@ cacosq (__complex128 x)
{
__complex128 y;
__complex128 res;
int rcls = fpclassifyq (__real__ x);
int icls = fpclassifyq (__imag__ x);
y = casinq (x);
if (rcls <= QUADFP_INFINITE || icls <= QUADFP_INFINITE
|| (rcls == QUADFP_ZERO && icls == QUADFP_ZERO))
{
y = casinq (x);
__real__ res = M_PI_2q - __real__ y;
__imag__ res = -__imag__ y;
__real__ res = (__float128) M_PI_2q - __real__ y;
if (__real__ res == 0)
__real__ res = 0;
__imag__ res = -__imag__ y;
}
else
{
__real__ y = -__imag__ x;
__imag__ y = __real__ x;
y = __quadmath_kernel_casinhq (y, 1);
__real__ res = __imag__ y;
__imag__ res = __real__ y;
}
return res;
}

34
libquadmath/math/casinhq.c
View File

@ -1,5 +1,5 @@
/* Return arc hyperbole sine for __float128 value.
Copyright (C) 1997, 1998 Free Software Foundation, Inc.
/* Return arc hyperbolic sine for a complex float type.
Copyright (C) 1997-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
@ -14,13 +14,11 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#include "quadmath-imp.h"
__complex128
casinhq (__complex128 x)
{
@ -37,15 +35,16 @@ casinhq (__complex128 x)
if (rcls == QUADFP_NAN)
__imag__ res = nanq ("");
else
__imag__ res = copysignq (rcls >= QUADFP_ZERO ? M_PI_2q : M_PI_4q,
__imag__ x);
__imag__ res = copysignq ((rcls >= QUADFP_ZERO
? M_PI_2q : M_PI_4q),
__imag__ x);
}
else if (rcls <= QUADFP_INFINITE)
{
__real__ res = __real__ x;
if ((rcls == QUADFP_INFINITE && icls >= QUADFP_ZERO)
|| (rcls == QUADFP_NAN && icls == QUADFP_ZERO))
__imag__ res = copysignq (0.0, __imag__ x);
__imag__ res = copysignq (0, __imag__ x);
else
__imag__ res = nanq ("");
}
@ -61,22 +60,7 @@ casinhq (__complex128 x)
}
else
{
__complex128 y;
__real__ y = (__real__ x - __imag__ x) * (__real__ x + __imag__ x) + 1.0;
__imag__ y = 2.0 * __real__ x * __imag__ x;
y = csqrtq (y);
__real__ y += __real__ x;
__imag__ y += __imag__ x;
res = clogq (y);
/* Ensure zeros have correct sign and results are correct if
very close to branch cuts. */
__real__ res = copysignq (__real__ res, __real__ x);
__imag__ res = copysignq (__imag__ res, __imag__ x);
res = __quadmath_kernel_casinhq (x, 0);
}
return res;

202
libquadmath/math/casinhq_kernel.c Normal file
View File

@ -0,0 +1,202 @@
/* Return arc hyperbolic sine for a complex float type, with the
imaginary part of the result possibly adjusted for use in
computing other functions.
Copyright (C) 1997-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#include "quadmath-imp.h"
/* Return the complex inverse hyperbolic sine of finite nonzero Z,
with the imaginary part of the result subtracted from pi/2 if ADJ
is nonzero. */
__complex128
__quadmath_kernel_casinhq (__complex128 x, int adj)
{
__complex128 res;
__float128 rx, ix;
__complex128 y;
/* Avoid cancellation by reducing to the first quadrant. */
rx = fabsq (__real__ x);
ix = fabsq (__imag__ x);
if (rx >= 1 / FLT128_EPSILON || ix >= 1 / FLT128_EPSILON)
{
/* For large x in the first quadrant, x + csqrt (1 + x * x)
is sufficiently close to 2 * x to make no significant
difference to the result; avoid possible overflow from
the squaring and addition. */
__real__ y = rx;
__imag__ y = ix;
if (adj)
{
__float128 t = __real__ y;
__real__ y = copysignq (__imag__ y, __imag__ x);
__imag__ y = t;
}
res = clogq (y);
__real__ res += (__float128) M_LN2q;
}
else if (rx >= 0.5Q && ix < FLT128_EPSILON / 8)
{
__float128 s = hypotq (1, rx);
__real__ res = logq (rx + s);
if (adj)
__imag__ res = atan2q (s, __imag__ x);
else
__imag__ res = atan2q (ix, s);
}
else if (rx < FLT128_EPSILON / 8 && ix >= 1.5Q)
{
__float128 s = sqrtq ((ix + 1) * (ix - 1));
__real__ res = logq (ix + s);
if (adj)
__imag__ res = atan2q (rx, copysignq (s, __imag__ x));
else
__imag__ res = atan2q (s, rx);
}
else if (ix > 1 && ix < 1.5Q && rx < 0.5Q)
{
if (rx < FLT128_EPSILON * FLT128_EPSILON)
{
__float128 ix2m1 = (ix + 1) * (ix - 1);
__float128 s = sqrtq (ix2m1);
__real__ res = log1pq (2 * (ix2m1 + ix * s)) / 2;
if (adj)
__imag__ res = atan2q (rx, copysignq (s, __imag__ x));
else
__imag__ res = atan2q (s, rx);
}
else
{
__float128 ix2m1 = (ix + 1) * (ix - 1);
__float128 rx2 = rx * rx;
__float128 f = rx2 * (2 + rx2 + 2 * ix * ix);
__float128 d = sqrtq (ix2m1 * ix2m1 + f);
__float128 dp = d + ix2m1;
__float128 dm = f / dp;
__float128 r1 = sqrtq ((dm + rx2) / 2);
__float128 r2 = rx * ix / r1;
__real__ res = log1pq (rx2 + dp + 2 * (rx * r1 + ix * r2)) / 2;
if (adj)
__imag__ res = atan2q (rx + r1, copysignq (ix + r2, __imag__ x));
else
__imag__ res = atan2q (ix + r2, rx + r1);
}
}
else if (ix == 1 && rx < 0.5Q)
{
if (rx < FLT128_EPSILON / 8)
{
__real__ res = log1pq (2 * (rx + sqrtq (rx))) / 2;
if (adj)
__imag__ res = atan2q (sqrtq (rx), copysignq (1, __imag__ x));
else
__imag__ res = atan2q (1, sqrtq (rx));
}
else
{
__float128 d = rx * sqrtq (4 + rx * rx);
__float128 s1 = sqrtq ((d + rx * rx) / 2);
__float128 s2 = sqrtq ((d - rx * rx) / 2);
__real__ res = log1pq (rx * rx + d + 2 * (rx * s1 + s2)) / 2;
if (adj)
__imag__ res = atan2q (rx + s1, copysignq (1 + s2, __imag__ x));
else
__imag__ res = atan2q (1 + s2, rx + s1);
}
}
else if (ix < 1 && rx < 0.5Q)
{
if (ix >= FLT128_EPSILON)
{
if (rx < FLT128_EPSILON * FLT128_EPSILON)
{
__float128 onemix2 = (1 + ix) * (1 - ix);
__float128 s = sqrtq (onemix2);
__real__ res = log1pq (2 * rx / s) / 2;
if (adj)
__imag__ res = atan2q (s, __imag__ x);
else
__imag__ res = atan2q (ix, s);
}
else
{
__float128 onemix2 = (1 + ix) * (1 - ix);
__float128 rx2 = rx * rx;
__float128 f = rx2 * (2 + rx2 + 2 * ix * ix);
__float128 d = sqrtq (onemix2 * onemix2 + f);
__float128 dp = d + onemix2;
__float128 dm = f / dp;
__float128 r1 = sqrtq ((dp + rx2) / 2);
__float128 r2 = rx * ix / r1;
__real__ res = log1pq (rx2 + dm + 2 * (rx * r1 + ix * r2)) / 2;
if (adj)
__imag__ res = atan2q (rx + r1, copysignq (ix + r2,
__imag__ x));
else
__imag__ res = atan2q (ix + r2, rx + r1);
}
}
else
{
__float128 s = hypotq (1, rx);
__real__ res = log1pq (2 * rx * (rx + s)) / 2;
if (adj)
__imag__ res = atan2q (s, __imag__ x);
else
__imag__ res = atan2q (ix, s);
}
math_check_force_underflow_nonneg (__real__ res);
}
else
{
__real__ y = (rx - ix) * (rx + ix) + 1;
__imag__ y = 2 * rx * ix;
y = csqrtq (y);
__real__ y += rx;
__imag__ y += ix;
if (adj)
{
__float128 t = __real__ y;
__real__ y = copysignq (__imag__ y, __imag__ x);
__imag__ y = t;
}
res = clogq (y);
}
/* Give results the correct sign for the original argument. */
__real__ res = copysignq (__real__ res, __real__ x);
__imag__ res = copysignq (__imag__ res, (adj ? 1 : __imag__ x));
return res;
}

12
libquadmath/math/casinq.c
View File

@ -1,5 +1,5 @@
/* Return arc sine of complex __float128 value.
Copyright (C) 1997 Free Software Foundation, Inc.
/* Return arc sine of a complex float type.
Copyright (C) 1997-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
@ -14,13 +14,11 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#include "quadmath-imp.h"
__complex128
casinq (__complex128 x)
{
@ -28,7 +26,7 @@ casinq (__complex128 x)
if (isnanq (__real__ x) || isnanq (__imag__ x))
{
if (__real__ x == 0.0)
if (__real__ x == 0)
{
res = x;
}

92
libquadmath/math/catanhq.c
View File

@ -1,5 +1,5 @@
/* Return arc hyperbole tangent for __float128 value.
Copyright (C) 1997, 1998 Free Software Foundation, Inc.
/* Return arc hyperbolic tangent for a complex float type.
Copyright (C) 1997-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
@ -14,13 +14,11 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#include "quadmath-imp.h"
__complex128
catanhq (__complex128 x)
{
@ -28,16 +26,16 @@ catanhq (__complex128 x)
int rcls = fpclassifyq (__real__ x);
int icls = fpclassifyq (__imag__ x);
if (rcls <= QUADFP_INFINITE || icls <= QUADFP_INFINITE)
if (__glibc_unlikely (rcls <= QUADFP_INFINITE || icls <= QUADFP_INFINITE))
{
if (icls == QUADFP_INFINITE)
{
__real__ res = copysignq (0.0, __real__ x);
__real__ res = copysignq (0, __real__ x);
__imag__ res = copysignq (M_PI_2q, __imag__ x);
}
else if (rcls == QUADFP_INFINITE || rcls == QUADFP_ZERO)
{
__real__ res = copysignq (0.0, __real__ x);
__real__ res = copysignq (0, __real__ x);
if (icls >= QUADFP_ZERO)
__imag__ res = copysignq (M_PI_2q, __imag__ x);
else
@ -49,27 +47,83 @@ catanhq (__complex128 x)
__imag__ res = nanq ("");
}
}
else if (rcls == QUADFP_ZERO && icls == QUADFP_ZERO)
else if (__glibc_unlikely (rcls == QUADFP_ZERO && icls == QUADFP_ZERO))
{
res = x;
}
else
{
__float128 i2, num, den;
if (fabsq (__real__ x) >= 16 / FLT128_EPSILON
|| fabsq (__imag__ x) >= 16 / FLT128_EPSILON)
{
__imag__ res = copysignq (M_PI_2q, __imag__ x);
if (fabsq (__imag__ x) <= 1)
__real__ res = 1 / __real__ x;
else if (fabsq (__real__ x) <= 1)
__real__ res = __real__ x / __imag__ x / __imag__ x;
else
{
__float128 h = hypotq (__real__ x / 2, __imag__ x / 2);
__real__ res = __real__ x / h / h / 4;
}
}
else
{
if (fabsq (__real__ x) == 1
&& fabsq (__imag__ x) < FLT128_EPSILON * FLT128_EPSILON)
__real__ res = (copysignq (0.5Q, __real__ x)
* ((__float128) M_LN2q
- logq (fabsq (__imag__ x))));
else
{
__float128 i2 = 0;
if (fabsq (__imag__ x) >= FLT128_EPSILON * FLT128_EPSILON)
i2 = __imag__ x * __imag__ x;
i2 = __imag__ x * __imag__ x;
__float128 num = 1 + __real__ x;
num = i2 + num * num;
num = 1.0 + __real__ x;
num = i2 + num * num;
__float128 den = 1 - __real__ x;
den = i2 + den * den;
den = 1.0 - __real__ x;
den = i2 + den * den;
__float128 f = num / den;
if (f < 0.5Q)
__real__ res = 0.25Q * logq (f);
else
{
num = 4 * __real__ x;
__real__ res = 0.25Q * log1pq (num / den);
}
}
__real__ res = 0.25 * (logq (num) - logq (den));
__float128 absx, absy, den;
den = 1 - __real__ x * __real__ x - i2;
absx = fabsq (__real__ x);
absy = fabsq (__imag__ x);
if (absx < absy)
{
__float128 t = absx;
absx = absy;
absy = t;
}
__imag__ res = 0.5 * atan2q (2.0 * __imag__ x, den);
if (absy < FLT128_EPSILON / 2)
{
den = (1 - absx) * (1 + absx);
if (den == 0)
den = 0;
}
else if (absx >= 1)
den = (1 - absx) * (1 + absx) - absy * absy;
else if (absx >= 0.75Q || absy >= 0.5Q)
den = -__quadmath_x2y2m1q (absx, absy);
else
den = (1 - absx) * (1 + absx) - absy * absy;
__imag__ res = 0.5Q * atan2q (2 * __imag__ x, den);
}
math_check_force_underflow_complex (res);
}
return res;

95
libquadmath/math/catanq.c
View File

@ -1,5 +1,5 @@
/* Return arc tangent of complex __float128 value.
Copyright (C) 1997, 1998 Free Software Foundation, Inc.
/* Return arc tangent of complex float type.
Copyright (C) 1997-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
@ -14,13 +14,11 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#include "quadmath-imp.h"
__complex128
catanq (__complex128 x)
{
@ -28,12 +26,12 @@ catanq (__complex128 x)
int rcls = fpclassifyq (__real__ x);
int icls = fpclassifyq (__imag__ x);
if (rcls <= QUADFP_INFINITE || icls <= QUADFP_INFINITE)
if (__glibc_unlikely (rcls <= QUADFP_INFINITE || icls <= QUADFP_INFINITE))
{
if (rcls == QUADFP_INFINITE)
{
__real__ res = copysignq (M_PI_2q, __real__ x);
__imag__ res = copysignq (0.0, __imag__ x);
__imag__ res = copysignq (0, __imag__ x);
}
else if (icls == QUADFP_INFINITE)
{
@ -41,12 +39,12 @@ catanq (__complex128 x)
__real__ res = copysignq (M_PI_2q, __real__ x);
else
__real__ res = nanq ("");
__imag__ res = copysignq (0.0, __imag__ x);
__imag__ res = copysignq (0, __imag__ x);
}
else if (icls == QUADFP_ZERO || icls == QUADFP_INFINITE)
{
__real__ res = nanq ("");
__imag__ res = copysignq (0.0, __imag__ x);
__imag__ res = copysignq (0, __imag__ x);
}
else
{
@ -54,27 +52,84 @@ catanq (__complex128 x)
__imag__ res = nanq ("");
}
}
else if (rcls == QUADFP_ZERO && icls == QUADFP_ZERO)
else if (__glibc_unlikely (rcls == QUADFP_ZERO && icls == QUADFP_ZERO))
{
res = x;
}
else
{
__float128 r2, num, den;
if (fabsq (__real__ x) >= 16 / FLT128_EPSILON
|| fabsq (__imag__ x) >= 16 / FLT128_EPSILON)
{
__real__ res = copysignq (M_PI_2q, __real__ x);
if (fabsq (__real__ x) <= 1)
__imag__ res = 1 / __imag__ x;
else if (fabsq (__imag__ x) <= 1)
__imag__ res = __imag__ x / __real__ x / __real__ x;
else
{
__float128 h = hypotq (__real__ x / 2, __imag__ x / 2);
__imag__ res = __imag__ x / h / h / 4;
}
}
else
{
__float128 den, absx, absy;
r2 = __real__ x * __real__ x;
absx = fabsq (__real__ x);
absy = fabsq (__imag__ x);
if (absx < absy)
{
__float128 t = absx;
absx = absy;
absy = t;
}
den = 1 - r2 - __imag__ x * __imag__ x;
if (absy < FLT128_EPSILON / 2)
{
den = (1 - absx) * (1 + absx);
if (den == 0)
den = 0;
}
else if (absx >= 1)
den = (1 - absx) * (1 + absx) - absy * absy;
else if (absx >= 0.75Q || absy >= 0.5Q)
den = -__quadmath_x2y2m1q (absx, absy);
else
den = (1 - absx) * (1 + absx) - absy * absy;
__real__ res = 0.5 * atan2q (2.0 * __real__ x, den);
__real__ res = 0.5Q * atan2q (2 * __real__ x, den);
num = __imag__ x + 1.0;
num = r2 + num * num;
if (fabsq (__imag__ x) == 1
&& fabsq (__real__ x) < FLT128_EPSILON * FLT128_EPSILON)
__imag__ res = (copysignq (0.5Q, __imag__ x)
* ((__float128) M_LN2q
- logq (fabsq (__real__ x))));
else
{
__float128 r2 = 0, num, f;
den = __imag__ x - 1.0;
den = r2 + den * den;
if (fabsq (__real__ x) >= FLT128_EPSILON * FLT128_EPSILON)
r2 = __real__ x * __real__ x;
__imag__ res = 0.25 * logq (num / den);
num = __imag__ x + 1;
num = r2 + num * num;
den = __imag__ x - 1;
den = r2 + den * den;
f = num / den;
if (f < 0.5Q)
__imag__ res = 0.25Q * logq (f);
else
{
num = 4 * __imag__ x;
__imag__ res = 0.25Q * log1pq (num / den);
}
}
}
math_check_force_underflow_complex (res);
}
return res;

7
libquadmath/math/cbrtq.c
View File

@ -1,12 +1,12 @@
/* cbrtq.c
*
* Cube root, __float128 precision
* Cube root, long double precision
*
*
*
* SYNOPSIS:
*
* __float128 x, y, cbrtq();
* long double x, y, cbrtq();
*
* y = cbrtq( x );
*
@ -53,7 +53,6 @@ Adapted for glibc October, 2001.
License along with this library; if not, see
<http://www.gnu.org/licenses/>. */
#include "quadmath-imp.h"
static const __float128 CBRT2 = 1.259921049894873164767210607278228350570251Q;
@ -63,7 +62,7 @@ static const __float128 CBRT4I = 0.6299605249474365823836053036391141752851257Q;
__float128
cbrtq ( __float128 x)
cbrtq (__float128 x)
{
int e, rem, sign;
__float128 z;

56
libquadmath/math/ccoshq.c
View File

@ -1,5 +1,5 @@
/* Complex cosine hyperbole function for complex __float128.
Copyright (C) 1997-2012 Free Software Foundation, Inc.
/* Complex cosine hyperbolic function for float types.
Copyright (C) 1997-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
@ -19,11 +19,6 @@
#include "quadmath-imp.h"
#ifdef HAVE_FENV_H
# include <fenv.h>
#endif
__complex128
ccoshq (__complex128 x)
{
@ -31,23 +26,23 @@ ccoshq (__complex128 x)
int rcls = fpclassifyq (__real__ x);
int icls = fpclassifyq (__imag__ x);
if (__builtin_expect (rcls >= QUADFP_ZERO, 1))
if (__glibc_likely (rcls >= QUADFP_ZERO))
{
/* Real part is finite. */
if (__builtin_expect (icls >= QUADFP_ZERO, 1))
if (__glibc_likely (icls >= QUADFP_ZERO))
{
/* Imaginary part is finite. */
const int t = (int) ((FLT128_MAX_EXP - 1) * M_LN2q);
__float128 sinix, cosix;
if (__builtin_expect (icls != QUADFP_SUBNORMAL, 1))
if (__glibc_likely (fabsq (__imag__ x) > FLT128_MIN))
{
sincosq (__imag__ x, &sinix, &cosix);
}
else
{
sinix = __imag__ x;
cosix = 1.0Q;
cosix = 1;
}
if (fabsq (__real__ x) > t)
@ -57,8 +52,8 @@ ccoshq (__complex128 x)
if (signbitq (__real__ x))
sinix = -sinix;
rx -= t;
sinix *= exp_t / 2.0Q;
cosix *= exp_t / 2.0Q;
sinix *= exp_t / 2;
cosix *= exp_t / 2;
if (rx > t)
{
rx -= t;
@ -83,62 +78,53 @@ ccoshq (__complex128 x)
__real__ retval = coshq (__real__ x) * cosix;
__imag__ retval = sinhq (__real__ x) * sinix;
}
math_check_force_underflow_complex (retval);
}
else
{
__imag__ retval = __real__ x == 0.0Q ? 0.0Q : nanq ("");
__real__ retval = nanq ("") + nanq ("");
#ifdef HAVE_FENV_H
if (icls == QUADFP_INFINITE)
feraiseexcept (FE_INVALID);
#endif
}
__imag__ retval = __real__ x == 0 ? 0 : nanq ("");
__real__ retval = __imag__ x - __imag__ x;
}
}
else if (rcls == QUADFP_INFINITE)
{
/* Real part is infinite. */
if (__builtin_expect (icls > QUADFP_ZERO, 1))
if (__glibc_likely (icls > QUADFP_ZERO))
{
/* Imaginary part is finite. */
__float128 sinix, cosix;
if (__builtin_expect (icls != QUADFP_SUBNORMAL, 1))
if (__glibc_likely (fabsq (__imag__ x) > FLT128_MIN))
{
sincosq (__imag__ x, &sinix, &cosix);
}
else
{
sinix = __imag__ x;
cosix = 1.0Q;
cosix = 1;
}
__real__ retval = copysignq (HUGE_VALQ, cosix);
__imag__ retval = (copysignq (HUGE_VALQ, sinix)
* copysignq (1.0Q, __real__ x));
* copysignq (1, __real__ x));
}
else if (icls == QUADFP_ZERO)
{
/* Imaginary part is 0.0. */
__real__ retval = HUGE_VALQ;
__imag__ retval = __imag__ x * copysignq (1.0Q, __real__ x);
__imag__ retval = __imag__ x * copysignq (1, __real__ x);
}
else
{
/* The addition raises the invalid exception. */
__real__ retval = HUGE_VALQ;
__imag__ retval = nanq ("") + nanq ("");
#ifdef HAVE_FENV_H
if (icls == QUADFP_INFINITE)
feraiseexcept (FE_INVALID);
#endif
}
__imag__ retval = __imag__ x - __imag__ x;
}
}
else
{
__real__ retval = nanq ("");
__imag__ retval = __imag__ x == 0.0 ? __imag__ x : nanq ("");
__imag__ retval = __imag__ x == 0 ? __imag__ x : nanq ("");
}
return retval;

18
libquadmath/math/ceilq.c
View File

@ -1,4 +1,4 @@
/* ceilq.c -- __float128 version of s_ceil.c.
/* s_ceill.c -- long double version of s_ceil.c.
* Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
@ -13,10 +13,22 @@
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: $";
#endif
/*
* ceilq(x)
* Return x rounded toward -inf to integral value
* Method:
* Bit twiddling.
*/
#define NO_MATH_REDIRECT
#include "quadmath-imp.h"
__float128
ceilq (__float128 x)
__float128 ceilq(__float128 x)
{
int64_t i0,i1,j0;
uint64_t i,j;

57
libquadmath/math/cexpq.c
View File

@ -1,5 +1,5 @@
/* Return value of complex exponential function for complex __float128 value.
Copyright (C) 1997-2012 Free Software Foundation, Inc.
/* Return value of complex exponential function for a float type.
Copyright (C) 1997-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
@ -19,11 +19,6 @@
#include "quadmath-imp.h"
#ifdef HAVE_FENV_H
# include <fenv.h>
#endif
__complex128
cexpq (__complex128 x)
{
@ -31,23 +26,23 @@ cexpq (__complex128 x)
int rcls = fpclassifyq (__real__ x);
int icls = fpclassifyq (__imag__ x);
if (__builtin_expect (rcls >= QUADFP_ZERO, 1))
if (__glibc_likely (rcls >= QUADFP_ZERO))
{
/* Real part is finite. */
if (__builtin_expect (icls >= QUADFP_ZERO, 1))
if (__glibc_likely (icls >= QUADFP_ZERO))
{
/* Imaginary part is finite. */
const int t = (int) ((FLT128_MAX_EXP - 1) * M_LN2q);
__float128 sinix, cosix;
if (__builtin_expect (icls != QUADFP_SUBNORMAL, 1))
if (__glibc_likely (fabsq (__imag__ x) > FLT128_MIN))
{
sincosq (__imag__ x, &sinix, &cosix);
}
else
{
sinix = __imag__ x;
cosix = 1.0Q;
cosix = 1;
}
if (__real__ x > t)
@ -75,6 +70,7 @@ cexpq (__complex128 x)
__real__ retval = exp_val * cosix;
__imag__ retval = exp_val * sinix;
}
math_check_force_underflow_complex (retval);
}
else
{
@ -83,18 +79,16 @@ cexpq (__complex128 x)
__real__ retval = nanq ("");
__imag__ retval = nanq ("");
#ifdef HAVE_FENV_H
feraiseexcept (FE_INVALID);
#endif
}
}
else if (__builtin_expect (rcls == QUADFP_INFINITE, 1))
else if (__glibc_likely (rcls == QUADFP_INFINITE))
{
/* Real part is infinite. */
if (__builtin_expect (icls >= QUADFP_ZERO, 1))
if (__glibc_likely (icls >= QUADFP_ZERO))
{
/* Imaginary part is finite. */
__float128 value = signbitq (__real__ x) ? 0.0Q : HUGE_VALQ;
__float128 value = signbitq (__real__ x) ? 0 : HUGE_VALQ;
if (icls == QUADFP_ZERO)
{
@ -106,14 +100,14 @@ cexpq (__complex128 x)
{
__float128 sinix, cosix;
if (__builtin_expect (icls != QUADFP_SUBNORMAL, 1))
if (__glibc_likely (fabsq (__imag__ x) > FLT128_MIN))
{
sincosq (__imag__ x, &sinix, &cosix);
}
else
{
sinix = __imag__ x;
cosix = 1.0Q;
cosix = 1;
}
__real__ retval = copysignq (value, cosix);
@ -123,29 +117,28 @@ cexpq (__complex128 x)
else if (signbitq (__real__ x) == 0)
{
__real__ retval = HUGE_VALQ;
__imag__ retval = nanq ("");
#ifdef HAVE_FENV_H
if (icls == QUADFP_INFINITE)
feraiseexcept (FE_INVALID);
#endif
__imag__ retval = __imag__ x - __imag__ x;
}
else
{
__real__ retval = 0.0Q;
__imag__ retval = copysignq (0.0Q, __imag__ x);
__real__ retval = 0;
__imag__ retval = copysignq (0, __imag__ x);
}
}
else
{
/* If the real part is NaN the result is NaN + iNaN. */
/* If the real part is NaN the result is NaN + iNaN unless the
imaginary part is zero. */
__real__ retval = nanq ("");
__imag__ retval = nanq ("");
if (icls == QUADFP_ZERO)
__imag__ retval = __imag__ x;
else
{
__imag__ retval = nanq ("");
#ifdef HAVE_FENV_H
if (rcls != QUADFP_NAN || icls != QUADFP_NAN)
feraiseexcept (FE_INVALID);
#endif
if (rcls != QUADFP_NAN || icls != QUADFP_NAN)
feraiseexcept (FE_INVALID);
}
}
return retval;

9
libquadmath/math/cimagq.c
View File

@ -1,5 +1,5 @@
/* Return imaginary part of complex __float128 value.
Copyright (C) 1997, 1998 Free Software Foundation, Inc.
/* Return imaginary part of complex float type.
Copyright (C) 1997-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
@ -14,9 +14,8 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#include "quadmath-imp.h"

57
libquadmath/math/clog10q.c
View File

@ -1,5 +1,5 @@
/* Compute complex base 10 logarithm for complex __float128.
Copyright (C) 1997-2012 Free Software Foundation, Inc.
/* Compute complex base 10 logarithm.
Copyright (C) 1997-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
@ -19,10 +19,11 @@
#include "quadmath-imp.h"
/* log_10 (2). */
#define M_LOG10_2q 0.3010299956639811952137388947244930267682Q
#define LOG10_2 0.3010299956639811952137388947244930267682Q
/* pi * log10 (e). */
#define PI_LOG10E 1.364376353841841347485783625431355770210Q
__complex128
clog10q (__complex128 x)
@ -31,15 +32,15 @@ clog10q (__complex128 x)
int rcls = fpclassifyq (__real__ x);
int icls = fpclassifyq (__imag__ x);
if (__builtin_expect (rcls == QUADFP_ZERO && icls == QUADFP_ZERO, 0))
if (__glibc_unlikely (rcls == QUADFP_ZERO && icls == QUADFP_ZERO))
{
/* Real and imaginary part are 0.0. */
__imag__ result = signbitq (__real__ x) ? M_PIq : 0.0Q;
__imag__ result = signbitq (__real__ x) ? PI_LOG10E : 0;
__imag__ result = copysignq (__imag__ result, __imag__ x);
/* Yes, the following line raises an exception. */
__real__ result = -1.0Q / fabsq (__real__ x);
__real__ result = -1 / fabsq (__real__ x);
}
else if (__builtin_expect (rcls != QUADFP_NAN && icls != QUADFP_NAN, 1))
else if (__glibc_likely (rcls != QUADFP_NAN && icls != QUADFP_NAN))
{
/* Neither real nor imaginary part is NaN. */
__float128 absx = fabsq (__real__ x), absy = fabsq (__imag__ x);
@ -52,11 +53,11 @@ clog10q (__complex128 x)
absy = t;
}
if (absx > FLT128_MAX / 2.0Q)
if (absx > FLT128_MAX / 2)
{
scale = -1;
absx = scalbnq (absx, scale);
absy = (absy >= FLT128_MIN * 2.0Q ? scalbnq (absy, scale) : 0.0Q);
absy = (absy >= FLT128_MIN * 2 ? scalbnq (absy, scale) : 0);
}
else if (absx < FLT128_MIN && absy < FLT128_MIN)
{
@ -65,39 +66,39 @@ clog10q (__complex128 x)
absy = scalbnq (absy, scale);
}
if (absx == 1.0Q && scale == 0)
if (absx == 1 && scale == 0)
{
__float128 absy2 = absy * absy;
if (absy2 <= FLT128_MIN * 2.0Q * M_LN10q)
__real__ result
= (absy2 / 2.0Q - absy2 * absy2 / 4.0Q) * M_LOG10Eq;
else
__real__ result = log1pq (absy2) * (M_LOG10Eq / 2.0Q);
__real__ result = (log1pq (absy * absy)
* ((__float128) M_LOG10Eq / 2));
math_check_force_underflow_nonneg (__real__ result);
}
else if (absx > 1.0Q && absx < 2.0Q && absy < 1.0Q && scale == 0)
else if (absx > 1 && absx < 2 && absy < 1 && scale == 0)
{
__float128 d2m1 = (absx - 1.0Q) * (absx + 1.0Q);
__float128 d2m1 = (absx - 1) * (absx + 1);
if (absy >= FLT128_EPSILON)
d2m1 += absy * absy;
__real__ result = log1pq (d2m1) * (M_LOG10Eq / 2.0Q);
__real__ result = log1pq (d2m1) * ((__float128) M_LOG10Eq / 2);
}
else if (absx < 1.0Q
&& absx >= 0.75Q
&& absy < FLT128_EPSILON / 2.0Q
else if (absx < 1
&& absx >= 0.5Q
&& absy < FLT128_EPSILON / 2
&& scale == 0)
{
__float128 d2m1 = (absx - 1.0Q) * (absx + 1.0Q);
__real__ result = log1pq (d2m1) * (M_LOG10Eq / 2.0Q);
__float128 d2m1 = (absx - 1) * (absx + 1);
__real__ result = log1pq (d2m1) * ((__float128) M_LOG10Eq / 2);
}
else if (absx < 1.0Q && (absx >= 0.75Q || absy >= 0.5Q) && scale == 0)
else if (absx < 1
&& absx >= 0.5Q
&& scale == 0
&& absx * absx + absy * absy >= 0.5Q)
{
__float128 d2m1 = __quadmath_x2y2m1q (absx, absy);
__real__ result = log1pq (d2m1) * (M_LOG10Eq / 2.0Q);
__real__ result = log1pq (d2m1) * ((__float128) M_LOG10Eq / 2);
}
else
{
__float128 d = hypotq (absx, absy);
__real__ result = log10q (d) - scale * M_LOG10_2q;
__real__ result = log10q (d) - scale * LOG10_2;
}
__imag__ result = M_LOG10Eq * atan2q (__imag__ x, __real__ x);

51
libquadmath/math/clogq.c
View File

@ -1,5 +1,5 @@
/* Compute complex natural logarithm for complex __float128.
Copyright (C) 1997-2012 Free Software Foundation, Inc.
/* Compute complex natural logarithm.
Copyright (C) 1997-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
@ -19,7 +19,6 @@
#include "quadmath-imp.h"
__complex128
clogq (__complex128 x)
{
@ -27,15 +26,15 @@ clogq (__complex128 x)
int rcls = fpclassifyq (__real__ x);
int icls = fpclassifyq (__imag__ x);
if (__builtin_expect (rcls == QUADFP_ZERO && icls == QUADFP_ZERO, 0))
if (__glibc_unlikely (rcls == QUADFP_ZERO && icls == QUADFP_ZERO))
{
/* Real and imaginary part are 0.0. */
__imag__ result = signbitq (__real__ x) ? M_PIq : 0.0Q;
__imag__ result = signbitq (__real__ x) ? (__float128) M_PIq : 0;
__imag__ result = copysignq (__imag__ result, __imag__ x);
/* Yes, the following line raises an exception. */
__real__ result = -1.0Q / fabsq (__real__ x);
__real__ result = -1 / fabsq (__real__ x);
}
else if (__builtin_expect (rcls != QUADFP_NAN && icls != QUADFP_NAN, 1))
else if (__glibc_likely (rcls != QUADFP_NAN && icls != QUADFP_NAN))
{
/* Neither real nor imaginary part is NaN. */
__float128 absx = fabsq (__real__ x), absy = fabsq (__imag__ x);
@ -48,11 +47,11 @@ clogq (__complex128 x)
absy = t;
}
if (absx > FLT128_MAX / 2.0)
if (absx > FLT128_MAX / 2)
{
scale = -1;
absx = scalbnq (absx, scale);
absy = (absy >= FLT128_MIN * 2.0Q ? scalbnq (absy, scale) : 0.0Q);
absy = (absy >= FLT128_MIN * 2 ? scalbnq (absy, scale) : 0);
}
else if (absx < FLT128_MIN && absy < FLT128_MIN)
{
@ -61,38 +60,38 @@ clogq (__complex128 x)
absy = scalbnq (absy, scale);
}
if (absx == 1.0Q && scale == 0)
if (absx == 1 && scale == 0)
{
__float128 absy2 = absy * absy;
if (absy2 <= FLT128_MIN * 2.0Q)
__real__ result = absy2 / 2.0Q - absy2 * absy2 / 4.0Q;
else
__real__ result = log1pq (absy2) / 2.0Q;
__real__ result = log1pq (absy * absy) / 2;
math_check_force_underflow_nonneg (__real__ result);
}
else if (absx > 1.0Q && absx < 2.0Q && absy < 1.0Q && scale == 0)
else if (absx > 1 && absx < 2 && absy < 1 && scale == 0)
{
__float128 d2m1 = (absx - 1.0Q) * (absx + 1.0Q);
__float128 d2m1 = (absx - 1) * (absx + 1);
if (absy >= FLT128_EPSILON)
d2m1 += absy * absy;
__real__ result = log1pq (d2m1) / 2.0Q;
__real__ result = log1pq (d2m1) / 2;
}
else if (absx < 1.0Q
&& absx >= 0.75Q
&& absy < FLT128_EPSILON / 2.0Q
else if (absx < 1
&& absx >= 0.5Q
&& absy < FLT128_EPSILON / 2
&& scale == 0)
{
__float128 d2m1 = (absx - 1.0Q) * (absx + 1.0Q);
__real__ result = log1pq (d2m1) / 2.0Q;
__float128 d2m1 = (absx - 1) * (absx + 1);
__real__ result = log1pq (d2m1) / 2;
}
else if (absx < 1.0 && (absx >= 0.75Q || absy >= 0.5Q) && scale == 0)
else if (absx < 1
&& absx >= 0.5Q
&& scale == 0
&& absx * absx + absy * absy >= 0.5Q)
{
__float128 d2m1 = __quadmath_x2y2m1q (absx, absy);
__real__ result = log1pq (d2m1) / 2.0Q;
__real__ result = log1pq (d2m1) / 2;
}
else
{
__float128 d = hypotq (absx, absy);
__real__ result = logq (d) - scale * M_LN2q;
__real__ result = logq (d) - scale * (__float128) M_LN2q;
}
__imag__ result = atan2q (__imag__ x, __real__ x);

9
libquadmath/math/conjq.c
View File

@ -1,5 +1,5 @@
/* Return complex conjugate of complex __float128 value.
Copyright (C) 1997, 1998 Free Software Foundation, Inc.
/* Return complex conjugate of complex float type.
Copyright (C) 1997-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
@ -14,9 +14,8 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#include "quadmath-imp.h"

28
libquadmath/math/copysignq.c
View File

@ -1,4 +1,4 @@
/* copysignq.c -- __float128 version of s_copysign.c.
/* s_copysignl.c -- long double version of s_copysign.c.
* Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
@ -13,14 +13,26 @@
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: $";
#endif
/*
* copysignq(long double x, long double y)
* copysignq(x,y) returns a value with the magnitude of x and
* with the sign bit of y.
*/
#define NO_MATH_REDIRECT
#include "quadmath-imp.h"
__float128
copysignq (__float128 x, __float128 y)
__float128 copysignq(__float128 x, __float128 y)
{
uint64_t hx,hy;
GET_FLT128_MSW64(hx,x);
GET_FLT128_MSW64(hy,y);
SET_FLT128_MSW64(x,(hx&0x7fffffffffffffffULL)|(hy&0x8000000000000000ULL));
return x;
uint64_t hx,hy;
GET_FLT128_MSW64(hx,x);
GET_FLT128_MSW64(hy,y);
SET_FLT128_MSW64(x,(hx&0x7fffffffffffffffULL)
|(hy&0x8000000000000000ULL));
return x;
}

34
libquadmath/math/coshq.c
View File

@ -9,11 +9,11 @@
* ====================================================
*/
/* Changes for 128-bit __float128 are
/* Changes for 128-bit long double are
Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
and are incorporated herein by permission of the author. The author
and are incorporated herein by permission of the author. The author
reserves the right to distribute this material elsewhere under different
copying permissions. These modifications are distributed here under
copying permissions. These modifications are distributed here under
the following terms:
This library is free software; you can redistribute it and/or
@ -27,34 +27,34 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
License along with this library; if not, see
<http://www.gnu.org/licenses/>. */
/* coshq(x)
* Method :
* mathematically coshq(x) if defined to be (exp(x)+exp(-x))/2
* 1. Replace x by |x| (coshq(x) = coshq(-x)).
* mathematically coshl(x) if defined to be (exp(x)+exp(-x))/2
* 1. Replace x by |x| (coshl(x) = coshl(-x)).
* 2.
* [ exp(x) - 1 ]^2
* 0 <= x <= ln2/2 : coshq(x) := 1 + -------------------
* 0 <= x <= ln2/2 : coshl(x) := 1 + -------------------
* 2*exp(x)
*
* exp(x) + 1/exp(x)
* ln2/2 <= x <= 22 : coshq(x) := -------------------
* ln2/2 <= x <= 22 : coshl(x) := -------------------
* 2
* 22 <= x <= lnovft : coshq(x) := expq(x)/2
* lnovft <= x <= ln2ovft: coshq(x) := expq(x/2)/2 * expq(x/2)
* ln2ovft < x : coshq(x) := huge*huge (overflow)
* 22 <= x <= lnovft : coshl(x) := expq(x)/2
* lnovft <= x <= ln2ovft: coshl(x) := expq(x/2)/2 * expq(x/2)
* ln2ovft < x : coshl(x) := huge*huge (overflow)
*
* Special cases:
* coshq(x) is |x| if x is +INF, -INF, or NaN.
* only coshq(0)=1 is exact for finite x.
* coshl(x) is |x| if x is +INF, -INF, or NaN.
* only coshl(0)=1 is exact for finite x.
*/
#include "quadmath-imp.h"
static const __float128 one = 1.0Q, half = 0.5Q, huge = 1.0e4900Q,
ovf_thresh = 1.1357216553474703894801348310092223067821E4Q;
static const __float128 one = 1.0, half = 0.5, huge = 1.0e4900Q,
ovf_thresh = 1.1357216553474703894801348310092223067821E4Q;
__float128
coshq (__float128 x)
@ -73,7 +73,7 @@ coshq (__float128 x)
if (ex >= 0x7fff0000)
return x * x;
/* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expq(|x|)) */
/* |x| in [0,0.5*ln2], return 1+expm1q(|x|)^2/(2*expq(|x|)) */
if (ex < 0x3ffd62e4) /* 0.3465728759765625 */
{
if (ex < 0x3fb80000) /* |x| < 2^-116 */

13
libquadmath/math/cosq.c
View File

@ -1,4 +1,4 @@
/* cosq.c -- __float128 version of s_cos.c.
/* s_cosl.c -- long double version of s_cos.c.
* Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
@ -17,8 +17,8 @@
* Return cosine function of x.
*
* kernel function:
* __quadmath_kernel_sinq ... sine function on [-pi/4,pi/4]
* __quadmath_kernel_cosq ... cosine function on [-pi/4,pi/4]
* __quadmath_kernel_sinq ... sine function on [-pi/4,pi/4]
* __quadmath_kernel_cosq ... cosine function on [-pi/4,pi/4]
* __quadmath_rem_pio2q ... argument reduction routine
*
* Method.
@ -46,10 +46,9 @@
#include "quadmath-imp.h"
__float128
cosq (__float128 x)
__float128 cosq(__float128 x)
{
__float128 y[2],z=0.0Q;
__float128 y[2],z=0;
int64_t n, ix;
/* High word of x. */
@ -64,6 +63,8 @@ cosq (__float128 x)
else if (ix>=0x7fff000000000000LL) {
if (ix == 0x7fff000000000000LL) {
GET_FLT128_LSW64(n,x);
if (n == 0)
errno = EDOM;
}
return x-x;
}

35
libquadmath/math/cosq_kernel.c
View File

@ -1,5 +1,5 @@
/* Quad-precision floating point cosine on <-pi/4,pi/4>.
Copyright (C) 1999 Free Software Foundation, Inc.
Copyright (C) 1999-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Jakub Jelinek <jj@ultra.linux.cz>
@ -14,9 +14,8 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#include "quadmath-imp.h"
@ -70,14 +69,14 @@ static const __float128 c[] = {
-2.50521016467996193495359189395805639E-08Q, /* bfe5ae644ee90c47dc71839de75b2787 */
};
#define SINCOSQ_COS_HI 0
#define SINCOSQ_COS_LO 1
#define SINCOSQ_SIN_HI 2
#define SINCOSQ_SIN_LO 3
#define SINCOSL_COS_HI 0
#define SINCOSL_COS_LO 1
#define SINCOSL_SIN_HI 2
#define SINCOSL_SIN_LO 3
extern const __float128 __sincosq_table[];
__float128
__quadmath_kernel_cosq (__float128 x, __float128 y)
__quadmath_kernel_cosq(__float128 x, __float128 y)
{
__float128 h, l, z, sin_l, cos_l_m1;
int64_t ix;
@ -98,7 +97,7 @@ __quadmath_kernel_cosq (__float128 x, __float128 y)
else
{
/* So that we don't have to use too large polynomial, we find
l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83
l and h such that x = l + h, where fabsq(l) <= 1.0/256 with 83
possible values for h. We look up cosq(h) and sinq(h) in
pre-computed tables, compute cosq(l) and sinq(l) using a
Chebyshev polynomial of degree 10(11) and compute
@ -106,10 +105,10 @@ __quadmath_kernel_cosq (__float128 x, __float128 y)
index = 0x3ffe - (tix >> 16);
hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
if (signbitq (x))
{
x = -x;
y = -y;
}
{
x = -x;
y = -y;
}
switch (index)
{
case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break;
@ -123,9 +122,9 @@ __quadmath_kernel_cosq (__float128 x, __float128 y)
z = l * l;
sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
return __sincosq_table [index + SINCOSQ_COS_HI]
+ (__sincosq_table [index + SINCOSQ_COS_LO]
- (__sincosq_table [index + SINCOSQ_SIN_HI] * sin_l
- __sincosq_table [index + SINCOSQ_COS_HI] * cos_l_m1));
return __sincosq_table [index + SINCOSL_COS_HI]
+ (__sincosq_table [index + SINCOSL_COS_LO]
- (__sincosq_table [index + SINCOSL_SIN_HI] * sin_l
- __sincosq_table [index + SINCOSL_COS_HI] * cos_l_m1));
}
}

