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New expf, exp2f, logf, log2f and powf implementations 

Based on code from https://github.com/ARM-software/optimized-routines/

This patch adds a highly optimized generic implementation of expf,
exp2f, logf, log2f and powf.  The new functions are not only
faster (6x for powf!), but are also smaller and more accurate.
In order to achieve this, the algorithm uses double precision
arithmetic for accuracy, avoids divisions and uses small table
lookups to minimize the polynomials.  Special cases are handled
inline to avoid the unnecessary overhead of wrapper functions and
set errno to POSIX requirements.

The new functions are added under newlib/libm/common, but the old
implementations are kept (in newlib/libm/math) for non-IEEE or
pre-C99 systems.  Targets can enable the new math code by defining
__OBSOLETE_MATH_DEFAULT to 0 in newlib/libc/include/machine/ieeefp.h,
users can override the default by defining __OBSOLETE_MATH.
Currently the new code is enabled for AArch64 and AArch32 with VFP.
Targets with a single precision FPU may still prefer the old
implementation.

libm.a size changes:
arm: -1692
arm/thumb/v7-a/nofp: -878
arm/thumb/v7-a+fp/hard: -864
arm/thumb/v7-a+fp/softfp: -908
aarch64: -1476
This commit is contained in:
Szabolcs Nagy 2017-05-25 16:41:38 +01:00 committed by Corinna Vinschen
parent c165a27c01
commit c156098271
24 changed files with 1337 additions and 86 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

27
newlib/libc/include/machine/ieeefp.h
View File

@ -48,6 +48,23 @@
This represents what type a float arg is passed as. It is used when the type is
not promoted to double.
__OBSOLETE_MATH_DEFAULT
Default value for __OBSOLETE_MATH if that's not set by the user.
It should be set here based on predefined feature macros.
__OBSOLETE_MATH
If set to 1 then some new math code will be disabled and older libm
code will be used instead. This is necessary because the new math
code does not support all targets, it assumes that the toolchain has
ISO C99 support (hexfloat literals, standard fenv semantics), the
target has IEEE-754 conforming binary32 float and binary64 double
(not mixed endian) representation, standard SNaN representation,
double and single precision arithmetics has similar latency and it
has no legacy SVID matherr support, only POSIX errno and fenv
exception based error handling.
*/
#if (defined(__arm__) || defined(__thumb__)) && !defined(__MAVERICK__)
@ -61,6 +78,7 @@
# else
# define __IEEE_BIG_ENDIAN
# endif
# define __OBSOLETE_MATH_DEFAULT 0
#else
# define __IEEE_BIG_ENDIAN
# ifdef __ARMEL__
@ -75,6 +93,7 @@
#else
#define __IEEE_BIG_ENDIAN
#endif
#define __OBSOLETE_MATH_DEFAULT 0
#endif
#ifdef __epiphany__
@ -427,6 +446,14 @@
#define __IEEE_BIG_ENDIAN
#endif
#ifndef __OBSOLETE_MATH_DEFAULT
/* Use old math code by default. */
#define __OBSOLETE_MATH_DEFAULT 1
#endif
#ifndef __OBSOLETE_MATH
#define __OBSOLETE_MATH __OBSOLETE_MATH_DEFAULT
#endif
#ifndef __IEEE_BIG_ENDIAN
#ifndef __IEEE_LITTLE_ENDIAN
#error Endianess not declared!!

7
newlib/libm/common/Makefile.am
View File

@ -18,11 +18,14 @@ fsrc = sf_finite.c sf_copysign.c sf_modf.c sf_scalbn.c \
sf_cbrt.c sf_exp10.c sf_expm1.c sf_ilogb.c \
sf_infinity.c sf_isinf.c sf_isinff.c sf_isnan.c sf_isnanf.c \
sf_log1p.c sf_nan.c sf_nextafter.c sf_pow10.c \
sf_rint.c sf_logb.c sf_log2.c \
sf_rint.c sf_logb.c \
sf_fdim.c sf_fma.c sf_fmax.c sf_fmin.c sf_fpclassify.c \
sf_lrint.c sf_llrint.c \
sf_lround.c sf_llround.c sf_nearbyint.c sf_remquo.c sf_round.c \
sf_scalbln.c sf_trunc.c
sf_scalbln.c sf_trunc.c \
sf_exp.c sf_exp2.c sf_exp2_data.c sf_log.c sf_log_data.c \
sf_log2.c sf_log2_data.c sf_pow_log2_data.c sf_pow.c \
math_errf.c
lsrc = atanl.c cosl.c sinl.c tanl.c tanhl.c frexpl.c modfl.c ceill.c fabsl.c \
floorl.c log1pl.c expm1l.c acosl.c asinl.c atan2l.c coshl.c sinhl.c \

