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421 lines
10 KiB
421 lines
10 KiB
/*
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* Configuration for math routines.
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*
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* Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
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* See https://llvm.org/LICENSE.txt for license information.
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* SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
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*/
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#ifndef _MATH_CONFIG_H
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#define _MATH_CONFIG_H
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#include <math.h>
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#include <stdint.h>
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#ifndef WANT_ROUNDING
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/* If defined to 1, return correct results for special cases in non-nearest
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rounding modes (logf (1.0f) returns 0.0f with FE_DOWNWARD rather than -0.0f).
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This may be set to 0 if there is no fenv support or if math functions only
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get called in round to nearest mode. */
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# define WANT_ROUNDING 1
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#endif
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#ifndef WANT_ERRNO
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/* If defined to 1, set errno in math functions according to ISO C. Many math
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libraries do not set errno, so this is 0 by default. It may need to be
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set to 1 if math.h has (math_errhandling & MATH_ERRNO) != 0. */
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# define WANT_ERRNO 0
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#endif
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#ifndef WANT_ERRNO_UFLOW
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/* Set errno to ERANGE if result underflows to 0 (in all rounding modes). */
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# define WANT_ERRNO_UFLOW (WANT_ROUNDING && WANT_ERRNO)
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#endif
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/* Compiler can inline round as a single instruction. */
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#ifndef HAVE_FAST_ROUND
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# if __aarch64__
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# define HAVE_FAST_ROUND 1
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# else
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# define HAVE_FAST_ROUND 0
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# endif
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#endif
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/* Compiler can inline lround, but not (long)round(x). */
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#ifndef HAVE_FAST_LROUND
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# if __aarch64__ && (100*__GNUC__ + __GNUC_MINOR__) >= 408 && __NO_MATH_ERRNO__
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# define HAVE_FAST_LROUND 1
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# else
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# define HAVE_FAST_LROUND 0
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# endif
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#endif
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/* Compiler can inline fma as a single instruction. */
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#ifndef HAVE_FAST_FMA
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# if defined FP_FAST_FMA || __aarch64__
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# define HAVE_FAST_FMA 1
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# else
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# define HAVE_FAST_FMA 0
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# endif
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#endif
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/* Provide *_finite symbols and some of the glibc hidden symbols
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so libmathlib can be used with binaries compiled against glibc
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to interpose math functions with both static and dynamic linking. */
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#ifndef USE_GLIBC_ABI
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# if __GNUC__
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# define USE_GLIBC_ABI 1
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# else
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# define USE_GLIBC_ABI 0
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# endif
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#endif
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/* Optionally used extensions. */
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#ifdef __GNUC__
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# define HIDDEN __attribute__ ((__visibility__ ("hidden")))
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# define NOINLINE __attribute__ ((noinline))
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# define UNUSED __attribute__ ((unused))
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# define likely(x) __builtin_expect (!!(x), 1)
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# define unlikely(x) __builtin_expect (x, 0)
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# if __GNUC__ >= 9
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# define attribute_copy(f) __attribute__ ((copy (f)))
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# else
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# define attribute_copy(f)
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# endif
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# define strong_alias(f, a) \
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extern __typeof (f) a __attribute__ ((alias (#f))) attribute_copy (f);
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# define hidden_alias(f, a) \
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extern __typeof (f) a __attribute__ ((alias (#f), visibility ("hidden"))) \
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attribute_copy (f);
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#else
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# define HIDDEN
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# define NOINLINE
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# define UNUSED
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# define likely(x) (x)
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# define unlikely(x) (x)
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#endif
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#if HAVE_FAST_ROUND
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/* When set, the roundtoint and converttoint functions are provided with
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the semantics documented below. */
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# define TOINT_INTRINSICS 1
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/* Round x to nearest int in all rounding modes, ties have to be rounded
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consistently with converttoint so the results match. If the result
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would be outside of [-2^31, 2^31-1] then the semantics is unspecified. */
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static inline double_t
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roundtoint (double_t x)
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{
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return round (x);
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}
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/* Convert x to nearest int in all rounding modes, ties have to be rounded
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consistently with roundtoint. If the result is not representable in an
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int32_t then the semantics is unspecified. */
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static inline int32_t
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converttoint (double_t x)
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{
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# if HAVE_FAST_LROUND
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return lround (x);
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# else
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return (long) round (x);
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# endif
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}
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#endif
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static inline uint32_t
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asuint (float f)
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{
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union
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{
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float f;
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uint32_t i;
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} u = {f};
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return u.i;
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}
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static inline float
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asfloat (uint32_t i)
