New exp and exp2 implementations
The new implementations are provided under !__OBSOLETE_MATH, they use ISO C99 code. There are several settings, with the default one the worst case error in nearest rounding mode is 0.509 ULP for exp and 0.507 ULP for exp2 when a multiply and add is contracted into an fma. They use a shared 2 KB lookup table, on aarch64 .text+.rodata size of libm.a is increased by 1868 bytes. The w_*.c wrappers are disabled for the new code as it takes care of error handling inline. The old exp2(x) code used to be just pow(2,x) so the speedup there is more significant. The file name has no special prefix to avoid any name collision with existing files. Improvements on Cortex-A72: exp latency: 3.2x exp thruput: 4.1x exp2 latency: 7.8x exp2 thruput: 18.8x
This commit is contained in:
Szabolcs Nagy
Corinna Vinschen
parent
cfbcbd1c95
commit
fb929067db
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@ -12,7 +12,8 @@ src = s_finite.c s_copysign.c s_modf.c s_scalbn.c \
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s_fdim.c s_fma.c s_fmax.c s_fmin.c s_fpclassify.c \
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s_lrint.c s_llrint.c \
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s_lround.c s_llround.c s_nearbyint.c s_remquo.c s_round.c s_scalbln.c \
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s_signbit.c s_trunc.c
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s_signbit.c s_trunc.c \
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exp.c exp2.c exp_data.c math_err.c
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fsrc = sf_finite.c sf_copysign.c sf_modf.c sf_scalbn.c \
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sf_cbrt.c sf_exp10.c sf_expm1.c sf_ilogb.c \
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@ -93,7 +93,9 @@ am__objects_1 = lib_a-s_finite.$(OBJEXT) lib_a-s_copysign.$(OBJEXT) \
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lib_a-s_llround.$(OBJEXT) lib_a-s_nearbyint.$(OBJEXT) \
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lib_a-s_remquo.$(OBJEXT) lib_a-s_round.$(OBJEXT) \
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lib_a-s_scalbln.$(OBJEXT) lib_a-s_signbit.$(OBJEXT) \
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lib_a-s_trunc.$(OBJEXT)
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lib_a-s_trunc.$(OBJEXT) lib_a-exp.$(OBJEXT) \
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lib_a-exp2.$(OBJEXT) lib_a-exp_data.$(OBJEXT) \
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lib_a-math_err.$(OBJEXT)
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am__objects_2 = lib_a-sf_finite.$(OBJEXT) lib_a-sf_copysign.$(OBJEXT) \
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lib_a-sf_modf.$(OBJEXT) lib_a-sf_scalbn.$(OBJEXT) \
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lib_a-sf_cbrt.$(OBJEXT) lib_a-sf_exp10.$(OBJEXT) \
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@ -162,7 +164,8 @@ am__objects_5 = s_finite.lo s_copysign.lo s_modf.lo s_scalbn.lo \
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s_log2.lo s_matherr.lo s_lib_ver.lo s_fdim.lo s_fma.lo \
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s_fmax.lo s_fmin.lo s_fpclassify.lo s_lrint.lo s_llrint.lo \
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s_lround.lo s_llround.lo s_nearbyint.lo s_remquo.lo s_round.lo \
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s_scalbln.lo s_signbit.lo s_trunc.lo
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s_scalbln.lo s_signbit.lo s_trunc.lo exp.lo exp2.lo \
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exp_data.lo math_err.lo
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am__objects_6 = sf_finite.lo sf_copysign.lo sf_modf.lo sf_scalbn.lo \
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sf_cbrt.lo sf_exp10.lo sf_expm1.lo sf_ilogb.lo sf_infinity.lo \
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sf_isinf.lo sf_isinff.lo sf_isnan.lo sf_isnanf.lo sf_log1p.lo \
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@ -352,7 +355,8 @@ src = s_finite.c s_copysign.c s_modf.c s_scalbn.c \
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s_fdim.c s_fma.c s_fmax.c s_fmin.c s_fpclassify.c \
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s_lrint.c s_llrint.c \
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s_lround.c s_llround.c s_nearbyint.c s_remquo.c s_round.c s_scalbln.c \
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s_signbit.c s_trunc.c
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s_signbit.c s_trunc.c \
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exp.c exp2.c exp_data.c math_err.c
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fsrc = sf_finite.c sf_copysign.c sf_modf.c sf_scalbn.c \
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sf_cbrt.c sf_exp10.c sf_expm1.c sf_ilogb.c \
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@ -696,6 +700,30 @@ lib_a-s_trunc.o: s_trunc.c
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lib_a-s_trunc.obj: s_trunc.c
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$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-s_trunc.obj `if test -f 's_trunc.c'; then $(CYGPATH_W) 's_trunc.c'; else $(CYGPATH_W) '$(srcdir)/s_trunc.c'; fi`
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lib_a-exp.o: exp.c
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$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-exp.o `test -f 'exp.c' || echo '$(srcdir)/'`exp.c
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lib_a-exp.obj: exp.c
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$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-exp.obj `if test -f 'exp.c'; then $(CYGPATH_W) 'exp.c'; else $(CYGPATH_W) '$(srcdir)/exp.c'; fi`
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lib_a-exp2.o: exp2.c
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$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-exp2.o `test -f 'exp2.c' || echo '$(srcdir)/'`exp2.c
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lib_a-exp2.obj: exp2.c
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$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-exp2.obj `if test -f 'exp2.c'; then $(CYGPATH_W) 'exp2.c'; else $(CYGPATH_W) '$(srcdir)/exp2.c'; fi`
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lib_a-exp_data.o: exp_data.c
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$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-exp_data.o `test -f 'exp_data.c' || echo '$(srcdir)/'`exp_data.c
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lib_a-exp_data.obj: exp_data.c
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$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-exp_data.obj `if test -f 'exp_data.c'; then $(CYGPATH_W) 'exp_data.c'; else $(CYGPATH_W) '$(srcdir)/exp_data.c'; fi`
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lib_a-math_err.o: math_err.c
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$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-math_err.o `test -f 'math_err.c' || echo '$(srcdir)/'`math_err.c
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lib_a-math_err.obj: math_err.c
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$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-math_err.obj `if test -f 'math_err.c'; then $(CYGPATH_W) 'math_err.c'; else $(CYGPATH_W) '$(srcdir)/math_err.c'; fi`
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lib_a-sf_finite.o: sf_finite.c
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$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_finite.o `test -f 'sf_finite.c' || echo '$(srcdir)/'`sf_finite.c
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@ -0,0 +1,165 @@
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/* Double-precision e^x function.
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Copyright (c) 2018 Arm Ltd. All rights reserved.
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SPDX-License-Identifier: BSD-3-Clause
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Redistribution and use in source and binary forms, with or without
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modification, are permitted provided that the following conditions
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are met:
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1. Redistributions of source code must retain the above copyright
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notice, this list of conditions and the following disclaimer.
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2. Redistributions in binary form must reproduce the above copyright
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notice, this list of conditions and the following disclaimer in the
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documentation and/or other materials provided with the distribution.
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3. The name of the company may not be used to endorse or promote
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products derived from this software without specific prior written
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permission.