148
newlib/libm/common/Makefile.in
View File

@ -78,21 +78,21 @@ am__objects_1 = lib_a-s_finite.$(OBJEXT) lib_a-s_copysign.$(OBJEXT) \
lib_a-s_modf.$(OBJEXT) lib_a-s_scalbn.$(OBJEXT) \
lib_a-s_cbrt.$(OBJEXT) lib_a-s_exp10.$(OBJEXT) \
lib_a-s_expm1.$(OBJEXT) lib_a-s_ilogb.$(OBJEXT) \
lib_a-s_infinity.$(OBJEXT) \
lib_a-s_isinf.$(OBJEXT) lib_a-s_isinfd.$(OBJEXT) \
lib_a-s_isnan.$(OBJEXT) lib_a-s_isnand.$(OBJEXT) \
lib_a-s_log1p.$(OBJEXT) lib_a-s_nan.$(OBJEXT) \
lib_a-s_nextafter.$(OBJEXT) lib_a-s_pow10.$(OBJEXT) \
lib_a-s_rint.$(OBJEXT) lib_a-s_logb.$(OBJEXT) \
lib_a-s_log2.$(OBJEXT) lib_a-s_matherr.$(OBJEXT) \
lib_a-s_lib_ver.$(OBJEXT) lib_a-s_fdim.$(OBJEXT) \
lib_a-s_fma.$(OBJEXT) lib_a-s_fmax.$(OBJEXT) \
lib_a-s_fmin.$(OBJEXT) lib_a-s_fpclassify.$(OBJEXT) \
lib_a-s_lrint.$(OBJEXT) lib_a-s_llrint.$(OBJEXT) \
lib_a-s_lround.$(OBJEXT) lib_a-s_llround.$(OBJEXT) \
lib_a-s_nearbyint.$(OBJEXT) lib_a-s_remquo.$(OBJEXT) \
lib_a-s_round.$(OBJEXT) lib_a-s_scalbln.$(OBJEXT) \
lib_a-s_signbit.$(OBJEXT) lib_a-s_trunc.$(OBJEXT)
lib_a-s_infinity.$(OBJEXT) lib_a-s_isinf.$(OBJEXT) \
lib_a-s_isinfd.$(OBJEXT) lib_a-s_isnan.$(OBJEXT) \
lib_a-s_isnand.$(OBJEXT) lib_a-s_log1p.$(OBJEXT) \
lib_a-s_nan.$(OBJEXT) lib_a-s_nextafter.$(OBJEXT) \
lib_a-s_pow10.$(OBJEXT) lib_a-s_rint.$(OBJEXT) \
lib_a-s_logb.$(OBJEXT) lib_a-s_log2.$(OBJEXT) \
lib_a-s_matherr.$(OBJEXT) lib_a-s_lib_ver.$(OBJEXT) \
lib_a-s_fdim.$(OBJEXT) lib_a-s_fma.$(OBJEXT) \
lib_a-s_fmax.$(OBJEXT) lib_a-s_fmin.$(OBJEXT) \
lib_a-s_fpclassify.$(OBJEXT) lib_a-s_lrint.$(OBJEXT) \
lib_a-s_llrint.$(OBJEXT) lib_a-s_lround.$(OBJEXT) \
lib_a-s_llround.$(OBJEXT) lib_a-s_nearbyint.$(OBJEXT) \
lib_a-s_remquo.$(OBJEXT) lib_a-s_round.$(OBJEXT) \
lib_a-s_scalbln.$(OBJEXT) lib_a-s_signbit.$(OBJEXT) \
lib_a-s_trunc.$(OBJEXT)
am__objects_2 = lib_a-sf_finite.$(OBJEXT) lib_a-sf_copysign.$(OBJEXT) \
lib_a-sf_modf.$(OBJEXT) lib_a-sf_scalbn.$(OBJEXT) \
lib_a-sf_cbrt.$(OBJEXT) lib_a-sf_exp10.$(OBJEXT) \
@ -102,14 +102,19 @@ am__objects_2 = lib_a-sf_finite.$(OBJEXT) lib_a-sf_copysign.$(OBJEXT) \
lib_a-sf_isnanf.$(OBJEXT) lib_a-sf_log1p.$(OBJEXT) \
lib_a-sf_nan.$(OBJEXT) lib_a-sf_nextafter.$(OBJEXT) \
lib_a-sf_pow10.$(OBJEXT) lib_a-sf_rint.$(OBJEXT) \
lib_a-sf_logb.$(OBJEXT) lib_a-sf_log2.$(OBJEXT) \
lib_a-sf_fdim.$(OBJEXT) lib_a-sf_fma.$(OBJEXT) \
lib_a-sf_fmax.$(OBJEXT) lib_a-sf_fmin.$(OBJEXT) \
lib_a-sf_fpclassify.$(OBJEXT) lib_a-sf_lrint.$(OBJEXT) \
lib_a-sf_llrint.$(OBJEXT) lib_a-sf_lround.$(OBJEXT) \
lib_a-sf_llround.$(OBJEXT) lib_a-sf_nearbyint.$(OBJEXT) \
lib_a-sf_remquo.$(OBJEXT) lib_a-sf_round.$(OBJEXT) \
lib_a-sf_scalbln.$(OBJEXT) lib_a-sf_trunc.$(OBJEXT)
lib_a-sf_logb.$(OBJEXT) lib_a-sf_fdim.$(OBJEXT) \
lib_a-sf_fma.$(OBJEXT) lib_a-sf_fmax.$(OBJEXT) \
lib_a-sf_fmin.$(OBJEXT) lib_a-sf_fpclassify.$(OBJEXT) \
lib_a-sf_lrint.$(OBJEXT) lib_a-sf_llrint.$(OBJEXT) \
lib_a-sf_lround.$(OBJEXT) lib_a-sf_llround.$(OBJEXT) \
lib_a-sf_nearbyint.$(OBJEXT) lib_a-sf_remquo.$(OBJEXT) \
lib_a-sf_round.$(OBJEXT) lib_a-sf_scalbln.$(OBJEXT) \
lib_a-sf_trunc.$(OBJEXT) lib_a-sf_exp.$(OBJEXT) \
lib_a-sf_exp2.$(OBJEXT) lib_a-sf_exp2_data.$(OBJEXT) \
lib_a-sf_log.$(OBJEXT) lib_a-sf_log_data.$(OBJEXT) \
lib_a-sf_log2.$(OBJEXT) lib_a-sf_log2_data.$(OBJEXT) \
lib_a-sf_pow_log2_data.$(OBJEXT) lib_a-sf_pow.$(OBJEXT) \
lib_a-math_errf.$(OBJEXT)
am__objects_3 = lib_a-atanl.$(OBJEXT) lib_a-cosl.$(OBJEXT) \
lib_a-sinl.$(OBJEXT) lib_a-tanl.$(OBJEXT) \
lib_a-tanhl.$(OBJEXT) lib_a-frexpl.$(OBJEXT) \
@ -148,21 +153,23 @@ lib_a_OBJECTS = $(am_lib_a_OBJECTS)
LTLIBRARIES = $(noinst_LTLIBRARIES)
libcommon_la_LIBADD =
am__objects_5 = s_finite.lo s_copysign.lo s_modf.lo s_scalbn.lo \
s_cbrt.lo s_exp10.lo s_expm1.lo s_ilogb.lo \
s_infinity.lo s_isinf.lo s_isinfd.lo s_isnan.lo s_isnand.lo \
s_log1p.lo s_nan.lo s_nextafter.lo s_pow10.lo s_rint.lo \
s_logb.lo s_log2.lo s_matherr.lo s_lib_ver.lo s_fdim.lo \
s_fma.lo s_fmax.lo s_fmin.lo s_fpclassify.lo s_lrint.lo \
s_llrint.lo s_lround.lo s_llround.lo s_nearbyint.lo \
s_remquo.lo s_round.lo s_scalbln.lo s_signbit.lo s_trunc.lo
s_cbrt.lo s_exp10.lo s_expm1.lo s_ilogb.lo s_infinity.lo \
s_isinf.lo s_isinfd.lo s_isnan.lo s_isnand.lo s_log1p.lo \
s_nan.lo s_nextafter.lo s_pow10.lo s_rint.lo s_logb.lo \
s_log2.lo s_matherr.lo s_lib_ver.lo s_fdim.lo s_fma.lo \
s_fmax.lo s_fmin.lo s_fpclassify.lo s_lrint.lo s_llrint.lo \
s_lround.lo s_llround.lo s_nearbyint.lo s_remquo.lo s_round.lo \
s_scalbln.lo s_signbit.lo s_trunc.lo
am__objects_6 = sf_finite.lo sf_copysign.lo sf_modf.lo sf_scalbn.lo \
sf_cbrt.lo sf_exp10.lo sf_expm1.lo sf_ilogb.lo sf_infinity.lo \
sf_isinf.lo sf_isinff.lo sf_isnan.lo sf_isnanf.lo sf_log1p.lo \
sf_nan.lo sf_nextafter.lo sf_pow10.lo sf_rint.lo sf_logb.lo \
sf_log2.lo sf_fdim.lo sf_fma.lo sf_fmax.lo sf_fmin.lo \
sf_fpclassify.lo sf_lrint.lo sf_llrint.lo sf_lround.lo \
sf_llround.lo sf_nearbyint.lo sf_remquo.lo sf_round.lo \
sf_scalbln.lo sf_trunc.lo
sf_fdim.lo sf_fma.lo sf_fmax.lo sf_fmin.lo sf_fpclassify.lo \
sf_lrint.lo sf_llrint.lo sf_lround.lo sf_llround.lo \
sf_nearbyint.lo sf_remquo.lo sf_round.lo sf_scalbln.lo \
sf_trunc.lo sf_exp.lo sf_exp2.lo sf_exp2_data.lo sf_log.lo \
sf_log_data.lo sf_log2.lo sf_log2_data.lo sf_pow_log2_data.lo \
sf_pow.lo math_errf.lo
am__objects_7 = atanl.lo cosl.lo sinl.lo tanl.lo tanhl.lo frexpl.lo \
modfl.lo ceill.lo fabsl.lo floorl.lo log1pl.lo expm1l.lo \
acosl.lo asinl.lo atan2l.lo coshl.lo sinhl.lo expl.lo \
@ -347,11 +354,14 @@ fsrc = sf_finite.c sf_copysign.c sf_modf.c sf_scalbn.c \
sf_cbrt.c sf_exp10.c sf_expm1.c sf_ilogb.c \
sf_infinity.c sf_isinf.c sf_isinff.c sf_isnan.c sf_isnanf.c \
sf_log1p.c sf_nan.c sf_nextafter.c sf_pow10.c \
sf_rint.c sf_logb.c sf_log2.c \
sf_rint.c sf_logb.c \
sf_fdim.c sf_fma.c sf_fmax.c sf_fmin.c sf_fpclassify.c \
sf_lrint.c sf_llrint.c \
sf_lround.c sf_llround.c sf_nearbyint.c sf_remquo.c sf_round.c \
sf_scalbln.c sf_trunc.c
sf_scalbln.c sf_trunc.c \
sf_exp.c sf_exp2.c sf_exp2_data.c sf_log.c sf_log_data.c \
sf_log2.c sf_log2_data.c sf_pow_log2_data.c sf_pow.c \
math_errf.c
lsrc = atanl.c cosl.c sinl.c tanl.c tanhl.c frexpl.c modfl.c ceill.c fabsl.c \
floorl.c log1pl.c expm1l.c acosl.c asinl.c atan2l.c coshl.c sinhl.c \
@ -796,12 +806,6 @@ lib_a-sf_logb.o: sf_logb.c
lib_a-sf_logb.obj: sf_logb.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_logb.obj `if test -f 'sf_logb.c'; then $(CYGPATH_W) 'sf_logb.c'; else $(CYGPATH_W) '$(srcdir)/sf_logb.c'; fi`
lib_a-sf_log2.o: sf_log2.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_log2.o `test -f 'sf_log2.c' || echo '$(srcdir)/'`sf_log2.c
lib_a-sf_log2.obj: sf_log2.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_log2.obj `if test -f 'sf_log2.c'; then $(CYGPATH_W) 'sf_log2.c'; else $(CYGPATH_W) '$(srcdir)/sf_log2.c'; fi`
lib_a-sf_fdim.o: sf_fdim.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_fdim.o `test -f 'sf_fdim.c' || echo '$(srcdir)/'`sf_fdim.c
@ -886,6 +890,66 @@ lib_a-sf_trunc.o: sf_trunc.c
lib_a-sf_trunc.obj: sf_trunc.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_trunc.obj `if test -f 'sf_trunc.c'; then $(CYGPATH_W) 'sf_trunc.c'; else $(CYGPATH_W) '$(srcdir)/sf_trunc.c'; fi`
lib_a-sf_exp.o: sf_exp.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_exp.o `test -f 'sf_exp.c' || echo '$(srcdir)/'`sf_exp.c
lib_a-sf_exp.obj: sf_exp.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_exp.obj `if test -f 'sf_exp.c'; then $(CYGPATH_W) 'sf_exp.c'; else $(CYGPATH_W) '$(srcdir)/sf_exp.c'; fi`
lib_a-sf_exp2.o: sf_exp2.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_exp2.o `test -f 'sf_exp2.c' || echo '$(srcdir)/'`sf_exp2.c
lib_a-sf_exp2.obj: sf_exp2.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_exp2.obj `if test -f 'sf_exp2.c'; then $(CYGPATH_W) 'sf_exp2.c'; else $(CYGPATH_W) '$(srcdir)/sf_exp2.c'; fi`
lib_a-sf_exp2_data.o: sf_exp2_data.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_exp2_data.o `test -f 'sf_exp2_data.c' || echo '$(srcdir)/'`sf_exp2_data.c
lib_a-sf_exp2_data.obj: sf_exp2_data.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_exp2_data.obj `if test -f 'sf_exp2_data.c'; then $(CYGPATH_W) 'sf_exp2_data.c'; else $(CYGPATH_W) '$(srcdir)/sf_exp2_data.c'; fi`
lib_a-sf_log.o: sf_log.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_log.o `test -f 'sf_log.c' || echo '$(srcdir)/'`sf_log.c
lib_a-sf_log.obj: sf_log.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_log.obj `if test -f 'sf_log.c'; then $(CYGPATH_W) 'sf_log.c'; else $(CYGPATH_W) '$(srcdir)/sf_log.c'; fi`
lib_a-sf_log_data.o: sf_log_data.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_log_data.o `test -f 'sf_log_data.c' || echo '$(srcdir)/'`sf_log_data.c
lib_a-sf_log_data.obj: sf_log_data.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_log_data.obj `if test -f 'sf_log_data.c'; then $(CYGPATH_W) 'sf_log_data.c'; else $(CYGPATH_W) '$(srcdir)/sf_log_data.c'; fi`
lib_a-sf_log2.o: sf_log2.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_log2.o `test -f 'sf_log2.c' || echo '$(srcdir)/'`sf_log2.c
lib_a-sf_log2.obj: sf_log2.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_log2.obj `if test -f 'sf_log2.c'; then $(CYGPATH_W) 'sf_log2.c'; else $(CYGPATH_W) '$(srcdir)/sf_log2.c'; fi`
lib_a-sf_log2_data.o: sf_log2_data.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_log2_data.o `test -f 'sf_log2_data.c' || echo '$(srcdir)/'`sf_log2_data.c
lib_a-sf_log2_data.obj: sf_log2_data.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_log2_data.obj `if test -f 'sf_log2_data.c'; then $(CYGPATH_W) 'sf_log2_data.c'; else $(CYGPATH_W) '$(srcdir)/sf_log2_data.c'; fi`
lib_a-sf_pow_log2_data.o: sf_pow_log2_data.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_pow_log2_data.o `test -f 'sf_pow_log2_data.c' || echo '$(srcdir)/'`sf_pow_log2_data.c
lib_a-sf_pow_log2_data.obj: sf_pow_log2_data.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_pow_log2_data.obj `if test -f 'sf_pow_log2_data.c'; then $(CYGPATH_W) 'sf_pow_log2_data.c'; else $(CYGPATH_W) '$(srcdir)/sf_pow_log2_data.c'; fi`
lib_a-sf_pow.o: sf_pow.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_pow.o `test -f 'sf_pow.c' || echo '$(srcdir)/'`sf_pow.c
lib_a-sf_pow.obj: sf_pow.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_pow.obj `if test -f 'sf_pow.c'; then $(CYGPATH_W) 'sf_pow.c'; else $(CYGPATH_W) '$(srcdir)/sf_pow.c'; fi`
lib_a-math_errf.o: math_errf.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-math_errf.o `test -f 'math_errf.c' || echo '$(srcdir)/'`math_errf.c
lib_a-math_errf.obj: math_errf.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-math_errf.obj `if test -f 'math_errf.c'; then $(CYGPATH_W) 'math_errf.c'; else $(CYGPATH_W) '$(srcdir)/math_errf.c'; fi`
lib_a-atanl.o: atanl.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-atanl.o `test -f 'atanl.c' || echo '$(srcdir)/'`atanl.c