16
libquadmath/math/cprojq.c
View File

@ -1,5 +1,5 @@
/* Compute projection of complex __float128 value to Riemann sphere.
Copyright (C) 1997, 1999, 2010 Free Software Foundation, Inc.
/* Compute projection of complex float type value to Riemann sphere.
Copyright (C) 1997-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
@ -14,24 +14,20 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#include "quadmath-imp.h"
__complex128
cprojq (__complex128 x)
{
if (isnanq (__real__ x) && isnanq (__imag__ x))
return x;
else if (!finiteq (__real__ x) || !finiteq (__imag__ x))
if (isinfq (__real__ x) || isinfq (__imag__ x))
{
__complex128 res;
__real__ res = __builtin_inf ();
__imag__ res = copysignq (0.0, __imag__ x);
__imag__ res = copysignq (0, __imag__ x);
return res;
}

9
libquadmath/math/crealq.c
View File

@ -1,5 +1,5 @@
/* Return real part of complex __float128 value.
Copyright (C) 1997, 1998 Free Software Foundation, Inc.
/* Return real part of complex float type.
Copyright (C) 1997-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
@ -14,9 +14,8 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#include "quadmath-imp.h"

54
libquadmath/math/csinhq.c
View File

@ -1,5 +1,5 @@
/* Complex sine hyperbole function for complex __float128.
Copyright (C) 1997-2012 Free Software Foundation, Inc.
/* Complex sine hyperbole function for float types.
Copyright (C) 1997-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
@ -19,11 +19,6 @@
#include "quadmath-imp.h"
#ifdef HAVE_FENV_H
# include <fenv.h>
#endif
__complex128
csinhq (__complex128 x)
{
@ -34,25 +29,28 @@ csinhq (__complex128 x)
__real__ x = fabsq (__real__ x);
if (__builtin_expect (rcls >= QUADFP_ZERO, 1))
if (__glibc_likely (rcls >= QUADFP_ZERO))
{
/* Real part is finite. */
if (__builtin_expect (icls >= QUADFP_ZERO, 1))
if (__glibc_likely (icls >= QUADFP_ZERO))
{
/* Imaginary part is finite. */
const int t = (int) ((FLT128_MAX_EXP - 1) * M_LN2q);
__float128 sinix, cosix;
if (__builtin_expect (icls != QUADFP_SUBNORMAL, 1))
if (__glibc_likely (fabsq (__imag__ x) > FLT128_MIN))
{
sincosq (__imag__ x, &sinix, &cosix);
}
else
{
sinix = __imag__ x;
cosix = 1.0Q;
cosix = 1;
}
if (negate)
cosix = -cosix;
if (fabsq (__real__ x) > t)
{
__float128 exp_t = expq (t);
@ -60,8 +58,8 @@ csinhq (__complex128 x)
if (signbitq (__real__ x))
cosix = -cosix;
rx -= t;
sinix *= exp_t / 2.0Q;
cosix *= exp_t / 2.0Q;
sinix *= exp_t / 2;
cosix *= exp_t / 2;
if (rx > t)
{
rx -= t;
@ -87,49 +85,41 @@ csinhq (__complex128 x)
__imag__ retval = coshq (__real__ x) * sinix;
}
if (negate)
__real__ retval = -__real__ retval;
math_check_force_underflow_complex (retval);
}
else
{
if (rcls == QUADFP_ZERO)
{
/* Real part is 0.0. */
__real__ retval = copysignq (0.0Q, negate ? -1.0Q : 1.0Q);
__imag__ retval = nanq ("") + nanq ("");
#ifdef HAVE_FENV_H
if (icls == QUADFP_INFINITE)
feraiseexcept (FE_INVALID);
#endif
__real__ retval = copysignq (0, negate ? -1 : 1);
__imag__ retval = __imag__ x - __imag__ x;
}
else
{
__real__ retval = nanq ("");
__imag__ retval = nanq ("");
#ifdef HAVE_FENV_H
feraiseexcept (FE_INVALID);
#endif
}
}
}
else if (rcls == QUADFP_INFINITE)
{
/* Real part is infinite. */
if (__builtin_expect (icls > QUADFP_ZERO, 1))
if (__glibc_likely (icls > QUADFP_ZERO))
{
/* Imaginary part is finite. */
__float128 sinix, cosix;
if (__builtin_expect (icls != QUADFP_SUBNORMAL, 1))
if (__glibc_likely (fabsq (__imag__ x) > FLT128_MIN))
{
sincosq (__imag__ x, &sinix, &cosix);
}
else
{
sinix = __imag__ x;
cosix = 1.0;
cosix = 1;
}
__real__ retval = copysignq (HUGE_VALQ, cosix);
@ -146,20 +136,14 @@ csinhq (__complex128 x)
}
else
{
/* The addition raises the invalid exception. */
__real__ retval = HUGE_VALQ;
__imag__ retval = nanq ("") + nanq ("");
#ifdef HAVE_FENV_H
if (icls == QUADFP_INFINITE)
feraiseexcept (FE_INVALID);
#endif
__imag__ retval = __imag__ x - __imag__ x;
}
}
else
{
__real__ retval = nanq ("");
__imag__ retval = __imag__ x == 0.0Q ? __imag__ x : nanq ("");
__imag__ retval = __imag__ x == 0 ? __imag__ x : nanq ("");
}
return retval;

52
libquadmath/math/csinq.c
View File

@ -1,5 +1,5 @@
/* Complex sine function for complex __float128.
Copyright (C) 1997-2012 Free Software Foundation, Inc.
/* Complex sine function for float types.
Copyright (C) 1997-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
@ -19,11 +19,6 @@
#include "quadmath-imp.h"
#ifdef HAVE_FENV_H
# include <fenv.h>
#endif
__complex128
csinq (__complex128 x)
{
@ -34,25 +29,28 @@ csinq (__complex128 x)
__real__ x = fabsq (__real__ x);
if (__builtin_expect (icls >= QUADFP_ZERO, 1))
if (__glibc_likely (icls >= QUADFP_ZERO))
{
/* Imaginary part is finite. */
if (__builtin_expect (rcls >= QUADFP_ZERO, 1))
if (__glibc_likely (rcls >= QUADFP_ZERO))
{
/* Real part is finite. */
const int t = (int) ((FLT128_MAX_EXP - 1) * M_LN2q);
__float128 sinix, cosix;
if (__builtin_expect (rcls != QUADFP_SUBNORMAL, 1))
if (__glibc_likely (__real__ x > FLT128_MIN))
{
sincosq (__real__ x, &sinix, &cosix);
}
else
{
sinix = __real__ x;
cosix = 1.0Q;
cosix = 1;
}
if (negate)
sinix = -sinix;
if (fabsq (__imag__ x) > t)
{
__float128 exp_t = expq (t);
@ -60,8 +58,8 @@ csinq (__complex128 x)
if (signbitq (__imag__ x))
cosix = -cosix;
ix -= t;
sinix *= exp_t / 2.0Q;
cosix *= exp_t / 2.0Q;
sinix *= exp_t / 2;
cosix *= exp_t / 2;
if (ix > t)
{
ix -= t;
@ -87,30 +85,22 @@ csinq (__complex128 x)
__imag__ retval = sinhq (__imag__ x) * cosix;
}
if (negate)
__real__ retval = -__real__ retval;
math_check_force_underflow_complex (retval);
}
else
{
if (icls == QUADFP_ZERO)
{
/* Imaginary part is 0.0. */
__real__ retval = nanq ("");
__real__ retval = __real__ x - __real__ x;
__imag__ retval = __imag__ x;
#ifdef HAVE_FENV_H
if (rcls == QUADFP_INFINITE)
feraiseexcept (FE_INVALID);
#endif
}
else
{
__real__ retval = nanq ("");
__imag__ retval = nanq ("");
#ifdef HAVE_FENV_H
feraiseexcept (FE_INVALID);
#endif
}
}
}
@ -120,7 +110,7 @@ csinq (__complex128 x)
if (rcls == QUADFP_ZERO)
{
/* Real part is 0.0. */
__real__ retval = copysignq (0.0Q, negate ? -1.0Q : 1.0Q);
__real__ retval = copysignq (0, negate ? -1 : 1);
__imag__ retval = __imag__ x;
}
else if (rcls > QUADFP_ZERO)
@ -128,14 +118,14 @@ csinq (__complex128 x)
/* Real part is finite. */
__float128 sinix, cosix;
if (__builtin_expect (rcls != QUADFP_SUBNORMAL, 1))
if (__glibc_likely (__real__ x > FLT128_MIN))
{
sincosq (__real__ x, &sinix, &cosix);
}
else
{
sinix = __real__ x;
cosix = 1.0;
cosix = 1;
}
__real__ retval = copysignq (HUGE_VALQ, sinix);
@ -148,20 +138,14 @@ csinq (__complex128 x)
}
else
{
/* The addition raises the invalid exception. */
__real__ retval = nanq ("");
__real__ retval = __real__ x - __real__ x;
__imag__ retval = HUGE_VALQ;
#ifdef HAVE_FENV_H
if (rcls == QUADFP_INFINITE)
feraiseexcept (FE_INVALID);
#endif
}
}
else
{
if (rcls == QUADFP_ZERO)
__real__ retval = copysignq (0.0Q, negate ? -1.0Q : 1.0Q);
__real__ retval = copysignq (0, negate ? -1 : 1);
else
__real__ retval = nanq ("");
__imag__ retval = nanq ("");

69
libquadmath/math/csqrtq.c
View File

@ -1,5 +1,5 @@
/* Complex square root of __float128 value.
Copyright (C) 1997-2012 Free Software Foundation, Inc.
/* Complex square root of a float type.
Copyright (C) 1997-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Based on an algorithm by Stephen L. Moshier <moshier@world.std.com>.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
@ -20,11 +20,6 @@
#include "quadmath-imp.h"
#ifdef HAVE_FENV_H
# include <fenv.h>
#endif
__complex128
csqrtq (__complex128 x)
{
@ -32,7 +27,7 @@ csqrtq (__complex128 x)
int rcls = fpclassifyq (__real__ x);
int icls = fpclassifyq (__imag__ x);
if (__builtin_expect (rcls <= QUADFP_INFINITE || icls <= QUADFP_INFINITE, 0))
if (__glibc_unlikely (rcls <= QUADFP_INFINITE || icls <= QUADFP_INFINITE))
{
if (icls == QUADFP_INFINITE)
{
@ -41,7 +36,7 @@ csqrtq (__complex128 x)
}
else if (rcls == QUADFP_INFINITE)
{
if (__real__ x < 0.0Q)
if (__real__ x < 0)
{
__real__ res = icls == QUADFP_NAN ? nanq ("") : 0;
__imag__ res = copysignq (HUGE_VALQ, __imag__ x);
@ -50,7 +45,7 @@ csqrtq (__complex128 x)
{
__real__ res = __real__ x;
__imag__ res = (icls == QUADFP_NAN
? nanq ("") : copysignq (0.0Q, __imag__ x));
? nanq ("") : copysignq (0, __imag__ x));
}
}
else
@ -61,27 +56,26 @@ csqrtq (__complex128 x)
}
else
{
if (__builtin_expect (icls == QUADFP_ZERO, 0))
if (__glibc_unlikely (icls == QUADFP_ZERO))
{
if (__real__ x < 0.0Q)
if (__real__ x < 0)
{
__real__ res = 0.0Q;
__imag__ res = copysignq (sqrtq (-__real__ x),
__imag__ x);
__real__ res = 0;
__imag__ res = copysignq (sqrtq (-__real__ x), __imag__ x);
}
else
{
__real__ res = fabsq (sqrtq (__real__ x));
__imag__ res = copysignq (0.0Q, __imag__ x);
__imag__ res = copysignq (0, __imag__ x);
}
}
else if (__builtin_expect (rcls == QUADFP_ZERO, 0))
else if (__glibc_unlikely (rcls == QUADFP_ZERO))
{
__float128 r;
if (fabsq (__imag__ x) >= 2.0Q * FLT128_MIN)
if (fabsq (__imag__ x) >= 2 * FLT128_MIN)
r = sqrtq (0.5Q * fabsq (__imag__ x));
else
r = 0.5Q * sqrtq (2.0Q * fabsq (__imag__ x));
r = 0.5Q * sqrtq (2 * fabsq (__imag__ x));
__real__ res = r;
__imag__ res = copysignq (r, __imag__ x);
@ -91,25 +85,25 @@ csqrtq (__complex128 x)
__float128 d, r, s;
int scale = 0;
if (fabsq (__real__ x) > FLT128_MAX / 4.0Q)
if (fabsq (__real__ x) > FLT128_MAX / 4)
{
scale = 1;
__real__ x = scalbnq (__real__ x, -2 * scale);
__imag__ x = scalbnq (__imag__ x, -2 * scale);
}
else if (fabsq (__imag__ x) > FLT128_MAX / 4.0Q)
else if (fabsq (__imag__ x) > FLT128_MAX / 4)
{
scale = 1;
if (fabsq (__real__ x) >= 4.0Q * FLT128_MIN)
if (fabsq (__real__ x) >= 4 * FLT128_MIN)
__real__ x = scalbnq (__real__ x, -2 * scale);
else
__real__ x = 0.0Q;
__real__ x = 0;
__imag__ x = scalbnq (__imag__ x, -2 * scale);
}
else if (fabsq (__real__ x) < FLT128_MIN
&& fabsq (__imag__ x) < FLT128_MIN)
else if (fabsq (__real__ x) < 2 * FLT128_MIN
&& fabsq (__imag__ x) < 2 * FLT128_MIN)
{
scale = -(FLT128_MANT_DIG / 2);
scale = -((FLT128_MANT_DIG + 1) / 2);
__real__ x = scalbnq (__real__ x, -2 * scale);
__imag__ x = scalbnq (__imag__ x, -2 * scale);
}
@ -120,12 +114,28 @@ csqrtq (__complex128 x)
if (__real__ x > 0)
{
r = sqrtq (0.5Q * (d + __real__ x));
s = 0.5Q * (__imag__ x / r);
if (scale == 1 && fabsq (__imag__ x) < 1)
{
/* Avoid possible intermediate underflow. */
s = __imag__ x / r;
r = scalbnq (r, scale);
scale = 0;
}
else
s = 0.5Q * (__imag__ x / r);
}
else
{
s = sqrtq (0.5Q * (d - __real__ x));
r = fabsq (0.5Q * (__imag__ x / s));
if (scale == 1 && fabsq (__imag__ x) < 1)
{
/* Avoid possible intermediate underflow. */
r = fabsq (__imag__ x / s);
s = scalbnq (s, scale);
scale = 0;
}
else
r = fabsq (0.5Q * (__imag__ x / s));
}
if (scale)
@ -134,6 +144,9 @@ csqrtq (__complex128 x)
s = scalbnq (s, scale);
}
math_check_force_underflow (r);
math_check_force_underflow (s);
__real__ res = r;
__imag__ res = copysignq (s, __imag__ x);
}

45
libquadmath/math/ctanhq.c
View File

@ -1,5 +1,5 @@
/* Complex hyperbole tangent for __float128.
Copyright (C) 1997-2012 Free Software Foundation, Inc.
/* Complex hyperbolic tangent for float types.
Copyright (C) 1997-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
@ -19,36 +19,39 @@
#include "quadmath-imp.h"
#ifdef HAVE_FENV_H
# include <fenv.h>
#endif
__complex128
ctanhq (__complex128 x)
{
__complex128 res;
if (__builtin_expect (!finiteq (__real__ x) || !finiteq (__imag__ x), 0))
if (__glibc_unlikely (!finiteq (__real__ x) || !finiteq (__imag__ x)))
{
if (__quadmath_isinf_nsq (__real__ x))
if (isinfq (__real__ x))
{
__real__ res = copysignq (1.0Q, __real__ x);
__imag__ res = copysignq (0.0Q, __imag__ x);
__real__ res = copysignq (1, __real__ x);
if (finiteq (__imag__ x) && fabsq (__imag__ x) > 1)
{
__float128 sinix, cosix;
sincosq (__imag__ x, &sinix, &cosix);
__imag__ res = copysignq (0, sinix * cosix);
}
else
__imag__ res = copysignq (0, __imag__ x);
}
else if (__imag__ x == 0.0Q)
else if (__imag__ x == 0)
{
res = x;
}
else
{
__real__ res = nanq ("");
if (__real__ x == 0)
__real__ res = __real__ x;
else
__real__ res = nanq ("");
__imag__ res = nanq ("");
#ifdef HAVE_FENV_H
if (__quadmath_isinf_nsq (__imag__ x))
if (isinfq (__imag__ x))
feraiseexcept (FE_INVALID);
#endif
}
}
else
@ -56,19 +59,18 @@ ctanhq (__complex128 x)
__float128 sinix, cosix;
__float128 den;
const int t = (int) ((FLT128_MAX_EXP - 1) * M_LN2q / 2);
int icls = fpclassifyq (__imag__ x);
/* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y))
= (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2). */
if (__builtin_expect (icls != QUADFP_SUBNORMAL, 1))
if (__glibc_likely (fabsq (__imag__ x) > FLT128_MIN))
{
sincosq (__imag__ x, &sinix, &cosix);
}
else
{
sinix = __imag__ x;
cosix = 1.0Q;
cosix = 1;
}
if (fabsq (__real__ x) > t)
@ -79,7 +81,7 @@ ctanhq (__complex128 x)
sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x). */
__float128 exp_2t = expq (2 * t);
__real__ res = copysignq (1.0, __real__ x);
__real__ res = copysignq (1, __real__ x);
__imag__ res = 4 * sinix * cosix;
__real__ x = fabsq (__real__ x);
__real__ x -= t;
@ -104,7 +106,7 @@ ctanhq (__complex128 x)
else
{
sinhrx = __real__ x;
coshrx = 1.0Q;
coshrx = 1;
}
if (fabsq (sinhrx) > fabsq (cosix) * FLT128_EPSILON)
@ -114,6 +116,7 @@ ctanhq (__complex128 x)
__real__ res = sinhrx * coshrx / den;
__imag__ res = sinix * cosix / den;
}
math_check_force_underflow_complex (res);
}
return res;

47
libquadmath/math/ctanq.c
View File

@ -1,5 +1,5 @@
/* Complex tangent function for complex __float128.
Copyright (C) 1997-2012 Free Software Foundation, Inc.
/* Complex tangent function for a complex float type.
Copyright (C) 1997-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
@ -19,56 +19,58 @@
#include "quadmath-imp.h"
#ifdef HAVE_FENV_H
# include <fenv.h>
#endif
__complex128
ctanq (__complex128 x)
{
__complex128 res;
if (__builtin_expect (!finiteq (__real__ x) || !finiteq (__imag__ x), 0))
if (__glibc_unlikely (!finiteq (__real__ x) || !finiteq (__imag__ x)))
{
if (__quadmath_isinf_nsq (__imag__ x))
if (isinfq (__imag__ x))
{
__real__ res = copysignq (0.0Q, __real__ x);
__imag__ res = copysignq (1.0Q, __imag__ x);
if (finiteq (__real__ x) && fabsq (__real__ x) > 1)
{
__float128 sinrx, cosrx;
sincosq (__real__ x, &sinrx, &cosrx);
__real__ res = copysignq (0, sinrx * cosrx);
}
else
__real__ res = copysignq (0, __real__ x);
__imag__ res = copysignq (1, __imag__ x);
}
else if (__real__ x == 0.0Q)
else if (__real__ x == 0)
{
res = x;
}
else
{
__real__ res = nanq ("");
__imag__ res = nanq ("");
if (__imag__ x == 0)
__imag__ res = __imag__ x;
else
__imag__ res = nanq ("");
#ifdef HAVE_FENV_H
if (__quadmath_isinf_nsq (__real__ x))
if (isinfq (__real__ x))
feraiseexcept (FE_INVALID);
#endif
}
}
else
{
__float128 sinrx, cosrx;
__float128 den;
const int t = (int) ((FLT128_MAX_EXP - 1) * M_LN2q / 2.0Q);
int rcls = fpclassifyq (__real__ x);
const int t = (int) ((FLT128_MAX_EXP - 1) * M_LN2q / 2);
/* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y))
= (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */
if (__builtin_expect (rcls != QUADFP_SUBNORMAL, 1))
if (__glibc_likely (fabsq (__real__ x) > FLT128_MIN))
{
sincosq (__real__ x, &sinrx, &cosrx);
}
else
{
sinrx = __real__ x;
cosrx = 1.0Q;
cosrx = 1;
}
if (fabsq (__imag__ x) > t)
@ -79,7 +81,7 @@ ctanq (__complex128 x)
sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y). */
__float128 exp_2t = expq (2 * t);
__imag__ res = copysignq (1.0Q, __imag__ x);
__imag__ res = copysignq (1, __imag__ x);
__real__ res = 4 * sinrx * cosrx;
__imag__ x = fabsq (__imag__ x);
__imag__ x -= t;
@ -104,7 +106,7 @@ ctanq (__complex128 x)
else
{
sinhix = __imag__ x;
coshix = 1.0Q;
coshix = 1;
}
if (fabsq (sinhix) > fabsq (cosrx) * FLT128_EPSILON)
@ -114,6 +116,7 @@ ctanq (__complex128 x)
__real__ res = sinrx * cosrx / den;
__imag__ res = sinhix * coshix / den;
}
math_check_force_underflow_complex (res);
}
return res;

27
libquadmath/math/erfq.c
View File

@ -27,11 +27,11 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
License along with this library; if not, see
<http://www.gnu.org/licenses/>. */
/* __float128 erfq(__float128 x)
* __float128 erfcq(__float128 x)
/* double erf(double x)
* double erfc(double x)
* x
* 2 |\
* erf(x) = --------- | exp(-t*t)dt
@ -96,14 +96,8 @@
* erfc/erf(NaN) is NaN
*/
#include <errno.h>
#include "quadmath-imp.h"
__float128 erfcq (__float128);
/* Evaluate P[n] x^n + P[n-1] x^(n-1) + ... + P[0] */
static __float128
@ -143,8 +137,8 @@ deval (__float128 x, const __float128 *p, int n)
static const __float128
tiny = 1e-4931Q,
one = 1.0Q,
two = 2.0Q,
one = 1,
two = 2,
/* 2/sqrt(pi) - 1 */
efx = 1.2837916709551257389615890312154517168810E-1Q;
@ -810,7 +804,7 @@ erfq (__float128 x)
__float128
erfcq (__float128 x)
{
__float128 y = 0.0Q, z, p, r;
__float128 y, z, p, r;
int32_t i, ix, sign;
ieee854_float128 u;
@ -868,7 +862,7 @@ erfcq (__float128 x)
y += C18a;
break;
case 8:
z = x - 1.0Q;
z = x - 1;
y = C19b + z * neval (z, RNr19, NRNr19) / deval (z, RDr19, NRDr19);
y += C19a;
break;
@ -879,7 +873,7 @@ erfcq (__float128 x)
break;
}
if (sign & 0x80000000)
y = 2.0Q - y;
y = 2 - y;
return y;
}
/* 1.25 < |x| < 107 */
@ -924,7 +918,8 @@ erfcq (__float128 x)
u.words32.w3 = 0;
u.words32.w2 &= 0xfe000000;
z = u.value;
r = expq (-z * z - 0.5625) * expq ((z - x) * (z + x) + p);
r = expq (-z * z - 0.5625) *
expq ((z - x) * (z + x) + p);
if ((sign & 0x80000000) == 0)
{
__float128 ret = r / x;

51
libquadmath/math/exp2q.c Normal file
View File

@ -0,0 +1,51 @@
/* Compute 2^x.
Copyright (C) 2012-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#include "quadmath-imp.h"
__float128
exp2q (__float128 x)
{
if (__glibc_likely (__builtin_isless (x, (__float128) FLT128_MAX_EXP)))
{
if (__builtin_expect (__builtin_isgreaterequal (x, (__float128) (FLT128_MIN_EXP - FLT128_MANT_DIG
- 1)), 1))
{
int intx = (int) x;
__float128 fractx = x - intx;
__float128 result;
if (fabsq (fractx) < FLT128_EPSILON / 4)
result = scalbnq (1 + fractx, intx);
else
result = scalbnq (expq (M_LN2q * fractx), intx);
math_check_force_underflow_nonneg (result);
return result;
}
else
{
/* Underflow or exact zero. */
if (isinfq (x))
return 0;
else
return FLT128_MIN * FLT128_MIN;
}
}
else
/* Infinity, NaN or overflow. */
return FLT128_MAX * x;
}

23
libquadmath/math/expm1q.c
View File

@ -1,15 +1,15 @@
/* expm1l.c
/* expm1q.c
*
* Exponential function, minus 1
* 128-bit __float128 precision
* 128-bit long double precision
*
*
*
* SYNOPSIS:
*
* __float128 x, y, expm1l();
* long double x, y, expm1q();
*
* y = expm1l( x );
* y = expm1q( x );
*
*
*
@ -48,12 +48,9 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
License along with this library; if not, see
<http://www.gnu.org/licenses/>. */
#include <errno.h>
#include "quadmath-imp.h"
/* exp(x) - 1 = x + 0.5 x^2 + x^3 P(x)/Q(x)
@ -83,7 +80,7 @@ static const __float128
C1 = 6.93145751953125E-1Q,
C2 = 1.428606820309417232121458176568075500134E-6Q,
/* ln 2^-114 */
minarg = -7.9018778583833765273564461846232128760607E1Q;
minarg = -7.9018778583833765273564461846232128760607E1Q, big = 1e4932Q;
__float128
@ -108,7 +105,7 @@ expm1q (__float128 x)
{
/* Infinity (which must be negative infinity). */
if (((ix & 0xffff) | u.words32.w1 | u.words32.w2 | u.words32.w3) == 0)
return -1.0Q;
return -1;
/* NaN. Invalid exception if signaling. */
return x + x;
}
@ -119,7 +116,7 @@ expm1q (__float128 x)
/* Minimum value. */
if (x < minarg)
return (4.0/HUGE_VALQ - 1.0Q);
return (4.0/big - 1);
/* Avoid internal underflow when result does not underflow, while
ensuring underflow (without returning a zero of the wrong sign)
@ -156,7 +153,7 @@ expm1q (__float128 x)
exp(x) - 1 = 2^k (qx + 1) - 1
= 2^k qx + 2^k - 1. */
px = ldexpq (1.0Q, k);
px = ldexpq (1, k);
x = px * qx + (px - 1.0);
return x;
}

