| /* |
| * Configuration for math routines. |
| * |
| * Copyright (c) 2017-2018, Arm Limited. |
| * SPDX-License-Identifier: MIT |
| */ |
| |
| #ifndef _MATH_CONFIG_H |
| #define _MATH_CONFIG_H |
| |
| #include <math.h> |
| #include <stdint.h> |
| |
| #ifndef WANT_ROUNDING |
| /* If defined to 1, return correct results for special cases in non-nearest |
| rounding modes (logf (1.0f) returns 0.0f with FE_DOWNWARD rather than -0.0f). |
| This may be set to 0 if there is no fenv support or if math functions only |
| get called in round to nearest mode. */ |
| # define WANT_ROUNDING 1 |
| #endif |
| #ifndef WANT_ERRNO |
| /* If defined to 1, set errno in math functions according to ISO C. Many math |
| libraries do not set errno, so this is 0 by default. It may need to be |
| set to 1 if math.h has (math_errhandling & MATH_ERRNO) != 0. */ |
| # define WANT_ERRNO 0 |
| #endif |
| #ifndef WANT_ERRNO_UFLOW |
| /* Set errno to ERANGE if result underflows to 0 (in all rounding modes). */ |
| # define WANT_ERRNO_UFLOW (WANT_ROUNDING && WANT_ERRNO) |
| #endif |
| |
| /* Compiler can inline round as a single instruction. */ |
| #ifndef HAVE_FAST_ROUND |
| # if __aarch64__ |
| # define HAVE_FAST_ROUND 1 |
| # else |
| # define HAVE_FAST_ROUND 0 |
| # endif |
| #endif |
| |
| /* Compiler can inline lround, but not (long)round(x). */ |
| #ifndef HAVE_FAST_LROUND |
| # if __aarch64__ && (100*__GNUC__ + __GNUC_MINOR__) >= 408 && __NO_MATH_ERRNO__ |
| # define HAVE_FAST_LROUND 1 |
| # else |
| # define HAVE_FAST_LROUND 0 |
| # endif |
| #endif |
| |
| /* Compiler can inline fma as a single instruction. */ |
| #ifndef HAVE_FAST_FMA |
| # if defined FP_FAST_FMA || __aarch64__ |
| # define HAVE_FAST_FMA 1 |
| # else |
| # define HAVE_FAST_FMA 0 |
| # endif |
| #endif |
| |
| /* Provide *_finite symbols and some of the glibc hidden symbols |
| so libmathlib can be used with binaries compiled against glibc |
| to interpose math functions with both static and dynamic linking. */ |
| #ifndef USE_GLIBC_ABI |
| # if __GNUC__ |
| # define USE_GLIBC_ABI 1 |
| # else |
| # define USE_GLIBC_ABI 0 |
| # endif |
| #endif |
| |
| /* Optionally used extensions. */ |
| #ifdef __GNUC__ |
| # define HIDDEN __attribute__ ((__visibility__ ("hidden"))) |
| # define NOINLINE __attribute__ ((noinline)) |
| # define UNUSED __attribute__ ((unused)) |
| # define likely(x) __builtin_expect (!!(x), 1) |
| # define unlikely(x) __builtin_expect (x, 0) |
| # if __GNUC__ >= 9 |
| # define attribute_copy(f) __attribute__ ((copy (f))) |
| # else |
| # define attribute_copy(f) |
| # endif |
| # define strong_alias(f, a) \ |
| extern __typeof (f) a __attribute__ ((alias (#f))) attribute_copy (f); |
| # define hidden_alias(f, a) \ |
| extern __typeof (f) a __attribute__ ((alias (#f), visibility ("hidden"))) \ |
| attribute_copy (f); |
| #else |
| # define HIDDEN |
| # define NOINLINE |
| # define UNUSED |
| # define likely(x) (x) |
| # define unlikely(x) (x) |
| #endif |
| |
| #if HAVE_FAST_ROUND |
| /* When set, the roundtoint and converttoint functions are provided with |
| the semantics documented below. */ |
| # define TOINT_INTRINSICS 1 |
| |
| /* Round x to nearest int in all rounding modes, ties have to be rounded |