179
newlib/libm/common/math_config.h Normal file
View File

@ -0,0 +1,179 @@
/* Configuration for math routines.
Copyright (c) 2017 ARM Ltd. All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
are met:
1. Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
3. The name of the company may not be used to endorse or promote
products derived from this software without specific prior written
permission.
THIS SOFTWARE IS PROVIDED BY ARM LTD ``AS IS AND ANY EXPRESS OR IMPLIED
WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
IN NO EVENT SHALL ARM LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
#ifndef _MATH_CONFIG_H
#define _MATH_CONFIG_H
#include <math.h>
#include <stdint.h>
#ifndef WANT_ROUNDING
/* Correct special case results in non-nearest rounding modes. */
# define WANT_ROUNDING 1
#endif
#ifndef WANT_ERRNO
/* Set errno according to ISO C with (math_errhandling & MATH_ERRNO) != 0. */
# define WANT_ERRNO 1
#endif
#ifndef WANT_ERRNO_UFLOW
/* Set errno to ERANGE if result underflows to 0 (in all rounding modes). */
# define WANT_ERRNO_UFLOW (WANT_ROUNDING && WANT_ERRNO)
#endif
#ifndef TOINT_INTRINSICS
# define TOINT_INTRINSICS 0
#endif
#ifndef TOINT_RINT
# define TOINT_RINT 0
#endif
#ifndef TOINT_SHIFT
# define TOINT_SHIFT 1
#endif
static inline uint32_t
asuint (float f)
{
union
{
float f;
uint32_t i;
} u = {f};
return u.i;
}
static inline float
asfloat (uint32_t i)
{
union
{
uint32_t i;
float f;
} u = {i};
return u.f;
}
static inline uint64_t
asuint64 (double f)
{
union
{
double f;
uint64_t i;
} u = {f};
return u.i;
}
static inline double
asdouble (uint64_t i)
{
union
{
uint64_t i;
double f;
} u = {i};
return u.f;
}
#ifndef IEEE_754_2008_SNAN
# define IEEE_754_2008_SNAN 1
#endif
static inline int
issignalingf_inline (float x)
{
uint32_t ix = asuint (x);
if (!IEEE_754_2008_SNAN)
return (ix & 0x7fc00000) == 0x7fc00000;
return 2 * (ix ^ 0x00400000) > 2u * 0x7fc00000;
}
#ifdef __GNUC__
# define HIDDEN __attribute__ ((__visibility__ ("hidden")))
# define NOINLINE __attribute__ ((noinline))
#else
# define HIDDEN
# define NOINLINE
#endif
HIDDEN float __math_oflowf (unsigned long);
HIDDEN float __math_uflowf (unsigned long);
HIDDEN float __math_may_uflowf (unsigned long);
HIDDEN float __math_divzerof (unsigned long);
HIDDEN float __math_invalidf (float);
/* Shared between expf, exp2f and powf. */
#define EXP2F_TABLE_BITS 5
#define EXP2F_POLY_ORDER 3
extern const struct exp2f_data
{
uint64_t tab[1 << EXP2F_TABLE_BITS];
double shift_scaled;
double poly[EXP2F_POLY_ORDER];
double shift;
double invln2_scaled;
double poly_scaled[EXP2F_POLY_ORDER];
} __exp2f_data HIDDEN;
#define LOGF_TABLE_BITS 4
#define LOGF_POLY_ORDER 4
extern const struct logf_data
{
struct
{
double invc, logc;
} tab[1 << LOGF_TABLE_BITS];
double ln2;
double poly[LOGF_POLY_ORDER - 1]; /* First order coefficient is 1. */
} __logf_data HIDDEN;
#define LOG2F_TABLE_BITS 4
#define LOG2F_POLY_ORDER 4
extern const struct log2f_data
{
struct
{
double invc, logc;
} tab[1 << LOG2F_TABLE_BITS];
double poly[LOG2F_POLY_ORDER];
} __log2f_data HIDDEN;
#define POWF_LOG2_TABLE_BITS 4
#define POWF_LOG2_POLY_ORDER 5
#if TOINT_INTRINSICS
# define POWF_SCALE_BITS EXP2F_TABLE_BITS
#else
# define POWF_SCALE_BITS 0
#endif
#define POWF_SCALE ((double) (1 << POWF_SCALE_BITS))
extern const struct powf_log2_data
{
struct
{
double invc, logc;
} tab[1 << POWF_LOG2_TABLE_BITS];
double poly[POWF_LOG2_POLY_ORDER];
} __powf_log2_data HIDDEN;
#endif