1020
libquadmath/math/expq.c
View File

File diff suppressed because it is too large Load Diff

970
libquadmath/math/expq_table.h Normal file
View File

@ -0,0 +1,970 @@
/* Accurate table for expq().
Copyright (C) 1999-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Jakub Jelinek <jj@ultra.linux.cz>
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
/* __expq_table basically consists of four tables, T_EXPL_ARG{1,2} and
T_EXPL_RES{1,2}. All tables use positive and negative indexes, the 0 points
are marked by T_EXPL_* defines.
For ARG1 and RES1 tables lets B be 89 and S 256.0, for ARG2 and RES2 B is 65
and S 32768.0.
These table have the property that, for all integers -B <= i <= B
expq(__expq_table[T_EXPL_ARGN+2*i]+__expq_table[T_EXPL_ARGN+2*i+1]+r) ==
__expq_table[T_EXPL_RESN+i], __expq_table[T_EXPL_RESN+i] is some exact number
with the low 58 bits of the mantissa 0,
__expq_table[T_EXPL_ARGN+2*i] == i/S+s
where absl(s) <= 2^-54 and absl(r) <= 2^-212. */
static const __float128 __expq_table [] = {
-3.47656250000000000584188889839535373E-01Q, /* bffd640000000000002b1b04213cf000 */
6.90417668990715641167244540876988960E-32Q, /* 3f97667c3fdb588a6ae1af8748357a17 */
-3.43749999999999981853132895957607418E-01Q, /* bffd5ffffffffffffac4ff5f4050b000 */
-7.16021898043268093462818380603370350E-33Q, /* bf94296c8219427edc1431ac2498583e */
-3.39843750000000013418643523138766329E-01Q, /* bffd5c000000000003de1f027a30e000 */
8.16920774283317801641347327589583265E-32Q, /* 3f97a82b65774bdca1b4440d749ed8d3 */
-3.35937500000000014998092453039303051E-01Q, /* bffd5800000000000452a9f4d8857000 */
-6.55865578425428447938248396879359670E-32Q, /* bf97548b7d240f3d034b395e6eecfac8 */
-3.32031250000000000981984049529998541E-01Q, /* bffd540000000000004875277cda5000 */
6.91213046334032232108944519541512737E-32Q, /* 3f9766e5f925338a19045c94443b66e1 */
-3.28124999999999986646017645350399708E-01Q, /* bffd4ffffffffffffc26a667bf44d000 */
-6.16281060996110316602421505683742661E-32Q, /* bf973ffdcdcffb6fbffc86b2b8d42f5d */
-3.24218749999999991645717430645867963E-01Q, /* bffd4bfffffffffffd97901063e48000 */
-7.90797211087760527593856542417304137E-32Q, /* bf979a9afaaca1ada6a8ed1c80584d60 */
-3.20312499999999998918211610690789652E-01Q, /* bffd47ffffffffffffb02d9856d71000 */
8.64024799457616856987630373786503376E-32Q, /* 3f97c0a098623f95579d5d9b2b67342d */
-3.16406249999999998153974811017181883E-01Q, /* bffd43ffffffffffff77c991f1076000 */
-2.73176610180696076418536105483668404E-32Q, /* bf961baeccb32f9b1fcbb8e60468e95a */
-3.12500000000000011420976192575972779E-01Q, /* bffd400000000000034ab8240483d000 */
7.16573502812389453744433792609989420E-32Q, /* 3f977410f4c2cfc4335f28446c0fb363 */
-3.08593750000000001735496343854851414E-01Q, /* bffd3c000000000000800e995c176000 */
-1.56292999645122272621237565671593071E-32Q, /* bf95449b9cbdaff6ac1246adb2c826ac */
-3.04687499999999982592401295899221626E-01Q, /* bffd37fffffffffffafb8bc1e061a000 */
6.48993208584888904958594509625158417E-32Q, /* 3f9750f9fe8366d82d77afa0031a92e1 */
-3.00781249999999999230616898937763959E-01Q, /* bffd33ffffffffffffc73ac39da54000 */
6.57082437496961397305801409357792029E-32Q, /* 3f97552d3cb598ea80135cf3feb27ec4 */
-2.96874999999999998788769281703245722E-01Q, /* bffd2fffffffffffffa6a07fa5021000 */
-3.26588297198283968096426564544269170E-32Q, /* bf9653260fc1802f46b629aee171809b */
-2.92968750000000015318089182805941695E-01Q, /* bffd2c0000000000046a468614bd6000 */
-1.73291974845198589684358727559290718E-32Q, /* bf9567e9d158f52e483c8d8dcb5961dd */
-2.89062500000000007736778942676309681E-01Q, /* bffd280000000000023adf9f4c3d3000 */
-6.83629745986675744404029225571026236E-32Q, /* bf9762f5face6281c1daf1c6aedbdb45 */
-2.85156250000000001367091555763661937E-01Q, /* bffd2400000000000064dfa11e3fb000 */
-5.44898442619766878281110054067026237E-32Q, /* bf971aed6d2db9f542986a785edae072 */
-2.81249999999999986958718100227029406E-01Q, /* bffd1ffffffffffffc3db9265ca9d000 */
1.13007318374506125723591889451107046E-32Q, /* 3f94d569fe387f456a97902907ac3856 */
-2.77343750000000000356078829380495179E-01Q, /* bffd1c0000000000001a462390083000 */
-4.98979365468978332358409063436543102E-32Q, /* bf970315bbf3e0d14b5c94c900702d4c */
-2.73437499999999990276993957508540484E-01Q, /* bffd17fffffffffffd32919bcdc94000 */
-8.79390484115892344533724650295100871E-32Q, /* bf97c89b0b89cc19c3ab2b60da9bbbc3 */
-2.69531250000000002434203866460082225E-01Q, /* bffd14000000000000b39ccf9e130000 */
9.44060754687026590886751809927191596E-32Q, /* 3f97ea2f32cfecca5c64a26137a9210f */
-2.65624999999999997296320716986257179E-01Q, /* bffd0fffffffffffff3880f13a2bc000 */
2.07142664067265697791007875348396921E-32Q, /* 3f95ae37ee685b9122fbe377bd205ee4 */
-2.61718750000000010237478733739017956E-01Q, /* bffd0c000000000002f3648179d40000 */
-6.10552936159265665298996309192680256E-32Q, /* bf973d0467d31e407515a3cca0f3b4e2 */
-2.57812500000000011948220522778370303E-01Q, /* bffd08000000000003719f81275bd000 */
6.72477169058908902499239631466443836E-32Q, /* 3f975d2b8c475d3160cf72d227d8e6f9 */
-2.53906249999999991822993360536596860E-01Q, /* bffd03fffffffffffda4a4b62f818000 */
-2.44868296623215865054704392917190994E-32Q, /* bf95fc92516c6d057d29fc2528855976 */
-2.49999999999999986862019457428548084E-01Q, /* bffcfffffffffffff86d2d20d5ff4000 */
-3.85302898949105073614122724961613078E-32Q, /* bf96901f147cb7d643af71b6129ce929 */
-2.46093750000000000237554160737318435E-01Q, /* bffcf8000000000000230e8ade26b000 */
-1.52823675242678363494345369284988589E-32Q, /* bf953d6700c5f3fc303f79d0ec8c680a */
-2.42187500000000003023380963205457065E-01Q, /* bffcf0000000000001be2c1a78bb0000 */
-7.78402037952209709489481182714311699E-34Q, /* bf9102ab1f3998e887f0ee4cf940faa5 */
-2.38281249999999995309623303145485725E-01Q, /* bffce7fffffffffffd4bd2940f43f000 */
-3.54307216794236899443913216397197696E-32Q, /* bf966fef03ab69c3f289436205b21d02 */
-2.34374999999999998425804947623207526E-01Q, /* bffcdfffffffffffff17b097a6092000 */
-2.86038428948386602859761879407549696E-32Q, /* bf96290a0eba0131efe3a05fe188f2e3 */
-2.30468749999999993822207406785200832E-01Q, /* bffcd7fffffffffffc70519834eae000 */
-2.54339521031747516806893838749365762E-32Q, /* bf96081f0ad7f9107ae6cddb32c178ab */
-2.26562499999999997823524030344489884E-01Q, /* bffccffffffffffffebecf10093df000 */
4.31904611473158635644635628922959401E-32Q, /* 3f96c083f0b1faa7c4c686193e38d67c */
-2.22656250000000004835132405125162742E-01Q, /* bffcc8000000000002c98a233f19f000 */
2.54709791629335691650310168420597566E-33Q, /* 3f92a735903f5eed07a716ab931e20d9 */
-2.18749999999999988969454021829236626E-01Q, /* bffcbffffffffffff9a42dc14ce36000 */
-3.77236096429336082213752014054909454E-32Q, /* bf9687be8e5b2fca54d3e81157eac660 */
-2.14843750000000010613256919115758495E-01Q, /* bffcb80000000000061e3d828ecac000 */
-4.55194148712216691177097854305964738E-32Q, /* bf96d8b35c776aa3e1a4768271380503 */
-2.10937499999999993204656148110447201E-01Q, /* bffcaffffffffffffc152f2aea118000 */
-2.95044199165561453749332254271716417E-32Q, /* bf96326433b00b2439094d9bef22ddd1 */
-2.07031250000000012233944895423355677E-01Q, /* bffca80000000000070d695ee0e94000 */
1.93146788688385419095981415411012357E-32Q, /* 3f959126729135a5e390d4bb802a0bde */
-2.03125000000000008030983633336321863E-01Q, /* bffca0000000000004a129fbc51af000 */
2.37361904671826193563212931215900137E-32Q, /* 3f95ecfb3c4ba1b97ea3ad45cbb1e68a */
-1.99218750000000001763815712796132779E-01Q, /* bffc98000000000001044b12d9950000 */
-3.63171243370923753295192486732883239E-33Q, /* bf932db5fb3f27c38e0fa7bbcfc64f55 */
-1.95312500000000004883660234506677272E-01Q, /* bffc90000000000002d0b3779d1f9000 */
-3.19989507343607877747980892249711601E-33Q, /* bf9309d63de96bb3ef744c865f22f1bd */
-1.91406250000000013720152363227519348E-01Q, /* bffc88000000000007e8bcb387121000 */
-1.89295754093147174148371614722178860E-32Q, /* bf958926e2e67dfe812c508290add2e7 */
-1.87500000000000000182342082774432620E-01Q, /* bffc800000000000001ae8b06a39f000 */
-2.96812835183184815200854214892983927E-32Q, /* bf96343a62d156bbe71f55d14ca4b6e5 */
-1.83593750000000012410147185883290345E-01Q, /* bffc78000000000007276a1adda8d000 */
-2.02191931237489669058466239995304587E-32Q, /* bf95a3efab92d26ec2df90df036a117f */
-1.79687499999999997439177363346082917E-01Q, /* bffc6ffffffffffffe8616db2927d000 */
-9.92752326937775530007399526834009465E-33Q, /* bf949c5f88ed17041e1a3f1829d543cd */
-1.75781249999999995824373974504785174E-01Q, /* bffc67fffffffffffd97c94f13ea3000 */
1.44184772065335613487885714828816178E-32Q, /* 3f952b75c63476e7fcc2f5841c27bcce */
-1.71874999999999986685050259043077809E-01Q, /* bffc5ffffffffffff8530f6bc531a000 */
-3.49007014971241147689894940544402482E-32Q, /* bf966a6dfaa012aea8ffe6d90b02330f */
-1.67968749999999997316058782350439701E-01Q, /* bffc57fffffffffffe73eb914f2aa000 */
3.34025733574205019081305778794376391E-32Q, /* 3f965adf4572561fd5456a6c13d8babf */
-1.64062499999999993322730602128318480E-01Q, /* bffc4ffffffffffffc269be4f68f3000 */
-1.83345916769684984022099095506340635E-32Q, /* bf957ccb69026cb2f6024c211576d5f4 */
-1.60156249999999992419000744447607979E-01Q, /* bffc47fffffffffffba13df21784a000 */
2.73442789798110494773517431626534726E-32Q, /* 3f961bf58ff22c9b30f1e2b39f26d7d5 */
-1.56249999999999987665010524130393080E-01Q, /* bffc3ffffffffffff8e3ad45e7508000 */
2.02695576464836145806428118889332191E-32Q, /* 3f95a4fb7435a4a2f71de81eb8ae75d1 */
-1.52343749999999989905291167951491803E-01Q, /* bffc37fffffffffffa2e48aecfc24000 */
-3.61436631548815190395331054871041524E-32Q, /* bf967756567ebd108075ae527cc2e7f0 */
-1.48437500000000006686107754967759751E-01Q, /* bffc30000000000003dab20261b3c000 */
-2.15524270159131591469319477922198390E-32Q, /* bf95bfa05b82ef3a708c4f0395e9fcf6 */
-1.44531250000000005132889939177166485E-01Q, /* bffc28000000000002f57b1969e7b000 */
2.74741116529653547935086189244019604E-32Q, /* 3f961d4eb77c1185d34fe1b04a3f3cf5 */
-1.40625000000000000707469094533647325E-01Q, /* bffc2000000000000068676d3d5c4000 */
4.40607097220049957013547629906723266E-33Q, /* 3f936e0ac425daf795b42913cf0ef881 */
-1.36718749999999995713752139187543306E-01Q, /* bffc17fffffffffffd87762255991000 */
-3.73751317180116492404578048203389108E-32Q, /* bf9684202491e9cbb7ceb67d9ff7e0c9 */
-1.32812500000000007198453630478482191E-01Q, /* bffc10000000000004264de3a4379000 */
-3.97050085179660203884930593717220728E-32Q, /* bf969c52048de14be3c9c1971e50869c */
-1.28906250000000006070486371645733082E-01Q, /* bffc080000000000037fd87db2cb0000 */
3.59610068058504988294019521946586131E-32Q, /* 3f967570c10687cb8e9ebd0b280abf5a */
-1.25000000000000003700729208608337966E-01Q, /* bffc00000000000002222198bbc74000 */
3.23464851393124362331846965931995969E-33Q, /* 3f930cb95da3bfc847e593716c91d57a */
-1.21093750000000013729038501177102555E-01Q, /* bffbf000000000000fd418d1f5fda000 */
2.45242487730722066611358741283977619E-32Q, /* 3f95fd5945ad86a464292e26ac192a84 */
-1.17187499999999999765305306880205578E-01Q, /* bffbdfffffffffffffbabaf869845000 */
-1.14557520298960389903199646350205537E-32Q, /* bf94dbda735322179d9bcf392e1dd06d */
-1.13281250000000009579647893740755690E-01Q, /* bffbd000000000000b0b69bae7ab9000 */
2.37873962873837390105423621772752350E-32Q, /* 3f95ee0b7e0bd5ac1f6fab1e2a71abc3 */
-1.09375000000000008981153004560108539E-01Q, /* bffbc000000000000a5ac4bc1d2c3000 */
1.53152444860014076105003555837231015E-32Q, /* 3f953e15ce931e12ef9a152522e32bdd */
-1.05468749999999992399063850363228723E-01Q, /* bffbaffffffffffff73c998091408000 */
-8.75920903597804862471749360196688834E-33Q, /* bf946bd7e310a01bae5687ebdc47fcc5 */
-1.01562500000000007685885179918350550E-01Q, /* bffba0000000000008dc7910a648c000 */
-4.63820993797174451904075397785059501E-33Q, /* bf938153d0e54001a472da180fb5e8aa */
-9.76562499999999887262211517861331814E-02Q, /* bffb8ffffffffffff300915aa6fd6000 */
-2.63767025974952608658936466715705903E-33Q, /* bf92b64215bb8d520be5404620d38088 */
-9.37499999999999939650246024457439795E-02Q, /* bffb7ffffffffffff90aca26bd0fc000 */
-1.72047822349322956713582039121348377E-32Q, /* bf9565545015c5b9b56d02cfefca2c7d */
-8.98437500000000033088896383977486369E-02Q, /* bffb70000000000003d09ca1e3cbe000 */
3.04831994420989436248526129869697270E-33Q, /* 3f92fa7d30d2ed90e7ebbd6231fd08b1 */
-8.59374999999999947312400115121319225E-02Q, /* bffb5ffffffffffff9ecefc03376e000 */
1.50416954438393392150792422537312281E-32Q, /* 3f9538675ee99bd722fad0023c09c915 */
-8.20312500000000054182280847004695514E-02Q, /* bffb500000000000063f2dbd40200000 */
2.68399664523430004488075638997207289E-33Q, /* 3f92bdf49766629882c49a3da88928ed */
-7.81250000000000114767533968079748798E-02Q, /* bffb4000000000000d3b56f81ba70000 */
1.72318124201659121296305402819694281E-32Q, /* 3f9565e407aaabfb359e8a567d760de3 */
-7.42187500000000035531829472486812869E-02Q, /* bffb3000000000000418b6e9b5388000 */
2.09401756478514117051383998628099655E-32Q, /* 3f95b2e91221fcd74be0a86d8ad658d2 */
-7.03124999999999987474933134860732535E-02Q, /* bffb1ffffffffffffe8e53453d2ac000 */
2.28515798224350800271565551341211666E-32Q, /* 3f95da9bd6adf00894f05b5cc5530125 */
-6.64062500000000042267533361089054159E-02Q, /* bffb10000000000004df8473dbcf2000 */
1.97576478800281368377376002585430031E-32Q, /* 3f959a59acbddb2f53bd3096b66370e9 */
-6.25000000000000066329769382774201686E-02Q, /* bffb00000000000007a5b5914e336000 */
-1.46422615813786836245343723048221678E-33Q, /* bf91e69295f069fc0c4a9db181ea25a3 */
-5.85937500000000002823707957982406053E-02Q, /* bffae0000000000000a6aeab10592000 */
9.25637741701318872896718218457555829E-33Q, /* 3f94807eb021f1f40a37d4015b1eb76b */
-5.46875000000000081586888005226044448E-02Q, /* bffac0000000000012d00a3171e3a000 */
-4.87144542459404765480424673678105050E-33Q, /* bf9394b42faba6b7036fe7b36269daf3 */
-5.07812499999999927720348253140567013E-02Q, /* bffa9fffffffffffef555cc8dd914000 */
-3.01901021987395945826043649523451725E-33Q, /* bf92f59e7e3025691f290f8f67277faf */
-4.68749999999999935349476738962633103E-02Q, /* bffa7ffffffffffff117b4ea2b876000 */
1.21521638219189777347767475937119750E-32Q, /* 3f94f8c7f88c5b56674b94d984ac8ecb */
-4.29687500000000056305562847814228219E-02Q, /* bffa6000000000000cfbb19be30c0000 */
-1.18643699217679276275559592978275214E-32Q, /* bf94ecd39f0833a876550e83eb012b99 */
-3.90624999999999962692914526031373542E-02Q, /* bffa3ffffffffffff765c743922f9000 */
-4.91277156857520035712509544689973679E-33Q, /* bf939823189996193872e58ac0dececb */
-3.51562500000000108152468207687602886E-02Q, /* bffa20000000000018f031e41177f000 */
1.18599806302656253755207072755609820E-32Q, /* 3f94eca4f23e787fab73ce8f6b9b8d64 */
-3.12500000000000077376981036742289578E-02Q, /* bffa00000000000011d787e0b386f000 */
9.97730386477005171963635210799577079E-33Q, /* 3f949e70e498c46a0173ac0d46c699fc */
-2.73437500000000139436129596418623235E-02Q, /* bff9c00000000000404db66e70a08000 */
2.25755321633070123579875157841633859E-33Q, /* 3f927719b1a93074bdf9f3c2cb784785 */
-2.34375000000000088003629211828324876E-02Q, /* bff98000000000002895a27d45feb000 */
2.84374279216848803102126617873942975E-33Q, /* 3f92d87f70e749d6da6c260b68dc210b */
-1.95312500000000107408831063404855424E-02Q, /* bff9400000000000318898ba69f71000 */
2.47348089686935458989103979140011912E-33Q, /* 3f929afa3de45086fe909fdddb41edce */
-1.56250000000000081443917555362290635E-02Q, /* bff9000000000000258f335e9cdd6000 */
-2.43379314483517422161458863218426254E-33Q, /* bf9294621c8a9ccacf2b020ec19cad27 */
-1.17187500000000051490597418161403184E-02Q, /* bff88000000000002f7ddfa26221f000 */
1.83405297208145390679150568810924707E-33Q, /* 3f9230bbfc5d5fe1b534fbcda0465bb9 */
-7.81249999999999715861805208310174953E-03Q, /* bff7ffffffffffffcb95f3fff157d000 */
3.51548384878710915171654413641872451E-34Q, /* 3f8fd349b76c22966f77a39fc37ed704 */
-3.90625000000000309326013918295097128E-03Q, /* bff7000000000000390f820c8e153000 */
6.38058004651791109324060099097251911E-36Q, /* 3f8a0f665d3ac25a1ac94d688273dbcd */
#define T_EXPL_ARG1 (2*89)
0.00000000000000000000000000000000000E+00Q, /* 00000000000000000000000000000000 */
0.00000000000000000000000000000000000E+00Q, /* 00000000000000000000000000000000 */
3.90625000000000245479958859972588985E-03Q, /* 3ff70000000000002d48769ac9874000 */
-6.58439598384342854976169982902779828E-36Q, /* bf8a1811b923e6c626b07ef29761482a */
7.81250000000001311374391093664996358E-03Q, /* 3ff800000000000078f3f3cd89111000 */
2.60265650555493781464273319671555602E-33Q, /* 3f92b070c3b635b87af426735a71fc87 */
1.17187500000000269581156218247101912E-02Q, /* 3ff8800000000000f8a50d02fe20d000 */
1.00961747974945520631836275894919326E-33Q, /* 3f914f80c1a4f8042044fe3b757b030b */
1.56249999999999797878275270751825475E-02Q, /* 3ff8ffffffffffff45935b69da62e000 */
2.03174577741375590087897353146748580E-33Q, /* 3f925194e863496e0f6e91cbf6b22e26 */
1.95312499999999760319884511789111533E-02Q, /* 3ff93fffffffffff917790ff9a8f4000 */
4.62788519658803722282100289809515007E-33Q, /* 3f9380783ba81295feeb3e4879d7d52d */
2.34374999999999822953909016349145918E-02Q, /* 3ff97fffffffffffae5a163bd3cd5000 */
-3.19499956304699705390404384504876533E-33Q, /* bf93096e2037ced8194cf344c692f8d6 */
2.73437500000000137220327275871555682E-02Q, /* 3ff9c000000000003f481dea5dd51000 */
-2.25757776523031994464630107442723424E-33Q, /* bf92771abcf988a02b414bf2614e3734 */
3.12499999999999790857640618332718621E-02Q, /* 3ff9ffffffffffff9f8cd40b51509000 */
-4.22479470489989916319395454536511458E-33Q, /* bf935efb7245612f371deca17cb7b30c */
3.51562499999999840753382405747597346E-02Q, /* 3ffa1fffffffffffdb47bd275f722000 */
1.08459658374118041980976756063083500E-34Q, /* 3f8e2055d18b7117c9db1c318b1e889b */
3.90624999999999989384433621470426757E-02Q, /* 3ffa3ffffffffffffd8d5e18b042e000 */
-7.41674226146122000759491297811091830E-33Q, /* bf94341454e48029e5b0205d91baffdc */
4.29687500000000107505739500500200462E-02Q, /* 3ffa60000000000018ca04cd9085c000 */
-4.74689012756713017494437969420919847E-34Q, /* bf903b7c268103c6f7fbaaa24142e287 */
4.68749999999999978700749928325717352E-02Q, /* 3ffa7ffffffffffffb16b6d5479e3000 */
-1.06208165308448830117773486334902917E-32Q, /* bf94b92be4b3b5b5a596a0a5187cc955 */
5.07812499999999815072625435955786253E-02Q, /* 3ffa9fffffffffffd55bd086d5cbc000 */
-9.37038897148383660401929567549111394E-33Q, /* bf94853b111b0175b491c80d00419416 */
5.46874999999999809511553152189867394E-02Q, /* 3ffabfffffffffffd4138bfa74a61000 */
1.06642963074562437340498606682822123E-32Q, /* 3f94bafa3fe991b39255d563dfa05d89 */
5.85937500000000184331996330905145551E-02Q, /* 3ffae000000000002a810a5f2f8bf000 */
-1.76639977694797200820296641773791945E-34Q, /* bf8ed596f07ce4408f1705c8ec16864c */
6.25000000000000021544696744852045001E-02Q, /* 3ffb000000000000027be32045e2b000 */
1.68616371995798354366633034788947149E-32Q, /* 3f955e33d7440794d8a1b25233d086ab */
6.64062499999999965563110718495802889E-02Q, /* 3ffb0ffffffffffffc079a38a3fed000 */
-1.82463217667830160048872113565316215E-32Q, /* bf957af6163bcdb97cefab44a942482a */
7.03124999999999759989183341261898222E-02Q, /* 3ffb1fffffffffffe454218acea05000 */
-1.07843770101525495515646940862541503E-32Q, /* bf94bff72aada26d94e76e71c07e0580 */
7.42187499999999898968873730710101412E-02Q, /* 3ffb2ffffffffffff45a166496dc1000 */
1.28629441689592874462780757154138223E-32Q, /* 3f950b2724597b8b93ce1e9d1cf4d035 */
7.81249999999999957198938523510804668E-02Q, /* 3ffb3ffffffffffffb10bc52adbc5000 */
1.13297573459968118467100063135856856E-33Q, /* 3f91787eea895b3c245899cf34ad0abd */
8.20312500000000199911640621145851159E-02Q, /* 3ffb500000000000170c59a661a89000 */
-1.51161335208135146756554123073528707E-32Q, /* bf9539f326c5ca84e7db5401566f3775 */
8.59375000000000134175373433347670743E-02Q, /* 3ffb6000000000000f78287547af0000 */
1.09763629458404270323909815379924900E-32Q, /* 3f94c7f0b61b6e3e27d44b9f5bbc7e9d */
8.98437500000000036533922600308306335E-02Q, /* 3ffb70000000000004364a83b7a14000 */
3.11459653680110433194288029777718358E-33Q, /* 3f9302c0248136d65cebeab69488d949 */
9.37500000000000184977946245216914691E-02Q, /* 3ffb800000000000155395d870b17000 */
-4.66656154468277949130395786965043927E-33Q, /* bf9383aec9b993b6db492b1ede786d8a */
9.76562500000000237839723100419376084E-02Q, /* 3ffb9000000000001b6bca237f6c4000 */
-1.03028043424658760249140747856831301E-32Q, /* bf94abf6352e3d2bb398e47919a343fb */
1.01562500000000012345545575236836572E-01Q, /* 3ffba000000000000e3bc30cd9a1f000 */
2.15755372310795701322789783729456319E-32Q, /* 3f95c01b3b819edd9d07548fafd61550 */
1.05468749999999976493840484471911438E-01Q, /* 3ffbafffffffffffe4e634cd77985000 */
1.78771847038773333029677216592309083E-32Q, /* 3f95734b6ae650f33dd43c49a1df9fc0 */
1.09375000000000002267015055992785402E-01Q, /* 3ffbc00000000000029d1ad08de7b000 */
6.23263106693943817730045115112427717E-33Q, /* 3f9402e4b39ce2198a45e1d045868cd6 */
1.13281250000000022354208618429577398E-01Q, /* 3ffbd0000000000019c5cc3f9d2b5000 */
5.40514416644786448581426756221178868E-33Q, /* 3f93c10ab4021472c662f69435de9269 */
1.17187500000000013252367133076817603E-01Q, /* 3ffbe000000000000f47688cc561b000 */
-7.12412585457324989451327215568641325E-33Q, /* bf9427ecb343a8d1758990565fcfbf45 */
1.21093750000000020759863992944300792E-01Q, /* 3ffbf0000000000017ef3af97bf04000 */
6.26591408357572503875647872077266444E-33Q, /* 3f940446a09a2da771b45fc075514d12 */
1.25000000000000004739659392396765618E-01Q, /* 3ffc00000000000002bb7344ecd89000 */
-1.55611398459729463981000080101758830E-32Q, /* bf95433135febefa9e6aa4db39e263d2 */
1.28906249999999982360888081057894783E-01Q, /* 3ffc07fffffffffff5d4ed3154361000 */
-1.77531518652835570781208599686606474E-32Q, /* bf9570b7f225ea076f97f418d11359c1 */
1.32812500000000010568583998727400436E-01Q, /* 3ffc1000000000000617a5d09526a000 */
2.12104021624990594668286391598300893E-32Q, /* 3f95b885d767a1048d93055927a27adc */
1.36718749999999998434125157367005292E-01Q, /* 3ffc17ffffffffffff18eaebc7970000 */
2.50454798592543203967309921276955297E-32Q, /* 3f9604164e5598528a76faff26cd1c97 */
1.40625000000000015550032422969330356E-01Q, /* 3ffc20000000000008f6c79d8928c000 */
7.80972982879849783680252962992639832E-33Q, /* 3f9444674acf2b3225c7647e0d95edf3 */
1.44531250000000012402535562111122522E-01Q, /* 3ffc28000000000007264a8bc1ff1000 */
2.79662468716455159585514763921671876E-32Q, /* 3f96226b095bd78aa650faf95a221993 */
1.48437500000000007761020440087419948E-01Q, /* 3ffc3000000000000479530ff8fe3000 */
2.15518492972728435680556239996258527E-32Q, /* 3f95bf9d49295e73a957906a029768cb */
1.52343750000000001733189947520484032E-01Q, /* 3ffc38000000000000ffc6109f71f000 */
8.34032236093545825619420380704500188E-33Q, /* 3f945a71851226a1d0ce5e656693153e */
1.56249999999999988073295321246958484E-01Q, /* 3ffc3ffffffffffff91fedd62ae0f000 */
2.44119337150624789345260194989620908E-32Q, /* 3f95fb041a57bc1c1280680ac1620bea */
1.60156250000000002076894210913572460E-01Q, /* 3ffc48000000000001327ed84a199000 */
-7.36124501128859978061216696286151753E-33Q, /* bf9431c62f01e59d2c1e00f195a0037f */
1.64062500000000000950861276373482172E-01Q, /* 3ffc500000000000008c5285fba85000 */
-4.80566184447001164583855800470217373E-33Q, /* bf938f3d1fcafd390f22f80e6c19421f */
1.67968749999999989878071706155265999E-01Q, /* 3ffc57fffffffffffa2a445c548c5000 */
-4.42154428718618459799673088733365064E-32Q, /* bf96cb28cf1c1b28006d53ffe633b22a */
1.71874999999999999459734108403218175E-01Q, /* 3ffc5fffffffffffffb04554e9dd4000 */
-3.29736288190321377985697972236270628E-32Q, /* bf96566af0ebc852e84be12859b24a31 */
1.75781249999999997987525759778901845E-01Q, /* 3ffc67fffffffffffed702df6ffff000 */
-1.28800728638468399687523924685844352E-32Q, /* bf950b8236b88ca0c1b739dc91a7e3fc */
1.79687500000000004929565820437175783E-01Q, /* 3ffc70000000000002d779bb32d2e000 */
1.60624461317978482424582320675174225E-32Q, /* 3f954d9a9cc0c963fd081f3dc922d04e */
1.83593750000000016873727045739708856E-01Q, /* 3ffc78000000000009ba1f6263c9a000 */
-3.83390389582056606880506003118452558E-32Q, /* bf968e22a5d826f77f19ee788474df22 */
1.87500000000000013443068740761666872E-01Q, /* 3ffc80000000000007bfd8c72a1bf000 */
-2.74141662712926256150154726565203091E-32Q, /* bf961caf5ac59c7f941f928e324c2cc1 */
1.91406249999999981494101786848611970E-01Q, /* 3ffc87fffffffffff55502eeae001000 */
3.68992437075565165346469517256118001E-32Q, /* 3f967f2f03f9096793372a27b92ad79d */
1.95312499999999989069921848800501648E-01Q, /* 3ffc8ffffffffffff9b3015280394000 */
3.69712249337856518452988332367785220E-32Q, /* 3f967fee5fdb5bd501ff93516999faa0 */
1.99218750000000021148042946919300804E-01Q, /* 3ffc9800000000000c30e67939095000 */
2.50142536781142175091322844848566649E-32Q, /* 3f9603c34ae58e10b300b07137ee618a */
2.03124999999999977732559198825437141E-01Q, /* 3ffc9ffffffffffff329e7df079e4000 */
-2.41951877287895024779300892731537816E-32Q, /* bf95f683aefe6965f080df8f59dd34a1 */
2.07031249999999996744030653771913124E-01Q, /* 3ffca7fffffffffffe1f80f4b73ca000 */
-1.94346475904454000031592792989765585E-32Q, /* bf9593a44f87870a3d100d498501ecc7 */
2.10937500000000000251399259834392298E-01Q, /* 3ffcb000000000000025199873310000 */
-1.33528748788094249098998693871759411E-33Q, /* bf91bbb9b25c813668d6103d08acac35 */
2.14843749999999993936323609611875097E-01Q, /* 3ffcb7fffffffffffc8128c866236000 */
1.14839877977014974625242788556545292E-32Q, /* 3f94dd06b4655c9b83a1305b240e7a42 */
2.18750000000000015181732784749663837E-01Q, /* 3ffcc0000000000008c06da5fff24000 */
1.42689085313142539755499441881408391E-32Q, /* 3f95285a87dfa7ea7dad5b3be8c669f4 */
2.22656249999999992172647770539596569E-01Q, /* 3ffcc7fffffffffffb7ce2fe531f6000 */
-3.34421462850496887359128610229650547E-32Q, /* bf965b487962b5c2d9056ca6ac0c2e5c */
2.26562499999999989595607223847082419E-01Q, /* 3ffccffffffffffffa0095277be5c000 */
-3.08983588107248752517344356508205569E-32Q, /* bf9640dded57157f8eded311213bdbcd */
2.30468749999999979130462438434567117E-01Q, /* 3ffcd7fffffffffff3f8332996560000 */
-3.01407539802851697849105682795217019E-32Q, /* bf9638ffde35dbdfe1a1ffe45185de5d */
2.34375000000000012194252337217891971E-01Q, /* 3ffce0000000000007078dd402c86000 */
-8.46879710915628592284714319904522657E-33Q, /* bf945fc7b29a2ac6c9eff9eb258a510f */
2.38281249999999982991877076137149870E-01Q, /* 3ffce7fffffffffff6320b486eece000 */
-2.93563878880439245627127095245798544E-32Q, /* bf9630daaa4f40ff05caf29ace2ea7d4 */
2.42187499999999981447559841442773990E-01Q, /* 3ffceffffffffffff54e24a09a8d5000 */
-4.56766746558806021264215486909850481E-32Q, /* bf96da556dee11f3113e5a3467b908e6 */
2.46093749999999991067720539980207318E-01Q, /* 3ffcf7fffffffffffad9d405dcb5d000 */
2.14033004219908074003010247652128251E-32Q, /* 3f95bc8776e8f9ae098884aa664cc3df */
2.50000000000000016613825838126835953E-01Q, /* 3ffd00000000000004c9e24c12bb3000 */
2.57617532593749185996714235009382870E-32Q, /* 3f960b867cc01178c0ec68226c6cb47d */
2.53906250000000013372004437827044321E-01Q, /* 3ffd04000000000003daae05b3168000 */
7.20177123439204414298152646284640101E-32Q, /* 3f9775eff59ddad7e7530b83934af87f */
2.57812499999999995765234725413886085E-01Q, /* 3ffd07fffffffffffec7878bad9d5000 */
6.51253187532920882777046064603770602E-32Q, /* 3f975226659ca241402e71c2011583b0 */
2.61718750000000007647689994011222248E-01Q, /* 3ffd0c000000000002344cc793a0f000 */
3.02370610028725823590045201871491395E-32Q, /* 3f9639ffe55fa2fa011674448b4e5b96 */
2.65624999999999986893899042596554269E-01Q, /* 3ffd0ffffffffffffc38f0c0a1e9f000 */
-2.07683715950724761146070082510569258E-32Q, /* bf95af579a92e872fef81abfdf06bae8 */
2.69531249999999979842788204900639327E-01Q, /* 3ffd13fffffffffffa30a908d67db000 */
8.71465252506557329027658736641075706E-32Q, /* 3f97c47d99e19830447a42b1c0ffac61 */
2.73437500000000006712165837793818271E-01Q, /* 3ffd18000000000001ef453a58edb000 */
-6.62704045767568912140550474455810301E-32Q, /* bf9758187a204dcb06ece46588aeeaba */
2.77343749999999994411329302988535617E-01Q, /* 3ffd1bfffffffffffe63a0fec9c9e000 */
-4.87273466291944117406493607771338767E-32Q, /* bf96fa0381b0844a0be46bac2d673f0c */
2.81250000000000012677892447379453135E-01Q, /* 3ffd20000000000003a7769e125d6000 */
-8.55871796664700790726282049552906783E-32Q, /* bf97bc64e01332cf7616b0091b8dff2c */
2.85156249999999998558643013736363981E-01Q, /* 3ffd23ffffffffffff95a5894bccf000 */
-1.33068334720606220176455289635046875E-32Q, /* bf95145f43290ecf5b7adcb24697bc73 */
2.89062500000000008831431235621753924E-01Q, /* 3ffd280000000000028ba504fac59000 */
-9.34157398616814623985483776710704237E-32Q, /* bf97e50ad1115b941fcb5f0c88a428f7 */
2.92968750000000019840235286110877063E-01Q, /* 3ffd2c000000000005b7f372d184f000 */
4.99302093775173155906059132992249671E-33Q, /* 3f939ecdcfb97bad3f8dbec5df5ec67d */
2.96875000000000015867911730971630513E-01Q, /* 3ffd3000000000000492d860c79db000 */
7.86107787827057767235127454590866211E-33Q, /* 3f944689517ee8f16cdb97d6a6938f32 */
3.00781250000000015814100002286124758E-01Q, /* 3ffd340000000000048edfe73a17d000 */
-1.65419431293024229981937172317171504E-32Q, /* bf9557900e3efca16c89646b57f68dc0 */
3.04687499999999985213157159965287195E-01Q, /* 3ffd37fffffffffffbbcec6f99b36000 */
9.68753602893894024018934325652944198E-32Q, /* 3f97f70170e5458660c33a7e8d43d049 */
3.08593749999999989969324338045156215E-01Q, /* 3ffd3bfffffffffffd1bdde4d0fb1000 */
7.10268609610294706092252562643261106E-32Q, /* 3f9770cae45cdf615010401a4b37d8d4 */
3.12500000000000002971606591018488854E-01Q, /* 3ffd40000000000000db440fbc06b000 */
6.38924218802905979887732294952782964E-32Q, /* 3f974bbf988bb5622bd8fbaa46e8b811 */
3.16406250000000006594921047402056305E-01Q, /* 3ffd44000000000001e69e8954814000 */
3.96079878754651470094149874444850097E-32Q, /* 3f969b5017b9fa7a1e86975258c73d3d */
3.20312500000000006713799366908329147E-01Q, /* 3ffd48000000000001ef64159c065000 */
-1.86401314975634286055150437995880517E-32Q, /* bf958323f0434911794e5fb8bfe136ba */
3.24218749999999987061246567584951210E-01Q, /* 3ffd4bfffffffffffc4549db9b928000 */
-3.18643523744758601387071062700407431E-32Q, /* bf964ae5fa7e26c2c3981bed12e14372 */
3.28124999999999991782776266707412953E-01Q, /* 3ffd4ffffffffffffda1ad0840ca8000 */
-4.46964199751314296839915534813144652E-32Q, /* bf96d0277729ffd74727150df6d15547 */
3.32031250000000000393816557756032682E-01Q, /* 3ffd540000000000001d0efc04fad000 */
-9.03246333902065439930373230002688649E-33Q, /* bf947731a008748cc6dee948839ef7ae */
3.35937499999999983810482995064392173E-01Q, /* 3ffd57fffffffffffb556cab8ae61000 */
5.27742727066129518825981597650621794E-32Q, /* 3f9712050a6ddbf1cabf1b971f4b5d0b */
3.39843750000000004310441349760912471E-01Q, /* 3ffd5c0000000000013e0def5ddc4000 */
-3.85927263474732591932884416445586106E-32Q, /* bf9690c51088ef3db9ca000829c450c2 */
3.43749999999999990248130003997484364E-01Q, /* 3ffd5ffffffffffffd3070624a0af000 */
9.62005170171527308106468341512327487E-34Q, /* 3f913fae595cea84432eb01430817fca */
3.47656250000000004085726414568625697E-01Q, /* 3ffd640000000000012d79309e291000 */
-6.59664093705705297250259434519072507E-32Q, /* bf97568465eafb0e662e64a5dbfaf35f */
-1.98364257812501251077851763965418372E-03Q, /* bff6040000000001cd90f658cf0b1000 */
-3.71984513103117734260309047540278737E-34Q, /* bf8fee73c54483194782aac4a6154d11 */
-1.95312500000000378520649630233891879E-03Q, /* bff60000000000008ba643bb5e2e8000 */
-1.12194202736719050440745599339855038E-34Q, /* bf8e2a436aeff7bc529873354f47a3f5 */
-1.92260742187499397430259771221991482E-03Q, /* bff5f7fffffffffe4361cb51170da000 */
-2.30068299876822157331268484824540848E-34Q, /* bf8f31d02f85cfe8c0cc02276ce0f437 */
-1.89208984375001137424603270262074989E-03Q, /* bff5f0000000000347456ed490c23000 */
-1.15012507244426243338260435466985403E-34Q, /* bf8e31c174d5677a937a34ad8d2a70b4 */
-1.86157226562500172319250342061336738E-03Q, /* bff5e800000000007f262fa3617b4000 */
-3.12438344643346437509767736937785561E-34Q, /* bf8f9f4d426a2457c273d34ef7d9bde9 */
-1.83105468749999505256246872355430379E-03Q, /* bff5dffffffffffe92f18c1c2b6fa000 */
-5.91130415288336591179087455220308942E-35Q, /* bf8d3a4c80b42dc036bae446c9807f78 */
-1.80053710937499445182387245573120522E-03Q, /* bff5d7fffffffffe669dea82b4a4c000 */
-1.92396289352411531324908916321392100E-34Q, /* bf8eff7a2123fb573ba9778550d669bd */
-1.77001953125000387737631542516323906E-03Q, /* bff5d000000000011e19915c3ddb7000 */
7.91101758977203355387806553469731354E-36Q, /* 3f8a507f5a70faaccf469e3461873dea */
-1.73950195312500034854670281415554486E-03Q, /* bff5c8000000000019b7dc6ef97bd000 */
1.55906551582436824067407021178835755E-34Q, /* 3f8e9e7880333e34955aebcde3cfb053 */
-1.70898437499998955782591472611429852E-03Q, /* bff5bffffffffffcfd80e88aa6b96000 */
8.22951661962611381718215899498500357E-35Q, /* 3f8db58e6031a779b59f6ece191de7cc */
-1.67846679687500586652037711131708544E-03Q, /* bff5b80000000001b0df6fd21c133000 */
-8.96642618848426299713145894522897419E-35Q, /* bf8ddcbcab46d531801bfae4121f2f8a */
-1.64794921875000109499161354039904782E-03Q, /* bff5b0000000000050cbce8915575000 */
-2.88077905394253859590587789680486639E-34Q, /* bf8f7eebd4dd860ef73b674d5e707959 */
-1.61743164062501133830507079150388351E-03Q, /* bff5a80000000003449e8700c3e82000 */
-3.68271725851639066312899986829350273E-34Q, /* bf8fe9845fe20a5fe74059e0cae185d6 */
-1.58691406249999015546015764131101956E-03Q, /* bff59ffffffffffd2999e668cdd28000 */
8.48197657099957029953716507898788812E-35Q, /* 3f8dc2faaebb97392e451b07b28c4b12 */
-1.55639648437500317366570219290722587E-03Q, /* bff5980000000000ea2cd9a40d256000 */
-3.45156704719737676412949957712570373E-36Q, /* bf8925a079505516c8e317ac1ff53255 */
-1.52587890625000568759013197767046039E-03Q, /* bff5900000000001a3ab8a3f6b698000 */
-1.01902948542497496574967177677556729E-34Q, /* bf8e0ee78d94d9b5ad3d63ae35c9b554 */
-1.49536132812500945889014955936485340E-03Q, /* bff5880000000002b9f1621b57743000 */
-3.32264697086631598830366079048117140E-34Q, /* bf8fb9a7d14c32289204fbb0c9eb20e0 */
-1.46484374999999931883259902869504725E-03Q, /* bff57fffffffffffcdbd1c90e1b4a000 */
-1.76487524793892929381101031660811433E-34Q, /* bf8ed52f2f724bc1ae870b18356337b4 */
-1.43432617187498876325946983333888768E-03Q, /* bff577fffffffffcc2dff8faa5570000 */
-3.54550084538495708816233114576143814E-34Q, /* bf8fd74724576915868c1e8ce9f430f1 */
-1.40380859374999215367421282192718062E-03Q, /* bff56ffffffffffdbd0b18aac65ed000 */
-1.90585907028351204486765167064669639E-34Q, /* bf8efaaa0c0e23e50c11b2120348054f */
-1.37329101562499692341771212945644892E-03Q, /* bff567ffffffffff1cfd00f1b0577000 */
-3.59631150411372589637918252836880320E-34Q, /* bf8fde08239ac74942a46298ea4fb715 */
-1.34277343749999137467356674296739172E-03Q, /* bff55ffffffffffd839030b05d53d000 */
-1.49571076125940368185068762485268117E-35Q, /* bf8b3e1a3d5c684b27a9f835b1d8d3c9 */
-1.31225585937499247038404301859788734E-03Q, /* bff557fffffffffdd469936e691e3000 */
3.10375845385355395586146533282311300E-34Q, /* 3f8f9c8f6d63b7a4145716ffd92491fb */
-1.28173828124999024755581675764821898E-03Q, /* bff54ffffffffffd306589b0ab21d000 */
-1.98541096105909793397376077900810019E-34Q, /* bf8f07e808bbb1e35106c294ffbb9687 */
-1.25122070312500340204619591143332523E-03Q, /* bff5480000000000fb06d5f16ad2c000 */
3.62884195935761446237911443317457521E-34Q, /* 3f8fe25b17d623178a386a6fa6c5afb2 */
-1.22070312499999591578388993012071279E-03Q, /* bff53ffffffffffed2a356c440074000 */
-2.96756662615653130862526710937493307E-35Q, /* bf8c3b90d8ff2a991e5bd16718fb0645 */
-1.19018554687498821966212632349422735E-03Q, /* bff537fffffffffc9ac3b585dda89000 */
1.44659971891167323357060028901142644E-34Q, /* 3f8e809279ab249edf1dad9fe13fb0bf */
-1.15966796875000160938908064907298384E-03Q, /* bff530000000000076c0800db9639000 */
2.50088010538742402346270685365928513E-34Q, /* 3f8f4c6c8a483b60201d30c1a83c3cb7 */
-1.12915039062500267151512523291939657E-03Q, /* bff5280000000000c51f7e7315137000 */
7.56402096465615210500092443924888831E-35Q, /* 3f8d922c1e485d99aea2668ed32b55a6 */
-1.09863281249998665006360103291051571E-03Q, /* bff51ffffffffffc26f2d4c9ce2ba000 */
1.43982174467233642713619821353592061E-34Q, /* 3f8e7ec530b3d92b6303bec1c81214d1 */
-1.06811523437500522742248711752028025E-03Q, /* bff518000000000181b7380f10446000 */
5.41265133745862349181293024531133174E-35Q, /* 3f8d1fc9313d018b30e790e06b6be723 */
-1.03759765624999980942114138999770552E-03Q, /* bff50ffffffffffff1f01130490e1000 */
1.21525139612685854366189534669623436E-34Q, /* 3f8e4311b96b6fcde412caf3f0d86fb9 */
-1.00708007812499602697537601515759439E-03Q, /* bff507fffffffffedad7afcce7051000 */
1.00020246351201558505328236381833392E-34Q, /* 3f8e09e640992512b1300744a7e984ed */
-9.76562499999992592487302113340463694E-04Q, /* bff4fffffffffffbbad8151f8adf6000 */
-1.64984406575162932060422892046851002E-34Q, /* bf8eb69a919986e8054b86fc34300f24 */
-9.46044921874989085824996924138179594E-04Q, /* bff4effffffffff9b55a204fd9792000 */
-9.29539174108308550334255350011347171E-35Q, /* bf8dee3a50ed896b4656fa577a1df3d7 */
-9.15527343750013735214860599791540029E-04Q, /* bff4e00000000007eaf5bf103f82d000 */
3.07557018309280519949818825519490586E-35Q, /* 3f8c470cfbef77d32c74cb8042f6ee81 */
-8.85009765625012292294986105781516428E-04Q, /* bff4d000000000071605c65403b97000 */
4.77499983783821950338363358545463558E-35Q, /* 3f8cfbc3dc18884c4c4f9e07d90d7bd3 */
-8.54492187499986941239470706817188192E-04Q, /* bff4bffffffffff878ddf9cab264a000 */
-1.60128240346239526958630011447901568E-34Q, /* bf8ea9b1a21e19e2d5bd84b0fbffcf95 */
-8.23974609374996290174598690241743810E-04Q, /* bff4affffffffffddc86c249ebe06000 */
1.61677540391961912631535763471935882E-34Q, /* 3f8eadd00841366b0dc2bc262c2c8c36 */
-7.93457031249988696952538334288757473E-04Q, /* bff49ffffffffff97bf6f0aa85a5f000 */
1.22318577008381887076634753347515709E-34Q, /* 3f8e452db5b5d250878f71040da06d14 */
-7.62939453124996723316499040007097041E-04Q, /* bff48ffffffffffe1c7265b431108000 */
-1.03845161748762410745671891558398468E-34Q, /* bf8e14115ad884c96d1a820c73647220 */
-7.32421874999998242520117923997325794E-04Q, /* bff47ffffffffffefca4498b7aa8a000 */
5.64005211953031009549514026639438083E-35Q, /* 3f8d2be06950f68f1a6d8ff829a6928e */
-7.01904296874999772890934814265622012E-04Q, /* bff46fffffffffffde7c0fe5d8041000 */
5.90245467325173644235991233229525762E-35Q, /* 3f8d39d40cc49002189243c194b1db0e */
-6.71386718750008699269643939210658742E-04Q, /* bff460000000000503c91d798b60c000 */
-5.20515801723324452151498579012322191E-35Q, /* bf8d14c0f08a6a9285b32b8bda003eb5 */
-6.40869140625005499535275057463709988E-04Q, /* bff45000000000032b969184e9751000 */
-6.69469163285461870099846471658294534E-35Q, /* bf8d63f36bab7b24d936c9380e3d3fa6 */
-6.10351562499999293780097329596079841E-04Q, /* bff43fffffffffff97c7c433e35ed000 */
-1.16941808547394177991845382085515086E-34Q, /* bf8e36e27886f10b234a7dd8fc588bf0 */
-5.79833984375000068291972326409994795E-04Q, /* bff43000000000000a13ff6dcf2bf000 */
1.17885044988246219185041488459766001E-34Q, /* 3f8e3964677e001a00412aab52790842 */
-5.49316406249990904622170867910987793E-04Q, /* bff41ffffffffffac1c25739c716b000 */
-3.31875702128137033065075734368960972E-35Q, /* bf8c60e928d8982c3c99aef4f885a121 */
-5.18798828125011293653756992177727236E-04Q, /* bff410000000000682a62cff36775000 */
-5.69971237642088463334239430962628187E-35Q, /* bf8d2f0c76f8757d61cd1abc7ea7d066 */
-4.88281249999990512232251384917893121E-04Q, /* bff3fffffffffff50fb48992320df000 */
1.02144616714408655325510171265051108E-35Q, /* 3f8ab279a3626612710b9b3ac71734ac */
-4.57763671874997554564967307956493434E-04Q, /* bff3dffffffffffd2e3c272e3cca9000 */
-8.25484058867957231164162481843653503E-35Q, /* bf8db6e71158e7bf93e2e683f07aa841 */
-4.27246093749991203999790346349633286E-04Q, /* bff3bffffffffff5dbe103cba0eb2000 */
-3.51191203319375193921924105905691755E-35Q, /* bf8c757356d0f3dd7fbefc0dd419ab50 */
-3.96728515624986649402960638705483281E-04Q, /* bff39ffffffffff09b996882706ec000 */
-5.51925962073095883016589497244931171E-36Q, /* bf89d586d49f22289cfc860bebb99056 */
-3.66210937499999945095511981300980754E-04Q, /* bff37fffffffffffefcb88bfc7df6000 */
-2.11696465278144529364423332249588595E-35Q, /* bf8bc23a84d28e5496c874ef9833be25 */
-3.35693359374992480958458008559640163E-04Q, /* bff35ffffffffff754c548a8798f2000 */
-8.58941791799705081104736787493668352E-35Q, /* bf8dc8b1192fb7c3662826d43acb7c68 */
-3.05175781250009811036303273640122156E-04Q, /* bff340000000000b4fb4f1aad1c76000 */
-8.61173897858769926480551302277426632E-35Q, /* bf8dc9e0eabb1c0b33051011b64769fa */
-2.74658203124987298321920308390303850E-04Q, /* bff31ffffffffff15b2056ac252fd000 */
3.35152809454778381053519808988046631E-37Q, /* 3f85c82fb59ff8d7c80d44e635420ab1 */
-2.44140624999999992770514819575735516E-04Q, /* bff2fffffffffffffbbb82d6a7636000 */
3.54445837111124472730013879165516908E-35Q, /* 3f8c78e955b01378be647b1c92aa9a77 */
-2.13623046875012756463165168672749438E-04Q, /* bff2c0000000001d6a1635fea6bbf000 */
1.50050816288650121729916777279129473E-35Q, /* 3f8b3f1f6f616a61129a58e131cbd31d */
-1.83105468749991323078784464300306893E-04Q, /* bff27fffffffffebfe0cbd0c82399000 */
-9.14919506501448661140572099029756008E-37Q, /* bf873754bacaa9d9513b6127e791eb47 */
-1.52587890625013337032336300236461546E-04Q, /* bff240000000001ec0cb57f2cc995000 */
2.84906084373176180870418394956384516E-35Q, /* 3f8c2ef6d03a7e6ab087c4f099e4de89 */
-1.22070312499990746786116828458007518E-04Q, /* bff1ffffffffffd553bbb49f35a34000 */
6.71618008964968339584520728412444537E-36Q, /* 3f8a1dacb99c60071fc9cd2349495bf0 */
-9.15527343750029275602791047595142231E-05Q, /* bff180000000000d8040cd6ecde28000 */
-1.95753652091078750312541716951402172E-35Q, /* bf8ba0526cfb24d8d59122f1c7a09a14 */
-6.10351562499913258461494008080572701E-05Q, /* bff0ffffffffffaffebbb92d7f6a9000 */
5.69868489273961111703398456218119973E-36Q, /* 3f89e4ca5df09ef4a4386dd5b3bf0331 */
-3.05175781250092882818419203884960853E-05Q, /* bff0000000000055ab55de88fac1d000 */
9.03341100018476837609128961872915953E-36Q, /* 3f8a803d229fa3a0e834a63abb06662b */
#define T_EXPL_ARG2 (2*T_EXPL_ARG1 + 2 + 2*65)
0.00000000000000000000000000000000000E+00Q, /* 00000000000000000000000000000000 */
0.00000000000000000000000000000000000E+00Q, /* 00000000000000000000000000000000 */
3.05175781249814607084128277672749162E-05Q, /* 3feffffffffffeaa02abb9102f499000 */
1.00271855391179733380665816525889949E-36Q, /* 3f8755351afa042ac3f58114824d4c10 */
6.10351562500179243748093427073421439E-05Q, /* 3ff1000000000052a95de07a4c26d000 */
1.67231624299180373502350811501181670E-36Q, /* 3f881c87a53691cae9d77f4e40d66616 */
9.15527343749970728685313252158399200E-05Q, /* 3ff17ffffffffff28040cc2acde28000 */
2.43665747834893104318707597514407880E-36Q, /* 3f889e9366c7c6c6a2ecb78dc9b0509e */
1.22070312500027751961838150070880064E-04Q, /* 3ff200000000003ffddde6c153b53000 */
-1.73322146370624186623546452226755405E-35Q, /* bf8b709d8d658ed5dbbe943de56ee84e */
1.52587890624995916105682628143179430E-04Q, /* 3ff23ffffffffff6954b56e285d23000 */
1.23580432650945898349135528000443828E-35Q, /* 3f8b06d396601dde16de7d7bc27346e6 */
1.83105468750008670314358488289621794E-04Q, /* 3ff2800000000013fe0cdc8c823b7000 */
4.30446229148833293310207915930740796E-35Q, /* 3f8cc9ba9bfe554a4f7f2fece291eb23 */
2.13623046875005741337455947623248132E-04Q, /* 3ff2c0000000000d3d1662de21a3f000 */
-3.96110759869520786681660669615255057E-35Q, /* bf8ca5379b04ff4a31aab0ceacc917e6 */
2.44140624999981493573336463433440506E-04Q, /* 3ff2ffffffffffd553bbdf48e0534000 */
-1.39617373942387888957350179316792928E-35Q, /* bf8b28eeedc286015802b63f96b8c5cd */
2.74658203124984920706309918754626834E-04Q, /* 3ff31fffffffffee9d60c8439ec1d000 */
-3.16168080483901830349738314447356223E-36Q, /* bf890cf74f81c77a611abc1243812444 */
3.05175781250008648918265055410966055E-04Q, /* 3ff3400000000009f8b5c9a346636000 */
8.54421306185008998867856704677221443E-35Q, /* 3f8dc649cd40922fc08adc6b6b20ead0 */
3.35693359374988945462612499316774515E-04Q, /* 3ff35ffffffffff34146c540f15b2000 */
7.96443137431639500475160850431097078E-35Q, /* 3f8da77638ed3148fc4d99d1c9e13446 */
3.66210937500027690542093987739604535E-04Q, /* 3ff380000000001fecce34bea89c4000 */
2.14507323877752361258862577769090367E-35Q, /* 3f8bc834e554d38894cf91957b0253d3 */
3.96728515625003928083564943615052121E-04Q, /* 3ff3a00000000004875d9a4acf6ab000 */
4.88358523466632050664019922448605508E-35Q, /* 3f8d03a7eaeef1a9f78c71a12c44dd28 */
4.27246093750017799227172345607351585E-04Q, /* 3ff3c00000000014856794c3ee850000 */
6.66520494592631402182216588784828935E-35Q, /* 3f8d6262118fcdb59b8f16108f5f1a6c */
4.57763671875002108342364320152138181E-04Q, /* 3ff3e000000000026e45d855410b9000 */
7.21799615960261390920033272189522298E-35Q, /* 3f8d7fc645cff8879462296af975c9fd */
4.88281249999999768797631616370963356E-04Q, /* 3ff3ffffffffffffbbc2d7cc004df000 */
-5.30564629906905979452258114088325361E-35Q, /* bf8d1a18b71929a30d67a217a27ae851 */
5.18798828124997339054881383202487041E-04Q, /* 3ff40ffffffffffe775055eea5851000 */
-4.03682911253647925867848180522846377E-35Q, /* bf8cad44f0f3e5199d8a589d9332acad */
5.49316406249980511907933706754958501E-04Q, /* 3ff41ffffffffff4c410b29bb62fb000 */
-2.08166843948323917121806956728438051E-35Q, /* bf8bbab8cf691403249fe5b699e25143 */
5.79833984374989593561576568548497165E-04Q, /* 3ff42ffffffffffa0047df328d817000 */
-1.72745033420153042445343706432627539E-34Q, /* bf8ecb3c2d7d3a9e6e960576be901fdf */
6.10351562500008540711511259540838154E-04Q, /* 3ff4400000000004ec62f54f8c271000 */
7.41889382604319545724663095428976499E-35Q, /* 3f8d8a74c002c81a47c93b8e05d15f8e */
6.40869140625020444702875407535884986E-04Q, /* 3ff450000000000bc91b09718515d000 */
-4.47321009727305792048065440180490107E-35Q, /* bf8cdbac5c8fe70822081d8993eb5cb6 */
6.71386718750007531635964622352684074E-04Q, /* 3ff460000000000457792973db05c000 */
5.13698959677949336513874456684462092E-35Q, /* 3f8d112114436949c5ef38d8049004ab */
7.01904296875006634673332887754430334E-04Q, /* 3ff4700000000003d31adf2cb8b1d000 */
-8.25665755717729437292989870760751482E-35Q, /* bf8db6ffcc8ef71f8e648e3a8b160f5a */
7.32421874999998244664170215504673504E-04Q, /* 3ff47ffffffffffefcf5498bd5c8a000 */
-5.64005234937832153139057628112753364E-35Q, /* bf8d2be06a1dfe90e7bf90fba7c12a98 */
7.62939453125017456345986752604096408E-04Q, /* 3ff490000000000a101a1b093d4a8000 */
-1.11084094120417622468550608896588329E-34Q, /* bf8e274feabd2d94f6694507a46accb1 */
7.93457031249987558617598988993908016E-04Q, /* 3ff49ffffffffff8d3f9dcab74bbf000 */
-1.22966480225449015129079129940978828E-34Q, /* bf8e46e6a65eef8fa9e42eddf3da305e */
8.23974609374997378723747633335135819E-04Q, /* 3ff4affffffffffe7d2afbaa55b26000 */
-1.62270010016794279091906973366704963E-34Q, /* bf8eaf633f057ebdb664a34566401c4e */
8.54492187500023938282350821569920958E-04Q, /* 3ff4c0000000000dccaabce399e59000 */
-1.39076361712838158775374263169606160E-34Q, /* bf8e71ba779364b3bbdba7841f2c4ca1 */
8.85009765624987932362186815286691297E-04Q, /* 3ff4cffffffffff90b218886edc2a000 */
4.07328275060905585228261577392403980E-35Q, /* 3f8cb1254dbb6ea4b8cfa5ed4cf28d24 */
9.15527343749975579461305518559161974E-04Q, /* 3ff4dffffffffff1ec2a21f25df33000 */
1.16855112459192484947855553716334015E-35Q, /* 3f8af10bf319e9f5270cf249eeffbe5c */
9.46044921875016761584725882821122521E-04Q, /* 3ff4f00000000009a992c46c16d71000 */
9.51660680007524262741115611071680436E-35Q, /* 3f8df9fd56e81f8edf133843910ee831 */
9.76562499999974118878133088548272636E-04Q, /* 3ff4fffffffffff1149edc46a6df6000 */
-5.65271128977550656964071208289181661E-36Q, /* bf89e0e12689dd721aa2314c81eb6429 */
1.00708007812498671732140389760347830E-03Q, /* 3ff507fffffffffc2be94b90ed091000 */
-1.43355074891483635310132767255371379E-34Q, /* bf8e7d1a688c247b16022daab1316d55 */
1.03759765625002637786192745235343007E-03Q, /* 3ff51000000000079a57b966bc158000 */
2.95905815240957629366749917020106928E-34Q, /* 3f8f895387fc73bb38f8a1b254c01a60 */
1.06811523437500860568717813047520763E-03Q, /* 3ff51800000000027afcd5b35f5e6000 */
-5.98328495358586628195372356742878314E-35Q, /* bf8d3e204130013bf6328f1b70ff8c76 */
1.09863281250001439958487251556220070E-03Q, /* 3ff5200000000004268077c6c66bd000 */
2.41371837889426603334113000868144760E-34Q, /* 3f8f40d6948edf864054ccf151f9815e */
1.12915039062501298413451613770002366E-03Q, /* 3ff5280000000003be0f5dd8fe81b000 */
-1.28815268997394164973472617519705703E-34Q, /* bf8e567321172ea089dce4bc8354ecb7 */
1.15966796874997272036339054191407232E-03Q, /* 3ff52ffffffffff8231e3bcfff1e8000 */
1.02996064554316248496839462594377804E-34Q, /* 3f8e11cf7d402789244f68e2d4f985b1 */
1.19018554687502744121802585360546796E-03Q, /* 3ff5380000000007e8cdf3f8f6c20000 */
-1.43453217726255628994625761307322163E-34Q, /* bf8e7d5d3370d85a374f5f4802fc517a */
1.22070312499997743541996266398850614E-03Q, /* 3ff53ffffffffff97f0722561f454000 */
-1.41086259180534339713692694428211646E-34Q, /* bf8e77125519ff76244dfec5fbd58402 */
1.25122070312501024092560690174507039E-03Q, /* 3ff5480000000002f3a59d8820691000 */
3.84102646020099293168698506729765213E-34Q, /* 3f8ffe8f5b86f9c3569c8f26e19b1f50 */
1.28173828124997986521442660131425390E-03Q, /* 3ff54ffffffffffa3250a764439d9000 */
1.44644589735033114377952806106652650E-34Q, /* 3f8e808801b80dcf38323cdbfdca2549 */
1.31225585937501665804856968749058137E-03Q, /* 3ff5580000000004cd25a414c6d62000 */
1.67474574742200577294563576414361377E-34Q, /* 3f8ebd394a151dbda4f81d5d83c0f1e9 */
1.34277343749997290265837386401818888E-03Q, /* 3ff55ffffffffff83091b042cfd59000 */
-1.55650565030381326742591837551559103E-34Q, /* bf8e9dca490d7fecfadba9625ffb91c5 */
1.37329101562497720784949380297774268E-03Q, /* 3ff567fffffffff96e3c7312f5ccf000 */
1.65279335325630026116581677369221748E-34Q, /* 3f8eb763496f5bd7404f2298b402074f */
1.40380859374999099958354100336136647E-03Q, /* 3ff56ffffffffffd67e2f09f2a381000 */
1.89919944388961890195706641264717076E-34Q, /* 3f8ef8e4d0ffdfeba982aa8829501389 */
1.43432617187497484122173130998160625E-03Q, /* 3ff577fffffffff8bf9c1d71af8a8000 */
2.57638517142061429772064578590009568E-34Q, /* 3f8f5675d82c1cc4ada70fd3a957b89a */
1.46484374999999929342158925502052945E-03Q, /* 3ff57fffffffffffcbdd1c7671b46000 */
1.76487201934184070490166772482073801E-34Q, /* 3f8ed52ef732458f6e4c5c07504f33cc */
1.49536132812502318451070466256902933E-03Q, /* 3ff5880000000006aeb7066c8ad43000 */
2.38068367275295804321313550609246656E-34Q, /* 3f8f3c7277ae6fc390ace5e06c0b025b */
1.52587890625000448053340248672949543E-03Q, /* 3ff59000000000014a9ae2104b3bc000 */
1.01174455568392813258454590274740959E-34Q, /* 3f8e0cf7c434762991bb38e12acee215 */
1.55639648437501113499837053523090913E-03Q, /* 3ff5980000000003359e2c204355e000 */
-2.82398418808099749023517211651363693E-35Q, /* bf8c2c4c2971d88caa95e15fb1ccb1a1 */
1.58691406249999937955142588308171026E-03Q, /* 3ff59fffffffffffd2380ecbc87c2000 */
-1.27361695572422741562701199136538047E-34Q, /* bf8e5295e0e206dfb0f0266c07225448 */
1.61743164062498000531048954475329309E-03Q, /* 3ff5a7fffffffffa3ca6fe61ed94c000 */
-1.22606548862580061633942923016222044E-34Q, /* bf8e45f1b17bb61039d21a351bb207b8 */
1.64794921875001835451453858682255576E-03Q, /* 3ff5b000000000054a52fa20f6565000 */
1.39132339594152335892305491425264583E-34Q, /* 3f8e71e0904c5449b414ee49b191cef2 */
1.67846679687501263995029340691547953E-03Q, /* 3ff5b80000000003a4a9e912c910b000 */
6.67245854693585315412242764786197029E-35Q, /* 3f8d62c4ccac1e7511a617d469468ccd */
1.70898437500002646861403514115369655E-03Q, /* 3ff5c00000000007a109fbaa7e015000 */
6.87367172354719289559624829652240928E-36Q, /* 3f8a245fa835eceb42bae8128d9336db */
1.73950195312501174308226096992992128E-03Q, /* 3ff5c80000000003627c8d637a005000 */
-2.20824271875474985927385878948759352E-34Q, /* bf8f25869b1cbefb25e735992f232f57 */
1.77001953124997491747605207736194513E-03Q, /* 3ff5cffffffffff8c53c84b6883b8000 */
3.43123048533596296514343180408963705E-34Q, /* 3f8fc816b91d173ddadbbf09b1287906 */
1.80053710937497698911127570705069398E-03Q, /* 3ff5d7fffffffff95e1899f4a8430000 */
3.99231237340890073475077494556136100E-35Q, /* 3f8ca889148f62fa854da5674df41279 */
1.83105468750002267094899598630423914E-03Q, /* 3ff5e0000000000688d21e62ba674000 */
-3.22274595655810623999007524769365273E-34Q, /* bf8fac605cb9ae01eb719675ced25560 */
1.86157226562500499224728040579690330E-03Q, /* 3ff5e80000000001705ce28a6d89e000 */
3.07094985075881613489605622068441083E-34Q, /* 3f8f98330225ec7e2c8f3c0d1c432b91 */
1.89208984374998234666824993196980949E-03Q, /* 3ff5effffffffffae969fdc7cd8cf000 */
-3.06287628722973914692165056776495733E-34Q, /* bf8f9720477d9cfa10e464df7f91020c */
1.92260742187501225343755557292811682E-03Q, /* 3ff5f800000000038824e428ed49a000 */
6.30049124729794620592961282769623368E-35Q, /* 3f8d4efdd7cd4336d88a6aa49e1e96bc */
1.95312499999998514894032051116231258E-03Q, /* 3ff5fffffffffffbb82f6a04f1ae0000 */
-6.14610057507500948543216998736262902E-35Q, /* bf8d46c862d39255370e7974d48daa7e */
1.98364257812501222021119324146882732E-03Q, /* 3ff6040000000001c2d8a1aa5188d000 */
3.71942298418113774118754986159801984E-34Q, /* 3f8fee6567d9940495519ffe62cbc9a4 */
7.06341639425619532977052017486130353E-01Q, /* 3ffe69a59c8245a9ac00000000000000 */
7.09106182437398424589503065362805501E-01Q, /* 3ffe6b0ff72deb89d000000000000000 */
7.11881545564596485142772053222870454E-01Q, /* 3ffe6c7bbce9a6d93000000000000000 */
7.14667771155948150507697391731198877E-01Q, /* 3ffe6de8ef213d71e000000000000000 */
7.17464901725936049503573599395167548E-01Q, /* 3ffe6f578f41e1a9e400000000000000 */
7.20272979955439790478166628417966422E-01Q, /* 3ffe70c79eba33c06c00000000000000 */
7.23092048692387218133958981525211129E-01Q, /* 3ffe72391efa434c7400000000000000 */
7.25922150952408251622927082280511968E-01Q, /* 3ffe73ac117390acd800000000000000 */
7.28763329919491220643124052003258839E-01Q, /* 3ffe752077990e79d000000000000000 */
7.31615628946641782803794740175362676E-01Q, /* 3ffe769652df22f7e000000000000000 */
7.34479091556544505525749855223693885E-01Q, /* 3ffe780da4bba98c4800000000000000 */
7.37353761442226890432394270646909717E-01Q, /* 3ffe79866ea5f432d400000000000000 */
7.40239682467726090031590047146892175E-01Q, /* 3ffe7b00b216ccf53000000000000000 */
7.43136898668758316688354170764796436E-01Q, /* 3ffe7c7c70887763c000000000000000 */
7.46045454253390638577059235103661194E-01Q, /* 3ffe7df9ab76b20fd000000000000000 */
7.48965393602715662213498148958024103E-01Q, /* 3ffe7f78645eb8076400000000000000 */
7.51896761271528629722027403659012634E-01Q, /* 3ffe80f89cbf42526400000000000000 */
7.54839601989007347171423134568613023E-01Q, /* 3ffe827a561889716000000000000000 */
7.57793960659394638668118204805068672E-01Q, /* 3ffe83fd91ec46ddc000000000000000 */
7.60759882362683631518152083117456641E-01Q, /* 3ffe858251bdb68b8c00000000000000 */
7.63737412355305483879774897104653064E-01Q, /* 3ffe87089711986c9400000000000000 */
7.66726596070820082262642358728044201E-01Q, /* 3ffe8890636e31f54400000000000000 */
7.69727479120609181517664865168626420E-01Q, /* 3ffe8a19b85b4fa2d800000000000000 */
7.72740107294572486917871856348938309E-01Q, /* 3ffe8ba4976246833800000000000000 */
7.75764526561826289752232810315035749E-01Q, /* 3ffe8d31020df5be4400000000000000 */
7.78800783071404878477039801509818062E-01Q, /* 3ffe8ebef9eac820b000000000000000 */
7.81848923152964780936002853195532225E-01Q, /* 3ffe904e8086b5a87800000000000000 */
7.84908993317491698871180005880887620E-01Q, /* 3ffe91df97714512d800000000000000 */
7.87981040258010162480317717381694820E-01Q, /* 3ffe9372403b8d6bcc00000000000000 */
7.91065110850296016042904057030682452E-01Q, /* 3ffe95067c78379f2800000000000000 */
7.94161252153591734614934694036492147E-01Q, /* 3ffe969c4dbb800b4800000000000000 */
7.97269511411324433014513601847284008E-01Q, /* 3ffe9833b59b38154400000000000000 */
8.00389936051826789142893403550260700E-01Q, /* 3ffe99ccb5aec7bec800000000000000 */
8.03522573689060742863077280162542593E-01Q, /* 3ffe9b674f8f2f3d7c00000000000000 */
8.06667472123343942680406826184480451E-01Q, /* 3ffe9d0384d70893f800000000000000 */
8.09824679342079301047618855591281317E-01Q, /* 3ffe9ea15722892c7800000000000000 */
8.12994243520486992160556383169023320E-01Q, /* 3ffea040c80f8374f000000000000000 */
8.16176213022339780422953481320291758E-01Q, /* 3ffea1e1d93d687d0000000000000000 */
8.19370636400700819157449927843117621E-01Q, /* 3ffea3848c4d49954c00000000000000 */
8.22577562398664585696650419777142815E-01Q, /* 3ffea528e2e1d9f09800000000000000 */
8.25797039950100647542896581398963463E-01Q, /* 3ffea6cede9f70467c00000000000000 */
8.29029118180400342863478613253391813E-01Q, /* 3ffea876812c0877bc00000000000000 */
8.32273846407226292054559735333896242E-01Q, /* 3ffeaa1fcc2f45343800000000000000 */
8.35531274141265073440720811959181447E-01Q, /* 3ffeabcac15271a2a400000000000000 */
8.38801451086982535754188461396552157E-01Q, /* 3ffead7762408309bc00000000000000 */
8.42084427143382358016410194068157580E-01Q, /* 3ffeaf25b0a61a7b4c00000000000000 */
8.45380252404767357221615498019673396E-01Q, /* 3ffeb0d5ae318680c400000000000000 */
8.48688977161503960155997106085123960E-01Q, /* 3ffeb2875c92c4c99400000000000000 */
8.52010651900789478530029441571969073E-01Q, /* 3ffeb43abd7b83db1c00000000000000 */
8.55345327307422548246407245642330963E-01Q, /* 3ffeb5efd29f24c26400000000000000 */
8.58693054264576483003423845730139874E-01Q, /* 3ffeb7a69db2bcc77800000000000000 */
8.62053883854575708767242758767679334E-01Q, /* 3ffeb95f206d17228000000000000000 */
8.65427867359675251357487013592617586E-01Q, /* 3ffebb195c86b6b29000000000000000 */
8.68815056262843166123843730019871145E-01Q, /* 3ffebcd553b9d7b62000000000000000 */
8.72215502248546159513864495238522068E-01Q, /* 3ffebe9307c271855000000000000000 */
8.75629257203538208242932228131394368E-01Q, /* 3ffec0527a5e384ddc00000000000000 */
8.79056373217652342599848225290770642E-01Q, /* 3ffec213ad4c9ed0d800000000000000 */
8.82496902584595399599010079327854328E-01Q, /* 3ffec3d6a24ed8221800000000000000 */
8.85950897802745995779361010136199184E-01Q, /* 3ffec59b5b27d9696800000000000000 */
8.89418411575955636383383762222365476E-01Q, /* 3ffec761d99c5ba58800000000000000 */
8.92899496814352794382685374330321793E-01Q, /* 3ffec92a1f72dd70d400000000000000 */
8.96394206635150403439382671422208659E-01Q, /* 3ffecaf42e73a4c7d800000000000000 */
8.99902594363456265202927397695020773E-01Q, /* 3ffeccc00868c0d18800000000000000 */
9.03424713533086704009278378180169966E-01Q, /* 3ffece8daf1e0ba94c00000000000000 */
9.06960617887383580004723171441582963E-01Q, /* 3ffed05d24612c2af000000000000000 */
9.10510361380034133338412516422977205E-01Q, /* 3ffed22e6a0197c02c00000000000000 */
9.14073998175894436579724811053893063E-01Q, /* 3ffed40181d094303400000000000000 */
9.17651582651815816982221463149471674E-01Q, /* 3ffed5d66da13970f400000000000000 */
9.21243169397474526149949269893113524E-01Q, /* 3ffed7ad2f48737a2000000000000000 */
9.24848813216204823639543519675498828E-01Q, /* 3ffed985c89d041a3000000000000000 */
9.28468569125835141431224428743007593E-01Q, /* 3ffedb603b7784cd1800000000000000 */
9.32102492359527579068867453315760940E-01Q, /* 3ffedd3c89b26894e000000000000000 */
9.35750638366620729469147477175283711E-01Q, /* 3ffedf1ab529fdd41c00000000000000 */
9.39413062813475779888605643463961314E-01Q, /* 3ffee0fabfbc702a3c00000000000000 */
9.43089821584325888048638830696290825E-01Q, /* 3ffee2dcab49ca51b400000000000000 */
9.46780970782128888929563004239753354E-01Q, /* 3ffee4c079b3f8000400000000000000 */
9.50486566729423443256052905780961737E-01Q, /* 3ffee6a62cdec7c7b000000000000000 */
9.54206665969188322362626308859034907E-01Q, /* 3ffee88dc6afecfbfc00000000000000 */
9.57941325265705301283958306157728657E-01Q, /* 3ffeea77490f0196b000000000000000 */
9.61690601605425299247542625380447134E-01Q, /* 3ffeec62b5e5881fb000000000000000 */
9.65454552197837823079851204965962097E-01Q, /* 3ffeee500f1eed967000000000000000 */
9.69233234476344074348475032820715569E-01Q, /* 3ffef03f56a88b5d7800000000000000 */
9.73026706099133165128733935489435680E-01Q, /* 3ffef2308e71a927a800000000000000 */
9.76835024950062025261843245971249416E-01Q, /* 3ffef423b86b7ee79000000000000000 */
9.80658249139538557015427500118676107E-01Q, /* 3ffef618d68936c09c00000000000000 */
9.84496437005408397968864164795377292E-01Q, /* 3ffef80feabfeefa4800000000000000 */
9.88349647113845042323276857132441364E-01Q, /* 3ffefa08f706bbf53800000000000000 */
9.92217938260243514925207364285597578E-01Q, /* 3ffefc03fd56aa225000000000000000 */
9.96101369470117486981664001177705359E-01Q, /* 3ffefe00ffaabffbbc00000000000000 */
#define T_EXPL_RES1 (T_EXPL_ARG2 + 2 + 2*65 + 89)
1.00000000000000000000000000000000000E+00Q, /* 3fff0000000000000000000000000000 */
1.00391388933834757590801700644078664E+00Q, /* 3fff0100802ab5577800000000000000 */
1.00784309720644799091004983893071767E+00Q, /* 3fff0202015600445c00000000000000 */
1.01178768355933151879000320150225889E+00Q, /* 3fff0304848362076c00000000000000 */
1.01574770858668572692806719715008512E+00Q, /* 3fff04080ab55de39000000000000000 */
1.01972323271377413034244341361045372E+00Q, /* 3fff050c94ef7a206c00000000000000 */
1.02371431660235789884438872832106426E+00Q, /* 3fff06122436410dd000000000000000 */
1.02772102115162167201845022646011785E+00Q, /* 3fff0718b98f42085000000000000000 */
1.03174340749910264936062276319717057E+00Q, /* 3fff08205601127ec800000000000000 */
1.03578153702162378824169763902318664E+00Q, /* 3fff0928fa934ef90800000000000000 */
1.03983547133622999947277776300325058E+00Q, /* 3fff0a32a84e9c1f5800000000000000 */
1.04390527230112850620713516036630608E+00Q, /* 3fff0b3d603ca7c32800000000000000 */
1.04799100201663270004459604933799710E+00Q, /* 3fff0c49236829e8bc00000000000000 */
1.05209272282610977189420964350574650E+00Q, /* 3fff0d55f2dce5d1e800000000000000 */
1.05621049731693195106174698594259098E+00Q, /* 3fff0e63cfa7ab09d000000000000000 */
1.06034438832143151909548350886325352E+00Q, /* 3fff0f72bad65671b800000000000000 */
1.06449445891785943185681162503897212E+00Q, /* 3fff1082b577d34ed800000000000000 */
1.06866077243134810492719566354935523E+00Q, /* 3fff1193c09c1c595c00000000000000 */
1.07284339243487741866189821848820429E+00Q, /* 3fff12a5dd543ccc4c00000000000000 */
1.07704238275024494209120007326419000E+00Q, /* 3fff13b90cb25176a400000000000000 */
1.08125780744903959851299646288680378E+00Q, /* 3fff14cd4fc989cd6400000000000000 */
1.08548973085361949442173568058933597E+00Q, /* 3fff15e2a7ae28fecc00000000000000 */
1.08973821753809324563988525369495619E+00Q, /* 3fff16f9157587069400000000000000 */
1.09400333232930546678574046381982043E+00Q, /* 3fff18109a3611c35000000000000000 */
1.09828514030782586896606289883493446E+00Q, /* 3fff192937074e0cd800000000000000 */
1.10258370680894224324930519287590869E+00Q, /* 3fff1a42ed01d8cbc800000000000000 */
1.10689909742365749645287564817408565E+00Q, /* 3fff1b5dbd3f68122400000000000000 */
1.11123137799969046168868658241990488E+00Q, /* 3fff1c79a8dacc350c00000000000000 */
1.11558061464248076122274255794764031E+00Q, /* 3fff1d96b0eff0e79400000000000000 */
1.11994687371619722204840741142106708E+00Q, /* 3fff1eb4d69bde569c00000000000000 */
1.12433022184475073235176978414529003E+00Q, /* 3fff1fd41afcba45e800000000000000 */
1.12873072591281087273529237791080959E+00Q, /* 3fff20f47f31c92e4800000000000000 */
1.13314845306682632219974493636982515E+00Q, /* 3fff2216045b6f5cd000000000000000 */
1.13758347071604959399593326452304609E+00Q, /* 3fff2338ab9b32134800000000000000 */
1.14203584653356560174586320499656722E+00Q, /* 3fff245c7613b8a9b000000000000000 */
1.14650564845732405583333957110880874E+00Q, /* 3fff258164e8cdb0d800000000000000 */
1.15099294469117646722011727433709893E+00Q, /* 3fff26a7793f60164400000000000000 */
1.15549780370591653744227755851170514E+00Q, /* 3fff27ceb43d84490400000000000000 */
1.16002029424032515603215642840950750E+00Q, /* 3fff28f7170a755fd800000000000000 */
1.16456048530221917269855680387991015E+00Q, /* 3fff2a20a2ce96406400000000000000 */
1.16911844616950438835445424956560601E+00Q, /* 3fff2b4b58b372c79400000000000000 */
1.17369424639123270948104504896036815E+00Q, /* 3fff2c7739e3c0f32c00000000000000 */
1.17828795578866324378353169777255971E+00Q, /* 3fff2da4478b620c7400000000000000 */
1.18289964445632783673900689791480545E+00Q, /* 3fff2ed282d763d42400000000000000 */
1.18752938276310060494722620205720887E+00Q, /* 3fff3001ecf601af7000000000000000 */
1.19217724135327157730657177125976887E+00Q, /* 3fff31328716a5d63c00000000000000 */
1.19684329114762477708211463323095813E+00Q, /* 3fff32645269ea829000000000000000 */
1.20152760334452030077656559114984702E+00Q, /* 3fff339750219b212c00000000000000 */
1.20623024942098072687102217059873510E+00Q, /* 3fff34cb8170b5835400000000000000 */
1.21095130113378179892436037334846333E+00Q, /* 3fff3600e78b6b11d000000000000000 */
1.21569083052054743854242246925423387E+00Q, /* 3fff373783a722012400000000000000 */
1.22044890990084875515009343871497549E+00Q, /* 3fff386f56fa7686e800000000000000 */
1.22522561187730755216662714701669756E+00Q, /* 3fff39a862bd3c106400000000000000 */
1.23002100933670455162882717559114099E+00Q, /* 3fff3ae2a8287e7a8000000000000000 */
1.23483517545109100499445276000187732E+00Q, /* 3fff3c1e2876834aa800000000000000 */
1.23966818367890557750499169742397498E+00Q, /* 3fff3d5ae4e2cae92c00000000000000 */
1.24452010776609517384017067342938390E+00Q, /* 3fff3e98deaa11dcbc00000000000000 */
1.24939102174724003813111039562500082E+00Q, /* 3fff3fd8170a52071800000000000000 */
1.25428099994668373895478907797951251E+00Q, /* 3fff41188f42c3e32000000000000000 */
1.25919011697966698459794088194030337E+00Q, /* 3fff425a4893dfc3f800000000000000 */
1.26411844775346637881341393949696794E+00Q, /* 3fff439d443f5f159000000000000000 */
1.26906606746853711786826579555054195E+00Q, /* 3fff44e183883d9e4800000000000000 */
1.27403305161966090564007458851847332E+00Q, /* 3fff462707b2bac20c00000000000000 */
1.27901947599709753244923149395617656E+00Q, /* 3fff476dd2045ac67800000000000000 */
1.28402541668774150540599521264084615E+00Q, /* 3fff48b5e3c3e8186800000000000000 */
1.28905095007628295311619126550795045E+00Q, /* 3fff49ff3e397492bc00000000000000 */
1.29409615284637330434591717676084954E+00Q, /* 3fff4b49e2ae5ac67400000000000000 */
1.29916110198179535206719492634874769E+00Q, /* 3fff4c95d26d3f440800000000000000 */
1.30424587476763775839572190307080746E+00Q, /* 3fff4de30ec211e60000000000000000 */
1.30935054879147461104338390214252286E+00Q, /* 3fff4f3198fa0f1cf800000000000000 */
1.31447520194454914310711046709911898E+00Q, /* 3fff50817263c13cd000000000000000 */
1.31961991242296217130558488861424848E+00Q, /* 3fff51d29c4f01cb3000000000000000 */
1.32478475872886558573071624778094701E+00Q, /* 3fff5325180cfacf7800000000000000 */
1.32996981967165983640200010995613411E+00Q, /* 3fff5478e6f02823d000000000000000 */
1.33517517436919680440254865061433520E+00Q, /* 3fff55ce0a4c58c7bc00000000000000 */
1.34040090224898678084031189428060316E+00Q, /* 3fff57248376b033d800000000000000 */
1.34564708304941055283521222918352578E+00Q, /* 3fff587c53c5a7af0400000000000000 */
1.35091379682093615244298234756570309E+00Q, /* 3fff59d57c910fa4e000000000000000 */
1.35620112392734021300455538039386738E+00Q, /* 3fff5b2fff3210fd9400000000000000 */
1.36150914504693443252136830778908916E+00Q, /* 3fff5c8bdd032e770800000000000000 */
1.36683794117379636690046140756749082E+00Q, /* 3fff5de9176045ff5400000000000000 */
1.37218759361900544124779344201670028E+00Q, /* 3fff5f47afa69210a800000000000000 */
1.37755818401188367960941150158760138E+00Q, /* 3fff60a7a734ab0e8800000000000000 */
1.38294979430124120867162673675920814E+00Q, /* 3fff6208ff6a88a46000000000000000 */
1.38836250675662681297595213436579797E+00Q, /* 3fff636bb9a983258400000000000000 */
1.39379640396958309755959248832368758E+00Q, /* 3fff64cfd75454ee7c00000000000000 */
1.39925156885490681313299887733592186E+00Q, /* 3fff663559cf1bc7c400000000000000 */
1.40472808465191417726103395580139477E+00Q, /* 3fff679c427f5a49f400000000000000 */
1.41022603492571069194738697660795879E+00Q, /* 3fff690492cbf9432c00000000000000 */
1.41574550356846662335641440222389065E+00Q, /* 3fff6a6e4c1d491e1800000000000000 */
9.98018323540573404351050612604012713E-01Q, /* 3ffefefc41f8d4bdb000000000000000 */
9.98048781107475468932221929208026268E-01Q, /* 3ffeff003ff556aa8800000000000000 */
9.98079239603882895082165305211674422E-01Q, /* 3ffeff043df9d4986000000000000000 */
9.98109699029824021243584297735651489E-01Q, /* 3ffeff083c064e972c00000000000000 */
9.98140159385327269125909310787392315E-01Q, /* 3ffeff0c3a1ac4b6ec00000000000000 */
9.98170620670420977171843901487591211E-01Q, /* 3ffeff10383737079400000000000000 */
9.98201082885133511579667242585856002E-01Q, /* 3ffeff14365ba5991c00000000000000 */
9.98231546029493238547658506831794512E-01Q, /* 3ffeff183488107b7c00000000000000 */
9.98262010103528552029672482603928074E-01Q, /* 3ffeff1c32bc77beb000000000000000 */
9.98292475107267818223988342651864514E-01Q, /* 3ffeff2030f8db72b000000000000000 */
9.98322941040739375573309644096298143E-01Q, /* 3ffeff242f3d3ba77000000000000000 */
9.98353407903971645787066790944663808E-01Q, /* 3ffeff282d89986cf000000000000000 */
9.98383875696992967307963340317655820E-01Q, /* 3ffeff2c2bddf1d32400000000000000 */
9.98414344419831761845429696222709026E-01Q, /* 3ffeff302a3a47ea0c00000000000000 */
9.98444814072516340086593800151604228E-01Q, /* 3ffeff34289e9ac19800000000000000 */
9.98475284655075123740886056111776270E-01Q, /* 3ffeff38270aea69c800000000000000 */
9.98505756167536479006585636852832977E-01Q, /* 3ffeff3c257f36f29400000000000000 */
9.98536228609928799837547330753295682E-01Q, /* 3ffeff4023fb806bf800000000000000 */
9.98566701982280452432050310562772211E-01Q, /* 3ffeff44227fc6e5ec00000000000000 */
9.98597176284619802988373749030870385E-01Q, /* 3ffeff48210c0a706800000000000000 */
9.98627651516975245460372434536111541E-01Q, /* 3ffeff4c1fa04b1b6800000000000000 */
9.98658127679375173801901155457017012E-01Q, /* 3ffeff501e3c88f6e800000000000000 */
9.98688604771847954211239084543194622E-01Q, /* 3ffeff541ce0c412e000000000000000 */
9.98719082794421980642241010173165705E-01Q, /* 3ffeff581b8cfc7f4c00000000000000 */
9.98749561747125619293186105096538085E-01Q, /* 3ffeff5c1a41324c2400000000000000 */
9.98780041629987291873504773320746608E-01Q, /* 3ffeff6018fd65896800000000000000 */
9.98810522443035364581476187595399097E-01Q, /* 3ffeff6417c196471000000000000000 */
9.98841004186298203615379520670103375E-01Q, /* 3ffeff68168dc4951400000000000000 */
9.98871486859804230684645176552294288E-01Q, /* 3ffeff6c1561f0837400000000000000 */
9.98901970463581839743127943620493170E-01Q, /* 3ffeff70143e1a222c00000000000000 */
9.98932454997659369233531378995394334E-01Q, /* 3ffeff74132241813000000000000000 */
9.98962940462065268620861502313346136E-01Q, /* 3ffeff78120e66b08400000000000000 */
9.98993426856827904103397486323956400E-01Q, /* 3ffeff7c110289c02000000000000000 */
9.99023914181975669634994119405746460E-01Q, /* 3ffeff800ffeaac00000000000000000 */
9.99054402437536959169506189937237650E-01Q, /* 3ffeff840f02c9c02000000000000000 */
9.99084891623540138905212870668037795E-01Q, /* 3ffeff880e0ee6d07800000000000000 */
9.99115381740013658307120181234495249E-01Q, /* 3ffeff8c0d2302010c00000000000000 */
9.99145872786985911329082910015131347E-01Q, /* 3ffeff900c3f1b61d800000000000000 */
9.99176364764485236413804614130640402E-01Q, /* 3ffeff940b633302d000000000000000 */
9.99206857672540083026291313217370771E-01Q, /* 3ffeff980a8f48f3f800000000000000 */
9.99237351511178817364822180024930276E-01Q, /* 3ffeff9c09c35d454800000000000000 */
9.99267846280429861138827618560753763E-01Q, /* 3ffeffa008ff7006c000000000000000 */
9.99298341980321608302162417203362565E-01Q, /* 3ffeffa4084381485c00000000000000 */
9.99328838610882452808681364331278019E-01Q, /* 3ffeffa8078f911a1800000000000000 */
9.99359336172140816367814863951934967E-01Q, /* 3ffeffac06e39f8bf400000000000000 */
9.99389834664125092933417704443854745E-01Q, /* 3ffeffb0063facadec00000000000000 */
9.99420334086863676459344674185558688E-01Q, /* 3ffeffb405a3b88ffc00000000000000 */
9.99450834440384988655026177184481639E-01Q, /* 3ffeffb8050fc3422400000000000000 */
9.99481335724717395718741386190231424E-01Q, /* 3ffeffbc0483ccd45c00000000000000 */
9.99511837939889374871071936468069907E-01Q, /* 3ffeffc003ffd556ac00000000000000 */
9.99542341085929264554721385138691403E-01Q, /* 3ffeffc40383dcd90800000000000000 */
9.99572845162865514234695751838444266E-01Q, /* 3ffeffc8030fe36b7400000000000000 */
9.99603350170726517864849824945849832E-01Q, /* 3ffeffcc02a3e91dec00000000000000 */
9.99633856109540669399038392839429434E-01Q, /* 3ffeffd0023fee006c00000000000000 */
9.99664362979336418302267475155531429E-01Q, /* 3ffeffd401e3f222f800000000000000 */
9.99694870780142130772816244643763639E-01Q, /* 3ffeffd8018ff5958800000000000000 */
9.99725379511986284031266336569387931E-01Q, /* 3ffeffdc0143f8682400000000000000 */
9.99755889174897216520321308053098619E-01Q, /* 3ffeffe000fffaaac000000000000000 */
9.99786399768903377704987178731244057E-01Q, /* 3ffeffe400c3fc6d6000000000000000 */
9.99816911294033217050269968240172602E-01Q, /* 3ffeffe8008ffdc00800000000000000 */
9.99847423750315072998873233700578567E-01Q, /* 3ffeffec0063feb2ac00000000000000 */
9.99877937137777450526954226006637327E-01Q, /* 3ffefff0003fff555800000000000000 */
9.99908451456448688077216502279043198E-01Q, /* 3ffefff40023ffb80000000000000000 */
9.99938966706357262870241697783058044E-01Q, /* 3ffefff8000fffeaac00000000000000 */
9.99969482887531541104308985268289689E-01Q, /* 3ffefffc0003fffd5400000000000000 */
#define T_EXPL_RES2 (T_EXPL_RES1 + 1 + 89 + 65)
1.00000000000000000000000000000000000E+00Q, /* 3fff0000000000000000000000000000 */
1.00003051804379100575559391472779680E+00Q, /* 3fff0002000200015400000000000000 */
1.00006103701893306334724798034585547E+00Q, /* 3fff00040008000aac00000000000000 */
1.00009155692545448346209013834595680E+00Q, /* 3fff0006001200240000000000000000 */
1.00012207776338379883185325525118969E+00Q, /* 3fff0008002000555800000000000000 */
1.00015259953274932014366527255333494E+00Q, /* 3fff000a003200a6ac00000000000000 */
1.00018312223357958012925905677548144E+00Q, /* 3fff000c004801200400000000000000 */
1.00021364586590294498691378066723701E+00Q, /* 3fff000e006201c95c00000000000000 */
1.00024417042974783642605984823603649E+00Q, /* 3fff0010008002aab400000000000000 */
1.00027469592514273166727889474714175E+00Q, /* 3fff001200a203cc1000000000000000 */
1.00030522235211605242000132420798764E+00Q, /* 3fff001400c805357000000000000000 */
1.00033574971069616488250630936818197E+00Q, /* 3fff001600f206eed000000000000000 */
1.00036627800091160178652671675081365E+00Q, /* 3fff0018012009003800000000000000 */
1.00039680722279067381919048784766346E+00Q, /* 3fff001a01520b71a000000000000000 */
1.00042733737636191371223048918182030E+00Q, /* 3fff001c01880e4b1000000000000000 */
1.00045786846165368766392589350289200E+00Q, /* 3fff001e01c211948400000000000000 */
1.00048840047869447289485833607614040E+00Q, /* 3fff0020020015560000000000000000 */
1.00051893342751269111445822090900037E+00Q, /* 3fff0022024219978400000000000000 */
1.00054946730813676403215595200890675E+00Q, /* 3fff002402881e611000000000000000 */
1.00058000212059516886853316464112140E+00Q, /* 3fff002602d223baa800000000000000 */
1.00061053786491632733302026281307917E+00Q, /* 3fff0028032029ac4c00000000000000 */
1.00064107454112866113504765053221490E+00Q, /* 3fff002a0372303dfc00000000000000 */
1.00067161214926059198404573180596344E+00Q, /* 3fff002c03c83777b800000000000000 */
1.00070215068934059710059614189958666E+00Q, /* 3fff002e04223f618400000000000000 */
1.00073269016139709819412928482051939E+00Q, /* 3fff0030048048036000000000000000 */
1.00076323056545857248522679583402351E+00Q, /* 3fff003204e251655000000000000000 */
1.00079377190155338617216784768970683E+00Q, /* 3fff003405485b8f5000000000000000 */
1.00082431416971007198668530691065826E+00Q, /* 3fff003605b266896800000000000000 */
1.00085485736995705163820957750431262E+00Q, /* 3fff00380620725b9800000000000000 */
1.00088540150232269132501983222027775E+00Q, /* 3fff003a06927f0ddc00000000000000 */
1.00091594656683552377884893758164253E+00Q, /* 3fff003c07088ca83c00000000000000 */
1.00094649256352402622027852885366883E+00Q, /* 3fff003e07829b32bc00000000000000 */
1.00097703949241650933643654752813745E+00Q, /* 3fff00400800aab55400000000000000 */
1.00100758735354156137020709138596430E+00Q, /* 3fff00420882bb381000000000000000 */
1.00103813614692760403102056443458423E+00Q, /* 3fff00440908ccc2f000000000000000 */
1.00106868587260300351715613942360505E+00Q, /* 3fff00460992df5df000000000000000 */
1.00109923653059629256034668287611566E+00Q, /* 3fff00480a20f3111800000000000000 */
1.00112978812093589287002259879955091E+00Q, /* 3fff004a0ab307e46800000000000000 */
1.00116034064365022615561429120134562E+00Q, /* 3fff004c0b491ddfe000000000000000 */
1.00119089409876788066000585786241572E+00Q, /* 3fff004e0be3350b8c00000000000000 */
1.00122144848631711155917400901671499E+00Q, /* 3fff00500c814d6f6000000000000000 */
1.00125200380632656260715407370298635E+00Q, /* 3fff00520d2367136c00000000000000 */
1.00128256005882454449107399341301061E+00Q, /* 3fff00540dc981ffa800000000000000 */
1.00131311724383964545381786592770368E+00Q, /* 3fff00560e739e3c2000000000000000 */
1.00134367536140017618251363273884635E+00Q, /* 3fff00580f21bbd0cc00000000000000 */
1.00137423441153472492004539162735455E+00Q, /* 3fff005a0fd3dac5b800000000000000 */
1.00140479439427171337584354660066310E+00Q, /* 3fff005c1089fb22e400000000000000 */
1.00143535530963956325933850166620687E+00Q, /* 3fff005e11441cf05000000000000000 */
1.00146591715766680730226312334707472E+00Q, /* 3fff0060120240360400000000000000 */
1.00149647993838186721404781565070152E+00Q, /* 3fff006212c464fc0000000000000000 */
1.00152704365181316470412298258452211E+00Q, /* 3fff0064138a8b4a4400000000000000 */
1.00155760829798923250422149067162536E+00Q, /* 3fff00661454b328d800000000000000 */
1.00158817387693849232377374391944613E+00Q, /* 3fff00681522dc9fbc00000000000000 */
1.00161874038868942138336137759324629E+00Q, /* 3fff006a15f507b6f400000000000000 */
1.00164930783327055241471725821611471E+00Q, /* 3fff006c16cb34768800000000000000 */
1.00167987621071025161612055853765924E+00Q, /* 3fff006e17a562e67400000000000000 */
1.00171044552103705171930414508096874E+00Q, /* 3fff00701883930ec000000000000000 */
1.00174101576427937443369842185347807E+00Q, /* 3fff00721965c4f76c00000000000000 */
1.00177158694046569697988502412044909E+00Q, /* 3fff00741a4bf8a87c00000000000000 */
1.00180215904962455208959681840497069E+00Q, /* 3fff00761b362e29f800000000000000 */
1.00183273209178441698341543997230474E+00Q, /* 3fff00781c246583e400000000000000 */
1.00186330606697365785962006157205906E+00Q, /* 3fff007a1d169ebe3c00000000000000 */
1.00189388097522080744994354972732253E+00Q, /* 3fff007c1e0cd9e10800000000000000 */
1.00192445681655439848611877096118405E+00Q, /* 3fff007e1f0716f45000000000000000 */
1.00195503359100279716642489802325144E+00Q, /* 3fff0080200556001000000000000000 */
1.00198561129859459173374602869444061E+00Q, /* 3fff00822107970c5400000000000000 */
};