| consistently with converttoint so the results match. If the result |
| would be outside of [-2^31, 2^31-1] then the semantics is unspecified. */ |
| static inline double_t |
| roundtoint (double_t x) |
| { |
| return round (x); |
| } |
| |
| /* Convert x to nearest int in all rounding modes, ties have to be rounded |
| consistently with roundtoint. If the result is not representible in an |
| int32_t then the semantics is unspecified. */ |
| static inline int32_t |
| converttoint (double_t x) |
| { |
| # if HAVE_FAST_LROUND |
| return lround (x); |
| # else |
| return (long) round (x); |
| # endif |
| } |
| #endif |
| |
| static inline uint32_t |
| asuint (float f) |
| { |
| union |
| { |
| float f; |
| uint32_t i; |
| } u = {f}; |
| return u.i; |
| } |
| |
| static inline float |
| asfloat (uint32_t i) |
| { |
| union |
| { |
| uint32_t i; |
| float f; |
| } u = {i}; |
| return u.f; |
| } |
| |
| static inline uint64_t |
| asuint64 (double f) |
| { |
| union |
| { |
| double f; |
| uint64_t i; |
| } u = {f}; |
| return u.i; |
| } |
| |
| static inline double |
| asdouble (uint64_t i) |
| { |
| union |
| { |
| uint64_t i; |
| double f; |
| } u = {i}; |
| return u.f; |
| } |
| |
| #ifndef IEEE_754_2008_SNAN |
| # define IEEE_754_2008_SNAN 1 |
| #endif |
| static inline int |
| issignalingf_inline (float x) |
| { |
| uint32_t ix = asuint (x); |
| if (!IEEE_754_2008_SNAN) |
| return (ix & 0x7fc00000) == 0x7fc00000; |
| return 2 * (ix ^ 0x00400000) > 2u * 0x7fc00000; |
| } |
| |
| static inline int |
| issignaling_inline (double x) |
| { |
| uint64_t ix = asuint64 (x); |
| if (!IEEE_754_2008_SNAN) |
| return (ix & 0x7ff8000000000000) == 0x7ff8000000000000; |
| return 2 * (ix ^ 0x0008000000000000) > 2 * 0x7ff8000000000000ULL; |
| } |
| |
| #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) |
| { |
| __asm__ __volatile__ ("" : "+w" (x)); |
| } |
| static inline void |
| 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) |
| { |
| volatile float y UNUSED = x; |
| } |
| static inline void |
| force_eval_double (double x) |
| { |
| volatile double y UNUSED = x; |
| } |
| #endif |
| |
| /* Evaluate an expression as the specified type, normally a type |
| cast should be enough, but compilers implement non-standard |
| excess-precision handling, so when FLT_EVAL_METHOD != 0 then |
| these functions may need to be customized. */ |
| static inline float |
| eval_as_float (float x) |
| { |
| return x; |
| } |
| static inline double |
| eval_as_double (double x) |
| { |
| return x; |
| } |
| |
| /* Error handling tail calls for special cases, with a sign argument. |
| The sign of the return value is set if the argument is non-zero. */ |
| |
| /* The result overflows. */ |
| HIDDEN float __math_oflowf (uint32_t); |
| /* The result underflows to 0 in nearest rounding mode. */ |
| HIDDEN float __math_uflowf (uint32_t); |
| /* The result underflows to 0 in some directed rounding mode only. */ |
| HIDDEN float __math_may_uflowf (uint32_t); |
| /* Division by zero. */ |
| HIDDEN float __math_divzerof (uint32_t); |
| /* The result overflows. */ |
| HIDDEN double __math_oflow (uint32_t); |
| /* The result underflows to 0 in nearest rounding mode. */ |