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/* Single-precision math error handling.
Copyright (c) 2017 ARM Ltd. All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
are met:
1. Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
3. The name of the company may not be used to endorse or promote
products derived from this software without specific prior written
permission.
THIS SOFTWARE IS PROVIDED BY ARM LTD ``AS IS AND ANY EXPRESS OR IMPLIED
WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
IN NO EVENT SHALL ARM LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
#include "fdlibm.h"
#if !__OBSOLETE_MATH
#include "math_config.h"
#if WANT_ERRNO
#include <errno.h>
/* NOINLINE reduces code size and avoids making math functions non-leaf
when the error handling is inlined. */
NOINLINE static float
with_errnof (float y, int e)
{
errno = e;
return y;
}
#else
#define with_errnof(x, e) (x)
#endif
/* NOINLINE prevents fenv semantics breaking optimizations. */
NOINLINE static float
xflowf (unsigned long sign, float y)
{
y = (sign ? -y : y) * y;
return with_errnof (y, ERANGE);
}
HIDDEN float
__math_uflowf (unsigned long sign)
{
return xflowf (sign, 0x1p-95f);
}
#if WANT_ERRNO_UFLOW
/* Underflows to zero in some non-nearest rounding mode, setting errno
is valid even if the result is non-zero, but in the subnormal range. */
HIDDEN float
__math_may_uflowf (unsigned long sign)
{
return xflowf (sign, 0x1.4p-75f);
}
#endif
HIDDEN float
__math_oflowf (unsigned long sign)
{
return xflowf (sign, 0x1p97f);
}
HIDDEN float
__math_divzerof (unsigned long sign)
{
float y = 0;
return with_errnof ((sign ? -1 : 1) / y, ERANGE);
}
HIDDEN float
__math_invalidf (float x)
{
float y = (x - x) / (x - x);
return isnan (x) ? y : with_errnof (y, EDOM);
}
#endif /* !__OBSOLETE_MATH */

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/* Single-precision e^x function.
Copyright (c) 2017 ARM Ltd. All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
are met:
1. Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
3. The name of the company may not be used to endorse or promote
products derived from this software without specific prior written
permission.
THIS SOFTWARE IS PROVIDED BY ARM LTD ``AS IS AND ANY EXPRESS OR IMPLIED
WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
IN NO EVENT SHALL ARM LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
#include "fdlibm.h"
#if !__OBSOLETE_MATH
#include <math.h>
#include <stdint.h>
#include "math_config.h"
/*
EXP2F_TABLE_BITS = 5
EXP2F_POLY_ORDER = 3
ULP error: 0.502 (nearest rounding.)
Relative error: 1.69 * 2^-34 in [-ln2/64, ln2/64] (before rounding.)
Wrong count: 170635 (all nearest rounding wrong results with fma.)
Non-nearest ULP error: 1 (rounded ULP error)
*/
#define N (1 << EXP2F_TABLE_BITS)
#define InvLn2N __exp2f_data.invln2_scaled
#define T __exp2f_data.tab
#define C __exp2f_data.poly_scaled
static inline uint32_t
top12 (float x)
{
return asuint (x) >> 20;
}
float
expf (float x)
{
uint32_t abstop;
uint64_t ki, t;
/* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
double_t kd, xd, z, r, r2, y, s;
xd = (double_t) x;
abstop = top12 (x) & 0x7ff;
if (__builtin_expect (abstop >= top12 (88.0f), 0))
{
/* |x| >= 88 or x is nan. */
if (asuint (x) == asuint (-INFINITY))
return 0.0f;
if (abstop >= top12 (INFINITY))
return x + x;
if (x > 0x1.62e42ep6f) /* x > log(0x1p128) ~= 88.72 */
return __math_oflowf (0);
if (x < -0x1.9fe368p6f) /* x < log(0x1p-150) ~= -103.97 */
return __math_uflowf (0);
#if WANT_ERRNO_UFLOW
if (x < -0x1.9d1d9ep6f) /* x < log(0x1p-149) ~= -103.28 */
return __math_may_uflowf (0);
#endif
}
/* x*N/Ln2 = k + r with r in [-1/2, 1/2] and int k. */
z = InvLn2N * xd;
/* Round and convert z to int, the result is in [-150*N, 128*N] and
ideally ties-to-even rule is used, otherwise the magnitude of r
can be bigger which gives larger approximation error. */
#if TOINT_INTRINSICS
kd = roundtoint (z);
ki = converttoint (z);
#elif TOINT_RINT
kd = rint (z);
ki = (long) kd;
#elif TOINT_SHIFT
# define SHIFT __exp2f_data.shift
kd = (double) (z + SHIFT); /* Rounding to double precision is required. */
ki = asuint64 (kd);
kd -= SHIFT;
#endif
r = z - kd;
/* exp(x) = 2^(k/N) * 2^(r/N) ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
t = T[ki % N];
t += ki << (52 - EXP2F_TABLE_BITS);
s = asdouble (t);
z = C[0] * r + C[1];
r2 = r * r;
y = C[2] * r + 1;
y = z * r2 + y;
y = y * s;
return (float) y;
}
#endif /* !__OBSOLETE_MATH */