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THIS SOFTWARE IS PROVIDED BY Arm LTD ``AS IS AND ANY EXPRESS OR IMPLIED
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WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
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MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
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IN NO EVENT SHALL Arm LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
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TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
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LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
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NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
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#include "fdlibm.h"
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#if !__OBSOLETE_MATH
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#include <math.h>
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#include <stdint.h>
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#include "math_config.h"
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#define N (1 << EXP_TABLE_BITS)
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#define InvLn2N __exp_data.invln2N
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#define NegLn2hiN __exp_data.negln2hiN
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#define NegLn2loN __exp_data.negln2loN
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#define Shift __exp_data.shift
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#define T __exp_data.tab
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#define C2 __exp_data.poly[5 - EXP_POLY_ORDER]
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#define C3 __exp_data.poly[6 - EXP_POLY_ORDER]
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#define C4 __exp_data.poly[7 - EXP_POLY_ORDER]
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#define C5 __exp_data.poly[8 - EXP_POLY_ORDER]
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#define C6 __exp_data.poly[9 - EXP_POLY_ORDER]
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static inline double
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specialcase (double_t tmp, uint64_t sbits, uint64_t ki)
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{
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double_t scale, y;
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if ((ki & 0x80000000) == 0)
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{
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/* k > 0, the exponent of scale might have overflowed by <= 460. */
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sbits -= 1009ull << 52;
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scale = asdouble (sbits);
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y = 0x1p1009 * (scale + scale * tmp);
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return check_oflow (y);
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}
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/* k < 0, need special care in the subnormal range. */
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sbits += 1022ull << 52;
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scale = asdouble (sbits);
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y = scale + scale * tmp;
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if (y < 1.0)
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{
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/* Round y to the right precision before scaling it into the subnormal
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range to avoid double rounding that can cause 0.5+E/2 ulp error where
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E is the worst-case ulp error outside the subnormal range. So this
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is only useful if the goal is better than 1 ulp worst-case error. */
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double_t hi, lo;
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lo = scale - y + scale * tmp;
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hi = 1.0 + y;
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lo = 1.0 - hi + y + lo;
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y = eval_as_double (hi + lo) - 1.0;
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/* Avoid -0.0 with downward rounding. */
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if (WANT_ROUNDING && y == 0.0)
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y = 0.0;
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/* The underflow exception needs to be signaled explicitly. */
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force_eval_double (opt_barrier_double (0x1p-1022) * 0x1p-1022);
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}
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y = 0x1p-1022 * y;
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return check_uflow (y);
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}
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static inline uint32_t
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top12 (double x)
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{
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return asuint64 (x) >> 52;
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}
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double
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exp (double x)
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{
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uint32_t abstop;
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uint64_t ki, idx, top, sbits;
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/* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
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double_t kd, z, r, r2, scale, tail, tmp;
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abstop = top12 (x) & 0x7ff;
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if (unlikely (abstop - top12 (0x1p-54) >= top12 (512.0) - top12 (0x1p-54)))
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{
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if (abstop - top12 (0x1p-54) >= 0x80000000)
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/* Avoid spurious underflow for tiny x. */
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/* Note: 0 is common input. */
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return WANT_ROUNDING ? 1.0 + x : 1.0;
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if (abstop >= top12 (1024.0))
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{
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if (asuint64 (x) == asuint64 (-INFINITY))
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return 0.0;
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if (abstop >= top12 (INFINITY))
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return 1.0 + x;
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if (asuint64 (x) >> 63)
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return __math_uflow (0);
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else
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return __math_oflow (0);
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}
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/* Large x is special cased below. */
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abstop = 0;
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}
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/* exp(x) = 2^(k/N) * exp(r), with exp(r) in [2^(-1/2N),2^(1/2N)]. */
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/* x = ln2/N*k + r, with int k and r in [-ln2/2N, ln2/2N]. */
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z = InvLn2N * x;
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#if TOINT_INTRINSICS
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kd = roundtoint (z);
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ki = converttoint (z);
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#elif EXP_USE_TOINT_NARROW
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/* z - kd is in [-0.5-2^-16, 0.5] in all rounding modes. */
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kd = eval_as_double (z + Shift);
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ki = asuint64 (kd) >> 16;
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kd = (double_t) (int32_t) ki;
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#else
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/* z - kd is in [-1, 1] in non-nearest rounding modes. */
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kd = eval_as_double (z + Shift);
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ki = asuint64 (kd);
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kd -= Shift;
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#endif
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r = x + kd*NegLn2hiN + kd*NegLn2loN;
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/* 2^(k/N) ~= scale * (1 + tail). */
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idx = 2*(ki % N);
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top = ki << (52 - EXP_TABLE_BITS);
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tail = asdouble (T[idx]);
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/* This is only a valid scale when -1023*N < k < 1024*N. */
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sbits = T[idx + 1] + top;
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/* exp(x) = 2^(k/N) * exp(r) ~= scale + scale * (tail + exp(r) - 1). */
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/* Evaluation is optimized assuming superscalar pipelined execution. */
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r2 = r*r;
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/* Without fma the worst case error is 0.25/N ulp larger. */
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/* Worst case error is less than 0.5+1.11/N+(abs poly error * 2^53) ulp. */
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#if EXP_POLY_ORDER == 4
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tmp = tail + r + r2*C2 + r*r2*(C3 + r*C4);
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#elif EXP_POLY_ORDER == 5
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tmp = tail + r + r2*(C2 + r*C3) + r2*r2*(C4 + r*C5);
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#elif EXP_POLY_ORDER == 6
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tmp = tail + r + r2*(0.5 + r*C3) + r2*r2*(C4 + r*C5 + r2*C6);
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#endif
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if (unlikely (abstop == 0))
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return specialcase (tmp, sbits, ki);
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scale = asdouble (sbits);
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/* Note: tmp == 0 or |tmp| > 2^-200 and scale > 2^-739, so there
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is no spurious underflow here even without fma. */
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return scale + scale * tmp;
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}
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#endif
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@ -0,0 +1,152 @@
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/* Double-precision 2^x function.
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Copyright (c) 2018 Arm Ltd. All rights reserved.
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SPDX-License-Identifier: BSD-3-Clause
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|
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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. */
|
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|
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#include "fdlibm.h"
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#if !__OBSOLETE_MATH
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#include <math.h>
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#include <stdint.h>
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#include "math_config.h"
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#define N (1 << EXP_TABLE_BITS)
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#define Shift __exp_data.exp2_shift
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#define T __exp_data.tab
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#define C1 __exp_data.exp2_poly[0]
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#define C2 __exp_data.exp2_poly[1]
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#define C3 __exp_data.exp2_poly[2]
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#define C4 __exp_data.exp2_poly[3]
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#define C5 __exp_data.exp2_poly[4]
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#define C6 __exp_data.exp2_poly[5]
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static inline double
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specialcase (double_t tmp, uint64_t sbits, uint64_t ki)
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{
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double_t scale, y;
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if ((ki & 0x80000000) == 0)
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{
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/* k > 0, the exponent of scale might have overflowed by 1. */
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sbits -= 1ull << 52;
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scale = asdouble (sbits);
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y = 2 * (scale + scale * tmp);
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return check_oflow (y);
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}
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/* k < 0, need special care in the subnormal range. */
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sbits += 1022ull << 52;
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scale = asdouble (sbits);
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y = scale + scale * tmp;
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if (y < 1.0)
|
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{
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/* Round y to the right precision before scaling it into the subnormal
|
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range to avoid double rounding that can cause 0.5+E/2 ulp error where
|
||||
E is the worst-case ulp error outside the subnormal range. So this
|
||||
is only useful if the goal is better than 1 ulp worst-case error. */
|
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double_t hi, lo;
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lo = scale - y + scale * tmp;
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hi = 1.0 + y;
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lo = 1.0 - hi + y + lo;
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y = eval_as_double (hi + lo) - 1.0;
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/* Avoid -0.0 with downward rounding. */
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if (WANT_ROUNDING && y == 0.0)
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y = 0.0;
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/* The underflow exception needs to be signaled explicitly. */
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force_eval_double (opt_barrier_double (0x1p-1022) * 0x1p-1022);
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}
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y = 0x1p-1022 * y;
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return check_uflow (y);
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}
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static inline uint32_t
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top12 (double x)
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{
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return asuint64 (x) >> 52;
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}
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double
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exp2 (double x)
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{
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uint32_t abstop;
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uint64_t ki, idx, top, sbits;
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/* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
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double_t kd, r, r2, scale, tail, tmp;
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abstop = top12 (x) & 0x7ff;
|
||||
if (unlikely (abstop - top12 (0x1p-54) >= top12 (512.0) - top12 (0x1p-54)))
|
||||
{
|
||||
if (abstop - top12 (0x1p-54) >= 0x80000000)
|
||||
/* Avoid spurious underflow for tiny x. */
|
||||
/* Note: 0 is common input. */
|
||||
return WANT_ROUNDING ? 1.0 + x : 1.0;
|
||||
if (abstop >= top12 (1024.0))
|
||||
{
|
||||
if (asuint64 (x) == asuint64 (-INFINITY))
|
||||
return 0.0;
|
||||
if (abstop >= top12 (INFINITY))
|
||||
return 1.0 + x;
|
||||
if (!(asuint64 (x) >> 63))
|
||||
return __math_oflow (0);
|
||||
else if (asuint64 (x) >= asuint64 (-1075.0))
|
||||
return __math_uflow (0);
|
||||
}
|
||||
if (2 * asuint64 (x) > 2 * asuint64 (928.0))
|
||||
/* Large x is special cased below. */
|
||||
abstop = 0;
|
||||
}
|
||||
|
||||
/* exp2(x) = 2^(k/N) * 2^r, with 2^r in [2^(-1/2N),2^(1/2N)]. */
|
||||
/* x = k/N + r, with int k and r in [-1/2N, 1/2N]. */
|
||||
kd = eval_as_double (x + Shift);
|
||||
ki = asuint64 (kd); /* k. */
|
||||
kd -= Shift; /* k/N for int k. */
|
||||
r = x - kd;
|
||||
/* 2^(k/N) ~= scale * (1 + tail). */
|
||||
idx = 2*(ki % N);
|
||||
top = ki << (52 - EXP_TABLE_BITS);
|
||||
tail = asdouble (T[idx]);
|
||||
/* This is only a valid scale when -1023*N < k < 1024*N. */
|
||||
sbits = T[idx + 1] + top;
|
||||
/* exp2(x) = 2^(k/N) * 2^r ~= scale + scale * (tail + 2^r - 1). */
|
||||
/* Evaluation is optimized assuming superscalar pipelined execution. */
|
||||
r2 = r*r;
|
||||
/* Without fma the worst case error is 0.5/N ulp larger. */
|
||||
/* Worst case error is less than 0.5+0.86/N+(abs poly error * 2^53) ulp. */
|
||||
#if EXP2_POLY_ORDER == 4
|
||||
tmp = tail + r*C1 + r2*C2 + r*r2*(C3 + r*C4);
|
||||
#elif EXP2_POLY_ORDER == 5
|
||||
tmp = tail + r*C1 + r2*(C2 + r*C3) + r2*r2*(C4 + r*C5);
|
||||
#elif EXP2_POLY_ORDER == 6
|
||||
tmp = tail + r*C1 + r2*(0.5 + r*C3) + r2*r2*(C4 + r*C5 + r2*C6);
|
||||
#endif
|
||||
if (unlikely (abstop == 0))
|
||||
return specialcase (tmp, sbits, ki);
|
||||
scale = asdouble (sbits);
|
||||
/* Note: tmp == 0 or |tmp| > 2^-65 and scale > 2^-928, so there
|
||||
is no spurious underflow here even without fma. */
|
||||
return scale + scale * tmp;
|
||||
}
|
||||
#endif
|
||||
|
|
@ -0,0 +1,611 @@
|
|||
/* Shared data between exp, exp2 and pow.