21
libquadmath/math/fabsq.c
View File

@ -1,4 +1,4 @@
/* fabsq.c -- __float128 version of s_fabs.c.
/* s_fabsl.c -- long double version of s_fabs.c.
* Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
@ -13,13 +13,20 @@
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: $";
#endif
/*
* fabsq(x) returns the absolute value of x.
*/
#include "quadmath-imp.h"
__float128
fabsq (__float128 x)
__float128 fabsq(__float128 x)
{
uint64_t hx;
GET_FLT128_MSW64(hx,x);
SET_FLT128_MSW64(x,hx&0x7fffffffffffffffLL);
return x;
uint64_t hx;
GET_FLT128_MSW64(hx,x);
SET_FLT128_MSW64(x,hx&0x7fffffffffffffffLL);
return x;
}

24
libquadmath/math/fdimq.c
View File

@ -1,5 +1,5 @@
/* Return positive difference between arguments.
Copyright (C) 1997, 2004, 2009 Free Software Foundation, Inc.
Copyright (C) 1997-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
@ -14,29 +14,19 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#include <errno.h>
#include "quadmath-imp.h"
__float128
fdimq (__float128 x, __float128 y)
{
int clsx = fpclassifyq (x);
int clsy = fpclassifyq (y);
if (__builtin_islessequal (x, y))
return 0;
if (clsx == QUADFP_NAN || clsy == QUADFP_NAN
|| (y < 0 && clsx == QUADFP_INFINITE && clsy == QUADFP_INFINITE))
/* Raise invalid flag. */
return x - y;
if (x <= y)
return 0.0Q;
__float128 r = x - y;
if (isinfq (r))
__float128 r = math_narrow_eval (x - y);
if (isinfq (r) && !isinfq (x) && !isinfq (y))
errno = ERANGE;
return r;

19
libquadmath/math/finiteq.c
View File

@ -1,4 +1,4 @@
/* finiteq.c -- __float128 version of s_finite.c.
/* s_finitel.c -- long double version of s_finite.c.
* Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
@ -13,18 +13,21 @@
* ====================================================
*/
#include "quadmath-imp.h"
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: $";
#endif
/*
* finiteq(x) returns 1 is x is finite, else 0;
* no branching!
*/
int
finiteq (const __float128 x)
#include "quadmath-imp.h"
int finiteq(__float128 x)
{
int64_t hx;
GET_FLT128_MSW64(hx,x);
return (int)((uint64_t)((hx&0x7fff000000000000LL)
-0x7fff000000000000LL)>>63);
int64_t hx;
GET_FLT128_MSW64(hx,x);
return (int)((uint64_t)((hx&0x7fff000000000000LL)
-0x7fff000000000000LL)>>63);
}

18
libquadmath/math/floorq.c
View File

@ -1,4 +1,4 @@
/* floorq.c -- __float128 version of s_floor.c.
/* s_floorl.c -- long double version of s_floor.c.
* Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
@ -13,10 +13,22 @@
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: $";
#endif
/*
* floorq(x)
* Return x rounded toward -inf to integral value
* Method:
* Bit twiddling.
*/
#define NO_MATH_REDIRECT
#include "quadmath-imp.h"
__float128
floorq (__float128 x)
__float128 floorq(__float128 x)
{
int64_t i0,i1,j0;
uint64_t i,j;

17
libquadmath/math/fmaxq.c
View File

@ -1,5 +1,5 @@
/* Return maximum numeric value of X and Y.
Copyright (C) 1997 Free Software Foundation, Inc.
Copyright (C) 1997-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
@ -14,15 +14,20 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#include "quadmath-imp.h"
__float128
fmaxq (__float128 x, __float128 y)
{
return (__builtin_isgreaterequal (x, y) || isnanq (y)) ? x : y;
if (__builtin_isgreaterequal (x, y))
return x;
else if (__builtin_isless (x, y))
return y;
else if (issignalingq (x) || issignalingq (y))
return x + y;
else
return isnanq (y) ? x : y;
}