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/* Single-precision 2^x function.
Copyright (c) 2017 ARM Ltd. All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
are met:
1. Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
3. The name of the company may not be used to endorse or promote
products derived from this software without specific prior written
permission.
THIS SOFTWARE IS PROVIDED BY ARM LTD ``AS IS AND ANY EXPRESS OR IMPLIED
WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
IN NO EVENT SHALL ARM LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
#include "fdlibm.h"
#if !__OBSOLETE_MATH
#include <math.h>
#include <stdint.h>
#include "math_config.h"
/*
EXP2F_TABLE_BITS = 5
EXP2F_POLY_ORDER = 3
ULP error: 0.502 (nearest rounding.)
Relative error: 1.69 * 2^-34 in [-1/64, 1/64] (before rounding.)
Wrong count: 168353 (all nearest rounding wrong results with fma.)
Non-nearest ULP error: 1 (rounded ULP error)
*/
#define N (1 << EXP2F_TABLE_BITS)
#define T __exp2f_data.tab
#define C __exp2f_data.poly
#define SHIFT __exp2f_data.shift_scaled
static inline uint32_t
top12 (float x)
{
return asuint (x) >> 20;
}
float
exp2f (float x)
{
uint32_t abstop;
uint64_t ki, t;
/* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
double_t kd, xd, z, r, r2, y, s;
xd = (double_t) x;
abstop = top12 (x) & 0x7ff;
if (__builtin_expect (abstop >= top12 (128.0f), 0))
{
/* |x| >= 128 or x is nan. */
if (asuint (x) == asuint (-INFINITY))
return 0.0f;
if (abstop >= top12 (INFINITY))
return x + x;
if (x > 0.0f)
return __math_oflowf (0);
if (x <= -150.0f)
return __math_uflowf (0);
#if WANT_ERRNO_UFLOW
if (x < -149.0f)
return __math_may_uflowf (0);
#endif
}
/* x = k/N + r with r in [-1/(2N), 1/(2N)] and int k. */
kd = (double) (xd + SHIFT); /* Rounding to double precision is required. */
ki = asuint64 (kd);
kd -= SHIFT; /* k/N for int k. */
r = xd - kd;
/* exp2(x) = 2^(k/N) * 2^r ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
t = T[ki % N];
t += ki << (52 - EXP2F_TABLE_BITS);
s = asdouble (t);
z = C[0] * r + C[1];
r2 = r * r;
y = C[2] * r + 1;
y = z * r2 + y;
y = y * s;
return (float) y;
}
#endif /* !__OBSOLETE_MATH */

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/* Shared data between expf, exp2f and powf.
Copyright (c) 2017 ARM Ltd. All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
are met:
1. Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
3. The name of the company may not be used to endorse or promote
products derived from this software without specific prior written
permission.
THIS SOFTWARE IS PROVIDED BY ARM LTD ``AS IS AND ANY EXPRESS OR IMPLIED
WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
IN NO EVENT SHALL ARM LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
#include "fdlibm.h"
#if !__OBSOLETE_MATH
#include "math_config.h"
#define N (1 << EXP2F_TABLE_BITS)
const struct exp2f_data __exp2f_data = {
/* tab[i] = uint(2^(i/N)) - (i << 52-BITS)
used for computing 2^(k/N) for an int |k| < 150 N as
double(tab[k%N] + (k << 52-BITS)) */
.tab = {
0x3ff0000000000000, 0x3fefd9b0d3158574, 0x3fefb5586cf9890f, 0x3fef9301d0125b51,
0x3fef72b83c7d517b, 0x3fef54873168b9aa, 0x3fef387a6e756238, 0x3fef1e9df51fdee1,
0x3fef06fe0a31b715, 0x3feef1a7373aa9cb, 0x3feedea64c123422, 0x3feece086061892d,
0x3feebfdad5362a27, 0x3feeb42b569d4f82, 0x3feeab07dd485429, 0x3feea47eb03a5585,
0x3feea09e667f3bcd, 0x3fee9f75e8ec5f74, 0x3feea11473eb0187, 0x3feea589994cce13,
0x3feeace5422aa0db, 0x3feeb737b0cdc5e5, 0x3feec49182a3f090, 0x3feed503b23e255d,
0x3feee89f995ad3ad, 0x3feeff76f2fb5e47, 0x3fef199bdd85529c, 0x3fef3720dcef9069,
0x3fef5818dcfba487, 0x3fef7c97337b9b5f, 0x3fefa4afa2a490da, 0x3fefd0765b6e4540,
},
.shift_scaled = 0x1.8p+52 / N,
.poly = { 0x1.c6af84b912394p-5, 0x1.ebfce50fac4f3p-3, 0x1.62e42ff0c52d6p-1 },
.shift = 0x1.8p+52,
.invln2_scaled = 0x1.71547652b82fep+0 * N,
.poly_scaled = {
0x1.c6af84b912394p-5/N/N/N, 0x1.ebfce50fac4f3p-3/N/N, 0x1.62e42ff0c52d6p-1/N
},
};
#endif /* !__OBSOLETE_MATH */

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/* Single-precision log function.
Copyright (c) 2017 ARM Ltd. All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
are met:
1. Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
3. The name of the company may not be used to endorse or promote
products derived from this software without specific prior written
permission.
THIS SOFTWARE IS PROVIDED BY ARM LTD ``AS IS AND ANY EXPRESS OR IMPLIED
WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
IN NO EVENT SHALL ARM LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
#include "fdlibm.h"
#if !__OBSOLETE_MATH
#include <math.h>
#include <stdint.h>
#include "math_config.h"
/*
LOGF_TABLE_BITS = 4
LOGF_POLY_ORDER = 4
ULP error: 0.818 (nearest rounding.)
Relative error: 1.957 * 2^-26 (before rounding.)
*/
#define T __logf_data.tab
#define A __logf_data.poly
#define Ln2 __logf_data.ln2
#define N (1 << LOGF_TABLE_BITS)
#define OFF 0x3f330000
float
logf (float x)
{
/* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
double_t z, r, r2, y, y0, invc, logc;
uint32_t ix, iz, tmp;
int k, i;
ix = asuint (x);
#if WANT_ROUNDING
/* Fix sign of zero with downward rounding when x==1. */
if (__builtin_expect (ix == 0x3f800000, 0))
return 0;
#endif
if (__builtin_expect (ix - 0x00800000 >= 0x7f800000 - 0x00800000, 0))
{
/* x < 0x1p-126 or inf or nan. */
if (ix * 2 == 0)
return __math_divzerof (1);
if (ix == 0x7f800000) /* log(inf) == inf. */
return x;
if ((ix & 0x80000000) || ix * 2 >= 0xff000000)
return __math_invalidf (x);
/* x is subnormal, normalize it. */
ix = asuint (x * 0x1p23f);
ix -= 23 << 23;
}
/* x = 2^k z; where z is in range [OFF,2*OFF] and exact.
The range is split into N subintervals.
The ith subinterval contains z and c is near its center. */
tmp = ix - OFF;
i = (tmp >> (23 - LOGF_TABLE_BITS)) % N;
k = (int32_t) tmp >> 23; /* arithmetic shift */
iz = ix - (tmp & 0x1ff << 23);
invc = T[i].invc;
logc = T[i].logc;
z = (double_t) asfloat (iz);
/* log(x) = log1p(z/c-1) + log(c) + k*Ln2 */
r = z * invc - 1;
y0 = logc + (double_t) k * Ln2;
/* Pipelined polynomial evaluation to approximate log1p(r). */
r2 = r * r;
y = A[1] * r + A[2];
y = A[0] * r2 + y;
y = y * r2 + (y0 + r);
return (float) y;
}
#endif /* !__OBSOLETE_MATH */