|
||||
Copyright (c) 2018 Arm Ltd. All rights reserved.
|
||||
|
||||
SPDX-License-Identifier: BSD-3-Clause
|
||||
|
||||
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 << EXP_TABLE_BITS)
|
||||
|
||||
const struct exp_data __exp_data = {
|
||||
// N/ln2
|
||||
.invln2N = 0x1.71547652b82fep0 * N,
|
||||
// -ln2/N
|
||||
#if N == 64
|
||||
.negln2hiN = -0x1.62e42fefa0000p-7,
|
||||
.negln2loN = -0x1.cf79abc9e3b3ap-46,
|
||||
#elif N == 128
|
||||
.negln2hiN = -0x1.62e42fefa0000p-8,
|
||||
.negln2loN = -0x1.cf79abc9e3b3ap-47,
|
||||
#elif N == 256
|
||||
.negln2hiN = -0x1.62e42fefc0000p-9,
|
||||
.negln2loN = 0x1.c610ca86c3899p-45,
|
||||
#endif
|
||||
// Used for rounding when !TOINT_INTRINSICS
|
||||
#if EXP_USE_TOINT_NARROW
|
||||
.shift = 0x1800000000.8p0,
|
||||
#else
|
||||
.shift = 0x1.8p52,
|
||||
#endif
|
||||
// exp polynomial coefficients.
|
||||
.poly = {
|
||||
#if N == 64 && EXP_POLY_ORDER == 5 && !EXP_POLY_WIDE
|
||||
// abs error: 1.5543*2^-60
|
||||
// ulp error: 0.529 (0.533 without fma)
|
||||
// if |x| < ln2/128+eps
|
||||
// abs error if |x| < ln2/64: 1.7157*2^-50
|
||||
0x1.fffffffffdbcdp-2,
|
||||
0x1.555555555444cp-3,
|
||||
0x1.555573c6a9f7dp-5,
|
||||
0x1.1111266d28935p-7,
|
||||
#elif N == 64 && EXP_POLY_ORDER == 6 && EXP_POLY_WIDE
|
||||
// abs error: 1.6735*2^-64
|
||||
// ulp error: 0.518 (0.522 without fma)
|
||||
// if |x| < ln2/64
|
||||
0x1.5555555548f9ap-3,
|
||||
0x1.555555554bf5dp-5,
|
||||
0x1.11115b75f0f4dp-7,
|
||||
0x1.6c171a6b6303ep-10,
|
||||
#elif N == 128 && EXP_POLY_ORDER == 5 && !EXP_POLY_WIDE
|
||||
// abs error: 1.555*2^-66
|
||||
// ulp error: 0.509 (0.511 without fma)
|
||||
// if |x| < ln2/256+eps
|
||||
// abs error if |x| < ln2/256+0x1p-15: 1.09*2^-65
|
||||
// abs error if |x| < ln2/128: 1.7145*2^-56
|
||||
0x1.ffffffffffdbdp-2,
|
||||
0x1.555555555543cp-3,
|
||||
0x1.55555cf172b91p-5,
|
||||
0x1.1111167a4d017p-7,
|
||||
#elif N == 128 && EXP_POLY_ORDER == 5 && EXP_POLY_WIDE
|
||||
// abs error: 1.5542*2^-60
|
||||
// ulp error: 0.521 (0.523 without fma)
|
||||
// if |x| < ln2/128
|
||||
0x1.fffffffffdbcep-2,
|
||||
0x1.55555555543c2p-3,
|
||||
0x1.555573c64f2e3p-5,
|
||||
0x1.111126b4eff73p-7,
|
||||
#elif N == 128 && EXP_POLY_ORDER == 6 && EXP_POLY_WIDE
|
||||
// abs error: 1.6861*2^-71
|
||||
// ulp error: 0.509 (0.511 without fma)
|
||||
// if |x| < ln2/128
|
||||
0x1.55555555548fdp-3,
|
||||
0x1.555555555658fp-5,
|
||||
0x1.111123a859bb6p-7,
|
||||
0x1.6c16ba6920cabp-10,
|
||||
#elif N == 256 && EXP_POLY_ORDER == 4 && !EXP_POLY_WIDE
|
||||
// abs error: 1.43*2^-58
|
||||
// ulp error: 0.549 (0.550 without fma)
|
||||
// if |x| < ln2/512
|
||||
0x1p0, // unused
|
||||
0x1.fffffffffffd4p-2,
|
||||
0x1.5555571d6ef9p-3,
|
||||
0x1.5555576a5adcep-5,
|
||||
#elif N == 256 && EXP_POLY_ORDER == 5 && EXP_POLY_WIDE
|
||||
// abs error: 1.5547*2^-66
|
||||
// ulp error: 0.505 (0.506 without fma)
|
||||
// if |x| < ln2/256
|
||||
0x1.ffffffffffdbdp-2,
|
||||
0x1.555555555543cp-3,
|
||||
0x1.55555cf16e1edp-5,
|
||||
0x1.1111167a4b553p-7,
|
||||
#endif
|
||||
},
|
||||
.exp2_shift = 0x1.8p52 / N,
|
||||
// exp2 polynomial coefficients.
|
||||
.exp2_poly = {
|
||||
#if N == 64 && EXP2_POLY_ORDER == 6 && EXP2_POLY_WIDE
|
||||
// abs error: 1.3054*2^-63
|
||||
// ulp error: 0.515
|
||||
// if |x| < 1/64
|
||||
0x1.62e42fefa39efp-1,
|
||||
0x1.ebfbdff82c58fp-3,
|
||||
0x1.c6b08d7045cf1p-5,
|
||||
0x1.3b2ab6fb8fd0ep-7,
|
||||
0x1.5d884afec48d7p-10,
|
||||
0x1.43097dc684ae1p-13,
|
||||
#elif N == 128 && EXP2_POLY_ORDER == 5 && !EXP2_POLY_WIDE
|
||||
// abs error: 1.2195*2^-65
|
||||
// ulp error: 0.507 (0.511 without fma)
|
||||
// if |x| < 1/256
|
||||
// abs error if |x| < 1/128: 1.9941*2^-56
|
||||
0x1.62e42fefa39efp-1,
|
||||
0x1.ebfbdff82c424p-3,
|
||||
0x1.c6b08d70cf4b5p-5,
|
||||
0x1.3b2abd24650ccp-7,
|
||||
0x1.5d7e09b4e3a84p-10,
|
||||
#elif N == 256 && EXP2_POLY_ORDER == 5 && EXP2_POLY_WIDE
|
||||
// abs error: 1.2195*2^-65
|
||||
// ulp error: 0.504 (0.508 without fma)
|
||||
// if |x| < 1/256
|
||||
0x1.62e42fefa39efp-1,
|
||||
0x1.ebfbdff82c424p-3,
|
||||
0x1.c6b08d70cf4b5p-5,
|
||||
0x1.3b2abd24650ccp-7,
|
||||
0x1.5d7e09b4e3a84p-10,
|
||||
#endif
|
||||
},
|
||||
// 2^(k/N) ~= H[k]*(1 + T[k]) for int k in [0,N)
|
||||
// tab[2*k] = asuint64(T[k])
|
||||
// tab[2*k+1] = asuint64(H[k]) - (k << 52)/N
|
||||
.tab = {
|
||||
#if N == 64
|
||||
0x0, 0x3ff0000000000000,
|
||||
0xbc7160139cd8dc5d, 0x3fefec9a3e778061,
|
||||
0x3c8cd2523567f613, 0x3fefd9b0d3158574,
|
||||
0x3c60f74e61e6c861, 0x3fefc74518759bc8,
|
||||
0x3c979aa65d837b6d, 0x3fefb5586cf9890f,
|
||||
0x3c3ebe3d702f9cd1, 0x3fefa3ec32d3d1a2,
|
||||
0xbc9556522a2fbd0e, 0x3fef9301d0125b51,
|
||||
0xbc91c923b9d5f416, 0x3fef829aaea92de0,
|
||||
0xbc801b15eaa59348, 0x3fef72b83c7d517b,
|
||||
0x3c8b898c3f1353bf, 0x3fef635beb6fcb75,
|
||||
0x3c9aecf73e3a2f60, 0x3fef54873168b9aa,
|
||||
0x3c8a6f4144a6c38d, 0x3fef463b88628cd6,
|
||||
0x3c968efde3a8a894, 0x3fef387a6e756238,
|
||||
0x3c80472b981fe7f2, 0x3fef2b4565e27cdd,
|
||||
0x3c82f7e16d09ab31, 0x3fef1e9df51fdee1,
|
||||
0x3c8b3782720c0ab4, 0x3fef1285a6e4030b,
|
||||
0x3c834d754db0abb6, 0x3fef06fe0a31b715,
|
||||
0x3c8fdd395dd3f84a, 0x3feefc08b26416ff,
|
||||
0xbc924aedcc4b5068, 0x3feef1a7373aa9cb,
|
||||
0xbc71d1e83e9436d2, 0x3feee7db34e59ff7,
|
||||
0x3c859f48a72a4c6d, 0x3feedea64c123422,
|
||||
0xbc58a78f4817895b, 0x3feed60a21f72e2a,
|