17
libquadmath/math/fminq.c
View File

@ -1,5 +1,5 @@
/* Return minimum numeric value of X and Y.
Copyright (C) 1997 Free Software Foundation, Inc.
Copyright (C) 1997-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
@ -14,15 +14,20 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#include "quadmath-imp.h"
__float128
fminq (__float128 x, __float128 y)
{
return (__builtin_islessequal (x, y) || isnanq (y)) ? x : y;
if (__builtin_islessequal (x, y))
return x;
else if (__builtin_isgreater (x, y))
return y;
else if (issignalingq (x) || issignalingq (y))
return x + y;
else
return isnanq (y) ? x : y;
}

196
libquadmath/math/fmodq.c
View File

@ -1,18 +1,18 @@
/* fmodq.c -- __float128 version of e_fmod.c.
/* e_fmodl.c -- long double version of e_fmod.c.
* Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
* Copyright (C) 1993, 2011 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
/*
* fmodq(x,y)
* Return x mod y in exact arithmetic
* Method: shift and subtract
@ -25,105 +25,105 @@ static const __float128 one = 1.0, Zero[] = {0.0, -0.0,};
__float128
fmodq (__float128 x, __float128 y)
{
int64_t n,hx,hy,hz,ix,iy,sx,i;
uint64_t lx,ly,lz;
int64_t n,hx,hy,hz,ix,iy,sx,i;
uint64_t lx,ly,lz;
GET_FLT128_WORDS64(hx,lx,x);
GET_FLT128_WORDS64(hy,ly,y);
sx = hx&0x8000000000000000ULL; /* sign of x */
hx ^=sx; /* |x| */
hy &= 0x7fffffffffffffffLL; /* |y| */
GET_FLT128_WORDS64(hx,lx,x);
GET_FLT128_WORDS64(hy,ly,y);
sx = hx&0x8000000000000000ULL; /* sign of x */
hx ^=sx; /* |x| */
hy &= 0x7fffffffffffffffLL; /* |y| */
/* purge off exception values */
if((hy|ly)==0||(hx>=0x7fff000000000000LL)|| /* y=0,or x not finite */
((hy|((ly|-ly)>>63))>0x7fff000000000000LL)) /* or y is NaN */
return (x*y)/(x*y);
if(hx<=hy) {
if((hx<hy)||(lx<ly)) return x; /* |x|<|y| return x */
if(lx==ly)
return Zero[(uint64_t)sx>>63]; /* |x|=|y| return x*0*/
}
/* purge off exception values */
if((hy|ly)==0||(hx>=0x7fff000000000000LL)|| /* y=0,or x not finite */
((hy|((ly|-ly)>>63))>0x7fff000000000000LL)) /* or y is NaN */
return (x*y)/(x*y);
if(hx<=hy) {
if((hx<hy)||(lx<ly)) return x; /* |x|<|y| return x */
if(lx==ly)
return Zero[(uint64_t)sx>>63]; /* |x|=|y| return x*0*/
}
/* determine ix = ilogb(x) */
if(hx<0x0001000000000000LL) { /* subnormal x */
if(hx==0) {
for (ix = -16431, i=lx; i>0; i<<=1) ix -=1;
} else {
for (ix = -16382, i=hx<<15; i>0; i<<=1) ix -=1;
}
} else ix = (hx>>48)-0x3fff;
/* determine ix = ilogb(x) */
if(hx<0x0001000000000000LL) { /* subnormal x */
if(hx==0) {
for (ix = -16431, i=lx; i>0; i<<=1) ix -=1;
} else {
for (ix = -16382, i=hx<<15; i>0; i<<=1) ix -=1;
}
} else ix = (hx>>48)-0x3fff;
/* determine iy = ilogb(y) */
if(hy<0x0001000000000000LL) { /* subnormal y */
if(hy==0) {
for (iy = -16431, i=ly; i>0; i<<=1) iy -=1;
} else {
for (iy = -16382, i=hy<<15; i>0; i<<=1) iy -=1;
}
} else iy = (hy>>48)-0x3fff;
/* determine iy = ilogb(y) */
if(hy<0x0001000000000000LL) { /* subnormal y */
if(hy==0) {
for (iy = -16431, i=ly; i>0; i<<=1) iy -=1;
} else {
for (iy = -16382, i=hy<<15; i>0; i<<=1) iy -=1;
}
} else iy = (hy>>48)-0x3fff;
/* set up {hx,lx}, {hy,ly} and align y to x */
if(ix >= -16382)
hx = 0x0001000000000000LL|(0x0000ffffffffffffLL&hx);
else { /* subnormal x, shift x to normal */
n = -16382-ix;
if(n<=63) {
hx = (hx<<n)|(lx>>(64-n));
lx <<= n;
} else {
hx = lx<<(n-64);
lx = 0;
}
}
if(iy >= -16382)
hy = 0x0001000000000000LL|(0x0000ffffffffffffLL&hy);
else { /* subnormal y, shift y to normal */
n = -16382-iy;
if(n<=63) {
hy = (hy<<n)|(ly>>(64-n));
ly <<= n;
} else {
hy = ly<<(n-64);
ly = 0;
}
}
/* set up {hx,lx}, {hy,ly} and align y to x */
if(ix >= -16382)
hx = 0x0001000000000000LL|(0x0000ffffffffffffLL&hx);
else { /* subnormal x, shift x to normal */
n = -16382-ix;
if(n<=63) {
hx = (hx<<n)|(lx>>(64-n));
lx <<= n;
} else {
hx = lx<<(n-64);
lx = 0;
}
}
if(iy >= -16382)
hy = 0x0001000000000000LL|(0x0000ffffffffffffLL&hy);
else { /* subnormal y, shift y to normal */
n = -16382-iy;
if(n<=63) {
hy = (hy<<n)|(ly>>(64-n));
ly <<= n;
} else {
hy = ly<<(n-64);
ly = 0;
}
}
/* fix point fmod */
n = ix - iy;
while(n--) {
hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
if(hz<0){hx = hx+hx+(lx>>63); lx = lx+lx;}
else {
if((hz|lz)==0) /* return sign(x)*0 */
return Zero[(uint64_t)sx>>63];
hx = hz+hz+(lz>>63); lx = lz+lz;
}
}
hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
if(hz>=0) {hx=hz;lx=lz;}
/* fix point fmod */
n = ix - iy;
while(n--) {
hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
if(hz<0){hx = hx+hx+(lx>>63); lx = lx+lx;}
else {
if((hz|lz)==0) /* return sign(x)*0 */
return Zero[(uint64_t)sx>>63];
hx = hz+hz+(lz>>63); lx = lz+lz;
}
}
hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
if(hz>=0) {hx=hz;lx=lz;}
/* convert back to floating value and restore the sign */
if((hx|lx)==0) /* return sign(x)*0 */
return Zero[(uint64_t)sx>>63];
while(hx<0x0001000000000000LL) { /* normalize x */
hx = hx+hx+(lx>>63); lx = lx+lx;
iy -= 1;
}
if(iy>= -16382) { /* normalize output */
hx = ((hx-0x0001000000000000LL)|((iy+16383)<<48));
SET_FLT128_WORDS64(x,hx|sx,lx);
} else { /* subnormal output */
n = -16382 - iy;
if(n<=48) {
lx = (lx>>n)|((uint64_t)hx<<(64-n));
hx >>= n;
} else if (n<=63) {
lx = (hx<<(64-n))|(lx>>n); hx = sx;
} else {
lx = hx>>(n-64); hx = sx;
}
SET_FLT128_WORDS64(x,hx|sx,lx);
x *= one; /* create necessary signal */
}
return x; /* exact output */
/* convert back to floating value and restore the sign */
if((hx|lx)==0) /* return sign(x)*0 */
return Zero[(uint64_t)sx>>63];
while(hx<0x0001000000000000LL) { /* normalize x */
hx = hx+hx+(lx>>63); lx = lx+lx;
iy -= 1;
}
if(iy>= -16382) { /* normalize output */
hx = ((hx-0x0001000000000000LL)|((iy+16383)<<48));
SET_FLT128_WORDS64(x,hx|sx,lx);
} else { /* subnormal output */
n = -16382 - iy;
if(n<=48) {
lx = (lx>>n)|((uint64_t)hx<<(64-n));
hx >>= n;
} else if (n<=63) {
lx = (hx<<(64-n))|(lx>>n); hx = sx;
} else {
lx = hx>>(n-64); hx = sx;
}
SET_FLT128_WORDS64(x,hx|sx,lx);
x *= one; /* create necessary signal */
}
return x; /* exact output */
}

41
libquadmath/math/frexpq.c
View File

@ -1,4 +1,4 @@
/* frexpq.c -- __float128 version of s_frexp.c.
/* s_frexpl.c -- long double version of s_frexp.c.
* Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
@ -13,10 +13,14 @@
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: $";
#endif
/*
* for non-zero x
* x = frexpq(arg,&exp);
* return a __float128 fp quantity x such that 0.5 <= |x| <1.0
* return a long double fp quantity x such that 0.5 <= |x| <1.0
* and the corresponding binary exponent "exp". That is
* arg = x*2^exp.
* If arg is inf, 0.0, or NaN, then frexpq(arg,&exp) returns arg
@ -28,22 +32,21 @@
static const __float128
two114 = 2.0769187434139310514121985316880384E+34Q; /* 0x4071000000000000, 0 */
__float128
frexpq (__float128 x, int *eptr)
__float128 frexpq(__float128 x, int *eptr)
{
uint64_t hx, lx, ix;
GET_FLT128_WORDS64(hx,lx,x);
ix = 0x7fffffffffffffffULL&hx;
*eptr = 0;
if(ix>=0x7fff000000000000ULL||((ix|lx)==0)) return x + x;/* 0,inf,nan */
if (ix<0x0001000000000000ULL) { /* subnormal */
x *= two114;
GET_FLT128_MSW64(hx,x);
ix = hx&0x7fffffffffffffffULL;
*eptr = -114;
}
*eptr += (ix>>48)-16382;
hx = (hx&0x8000ffffffffffffULL) | 0x3ffe000000000000ULL;
SET_FLT128_MSW64(x,hx);
return x;
uint64_t hx, lx, ix;
GET_FLT128_WORDS64(hx,lx,x);
ix = 0x7fffffffffffffffULL&hx;
*eptr = 0;
if(ix>=0x7fff000000000000ULL||((ix|lx)==0)) return x + x;/* 0,inf,nan */
if (ix<0x0001000000000000ULL) { /* subnormal */
x *= two114;
GET_FLT128_MSW64(hx,x);
ix = hx&0x7fffffffffffffffULL;
*eptr = -114;
}
*eptr += (ix>>48)-16382;
hx = (hx&0x8000ffffffffffffULL) | 0x3ffe000000000000ULL;
SET_FLT128_MSW64(x,hx);
return x;
}

189
libquadmath/math/hypotq.c
View File

@ -1,3 +1,7 @@
/* e_hypotl.c -- long double version of e_hypot.c.
* Conversion to long double by Jakub Jelinek, jakub@redhat.com.
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
@ -9,19 +13,14 @@
* ====================================================
*/
/* From e_hypotl.c -- long double version of e_hypot.c.
* Conversion to long double by Jakub Jelinek, jakub@redhat.com.
* Conversion to __float128 by FX Coudert, fxcoudert@gcc.gnu.org.
*/
/* hypotq(x,y)
*
* Method :
* If (assume round-to-nearest) z=x*x+y*y
* has error less than sqrtl(2)/2 ulp, than
* sqrtl(z) has error less than 1 ulp (exercise).
* has error less than sqrtq(2)/2 ulp, than
* sqrtq(z) has error less than 1 ulp (exercise).
*
* So, compute sqrtl(x*x+y*y) with some care as
* So, compute sqrtq(x*x+y*y) with some care as
* follows to get the error below 1 ulp:
*
* Assume x>y>0;
@ -38,100 +37,102 @@
* large or too tiny
*
* Special cases:
* hypotq(x,y) is INF if x or y is +INF or -INF; else
* hypotq(x,y) is NAN if x or y is NAN.
* hypotl(x,y) is INF if x or y is +INF or -INF; else
* hypotl(x,y) is NAN if x or y is NAN.
*
* Accuracy:
* hypotq(x,y) returns sqrtl(x^2+y^2) with error less
* than 1 ulps (units in the last place)
* hypotl(x,y) returns sqrtq(x^2+y^2) with error less
* than 1 ulps (units in the last place)
*/
#include "quadmath-imp.h"
__float128
hypotq (__float128 x, __float128 y)
hypotq(__float128 x, __float128 y)
{
__float128 a, b, t1, t2, y1, y2, w;
int64_t j, k, ha, hb;
__float128 a,b,t1,t2,y1,y2,w;
int64_t j,k,ha,hb;
GET_FLT128_MSW64(ha,x);
ha &= 0x7fffffffffffffffLL;
GET_FLT128_MSW64(hb,y);
hb &= 0x7fffffffffffffffLL;
if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
SET_FLT128_MSW64(a,ha); /* a <- |a| */
SET_FLT128_MSW64(b,hb); /* b <- |b| */
if((ha-hb)>0x78000000000000LL) {return a+b;} /* x/y > 2**120 */
k=0;
if(ha > 0x5f3f000000000000LL) { /* a>2**8000 */
if(ha >= 0x7fff000000000000LL) { /* Inf or NaN */
uint64_t low;
w = a+b; /* for sNaN */
GET_FLT128_LSW64(low,a);
if(((ha&0xffffffffffffLL)|low)==0) w = a;
GET_FLT128_LSW64(low,b);
if(((hb^0x7fff000000000000LL)|low)==0) w = b;
return w;
}
/* scale a and b by 2**-9600 */
ha -= 0x2580000000000000LL;
hb -= 0x2580000000000000LL; k += 9600;
SET_FLT128_MSW64(a,ha);
SET_FLT128_MSW64(b,hb);
}
if(hb < 0x20bf000000000000LL) { /* b < 2**-8000 */
if(hb <= 0x0000ffffffffffffLL) { /* subnormal b or 0 */
uint64_t low;
GET_FLT128_LSW64(low,b);
if((hb|low)==0) return a;
t1=0;
SET_FLT128_MSW64(t1,0x7ffd000000000000LL); /* t1=2^16382 */
b *= t1;
a *= t1;
k -= 16382;
GET_FLT128_MSW64 (ha, a);
GET_FLT128_MSW64 (hb, b);
if (hb > ha)
{
t1 = a;
a = b;
b = t1;
j = ha;
ha = hb;
hb = j;
}
} else { /* scale a and b by 2^9600 */
ha += 0x2580000000000000LL; /* a *= 2^9600 */
hb += 0x2580000000000000LL; /* b *= 2^9600 */
k -= 9600;
SET_FLT128_MSW64(a,ha);
SET_FLT128_MSW64(b,hb);
}
}
GET_FLT128_MSW64(ha,x);
ha &= 0x7fffffffffffffffLL;
GET_FLT128_MSW64(hb,y);
hb &= 0x7fffffffffffffffLL;
if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
SET_FLT128_MSW64(a,ha); /* a <- |a| */
SET_FLT128_MSW64(b,hb); /* b <- |b| */
if((ha-hb)>0x78000000000000LL) {return a+b;} /* x/y > 2**120 */
k=0;
if(ha > 0x5f3f000000000000LL) { /* a>2**8000 */
if(ha >= 0x7fff000000000000LL) { /* Inf or NaN */
uint64_t low;
w = a+b; /* for sNaN */
if (issignalingq (a) || issignalingq (b))
return w;
GET_FLT128_LSW64(low,a);
if(((ha&0xffffffffffffLL)|low)==0) w = a;
GET_FLT128_LSW64(low,b);
if(((hb^0x7fff000000000000LL)|low)==0) w = b;
return w;
}
/* scale a and b by 2**-9600 */
ha -= 0x2580000000000000LL;
hb -= 0x2580000000000000LL; k += 9600;
SET_FLT128_MSW64(a,ha);
SET_FLT128_MSW64(b,hb);
}
if(hb < 0x20bf000000000000LL) { /* b < 2**-8000 */
if(hb <= 0x0000ffffffffffffLL) { /* subnormal b or 0 */
uint64_t low;
GET_FLT128_LSW64(low,b);
if((hb|low)==0) return a;
t1=0;
SET_FLT128_MSW64(t1,0x7ffd000000000000LL); /* t1=2^16382 */
b *= t1;
a *= t1;
k -= 16382;
GET_FLT128_MSW64 (ha, a);
GET_FLT128_MSW64 (hb, b);
if (hb > ha)
{
t1 = a;
a = b;
b = t1;
j = ha;
ha = hb;
hb = j;
}
} else { /* scale a and b by 2^9600 */
ha += 0x2580000000000000LL; /* a *= 2^9600 */
hb += 0x2580000000000000LL; /* b *= 2^9600 */
k -= 9600;
SET_FLT128_MSW64(a,ha);
SET_FLT128_MSW64(b,hb);
}
}
/* medium size a and b */
w = a-b;
if (w>b) {
t1 = 0;
SET_FLT128_MSW64(t1,ha);
t2 = a-t1;
w = sqrtq(t1*t1-(b*(-b)-t2*(a+t1)));
} else {
a = a+a;
y1 = 0;
SET_FLT128_MSW64(y1,hb);
y2 = b - y1;
t1 = 0;
SET_FLT128_MSW64(t1,ha+0x0001000000000000LL);
t2 = a - t1;
w = sqrtq(t1*y1-(w*(-w)-(t1*y2+t2*b)));
}
if(k!=0) {
uint64_t high;
t1 = 1.0Q;
GET_FLT128_MSW64(high,t1);
SET_FLT128_MSW64(t1,high+(k<<48));
w *= t1;
math_check_force_underflow_nonneg (w);
return w;
} else return w;
w = a-b;
if (w>b) {
t1 = 0;
SET_FLT128_MSW64(t1,ha);
t2 = a-t1;
w = sqrtq(t1*t1-(b*(-b)-t2*(a+t1)));
} else {
a = a+a;
y1 = 0;
SET_FLT128_MSW64(y1,hb);
y2 = b - y1;
t1 = 0;
SET_FLT128_MSW64(t1,ha+0x0001000000000000LL);
t2 = a - t1;
w = sqrtq(t1*y1-(w*(-w)-(t1*y2+t2*b)));
}
if(k!=0) {
uint64_t high;
t1 = 1;
GET_FLT128_MSW64(high,t1);
SET_FLT128_MSW64(t1,high+(k<<48));
w *= t1;
math_check_force_underflow_nonneg (w);
return w;
} else return w;
}

33
libquadmath/math/ilogbq.c
View File

@ -1,4 +1,4 @@
/* ilogbq.c -- __float128 version of s_ilogb.c.
/* s_ilogbl.c -- long double version of s_ilogb.c.
* Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
@ -17,18 +17,15 @@
static char rcsid[] = "$NetBSD: $";
#endif
/* ilogbl(__float128 x)
/* ilogbl(long double x)
* return the binary exponent of non-zero x
* ilogbl(0) = FP_ILOGB0
* ilogbl(NaN) = FP_ILOGBNAN (no signal is raised)
* ilogbl(+-Inf) = INT_MAX (no signal is raised)
*/
#include <limits.h>
#include <math.h>
#include <errno.h>
#include "quadmath-imp.h"
#ifndef FP_ILOGB0
# define FP_ILOGB0 INT_MIN
#endif
@ -36,8 +33,7 @@ static char rcsid[] = "$NetBSD: $";
# define FP_ILOGBNAN INT_MAX
#endif
int
ilogbq (__float128 x)
int ilogbq (__float128 x)
{
int64_t hx,lx;
int ix;
@ -46,13 +42,7 @@ ilogbq (__float128 x)
hx &= 0x7fffffffffffffffLL;
if(hx <= 0x0001000000000000LL) {
if((hx|lx)==0)
{
errno = EDOM;
#ifdef USE_FENV_H
feraiseexcept (FE_INVALID);
#endif
return FP_ILOGB0; /* ilogbl(0) = FP_ILOGB0 */
}
{ errno = EDOM; feraiseexcept (FE_INVALID); return FP_ILOGB0; } /* ilogbl(0) = FP_ILOGB0 */
else /* subnormal x */
if(hx==0) {
for (ix = -16431; lx>0; lx<<=1) ix -=1;
@ -65,18 +55,7 @@ ilogbq (__float128 x)
else if (FP_ILOGBNAN != INT_MAX) {
/* ISO C99 requires ilogbl(+-Inf) == INT_MAX. */
if (((hx^0x7fff000000000000LL)|lx) == 0)
{
errno = EDOM;
#ifdef USE_FENV_H
feraiseexcept (FE_INVALID);
#endif
return INT_MAX;
}
{ errno = EDOM; feraiseexcept (FE_INVALID); return INT_MAX; }
}
errno = EDOM;
#ifdef USE_FENV_H
feraiseexcept (FE_INVALID);
#endif
return FP_ILOGBNAN;
{ errno = EDOM; feraiseexcept (FE_INVALID); return FP_ILOGBNAN; }
}

19
libquadmath/math/isinf_nsq.c
View File

@ -1,19 +0,0 @@
/*
* Written by Ulrich Drepper <drepper@gmail.com>
*/
/*
* __quadmath_isinf_nsq (x) returns != 0 if x is ±inf, else 0;
* no branching!
*/
#include "quadmath-imp.h"
int
__quadmath_isinf_nsq (__float128 x)
{
int64_t hx,lx;
GET_FLT128_WORDS64(hx,lx,x);
return !(lx | ((hx & 0x7fffffffffffffffLL) ^ 0x7fff000000000000LL));
}

19
libquadmath/math/isinfq.c
View File

@ -4,14 +4,23 @@
* Public domain.
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: $";
#endif
/*
* isinfq(x) returns 1 if x is inf, -1 if x is -inf, else 0;
* no branching!
*/
#include "quadmath-imp.h"
int
isinfq (__float128 x)
{
int64_t hx,lx;
GET_FLT128_WORDS64(hx,lx,x);
lx |= (hx & 0x7fffffffffffffffLL) ^ 0x7fff000000000000LL;
lx |= -lx;
return ~(lx >> 63) & (hx >> 62);
int64_t hx,lx;
GET_FLT128_WORDS64(hx,lx,x);
lx |= (hx & 0x7fffffffffffffffLL) ^ 0x7fff000000000000LL;
lx |= -lx;
return ~(lx >> 63) & (hx >> 62);
}

26
libquadmath/math/isnanq.c
View File

@ -1,4 +1,4 @@
/* isnanq.c -- __float128 version of s_isnan.c.
/* s_isnanl.c -- long double version of s_isnan.c.
* Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
@ -13,15 +13,23 @@
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: $";
#endif
/*
* isnanq(x) returns 1 is x is nan, else 0;
* no branching!
*/
#include "quadmath-imp.h"
int
isnanq (const __float128 x)
int isnanq(__float128 x)
{
int64_t hx,lx;
GET_FLT128_WORDS64(hx,lx,x);
hx &= 0x7fffffffffffffffLL;
hx |= (uint64_t)(lx|(-lx))>>63;
hx = 0x7fff000000000000LL - hx;
return (int)((uint64_t)hx>>63);
int64_t hx,lx;
GET_FLT128_WORDS64(hx,lx,x);
hx &= 0x7fffffffffffffffLL;
hx |= (uint64_t)(lx|(-lx))>>63;
hx = 0x7fff000000000000LL - hx;
return (int)((uint64_t)hx>>63);
}

43
libquadmath/math/issignalingq.c Normal file
View File

@ -0,0 +1,43 @@
/* Test for signaling NaN.
Copyright (C) 2013-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#include "quadmath-imp.h"
int
issignalingq (__float128 x)
{
uint64_t hxi, lxi __attribute__ ((unused));
GET_FLT128_WORDS64 (hxi, lxi, x);
#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN
/* We only have to care about the high-order bit of x's significand, because
having it set (sNaN) already makes the significand different from that
used to designate infinity. */
return ((hxi & UINT64_C (0x7fff800000000000))
== UINT64_C (0x7fff800000000000));
#else
/* To keep the following comparison simple, toggle the quiet/signaling bit,
so that it is set for sNaNs. This is inverse to IEEE 754-2008 (as well as
common practice for IEEE 754-1985). */
hxi ^= UINT64_C (0x0000800000000000);
/* If lxi != 0, then set any suitable bit of the significand in hxi. */
hxi |= (lxi | -lxi) >> 63;
/* We have to compare for greater (instead of greater or equal), because x's
significand being all-zero designates infinity not NaN. */
return (hxi & UINT64_C (0x7fffffffffffffff)) > UINT64_C (0x7fff800000000000);
#endif
}

47
libquadmath/math/j0q.c
View File

@ -6,7 +6,7 @@
*
* SYNOPSIS:
*
* __float128 x, y, j0l();
* long double x, y, j0l();
*
* y = j0l( x );
*
@ -52,7 +52,7 @@
*
* SYNOPSIS:
*
* __float128 x, y, y0l();
* double x, y, y0l();
*
* y = y0l( x );
*
@ -88,8 +88,8 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
License along with this library; if not, see
<http://www.gnu.org/licenses/>. */
#include "quadmath-imp.h"
@ -97,7 +97,7 @@
static const __float128 ONEOSQPI = 5.6418958354775628694807945156077258584405E-1Q;
/* 2 / pi */
static const __float128 TWOOPI = 6.3661977236758134307553505349005744813784E-1Q;
static const __float128 zero = 0.0Q;
static const __float128 zero = 0;
/* J0(x) = 1 - x^2/4 + x^2 x^2 R(x^2)
Peak relative error 3.4e-37
@ -683,21 +683,21 @@ j0q (__float128 x)
if (x != x)
return x + x;
else
return 0.0Q;
return 0;
}
if (x == 0.0Q)
return 1.0Q;
if (x == 0)
return 1;
xx = fabsq (x);
if (xx <= 2.0Q)
if (xx <= 2)
{
if (xx < 0x1p-57Q)
return 1.0Q;
return 1;
/* 0 <= x <= 2 */
z = xx * xx;
p = z * z * neval (z, J0_2N, NJ0_2N) / deval (z, J0_2D, NJ0_2D);
p -= 0.25Q * z;
p += 1.0Q;
p += 1;
return p;
}
@ -711,7 +711,7 @@ j0q (__float128 x)
sincosq (xx, &s, &c);
ss = s - c;
cc = s + c;
if (xx <= FLT128_MAX / 2.0Q)
if (xx <= FLT128_MAX / 2)
{
z = -cosq (xx + xx);
if ((s * c) < 0)
@ -723,7 +723,7 @@ j0q (__float128 x)
if (xx > 0x1p256Q)
return ONEOSQPI * cc / sqrtq (xx);
xinv = 1.0Q / xx;
xinv = 1 / xx;
z = xinv * xinv;
if (xinv <= 0.25)
{
@ -781,7 +781,7 @@ j0q (__float128 x)
q = neval (z, Q2_2r3N, NQ2_2r3N) / deval (z, Q2_2r3D, NQ2_2r3D);
}
}
p = 1.0Q + z * p;
p = 1 + z * p;
q = z * xinv * q;
q = q - 0.125Q * xinv;
z = ONEOSQPI * (p * cc - q * ss) / sqrtq (xx);
@ -789,11 +789,12 @@ j0q (__float128 x)
}
/* Y0(x) = 2/pi * log(x) * J0(x) + R(x^2)
Peak absolute error 1.7e-36 (relative where Y0 > 1)
0 <= x <= 2 */
#define NY0_2N 7
static __float128 Y0_2N[NY0_2N + 1] = {
static const __float128 Y0_2N[NY0_2N + 1] = {
-1.062023609591350692692296993537002558155E19Q,
2.542000883190248639104127452714966858866E19Q,
-1.984190771278515324281415820316054696545E18Q,
@ -804,7 +805,7 @@ static __float128 Y0_2N[NY0_2N + 1] = {
8.230845651379566339707130644134372793322E6Q,
};
#define NY0_2D 7
static __float128 Y0_2D[NY0_2D + 1] = {
static const __float128 Y0_2D[NY0_2D + 1] = {
1.438972634353286978700329883122253752192E20Q,
1.856409101981569254247700169486907405500E18Q,
1.219693352678218589553725579802986255614E16Q,
@ -821,22 +822,22 @@ static const __float128 U0 = -7.3804295108687225274343927948483016310862e-02Q;
/* Bessel function of the second kind, order zero. */
__float128
y0q (__float128 x)
y0q(__float128 x)
{
__float128 xx, xinv, z, p, q, c, s, cc, ss;
if (! finiteq (x))
return 1 / (x + x * x);
if (x <= 0.0Q)
if (x <= 0)
{
if (x < 0.0Q)
if (x < 0)
return (zero / (zero * x));
return -1 / zero; /* -inf and divide by zero exception. */
}
xx = fabsq (x);
if (xx <= 0x1p-57)
return U0 + TWOOPI * logq (x);
if (xx <= 2.0Q)
if (xx <= 2)
{
/* 0 <= x <= 2 */
z = xx * xx;
@ -855,7 +856,7 @@ y0q (__float128 x)
sincosq (x, &s, &c);
ss = s - c;
cc = s + c;
if (xx <= FLT128_MAX / 2.0Q)
if (xx <= FLT128_MAX / 2)
{
z = -cosq (x + x);
if ((s * c) < 0)
@ -867,7 +868,7 @@ y0q (__float128 x)
if (xx > 0x1p256Q)
return ONEOSQPI * ss / sqrtq (x);
xinv = 1.0Q / xx;
xinv = 1 / xx;
z = xinv * xinv;
if (xinv <= 0.25)
{
@ -925,7 +926,7 @@ y0q (__float128 x)
q = neval (z, Q2_2r3N, NQ2_2r3N) / deval (z, Q2_2r3D, NQ2_2r3D);
}
}
p = 1.0Q + z * p;
p = 1 + z * p;
q = z * xinv * q;
q = q - 0.125Q * xinv;
z = ONEOSQPI * (p * ss + q * cc) / sqrtq (x);

50
libquadmath/math/j1q.c
View File

@ -6,9 +6,9 @@
*
* SYNOPSIS:
*
* __float128 x, y, j1q();
* long double x, y, j1l();
*
* y = j1q( x );
* y = j1l( x );
*
*
*
@ -52,9 +52,9 @@
*
* SYNOPSIS:
*
* __float128, y, y1q();
* double x, y, y1l();
*
* y = y1q( x );
* y = y1l( x );
*
*
*
@ -92,17 +92,16 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
License along with this library; if not, see
<http://www.gnu.org/licenses/>. */
#include <errno.h>
#include "quadmath-imp.h"
/* 1 / sqrt(pi) */
static const __float128 ONEOSQPI = 5.6418958354775628694807945156077258584405E-1Q;
/* 2 / pi */
static const __float128 TWOOPI = 6.3661977236758134307553505349005744813784E-1Q;
static const __float128 zero = 0.0Q;
static const __float128 zero = 0;
/* J1(x) = .5x + x x^2 R(x^2)
Peak relative error 1.9e-35
@ -126,7 +125,7 @@ static const __float128 J0_2D[NJ0_2D + 1] = {
5.673775894803172808323058205986256928794E8Q,
1.080329960080981204840966206372671147224E6Q,
1.411951256636576283942477881535283304912E3Q,
/* 1.000000000000000000000000000000000000000E0Q */
/* 1.000000000000000000000000000000000000000E0L */
};
/* J1(x)cosX + Y1(x)sinX = sqrt( 2/(pi x)) P1(x), P1(x) = 1 + 1/x^2 R(1/x^2),
@ -690,9 +689,9 @@ j1q (__float128 x)
if (x != x)
return x + x;
else
return 0.0Q;
return 0;
}
if (x == 0.0Q)
if (x == 0)
return x;
xx = fabsq (x);
if (xx <= 0x1p-58Q)
@ -703,7 +702,7 @@ j1q (__float128 x)
errno = ERANGE;
return ret;
}
if (xx <= 2.0Q)
if (xx <= 2)
{
/* 0 <= x <= 2 */
z = xx * xx;
@ -723,7 +722,7 @@ j1q (__float128 x)
sincosq (xx, &s, &c);
ss = -s - c;
cc = s - c;
if (xx <= FLT128_MAX / 2.0Q)
if (xx <= FLT128_MAX / 2)
{
z = cosq (xx + xx);
if ((s * c) > 0)
@ -740,7 +739,7 @@ j1q (__float128 x)
return z;
}
xinv = 1.0Q / xx;
xinv = 1 / xx;
z = xinv * xinv;
if (xinv <= 0.25)
{
@ -798,7 +797,7 @@ j1q (__float128 x)
q = neval (z, Q2_2r3N, NQ2_2r3N) / deval (z, Q2_2r3D, NQ2_2r3D);
}
}
p = 1.0Q + z * p;
p = 1 + z * p;
q = z * q;
q = q * xinv + 0.375Q * xinv;
z = ONEOSQPI * (p * cc - q * ss) / sqrtq (xx);
@ -808,11 +807,12 @@ j1q (__float128 x)
}
/* Y1(x) = 2/pi * (log(x) * J1(x) - 1/x) + x R(x^2)
Peak relative error 6.2e-38
0 <= x <= 2 */
#define NY0_2N 7
static __float128 Y0_2N[NY0_2N + 1] = {
static const __float128 Y0_2N[NY0_2N + 1] = {
-6.804415404830253804408698161694720833249E19Q,
1.805450517967019908027153056150465849237E19Q,
-8.065747497063694098810419456383006737312E17Q,
@ -823,7 +823,7 @@ static __float128 Y0_2N[NY0_2N + 1] = {
9.541172044989995856117187515882879304461E5Q,
};
#define NY0_2D 7
static __float128 Y0_2D[NY0_2D + 1] = {
static const __float128 Y0_2D[NY0_2D + 1] = {
3.470629591820267059538637461549677594549E20Q,
4.120796439009916326855848107545425217219E18Q,
2.477653371652018249749350657387030814542E16Q,
@ -845,9 +845,9 @@ y1q (__float128 x)
if (! finiteq (x))
return 1 / (x + x * x);
if (x <= 0.0Q)
if (x <= 0)
{
if (x < 0.0Q)
if (x < 0)
return (zero / (zero * x));
return -1 / zero; /* -inf and divide by zero exception. */
}
@ -859,10 +859,10 @@ y1q (__float128 x)
errno = ERANGE;
return z;
}
if (xx <= 2.0Q)
{
if (xx <= 2)
{
/* 0 <= x <= 2 */
/* FIXME: SET_RESTORE_ROUNDL (FE_TONEAREST); */
SET_RESTORE_ROUNDF128 (FE_TONEAREST);
z = xx * xx;
p = xx * neval (z, Y0_2N, NY0_2N) / deval (z, Y0_2D, NY0_2D);
p = -TWOOPI / xx + p;
@ -879,7 +879,7 @@ y1q (__float128 x)
sincosq (xx, &s, &c);
ss = -s - c;
cc = s - c;
if (xx <= FLT128_MAX / 2.0Q)
if (xx <= FLT128_MAX / 2)
{
z = cosq (xx + xx);
if ((s * c) > 0)
@ -891,7 +891,7 @@ y1q (__float128 x)
if (xx > 0x1p256Q)
return ONEOSQPI * ss / sqrtq (xx);
xinv = 1.0Q / xx;
xinv = 1 / xx;
z = xinv * xinv;
if (xinv <= 0.25)
{
@ -949,7 +949,7 @@ y1q (__float128 x)
q = neval (z, Q2_2r3N, NQ2_2r3N) / deval (z, Q2_2r3D, NQ2_2r3D);
}
}
p = 1.0Q + z * p;
p = 1 + z * p;
q = z * q;
q = q * xinv + 0.375Q * xinv;
z = ONEOSQPI * (p * ss + q * cc) / sqrtq (xx);

535
libquadmath/math/jnq.c
View File

@ -27,8 +27,8 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
License along with this library; if not, see
<http://www.gnu.org/licenses/>. */
/*
* __ieee754_jn(n, x), __ieee754_yn(n, x)
@ -56,14 +56,13 @@
*
*/
#include <errno.h>
#include "quadmath-imp.h"
static const __float128
invsqrtpi = 5.6418958354775628694807945156077258584405E-1Q,
two = 2.0e0Q,
one = 1.0e0Q,
zero = 0.0Q;
two = 2,
one = 1,
zero = 0;
__float128
@ -71,7 +70,7 @@ jnq (int n, __float128 x)
{
uint32_t se;
int32_t i, ix, sgn;
__float128 a, b, temp, di;
__float128 a, b, temp, di, ret;
__float128 z, w;
ieee854_float128 u;
@ -104,201 +103,213 @@ jnq (int n, __float128 x)
sgn = (n & 1) & (se >> 31); /* even n -- 0, odd n -- sign(x) */
x = fabsq (x);
if (x == 0.0Q || ix >= 0x7fff0000) /* if x is 0 or inf */
b = zero;
else if ((__float128) n <= x)
{
SET_RESTORE_ROUNDF128 (FE_TONEAREST);
if (x == 0 || ix >= 0x7fff0000) /* if x is 0 or inf */
return sgn == 1 ? -zero : zero;
else if ((__float128) n <= x)
{
/* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
if (ix >= 0x412D0000)
{ /* x > 2**302 */
/* ??? Could use an expansion for large x here. */
/* (x >> n**2)
* Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
* Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
* Let s=sin(x), c=cos(x),
* xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
*
* n sin(xn)*sqt2 cos(xn)*sqt2
* ----------------------------------
* 0 s-c c+s
* 1 -s-c -c+s
* 2 -s+c -c-s
* 3 s+c c-s
*/
__float128 s;
__float128 c;
sincosq (x, &s, &c);
switch (n & 3)
{
case 0:
temp = c + s;
break;
case 1:
temp = -c + s;
break;
case 2:
temp = -c - s;
break;
case 3:
temp = c - s;
break;
}
b = invsqrtpi * temp / sqrtq (x);
}
else
{
a = j0q (x);
b = j1q (x);
for (i = 1; i < n; i++)
{
temp = b;
b = b * ((__float128) (i + i) / x) - a; /* avoid underflow */
a = temp;
}
}
}
else
{
if (ix < 0x3fc60000)
{ /* x < 2**-57 */
/* x is tiny, return the first Taylor expansion of J(n,x)
* J(n,x) = 1/n!*(x/2)^n - ...
*/
if (n >= 400) /* underflow, result < 10^-4952 */
b = zero;
else
{
temp = x * 0.5;
b = temp;
for (a = one, i = 2; i <= n; i++)
{
a *= (__float128) i; /* a = n! */
b *= temp; /* b = (x/2)^n */
}
b = b / a;
}
}
else
{
/* use backward recurrence */
/* x x^2 x^2
* J(n,x)/J(n-1,x) = ---- ------ ------ .....
* 2n - 2(n+1) - 2(n+2)
*
* 1 1 1
* (for large x) = ---- ------ ------ .....
* 2n 2(n+1) 2(n+2)
* -- - ------ - ------ -
* x x x
*
* Let w = 2n/x and h=2/x, then the above quotient
* is equal to the continued fraction:
* 1
* = -----------------------
* 1
* w - -----------------
* 1
* w+h - ---------
* w+2h - ...
*
* To determine how many terms needed, let
* Q(0) = w, Q(1) = w(w+h) - 1,
* Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
* When Q(k) > 1e4 good for single
* When Q(k) > 1e9 good for double
* When Q(k) > 1e17 good for quadruple
*/
/* determine k */
__float128 t, v;
__float128 q0, q1, h, tmp;
int32_t k, m;
w = (n + n) / (__float128) x;
h = 2 / (__float128) x;
q0 = w;
z = w + h;
q1 = w * z - 1;
k = 1;
while (q1 < 1.0e17Q)
{
k += 1;
z += h;
tmp = z * q1 - q0;
q0 = q1;
q1 = tmp;
}
m = n + n;
for (t = zero, i = 2 * (n + k); i >= m; i -= 2)
t = one / (i / x - t);
a = t;
b = one;
/* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
* Hence, if n*(log(2n/x)) > ...
* single 8.8722839355e+01
* double 7.09782712893383973096e+02
* long double 1.1356523406294143949491931077970765006170e+04
* then recurrent value may overflow and the result is
* likely underflow to zero
*/
tmp = n;
v = two / x;
tmp = tmp * logq (fabsq (v * tmp));
if (tmp < 1.1356523406294143949491931077970765006170e+04Q)
{
for (i = n - 1, di = (__float128) (i + i); i > 0; i--)
{
temp = b;
b *= di;
b = b / x - a;
a = temp;
di -= two;
}
}
else
{
for (i = n - 1, di = (__float128) (i + i); i > 0; i--)
{
temp = b;
b *= di;
b = b / x - a;
a = temp;
di -= two;
/* scale b to avoid spurious overflow */
if (b > 1e100Q)
{
a /= b;
t /= b;
b = one;
}
}
}
/* j0() and j1() suffer enormous loss of precision at and
* near zero; however, we know that their zero points never
* coincide, so just choose the one further away from zero.
*/
z = j0q (x);
w = j1q (x);
if (fabsq (z) >= fabsq (w))
b = (t * z / b);
else
b = (t * w / a);
}
}
if (sgn == 1)
ret = -b;
else
ret = b;
}
if (ret == 0)
{
/* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
if (ix >= 0x412D0000)
{ /* x > 2**302 */
/* ??? Could use an expansion for large x here. */
/* (x >> n**2)
* Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
* Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
* Let s=sin(x), c=cos(x),
* xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
*
* n sin(xn)*sqt2 cos(xn)*sqt2
* ----------------------------------
* 0 s-c c+s
* 1 -s-c -c+s
* 2 -s+c -c-s
* 3 s+c c-s
*/
__float128 s;
__float128 c;
sincosq (x, &s, &c);
switch (n & 3)
{
case 0:
temp = c + s;
break;
case 1:
temp = -c + s;
break;
case 2:
temp = -c - s;
break;
case 3:
temp = c - s;
break;
}
b = invsqrtpi * temp / sqrtq (x);
}
else
{
a = j0q (x);
b = j1q (x);
for (i = 1; i < n; i++)
{
temp = b;
b = b * ((__float128) (i + i) / x) - a; /* avoid underflow */
a = temp;
}
}
ret = copysignq (FLT128_MIN, ret) * FLT128_MIN;
errno = ERANGE;
}
else
{
if (ix < 0x3fc60000)
{ /* x < 2**-57 */
/* x is tiny, return the first Taylor expansion of J(n,x)
* J(n,x) = 1/n!*(x/2)^n - ...
*/
if (n >= 400) /* underflow, result < 10^-4952 */
b = zero;
else
{
temp = x * 0.5;
b = temp;
for (a = one, i = 2; i <= n; i++)
{
a *= (__float128) i; /* a = n! */
b *= temp; /* b = (x/2)^n */
}
b = b / a;
}
}
else
{
/* use backward recurrence */
/* x x^2 x^2
* J(n,x)/J(n-1,x) = ---- ------ ------ .....
* 2n - 2(n+1) - 2(n+2)
*
* 1 1 1
* (for large x) = ---- ------ ------ .....
* 2n 2(n+1) 2(n+2)
* -- - ------ - ------ -
* x x x
*
* Let w = 2n/x and h=2/x, then the above quotient
* is equal to the continued fraction:
* 1
* = -----------------------
* 1
* w - -----------------
* 1
* w+h - ---------
* w+2h - ...
*
* To determine how many terms needed, let
* Q(0) = w, Q(1) = w(w+h) - 1,
* Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
* When Q(k) > 1e4 good for single
* When Q(k) > 1e9 good for double
* When Q(k) > 1e17 good for quadruple
*/
/* determine k */
__float128 t, v;
__float128 q0, q1, h, tmp;
int32_t k, m;
w = (n + n) / (__float128) x;
h = 2.0Q / (__float128) x;
q0 = w;
z = w + h;
q1 = w * z - 1.0Q;
k = 1;
while (q1 < 1.0e17Q)
{
k += 1;
z += h;
tmp = z * q1 - q0;
q0 = q1;
q1 = tmp;
}
m = n + n;
for (t = zero, i = 2 * (n + k); i >= m; i -= 2)
t = one / (i / x - t);
a = t;
b = one;
/* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
* Hence, if n*(log(2n/x)) > ...
* single 8.8722839355e+01
* double 7.09782712893383973096e+02
* __float128 1.1356523406294143949491931077970765006170e+04
* then recurrent value may overflow and the result is
* likely underflow to zero
*/
tmp = n;
v = two / x;
tmp = tmp * logq (fabsq (v * tmp));
if (tmp < 1.1356523406294143949491931077970765006170e+04Q)
{
for (i = n - 1, di = (__float128) (i + i); i > 0; i--)
{
temp = b;
b *= di;
b = b / x - a;
a = temp;
di -= two;
}
}
else
{
for (i = n - 1, di = (__float128) (i + i); i > 0; i--)
{
temp = b;
b *= di;
b = b / x - a;
a = temp;
di -= two;
/* scale b to avoid spurious overflow */
if (b > 1e100Q)
{
a /= b;
t /= b;
b = one;
}
}
}
/* j0() and j1() suffer enormous loss of precision at and
* near zero; however, we know that their zero points never
* coincide, so just choose the one further away from zero.
*/
z = j0q (x);
w = j1q (x);
if (fabsq (z) >= fabsq (w))
b = (t * z / b);
else
b = (t * w / a);
}
}
if (sgn == 1)
return -b;
else
return b;
math_check_force_underflow (ret);
return ret;
}
__float128
ynq (int n, __float128 x)
{
uint32_t se;
int32_t i, ix;
int32_t sign;
__float128 a, b, temp;
__float128 a, b, temp, ret;
ieee854_float128 u;
u.value = x;
@ -311,10 +322,10 @@ ynq (int n, __float128 x)
if ((u.words32.w0 & 0xffff) | u.words32.w1 | u.words32.w2 | u.words32.w3)
return x + x;
}
if (x <= 0.0Q)
if (x <= 0)
{
if (x == 0.0Q)
return -HUGE_VALQ + x;
if (x == 0)
return ((n < 0 && (n & 1) != 0) ? 1 : -1) / 0.0Q;
if (se & 0x80000000)
return zero / (zero * x);
}
@ -326,69 +337,79 @@ ynq (int n, __float128 x)
}
if (n == 0)
return (y0q (x));
if (n == 1)
return (sign * y1q (x));
if (ix >= 0x7fff0000)
return zero;
if (ix >= 0x412D0000)
{ /* x > 2**302 */
{
SET_RESTORE_ROUNDF128 (FE_TONEAREST);
if (n == 1)
{
ret = sign * y1q (x);
goto out;
}
if (ix >= 0x7fff0000)
return zero;
if (ix >= 0x412D0000)
{ /* x > 2**302 */
/* ??? See comment above on the possible futility of this. */
/* ??? See comment above on the possible futility of this. */
/* (x >> n**2)
* Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
* Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
* Let s=sin(x), c=cos(x),
* xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
*
* n sin(xn)*sqt2 cos(xn)*sqt2
* ----------------------------------
* 0 s-c c+s
* 1 -s-c -c+s
* 2 -s+c -c-s
* 3 s+c c-s
*/
__float128 s;
__float128 c;
sincosq (x, &s, &c);
switch (n & 3)
{
case 0:
temp = s - c;
break;
case 1:
temp = -s - c;
break;
case 2:
temp = -s + c;
break;
case 3:
temp = s + c;
break;
}
b = invsqrtpi * temp / sqrtq (x);
}
else
{
a = y0q (x);
b = y1q (x);
/* quit if b is -inf */
u.value = b;
se = u.words32.w0 & 0xffff0000;
for (i = 1; i < n && se != 0xffff0000; i++)
{
temp = b;
b = ((__float128) (i + i) / x) * b - a;
u.value = b;
se = u.words32.w0 & 0xffff0000;
a = temp;
}
}
/* If B is +-Inf, set up errno accordingly. */
if (! finiteq (b))
errno = ERANGE;
if (sign > 0)
return b;
else
return -b;
/* (x >> n**2)
* Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
* Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
* Let s=sin(x), c=cos(x),
* xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
*
* n sin(xn)*sqt2 cos(xn)*sqt2
* ----------------------------------
* 0 s-c c+s
* 1 -s-c -c+s
* 2 -s+c -c-s
* 3 s+c c-s
*/
__float128 s;
__float128 c;
sincosq (x, &s, &c);
switch (n & 3)
{
case 0:
temp = s - c;
break;
case 1:
temp = -s - c;
break;
case 2:
temp = -s + c;
break;
case 3:
temp = s + c;
break;
}
b = invsqrtpi * temp / sqrtq (x);
}
else
{
a = y0q (x);
b = y1q (x);
/* quit if b is -inf */
u.value = b;
se = u.words32.w0 & 0xffff0000;
for (i = 1; i < n && se != 0xffff0000; i++)
{
temp = b;
b = ((__float128) (i + i) / x) * b - a;
u.value = b;
se = u.words32.w0 & 0xffff0000;
a = temp;
}
}
/* If B is +-Inf, set up errno accordingly. */
if (! finiteq (b))
errno = ERANGE;
if (sign > 0)
ret = b;
else
ret = -b;
}
out:
if (isinfq (ret))
ret = copysignq (FLT128_MAX, ret) * FLT128_MAX;
return ret;
}