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/* sf_log2.c -- float version of s_log2.c.
* Modification of sf_exp10.c by Yaakov Selkowitz 2009.
*/
/* Single-precision log2 function.
Copyright (c) 2017 ARM Ltd. All rights reserved.
/*
* ====================================================
* 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.
* ====================================================
*/
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
are met:
1. Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
3. The name of the company may not be used to endorse or promote
products derived from this software without specific prior written
permission.
/*
* wrapper log2f(x)
*/
THIS SOFTWARE IS PROVIDED BY ARM LTD ``AS IS AND ANY EXPRESS OR IMPLIED
WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
IN NO EVENT SHALL ARM LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
#include "fdlibm.h"
#include <errno.h>
#if !__OBSOLETE_MATH
#include <math.h>
#undef log2
#undef log2f
#include <stdint.h>
#include "math_config.h"
#ifdef __STDC__
float log2f(float x) /* wrapper log2f */
#else
float log2f(x) /* wrapper log2f */
float x;
#endif
/*
LOG2F_TABLE_BITS = 4
LOG2F_POLY_ORDER = 4
ULP error: 0.752 (nearest rounding.)
Relative error: 1.9 * 2^-26 (before rounding.)
*/
#define N (1 << LOG2F_TABLE_BITS)
#define T __log2f_data.tab
#define A __log2f_data.poly
#define OFF 0x3f330000
float
log2f (float x)
{
return (logf(x) / (float_t) M_LN2);
}
/* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
double_t z, r, r2, p, y, y0, invc, logc;
uint32_t ix, iz, top, tmp;
int k, i;
#ifdef _DOUBLE_IS_32BITS
#ifdef __STDC__
double log2(double x)
#else
double log2(x)
double x;
ix = asuint (x);
#if WANT_ROUNDING
/* Fix sign of zero with downward rounding when x==1. */
if (__builtin_expect (ix == 0x3f800000, 0))
return 0;
#endif
{
return (double) log2f((float) x);
}
if (__builtin_expect (ix - 0x00800000 >= 0x7f800000 - 0x00800000, 0))
{
/* x < 0x1p-126 or inf or nan. */
if (ix * 2 == 0)
return __math_divzerof (1);
if (ix == 0x7f800000) /* log2(inf) == inf. */
return x;
if ((ix & 0x80000000) || ix * 2 >= 0xff000000)
return __math_invalidf (x);
/* x is subnormal, normalize it. */
ix = asuint (x * 0x1p23f);
ix -= 23 << 23;
}
#endif /* defined(_DOUBLE_IS_32BITS) */
/* x = 2^k z; where z is in range [OFF,2*OFF] and exact.
The range is split into N subintervals.
The ith subinterval contains z and c is near its center. */
tmp = ix - OFF;
i = (tmp >> (23 - LOG2F_TABLE_BITS)) % N;
top = tmp & 0xff800000;
iz = ix - top;
k = (int32_t) tmp >> 23; /* arithmetic shift */
invc = T[i].invc;
logc = T[i].logc;
z = (double_t) asfloat (iz);
/* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */
r = z * invc - 1;
y0 = logc + (double_t) k;
/* Pipelined polynomial evaluation to approximate log1p(r)/ln2. */
r2 = r * r;
y = A[1] * r + A[2];
y = A[0] * r2 + y;
p = A[3] * r + y0;
y = y * r2 + p;
return (float) y;
}
#endif /* !__OBSOLETE_MATH */

56
newlib/libm/common/sf_log2_data.c Normal file
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@ -0,0 +1,56 @@
/* Data definition for log2f.
Copyright (c) 2017 ARM Ltd. All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
are met:
1. Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
3. The name of the company may not be used to endorse or promote
products derived from this software without specific prior written
permission.
THIS SOFTWARE IS PROVIDED BY ARM LTD ``AS IS AND ANY EXPRESS OR IMPLIED
WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
IN NO EVENT SHALL ARM LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
#include "fdlibm.h"
#if !__OBSOLETE_MATH
#include "math_config.h"
const struct log2f_data __log2f_data = {
.tab = {
{ 0x1.661ec79f8f3bep+0, -0x1.efec65b963019p-2 },
{ 0x1.571ed4aaf883dp+0, -0x1.b0b6832d4fca4p-2 },
{ 0x1.49539f0f010bp+0, -0x1.7418b0a1fb77bp-2 },
{ 0x1.3c995b0b80385p+0, -0x1.39de91a6dcf7bp-2 },
{ 0x1.30d190c8864a5p+0, -0x1.01d9bf3f2b631p-2 },
{ 0x1.25e227b0b8eap+0, -0x1.97c1d1b3b7afp-3 },
{ 0x1.1bb4a4a1a343fp+0, -0x1.2f9e393af3c9fp-3 },
{ 0x1.12358f08ae5bap+0, -0x1.960cbbf788d5cp-4 },
{ 0x1.0953f419900a7p+0, -0x1.a6f9db6475fcep-5 },
{ 0x1p+0, 0x0p+0 },
{ 0x1.e608cfd9a47acp-1, 0x1.338ca9f24f53dp-4 },
{ 0x1.ca4b31f026aap-1, 0x1.476a9543891bap-3 },
{ 0x1.b2036576afce6p-1, 0x1.e840b4ac4e4d2p-3 },
{ 0x1.9c2d163a1aa2dp-1, 0x1.40645f0c6651cp-2 },
{ 0x1.886e6037841edp-1, 0x1.88e9c2c1b9ff8p-2 },
{ 0x1.767dcf5534862p-1, 0x1.ce0a44eb17bccp-2 },
},
.poly = {
-0x1.712b6f70a7e4dp-2, 0x1.ecabf496832ep-2, -0x1.715479ffae3dep-1,
0x1.715475f35c8b8p0,
}
};
#endif /* !__OBSOLETE_MATH */

56
newlib/libm/common/sf_log_data.c Normal file
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@ -0,0 +1,56 @@
/* Data definition for logf.
Copyright (c) 2017 ARM Ltd. All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
are met:
1. Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
3. The name of the company may not be used to endorse or promote
products derived from this software without specific prior written
permission.
THIS SOFTWARE IS PROVIDED BY ARM LTD ``AS IS AND ANY EXPRESS OR IMPLIED
WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
IN NO EVENT SHALL ARM LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
#include "fdlibm.h"
#if !__OBSOLETE_MATH
#include "math_config.h"
const struct logf_data __logf_data = {
.tab = {
{ 0x1.661ec79f8f3bep+0, -0x1.57bf7808caadep-2 },
{ 0x1.571ed4aaf883dp+0, -0x1.2bef0a7c06ddbp-2 },
{ 0x1.49539f0f010bp+0, -0x1.01eae7f513a67p-2 },
{ 0x1.3c995b0b80385p+0, -0x1.b31d8a68224e9p-3 },
{ 0x1.30d190c8864a5p+0, -0x1.6574f0ac07758p-3 },
{ 0x1.25e227b0b8eap+0, -0x1.1aa2bc79c81p-3 },
{ 0x1.1bb4a4a1a343fp+0, -0x1.a4e76ce8c0e5ep-4 },
{ 0x1.12358f08ae5bap+0, -0x1.1973c5a611cccp-4 },
{ 0x1.0953f419900a7p+0, -0x1.252f438e10c1ep-5 },
{ 0x1p+0, 0x0p+0 },
{ 0x1.e608cfd9a47acp-1, 0x1.aa5aa5df25984p-5 },
{ 0x1.ca4b31f026aap-1, 0x1.c5e53aa362eb4p-4 },
{ 0x1.b2036576afce6p-1, 0x1.526e57720db08p-3 },
{ 0x1.9c2d163a1aa2dp-1, 0x1.bc2860d22477p-3 },
{ 0x1.886e6037841edp-1, 0x1.1058bc8a07ee1p-2 },
{ 0x1.767dcf5534862p-1, 0x1.4043057b6ee09p-2 },
},
.ln2 = 0x1.62e42fefa39efp-1,
.poly = {
-0x1.00ea348b88334p-2, 0x1.5575b0be00b6ap-2, -0x1.ffffef20a4123p-2,
}
};
#endif /* !__OBSOLETE_MATH */