||||
0x3c4363ed60c2ac11, 0x3feece086061892d,
|
||||
0x3c6ecce1daa10379, 0x3feec6a2b5c13cd0,
|
||||
0x3c7690cebb7aafb0, 0x3feebfdad5362a27,
|
||||
0xbc8f94340071a38e, 0x3feeb9b2769d2ca7,
|
||||
0xbc78dec6bd0f385f, 0x3feeb42b569d4f82,
|
||||
0x3c93350518fdd78e, 0x3feeaf4736b527da,
|
||||
0x3c9063e1e21c5409, 0x3feeab07dd485429,
|
||||
0x3c9432e62b64c035, 0x3feea76f15ad2148,
|
||||
0xbc8c33c53bef4da8, 0x3feea47eb03a5585,
|
||||
0xbc93cedd78565858, 0x3feea23882552225,
|
||||
0xbc93b3efbf5e2228, 0x3feea09e667f3bcd,
|
||||
0xbc6367efb86da9ee, 0x3fee9fb23c651a2f,
|
||||
0xbc781f647e5a3ecf, 0x3fee9f75e8ec5f74,
|
||||
0xbc8619321e55e68a, 0x3fee9feb564267c9,
|
||||
0xbc7b32dcb94da51d, 0x3feea11473eb0187,
|
||||
0x3c65ebe1abd66c55, 0x3feea2f336cf4e62,
|
||||
0xbc9369b6f13b3734, 0x3feea589994cce13,
|
||||
0xbc94d450d872576e, 0x3feea8d99b4492ed,
|
||||
0x3c8db72fc1f0eab4, 0x3feeace5422aa0db,
|
||||
0x3c7bf68359f35f44, 0x3feeb1ae99157736,
|
||||
0xbc5da9b88b6c1e29, 0x3feeb737b0cdc5e5,
|
||||
0xbc92434322f4f9aa, 0x3feebd829fde4e50,
|
||||
0x3c71affc2b91ce27, 0x3feec49182a3f090,
|
||||
0xbc87c50422622263, 0x3feecc667b5de565,
|
||||
0xbc91bbd1d3bcbb15, 0x3feed503b23e255d,
|
||||
0x3c8469846e735ab3, 0x3feede6b5579fdbf,
|
||||
0x3c8c1a7792cb3387, 0x3feee89f995ad3ad,
|
||||
0xbc55c3d956dcaeba, 0x3feef3a2b84f15fb,
|
||||
0xbc68d6f438ad9334, 0x3feeff76f2fb5e47,
|
||||
0x3c74ffd70a5fddcd, 0x3fef0c1e904bc1d2,
|
||||
0x3c736eae30af0cb3, 0x3fef199bdd85529c,
|
||||
0x3c84e08fd10959ac, 0x3fef27f12e57d14b,
|
||||
0x3c676b2c6c921968, 0x3fef3720dcef9069,
|
||||
0xbc8fad5d3ffffa6f, 0x3fef472d4a07897c,
|
||||
0x3c74a385a63d07a7, 0x3fef5818dcfba487,
|
||||
0x3c8e5a50d5c192ac, 0x3fef69e603db3285,
|
||||
0xbc82d52107b43e1f, 0x3fef7c97337b9b5f,
|
||||
0x3c74b604603a88d3, 0x3fef902ee78b3ff6,
|
||||
0xbc8ff7128fd391f0, 0x3fefa4afa2a490da,
|
||||
0x3c8ec3bc41aa2008, 0x3fefba1bee615a27,
|
||||
0x3c8a64a931d185ee, 0x3fefd0765b6e4540,
|
||||
0x3c77893b4d91cd9d, 0x3fefe7c1819e90d8,
|
||||
#elif N == 128
|
||||
0x0, 0x3ff0000000000000,
|
||||
0x3c9b3b4f1a88bf6e, 0x3feff63da9fb3335,
|
||||
0xbc7160139cd8dc5d, 0x3fefec9a3e778061,
|
||||
0xbc905e7a108766d1, 0x3fefe315e86e7f85,
|
||||
0x3c8cd2523567f613, 0x3fefd9b0d3158574,
|
||||
0xbc8bce8023f98efa, 0x3fefd06b29ddf6de,
|
||||
0x3c60f74e61e6c861, 0x3fefc74518759bc8,
|
||||
0x3c90a3e45b33d399, 0x3fefbe3ecac6f383,
|
||||
0x3c979aa65d837b6d, 0x3fefb5586cf9890f,
|
||||
0x3c8eb51a92fdeffc, 0x3fefac922b7247f7,
|
||||
0x3c3ebe3d702f9cd1, 0x3fefa3ec32d3d1a2,
|
||||
0xbc6a033489906e0b, 0x3fef9b66affed31b,
|
||||
0xbc9556522a2fbd0e, 0x3fef9301d0125b51,
|
||||
0xbc5080ef8c4eea55, 0x3fef8abdc06c31cc,
|
||||
0xbc91c923b9d5f416, 0x3fef829aaea92de0,
|
||||
0x3c80d3e3e95c55af, 0x3fef7a98c8a58e51,
|
||||
0xbc801b15eaa59348, 0x3fef72b83c7d517b,
|
||||
0xbc8f1ff055de323d, 0x3fef6af9388c8dea,
|
||||
0x3c8b898c3f1353bf, 0x3fef635beb6fcb75,
|
||||
0xbc96d99c7611eb26, 0x3fef5be084045cd4,
|
||||
0x3c9aecf73e3a2f60, 0x3fef54873168b9aa,
|
||||
0xbc8fe782cb86389d, 0x3fef4d5022fcd91d,
|
||||
0x3c8a6f4144a6c38d, 0x3fef463b88628cd6,
|
||||
0x3c807a05b0e4047d, 0x3fef3f49917ddc96,
|
||||
0x3c968efde3a8a894, 0x3fef387a6e756238,
|
||||
0x3c875e18f274487d, 0x3fef31ce4fb2a63f,
|
||||
0x3c80472b981fe7f2, 0x3fef2b4565e27cdd,
|
||||
0xbc96b87b3f71085e, 0x3fef24dfe1f56381,
|
||||
0x3c82f7e16d09ab31, 0x3fef1e9df51fdee1,
|
||||
0xbc3d219b1a6fbffa, 0x3fef187fd0dad990,
|
||||
0x3c8b3782720c0ab4, 0x3fef1285a6e4030b,
|
||||
0x3c6e149289cecb8f, 0x3fef0cafa93e2f56,
|
||||
0x3c834d754db0abb6, 0x3fef06fe0a31b715,
|
||||
0x3c864201e2ac744c, 0x3fef0170fc4cd831,
|
||||
0x3c8fdd395dd3f84a, 0x3feefc08b26416ff,
|
||||
0xbc86a3803b8e5b04, 0x3feef6c55f929ff1,
|
||||
0xbc924aedcc4b5068, 0x3feef1a7373aa9cb,
|
||||
0xbc9907f81b512d8e, 0x3feeecae6d05d866,
|
||||
0xbc71d1e83e9436d2, 0x3feee7db34e59ff7,
|
||||
0xbc991919b3ce1b15, 0x3feee32dc313a8e5,
|
||||
0x3c859f48a72a4c6d, 0x3feedea64c123422,
|
||||
0xbc9312607a28698a, 0x3feeda4504ac801c,
|
||||
0xbc58a78f4817895b, 0x3feed60a21f72e2a,
|
||||
0xbc7c2c9b67499a1b, 0x3feed1f5d950a897,
|
||||
0x3c4363ed60c2ac11, 0x3feece086061892d,
|
||||
0x3c9666093b0664ef, 0x3feeca41ed1d0057,
|
||||
0x3c6ecce1daa10379, 0x3feec6a2b5c13cd0,
|
||||
0x3c93ff8e3f0f1230, 0x3feec32af0d7d3de,
|
||||
0x3c7690cebb7aafb0, 0x3feebfdad5362a27,
|
||||
0x3c931dbdeb54e077, 0x3feebcb299fddd0d,
|
||||
0xbc8f94340071a38e, 0x3feeb9b2769d2ca7,
|
||||
0xbc87deccdc93a349, 0x3feeb6daa2cf6642,
|
||||
0xbc78dec6bd0f385f, 0x3feeb42b569d4f82,
|
||||
0xbc861246ec7b5cf6, 0x3feeb1a4ca5d920f,
|
||||
0x3c93350518fdd78e, 0x3feeaf4736b527da,
|
||||
0x3c7b98b72f8a9b05, 0x3feead12d497c7fd,
|
||||
0x3c9063e1e21c5409, 0x3feeab07dd485429,
|
||||
0x3c34c7855019c6ea, 0x3feea9268a5946b7,
|
||||
0x3c9432e62b64c035, 0x3feea76f15ad2148,
|
||||
0xbc8ce44a6199769f, 0x3feea5e1b976dc09,
|
||||
0xbc8c33c53bef4da8, 0x3feea47eb03a5585,
|
||||
0xbc845378892be9ae, 0x3feea34634ccc320,
|
||||
0xbc93cedd78565858, 0x3feea23882552225,
|
||||
0x3c5710aa807e1964, 0x3feea155d44ca973,
|
||||
0xbc93b3efbf5e2228, 0x3feea09e667f3bcd,
|
||||
0xbc6a12ad8734b982, 0x3feea012750bdabf,
|
||||
0xbc6367efb86da9ee, 0x3fee9fb23c651a2f,
|
||||
0xbc80dc3d54e08851, 0x3fee9f7df9519484,
|
||||
0xbc781f647e5a3ecf, 0x3fee9f75e8ec5f74,
|
||||
0xbc86ee4ac08b7db0, 0x3fee9f9a48a58174,
|
||||
0xbc8619321e55e68a, 0x3fee9feb564267c9,
|
||||
0x3c909ccb5e09d4d3, 0x3feea0694fde5d3f,
|
||||
0xbc7b32dcb94da51d, 0x3feea11473eb0187,