25
libquadmath/math/ldexpq.c
View File

@ -1,8 +1,4 @@
/* ldexpq.c -- __float128 version of s_ldexp.c.
* Conversion to long double by Ulrich Drepper,
* Cygnus Support, drepper@cygnus.com.
*/
/* @(#)s_ldexp.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
@ -14,14 +10,23 @@
* ====================================================
*/
#include <errno.h>
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: s_ldexp.c,v 1.6 1995/05/10 20:47:40 jtc Exp $";
#endif
#include "quadmath-imp.h"
__float128
ldexpq (__float128 value, int exp)
{
if(!finiteq(value)||value==0.0Q) return value;
value = scalbnq(value,exp);
if(!finiteq(value)||value==0.0Q) errno = ERANGE;
return value;
if(!finiteq(value)||value==0) return value + value;
value = scalbnq(value,exp);
if(!finiteq(value)||value==0) errno = ERANGE;
return value;
}
/* Note, versioning issues are punted to ldbl-opt in this case. */

151
libquadmath/math/lgammaq.c
View File

@ -6,7 +6,7 @@
*
* SYNOPSIS:
*
* __float128 x, y, lgammal();
* long double x, y, lgammal();
* extern int sgngam;
*
* y = lgammal(x);
@ -18,7 +18,7 @@
* Returns the base e (2.718...) logarithm of the absolute
* value of the gamma function of the argument.
* The sign (+1 or -1) of the gamma function is returned in a
* global (extern) variable named signgam.
* global (extern) variable named sgngam.
*
* The positive domain is partitioned into numerous segments for approximation.
* For x > 10,
@ -65,20 +65,26 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
License along with this library; if not, see
<http://www.gnu.org/licenses/>. */
#include "quadmath-imp.h"
#ifdef HAVE_MATH_H_SIGNGAM
#include <math.h> /* For POSIX's extern int signgam. */
# include <math.h>
#endif
__float128
lgammaq (__float128 x)
{
#ifndef HAVE_MATH_H_SIGNGAM
int signgam;
#endif
return __quadmath_lgammaq_r (x, &signgam);
}
static const __float128 PIQ = 3.1415926535897932384626433832795028841972E0Q;
static const __float128 PIL = 3.1415926535897932384626433832795028841972E0Q;
static const __float128 MAXLGM = 1.0485738685148938358098967157129705071571E4928Q;
static const __float128 one = 1.0Q;
static const __float128 zero = 0.0Q;
static const __float128 huge = 1.0e4000Q;
static const __float128 one = 1;
static const __float128 huge = FLT128_MAX;
/* log gamma(x) = ( x - 0.5 ) * log(x) - x + LS2PI + 1/x P(1/x^2)
1/x <= 0.0741 (x >= 13.495...)
@ -131,7 +137,7 @@ static const __float128 RD13[NRD13 + 1] =
1.178186288833066430952276702931512870676E7Q,
1.519928623743264797939103740132278337476E5Q,
7.989298844938119228411117593338850892311E2Q
/* 1.0E0Q */
/* 1.0E0L */
};
@ -163,7 +169,7 @@ static const __float128 RD12[NRD12 + 1] =
9.236680081763754597872713592701048455890E6Q,
1.292246897881650919242713651166596478850E5Q,
7.366532445427159272584194816076600211171E2Q
/* 1.0E0Q */
/* 1.0E0L */
};
@ -195,7 +201,7 @@ static const __float128 RD11[NRD11 + 1] =
7.089478198662651683977290023829391596481E6Q,
1.083246385105903533237139380509590158658E5Q,
6.744420991491385145885727942219463243597E2Q
/* 1.0E0Q */
/* 1.0E0L */
};
@ -228,7 +234,7 @@ static const __float128 RD10[NRD10 + 1] =
-1.632090155573373286153427982504851867131E8Q,
-1.483575879240631280658077826889223634921E6Q,
-4.002806669713232271615885826373550502510E3Q
/* 1.0E0Q */
/* 1.0E0L */
};
@ -261,7 +267,7 @@ static const __float128 RD9[NRD9 + 1] =
-1.164573656694603024184768200787835094317E8Q,
-1.177343939483908678474886454113163527909E6Q,
-3.529391059783109732159524500029157638736E3Q
/* 1.0E0Q */
/* 1.0E0L */
};
@ -295,7 +301,7 @@ static const __float128 RD8[NRD8 + 1] =
5.790862854275238129848491555068073485086E6Q,
9.305213264307921522842678835618803553589E4Q,
6.216974105861848386918949336819572333622E2Q
/* 1.0E0Q */
/* 1.0E0L */
};
@ -329,7 +335,7 @@ static const __float128 RD7[NRD7 + 1] =
3.845638971184305248268608902030718674691E6Q,
7.081730675423444975703917836972720495507E4Q,
5.423122582741398226693137276201344096370E2Q
/* 1.0E0Q */
/* 1.0E0L */
};
@ -364,7 +370,7 @@ static const __float128 RD6[NRD6 + 1] =
-6.564058379709759600836745035871373240904E7Q,
-7.861511116647120540275354855221373571536E5Q,
-2.821943442729620524365661338459579270561E3Q
/* 1.0E0Q */
/* 1.0E0L */
};
@ -400,7 +406,7 @@ static const __float128 RD5[NRD5 + 1] =
2.698552646016599923609773122139463150403E6Q,
5.526516251532464176412113632726150253215E4Q,
4.772343321713697385780533022595450486932E2Q
/* 1.0E0Q */
/* 1.0E0L */
};
@ -437,7 +443,7 @@ static const __float128 RD4[NRD4 + 1] =
-3.416703082301143192939774401370222822430E7Q,
-4.981791914177103793218433195857635265295E5Q,
-2.192507743896742751483055798411231453733E3Q
/* 1.0E0Q */
/* 1.0E0L */
};
@ -475,7 +481,7 @@ static const __float128 RD3[NRD3 + 1] =
-1.505316381525727713026364396635522516989E7Q,
-2.856327162923716881454613540575964890347E5Q,
-1.622140448015769906847567212766206894547E3Q
/* 1.0E0Q */
/* 1.0E0L */
};
@ -509,7 +515,7 @@ static const __float128 RD2r5[NRD2r5 + 1] =
-4.101991193844953082400035444146067511725E6Q,
-1.174082735875715802334430481065526664020E5Q,
-9.932840389994157592102947657277692978511E2Q
/* 1.0E0Q */
/* 1.0E0L */
};
@ -579,7 +585,7 @@ static const __float128 RD1r75[NRD1r75 + 1] =
-1.201296501404876774861190604303728810836E6Q,
-5.007966406976106636109459072523610273928E4Q,
-6.155817990560743422008969155276229018209E2Q
/* 1.0E0Q */
/* 1.0E0L */
};
@ -616,7 +622,7 @@ static const __float128 RD1r5[NRD1r5 + 1] =
5.741463295366557346748361781768833633256E4Q,
4.226404539738182992856094681115746692030E3Q,
1.316980975410327975566999780608618774469E2Q,
/* 1.0E0Q */
/* 1.0E0L */
};
@ -652,7 +658,7 @@ static const __float128 RD1r25[NRD1r25 + 1] =
3.822267399625696880571810137601310855419E4Q,
3.228463206479133236028576845538387620856E3Q,
1.152133170470059555646301189220117965514E2Q
/* 1.0E0Q */
/* 1.0E0L */
};
@ -758,60 +764,61 @@ deval (__float128 x, const __float128 *p, int n)
__float128
lgammaq (__float128 x)
__quadmath_lgammaq_r (__float128 x, int *signgamp)
{
__float128 p, q, w, z, nx;
int i, nn;
#ifndef HAVE_MATH_H_SIGNGAM
int signgam;
#endif
signgam = 1;
*signgamp = 1;
if (! finiteq (x))
return x * x;
if (x == 0.0Q)
if (x == 0)
{
if (signbitq (x))
signgam = -1;
*signgamp = -1;
}
if (x < 0.0Q)
if (x < 0)
{
if (x < -2 && x > -50)
return __quadmath_lgamma_negq (x, signgamp);
q = -x;
p = floorq (q);
if (p == q)
return (one / (p - p));
i = p;
if ((i & 1) == 0)
signgam = -1;
return (one / fabsq (p - p));
__float128 halfp = p * 0.5Q;
if (halfp == floorq (halfp))
*signgamp = -1;
else
signgam = 1;
*signgamp = 1;
if (q < 0x1p-120Q)
return -logq (q);
z = q - p;
if (z > 0.5Q)
{
p += 1.0Q;
p += 1;
z = p - q;
}
z = q * sinq (PIQ * z);
if (z == 0.0Q)
return (signgam * huge * huge);
w = lgammaq (q);
z = logq (PIQ / z) - w;
z = q * sinq (PIL * z);
w = __quadmath_lgammaq_r (q, &i);
z = logq (PIL / z) - w;
return (z);
}
if (x < 13.5Q)
{
p = 0.0Q;
p = 0;
nx = floorq (x + 0.5Q);
nn = nx;
switch (nn)
{
case 0:
/* log gamma (x + 1) = log(x) + log gamma(x) */
if (x <= 0.125)
if (x < 0x1p-120Q)
return -logq (x);
else if (x <= 0.125)
{
p = x * neval (x, RN1, NRN1) / deval (x, RD1, NRD1);
}
@ -824,7 +831,7 @@ lgammaq (__float128 x)
}
else if (x <= 0.625)
{
z = x + (1.0Q - x0a);
z = x + (1 - x0a);
z = z - x0b;
p = neval (z, RN1r5, NRN1r5) / deval (z, RD1r5, NRD1r5);
p = p * z * z;
@ -840,7 +847,7 @@ lgammaq (__float128 x)
}
else
{
z = x - 1.0Q;
z = x - 1;
p = z * neval (z, RN2, NRN2) / deval (z, RD2, NRD2);
}
p = p - logq (x);
@ -851,7 +858,7 @@ lgammaq (__float128 x)
{
if (x <= 0.625)
{
z = x + (1.0Q - x0a);
z = x + (1 - x0a);
z = z - x0b;
p = neval (z, RN1r5, NRN1r5) / deval (z, RD1r5, NRD1r5);
p = p * z * z;
@ -868,21 +875,21 @@ lgammaq (__float128 x)
}
else
{
z = x - 1.0Q;
z = x - 1;
p = z * neval (z, RN2, NRN2) / deval (z, RD2, NRD2);
}
p = p - logq (x);
}
else if (x < 1.0Q)
else if (x < 1)
{
z = x - 1.0Q;
z = x - 1;
p = z * neval (z, RNr9, NRNr9) / deval (z, RDr9, NRDr9);
}
else if (x == 1.0Q)
p = 0.0Q;
else if (x == 1)
p = 0;
else if (x <= 1.125Q)
{
z = x - 1.0Q;
z = x - 1;
p = z * neval (z, RN1, NRN1) / deval (z, RD1, NRD1);
}
else if (x <= 1.375)
@ -921,11 +928,11 @@ lgammaq (__float128 x)
p += lgam1r75b;
p += lgam1r75a;
}
else if (x == 2.0Q)
p = 0.0Q;
else if (x == 2)
p = 0;
else if (x < 2.375Q)
{
z = x - 2.0Q;
z = x - 2;
p = z * neval (z, RN2, NRN2) / deval (z, RD2, NRD2);
}
else
@ -947,7 +954,7 @@ lgammaq (__float128 x)
}
else
{
z = x - 3.0Q;
z = x - 3;
p = z * neval (z, RN3, NRN3) / deval (z, RD3, NRD3);
p += lgam3b;
p += lgam3a;
@ -955,70 +962,70 @@ lgammaq (__float128 x)
break;
case 4:
z = x - 4.0Q;
z = x - 4;
p = z * neval (z, RN4, NRN4) / deval (z, RD4, NRD4);
p += lgam4b;
p += lgam4a;
break;
case 5:
z = x - 5.0Q;
z = x - 5;
p = z * neval (z, RN5, NRN5) / deval (z, RD5, NRD5);
p += lgam5b;
p += lgam5a;
break;
case 6:
z = x - 6.0Q;
z = x - 6;
p = z * neval (z, RN6, NRN6) / deval (z, RD6, NRD6);
p += lgam6b;
p += lgam6a;
break;
case 7:
z = x - 7.0Q;
z = x - 7;
p = z * neval (z, RN7, NRN7) / deval (z, RD7, NRD7);
p += lgam7b;
p += lgam7a;
break;
case 8:
z = x - 8.0Q;
z = x - 8;
p = z * neval (z, RN8, NRN8) / deval (z, RD8, NRD8);
p += lgam8b;
p += lgam8a;
break;
case 9:
z = x - 9.0Q;
z = x - 9;
p = z * neval (z, RN9, NRN9) / deval (z, RD9, NRD9);
p += lgam9b;
p += lgam9a;
break;
case 10:
z = x - 10.0Q;
z = x - 10;
p = z * neval (z, RN10, NRN10) / deval (z, RD10, NRD10);
p += lgam10b;
p += lgam10a;
break;
case 11:
z = x - 11.0Q;
z = x - 11;
p = z * neval (z, RN11, NRN11) / deval (z, RD11, NRD11);
p += lgam11b;
p += lgam11a;
break;
case 12:
z = x - 12.0Q;
z = x - 12;
p = z * neval (z, RN12, NRN12) / deval (z, RD12, NRD12);
p += lgam12b;
p += lgam12a;
break;
case 13:
z = x - 13.0Q;
z = x - 13;
p = z * neval (z, RN13, NRN13) / deval (z, RD13, NRD13);
p += lgam13b;
p += lgam13a;
@ -1028,14 +1035,16 @@ lgammaq (__float128 x)
}
if (x > MAXLGM)
return (signgam * huge * huge);
return (*signgamp * huge * huge);
if (x > 0x1p120Q)
return x * (logq (x) - 1);
q = ls2pi - x;
q = (x - 0.5Q) * logq (x) + q;
if (x > 1.0e18Q)
return (q);
p = 1.0Q / (x * x);
p = 1 / (x * x);
q += neval (p, RASY, NRASY) / x;
return (q);
}

549
libquadmath/math/lgammaq_neg.c Normal file
View File

@ -0,0 +1,549 @@
/* lgammal expanding around zeros.
Copyright (C) 2015-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#include "quadmath-imp.h"
static const __float128 lgamma_zeros[][2] =
{
{ -0x2.74ff92c01f0d82abec9f315f1a08p+0Q, 0xe.d3ccb7fb2658634a2b9f6b2ba81p-116Q },
{ -0x2.bf6821437b20197995a4b4641eaep+0Q, -0xb.f4b00b4829f961e428533e6ad048p-116Q },
{ -0x3.24c1b793cb35efb8be699ad3d9bap+0Q, -0x6.5454cb7fac60e3f16d9d7840c2ep-116Q },
{ -0x3.f48e2a8f85fca170d4561291236cp+0Q, -0xc.320a4887d1cb4c711828a75d5758p-116Q },
{ -0x4.0a139e16656030c39f0b0de18114p+0Q, 0x1.53e84029416e1242006b2b3d1cfp-112Q },
{ -0x4.fdd5de9bbabf3510d0aa40769884p+0Q, -0x1.01d7d78125286f78d1e501f14966p-112Q },
{ -0x5.021a95fc2db6432a4c56e595394cp+0Q, -0x1.ecc6af0430d4fe5746fa7233356fp-112Q },
{ -0x5.ffa4bd647d0357dd4ed62cbd31ecp+0Q, -0x1.f8e3f8e5deba2d67dbd70dd96ce1p-112Q },
{ -0x6.005ac9625f233b607c2d96d16384p+0Q, -0x1.cb86ac569340cf1e5f24df7aab7bp-112Q },
{ -0x6.fff2fddae1bbff3d626b65c23fd4p+0Q, 0x1.e0bfcff5c457ebcf4d3ad9674167p-112Q },
{ -0x7.000cff7b7f87adf4482dcdb98784p+0Q, 0x1.54d99e35a74d6407b80292df199fp-112Q },
{ -0x7.fffe5fe05673c3ca9e82b522b0ccp+0Q, 0x1.62d177c832e0eb42c2faffd1b145p-112Q },
{ -0x8.0001a01459fc9f60cb3cec1cec88p+0Q, 0x2.8998835ac7277f7bcef67c47f188p-112Q },
{ -0x8.ffffd1c425e80ffc864e95749258p+0Q, -0x1.e7e20210e7f81cf781b44e9d2b02p-112Q },
{ -0x9.00002e3bb47d86d6d843fedc352p+0Q, 0x2.14852f613a16291751d2ab751f7ep-112Q },
{ -0x9.fffffb606bdfdcd062ae77a50548p+0Q, 0x3.962d1490cc2e8f031c7007eaa1ap-116Q },
{ -0xa.0000049f93bb9927b45d95e1544p+0Q, -0x1.e03086db9146a9287bd4f2172d5ap-112Q },
{ -0xa.ffffff9466e9f1b36dacd2adbd18p+0Q, -0xd.05a4e458062f3f95345a4d9c9b6p-116Q },
{ -0xb.0000006b9915315d965a6ffea41p+0Q, 0x1.b415c6fff233e7b7fdc3a094246fp-112Q },
{ -0xb.fffffff7089387387de41acc3d4p+0Q, 0x3.687427c6373bd74a10306e10a28ep-112Q },
{ -0xc.00000008f76c7731567c0f0250fp+0Q, -0x3.87920df5675833859190eb128ef6p-112Q },
{ -0xc.ffffffff4f6dcf617f97a5ffc758p+0Q, 0x2.ab72d76f32eaee2d1a42ed515d3ap-116Q },
{ -0xd.00000000b092309c06683dd1b9p+0Q, -0x3.e3700857a15c19ac5a611de9688ap-112Q },
{ -0xd.fffffffff36345ab9e184a3e09dp+0Q, -0x1.176dc48e47f62d917973dd44e553p-112Q },
{ -0xe.000000000c9cba545e94e75ec57p+0Q, -0x1.8f753e2501e757a17cf2ecbeeb89p-112Q },
{ -0xe.ffffffffff28c060c6604ef3037p+0Q, -0x1.f89d37357c9e3dc17c6c6e63becap-112Q },
{ -0xf.0000000000d73f9f399bd0e420f8p+0Q, -0x5.e9ee31b0b890744fc0e3fbc01048p-116Q },
{ -0xf.fffffffffff28c060c6621f512e8p+0Q, 0xd.1b2eec9d960bd9adc5be5f5fa5p-116Q },
{ -0x1.000000000000d73f9f399da1424cp+4Q, 0x6.c46e0e88305d2800f0e414c506a8p-116Q },
{ -0x1.0ffffffffffff3569c47e7a93e1cp+4Q, -0x4.6a08a2e008a998ebabb8087efa2cp-112Q },
{ -0x1.1000000000000ca963b818568887p+4Q, -0x6.ca5a3a64ec15db0a95caf2c9ffb4p-112Q },
{ -0x1.1fffffffffffff4bec3ce234132dp+4Q, -0x8.b2b726187c841cb92cd5221e444p-116Q },
{ -0x1.20000000000000b413c31dcbeca5p+4Q, 0x3.c4d005344b6cd0e7231120294abcp-112Q },
{ -0x1.2ffffffffffffff685b25cbf5f54p+4Q, -0x5.ced932e38485f7dd296b8fa41448p-112Q },
{ -0x1.30000000000000097a4da340a0acp+4Q, 0x7.e484e0e0ffe38d406ebebe112f88p-112Q },
{ -0x1.3fffffffffffffff86af516ff7f7p+4Q, -0x6.bd67e720d57854502b7db75e1718p-112Q },
{ -0x1.40000000000000007950ae900809p+4Q, 0x6.bec33375cac025d9c073168c5d9p-112Q },
{ -0x1.4ffffffffffffffffa391c4248c3p+4Q, 0x5.c63022b62b5484ba346524db607p-112Q },
{ -0x1.500000000000000005c6e3bdb73dp+4Q, -0x5.c62f55ed5322b2685c5e9a51e6a8p-112Q },
{ -0x1.5fffffffffffffffffbcc71a492p+4Q, -0x1.eb5aeb96c74d7ad25e060528fb5p-112Q },
{ -0x1.6000000000000000004338e5b6ep+4Q, 0x1.eb5aec04b2f2eb663e4e3d8a018cp-112Q },
{ -0x1.6ffffffffffffffffffd13c97d9dp+4Q, -0x3.8fcc4d08d6fe5aa56ab04307ce7ep-112Q },
{ -0x1.70000000000000000002ec368263p+4Q, 0x3.8fcc4d090cee2f5d0b69a99c353cp-112Q },
{ -0x1.7fffffffffffffffffffe0d30fe7p+4Q, 0x7.2f577cca4b4c8cb1dc14001ac5ecp-112Q },
{ -0x1.800000000000000000001f2cf019p+4Q, -0x7.2f577cca4b3442e35f0040b3b9e8p-112Q },
{ -0x1.8ffffffffffffffffffffec0c332p+4Q, -0x2.e9a0572b1bb5b95f346a92d67a6p-112Q },
{ -0x1.90000000000000000000013f3ccep+4Q, 0x2.e9a0572b1bb5c371ddb3561705ap-112Q },
{ -0x1.9ffffffffffffffffffffff3b8bdp+4Q, -0x1.cad8d32e386fd783e97296d63dcbp-116Q },
{ -0x1.a0000000000000000000000c4743p+4Q, 0x1.cad8d32e386fd7c1ab8c1fe34c0ep-116Q },
{ -0x1.afffffffffffffffffffffff8b95p+4Q, -0x3.8f48cc5737d5979c39db806c5406p-112Q },
{ -0x1.b00000000000000000000000746bp+4Q, 0x3.8f48cc5737d5979c3b3a6bda06f6p-112Q },
{ -0x1.bffffffffffffffffffffffffbd8p+4Q, 0x6.2898d42174dcf171470d8c8c6028p-112Q },
{ -0x1.c000000000000000000000000428p+4Q, -0x6.2898d42174dcf171470d18ba412cp-112Q },
{ -0x1.cfffffffffffffffffffffffffdbp+4Q, -0x4.c0ce9794ea50a839e311320bde94p-112Q },
{ -0x1.d000000000000000000000000025p+4Q, 0x4.c0ce9794ea50a839e311322f7cf8p-112Q },
{ -0x1.dfffffffffffffffffffffffffffp+4Q, 0x3.932c5047d60e60caded4c298a174p-112Q },
{ -0x1.e000000000000000000000000001p+4Q, -0x3.932c5047d60e60caded4c298973ap-112Q },
{ -0x1.fp+4Q, 0xa.1a6973c1fade2170f7237d35fe3p-116Q },
{ -0x1.fp+4Q, -0xa.1a6973c1fade2170f7237d35fe08p-116Q },
{ -0x2p+4Q, 0x5.0d34b9e0fd6f10b87b91be9aff1p-120Q },
{ -0x2p+4Q, -0x5.0d34b9e0fd6f10b87b91be9aff0cp-120Q },
{ -0x2.1p+4Q, 0x2.73024a9ba1aa36a7059bff52e844p-124Q },
{ -0x2.1p+4Q, -0x2.73024a9ba1aa36a7059bff52e844p-124Q },
{ -0x2.2p+4Q, 0x1.2710231c0fd7a13f8a2b4af9d6b7p-128Q },
{ -0x2.2p+4Q, -0x1.2710231c0fd7a13f8a2b4af9d6b7p-128Q },
{ -0x2.3p+4Q, 0x8.6e2ce38b6c8f9419e3fad3f0312p-136Q },
{ -0x2.3p+4Q, -0x8.6e2ce38b6c8f9419e3fad3f0312p-136Q },
{ -0x2.4p+4Q, 0x3.bf30652185952560d71a254e4eb8p-140Q },
{ -0x2.4p+4Q, -0x3.bf30652185952560d71a254e4eb8p-140Q },
{ -0x2.5p+4Q, 0x1.9ec8d1c94e85af4c78b15c3d89d3p-144Q },
{ -0x2.5p+4Q, -0x1.9ec8d1c94e85af4c78b15c3d89d3p-144Q },
{ -0x2.6p+4Q, 0xa.ea565ce061d57489e9b85276274p-152Q },
{ -0x2.6p+4Q, -0xa.ea565ce061d57489e9b85276274p-152Q },
{ -0x2.7p+4Q, 0x4.7a6512692eb37804111dabad30ecp-156Q },
{ -0x2.7p+4Q, -0x4.7a6512692eb37804111dabad30ecp-156Q },
{ -0x2.8p+4Q, 0x1.ca8ed42a12ae3001a07244abad2bp-160Q },
{ -0x2.8p+4Q, -0x1.ca8ed42a12ae3001a07244abad2bp-160Q },
{ -0x2.9p+4Q, 0xb.2f30e1ce812063f12e7e8d8d96e8p-168Q },
{ -0x2.9p+4Q, -0xb.2f30e1ce812063f12e7e8d8d96e8p-168Q },
{ -0x2.ap+4Q, 0x4.42bd49d4c37a0db136489772e428p-172Q },
{ -0x2.ap+4Q, -0x4.42bd49d4c37a0db136489772e428p-172Q },
{ -0x2.bp+4Q, 0x1.95db45257e5122dcbae56def372p-176Q },
{ -0x2.bp+4Q, -0x1.95db45257e5122dcbae56def372p-176Q },
{ -0x2.cp+4Q, 0x9.3958d81ff63527ecf993f3fb6f48p-184Q },
{ -0x2.cp+4Q, -0x9.3958d81ff63527ecf993f3fb6f48p-184Q },
{ -0x2.dp+4Q, 0x3.47970e4440c8f1c058bd238c9958p-188Q },
{ -0x2.dp+4Q, -0x3.47970e4440c8f1c058bd238c9958p-188Q },
{ -0x2.ep+4Q, 0x1.240804f65951062ca46e4f25c608p-192Q },
{ -0x2.ep+4Q, -0x1.240804f65951062ca46e4f25c608p-192Q },
{ -0x2.fp+4Q, 0x6.36a382849fae6de2d15362d8a394p-200Q },
{ -0x2.fp+4Q, -0x6.36a382849fae6de2d15362d8a394p-200Q },
{ -0x3p+4Q, 0x2.123680d6dfe4cf4b9b1bcb9d8bdcp-204Q },
{ -0x3p+4Q, -0x2.123680d6dfe4cf4b9b1bcb9d8bdcp-204Q },
{ -0x3.1p+4Q, 0xa.d21786ff5842eca51fea0870919p-212Q },
{ -0x3.1p+4Q, -0xa.d21786ff5842eca51fea0870919p-212Q },
{ -0x3.2p+4Q, 0x3.766dedc259af040be140a68a6c04p-216Q },
};
static const __float128 e_hi = 0x2.b7e151628aed2a6abf7158809cf4p+0Q;
static const __float128 e_lo = 0xf.3c762e7160f38b4da56a784d9048p-116Q;
/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) in Stirling's
approximation to lgamma function. */
static const __float128 lgamma_coeff[] =
{
0x1.5555555555555555555555555555p-4Q,
-0xb.60b60b60b60b60b60b60b60b60b8p-12Q,
0x3.4034034034034034034034034034p-12Q,
-0x2.7027027027027027027027027028p-12Q,
0x3.72a3c5631fe46ae1d4e700dca8f2p-12Q,
-0x7.daac36664f1f207daac36664f1f4p-12Q,
0x1.a41a41a41a41a41a41a41a41a41ap-8Q,
-0x7.90a1b2c3d4e5f708192a3b4c5d7p-8Q,
0x2.dfd2c703c0cfff430edfd2c703cp-4Q,
-0x1.6476701181f39edbdb9ce625987dp+0Q,
0xd.672219167002d3a7a9c886459cp+0Q,
-0x9.cd9292e6660d55b3f712eb9e07c8p+4Q,
0x8.911a740da740da740da740da741p+8Q,
-0x8.d0cc570e255bf59ff6eec24b49p+12Q,
0xa.8d1044d3708d1c219ee4fdc446ap+16Q,
-0xe.8844d8a169abbc406169abbc406p+20Q,
0x1.6d29a0f6433b79890cede62433b8p+28Q,
-0x2.88a233b3c8cddaba9809357125d8p+32Q,
0x5.0dde6f27500939a85c40939a85c4p+36Q,
-0xb.4005bde03d4642a243581714af68p+40Q,
0x1.bc8cd6f8f1f755c78753cdb5d5c9p+48Q,
-0x4.bbebb143bb94de5a0284fa7ec424p+52Q,
0xe.2e1337f5af0bed90b6b0a352d4fp+56Q,
-0x2.e78250162b62405ad3e4bfe61b38p+64Q,
0xa.5f7eef9e71ac7c80326ab4cc8bfp+68Q,
-0x2.83be0395e550213369924971b21ap+76Q,
0xa.8ebfe48da17dd999790760b0cep+80Q,
};
#define NCOEFF (sizeof (lgamma_coeff) / sizeof (lgamma_coeff[0]))
/* Polynomial approximations to (|gamma(x)|-1)(x-n)/(x-x0), where n is
the integer end-point of the half-integer interval containing x and
x0 is the zero of lgamma in that half-integer interval. Each
polynomial is expressed in terms of x-xm, where xm is the midpoint
of the interval for which the polynomial applies. */
static const __float128 poly_coeff[] =
{
/* Interval [-2.125, -2] (polynomial degree 23). */
-0x1.0b71c5c54d42eb6c17f30b7aa8f5p+0Q,
-0xc.73a1dc05f34951602554c6d7506p-4Q,
-0x1.ec841408528b51473e6c425ee5ffp-4Q,
-0xe.37c9da26fc3c9a3c1844c8c7f1cp-4Q,
-0x1.03cd87c519305703b021fa33f827p-4Q,
-0xe.ae9ada65e09aa7f1c75216128f58p-4Q,
0x9.b11855a4864b5731cf85736015a8p-8Q,
-0xe.f28c133e697a95c28607c9701dep-4Q,
0x2.6ec14a1c586a72a7cc33ee569d6ap-4Q,
-0xf.57cab973e14464a262fc24723c38p-4Q,
0x4.5b0fc25f16e52997b2886bbae808p-4Q,
-0xf.f50e59f1a9b56e76e988dac9ccf8p-4Q,
0x6.5f5eae15e9a93369e1d85146c6fcp-4Q,
-0x1.0d2422daac459e33e0994325ed23p+0Q,
0x8.82000a0e7401fb1117a0e6606928p-4Q,
-0x1.1f492f178a3f1b19f58a2ca68e55p+0Q,
0xa.cb545f949899a04c160b19389abp-4Q,
-0x1.36165a1b155ba3db3d1b77caf498p+0Q,
0xd.44c5d5576f74302e5cf79e183eep-4Q,
-0x1.51f22e0cdd33d3d481e326c02f3ep+0Q,
0xf.f73a349c08244ac389c007779bfp-4Q,
-0x1.73317bf626156ba716747c4ca866p+0Q,
0x1.379c3c97b9bc71e1c1c4802dd657p+0Q,
-0x1.a72a351c54f902d483052000f5dfp+0Q,
/* Interval [-2.25, -2.125] (polynomial degree 24). */
-0xf.2930890d7d675a80c36afb0fd5e8p-4Q,
-0xc.a5cfde054eab5c6770daeca577f8p-4Q,
0x3.9c9e0fdebb07cdf89c61d41c9238p-4Q,
-0x1.02a5ad35605fcf4af65a6dbacb84p+0Q,
0x9.6e9b1185bb48be9de1918e00a2e8p-4Q,
-0x1.4d8332f3cfbfa116fd611e9ce90dp+0Q,
0x1.1c0c8cb4d9f4b1d490e1a41fae4dp+0Q,
-0x1.c9a6f5ae9130cd0299e293a42714p+0Q,
0x1.d7e9307fd58a2ea997f29573a112p+0Q,
-0x2.921cb3473d96178ca2a11d2a8d46p+0Q,
0x2.e8d59113b6f3409ff8db226e9988p+0Q,
-0x3.cbab931625a1ae2b26756817f264p+0Q,
0x4.7d9f0f05d5296d18663ca003912p+0Q,
-0x5.ade9cba12a14ea485667b7135bbp+0Q,
0x6.dc983a5da74fb48e767b7fec0a3p+0Q,
-0x8.8d9ed454ae31d9e138dd8ee0d1a8p+0Q,
0xa.6fa099d4e7c202e0c0fd6ed8492p+0Q,
-0xc.ebc552a8090a0f0115e92d4ebbc8p+0Q,
0xf.d695e4772c0d829b53fba9ca5568p+0Q,
-0x1.38c32ae38e5e9eb79b2a4c5570a9p+4Q,
0x1.8035145646cfab49306d0999a51bp+4Q,
-0x1.d930adbb03dd342a4c2a8c4e1af6p+4Q,
0x2.45c2edb1b4943ddb3686cd9c6524p+4Q,
-0x2.e818ebbfafe2f916fa21abf7756p+4Q,
0x3.9804ce51d0fb9a430a711fd7307p+4Q,
/* Interval [-2.375, -2.25] (polynomial degree 25). */
-0xd.7d28d505d6181218a25f31d5e45p-4Q,
-0xe.69649a3040985140cdf946829fap-4Q,
0xb.0d74a2827d053a8d44595012484p-4Q,
-0x1.924b0922853617cac181afbc08ddp+0Q,
0x1.d49b12bccf0a568582e2d3c410f3p+0Q,
-0x3.0898bb7d8c4093e636279c791244p+0Q,
0x4.207a6cac711cb53868e8a5057eep+0Q,
-0x6.39ee63ea4fb1dcab0c9144bf3ddcp+0Q,
0x8.e2e2556a797b649bf3f53bd26718p+0Q,
-0xd.0e83ac82552ef12af508589e7a8p+0Q,
0x1.2e4525e0ce6670563c6484a82b05p+4Q,
-0x1.b8e350d6a8f2b222fa390a57c23dp+4Q,
0x2.805cd69b919087d8a80295892c2cp+4Q,
-0x3.a42585424a1b7e64c71743ab014p+4Q,
0x5.4b4f409f98de49f7bfb03c05f984p+4Q,
-0x7.b3c5827fbe934bc820d6832fb9fcp+4Q,
0xb.33b7b90cc96c425526e0d0866e7p+4Q,
-0x1.04b77047ac4f59ee3775ca10df0dp+8Q,
0x1.7b366f5e94a34f41386eac086313p+8Q,
-0x2.2797338429385c9849ca6355bfc2p+8Q,
0x3.225273cf92a27c9aac1b35511256p+8Q,
-0x4.8f078aa48afe6cb3a4e89690f898p+8Q,
0x6.9f311d7b6654fc1d0b5195141d04p+8Q,
-0x9.a0c297b6b4621619ca9bacc48ed8p+8Q,
0xe.ce1f06b6f90d92138232a76e4cap+8Q,
-0x1.5b0e6806fa064daf011613e43b17p+12Q,
/* Interval [-2.5, -2.375] (polynomial degree 27). */
-0xb.74ea1bcfff94b2c01afba9daa7d8p-4Q,
-0x1.2a82bd590c37538cab143308de4dp+0Q,
0x1.88020f828b966fec66b8649fd6fcp+0Q,
-0x3.32279f040eb694970e9db24863dcp+0Q,
0x5.57ac82517767e68a721005853864p+0Q,
-0x9.c2aedcfe22833de43834a0a6cc4p+0Q,
0x1.12c132f1f5577f99e1a0ed3538e1p+4Q,
-0x1.ea94e26628a3de3597f7bb55a948p+4Q,
0x3.66b4ac4fa582f58b59f96b2f7c7p+4Q,
-0x6.0cf746a9cf4cba8c39afcc73fc84p+4Q,
0xa.c102ef2c20d75a342197df7fedf8p+4Q,
-0x1.31ebff06e8f14626782df58db3b6p+8Q,
0x2.1fd6f0c0e710994e059b9dbdb1fep+8Q,
-0x3.c6d76040407f447f8b5074f07706p+8Q,
0x6.b6d18e0d8feb4c2ef5af6a40ed18p+8Q,
-0xb.efaf542c529f91e34217f24ae6a8p+8Q,
0x1.53852d873210e7070f5d9eb2296p+12Q,
-0x2.5b977c0ddc6d540717173ac29fc8p+12Q,
0x4.310d452ae05100eff1e02343a724p+12Q,
-0x7.73a5d8f20c4f986a7dd1912b2968p+12Q,
0xd.3f5ea2484f3fca15eab1f4d1a218p+12Q,
-0x1.78d18aac156d1d93a2ffe7e08d3fp+16Q,
0x2.9df49ca75e5b567f5ea3e47106cp+16Q,
-0x4.a7149af8961a08aa7c3233b5bb94p+16Q,
0x8.3db10ffa742c707c25197d989798p+16Q,
-0xe.a26d6dd023cadd02041a049ec368p+16Q,
0x1.c825d90514e7c57c7fa5316f947cp+20Q,
-0x3.34bb81e5a0952df8ca1abdc6684cp+20Q,
/* Interval [-2.625, -2.5] (polynomial degree 28). */
-0x3.d10108c27ebafad533c20eac32bp-4Q,
0x1.cd557caff7d2b2085f41dbec5106p+0Q,
0x3.819b4856d399520dad9776ea2cacp+0Q,
0x6.8505cbad03dc34c5e42e8b12eb78p+0Q,
0xb.c1b2e653a9e38f82b399c94e7f08p+0Q,
0x1.50a53a38f148138105124df65419p+4Q,
0x2.57ae00cbe5232cbeeed34d89727ap+4Q,
0x4.2b156301b8604db85a601544bfp+4Q,
0x7.6989ed23ca3ca7579b3462592b5cp+4Q,
0xd.2dd2976557939517f831f5552cc8p+4Q,
0x1.76e1c3430eb860969bce40cd494p+8Q,
0x2.9a77bf5488742466db3a2c7c1ec6p+8Q,
0x4.a0d62ed7266e8eb36f725a8ebcep+8Q,
0x8.3a6184dd3021067df2f8b91e99c8p+8Q,
0xe.a0ade1538245bf55d39d7e436b1p+8Q,
0x1.a01359fae8617b5826dd74428e9p+12Q,
0x2.e3b0a32caae77251169acaca1ad4p+12Q,
0x5.2301257c81589f62b38fb5993ee8p+12Q,
0x9.21c9275db253d4e719b73b18cb9p+12Q,
0x1.03c104bc96141cda3f3fa4b112bcp+16Q,
0x1.cdc8ed65119196a08b0c78f1445p+16Q,
0x3.34f31d2eaacf34382cdb0073572ap+16Q,
0x5.b37628cadf12bf0000907d0ef294p+16Q,
0xa.22d8b332c0b1e6a616f425dfe5ap+16Q,
0x1.205b01444804c3ff922cd78b4c42p+20Q,
0x1.fe8f0cea9d1e0ff25be2470b4318p+20Q,
0x3.8872aebeb368399aee02b39340aep+20Q,
0x6.ebd560d351e84e26a4381f5b293cp+20Q,
0xc.c3644d094b0dae2fbcbf682cd428p+20Q,
/* Interval [-2.75, -2.625] (polynomial degree 26). */
-0x6.b5d252a56e8a75458a27ed1c2dd4p-4Q,
0x1.28d60383da3ac721aed3c5794da9p+0Q,
0x1.db6513ada8a66ea77d87d9a8827bp+0Q,
0x2.e217118f9d348a27f7506a707e6ep+0Q,
0x4.450112c5cbf725a0fb9802396c9p+0Q,
0x6.4af99151eae7810a75df2a0303c4p+0Q,
0x9.2db598b4a97a7f69aeef32aec758p+0Q,
0xd.62bef9c22471f5ee47ea1b9c0b5p+0Q,
0x1.379f294e412bd62328326d4222f9p+4Q,
0x1.c5827349d8865f1e8825c37c31c6p+4Q,
0x2.93a7e7a75b7568cc8cbe8c016c12p+4Q,
0x3.bf9bb882afe57edb383d41879d3ap+4Q,
0x5.73c737828cee095c43a5566731c8p+4Q,
0x7.ee4653493a7f81e0442062b3823cp+4Q,
0xb.891c6b83fc8b55bd973b5d962d6p+4Q,
0x1.0c775d7de3bf9b246c0208e0207ep+8Q,
0x1.867ee43ec4bd4f4fd56abc05110ap+8Q,
0x2.37fe9ba6695821e9822d8c8af0a6p+8Q,
0x3.3a2c667e37c942f182cd3223a936p+8Q,
0x4.b1b500eb59f3f782c7ccec88754p+8Q,
0x6.d3efd3b65b3d0d8488d30b79fa4cp+8Q,
0x9.ee8224e65bed5ced8b75eaec609p+8Q,
0xe.72416e510cca77d53fc615c1f3dp+8Q,
0x1.4fb538b0a2dfe567a8904b7e0445p+12Q,
0x1.e7f56a9266cf525a5b8cf4cb76cep+12Q,
0x2.f0365c983f68c597ee49d099cce8p+12Q,
0x4.53aa229e1b9f5b5e59625265951p+12Q,
/* Interval [-2.875, -2.75] (polynomial degree 24). */
-0x8.a41b1e4f36ff88dc820815607d68p-4Q,
0xc.da87d3b69dc0f2f9c6f368b8ca1p-4Q,
0x1.1474ad5c36158a7bea04fd2f98c6p+0Q,
0x1.761ecb90c555df6555b7dba955b6p+0Q,
0x1.d279bff9ae291caf6c4b4bcb3202p+0Q,
0x2.4e5d00559a6e2b9b5d7fe1f6689cp+0Q,
0x2.d57545a75cee8743ae2b17bc8d24p+0Q,
0x3.8514eee3aac88b89bec2307021bap+0Q,
0x4.5235e3b6e1891ffeb87fed9f8a24p+0Q,
0x5.562acdb10eef3c9a773b3e27a864p+0Q,
0x6.8ec8965c76efe03c26bff60b1194p+0Q,
0x8.15251aca144877af32658399f9b8p+0Q,
0x9.f08d56aba174d844138af782c0f8p+0Q,
0xc.3dbbeda2679e8a1346ccc3f6da88p+0Q,
0xf.0f5bfd5eacc26db308ffa0556fa8p+0Q,
0x1.28a6ccd84476fbc713d6bab49ac9p+4Q,
0x1.6d0a3ae2a3b1c8ff400641a3a21fp+4Q,
0x1.c15701b28637f87acfb6a91d33b5p+4Q,
0x2.28fbe0eccf472089b017651ca55ep+4Q,
0x2.a8a453004f6e8ffaacd1603bc3dp+4Q,
0x3.45ae4d9e1e7cd1a5dba0e4ec7f6cp+4Q,
0x4.065fbfacb7fad3e473cb577a61e8p+4Q,
0x4.f3d1473020927acac1944734a39p+4Q,
0x6.54bb091245815a36fb74e314dd18p+4Q,
0x7.d7f445129f7fb6c055e582d3f6ep+4Q,
/* Interval [-3, -2.875] (polynomial degree 23). */
-0xa.046d667e468f3e44dcae1afcc648p-4Q,
0x9.70b88dcc006c214d8d996fdf5ccp-4Q,
0xa.a8a39421c86d3ff24931a0929fp-4Q,
0xd.2f4d1363f324da2b357c8b6ec94p-4Q,
0xd.ca9aa1a3a5c00de11bf60499a97p-4Q,
0xf.cf09c31eeb52a45dfa7ebe3778dp-4Q,
0x1.04b133a39ed8a09691205660468bp+0Q,
0x1.22b547a06edda944fcb12fd9b5ecp+0Q,
0x1.2c57fce7db86a91df09602d344b3p+0Q,
0x1.4aade4894708f84795212fe257eep+0Q,
0x1.579c8b7b67ec4afed5b28c8bf787p+0Q,
0x1.776820e7fc80ae5284239733078ap+0Q,
0x1.883ab28c7301fde4ca6b8ec26ec8p+0Q,
0x1.aa2ef6e1ae52eb42c9ee83b206e3p+0Q,
0x1.bf4ad50f0a9a9311300cf0c51ee7p+0Q,
0x1.e40206e0e96b1da463814dde0d09p+0Q,
0x1.fdcbcffef3a21b29719c2bd9feb1p+0Q,
0x2.25e2e8948939c4d42cf108fae4bep+0Q,
0x2.44ce14d2b59c1c0e6bf2cfa81018p+0Q,
0x2.70ee80bbd0387162be4861c43622p+0Q,
0x2.954b64d2c2ebf3489b949c74476p+0Q,
0x2.c616e133a811c1c9446105208656p+0Q,
0x3.05a69dfe1a9ba1079f90fcf26bd4p+0Q,
0x3.410d2ad16a0506de29736e6aafdap+0Q,
};
static const size_t poly_deg[] =
{
23,
24,
25,
27,
28,
26,
24,
23,
};
static const size_t poly_end[] =
{
23,
48,
74,
102,
131,
158,
183,
207,
};
/* Compute sin (pi * X) for -0.25 <= X <= 0.5. */
static __float128
lg_sinpi (__float128 x)
{
if (x <= 0.25Q)
return sinq (M_PIq * x);
else
return cosq (M_PIq * (0.5Q - x));
}
/* Compute cos (pi * X) for -0.25 <= X <= 0.5. */
static __float128
lg_cospi (__float128 x)
{
if (x <= 0.25Q)
return cosq (M_PIq * x);
else
return sinq (M_PIq * (0.5Q - x));
}
/* Compute cot (pi * X) for -0.25 <= X <= 0.5. */
static __float128
lg_cotpi (__float128 x)
{
return lg_cospi (x) / lg_sinpi (x);
}
/* Compute lgamma of a negative argument -50 < X < -2, setting
*SIGNGAMP accordingly. */
__float128
__quadmath_lgamma_negq (__float128 x, int *signgamp)
{
/* Determine the half-integer region X lies in, handle exact
integers and determine the sign of the result. */
int i = floorq (-2 * x);
if ((i & 1) == 0 && i == -2 * x)
return 1.0Q / 0.0Q;
__float128 xn = ((i & 1) == 0 ? -i / 2 : (-i - 1) / 2);
i -= 4;
*signgamp = ((i & 2) == 0 ? -1 : 1);
SET_RESTORE_ROUNDF128 (FE_TONEAREST);
/* Expand around the zero X0 = X0_HI + X0_LO. */
__float128 x0_hi = lgamma_zeros[i][0], x0_lo = lgamma_zeros[i][1];
__float128 xdiff = x - x0_hi - x0_lo;
/* For arguments in the range -3 to -2, use polynomial
approximations to an adjusted version of the gamma function. */
if (i < 2)
{
int j = floorq (-8 * x) - 16;
__float128 xm = (-33 - 2 * j) * 0.0625Q;
__float128 x_adj = x - xm;
size_t deg = poly_deg[j];
size_t end = poly_end[j];
__float128 g = poly_coeff[end];
for (size_t j = 1; j <= deg; j++)
g = g * x_adj + poly_coeff[end - j];
return log1pq (g * xdiff / (x - xn));
}
/* The result we want is log (sinpi (X0) / sinpi (X))
+ log (gamma (1 - X0) / gamma (1 - X)). */
__float128 x_idiff = fabsq (xn - x), x0_idiff = fabsq (xn - x0_hi - x0_lo);
__float128 log_sinpi_ratio;
if (x0_idiff < x_idiff * 0.5Q)
/* Use log not log1p to avoid inaccuracy from log1p of arguments
close to -1. */
log_sinpi_ratio = logq (lg_sinpi (x0_idiff)
/ lg_sinpi (x_idiff));
else
{
/* Use log1p not log to avoid inaccuracy from log of arguments
close to 1. X0DIFF2 has positive sign if X0 is further from
XN than X is from XN, negative sign otherwise. */
__float128 x0diff2 = ((i & 1) == 0 ? xdiff : -xdiff) * 0.5Q;
__float128 sx0d2 = lg_sinpi (x0diff2);
__float128 cx0d2 = lg_cospi (x0diff2);
log_sinpi_ratio = log1pq (2 * sx0d2
* (-sx0d2 + cx0d2 * lg_cotpi (x_idiff)));
}
__float128 log_gamma_ratio;
__float128 y0 = 1 - x0_hi;
__float128 y0_eps = -x0_hi + (1 - y0) - x0_lo;
__float128 y = 1 - x;
__float128 y_eps = -x + (1 - y);
/* We now wish to compute LOG_GAMMA_RATIO
= log (gamma (Y0 + Y0_EPS) / gamma (Y + Y_EPS)). XDIFF
accurately approximates the difference Y0 + Y0_EPS - Y -
Y_EPS. Use Stirling's approximation. First, we may need to
adjust into the range where Stirling's approximation is
sufficiently accurate. */
__float128 log_gamma_adj = 0;
if (i < 20)
{
int n_up = (21 - i) / 2;
__float128 ny0, ny0_eps, ny, ny_eps;
ny0 = y0 + n_up;
ny0_eps = y0 - (ny0 - n_up) + y0_eps;
y0 = ny0;
y0_eps = ny0_eps;
ny = y + n_up;
ny_eps = y - (ny - n_up) + y_eps;
y = ny;
y_eps = ny_eps;
__float128 prodm1 = __quadmath_lgamma_productq (xdiff, y - n_up, y_eps, n_up);
log_gamma_adj = -log1pq (prodm1);
}
__float128 log_gamma_high
= (xdiff * log1pq ((y0 - e_hi - e_lo + y0_eps) / e_hi)
+ (y - 0.5Q + y_eps) * log1pq (xdiff / y) + log_gamma_adj);
/* Compute the sum of (B_2k / 2k(2k-1))(Y0^-(2k-1) - Y^-(2k-1)). */
__float128 y0r = 1 / y0, yr = 1 / y;
__float128 y0r2 = y0r * y0r, yr2 = yr * yr;
__float128 rdiff = -xdiff / (y * y0);
__float128 bterm[NCOEFF];
__float128 dlast = rdiff, elast = rdiff * yr * (yr + y0r);
bterm[0] = dlast * lgamma_coeff[0];
for (size_t j = 1; j < NCOEFF; j++)
{
__float128 dnext = dlast * y0r2 + elast;
__float128 enext = elast * yr2;
bterm[j] = dnext * lgamma_coeff[j];
dlast = dnext;
elast = enext;
}
__float128 log_gamma_low = 0;
for (size_t j = 0; j < NCOEFF; j++)
log_gamma_low += bterm[NCOEFF - 1 - j];
log_gamma_ratio = log_gamma_high + log_gamma_low;
return log_sinpi_ratio + log_gamma_ratio;
}