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{
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union
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{
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uint32_t i;
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float f;
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} u = {i};
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return u.f;
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}
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static inline uint64_t
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asuint64 (double f)
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{
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union
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{
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double f;
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uint64_t i;
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} u = {f};
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return u.i;
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}
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static inline double
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asdouble (uint64_t i)
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{
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union
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{
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uint64_t i;
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double f;
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} u = {i};
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return u.f;
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}
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#ifndef IEEE_754_2008_SNAN
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# define IEEE_754_2008_SNAN 1
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#endif
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static inline int
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issignalingf_inline (float x)
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{
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uint32_t ix = asuint (x);
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if (!IEEE_754_2008_SNAN)
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return (ix & 0x7fc00000) == 0x7fc00000;
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return 2 * (ix ^ 0x00400000) > 2u * 0x7fc00000;
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}
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static inline int
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issignaling_inline (double x)
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{
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uint64_t ix = asuint64 (x);
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if (!IEEE_754_2008_SNAN)
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return (ix & 0x7ff8000000000000) == 0x7ff8000000000000;
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return 2 * (ix ^ 0x0008000000000000) > 2 * 0x7ff8000000000000ULL;
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}
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#if __aarch64__ && __GNUC__
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/* Prevent the optimization of a floating-point expression. */
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static inline float
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opt_barrier_float (float x)
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{
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__asm__ __volatile__ ("" : "+w" (x));
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return x;
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}
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static inline double
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opt_barrier_double (double x)
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{
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__asm__ __volatile__ ("" : "+w" (x));
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return x;
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}
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/* Force the evaluation of a floating-point expression for its side-effect. */
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static inline void
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force_eval_float (float x)
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{
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__asm__ __volatile__ ("" : "+w" (x));
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}
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static inline void
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force_eval_double (double x)
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{
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__asm__ __volatile__ ("" : "+w" (x));
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}
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#else
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static inline float
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opt_barrier_float (float x)
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{
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volatile float y = x;
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return y;
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}
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static inline double
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opt_barrier_double (double x)
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{
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volatile double y = x;
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return y;
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}
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static inline void
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force_eval_float (float x)
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{
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volatile float y UNUSED = x;
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}
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static inline void
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force_eval_double (double x)
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{
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volatile double y UNUSED = x;
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}
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#endif
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/* Evaluate an expression as the specified type, normally a type
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cast should be enough, but compilers implement non-standard
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excess-precision handling, so when FLT_EVAL_METHOD != 0 then
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these functions may need to be customized. */
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static inline float
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eval_as_float (float x)
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{
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return x;
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}
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static inline double
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eval_as_double (double x)
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{
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return x;
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}
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/* Error handling tail calls for special cases, with a sign argument.
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The sign of the return value is set if the argument is non-zero. */
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/* The result overflows. */
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HIDDEN float __math_oflowf (uint32_t);
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/* The result underflows to 0 in nearest rounding mode. */
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HIDDEN float __math_uflowf (uint32_t);
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/* The result underflows to 0 in some directed rounding mode only. */
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HIDDEN float __math_may_uflowf (uint32_t);
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/* Division by zero. */
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HIDDEN float __math_divzerof (uint32_t);
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/* The result overflows. */
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HIDDEN double __math_oflow (uint32_t);
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/* The result underflows to 0 in nearest rounding mode. */
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HIDDEN double __math_uflow (uint32_t);
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/* The result underflows to 0 in some directed rounding mode only. */
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HIDDEN double __math_may_uflow (uint32_t);
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/* Division by zero. */
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HIDDEN double __math_divzero (uint32_t);
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/* Error handling using input checking. */
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/* Invalid input unless it is a quiet NaN. */
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HIDDEN float __math_invalidf (float);
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/* Invalid input unless it is a quiet NaN. */
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HIDDEN double __math_invalid (double);
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/* Error handling using output checking, only for errno setting. */