|
||||
0x3c94ecfd5467c06b, 0x3feea1ed0130c132,
|
||||
0x3c65ebe1abd66c55, 0x3feea2f336cf4e62,
|
||||
0xbc88a1c52fb3cf42, 0x3feea427543e1a12,
|
||||
0xbc9369b6f13b3734, 0x3feea589994cce13,
|
||||
0xbc805e843a19ff1e, 0x3feea71a4623c7ad,
|
||||
0xbc94d450d872576e, 0x3feea8d99b4492ed,
|
||||
0x3c90ad675b0e8a00, 0x3feeaac7d98a6699,
|
||||
0x3c8db72fc1f0eab4, 0x3feeace5422aa0db,
|
||||
0xbc65b6609cc5e7ff, 0x3feeaf3216b5448c,
|
||||
0x3c7bf68359f35f44, 0x3feeb1ae99157736,
|
||||
0xbc93091fa71e3d83, 0x3feeb45b0b91ffc6,
|
||||
0xbc5da9b88b6c1e29, 0x3feeb737b0cdc5e5,
|
||||
0xbc6c23f97c90b959, 0x3feeba44cbc8520f,
|
||||
0xbc92434322f4f9aa, 0x3feebd829fde4e50,
|
||||
0xbc85ca6cd7668e4b, 0x3feec0f170ca07ba,
|
||||
0x3c71affc2b91ce27, 0x3feec49182a3f090,
|
||||
0x3c6dd235e10a73bb, 0x3feec86319e32323,
|
||||
0xbc87c50422622263, 0x3feecc667b5de565,
|
||||
0x3c8b1c86e3e231d5, 0x3feed09bec4a2d33,
|
||||
0xbc91bbd1d3bcbb15, 0x3feed503b23e255d,
|
||||
0x3c90cc319cee31d2, 0x3feed99e1330b358,
|
||||
0x3c8469846e735ab3, 0x3feede6b5579fdbf,
|
||||
0xbc82dfcd978e9db4, 0x3feee36bbfd3f37a,
|
||||
0x3c8c1a7792cb3387, 0x3feee89f995ad3ad,
|
||||
0xbc907b8f4ad1d9fa, 0x3feeee07298db666,
|
||||
0xbc55c3d956dcaeba, 0x3feef3a2b84f15fb,
|
||||
0xbc90a40e3da6f640, 0x3feef9728de5593a,
|
||||
0xbc68d6f438ad9334, 0x3feeff76f2fb5e47,
|
||||
0xbc91eee26b588a35, 0x3fef05b030a1064a,
|
||||
0x3c74ffd70a5fddcd, 0x3fef0c1e904bc1d2,
|
||||
0xbc91bdfbfa9298ac, 0x3fef12c25bd71e09,
|
||||
0x3c736eae30af0cb3, 0x3fef199bdd85529c,
|
||||
0x3c8ee3325c9ffd94, 0x3fef20ab5fffd07a,
|
||||
0x3c84e08fd10959ac, 0x3fef27f12e57d14b,
|
||||
0x3c63cdaf384e1a67, 0x3fef2f6d9406e7b5,
|
||||
0x3c676b2c6c921968, 0x3fef3720dcef9069,
|
||||
0xbc808a1883ccb5d2, 0x3fef3f0b555dc3fa,
|
||||
0xbc8fad5d3ffffa6f, 0x3fef472d4a07897c,
|
||||
0xbc900dae3875a949, 0x3fef4f87080d89f2,
|
||||
0x3c74a385a63d07a7, 0x3fef5818dcfba487,
|
||||
0xbc82919e2040220f, 0x3fef60e316c98398,
|
||||
0x3c8e5a50d5c192ac, 0x3fef69e603db3285,
|
||||
0x3c843a59ac016b4b, 0x3fef7321f301b460,
|
||||
0xbc82d52107b43e1f, 0x3fef7c97337b9b5f,
|
||||
0xbc892ab93b470dc9, 0x3fef864614f5a129,
|
||||
0x3c74b604603a88d3, 0x3fef902ee78b3ff6,
|
||||
0x3c83c5ec519d7271, 0x3fef9a51fbc74c83,
|
||||
0xbc8ff7128fd391f0, 0x3fefa4afa2a490da,
|
||||
0xbc8dae98e223747d, 0x3fefaf482d8e67f1,
|
||||
0x3c8ec3bc41aa2008, 0x3fefba1bee615a27,
|
||||
0x3c842b94c3a9eb32, 0x3fefc52b376bba97,
|
||||
0x3c8a64a931d185ee, 0x3fefd0765b6e4540,
|
||||
0xbc8e37bae43be3ed, 0x3fefdbfdad9cbe14,
|
||||
0x3c77893b4d91cd9d, 0x3fefe7c1819e90d8,
|
||||
0x3c5305c14160cc89, 0x3feff3c22b8f71f1,
|
||||
#elif N == 256
|
||||
0x0, 0x3ff0000000000000,
|
||||
0xbc84e82fc61851ac, 0x3feffb1afa5abcbf,
|
||||
0x3c9b3b4f1a88bf6e, 0x3feff63da9fb3335,
|
||||
0xbc82985dd8521d32, 0x3feff168143b0281,
|
||||
0xbc7160139cd8dc5d, 0x3fefec9a3e778061,
|
||||
0x3c651e617061bfbd, 0x3fefe7d42e11bbcc,
|
||||
0xbc905e7a108766d1, 0x3fefe315e86e7f85,
|
||||
0x3c845fad437fa426, 0x3fefde5f72f654b1,
|
||||
0x3c8cd2523567f613, 0x3fefd9b0d3158574,
|
||||
0xbc954529642b232f, 0x3fefd50a0e3c1f89,
|
||||
0xbc8bce8023f98efa, 0x3fefd06b29ddf6de,
|
||||
0x3c8293708ef5c32e, 0x3fefcbd42b72a836,
|
||||
0x3c60f74e61e6c861, 0x3fefc74518759bc8,
|
||||
0xbc95b9280905b2a4, 0x3fefc2bdf66607e0,
|
||||
0x3c90a3e45b33d399, 0x3fefbe3ecac6f383,
|
||||
0x3c84f31f32c4b7e7, 0x3fefb9c79b1f3919,
|
||||
0x3c979aa65d837b6d, 0x3fefb5586cf9890f,
|
||||
0x3c9407fb30d06420, 0x3fefb0f145e46c85,
|
||||
0x3c8eb51a92fdeffc, 0x3fefac922b7247f7,
|
||||
0xbc9a5d04b3b9911b, 0x3fefa83b23395dec,
|
||||
0x3c3ebe3d702f9cd1, 0x3fefa3ec32d3d1a2,
|
||||
0xbc937a01f0739546, 0x3fef9fa55fdfa9c5,
|
||||
0xbc6a033489906e0b, 0x3fef9b66affed31b,
|
||||
0x3c8b8268b04ef0a5, 0x3fef973028d7233e,
|
||||
0xbc9556522a2fbd0e, 0x3fef9301d0125b51,
|
||||
0xbc9ac46e44a2ebcc, 0x3fef8edbab5e2ab6,
|
||||
0xbc5080ef8c4eea55, 0x3fef8abdc06c31cc,
|
||||
0xbc65704e90c9f860, 0x3fef86a814f204ab,
|
||||
0xbc91c923b9d5f416, 0x3fef829aaea92de0,
|
||||
0xbc897cea57e46280, 0x3fef7e95934f312e,
|
||||
0x3c80d3e3e95c55af, 0x3fef7a98c8a58e51,
|
||||
0x3c56f01429e2b9d2, 0x3fef76a45471c3c2,
|
||||
0xbc801b15eaa59348, 0x3fef72b83c7d517b,
|
||||
0x3c6e653b2459034b, 0x3fef6ed48695bbc0,
|
||||
0xbc8f1ff055de323d, 0x3fef6af9388c8dea,
|
||||
0x3c92cc7ea345b7dc, 0x3fef672658375d2f,
|
||||
0x3c8b898c3f1353bf, 0x3fef635beb6fcb75,
|
||||
0x3c957bfb2876ea9e, 0x3fef5f99f8138a1c,
|
||||
0xbc96d99c7611eb26, 0x3fef5be084045cd4,
|
||||
0x3c8cdc1873af2155, 0x3fef582f95281c6b,
|
||||
0x3c9aecf73e3a2f60, 0x3fef54873168b9aa,
|
||||
0xbc9493684653a131, 0x3fef50e75eb44027,
|
||||
0xbc8fe782cb86389d, 0x3fef4d5022fcd91d,
|
||||
0xbc98e2899077520a, 0x3fef49c18438ce4d,
|
||||
0x3c8a6f4144a6c38d, 0x3fef463b88628cd6,
|
||||
0x3c9120fcd4f59273, 0x3fef42be3578a819,
|
||||
0x3c807a05b0e4047d, 0x3fef3f49917ddc96,
|
||||
0x3c89b788c188c9b8, 0x3fef3bdda27912d1,
|
||||
0x3c968efde3a8a894, 0x3fef387a6e756238,
|
||||
0x3c877afbca90ef84, 0x3fef351ffb82140a,
|
||||
0x3c875e18f274487d, 0x3fef31ce4fb2a63f,
|
||||
0x3c91512f082876ee, 0x3fef2e85711ece75,
|
||||
0x3c80472b981fe7f2, 0x3fef2b4565e27cdd,
|
||||
0x3c9a02f0c7d75ec6, 0x3fef280e341ddf29,
|
||||
0xbc96b87b3f71085e, 0x3fef24dfe1f56381,
|
||||
0xbc803297e78260bf, 0x3fef21ba7591bb70,
|
||||
0x3c82f7e16d09ab31, 0x3fef1e9df51fdee1,
|
||||
0xbc95b77e5ccd9fbf, 0x3fef1b8a66d10f13,
|
||||
0xbc3d219b1a6fbffa, 0x3fef187fd0dad990,
|
||||