230
newlib/libm/common/sf_pow.c Normal file
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@ -0,0 +1,230 @@
/* Single-precision pow function.
Copyright (c) 2017 ARM Ltd. All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
are met:
1. Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
3. The name of the company may not be used to endorse or promote
products derived from this software without specific prior written
permission.
THIS SOFTWARE IS PROVIDED BY ARM LTD ``AS IS AND ANY EXPRESS OR IMPLIED
WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
IN NO EVENT SHALL ARM LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
#include "fdlibm.h"
#if !__OBSOLETE_MATH
#include <math.h>
#include <stdint.h>
#include "math_config.h"
/*
POWF_LOG2_POLY_ORDER = 5
EXP2F_TABLE_BITS = 5
ULP error: 0.82 (~ 0.5 + relerr*2^24)
relerr: 1.27 * 2^-26 (Relative error ~= 128*Ln2*relerr_log2 + relerr_exp2)
relerr_log2: 1.83 * 2^-33 (Relative error of logx.)
relerr_exp2: 1.69 * 2^-34 (Relative error of exp2(ylogx).)
*/
#define N (1 << POWF_LOG2_TABLE_BITS)
#define T __powf_log2_data.tab
#define A __powf_log2_data.poly
#define OFF 0x3f330000
/* Subnormal input is normalized so ix has negative biased exponent.
Output is multiplied by N (POWF_SCALE) if TOINT_INTRINICS is set. */
static inline double_t
log2_inline (uint32_t ix)
{
/* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
double_t z, r, r2, r4, p, q, y, y0, invc, logc;
uint32_t iz, top, tmp;
int k, i;
/* x = 2^k z; where z is in range [OFF,2*OFF] and exact.
The range is split into N subintervals.
The ith subinterval contains z and c is near its center. */
tmp = ix - OFF;
i = (tmp >> (23 - POWF_LOG2_TABLE_BITS)) % N;
top = tmp & 0xff800000;
iz = ix - top;
k = (int32_t) top >> (23 - POWF_SCALE_BITS); /* arithmetic shift */
invc = T[i].invc;
logc = T[i].logc;
z = (double_t) asfloat (iz);
/* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */
r = z * invc - 1;
y0 = logc + (double_t) k;
/* Pipelined polynomial evaluation to approximate log1p(r)/ln2. */
r2 = r * r;
y = A[0] * r + A[1];
p = A[2] * r + A[3];
r4 = r2 * r2;
q = A[4] * r + y0;
q = p * r2 + q;
y = y * r4 + q;
return y;
}
#undef N
#undef T
#define N (1 << EXP2F_TABLE_BITS)
#define T __exp2f_data.tab
#define SIGN_BIAS (1 << (EXP2F_TABLE_BITS + 11))
/* The output of log2 and thus the input of exp2 is either scaled by N
(in case of fast toint intrinsics) or not. The unscaled xd must be
in [-1021,1023], sign_bias sets the sign of the result. */
static inline double_t
exp2_inline (double_t xd, unsigned long sign_bias)
{
uint64_t ki, ski, t;
/* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
double_t kd, z, r, r2, y, s;
#if TOINT_INTRINSICS
# define C __exp2f_data.poly_scaled
/* N*x = k + r with r in [-1/2, 1/2] */
kd = roundtoint (xd); /* k */
ki = converttoint (xd);
#else
# define C __exp2f_data.poly
# define SHIFT __exp2f_data.shift_scaled
/* x = k/N + r with r in [-1/(2N), 1/(2N)] */
kd = (double) (xd + SHIFT); /* Rounding to double precision is required. */
ki = asuint64 (kd);
kd -= SHIFT; /* k/N */
#endif
r = xd - kd;
/* exp2(x) = 2^(k/N) * 2^r ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
t = T[ki % N];
ski = ki + sign_bias;
t += ski << (52 - EXP2F_TABLE_BITS);
s = asdouble (t);
z = C[0] * r + C[1];
r2 = r * r;
y = C[2] * r + 1;
y = z * r2 + y;
y = y * s;
return y;
}
/* Returns 0 if not int, 1 if odd int, 2 if even int. */
static inline int
checkint (uint32_t iy)
{
int e = iy >> 23 & 0xff;
if (e < 0x7f)
return 0;
if (e > 0x7f + 23)
return 2;
if (iy & ((1 << (0x7f + 23 - e)) - 1))
return 0;
if (iy & (1 << (0x7f + 23 - e)))
return 1;
return 2;
}
static inline int
zeroinfnan (uint32_t ix)
{
return 2 * ix - 1 >= 2u * 0x7f800000 - 1;
}
float
powf (float x, float y)
{
unsigned long sign_bias = 0;
uint32_t ix, iy;
ix = asuint (x);
iy = asuint (y);
if (__builtin_expect (ix - 0x00800000 >= 0x7f800000 - 0x00800000
|| zeroinfnan (iy),
0))
{
/* Either (x < 0x1p-126 or inf or nan) or (y is 0 or inf or nan). */
if (__builtin_expect (zeroinfnan (iy), 0))
{
if (2 * iy == 0)
return issignalingf_inline (x) ? x + y : 1.0f;
if (ix == 0x3f800000)
return issignalingf_inline (y) ? x + y : 1.0f;
if (2 * ix > 2u * 0x7f800000 || 2 * iy > 2u * 0x7f800000)
return x + y;
if (2 * ix == 2 * 0x3f800000)
return 1.0f;
if ((2 * ix < 2 * 0x3f800000) == !(iy & 0x80000000))
return 0.0f; /* |x|<1 && y==inf or |x|>1 && y==-inf. */
return y * y;
}
if (__builtin_expect (zeroinfnan (ix), 0))
{
float_t x2 = x * x;
if (ix & 0x80000000 && checkint (iy) == 1)
{
x2 = -x2;
sign_bias = 1;
}
#if WANT_ERRNO
if (2 * ix == 0 && iy & 0x80000000)
return __math_divzerof (sign_bias);
#endif
return iy & 0x80000000 ? 1 / x2 : x2;
}
/* x and y are non-zero finite. */
if (ix & 0x80000000)
{
/* Finite x < 0. */
int yint = checkint (iy);
if (yint == 0)
return __math_invalidf (x);
if (yint == 1)
sign_bias = SIGN_BIAS;
ix &= 0x7fffffff;
}
if (ix < 0x00800000)
{
/* Normalize subnormal x so exponent becomes negative. */
ix = asuint (x * 0x1p23f);
ix &= 0x7fffffff;
ix -= 23 << 23;
}
}
double_t logx = log2_inline (ix);
double_t ylogx = y * logx; /* Note: cannot overflow, y is single prec. */
if (__builtin_expect ((asuint64 (ylogx) >> 47 & 0xffff)
>= asuint64 (126.0 * POWF_SCALE) >> 47,
0))
{
/* |y*log(x)| >= 126. */
if (ylogx > 0x1.fffffffd1d571p+6 * POWF_SCALE)
return __math_oflowf (sign_bias);
if (ylogx <= -150.0 * POWF_SCALE)
return __math_uflowf (sign_bias);
#if WANT_ERRNO_UFLOW
if (ylogx < -149.0 * POWF_SCALE)
return __math_may_uflowf (sign_bias);
#endif
}
return (float) exp2_inline (ylogx, sign_bias);
}
#endif /* !__OBSOLETE_MATH */

57
newlib/libm/common/sf_pow_log2_data.c Normal file
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@ -0,0 +1,57 @@
/* Data definition for powf.
Copyright (c) 2017 ARM Ltd. All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
are met:
1. Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
3. The name of the company may not be used to endorse or promote
products derived from this software without specific prior written
permission.
THIS SOFTWARE IS PROVIDED BY ARM LTD ``AS IS AND ANY EXPRESS OR IMPLIED
WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
IN NO EVENT SHALL ARM LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
#include "fdlibm.h"
#if !__OBSOLETE_MATH
#include "math_config.h"
const struct powf_log2_data __powf_log2_data = {
.tab = {
{ 0x1.661ec79f8f3bep+0, -0x1.efec65b963019p-2 * POWF_SCALE },
{ 0x1.571ed4aaf883dp+0, -0x1.b0b6832d4fca4p-2 * POWF_SCALE },
{ 0x1.49539f0f010bp+0, -0x1.7418b0a1fb77bp-2 * POWF_SCALE },
{ 0x1.3c995b0b80385p+0, -0x1.39de91a6dcf7bp-2 * POWF_SCALE },
{ 0x1.30d190c8864a5p+0, -0x1.01d9bf3f2b631p-2 * POWF_SCALE },
{ 0x1.25e227b0b8eap+0, -0x1.97c1d1b3b7afp-3 * POWF_SCALE },
{ 0x1.1bb4a4a1a343fp+0, -0x1.2f9e393af3c9fp-3 * POWF_SCALE },
{ 0x1.12358f08ae5bap+0, -0x1.960cbbf788d5cp-4 * POWF_SCALE },
{ 0x1.0953f419900a7p+0, -0x1.a6f9db6475fcep-5 * POWF_SCALE },
{ 0x1p+0, 0x0p+0 * POWF_SCALE },
{ 0x1.e608cfd9a47acp-1, 0x1.338ca9f24f53dp-4 * POWF_SCALE },
{ 0x1.ca4b31f026aap-1, 0x1.476a9543891bap-3 * POWF_SCALE },
{ 0x1.b2036576afce6p-1, 0x1.e840b4ac4e4d2p-3 * POWF_SCALE },
{ 0x1.9c2d163a1aa2dp-1, 0x1.40645f0c6651cp-2 * POWF_SCALE },
{ 0x1.886e6037841edp-1, 0x1.88e9c2c1b9ff8p-2 * POWF_SCALE },
{ 0x1.767dcf5534862p-1, 0x1.ce0a44eb17bccp-2 * POWF_SCALE },
},
.poly = {
0x1.27616c9496e0bp-2 * POWF_SCALE, -0x1.71969a075c67ap-2 * POWF_SCALE,
0x1.ec70a6ca7baddp-2 * POWF_SCALE, -0x1.7154748bef6c8p-1 * POWF_SCALE,
0x1.71547652ab82bp0 * POWF_SCALE,
}
};
#endif /* !__OBSOLETE_MATH */