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/* Check if the result overflowed to infinity. */
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HIDDEN double __math_check_oflow (double);
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/* Check if the result underflowed to 0. */
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HIDDEN double __math_check_uflow (double);
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/* Check if the result overflowed to infinity. */
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static inline double
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check_oflow (double x)
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{
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return WANT_ERRNO ? __math_check_oflow (x) : x;
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}
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/* Check if the result underflowed to 0. */
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static inline double
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check_uflow (double x)
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{
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return WANT_ERRNO ? __math_check_uflow (x) : x;
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}
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/* Shared between expf, exp2f and powf. */
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#define EXP2F_TABLE_BITS 5
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#define EXP2F_POLY_ORDER 3
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extern const struct exp2f_data
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{
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uint64_t tab[1 << EXP2F_TABLE_BITS];
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double shift_scaled;
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double poly[EXP2F_POLY_ORDER];
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double shift;
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double invln2_scaled;
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double poly_scaled[EXP2F_POLY_ORDER];
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} __exp2f_data HIDDEN;
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#define LOGF_TABLE_BITS 4
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#define LOGF_POLY_ORDER 4
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extern const struct logf_data
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{
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struct
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{
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double invc, logc;
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} tab[1 << LOGF_TABLE_BITS];
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double ln2;
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double poly[LOGF_POLY_ORDER - 1]; /* First order coefficient is 1. */
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} __logf_data HIDDEN;
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#define LOG2F_TABLE_BITS 4
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#define LOG2F_POLY_ORDER 4
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extern const struct log2f_data
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{
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struct
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{
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double invc, logc;
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} tab[1 << LOG2F_TABLE_BITS];
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double poly[LOG2F_POLY_ORDER];
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} __log2f_data HIDDEN;
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#define POWF_LOG2_TABLE_BITS 4
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#define POWF_LOG2_POLY_ORDER 5
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#if TOINT_INTRINSICS
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# define POWF_SCALE_BITS EXP2F_TABLE_BITS
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#else
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# define POWF_SCALE_BITS 0
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#endif
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#define POWF_SCALE ((double) (1 << POWF_SCALE_BITS))
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extern const struct powf_log2_data
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{
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struct
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{
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double invc, logc;
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} tab[1 << POWF_LOG2_TABLE_BITS];
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double poly[POWF_LOG2_POLY_ORDER];
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} __powf_log2_data HIDDEN;
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#define EXP_TABLE_BITS 7
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#define EXP_POLY_ORDER 5
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/* Use polynomial that is optimized for a wider input range. This may be
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needed for good precision in non-nearest rounding and !TOINT_INTRINSICS. */
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#define EXP_POLY_WIDE 0
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/* Use close to nearest rounding toint when !TOINT_INTRINSICS. This may be
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needed for good precision in non-nearest rounding and !EXP_POLY_WIDE. */
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#define EXP_USE_TOINT_NARROW 0
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#define EXP2_POLY_ORDER 5
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#define EXP2_POLY_WIDE 0
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extern const struct exp_data
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{
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double invln2N;
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double shift;
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double negln2hiN;
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double negln2loN;
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double poly[4]; /* Last four coefficients. */
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double exp2_shift;
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double exp2_poly[EXP2_POLY_ORDER];
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uint64_t tab[2*(1 << EXP_TABLE_BITS)];
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} __exp_data HIDDEN;
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#define LOG_TABLE_BITS 7
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#define LOG_POLY_ORDER 6
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#define LOG_POLY1_ORDER 12
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extern const struct log_data
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{
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double ln2hi;
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double ln2lo;
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double poly[LOG_POLY_ORDER - 1]; /* First coefficient is 1. */
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double poly1[LOG_POLY1_ORDER - 1];
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struct {double invc, logc;} tab[1 << LOG_TABLE_BITS];
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#if !HAVE_FAST_FMA
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struct {double chi, clo;} tab2[1 << LOG_TABLE_BITS];
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#endif
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} __log_data HIDDEN;
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#define LOG2_TABLE_BITS 6
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#define LOG2_POLY_ORDER 7
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#define LOG2_POLY1_ORDER 11
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extern const struct log2_data
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{
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double invln2hi;
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double invln2lo;
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double poly[LOG2_POLY_ORDER - 1];
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double poly1[LOG2_POLY1_ORDER - 1];
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struct {double invc, logc;} tab[1 << LOG2_TABLE_BITS];
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#if !HAVE_FAST_FMA
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struct {double chi, clo;} tab2[1 << LOG2_TABLE_BITS];
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#endif
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} __log2_data HIDDEN;
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#define POW_LOG_TABLE_BITS 7
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#define POW_LOG_POLY_ORDER 8
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extern const struct pow_log_data
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{
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double ln2hi;
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double ln2lo;
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double poly[POW_LOG_POLY_ORDER - 1]; /* First coefficient is 1. */
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/* Note: the pad field is unused, but allows slightly faster indexing. */
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struct {double invc, pad, logc, logctail;} tab[1 << POW_LOG_TABLE_BITS];
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} __pow_log_data HIDDEN;
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#endif
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