0xbc91e75c40b4251e, 0x3fef157e39771b2f,
|
||||
0x3c8b3782720c0ab4, 0x3fef1285a6e4030b,
|
||||
0x3c98a911f1f7785a, 0x3fef0f961f641589,
|
||||
0x3c6e149289cecb8f, 0x3fef0cafa93e2f56,
|
||||
0xbc61e7c998db7dbb, 0x3fef09d24abd886b,
|
||||
0x3c834d754db0abb6, 0x3fef06fe0a31b715,
|
||||
0x3c85425c11faadf4, 0x3fef0432edeeb2fd,
|
||||
0x3c864201e2ac744c, 0x3fef0170fc4cd831,
|
||||
0xbc979517a03e2847, 0x3feefeb83ba8ea32,
|
||||
0x3c8fdd395dd3f84a, 0x3feefc08b26416ff,
|
||||
0xbc800e2a46da4bee, 0x3feef96266e3fa2d,
|
||||
0xbc86a3803b8e5b04, 0x3feef6c55f929ff1,
|
||||
0xbc87430803972b34, 0x3feef431a2de883b,
|
||||
0xbc924aedcc4b5068, 0x3feef1a7373aa9cb,
|
||||
0xbc954de30ae02d94, 0x3feeef26231e754a,
|
||||
0xbc9907f81b512d8e, 0x3feeecae6d05d866,
|
||||
0xbc94f2487e1c03ec, 0x3feeea401b7140ef,
|
||||
0xbc71d1e83e9436d2, 0x3feee7db34e59ff7,
|
||||
0x3c914a5432fcb2f4, 0x3feee57fbfec6cf4,
|
||||
0xbc991919b3ce1b15, 0x3feee32dc313a8e5,
|
||||
0x3c79c3bba5562a2f, 0x3feee0e544ede173,
|
||||
0x3c859f48a72a4c6d, 0x3feedea64c123422,
|
||||
0xbc85a71612e21658, 0x3feedc70df1c5175,
|
||||
0xbc9312607a28698a, 0x3feeda4504ac801c,
|
||||
0x3c86421f6f1d24d6, 0x3feed822c367a024,
|
||||
0xbc58a78f4817895b, 0x3feed60a21f72e2a,
|
||||
0xbc9348a6815fce65, 0x3feed3fb2709468a,
|
||||
0xbc7c2c9b67499a1b, 0x3feed1f5d950a897,
|
||||
0x3c835c43984d9871, 0x3feecffa3f84b9d4,
|
||||
0x3c4363ed60c2ac11, 0x3feece086061892d,
|
||||
0xbc632afc8d9473a0, 0x3feecc2042a7d232,
|
||||
0x3c9666093b0664ef, 0x3feeca41ed1d0057,
|
||||
0xbc95fc5e44de020e, 0x3feec86d668b3237,
|
||||
0x3c6ecce1daa10379, 0x3feec6a2b5c13cd0,
|
||||
0xbc7ea0148327c42f, 0x3feec4e1e192aed2,
|
||||
0x3c93ff8e3f0f1230, 0x3feec32af0d7d3de,
|
||||
0xbc7a843ad1a88022, 0x3feec17dea6db7d7,
|
||||
0x3c7690cebb7aafb0, 0x3feebfdad5362a27,
|
||||
0x3c892ca3bf144e63, 0x3feebe41b817c114,
|
||||
0x3c931dbdeb54e077, 0x3feebcb299fddd0d,
|
||||
0xbc902c99b04aa8b0, 0x3feebb2d81d8abff,
|
||||
0xbc8f94340071a38e, 0x3feeb9b2769d2ca7,
|
||||
0x3c73e34f67e67118, 0x3feeb8417f4531ee,
|
||||
0xbc87deccdc93a349, 0x3feeb6daa2cf6642,
|
||||
0xbc75a3b1197ba0f0, 0x3feeb57de83f4eef,
|
||||
0xbc78dec6bd0f385f, 0x3feeb42b569d4f82,
|
||||
0x3c81bd2888075068, 0x3feeb2e2f4f6ad27,
|
||||
0xbc861246ec7b5cf6, 0x3feeb1a4ca5d920f,
|
||||
0xbc896be8ae89ef8f, 0x3feeb070dde910d2,
|
||||
0x3c93350518fdd78e, 0x3feeaf4736b527da,
|
||||
0xbc88e6ac90348602, 0x3feeae27dbe2c4cf,
|
||||
0x3c7b98b72f8a9b05, 0x3feead12d497c7fd,
|
||||
0xbc91af7f1365c3ac, 0x3feeac0827ff07cc,
|
||||
0x3c9063e1e21c5409, 0x3feeab07dd485429,
|
||||
0xbc943a3540d1898a, 0x3feeaa11fba87a03,
|
||||
0x3c34c7855019c6ea, 0x3feea9268a5946b7,
|
||||
0xbc951f58ddaa8090, 0x3feea84590998b93,
|
||||
0x3c9432e62b64c035, 0x3feea76f15ad2148,
|
||||
0xbc82e1648e50a17c, 0x3feea6a320dceb71,
|
||||
0xbc8ce44a6199769f, 0x3feea5e1b976dc09,
|
||||
0x3c95f30eda98a575, 0x3feea52ae6cdf6f4,
|
||||
0xbc8c33c53bef4da8, 0x3feea47eb03a5585,
|
||||
0x3c917ecda8a72159, 0x3feea3dd1d1929fd,
|
||||
0xbc845378892be9ae, 0x3feea34634ccc320,
|
||||
0xbc9345f3cee1ae6e, 0x3feea2b9febc8fb7,
|
||||
0xbc93cedd78565858, 0x3feea23882552225,
|
||||
0xbc85c33fdf910406, 0x3feea1c1c70833f6,
|
||||
0x3c5710aa807e1964, 0x3feea155d44ca973,
|
||||
0x3c81079ab5789604, 0x3feea0f4b19e9538,
|
||||
0xbc93b3efbf5e2228, 0x3feea09e667f3bcd,
|
||||
0x3c727df161cd7778, 0x3feea052fa75173e,
|
||||
0xbc6a12ad8734b982, 0x3feea012750bdabf,
|
||||
0x3c93f9924a05b767, 0x3fee9fdcddd47645,
|
||||
0xbc6367efb86da9ee, 0x3fee9fb23c651a2f,
|
||||
0xbc87557939a8b5ef, 0x3fee9f9298593ae5,
|
||||
0xbc80dc3d54e08851, 0x3fee9f7df9519484,
|
||||
0x3c51ed2f56fa9d1a, 0x3fee9f7466f42e87,
|
||||
0xbc781f647e5a3ecf, 0x3fee9f75e8ec5f74,
|
||||
0xbc88e67a9006c909, 0x3fee9f8286ead08a,
|
||||
0xbc86ee4ac08b7db0, 0x3fee9f9a48a58174,
|
||||
0x3c86597566977ac8, 0x3fee9fbd35d7cbfd,
|
||||
0xbc8619321e55e68a, 0x3fee9feb564267c9,
|
||||
0x3c92c0b7028a5c3a, 0x3feea024b1ab6e09,
|
||||
0x3c909ccb5e09d4d3, 0x3feea0694fde5d3f,
|
||||
0x3c8a30faf49cc78c, 0x3feea0b938ac1cf6,
|
||||
0xbc7b32dcb94da51d, 0x3feea11473eb0187,
|
||||
0xbc92dad3519d7b5b, 0x3feea17b0976cfdb,
|
||||
0x3c94ecfd5467c06b, 0x3feea1ed0130c132,
|
||||
0x3c87d51410fd15c2, 0x3feea26a62ff86f0,
|
||||
0x3c65ebe1abd66c55, 0x3feea2f336cf4e62,
|
||||
0xbc760a3629969871, 0x3feea3878491c491,
|
||||
0xbc88a1c52fb3cf42, 0x3feea427543e1a12,
|
||||
0x3c8b18c6e3fdef5d, 0x3feea4d2add106d9,
|
||||
0xbc9369b6f13b3734, 0x3feea589994cce13,
|
||||
0x3c90ec1ddcb1390a, 0x3feea64c1eb941f7,
|
||||
0xbc805e843a19ff1e, 0x3feea71a4623c7ad,
|
||||
0xbc522cea4f3afa1e, 0x3feea7f4179f5b21,
|
||||
0xbc94d450d872576e, 0x3feea8d99b4492ed,
|
||||
0x3c7c88549b958471, 0x3feea9cad931a436,
|
||||
0x3c90ad675b0e8a00, 0x3feeaac7d98a6699,
|
||||
0x3c931143962f7877, 0x3feeabd0a478580f,
|
||||
0x3c8db72fc1f0eab4, 0x3feeace5422aa0db,
|
||||
0x3c93e9e96f112479, 0x3feeae05bad61778,
|
||||
0xbc65b6609cc5e7ff, 0x3feeaf3216b5448c,
|
||||
0xbc8dac42a4a38df0, 0x3feeb06a5e0866d9,
|
||||
0x3c7bf68359f35f44, 0x3feeb1ae99157736,
|
||||
0x3c8b99dd98b1ed84, 0x3feeb2fed0282c8a,
|
||||
0xbc93091fa71e3d83, 0x3feeb45b0b91ffc6,
|
||||
0xbc7885ad50cbb750, 0x3feeb5c353aa2fe2,
|
||||
0xbc5da9b88b6c1e29, 0x3feeb737b0cdc5e5,
|
||||
0xbc82d5e85f3e0301, 0x3feeb8b82b5f98e5,
|
||||
0xbc6c23f97c90b959, 0x3feeba44cbc8520f,
|
||||
0xbc51669428996971, 0x3feebbdd9a7670b3,
|
||||
0xbc92434322f4f9aa, 0x3feebd829fde4e50,
|
||||
0x3c71f2b2c1c4c014, 0x3feebf33e47a22a2,