3
newlib/libm/math/Makefile.am
View File

@ -48,7 +48,8 @@ fsrc = kf_rem_pio2.c \
sf_frexp.c sf_ldexp.c \
sf_signif.c sf_sin.c \
sf_tan.c sf_tanh.c \
wf_exp2.c wf_tgamma.c
wf_exp2.c wf_tgamma.c \
wf_log2.c
lsrc = el_hypot.c

14
newlib/libm/math/Makefile.in
View File

@ -137,7 +137,8 @@ am__objects_2 = lib_a-kf_rem_pio2.$(OBJEXT) lib_a-kf_cos.$(OBJEXT) \
lib_a-sf_frexp.$(OBJEXT) lib_a-sf_ldexp.$(OBJEXT) \
lib_a-sf_signif.$(OBJEXT) lib_a-sf_sin.$(OBJEXT) \
lib_a-sf_tan.$(OBJEXT) lib_a-sf_tanh.$(OBJEXT) \
lib_a-wf_exp2.$(OBJEXT) lib_a-wf_tgamma.$(OBJEXT)
lib_a-wf_exp2.$(OBJEXT) lib_a-wf_tgamma.$(OBJEXT) \
lib_a-wf_log2.$(OBJEXT)
am__objects_3 = lib_a-el_hypot.$(OBJEXT)
@USE_LIBTOOL_FALSE@am_lib_a_OBJECTS = $(am__objects_1) \
@USE_LIBTOOL_FALSE@ $(am__objects_2) $(am__objects_3)
@ -169,7 +170,7 @@ am__objects_5 = kf_rem_pio2.lo kf_cos.lo kf_sin.lo kf_tan.lo \
wf_sincos.lo wf_drem.lo sf_asinh.lo sf_atan.lo sf_ceil.lo \
sf_cos.lo sf_erf.lo sf_fabs.lo sf_floor.lo sf_frexp.lo \
sf_ldexp.lo sf_signif.lo sf_sin.lo sf_tan.lo sf_tanh.lo \
wf_exp2.lo wf_tgamma.lo
wf_exp2.lo wf_tgamma.lo wf_log2.lo
am__objects_6 = el_hypot.lo
@USE_LIBTOOL_TRUE@am_libmath_la_OBJECTS = $(am__objects_4) \
@USE_LIBTOOL_TRUE@ $(am__objects_5) $(am__objects_6)
@ -372,7 +373,8 @@ fsrc = kf_rem_pio2.c \
sf_frexp.c sf_ldexp.c \
sf_signif.c sf_sin.c \
sf_tan.c sf_tanh.c \
wf_exp2.c wf_tgamma.c
wf_exp2.c wf_tgamma.c \
wf_log2.c
lsrc = el_hypot.c
libmath_la_LDFLAGS = -Xcompiler -nostdlib
@ -1270,6 +1272,12 @@ lib_a-wf_tgamma.o: wf_tgamma.c
lib_a-wf_tgamma.obj: wf_tgamma.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-wf_tgamma.obj `if test -f 'wf_tgamma.c'; then $(CYGPATH_W) 'wf_tgamma.c'; else $(CYGPATH_W) '$(srcdir)/wf_tgamma.c'; fi`
lib_a-wf_log2.o: wf_log2.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-wf_log2.o `test -f 'wf_log2.c' || echo '$(srcdir)/'`wf_log2.c
lib_a-wf_log2.obj: wf_log2.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-wf_log2.obj `if test -f 'wf_log2.c'; then $(CYGPATH_W) 'wf_log2.c'; else $(CYGPATH_W) '$(srcdir)/wf_log2.c'; fi`
lib_a-el_hypot.o: el_hypot.c
$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-el_hypot.o `test -f 'el_hypot.c' || echo '$(srcdir)/'`el_hypot.c

2
newlib/libm/math/ef_exp.c
View File

@ -15,6 +15,7 @@
#include "fdlibm.h"
#if __OBSOLETE_MATH
#ifdef __v810__
#define const
#endif
@ -97,3 +98,4 @@ P5 = 4.1381369442e-08; /* 0x3331bb4c */
return y*twom100;
}
}
#endif /* __OBSOLETE_MATH */

2
newlib/libm/math/ef_log.c
View File

@ -15,6 +15,7 @@
#include "fdlibm.h"
#if __OBSOLETE_MATH
#ifdef __STDC__
static const float
#else
@ -90,3 +91,4 @@ static float zero = 0.0;
return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
}
}
#endif /* __OBSOLETE_MATH */

2
newlib/libm/math/ef_pow.c
View File

@ -15,6 +15,7 @@
#include "fdlibm.h"
#if __OBSOLETE_MATH
#ifdef __v810__
#define const
#endif
@ -253,3 +254,4 @@ ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
else SET_FLOAT_WORD(z,j);
return s*z;
}
#endif /* __OBSOLETE_MATH */

2
newlib/libm/math/wf_exp.c
View File

@ -18,6 +18,7 @@
*/
#include "fdlibm.h"
#if __OBSOLETE_MATH
#include <errno.h>
#ifdef __STDC__
@ -101,3 +102,4 @@ u_threshold= -1.0397208405e+02; /* 0xc2cff1b5 */
}
#endif /* defined(_DOUBLE_IS_32BITS) */
#endif /* __OBSOLETE_MATH */

2
newlib/libm/math/wf_exp2.c
View File

@ -18,6 +18,7 @@
*/
#include "fdlibm.h"
#if __OBSOLETE_MATH
#include <errno.h>
#include <math.h>
@ -44,3 +45,4 @@
}
#endif /* defined(_DOUBLE_IS_32BITS) */
#endif /* __OBSOLETE_MATH */

2
newlib/libm/math/wf_log.c
View File

@ -18,6 +18,7 @@
*/
#include "fdlibm.h"
#if __OBSOLETE_MATH
#include <errno.h>
#ifdef __STDC__
@ -84,3 +85,4 @@
}
#endif /* defined(_DOUBLE_IS_32BITS) */
#endif /* __OBSOLETE_MATH */

50
newlib/libm/math/wf_log2.c Normal file
View File

@ -0,0 +1,50 @@
/* wf_log2.c -- float version of s_log2.c.
* Modification of sf_exp10.c by Yaakov Selkowitz 2009.
*/
/*
* ====================================================
* 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.
* ====================================================
*/
/*
* wrapper log2f(x)
*/
#include "fdlibm.h"
#if __OBSOLETE_MATH
#include <errno.h>
#include <math.h>
#undef log2
#undef log2f
#ifdef __STDC__
float log2f(float x) /* wrapper log2f */
#else
float log2f(x) /* wrapper log2f */
float x;
#endif
{
return (logf(x) / (float_t) M_LN2);
}
#ifdef _DOUBLE_IS_32BITS
#ifdef __STDC__
double log2(double x)
#else
double log2(x)
double x;
#endif
{
return (double) log2f((float) x);
}
#endif /* defined(_DOUBLE_IS_32BITS) */
#endif /* __OBSOLETE_MATH */

2
newlib/libm/math/wf_pow.c
View File

@ -18,6 +18,7 @@
*/
#include "fdlibm.h"
#if __OBSOLETE_MATH
#include <errno.h>
#ifdef __STDC__
@ -177,3 +178,4 @@
}
#endif /* defined(_DOUBLE_IS_32BITS) */
#endif /* __OBSOLETE_MATH */