50
libquadmath/math/lgammaq_product.c Normal file
View File

@ -0,0 +1,50 @@
/* Compute a product of 1 + (T/X), 1 + (T/(X+1)), ....
Copyright (C) 2015-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#include "quadmath-imp.h"
/* Compute the product of 1 + (T / (X + X_EPS)), 1 + (T / (X + X_EPS +
1)), ..., 1 + (T / (X + X_EPS + N - 1)), minus 1. X is such that
all the values X + 1, ..., X + N - 1 are exactly representable, and
X_EPS / X is small enough that factors quadratic in it can be
neglected. */
__float128
__quadmath_lgamma_productq (__float128 t, __float128 x, __float128 x_eps, int n)
{
__float128 ret = 0, ret_eps = 0;
for (int i = 0; i < n; i++)
{
__float128 xi = x + i;
__float128 quot = t / xi;
__float128 mhi, mlo;
mul_splitq (&mhi, &mlo, quot, xi);
__float128 quot_lo = (t - mhi - mlo) / xi - t * x_eps / (xi * xi);
/* We want (1 + RET + RET_EPS) * (1 + QUOT + QUOT_LO) - 1. */
__float128 rhi, rlo;
mul_splitq (&rhi, &rlo, ret, quot);
__float128 rpq = ret + quot;
__float128 rpq_eps = (ret - rpq) + quot;
__float128 nret = rpq + rhi;
__float128 nret_eps = (rpq - nret) + rhi;
ret_eps += (rpq_eps + nret_eps + rlo + ret_eps * quot
+ quot_lo + quot_lo * (ret + ret_eps));
ret = nret;
}
return ret + ret_eps;
}

21
libquadmath/math/llrintq.c
View File

@ -1,6 +1,6 @@
/* Round argument to nearest integral value according to current rounding
direction.
Copyright (C) 1997-2017 Free Software Foundation, Inc.
Copyright (C) 1997-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and
Jakub Jelinek <jj@ultra.linux.cz>, 1999.
@ -16,9 +16,8 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#include "quadmath-imp.h"
@ -53,9 +52,7 @@ llrintq (__float128 x)
/* In the event of overflow we must raise the "invalid"
exception, but not "inexact". */
t = nearbyintq (x);
#ifdef USE_FENV_H
feraiseexcept (t == LLONG_MAX ? FE_INEXACT : FE_INVALID);
#endif
}
else
#endif
@ -82,21 +79,21 @@ llrintq (__float128 x)
unspecified. */
#if defined FE_INVALID || defined FE_INEXACT
if (x < (__float128) LLONG_MIN
&& x > (__float128) LLONG_MIN - 1.0Q)
&& x > (__float128) LLONG_MIN - 1)
{
/* If truncation produces LLONG_MIN, the cast will not raise
the exception, but may raise "inexact". */
t = nearbyintq (x);
#ifdef USE_FENV_H
feraiseexcept (t == LLONG_MIN ? FE_INEXACT : FE_INVALID);
#endif
return LLONG_MIN;
}
else if (FIX_FLT128_LLONG_CONVERT_OVERFLOW && x != (__float128) LLONG_MIN)
{
feraiseexcept (FE_INVALID);
return sx == 0 ? LLONG_MAX : LLONG_MIN;
}
#endif
/* The number is too large. It is left implementation defined
what happens. */
return (long long int) x;
}

23
libquadmath/math/llroundq.c
View File

@ -1,5 +1,5 @@
/* Round __float128 value to long long int.
Copyright (C) 1997-2017 Free Software Foundation, Inc.
/* Round long double value to long long int.
Copyright (C) 1997-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and
Jakub Jelinek <jj@ultra.linux.cz>, 1999.
@ -15,13 +15,11 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#include "quadmath-imp.h"
long long int
llroundq (__float128 x)
{
@ -61,7 +59,7 @@ llroundq (__float128 x)
else
{
result = ((long long int) i0 << (j0 - 48)) | (j >> (112 - j0));
#if defined FE_INVALID && defined USE_FENV_H
#ifdef FE_INVALID
if (sign == 1 && result == LLONG_MIN)
/* Rounding brought the value out of range. */
feraiseexcept (FE_INVALID);
@ -75,13 +73,18 @@ llroundq (__float128 x)
FE_INVALID must be raised and the return value is
unspecified. */
#ifdef FE_INVALID
if (x <= (__float128) LLONG_MIN - 0.5Q)
if (FIX_FLT128_LLONG_CONVERT_OVERFLOW
&& !(sign == -1 && x > (__float128) LLONG_MIN - 0.5Q))
{
feraiseexcept (FE_INVALID);
return sign == 1 ? LLONG_MAX : LLONG_MIN;
}
else if (!FIX_FLT128_LLONG_CONVERT_OVERFLOW
&& x <= (__float128) LLONG_MIN - 0.5Q)
{
/* If truncation produces LLONG_MIN, the cast will not raise
the exception, but may raise "inexact". */
#ifdef USE_FENV_H
feraiseexcept (FE_INVALID);
#endif
return LLONG_MIN;
}
#endif

26
libquadmath/math/log10q.c
View File

@ -1,14 +1,14 @@
/* log10q.c
/* log10l.c
*
* Common logarithm, 128-bit __float128 precision
* Common logarithm, 128-bit long double precision
*
*
*
* SYNOPSIS:
*
* __float128 x, y, log10l();
* long double x, y, log10l();
*
* y = log10q( x );
* y = log10l( x );
*
*
*
@ -57,9 +57,7 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
License along with this library; if not, see <http://www.gnu.org/licenses/>.
*/
#include "quadmath-imp.h"
@ -99,7 +97,7 @@ static const __float128 Q[12] =
9.147150349299596453976674231612674085381E3Q,
9.104928120962988414618126155557301584078E2Q,
4.839208193348159620282142911143429644326E1Q
/* 1.000000000000000000000000000000000000000E0Q, */
/* 1.000000000000000000000000000000000000000E0L, */
};
/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2),
@ -125,7 +123,7 @@ static const __float128 S[6] =
-5.748542087379434595104154610899551484314E4Q,
3.998526750980007367835804959888064681098E3Q,
-1.186359407982897997337150403816839480438E2Q
/* 1.000000000000000000000000000000000000000E0Q, */
/* 1.000000000000000000000000000000000000000E0L, */
};
static const __float128
@ -188,14 +186,14 @@ log10q (__float128 x)
/* Test for domain */
GET_FLT128_WORDS64 (hx, lx, x);
if (((hx & 0x7fffffffffffffffLL) | lx) == 0)
return (-1.0Q / fabsq (x)); /* log10l(+-0)=-inf */
return (-1 / fabsq (x)); /* log10l(+-0)=-inf */
if (hx < 0)
return (x - x) / (x - x);
if (hx >= 0x7fff000000000000LL)
return (x + x);
if (x == 1.0Q)
return 0.0Q;
if (x == 1)
return 0;
/* separate mantissa from exponent */
@ -234,11 +232,11 @@ log10q (__float128 x)
if (x < SQRTH)
{
e -= 1;
x = 2.0 * x - 1.0Q; /* 2x - 1 */
x = 2.0 * x - 1; /* 2x - 1 */
}
else
{
x = x - 1.0Q;
x = x - 1;
}
z = x * x;
y = x * (z * neval (x, P, 12) / deval (x, Q, 11));

33
libquadmath/math/log1pq.c
View File

@ -1,13 +1,13 @@
/* log1pl.c
/* log1pq.c
*
* Relative error logarithm
* Natural logarithm of 1+x for __float128 precision
* Natural logarithm of 1+x, 128-bit long double precision
*
*
*
* SYNOPSIS:
*
* __float128 x, y, log1pl();
* long double x, y, log1pq();
*
* y = log1pq( x );
*
@ -49,9 +49,8 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
License along with this library; if not, see
<http://www.gnu.org/licenses/>. */
#include "quadmath-imp.h"
@ -74,7 +73,7 @@ static const __float128
P2 = 2.014652742082537582487669938141683759923E5Q,
P1 = 7.771154681358524243729929227226708890930E4Q,
P0 = 1.313572404063446165910279910527789794488E4Q,
/* Q12 = 1.000000000000000000000000000000000000000E0Q, */
/* Q12 = 1.000000000000000000000000000000000000000E0L, */
Q11 = 4.839208193348159620282142911143429644326E1Q,
Q10 = 9.104928120962988414618126155557301584078E2Q,
Q9 = 9.147150349299596453976674231612674085381E3Q,
@ -101,7 +100,7 @@ static const __float128
R2 = 2.048819892795278657810231591630928516206E4Q,
R1 = -8.977257995689735303686582344659576526998E4Q,
R0 = 1.418134209872192732479751274970992665513E5Q,
/* S6 = 1.000000000000000000000000000000000000000E0Q, */
/* S6 = 1.000000000000000000000000000000000000000E0L, */
S5 = -1.186359407982897997337150403816839480438E2Q,
S4 = 3.998526750980007367835804959888064681098E3Q,
S3 = -5.748542087379434595104154610899551484314E4Q,
@ -114,8 +113,8 @@ static const __float128 C1 = 6.93145751953125E-1Q;
static const __float128 C2 = 1.428606820309417232121458176568075500134E-6Q;
static const __float128 sqrth = 0.7071067811865475244008443621048490392848Q;
static const __float128 zero = 0.0Q;
/* ln (2^16384 * (1 - 2^-113)) */
static const __float128 zero = 0;
__float128
log1pq (__float128 xm1)
@ -140,19 +139,19 @@ log1pq (__float128 xm1)
{
math_check_force_underflow (xm1);
if ((int) xm1 == 0)
return xm1;
return xm1;
}
if (xm1 >= 0x1p113Q)
x = xm1;
else
x = xm1 + 1.0Q;
x = xm1 + 1;
/* log1p(-1) = -inf */
if (x <= 0.0Q)
if (x <= 0)
{
if (x == 0.0Q)
return (-1.0Q / zero); /* log1p(-1) = -inf */
if (x == 0)
return (-1 / zero); /* log1p(-1) = -inf */
else
return (zero / (x - x));
}
@ -207,14 +206,14 @@ log1pq (__float128 xm1)
{
e -= 1;
if (e != 0)
x = 2.0Q * x - 1.0Q; /* 2x - 1 */
x = 2 * x - 1; /* 2x - 1 */
else
x = xm1;
}
else
{
if (e != 0)
x = x - 1.0Q;
x = x - 1;
else
x = xm1;
}

25
libquadmath/math/log2q.c
View File

@ -1,13 +1,13 @@
/* log2q.c
* Base 2 logarithm for __float128 precision
/* log2l.c
* Base 2 logarithm, 128-bit long double precision
*
*
*
* SYNOPSIS:
*
* __float128 x, y, log2q();
* long double x, y, log2l();
*
* y = log2q( x );
* y = log2l( x );
*
*
*
@ -56,8 +56,7 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
License along with this library; if not, see <http://www.gnu.org/licenses/>.
*/
#include "quadmath-imp.h"
@ -97,7 +96,7 @@ static const __float128 Q[12] =
9.147150349299596453976674231612674085381E3Q,
9.104928120962988414618126155557301584078E2Q,
4.839208193348159620282142911143429644326E1Q
/* 1.000000000000000000000000000000000000000E0Q, */
/* 1.000000000000000000000000000000000000000E0L, */
};
/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2),
@ -123,7 +122,7 @@ static const __float128 S[6] =
-5.748542087379434595104154610899551484314E4Q,
3.998526750980007367835804959888064681098E3Q,
-1.186359407982897997337150403816839480438E2Q
/* 1.000000000000000000000000000000000000000E0Q, */
/* 1.000000000000000000000000000000000000000E0L, */
};
static const __float128
@ -181,14 +180,14 @@ log2q (__float128 x)
/* Test for domain */
GET_FLT128_WORDS64 (hx, lx, x);
if (((hx & 0x7fffffffffffffffLL) | lx) == 0)
return (-1.0Q / fabsq (x)); /* log2l(+-0)=-inf */
return (-1 / fabsq (x)); /* log2l(+-0)=-inf */
if (hx < 0)
return (x - x) / (x - x);
if (hx >= 0x7fff000000000000LL)
return (x + x);
if (x == 1.0Q)
return 0.0Q;
if (x == 1)
return 0;
/* separate mantissa from exponent */
@ -227,11 +226,11 @@ log2q (__float128 x)
if (x < SQRTH)
{
e -= 1;
x = 2.0 * x - 1.0Q; /* 2x - 1 */
x = 2.0 * x - 1; /* 2x - 1 */
}
else
{
x = x - 1.0Q;
x = x - 1;
}
z = x * x;
y = x * (z * neval (x, P, 12) / deval (x, Q, 11));

6
libquadmath/math/logbq.c
View File

@ -13,8 +13,12 @@
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: $";
#endif
/*
* long double logbl(x)
* long double logbq(x)
* IEEE 754 logb. Included to pass IEEE test suite. Not recommend.
* Use ilogb instead.
*/

26
libquadmath/math/logq.c
View File

@ -1,12 +1,12 @@
/* logq.c
/* logll.c
*
* Natural logarithm for __float128 precision.
* Natural logarithm for 128-bit long double precision.
*
*
*
* SYNOPSIS:
*
* __float128 x, y, logq();
* long double x, y, logq();
*
* y = logq( x );
*
@ -42,7 +42,7 @@
*
*/
/* Copyright 2001 by Stephen L. Moshier <moshier@na-net.ornl.gov>
/* Copyright 2001 by Stephen L. Moshier <moshier@na-net.ornl.gov>
This library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
@ -55,8 +55,8 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
License along with this library; if not, see
<http://www.gnu.org/licenses/>. */
#include "quadmath-imp.h"
@ -183,7 +183,7 @@ static const __float128
ln2b = 1.4286068203094172321214581765680755001344E-6Q;
__float128
logq (__float128 x)
logq(__float128 x)
{
__float128 z, y, w;
ieee854_float128 u, t;
@ -240,11 +240,11 @@ logq (__float128 x)
/* On this interval the table is not used due to cancellation error. */
if ((x <= 1.0078125Q) && (x >= 0.9921875Q))
{
if (x == 1.0Q)
return 0.0Q;
z = x - 1.0Q;
if (x == 1)
return 0;
z = x - 1;
k = 64;
t.value = 1.0Q;
t.value = 1;
e = 0;
}
else
@ -252,7 +252,7 @@ logq (__float128 x)
/* log(u) = log( t u/t ) = log(t) + log(u/t)
log(t) is tabulated in the lookup table.
Express log(u/t) = log(1+z), where z = u/t - 1 = (u-t)/t.
cf. Cody & Waite. */
cf. Cody & Waite. */
z = (u.value - t.value) / t.value;
}
/* Series expansion of log(1+z). */
@ -274,7 +274,7 @@ logq (__float128 x)
y += e * ln2b; /* Base 2 exponent offset times ln(2). */
y += z;
y += logtbl[k-26]; /* log(t) - (t-1) */
y += (t.value - 1.0Q);
y += (t.value - 1);
y += e * ln2a;
return y;
}

21
libquadmath/math/lrintq.c
View File

@ -1,6 +1,6 @@
/* Round argument to nearest integral value according to current rounding
direction.
Copyright (C) 1997-2017 Free Software Foundation, Inc.
Copyright (C) 1997-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and
Jakub Jelinek <jj@ultra.linux.cz>, 1999.
@ -16,9 +16,8 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#include "quadmath-imp.h"
@ -56,9 +55,7 @@ lrintq (__float128 x)
/* In the event of overflow we must raise the "invalid"
exception, but not "inexact". */
t = nearbyintq (x);
#ifdef USE_FENV_H
feraiseexcept (t == LONG_MAX ? FE_INEXACT : FE_INVALID);
#endif
}
else
#endif
@ -85,9 +82,7 @@ lrintq (__float128 x)
/* In the event of overflow we must raise the "invalid"
exception, but not "inexact". */
t = nearbyintq (x);
#ifdef USE_FENV_H
feraiseexcept (t == LONG_MAX ? FE_INEXACT : FE_INVALID);
#endif
}
else
#endif
@ -113,16 +108,20 @@ lrintq (__float128 x)
unspecified. */
#if defined FE_INVALID || defined FE_INEXACT
if (x < (__float128) LONG_MIN
&& x > (__float128) LONG_MIN - 1.0Q)
&& x > (__float128) LONG_MIN - 1)
{
/* If truncation produces LONG_MIN, the cast will not raise
the exception, but may raise "inexact". */
t = nearbyintq (x);
#ifdef USE_FENV_H
feraiseexcept (t == LONG_MIN ? FE_INEXACT : FE_INVALID);
#endif
return LONG_MIN;
}
else if (FIX_FLT128_LONG_CONVERT_OVERFLOW && x != (__float128) LONG_MIN)
{
feraiseexcept (FE_INVALID);
return sx == 0 ? LONG_MAX : LONG_MIN;
}
#endif
return (long int) x;
}

27
libquadmath/math/lroundq.c
View File

@ -1,5 +1,5 @@
/* Round __float128 value to long int.
Copyright (C) 1997-2017 Free Software Foundation, Inc.
/* Round long double value to long int.
Copyright (C) 1997-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and
Jakub Jelinek <jj@ultra.linux.cz>, 1999.
@ -15,13 +15,11 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#include "quadmath-imp.h"
long int
lroundq (__float128 x)
{
@ -46,7 +44,7 @@ lroundq (__float128 x)
{
i0 += 0x0000800000000000LL >> j0;
result = i0 >> (48 - j0);
#if defined FE_INVALID && defined USE_FENV_H
#ifdef FE_INVALID
if (sizeof (long int) == 4
&& sign == 1
&& result == LONG_MIN)
@ -68,7 +66,7 @@ lroundq (__float128 x)
else
{
result = ((long int) i0 << (j0 - 48)) | (j >> (112 - j0));
#if defined FE_INVALID && defined USE_FENV_H
#ifdef FE_INVALID
if (sizeof (long int) == 8
&& sign == 1
&& result == LONG_MIN)
@ -84,16 +82,23 @@ lroundq (__float128 x)
FE_INVALID must be raised and the return value is
unspecified. */
#ifdef FE_INVALID
if (x <= (__float128) LONG_MIN - 0.5Q)
if (FIX_FLT128_LONG_CONVERT_OVERFLOW
&& !(sign == -1 && x > (__float128) LONG_MIN - 0.5Q))
{
feraiseexcept (FE_INVALID);
return sign == 1 ? LONG_MAX : LONG_MIN;
}
else if (!FIX_FLT128_LONG_CONVERT_OVERFLOW
&& x <= (__float128) LONG_MIN - 0.5Q)
{
/* If truncation produces LONG_MIN, the cast will not raise
the exception, but may raise "inexact". */
#ifdef USE_FENV_H
feraiseexcept (FE_INVALID);
#endif
return LONG_MIN;
}
#endif
/* The number is too large. It is left implementation defined
what happens. */
return (long int) x;
}

19
libquadmath/math/modfq.c
View File

@ -1,4 +1,4 @@
/* modfq.c -- __float128 version of s_modf.c.
/* s_modfl.c -- long double version of s_modf.c.
* Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
@ -13,12 +13,25 @@
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: $";
#endif
/*
* modfq(long double x, long double *iptr)
* return fraction part of x, and return x's integral part in *iptr.
* Method:
* Bit twiddling.
*
* Exception:
* No exception.
*/
#include "quadmath-imp.h"
static const __float128 one = 1.0;
__float128
modfq (__float128 x, __float128 *iptr)
__float128 modfq(__float128 x, __float128 *iptr)
{
int64_t i0,i1,j0;
uint64_t i;

25
libquadmath/math/nearbyintq.c
View File

@ -1,4 +1,4 @@
/* nearbyintq.c -- __float128 version of s_nearbyint.c.
/* s_nearbyintl.c -- long double version of s_nearbyint.c.
* Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
@ -24,12 +24,6 @@
*/
#include "quadmath-imp.h"
#ifdef HAVE_FENV_H
# include <fenv.h>
# if defined HAVE_FEHOLDEXCEPT && defined HAVE_FESETENV
# define USE_FENV_H
# endif
#endif
static const __float128
TWO112[2]={
@ -37,12 +31,9 @@ TWO112[2]={
-5.19229685853482762853049632922009600E+33Q /* 0xC06F000000000000, 0 */
};
__float128
nearbyintq(__float128 x)
__float128 nearbyintq(__float128 x)
{
#ifdef USE_FENV_H
fenv_t env;
#endif
int64_t i0,j0,sx;
uint64_t i1 __attribute__ ((unused));
__float128 w,t;
@ -51,15 +42,11 @@ nearbyintq(__float128 x)
j0 = ((i0>>48)&0x7fff)-0x3fff;
if(j0<112) {
if(j0<0) {
#ifdef USE_FENV_H
feholdexcept (&env);
#endif
w = TWO112[sx]+x;
w = TWO112[sx] + math_opt_barrier (x);
t = w-TWO112[sx];
math_force_eval (t);
#ifdef USE_FENV_H
fesetenv (&env);
#endif
GET_FLT128_MSW64(i0,t);
SET_FLT128_MSW64(t,(i0&0x7fffffffffffffffLL)|(sx<<63));
return t;
@ -68,14 +55,10 @@ nearbyintq(__float128 x)
if(j0==0x4000) return x+x; /* inf or NaN */
else return x; /* x is integral */
}
#ifdef USE_FENV_H
feholdexcept (&env);
#endif
w = TWO112[sx]+x;
w = TWO112[sx] + math_opt_barrier (x);
t = w-TWO112[sx];
math_force_eval (t);
#ifdef USE_FENV_H
fesetenv (&env);
#endif
return t;
}

25
libquadmath/math/nextafterq.c
View File

@ -1,4 +1,4 @@
/* nextafterq.c -- __float128 version of s_nextafter.c.
/* s_nextafterl.c -- long double version of s_nextafter.c.
* Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
@ -13,11 +13,20 @@
* ====================================================
*/
#include <errno.h>
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: $";
#endif
/* IEEE functions
* nextafterq(x,y)
* return the next machine floating-point number of x in the
* direction toward y.
* Special cases:
*/
#include "quadmath-imp.h"
__float128
nextafterq (__float128 x, __float128 y)
__float128 nextafterq(__float128 x, __float128 y)
{
int64_t hx,hy,ix,iy;
uint64_t lx,ly;
@ -32,9 +41,11 @@ nextafterq (__float128 x, __float128 y)
return x+y;
if(x==y) return y; /* x=y, return y */
if((ix|lx)==0) { /* x == 0 */
__float128 u;
SET_FLT128_WORDS64(x,hy&0x8000000000000000ULL,1);/* return +-minsubnormal */
/* here we should raise an underflow flag */
u = math_opt_barrier (x);
u = u * u;
math_force_eval (u); /* raise underflow flag */
return x;
}
if(hx>=0) { /* x > 0 */
@ -61,7 +72,7 @@ nextafterq (__float128 x, __float128 y)
errno = ERANGE;
}
if(hy==0) {
__float128 u = x*x; /* underflow */
__float128 u = x*x; /* underflow */
math_force_eval (u); /* raise underflow flag */
errno = ERANGE;
}

25
libquadmath/math/powq.c
View File

@ -11,9 +11,9 @@
/* Expansions and modifications for 128-bit long double are
Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
and are incorporated herein by permission of the author. The author
and are incorporated herein by permission of the author. The author
reserves the right to distribute this material elsewhere under different
copying permissions. These modifications are distributed here under
copying permissions. These modifications are distributed here under
the following terms:
This library is free software; you can redistribute it and/or
@ -27,8 +27,8 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
License along with this library; if not, see
<http://www.gnu.org/licenses/>. */
/* powq(x,y) return x**y
*
@ -67,7 +67,7 @@
#include "quadmath-imp.h"
static const __float128 bp[] = {
1.0Q,
1,
1.5Q,
};
@ -83,9 +83,9 @@ static const __float128 dp_l[] = {
1.0579781240112554492329533686862998106046E-16Q
};
static const __float128 zero = 0.0Q,
one = 1.0Q,
two = 2.0Q,
static const __float128 zero = 0,
one = 1,
two = 2,
two113 = 1.0384593717069655257060992658440192E34Q,
huge = 1.0e3000Q,
tiny = 1.0e-3000Q;
@ -164,13 +164,14 @@ powq (__float128 x, __float128 y)
/* y==zero: x**0 = 1 */
if ((iy | q.words32.w1 | q.words32.w2 | q.words32.w3) == 0)
if ((iy | q.words32.w1 | q.words32.w2 | q.words32.w3) == 0
&& !issignalingq (x))
return one;
/* 1.0**y = 1; -1.0**+-Inf = 1 */
if (x == one)
if (x == one && !issignalingq (y))
return one;
if (x == -1.0Q && iy == 0x7fff0000
if (x == -1 && iy == 0x7fff0000
&& (q.words32.w1 | q.words32.w2 | q.words32.w3) == 0)
return one;
@ -264,7 +265,7 @@ powq (__float128 x, __float128 y)
/* sgn (sign of result -ve**odd) = -1 else = 1 */
sgn = one;
if (((((uint32_t) hx >> 31) - 1) | (yisint - 1)) == 0)
sgn = -one; /* (-ve)**(odd int) */
sgn = -one; /* (-ve)**(odd int) */
/* |y| is huge.
2^-16495 = 1/2 of smallest representable value.

86
libquadmath/math/remainderq.c
View File

@ -1,4 +1,4 @@
/* fmodq.c -- __float128 version of e_fmod.c.
/* e_fmodl.c -- long double version of e_fmod.c.
* Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
/*
@ -7,61 +7,63 @@
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* remainderq(x,p)
* Return :
* returns x REM p = x - [x/p]*p as if in infinite
* precise arithmetic, where [x/p] is the (infinite bit)
* Return :
* returns x REM p = x - [x/p]*p as if in infinite
* precise arithmetic, where [x/p] is the (infinite bit)
* integer nearest x/p (in half way case choose the even one).
* Method :
* Based on fmodq() return x-[x/p]chopped*p exactlp.
* Method :
* Based on fmodl() return x-[x/p]chopped*p exactlp.
*/
#include "quadmath-imp.h"
static const __float128 zero = 0.0Q;
static const __float128 zero = 0;
__float128
remainderq (__float128 x, __float128 p)
remainderq(__float128 x, __float128 p)
{
int64_t hx,hp;
uint64_t sx,lx,lp;
__float128 p_half;
int64_t hx,hp;
uint64_t sx,lx,lp;
__float128 p_half;
GET_FLT128_WORDS64(hx,lx,x);
GET_FLT128_WORDS64(hp,lp,p);
sx = hx&0x8000000000000000ULL;
hp &= 0x7fffffffffffffffLL;
hx &= 0x7fffffffffffffffLL;
GET_FLT128_WORDS64(hx,lx,x);
GET_FLT128_WORDS64(hp,lp,p);
sx = hx&0x8000000000000000ULL;
hp &= 0x7fffffffffffffffLL;
hx &= 0x7fffffffffffffffLL;
/* purge off exception values */
if((hp|lp)==0) return (x*p)/(x*p); /* p = 0 */
if((hx>=0x7fff000000000000LL)|| /* x not finite */
((hp>=0x7fff000000000000LL)&& /* p is NaN */
(((hp-0x7fff000000000000LL)|lp)!=0)))
return (x*p)/(x*p);
/* purge off exception values */
if((hp|lp)==0) return (x*p)/(x*p); /* p = 0 */
if((hx>=0x7fff000000000000LL)|| /* x not finite */
((hp>=0x7fff000000000000LL)&& /* p is NaN */
(((hp-0x7fff000000000000LL)|lp)!=0)))
return (x*p)/(x*p);
if (hp<=0x7ffdffffffffffffLL) x = fmodq (x,p+p); /* now x < 2p */
if (((hx-hp)|(lx-lp))==0) return zero*x;
x = fabsq(x);
p = fabsq(p);
if (hp<0x0002000000000000LL) {
if(x+x>p) {
x-=p;
if(x+x>=p) x -= p;
}
} else {
p_half = 0.5Q*p;
if(x>p_half) {
x-=p;
if(x>=p_half) x -= p;
}
}
GET_FLT128_MSW64(hx,x);
SET_FLT128_MSW64(x,hx^sx);
return x;
if (hp<=0x7ffdffffffffffffLL) x = fmodq(x,p+p); /* now x < 2p */
if (((hx-hp)|(lx-lp))==0) return zero*x;
x = fabsq(x);
p = fabsq(p);
if (hp<0x0002000000000000LL) {
if(x+x>p) {
x-=p;
if(x+x>=p) x -= p;
}
} else {
p_half = 0.5Q*p;
if(x>p_half) {
x-=p;
if(x>=p_half) x -= p;
}
}
GET_FLT128_MSW64(hx,x);
SET_FLT128_MSW64(x,hx^sx);
return x;
}

12
libquadmath/math/remquoq.c
View File

@ -1,5 +1,5 @@
/* Compute remainder and a congruent to the quotient.
Copyright (C) 1997-2017 Free Software Foundation, Inc.
Copyright (C) 1997-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and
Jakub Jelinek <jj@ultra.linux.cz>, 1999.
@ -15,13 +15,11 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#include "quadmath-imp.h"
static const __float128 zero = 0.0;
@ -102,8 +100,8 @@ remquoq (__float128 x, __float128 y, int *quo)
*quo = qs ? -cquo : cquo;
/* Ensure correct sign of zero result in round-downward mode. */
if (x == 0.0Q)
x = 0.0Q;
if (x == 0)
x = 0;
if (sx)
x = -x;
return x;

15
libquadmath/math/rintq.c
View File

@ -1,4 +1,4 @@
/* rintq.c -- __float128 version of s_rint.c.
/* s_rintl.c -- long double version of s_rint.c.
* Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
@ -13,6 +13,10 @@
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: $";
#endif
/*
* rintq(x)
* Return x rounded to integral value according to the prevailing
@ -23,16 +27,17 @@
* Inexact flag raised if x not equal to rintq(x).
*/
#define NO_MATH_REDIRECT
#include "quadmath-imp.h"
static const __float128
TWO112[2]={
5.19229685853482762853049632922009600E+33Q, /* 0x406F000000000000, 0 */
-5.19229685853482762853049632922009600E+33Q /* 0xC06F000000000000, 0 */
5.19229685853482762853049632922009600E+33L, /* 0x406F000000000000, 0 */
-5.19229685853482762853049632922009600E+33L /* 0xC06F000000000000, 0 */
};
__float128
rintq (__float128 x)
__float128 rintq(__float128 x)
{
int64_t i0,j0,sx;
uint64_t i1 __attribute__ ((unused));

12
libquadmath/math/roundq.c
View File

@ -1,5 +1,5 @@
/* Round __float128 to integer away from zero.
Copyright (C) 1997-2017 Free Software Foundation, Inc.
/* Round long double to integer away from zero.
Copyright (C) 1997-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and
Jakub Jelinek <jj@ultra.linux.cz>, 1999.
@ -15,9 +15,10 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#define NO_MATH_REDIRECT
#include "quadmath-imp.h"
@ -44,6 +45,7 @@ roundq (__float128 x)
if (((i0 & i) | i1) == 0)
/* X is integral. */
return x;
i0 += 0x0000800000000000LL >> j0;
i0 &= ~i;
i1 = 0;

14
libquadmath/math/scalblnq.c
View File

@ -1,7 +1,8 @@
/* scalblnq.c -- __float128 version of s_scalbn.c.
/* s_scalblnl.c -- long double version of s_scalbn.c.
* Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
/* @(#)s_scalbn.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
@ -13,9 +14,13 @@
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: $";
#endif
/*
* scalblnq (_float128 x, long int n)
* scalblnq(x,n) returns x* 2**n computed by exponent
* scalblnl (long double x, long int n)
* scalblnl(x,n) returns x* 2**n computed by exponent
* manipulation rather than by actually performing an
* exponentiation or a multiplication.
*/
@ -28,8 +33,7 @@ twom114 = 4.8148248609680896326399448564623183E-35Q, /* 0x3F8D000000000000, 0 */
huge = 1.0E+4900Q,
tiny = 1.0E-4900Q;
__float128
scalblnq (__float128 x, long int n)
__float128 scalblnq (__float128 x, long int n)
{
int64_t k,hx,lx;
GET_FLT128_WORDS64(hx,lx,x);

11
libquadmath/math/scalbnq.c
View File

@ -1,7 +1,8 @@
/* scalbnq.c -- __float128 version of s_scalbn.c.
/* s_scalbnl.c -- long double version of s_scalbn.c.
* Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
/* @(#)s_scalbn.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
@ -13,9 +14,12 @@
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: $";
#endif
/*
* scalbnq (__float128 x, int n)
* scalbnq (long double x, int n)
* scalbnq(x,n) returns x* 2**n computed by exponent
* manipulation rather than by actually performing an
* exponentiation or a multiplication.
@ -29,8 +33,7 @@ twom114 = 4.8148248609680896326399448564623183E-35Q, /* 0x3F8D000000000000, 0 */
huge = 1.0E+4900Q,
tiny = 1.0E-4900Q;
__float128
scalbnq (__float128 x, int n)
__float128 scalbnq (__float128 x, int n)
{
int64_t k,hx,lx;
GET_FLT128_WORDS64(hx,lx,x);

26
libquadmath/math/signbitq.c
View File

@ -1,10 +1,26 @@
/* Return nonzero value if number is negative.
Copyright (C) 1997-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#include "quadmath-imp.h"
int
signbitq (const __float128 x)
signbitq (__float128 x)
{
ieee854_float128 f;
f.value = x;
return f.ieee.negative;
return __builtin_signbit (x);
}