|
||||
0xbc85ca6cd7668e4b, 0x3feec0f170ca07ba,
|
||||
0xbc9294f304f166b6, 0x3feec2bb4d53fe0d,
|
||||
0x3c71affc2b91ce27, 0x3feec49182a3f090,
|
||||
0xbc8a1e58414c07d3, 0x3feec674194bb8d5,
|
||||
0x3c6dd235e10a73bb, 0x3feec86319e32323,
|
||||
0xbc79740b58a20091, 0x3feeca5e8d07f29e,
|
||||
0xbc87c50422622263, 0x3feecc667b5de565,
|
||||
0x3c9165830a2b96c2, 0x3feece7aed8eb8bb,
|
||||
0x3c8b1c86e3e231d5, 0x3feed09bec4a2d33,
|
||||
0xbc903d5cbe27874b, 0x3feed2c980460ad8,
|
||||
0xbc91bbd1d3bcbb15, 0x3feed503b23e255d,
|
||||
0x3c5986178980fce0, 0x3feed74a8af46052,
|
||||
0x3c90cc319cee31d2, 0x3feed99e1330b358,
|
||||
0xbc89472975b1f2a5, 0x3feedbfe53c12e59,
|
||||
0x3c8469846e735ab3, 0x3feede6b5579fdbf,
|
||||
0x3c7d8157a34b7e7f, 0x3feee0e521356eba,
|
||||
0xbc82dfcd978e9db4, 0x3feee36bbfd3f37a,
|
||||
0x3c8c8a4e231ebb7d, 0x3feee5ff3a3c2774,
|
||||
0x3c8c1a7792cb3387, 0x3feee89f995ad3ad,
|
||||
0xbc888c8d11a142e5, 0x3feeeb4ce622f2ff,
|
||||
0xbc907b8f4ad1d9fa, 0x3feeee07298db666,
|
||||
0x3c889c2ea41433c7, 0x3feef0ce6c9a8952,
|
||||
0xbc55c3d956dcaeba, 0x3feef3a2b84f15fb,
|
||||
0xbc7274aedac8ff80, 0x3feef68415b749b1,
|
||||
0xbc90a40e3da6f640, 0x3feef9728de5593a,
|
||||
0x3c85c620ce76df06, 0x3feefc6e29f1c52a,
|
||||
0xbc68d6f438ad9334, 0x3feeff76f2fb5e47,
|
||||
0xbc8fda52e1b51e41, 0x3fef028cf22749e4,
|
||||
0xbc91eee26b588a35, 0x3fef05b030a1064a,
|
||||
0xbc32141a7b3e2cd8, 0x3fef08e0b79a6f1f,
|
||||
0x3c74ffd70a5fddcd, 0x3fef0c1e904bc1d2,
|
||||
0xbc302899507554e5, 0x3fef0f69c3f3a207,
|
||||
0xbc91bdfbfa9298ac, 0x3fef12c25bd71e09,
|
||||
0xbc80dda2d4c0010c, 0x3fef16286141b33d,
|
||||
0x3c736eae30af0cb3, 0x3fef199bdd85529c,
|
||||
0xbc8a007daadf8d68, 0x3fef1d1cd9fa652c,
|
||||
0x3c8ee3325c9ffd94, 0x3fef20ab5fffd07a,
|
||||
0x3c836909391181d3, 0x3fef244778fafb22,
|
||||
0x3c84e08fd10959ac, 0x3fef27f12e57d14b,
|
||||
0xbc811cd7dbdf9547, 0x3fef2ba88988c933,
|
||||
0x3c63cdaf384e1a67, 0x3fef2f6d9406e7b5,
|
||||
0xbc7ac28b7bef6621, 0x3fef33405751c4db,
|
||||
0x3c676b2c6c921968, 0x3fef3720dcef9069,
|
||||
0xbc7030587207b9e1, 0x3fef3b0f2e6d1675,
|
||||
0xbc808a1883ccb5d2, 0x3fef3f0b555dc3fa,
|
||||
0xbc8cc734592af7fc, 0x3fef43155b5bab74,
|
||||
0xbc8fad5d3ffffa6f, 0x3fef472d4a07897c,
|
||||
0x3c87752a44f587e8, 0x3fef4b532b08c968,
|
||||
0xbc900dae3875a949, 0x3fef4f87080d89f2,
|
||||
0x3c85b66fefeef52e, 0x3fef53c8eacaa1d6,
|
||||
0x3c74a385a63d07a7, 0x3fef5818dcfba487,
|
||||
0x3c5159d9d908a96e, 0x3fef5c76e862e6d3,
|
||||
0xbc82919e2040220f, 0x3fef60e316c98398,
|
||||
0x3c8c254d16117a68, 0x3fef655d71ff6075,
|
||||
0x3c8e5a50d5c192ac, 0x3fef69e603db3285,
|
||||
0xbc8d8c329fbd0e03, 0x3fef6e7cd63a8315,
|
||||
0x3c843a59ac016b4b, 0x3fef7321f301b460,
|
||||
0xbc8ea6e6fbd5f2a6, 0x3fef77d5641c0658,
|
||||
0xbc82d52107b43e1f, 0x3fef7c97337b9b5f,
|
||||
0xbc63e8e3eab2cbb4, 0x3fef81676b197d17,
|
||||
0xbc892ab93b470dc9, 0x3fef864614f5a129,
|
||||
0xbc8b7966cd0d2cd9, 0x3fef8b333b16ee12,
|
||||
0x3c74b604603a88d3, 0x3fef902ee78b3ff6,
|
||||
0xbc776caa4c2ff1cf, 0x3fef953924676d76,
|
||||
0x3c83c5ec519d7271, 0x3fef9a51fbc74c83,
|
||||
0xbc81d5fc525d9940, 0x3fef9f7977cdb740,
|
||||
0xbc8ff7128fd391f0, 0x3fefa4afa2a490da,
|
||||
0x3c855cd8aaea3d21, 0x3fefa9f4867cca6e,
|
||||
0xbc8dae98e223747d, 0x3fefaf482d8e67f1,
|
||||
0x3c8269947c2bed4a, 0x3fefb4aaa2188510,
|
||||
0x3c8ec3bc41aa2008, 0x3fefba1bee615a27,
|
||||
0xbc83b6137e9afe9e, 0x3fefbf9c1cb6412a,
|
||||
0x3c842b94c3a9eb32, 0x3fefc52b376bba97,
|
||||
0xbc69fa74878ba7c7, 0x3fefcac948dd7274,
|
||||
0x3c8a64a931d185ee, 0x3fefd0765b6e4540,
|
||||
0x3c901f3a75ee0efe, 0x3fefd632798844f8,
|
||||
0xbc8e37bae43be3ed, 0x3fefdbfdad9cbe14,
|
||||
0xbc516a9ce6ed84fa, 0x3fefe1d802243c89,
|
||||
0x3c77893b4d91cd9d, 0x3fefe7c1819e90d8,
|
||||
0xbc699c7db2effc76, 0x3fefedba3692d514,
|
||||
0x3c5305c14160cc89, 0x3feff3c22b8f71f1,
|
||||
0x3c64b458677f9840, 0x3feff9d96b2a23d9,
|
||||
#endif
|
||||
},
|
||||
};
|
||||
#endif /* __OBSOLETE_MATH */
|
||||
|
|
@ -231,6 +231,7 @@ extern float __ieee754_scalbf __P((float,float));
|
|||
This is valid as long as there are no namespace issues (the
|
||||
extern symbol is reserved whenever the caller is reserved)
|
||||
and there are no observable error handling side effects. */
|
||||
# define __ieee754_exp(x) exp(x)
|
||||
# define __ieee754_expf(x) expf(x)
|
||||
# define __ieee754_logf(x) logf(x)
|
||||
# define __ieee754_powf(x,y) powf(x,y)
|
||||
|
|
|
|||
|
|
@ -147,8 +147,21 @@ issignalingf_inline (float x)
|
|||
return 2 * (ix ^ 0x00400000) > 2u * 0x7fc00000;
|
||||
}
|
||||
|
||||
/* Force the evaluation of a floating-point expression for its side-effect. */
|
||||
#if __aarch64__ && __GNUC__
|
||||
/* Prevent the optimization of a floating-point expression. */
|
||||
static inline float
|
||||
opt_barrier_float (float x)
|
||||
{
|
||||
__asm__ __volatile__ ("" : "+w" (x));
|
||||
return x;
|
||||
}
|
||||
static inline double
|
||||
opt_barrier_double (double x)
|
||||
{
|
||||
__asm__ __volatile__ ("" : "+w" (x));
|
||||
return x;
|
||||
}
|
||||
/* Force the evaluation of a floating-point expression for its side-effect. */
|
||||
static inline void
|
||||
force_eval_float (float x)
|
||||
{
|
||||
|
|
@ -160,6 +173,18 @@ force_eval_double (double x)
|
|||
__asm__ __volatile__ ("" : "+w" (x));
|
||||
}
|
||||
#else
|
||||
static inline float
|
||||
opt_barrier_float (float x)
|
||||
{
|
||||
volatile float y = x;
|
||||
return y;
|
||||
}
|
||||
static inline double
|
||||
opt_barrier_double (double x)
|
||||
{
|
||||
volatile double y = x;
|
||||
return y;
|
||||
}
|
||||
static inline void
|
||||
force_eval_float (float x)
|
||||
{
|
||||
|
|
@ -199,11 +224,33 @@ eval_as_double (double x)
|
|||
# define unlikely(x) (x)
|
||||
#endif
|
||||
|
||||
/* Error handling tail calls for special cases, with sign argument. */
|
||||
HIDDEN float __math_oflowf (uint32_t);
|
||||
HIDDEN float __math_uflowf (uint32_t);
|
||||
HIDDEN float __math_may_uflowf (uint32_t);
|
||||
HIDDEN float __math_divzerof (uint32_t);
|
||||
HIDDEN double __math_oflow (uint32_t);
|
||||
HIDDEN double __math_uflow (uint32_t);
|
||||
HIDDEN double __math_may_uflow (uint32_t);
|
||||
HIDDEN double __math_divzero (uint32_t);
|
||||
/* Error handling using input checking. */
|
||||
HIDDEN float __math_invalidf (float);
|
||||
HIDDEN double __math_invalid (double);
|
||||
/* Error handling using output checking, only for errno setting. */
|
||||
HIDDEN double __math_check_oflow (double);
|
||||
HIDDEN double __math_check_uflow (double);
|
||||
|
||||
static inline double
|
||||
check_oflow (double x)
|
||||
{
|
||||
return WANT_ERRNO ? __math_check_oflow (x) : x;
|
||||
}
|
||||
|
||||
static inline double
|
||||
check_uflow (double x)
|
||||
{
|
||||
return WANT_ERRNO ? __math_check_uflow (x) : x;
|
||||
}
|
||||
|
||||
/* Shared between expf, exp2f and powf. */
|
||||
#define EXP2F_TABLE_BITS 5
|
||||
|
|
@ -258,4 +305,25 @@ extern const struct powf_log2_data
|
|||
double poly[POWF_LOG2_POLY_ORDER];
|
||||
} __powf_log2_data HIDDEN;
|
||||
|
||||
#define EXP_TABLE_BITS 7
|
||||
#define EXP_POLY_ORDER 5
|
||||
/* Use polynomial that is optimized for a wider input range. This may be
|
||||
needed for good precision in non-nearest rounding and !TOINT_INTRINSICS. */
|
||||
#define EXP_POLY_WIDE 0
|
||||
/* Use close to nearest rounding toint when !TOINT_INTRINSICS. This may be
|
||||
needed for good precision in non-nearest rouning and !EXP_POLY_WIDE. */
|
||||
#define EXP_USE_TOINT_NARROW 0
|
||||
#define EXP2_POLY_ORDER 5
|
||||
#define EXP2_POLY_WIDE 0
|
||||
extern const struct exp_data {
|
||||
double invln2N;
|
||||
double shift;
|
||||
double negln2hiN;
|
||||
double negln2loN;
|
||||
double poly[4]; /* Last four coefficients. */
|
||||
double exp2_shift;
|
||||
double exp2_poly[EXP2_POLY_ORDER];
|
||||
uint64_t tab[2*(1 << EXP_TABLE_BITS)];
|
||||
} __exp_data HIDDEN;
|
||||
|
||||
#endif
|
||||
|
|
|
|||
|
|
@ -0,0 +1,101 @@
|
|||
/* Double-precision math error handling.
|
||||
Copyright (c) 2018 ARM Ltd. All rights reserved.
|
||||
|
||||
SPDX-License-Identifier: BSD-3-Clause
|
||||
|
||||
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 "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 double
|
||||
with_errno (double y, int e)
|
||||
{
|
||||
errno = e;
|
||||
return y;
|
||||
}
|
||||
#else
|
||||
#define with_errno(x, e) (x)
|
||||
#endif
|
||||
|
||||
/* NOINLINE reduces code size. */
|
||||
NOINLINE static double
|
||||
xflow (uint32_t sign, double y)
|
||||
{
|
||||
y = opt_barrier_double (sign ? -y : y) * y;
|
||||
return with_errno (y, ERANGE);
|
||||
}
|
||||
|
||||
HIDDEN double
|
||||
__math_uflow (uint32_t sign)
|
||||
{
|
||||
return xflow (sign, 0x1p-767);
|
||||
}
|
||||
|
||||
#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 double
|
||||
__math_may_uflow (uint32_t sign)
|
||||
{
|
||||
return xflow (sign, 0x1.8p-538);
|
||||
}
|
||||
#endif
|
||||
|
||||
HIDDEN double
|
||||
__math_oflow (uint32_t sign)
|
||||
{
|
||||
return xflow (sign, 0x1p769);
|
||||
}
|
||||
|
||||
HIDDEN double
|
||||
__math_divzero (uint32_t sign)
|
||||
{
|
||||
double y = opt_barrier_double (sign ? -1.0 : 1.0) / 0.0;
|
||||
return with_errno (y, ERANGE);
|
||||
}
|
||||
|
||||
HIDDEN double
|
||||
__math_invalid (double x)
|
||||
{
|
||||
double y = (x - x) / (x - x);
|
||||
return isnan (x) ? y : with_errno (y, EDOM);
|
||||
}
|
||||
|
||||
/* Check result and set errno if necessary. */
|
||||
|
||||
HIDDEN double
|
||||
__math_check_uflow (double y)
|
||||
{
|
||||
return y == 0.0 ? with_errno (y, ERANGE) : y;
|
||||
}
|
||||
|
||||
HIDDEN double
|
||||
__math_check_oflow (double y)
|
||||
{
|
||||
return isinf (y) ? with_errno (y, ERANGE) : y;
|
||||
}
|
||||
|
|
@ -75,6 +75,7 @@
|
|||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
#if __OBSOLETE_MATH
|
||||
|
||||
#ifndef _DOUBLE_IS_32BITS
|
||||
|
||||
|
|
@ -164,3 +165,4 @@ P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */
|
|||
}
|
||||
|
||||
#endif /* defined(_DOUBLE_IS_32BITS) */
|
||||
#endif /* __OBSOLETE_MATH */
|
||||
|
|
|
|||
|
|
@ -53,6 +53,7 @@ PORTABILITY
|
|||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
#if __OBSOLETE_MATH
|
||||
#include <errno.h>
|
||||
|
||||
#ifndef _DOUBLE_IS_32BITS
|
||||
|
|
@ -126,3 +127,4 @@ u_threshold= -7.45133219101941108420e+02; /* 0xc0874910, 0xD52D3051 */
|
|||
}
|
||||
|
||||
#endif /* defined(_DOUBLE_IS_32BITS) */
|
||||
#endif /* __OBSOLETE_MATH */
|
||||
|
|
|
|||
|
|
@ -52,6 +52,7 @@ PORTABILITY
|
|||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
#if __OBSOLETE_MATH
|
||||
#include <errno.h>
|
||||
#include <math.h>
|
||||
|
||||
|
|
@ -68,3 +69,4 @@ PORTABILITY
|
|||
}
|
||||
|
||||
#endif /* defined(_DOUBLE_IS_32BITS) */
|
||||
#endif /* __OBSOLETE_MATH */
|
||||
|
|
|
|||
Loading…
Reference in New Issue