11
libquadmath/math/sincos_table.c
View File

@ -1,5 +1,5 @@
/* Quad-precision floating point sine and cosine tables.
Copyright (C) 1999-2017 Free Software Foundation, Inc.
Copyright (C) 1999-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Jakub Jelinek <jj@ultra.linux.cz>
@ -14,9 +14,8 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
/* For 0.1484375 + n/128.0, n=0..82 this table contains
first 113 bits of cosine, then at least 113 additional
@ -26,11 +25,13 @@
Computed using gmp.
*/
/* Include to grab typedefs and wrappers for __float128 and such. */
#include "quadmath-imp.h"
const __float128 __sincosq_table[] = {
/* x = 1.48437500000000000000000000000000000e-01Q 3ffc3000000000000000000000000000 */
/* x = 1.48437500000000000000000000000000000e-01L 3ffc3000000000000000000000000000 */
/* cos(x) = 0.fd2f5320e1b790209b4dda2f98f79caaa7b873aff1014b0fbc5243766d03cb006bc837c4358 */
9.89003367927322909016887196069562069e-01Q, /* 3ffefa5ea641c36f2041369bb45f31ef */
2.15663692029265697782289400027743703e-35Q, /* 3f8bcaaa7b873aff1014b0fbc5243767 */

10
libquadmath/math/sincosq.c
View File

@ -1,5 +1,5 @@
/* Compute sine and cosine of argument.
Copyright (C) 1997-2017 Free Software Foundation, Inc.
Copyright (C) 1997-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and
Jakub Jelinek <jj@ultra.linux.cz>.
@ -15,11 +15,9 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#include <errno.h>
#include "quadmath-imp.h"
void
@ -33,7 +31,7 @@ sincosq (__float128 x, __float128 *sinx, __float128 *cosx)
/* |x| ~< pi/4 */
ix &= 0x7fffffffffffffffLL;
if (ix <= 0x3ffe921fb54442d1LL)
__quadmath_kernel_sincosq (x, 0.0Q, sinx, cosx, 0);
__quadmath_kernel_sincosq (x, 0, sinx, cosx, 0);
else if (ix >= 0x7fff000000000000LL)
{
/* sin(Inf or NaN) is NaN */

44
libquadmath/math/sincosq_kernel.c
View File

@ -1,5 +1,5 @@
/* Quad-precision floating point sine and cosine on <-pi/4,pi/4>.
Copyright (C) 1999-2017 Free Software Foundation, Inc.
Copyright (C) 1999-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Jakub Jelinek <jj@ultra.linux.cz>
@ -14,9 +14,8 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#include "quadmath-imp.h"
@ -89,15 +88,14 @@ static const __float128 c[] = {
2.81068754939739570236322404393398135e-15Q, /* 3fce9510115aabf87aceb2022a9a9180 */
};
#define SINCOSQ_COS_HI 0
#define SINCOSQ_COS_LO 1
#define SINCOSQ_SIN_HI 2
#define SINCOSQ_SIN_LO 3
#define SINCOSL_COS_HI 0
#define SINCOSL_COS_LO 1
#define SINCOSL_SIN_HI 2
#define SINCOSL_SIN_LO 3
extern const __float128 __sincosq_table[];
void
__quadmath_kernel_sincosq(__float128 x, __float128 y, __float128 *sinx,
__float128 *cosx, int iy)
__quadmath_kernel_sincosq(__float128 x, __float128 y, __float128 *sinx, __float128 *cosx, int iy)
{
__float128 h, l, z, sin_l, cos_l_m1;
int64_t ix;
@ -128,7 +126,7 @@ __quadmath_kernel_sincosq(__float128 x, __float128 y, __float128 *sinx,
else
{
/* So that we don't have to use too large polynomial, we find
l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83
l and h such that x = l + h, where fabsq(l) <= 1.0/256 with 83
possible values for h. We look up cosq(h) and sinq(h) in
pre-computed tables, compute cosq(l) and sinq(l) using a
Chebyshev polynomial of degree 10(11) and compute
@ -137,10 +135,10 @@ __quadmath_kernel_sincosq(__float128 x, __float128 y, __float128 *sinx,
index = 0x3ffe - (tix >> 16);
hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
if (signbitq (x))
{
x = -x;
y = -y;
}
{
x = -x;
y = -y;
}
switch (index)
{
case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break;
@ -157,14 +155,14 @@ __quadmath_kernel_sincosq(__float128 x, __float128 y, __float128 *sinx,
z = l * l;
sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
z = __sincosq_table [index + SINCOSQ_SIN_HI]
+ (__sincosq_table [index + SINCOSQ_SIN_LO]
+ (__sincosq_table [index + SINCOSQ_SIN_HI] * cos_l_m1)
+ (__sincosq_table [index + SINCOSQ_COS_HI] * sin_l));
z = __sincosq_table [index + SINCOSL_SIN_HI]
+ (__sincosq_table [index + SINCOSL_SIN_LO]
+ (__sincosq_table [index + SINCOSL_SIN_HI] * cos_l_m1)
+ (__sincosq_table [index + SINCOSL_COS_HI] * sin_l));
*sinx = (ix < 0) ? -z : z;
*cosx = __sincosq_table [index + SINCOSQ_COS_HI]
+ (__sincosq_table [index + SINCOSQ_COS_LO]
- (__sincosq_table [index + SINCOSQ_SIN_HI] * sin_l
- __sincosq_table [index + SINCOSQ_COS_HI] * cos_l_m1));
*cosx = __sincosq_table [index + SINCOSL_COS_HI]
+ (__sincosq_table [index + SINCOSL_COS_LO]
- (__sincosq_table [index + SINCOSL_SIN_HI] * sin_l
- __sincosq_table [index + SINCOSL_COS_HI] * cos_l_m1));
}
}

38
libquadmath/math/sinhq.c
View File

@ -1,5 +1,5 @@
/* sinhq.c -- __float128 version of e_sinh.c.
* Conversion to __float128 by Ulrich Drepper,
/* e_sinhl.c -- long double version of e_sinh.c.
* Conversion to long double by Ulrich Drepper,
* Cygnus Support, drepper@cygnus.com.
*/
@ -14,11 +14,11 @@
* ====================================================
*/
/* Changes for 128-bit __float128 are
/* Changes for 128-bit long double are
Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
and are incorporated herein by permission of the author. The author
and are incorporated herein by permission of the author. The author
reserves the right to distribute this material elsewhere under different
copying permissions. These modifications are distributed here under
copying permissions. These modifications are distributed here under
the following terms:
This library is free software; you can redistribute it and/or
@ -32,31 +32,31 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
License along with this library; if not, see
<http://www.gnu.org/licenses/>. */
/* sinhq(x)
* Method :
* mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
* 1. Replace x by |x| (sinhq(-x) = -sinhq(x)).
* 1. Replace x by |x| (sinhl(-x) = -sinhl(x)).
* 2.
* E + E/(E+1)
* 0 <= x <= 25 : sinhq(x) := --------------, E=expm1q(x)
* 0 <= x <= 25 : sinhl(x) := --------------, E=expm1q(x)
* 2
*
* 25 <= x <= lnovft : sinhq(x) := expq(x)/2
* lnovft <= x <= ln2ovft: sinhq(x) := expq(x/2)/2 * expq(x/2)
* ln2ovft < x : sinhq(x) := x*shuge (overflow)
* 25 <= x <= lnovft : sinhl(x) := expq(x)/2
* lnovft <= x <= ln2ovft: sinhl(x) := expq(x/2)/2 * expq(x/2)
* ln2ovft < x : sinhl(x) := x*shuge (overflow)
*
* Special cases:
* sinhq(x) is |x| if x is +INF, -INF, or NaN.
* only sinhq(0)=0 is exact for finite x.
* sinhl(x) is |x| if x is +INF, -INF, or NaN.
* only sinhl(0)=0 is exact for finite x.
*/
#include "quadmath-imp.h"
static const __float128 one = 1.0, shuge = 1.0e4931Q,
ovf_thresh = 1.1357216553474703894801348310092223067821E4Q;
ovf_thresh = 1.1357216553474703894801348310092223067821E4Q;
__float128
sinhq (__float128 x)
@ -74,7 +74,7 @@ sinhq (__float128 x)
if (ix >= 0x7fff0000)
return x + x;
h = 0.5Q;
h = 0.5;
if (jx & 0x80000000)
h = -h;
@ -92,7 +92,7 @@ sinhq (__float128 x)
}
t = expm1q (u.value);
if (ix < 0x3fff0000)
return h * (2.0Q * t - t * t / (t + one));
return h * (2.0 * t - t * t / (t + one));
return h * (t + t / (t + one));
}
@ -104,11 +104,11 @@ sinhq (__float128 x)
Overflow threshold is log(2 * maxdouble). */
if (u.value <= ovf_thresh)
{
w = expq (0.5Q * u.value);
w = expq (0.5 * u.value);
t = h * w;
return t * w;
}
/* |x| > overflowthreshold, sinhq(x) overflow */
/* |x| > overflowthreshold, sinhl(x) overflow */
return x * shuge;
}

13
libquadmath/math/sinq.c
View File

@ -1,4 +1,4 @@
/* sinq.c -- __float128 version of s_sin.c.
/* s_sinl.c -- long double version of s_sin.c.
* Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
@ -17,8 +17,8 @@
* Return sine function of x.
*
* kernel function:
* __quadmath_kernel_sinq ... sine function on [-pi/4,pi/4]
* __quadmath_kernel_cosq ... cose function on [-pi/4,pi/4]
* __quadmath_kernel_sinq ... sine function on [-pi/4,pi/4]
* __quadmath_kernel_cosq ... cose function on [-pi/4,pi/4]
* __quadmath_rem_pio2q ... argument reduction routine
*
* Method.
@ -46,10 +46,9 @@
#include "quadmath-imp.h"
__float128
sinq (__float128 x)
__float128 sinq(__float128 x)
{
__float128 y[2],z=0.0Q;
__float128 y[2],z=0;
int64_t n, ix;
/* High word of x. */
@ -64,6 +63,8 @@ sinq (__float128 x)
else if (ix>=0x7fff000000000000LL) {
if (ix == 0x7fff000000000000LL) {
GET_FLT128_LSW64(n,x);
if (n == 0)
errno = EDOM;
}
return x-x;
}

27
libquadmath/math/sinq_kernel.c
View File

@ -1,5 +1,5 @@
/* Quad-precision floating point sine on <-pi/4,pi/4>.
Copyright (C) 1999 Free Software Foundation, Inc.
Copyright (C) 1999-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Jakub Jelinek <jj@ultra.linux.cz>
@ -14,9 +14,8 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#include "quadmath-imp.h"
@ -70,14 +69,14 @@ static const __float128 c[] = {
-2.50521016467996193495359189395805639E-08Q, /* bfe5ae644ee90c47dc71839de75b2787 */
};
#define SINCOSQ_COS_HI 0
#define SINCOSQ_COS_LO 1
#define SINCOSQ_SIN_HI 2
#define SINCOSQ_SIN_LO 3
#define SINCOSL_COS_HI 0
#define SINCOSL_COS_LO 1
#define SINCOSL_SIN_HI 2
#define SINCOSL_SIN_LO 3
extern const __float128 __sincosq_table[];
__float128
__quadmath_kernel_sinq (__float128 x, __float128 y, int iy)
__quadmath_kernel_sinq(__float128 x, __float128 y, int iy)
{
__float128 h, l, z, sin_l, cos_l_m1;
int64_t ix;
@ -101,7 +100,7 @@ __quadmath_kernel_sinq (__float128 x, __float128 y, int iy)
else
{
/* So that we don't have to use too large polynomial, we find
l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83
l and h such that x = l + h, where fabsq(l) <= 1.0/256 with 83
possible values for h. We look up cosq(h) and sinq(h) in
pre-computed tables, compute cosq(l) and sinq(l) using a
Chebyshev polynomial of degree 10(11) and compute
@ -125,10 +124,10 @@ __quadmath_kernel_sinq (__float128 x, __float128 y, int iy)
z = l * l;
sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
z = __sincosq_table [index + SINCOSQ_SIN_HI]
+ (__sincosq_table [index + SINCOSQ_SIN_LO]
+ (__sincosq_table [index + SINCOSQ_SIN_HI] * cos_l_m1)
+ (__sincosq_table [index + SINCOSQ_COS_HI] * sin_l));
z = __sincosq_table [index + SINCOSL_SIN_HI]
+ (__sincosq_table [index + SINCOSL_SIN_LO]
+ (__sincosq_table [index + SINCOSL_SIN_HI] * cos_l_m1)
+ (__sincosq_table [index + SINCOSL_COS_HI] * sin_l));
return (ix < 0) ? -z : z;
}
}

32
libquadmath/math/tanhq.c
View File

@ -1,5 +1,5 @@
/* s_tanhl.c -- __float128 version of s_tanh.c.
* Conversion to __float128 by Ulrich Drepper,
/* s_tanhl.c -- long double version of s_tanh.c.
* Conversion to long double by Ulrich Drepper,
* Cygnus Support, drepper@cygnus.com.
*/
@ -14,36 +14,36 @@
* ====================================================
*/
/* Changes for 128-bit __float128 contributed by
/* Changes for 128-bit long double contributed by
Stephen L. Moshier <moshier@na-net.ornl.gov> */
/* tanhl(x)
/* tanhq(x)
* Return the Hyperbolic Tangent of x
*
* Method :
* x -x
* e - e
* 0. tanhl(x) is defined to be -----------
* 0. tanhq(x) is defined to be -----------
* x -x
* e + e
* 1. reduce x to non-negative by tanhl(-x) = -tanhl(x).
* 2. 0 <= x <= 2**-57 : tanhl(x) := x*(one+x)
* 1. reduce x to non-negative by tanhq(-x) = -tanhq(x).
* 2. 0 <= x <= 2**-57 : tanhq(x) := x*(one+x)
* -t
* 2**-57 < x <= 1 : tanhl(x) := -----; t = expm1l(-2x)
* 2**-57 < x <= 1 : tanhq(x) := -----; t = expm1q(-2x)
* t + 2
* 2
* 1 <= x <= 40.0 : tanhl(x) := 1- ----- ; t=expm1l(2x)
* 1 <= x <= 40.0 : tanhq(x) := 1- ----- ; t=expm1q(2x)
* t + 2
* 40.0 < x <= INF : tanhl(x) := 1.
* 40.0 < x <= INF : tanhq(x) := 1.
*
* Special cases:
* tanhl(NaN) is NaN;
* only tanhl(0)=0 is exact for finite argument.
* tanhq(NaN) is NaN;
* only tanhq(0)=0 is exact for finite argument.
*/
#include "quadmath-imp.h"
static const __float128 one = 1.0Q, two = 2.0Q, tiny = 1.0e-4900Q;
static const __float128 one = 1.0, two = 2.0, tiny = 1.0e-4900Q;
__float128
tanhq (__float128 x)
@ -59,11 +59,11 @@ tanhq (__float128 x)
/* x is INF or NaN */
if (ix >= 0x7fff0000)
{
/* for NaN it's not important which branch: tanhl(NaN) = NaN */
/* for NaN it's not important which branch: tanhq(NaN) = NaN */
if (jx & 0x80000000)
return one / x - one; /* tanhl(-inf)= -1; */
return one / x - one; /* tanhq(-inf)= -1; */
else
return one / x + one; /* tanhl(+inf)=+1 */
return one / x + one; /* tanhq(+inf)=+1 */
}
/* |x| < 40 */

187
libquadmath/math/tanq.c
View File

@ -1,171 +1,4 @@
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
Long double expansions are
Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
and are incorporated herein by permission of the author. The author
reserves the right to distribute this material elsewhere under different
copying permissions. These modifications are distributed here under
the following terms:
This library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
This library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
/* __quadmath_kernel_tanq( x, y, k )
* kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854
* Input x is assumed to be bounded by ~pi/4 in magnitude.
* Input y is the tail of x.
* Input k indicates whether tan (if k=1) or
* -1/tan (if k= -1) is returned.
*
* Algorithm
* 1. Since tan(-x) = -tan(x), we need only to consider positive x.
* 2. if x < 2^-57, return x with inexact if x!=0.
* 3. tan(x) is approximated by a rational form x + x^3 / 3 + x^5 R(x^2)
* on [0,0.67433].
*
* Note: tan(x+y) = tan(x) + tan'(x)*y
* ~ tan(x) + (1+x*x)*y
* Therefore, for better accuracy in computing tan(x+y), let
* r = x^3 * R(x^2)
* then
* tan(x+y) = x + (x^3 / 3 + (x^2 *(r+y)+y))
*
* 4. For x in [0.67433,pi/4], let y = pi/4 - x, then
* tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
* = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
*/
#include "quadmath-imp.h"
static const __float128
one = 1.0Q,
pio4hi = 7.8539816339744830961566084581987569936977E-1Q,
pio4lo = 2.1679525325309452561992610065108379921906E-35Q,
/* tan x = x + x^3 / 3 + x^5 T(x^2)/U(x^2)
0 <= x <= 0.6743316650390625
Peak relative error 8.0e-36 */
TH = 3.333333333333333333333333333333333333333E-1Q,
T0 = -1.813014711743583437742363284336855889393E7Q,
T1 = 1.320767960008972224312740075083259247618E6Q,
T2 = -2.626775478255838182468651821863299023956E4Q,
T3 = 1.764573356488504935415411383687150199315E2Q,
T4 = -3.333267763822178690794678978979803526092E-1Q,
U0 = -1.359761033807687578306772463253710042010E8Q,
U1 = 6.494370630656893175666729313065113194784E7Q,
U2 = -4.180787672237927475505536849168729386782E6Q,
U3 = 8.031643765106170040139966622980914621521E4Q,
U4 = -5.323131271912475695157127875560667378597E2Q;
/* 1.000000000000000000000000000000000000000E0 */
static __float128
__quadmath_kernel_tanq (__float128 x, __float128 y, int iy)
{
__float128 z, r, v, w, s;
int32_t ix, sign = 1;
ieee854_float128 u, u1;
u.value = x;
ix = u.words32.w0 & 0x7fffffff;
if (ix < 0x3fc60000) /* x < 2**-57 */
{
if ((int) x == 0)
{ /* generate inexact */
if ((ix | u.words32.w1 | u.words32.w2 | u.words32.w3
| (iy + 1)) == 0)
return one / fabsq (x);
else if (iy == 1)
{
math_check_force_underflow (x);
return x;
}
else
return -one / x;
}
}
if (ix >= 0x3ffe5942) /* |x| >= 0.6743316650390625 */
{
if ((u.words32.w0 & 0x80000000) != 0)
{
x = -x;
y = -y;
sign = -1;
}
else
sign = 1;
z = pio4hi - x;
w = pio4lo - y;
x = z + w;
y = 0.0;
}
z = x * x;
r = T0 + z * (T1 + z * (T2 + z * (T3 + z * T4)));
v = U0 + z * (U1 + z * (U2 + z * (U3 + z * (U4 + z))));
r = r / v;
s = z * x;
r = y + z * (s * r + y);
r += TH * s;
w = x + r;
if (ix >= 0x3ffe5942)
{
v = (__float128) iy;
w = (v - 2.0Q * (x - (w * w / (w + v) - r)));
if (sign < 0)
w = -w;
return w;
}
if (iy == 1)
return w;
else
{ /* if allow error up to 2 ulp,
simply return -1.0/(x+r) here */
/* compute -1.0/(x+r) accurately */
u1.value = w;
u1.words32.w2 = 0;
u1.words32.w3 = 0;
v = r - (u1.value - x); /* u1+v = r+x */
z = -1.0 / w;
u.value = z;
u.words32.w2 = 0;
u.words32.w3 = 0;
s = 1.0 + u.value * u1.value;
return u.value + z * (s + u.value * v);
}
}
/* tanq.c -- __float128 version of s_tan.c.
/* s_tanl.c -- long double version of s_tan.c.
* Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
@ -181,11 +14,11 @@ __quadmath_kernel_tanq (__float128 x, __float128 y, int iy)
* ====================================================
*/
/* tanl(x)
/* tanq(x)
* Return tangent function of x.
*
* kernel function:
* __quadmath_kernel_tanq ... tangent function on [-pi/4,pi/4]
* __quadmath_kernel_tanq ... tangent function on [-pi/4,pi/4]
* __quadmath_rem_pio2q ... argument reduction routine
*
* Method.
@ -211,11 +44,11 @@ __quadmath_kernel_tanq (__float128 x, __float128 y, int iy)
* TRIG(x) returns trig(x) nearly rounded
*/
#include "quadmath-imp.h"
__float128
tanq (__float128 x)
__float128 tanq(__float128 x)
{
__float128 y[2],z=0.0Q;
__float128 y[2],z=0;
int64_t n, ix;
/* High word of x. */
@ -225,10 +58,12 @@ tanq (__float128 x)
ix &= 0x7fffffffffffffffLL;
if(ix <= 0x3ffe921fb54442d1LL) return __quadmath_kernel_tanq(x,z,1);
/* tanl(Inf or NaN) is NaN */
/* tanq(Inf or NaN) is NaN */
else if (ix>=0x7fff000000000000LL) {
if (ix == 0x7fff000000000000LL) {
GET_FLT128_LSW64(n,x);
if (n == 0)
errno = EDOM;
}
return x-x; /* NaN */
}
@ -236,7 +71,7 @@ tanq (__float128 x)
/* argument reduction needed */
else {
n = __quadmath_rem_pio2q(x,y);
/* 1 -- n even, -1 -- n odd */
return __quadmath_kernel_tanq(y[0],y[1],1-((n&1)<<1));
return __quadmath_kernel_tanq(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even
-1 -- n odd */
}
}

165
libquadmath/math/tanq_kernel.c Normal file
View File

@ -0,0 +1,165 @@
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
Long double expansions are
Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
and are incorporated herein by permission of the author. The author
reserves the right to distribute this material elsewhere under different
copying permissions. These modifications are distributed here under
the following terms:
This library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
This library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this library; if not, see
<http://www.gnu.org/licenses/>. */
/* __quadmath_kernel_tanq( x, y, k )
* kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854
* Input x is assumed to be bounded by ~pi/4 in magnitude.
* Input y is the tail of x.
* Input k indicates whether tan (if k=1) or
* -1/tan (if k= -1) is returned.
*
* Algorithm
* 1. Since tan(-x) = -tan(x), we need only to consider positive x.
* 2. if x < 2^-57, return x with inexact if x!=0.
* 3. tan(x) is approximated by a rational form x + x^3 / 3 + x^5 R(x^2)
* on [0,0.67433].
*
* Note: tan(x+y) = tan(x) + tan'(x)*y
* ~ tan(x) + (1+x*x)*y
* Therefore, for better accuracy in computing tan(x+y), let
* r = x^3 * R(x^2)
* then
* tan(x+y) = x + (x^3 / 3 + (x^2 *(r+y)+y))
*
* 4. For x in [0.67433,pi/4], let y = pi/4 - x, then
* tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
* = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
*/
#include "quadmath-imp.h"
static const __float128
one = 1,
pio4hi = 7.8539816339744830961566084581987569936977E-1Q,
pio4lo = 2.1679525325309452561992610065108379921906E-35Q,
/* tan x = x + x^3 / 3 + x^5 T(x^2)/U(x^2)
0 <= x <= 0.6743316650390625
Peak relative error 8.0e-36 */
TH = 3.333333333333333333333333333333333333333E-1Q,
T0 = -1.813014711743583437742363284336855889393E7Q,
T1 = 1.320767960008972224312740075083259247618E6Q,
T2 = -2.626775478255838182468651821863299023956E4Q,
T3 = 1.764573356488504935415411383687150199315E2Q,
T4 = -3.333267763822178690794678978979803526092E-1Q,
U0 = -1.359761033807687578306772463253710042010E8Q,
U1 = 6.494370630656893175666729313065113194784E7Q,
U2 = -4.180787672237927475505536849168729386782E6Q,
U3 = 8.031643765106170040139966622980914621521E4Q,
U4 = -5.323131271912475695157127875560667378597E2Q;
/* 1.000000000000000000000000000000000000000E0 */
__float128
__quadmath_kernel_tanq (__float128 x, __float128 y, int iy)
{
__float128 z, r, v, w, s;
int32_t ix, sign;
ieee854_float128 u, u1;
u.value = x;
ix = u.words32.w0 & 0x7fffffff;
if (ix < 0x3fc60000) /* x < 2**-57 */
{
if ((int) x == 0)
{ /* generate inexact */
if ((ix | u.words32.w1 | u.words32.w2 | u.words32.w3
| (iy + 1)) == 0)
return one / fabsq (x);
else if (iy == 1)
{
math_check_force_underflow (x);
return x;
}
else
return -one / x;
}
}
if (ix >= 0x3ffe5942) /* |x| >= 0.6743316650390625 */
{
if ((u.words32.w0 & 0x80000000) != 0)
{
x = -x;
y = -y;
sign = -1;
}
else
sign = 1;
z = pio4hi - x;
w = pio4lo - y;
x = z + w;
y = 0.0;
}
z = x * x;
r = T0 + z * (T1 + z * (T2 + z * (T3 + z * T4)));
v = U0 + z * (U1 + z * (U2 + z * (U3 + z * (U4 + z))));
r = r / v;
s = z * x;
r = y + z * (s * r + y);
r += TH * s;
w = x + r;
if (ix >= 0x3ffe5942)
{
v = (__float128) iy;
w = (v - 2.0 * (x - (w * w / (w + v) - r)));
/* SIGN is set for arguments that reach this code, but not
otherwise, resulting in warnings that it may be used
uninitialized although in the cases where it is used it has
always been set. */
if (sign < 0)
w = -w;
return w;
}
if (iy == 1)
return w;
else
{ /* if allow error up to 2 ulp,
simply return -1.0/(x+r) here */
/* compute -1.0/(x+r) accurately */
u1.value = w;
u1.words32.w2 = 0;
u1.words32.w3 = 0;
v = r - (u1.value - x); /* u1+v = r+x */
z = -1.0 / w;
u.value = z;
u.words32.w2 = 0;
u.words32.w3 = 0;
s = 1.0 + u.value * u1.value;
return u.value + z * (s + u.value * v);
}
}

216
libquadmath/math/tgammaq.c
View File

@ -1,8 +1,8 @@
/* Implementation of gamma function according to ISO C.
Copyright (C) 1997, 1999, 2002, 2004 Free Software Foundation, Inc.
Copyright (C) 1997-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and
Jakub Jelinek <jj@ultra.linux.cz, 1999.
Jakub Jelinek <jj@ultra.linux.cz, 1999.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
@ -15,39 +15,209 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#include "quadmath-imp.h"
__float128
tgammaq (__float128 x)
{
/* We don't have a real gamma implementation now. We'll use lgamma
and the exp function. But due to the required boundary
conditions we must check some values separately. */
int sign;
__float128 ret;
ret = __quadmath_gammaq_r (x, &sign);
return sign < 0 ? -ret : ret;
}
/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) inside exp in Stirling's
approximation to gamma function. */
static const __float128 gamma_coeff[] =
{
0x1.5555555555555555555555555555p-4Q,
-0xb.60b60b60b60b60b60b60b60b60b8p-12Q,
0x3.4034034034034034034034034034p-12Q,
-0x2.7027027027027027027027027028p-12Q,
0x3.72a3c5631fe46ae1d4e700dca8f2p-12Q,
-0x7.daac36664f1f207daac36664f1f4p-12Q,
0x1.a41a41a41a41a41a41a41a41a41ap-8Q,
-0x7.90a1b2c3d4e5f708192a3b4c5d7p-8Q,
0x2.dfd2c703c0cfff430edfd2c703cp-4Q,
-0x1.6476701181f39edbdb9ce625987dp+0Q,
0xd.672219167002d3a7a9c886459cp+0Q,
-0x9.cd9292e6660d55b3f712eb9e07c8p+4Q,
0x8.911a740da740da740da740da741p+8Q,
-0x8.d0cc570e255bf59ff6eec24b49p+12Q,
};
#define NCOEFF (sizeof (gamma_coeff) / sizeof (gamma_coeff[0]))
/* Return gamma (X), for positive X less than 1775, in the form R *
2^(*EXP2_ADJ), where R is the return value and *EXP2_ADJ is set to
avoid overflow or underflow in intermediate calculations. */
static __float128
gammal_positive (__float128 x, int *exp2_adj)
{
int local_signgam;
if (x < 0.5Q)
{
*exp2_adj = 0;
return expq (__quadmath_lgammaq_r (x + 1, &local_signgam)) / x;
}
else if (x <= 1.5Q)
{
*exp2_adj = 0;
return expq (__quadmath_lgammaq_r (x, &local_signgam));
}
else if (x < 12.5Q)
{
/* Adjust into the range for using exp (lgamma). */
*exp2_adj = 0;
__float128 n = ceilq (x - 1.5Q);
__float128 x_adj = x - n;
__float128 eps;
__float128 prod = __quadmath_gamma_productq (x_adj, 0, n, &eps);
return (expq (__quadmath_lgammaq_r (x_adj, &local_signgam))
* prod * (1 + eps));
}
else
{
__float128 eps = 0;
__float128 x_eps = 0;
__float128 x_adj = x;
__float128 prod = 1;
if (x < 24)
{
/* Adjust into the range for applying Stirling's
approximation. */
__float128 n = ceilq (24 - x);
x_adj = x + n;
x_eps = (x - (x_adj - n));
prod = __quadmath_gamma_productq (x_adj - n, x_eps, n, &eps);
}
/* The result is now gamma (X_ADJ + X_EPS) / (PROD * (1 + EPS)).
Compute gamma (X_ADJ + X_EPS) using Stirling's approximation,
starting by computing pow (X_ADJ, X_ADJ) with a power of 2
factored out. */
__float128 exp_adj = -eps;
__float128 x_adj_int = roundq (x_adj);
__float128 x_adj_frac = x_adj - x_adj_int;
int x_adj_log2;
__float128 x_adj_mant = frexpq (x_adj, &x_adj_log2);
if (x_adj_mant < M_SQRT1_2q)
{
x_adj_log2--;
x_adj_mant *= 2;
}
*exp2_adj = x_adj_log2 * (int) x_adj_int;
__float128 ret = (powq (x_adj_mant, x_adj)
* exp2q (x_adj_log2 * x_adj_frac)
* expq (-x_adj)
* sqrtq (2 * M_PIq / x_adj)
/ prod);
exp_adj += x_eps * logq (x_adj);
__float128 bsum = gamma_coeff[NCOEFF - 1];
__float128 x_adj2 = x_adj * x_adj;
for (size_t i = 1; i <= NCOEFF - 1; i++)
bsum = bsum / x_adj2 + gamma_coeff[NCOEFF - 1 - i];
exp_adj += bsum / x_adj;
return ret + ret * expm1q (exp_adj);
}
}
__float128
__quadmath_gammaq_r (__float128 x, int *signgamp)
{
int64_t hx;
uint64_t lx;
__float128 res;
int sign;
__float128 ret;
GET_FLT128_WORDS64 (hx, lx, x);
if (((hx & 0x7fffffffffffffffLL) | lx) == 0)
/* Return value for x == 0 is Inf with divide by zero exception. */
return 1.0 / x;
{
/* Return value for x == 0 is Inf with divide by zero exception. */
*signgamp = 0;
return 1.0 / x;
}
if (hx < 0 && (uint64_t) hx < 0xffff000000000000ULL && rintq (x) == x)
/* Return value for integer x < 0 is NaN with invalid exception. */
return (x - x) / (x - x);
{
/* Return value for integer x < 0 is NaN with invalid exception. */
*signgamp = 0;
return (x - x) / (x - x);
}
if (hx == 0xffff000000000000ULL && lx == 0)
/* x == -Inf. According to ISO this is NaN. */
return x - x;
{
/* x == -Inf. According to ISO this is NaN. */
*signgamp = 0;
return x - x;
}
if ((hx & 0x7fff000000000000ULL) == 0x7fff000000000000ULL)
{
/* Positive infinity (return positive infinity) or NaN (return
NaN). */
*signgamp = 0;
return x + x;
}
/* XXX FIXME. */
res = expq (lgammaq (x));
return signbitq (x) ? -res : res;
if (x >= 1756)
{
/* Overflow. */
*signgamp = 0;
return FLT128_MAX * FLT128_MAX;
}
else
{
SET_RESTORE_ROUNDF128 (FE_TONEAREST);
if (x > 0)
{
*signgamp = 0;
int exp2_adj;
ret = gammal_positive (x, &exp2_adj);
ret = scalbnq (ret, exp2_adj);
}
else if (x >= -FLT128_EPSILON / 4)
{
*signgamp = 0;
ret = 1 / x;
}
else
{
__float128 tx = truncq (x);
*signgamp = (tx == 2 * truncq (tx / 2)) ? -1 : 1;
if (x <= -1775)
/* Underflow. */
ret = FLT128_MIN * FLT128_MIN;
else
{
__float128 frac = tx - x;
if (frac > 0.5Q)
frac = 1 - frac;
__float128 sinpix = (frac <= 0.25Q
? sinq (M_PIq * frac)
: cosq (M_PIq * (0.5Q - frac)));
int exp2_adj;
ret = M_PIq / (-x * sinpix
* gammal_positive (-x, &exp2_adj));
ret = scalbnq (ret, -exp2_adj);
math_check_force_underflow_nonneg (ret);
}
}
}
if (isinfq (ret) && x != 0)
{
if (*signgamp < 0)
return -(-copysignq (FLT128_MAX, ret) * FLT128_MAX);
else
return copysignq (FLT128_MAX, ret) * FLT128_MAX;
}
else if (ret == 0)
{
if (*signgamp < 0)
return -(-copysignq (FLT128_MIN, ret) * FLT128_MIN);
else
return copysignq (FLT128_MIN, ret) * FLT128_MIN;
}
else
return ret;
}

43
libquadmath/math/tgammaq_product.c Normal file
View File

@ -0,0 +1,43 @@
/* Compute a product of X, X+1, ..., with an error estimate.
Copyright (C) 2013-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#include "quadmath-imp.h"
/* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N
- 1, in the form R * (1 + *EPS) where the return value R is an
approximation to the product and *EPS is set to indicate the
approximate error in the return value. X is such that all the
values X + 1, ..., X + N - 1 are exactly representable, and X_EPS /
X is small enough that factors quadratic in it can be
neglected. */
__float128
__quadmath_gamma_productq (__float128 x, __float128 x_eps, int n, __float128 *eps)
{
SET_RESTORE_ROUNDF128 (FE_TONEAREST);
__float128 ret = x;
*eps = x_eps / x;
for (int i = 1; i < n; i++)
{
*eps += x_eps / (x + i);
__float128 lo;
mul_splitq (&ret, &lo, ret, x + i);
*eps += lo / ret;
}
return ret;
}

10
libquadmath/math/truncq.c
View File

@ -1,5 +1,5 @@
/* Truncate argument to nearest integral value not larger than the argument.
Copyright (C) 1997-2017 Free Software Foundation, Inc.
Copyright (C) 1997-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and
Jakub Jelinek <jj@ultra.linux.cz>, 1999.
@ -15,13 +15,13 @@
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#define NO_MATH_REDIRECT
#include "quadmath-imp.h"
__float128
truncq (__float128 x)
{

45
libquadmath/math/x2y2m1q.c
View File

@ -1,5 +1,5 @@
/* Compute x^2 + y^2 - 1, without large cancellation error.
Copyright (C) 2012 Free Software Foundation, Inc.
Copyright (C) 2012-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
@ -17,7 +17,6 @@
<http://www.gnu.org/licenses/>. */
#include "quadmath-imp.h"
#include <stdlib.h>
/* Calculate X + Y exactly and store the result in *HI + *LO. It is
given that |X| >= |Y| and the values are small enough that no
@ -31,18 +30,6 @@ add_split (__float128 *hi, __float128 *lo, __float128 x, __float128 y)
*lo = (x - *hi) + y;
}
/* Calculate X * Y exactly and store the result in *HI + *LO. It is
given that the values are small enough that no overflow occurs and
large enough (or zero) that no underflow occurs. */
static inline void
mul_split (__float128 *hi, __float128 *lo, __float128 x, __float128 y)
{
/* Fast built-in fused multiply-add. */
*hi = x * y;
*lo = fmaq (x, y, -*hi);
}
/* Compare absolute values of floating-point values pointed to by P
and Q for qsort. */
@ -60,34 +47,26 @@ compare (const void *p, const void *q)
}
/* Return X^2 + Y^2 - 1, computed without large cancellation error.
It is given that 1 > X >= Y >= epsilon / 2, and that either X >=
0.75 or Y >= 0.5. */
It is given that 1 > X >= Y >= epsilon / 2, and that X^2 + Y^2 >=
0.5. */
__float128
__quadmath_x2y2m1q (__float128 x, __float128 y)
{
__float128 vals[4];
size_t i;
/* FIXME: SET_RESTORE_ROUNDL (FE_TONEAREST); */
mul_split (&vals[1], &vals[0], x, x);
mul_split (&vals[3], &vals[2], y, y);
if (x >= 0.75Q)
vals[1] -= 1.0Q;
else
{
vals[1] -= 0.5Q;
vals[3] -= 0.5Q;
}
qsort (vals, 4, sizeof (__float128), compare);
__float128 vals[5];
SET_RESTORE_ROUNDF128 (FE_TONEAREST);
mul_splitq (&vals[1], &vals[0], x, x);
mul_splitq (&vals[3], &vals[2], y, y);
vals[4] = -1;
qsort (vals, 5, sizeof (__float128), compare);
/* Add up the values so that each element of VALS has absolute value
at most equal to the last set bit of the next nonzero
element. */
for (i = 0; i <= 2; i++)
for (size_t i = 0; i <= 3; i++)
{
add_split (&vals[i + 1], &vals[i], vals[i + 1], vals[i]);
qsort (vals + i + 1, 3 - i, sizeof (__float128), compare);
qsort (vals + i + 1, 4 - i, sizeof (__float128), compare);
}
/* Now any error from this addition will be small. */
return vals[3] + vals[2] + vals[1] + vals[0];
return vals[4] + vals[3] + vals[2] + vals[1] + vals[0];
}

109
libquadmath/quadmath-imp.h
View File

@ -21,10 +21,16 @@ Boston, MA 02110-1301, USA. */
#ifndef QUADMATH_IMP_H
#define QUADMATH_IMP_H
#include <errno.h>
#include <limits.h>
#include <stdbool.h>
#include <stdint.h>
#include <stdlib.h>
#include "quadmath.h"
#include "config.h"
#ifdef HAVE_FENV_H
# include <fenv.h>
#endif
/* Under IEEE 754, an architecture may determine tininess of
@ -36,6 +42,10 @@ Boston, MA 02110-1301, USA. */
#define TININESS_AFTER_ROUNDING 1
#define HIGH_ORDER_BIT_IS_SET_FOR_SNAN 0
#define FIX_FLT128_LONG_CONVERT_OVERFLOW 0
#define FIX_FLT128_LLONG_CONVERT_OVERFLOW 0
/* Prototypes for internal functions. */
extern int32_t __quadmath_rem_pio2q (__float128, __float128 *);
@ -43,9 +53,24 @@ extern void __quadmath_kernel_sincosq (__float128, __float128, __float128 *,
__float128 *, int);
extern __float128 __quadmath_kernel_sinq (__float128, __float128, int);
extern __float128 __quadmath_kernel_cosq (__float128, __float128);
extern __float128 __quadmath_kernel_tanq (__float128, __float128, int);
extern __float128 __quadmath_gamma_productq (__float128, __float128, int,
__float128 *);
extern __float128 __quadmath_gammaq_r (__float128, int *);
extern __float128 __quadmath_lgamma_negq (__float128, int *);
extern __float128 __quadmath_lgamma_productq (__float128, __float128,
__float128, int);
extern __float128 __quadmath_lgammaq_r (__float128, int *);
extern __float128 __quadmath_x2y2m1q (__float128 x, __float128 y);
extern int __quadmath_isinf_nsq (__float128 x);
extern __complex128 __quadmath_kernel_casinhq (__complex128, int);
static inline void
mul_splitq (__float128 *hi, __float128 *lo, __float128 x, __float128 y)
{
/* Fast built-in fused multiply-add. */
*hi = x * y;
*lo = fmaq (x, y, -*hi);
}
@ -227,4 +252,86 @@ do { \
} \
while (0)
/* Likewise, for both real and imaginary parts of a complex
result. */
#define math_check_force_underflow_complex(x) \
do \
{ \
__typeof (x) force_underflow_complex_tmp = (x); \
math_check_force_underflow (__real__ force_underflow_complex_tmp); \
math_check_force_underflow (__imag__ force_underflow_complex_tmp); \
} \
while (0)
#ifndef HAVE_FENV_H
# define feraiseexcept(arg) ((void) 0)
typedef int fenv_t;
# define feholdexcept(arg) ((void) 0)
# define fesetround(arg) ((void) 0)
# define feupdateenv(arg) ((void) (arg))
# define fesetenv(arg) ((void) (arg))
# define fetestexcept(arg) 0
# define feclearexcept(arg) ((void) 0)
#else
# ifndef HAVE_FEHOLDEXCEPT
# define feholdexcept(arg) ((void) 0)
# endif
# ifndef HAVE_FESETROUND
# define fesetround(arg) ((void) 0)
# endif
# ifndef HAVE_FEUPDATEENV
# define feupdateenv(arg) ((void) (arg))
# endif
# ifndef HAVE_FESETENV
# define fesetenv(arg) ((void) (arg))
# endif
# ifndef HAVE_FETESTEXCEPT
# define fetestexcept(arg) 0
# endif
#endif
#ifndef __glibc_likely
# define __glibc_likely(cond) __builtin_expect ((cond), 1)
#endif
#ifndef __glibc_unlikely
# define __glibc_unlikely(cond) __builtin_expect ((cond), 0)
#endif
#if defined HAVE_FENV_H && defined HAVE_FESETROUND && defined HAVE_FEUPDATEENV
struct rm_ctx
{
fenv_t env;
bool updated_status;
};
# define SET_RESTORE_ROUNDF128(RM) \
struct rm_ctx ctx __attribute__((cleanup (libc_feresetround_ctx))); \
libc_feholdsetround_ctx (&ctx, (RM))
static inline __attribute__ ((always_inline)) void
libc_feholdsetround_ctx (struct rm_ctx *ctx, int round)
{
ctx->updated_status = false;
/* Update rounding mode only if different. */
if (__glibc_unlikely (round != fegetround ()))
{
ctx->updated_status = true;
fegetenv (&ctx->env);
fesetround (round);
}
}
static inline __attribute__ ((always_inline)) void
libc_feresetround_ctx (struct rm_ctx *ctx)
{
/* Restore the rounding mode if updated. */
if (__glibc_unlikely (ctx->updated_status))
feupdateenv (&ctx->env);
}
#else
# define SET_RESTORE_ROUNDF128(RM) ((void) 0)
#endif
#endif

2
libquadmath/quadmath.h
View File

@ -58,6 +58,7 @@ extern __float128 coshq (__float128) __quadmath_throw;
extern __float128 cosq (__float128) __quadmath_throw;
extern __float128 erfq (__float128) __quadmath_throw;
extern __float128 erfcq (__float128) __quadmath_throw;
extern __float128 exp2q (__float128) __quadmath_throw;
extern __float128 expq (__float128) __quadmath_throw;
extern __float128 expm1q (__float128) __quadmath_throw;
extern __float128 fabsq (__float128) __quadmath_throw;
@ -73,6 +74,7 @@ extern __float128 hypotq (__float128, __float128) __quadmath_throw;
extern int isinfq (__float128) __quadmath_throw;
extern int ilogbq (__float128) __quadmath_throw;
extern int isnanq (__float128) __quadmath_throw;
extern int issignalingq (__float128) __quadmath_throw;
extern __float128 j0q (__float128) __quadmath_throw;
extern __float128 j1q (__float128) __quadmath_throw;
extern __float128 jnq (int, __float128) __quadmath_throw;

6
libquadmath/quadmath.map
View File

@ -101,3 +101,9 @@ QUADMATH_1.1 {
global:
logbq;
} QUADMATH_1.0;
QUADMATH_1.2 {
global:
exp2q;
issignalingq;
} QUADMATH_1.1;

2
libquadmath/quadmath_weak.h
View File

@ -50,6 +50,7 @@ __qmath3 (coshq)
__qmath3 (cosq)
__qmath3 (erfq)
__qmath3 (erfcq)
__qmath3 (exp2q)
__qmath3 (expq)
__qmath3 (expm1q)
__qmath3 (fabsq)
@ -65,6 +66,7 @@ __qmath3 (hypotq)
__qmath3 (ilogbq)
__qmath3 (isinfq)
__qmath3 (isnanq)
__qmath3 (issignalingq)
__qmath3 (j0q)
__qmath3 (j1q)
__qmath3 (jnq)

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