| HIDDEN double __math_uflow (uint32_t); |
| /* The result underflows to 0 in some directed rounding mode only. */ |
| HIDDEN double __math_may_uflow (uint32_t); |
| /* Division by zero. */ |
| HIDDEN double __math_divzero (uint32_t); |
| |
| /* Error handling using input checking. */ |
| |
| /* Invalid input unless it is a quiet NaN. */ |
| HIDDEN float __math_invalidf (float); |
| /* Invalid input unless it is a quiet NaN. */ |
| HIDDEN double __math_invalid (double); |
| |
| /* Error handling using output checking, only for errno setting. */ |
| |
| /* Check if the result overflowed to infinity. */ |
| HIDDEN double __math_check_oflow (double); |
| /* Check if the result underflowed to 0. */ |
| HIDDEN double __math_check_uflow (double); |
| |
| /* Check if the result overflowed to infinity. */ |
| static inline double |
| check_oflow (double x) |
| { |
| return WANT_ERRNO ? __math_check_oflow (x) : x; |
| } |
| |
| /* Check if the result underflowed to 0. */ |
| 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 |
| #define EXP2F_POLY_ORDER 3 |
| extern const struct exp2f_data |
| { |
| uint64_t tab[1 << EXP2F_TABLE_BITS]; |
| double shift_scaled; |
| double poly[EXP2F_POLY_ORDER]; |
| double shift; |
| double invln2_scaled; |
| double poly_scaled[EXP2F_POLY_ORDER]; |
| } __exp2f_data HIDDEN; |
| |
| #define LOGF_TABLE_BITS 4 |
| #define LOGF_POLY_ORDER 4 |
| extern const struct logf_data |
| { |
| struct |
| { |
| double invc, logc; |
| } tab[1 << LOGF_TABLE_BITS]; |
| double ln2; |
| double poly[LOGF_POLY_ORDER - 1]; /* First order coefficient is 1. */ |
| } __logf_data HIDDEN; |
| |
| #define LOG2F_TABLE_BITS 4 |
| #define LOG2F_POLY_ORDER 4 |
| extern const struct log2f_data |
| { |
| struct |
| { |
| double invc, logc; |
| } tab[1 << LOG2F_TABLE_BITS]; |
| double poly[LOG2F_POLY_ORDER]; |
| } __log2f_data HIDDEN; |
| |
| #define POWF_LOG2_TABLE_BITS 4 |
| #define POWF_LOG2_POLY_ORDER 5 |
| #if TOINT_INTRINSICS |
| # define POWF_SCALE_BITS EXP2F_TABLE_BITS |
| #else |
| # define POWF_SCALE_BITS 0 |
| #endif |
| #define POWF_SCALE ((double) (1 << POWF_SCALE_BITS)) |
| extern const struct powf_log2_data |
| { |
| struct |
| { |
| double invc, logc; |
| } tab[1 << POWF_LOG2_TABLE_BITS]; |
| double poly[POWF_LOG2_POLY_ORDER]; |
| } __powf_log2_data HIDDEN; |
| |
| |
| #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; |
| |
| #define LOG_TABLE_BITS 7 |
| #define LOG_POLY_ORDER 6 |
| #define LOG_POLY1_ORDER 12 |
| extern const struct log_data |
| { |
| double ln2hi; |
| double ln2lo; |
| double poly[LOG_POLY_ORDER - 1]; /* First coefficient is 1. */ |
| double poly1[LOG_POLY1_ORDER - 1]; |
| struct {double invc, logc;} tab[1 << LOG_TABLE_BITS]; |
| #if !HAVE_FAST_FMA |
| struct {double chi, clo;} tab2[1 << LOG_TABLE_BITS]; |
| #endif |
| } __log_data HIDDEN; |
| |
| #define LOG2_TABLE_BITS 6 |
| #define LOG2_POLY_ORDER 7 |
| #define LOG2_POLY1_ORDER 11 |
| extern const struct log2_data |
| { |
| double invln2hi; |
| double invln2lo; |
| double poly[LOG2_POLY_ORDER - 1]; |
| double poly1[LOG2_POLY1_ORDER - 1]; |
| struct {double invc, logc;} tab[1 << LOG2_TABLE_BITS]; |
| #if !HAVE_FAST_FMA |
| struct {double chi, clo;} tab2[1 << LOG2_TABLE_BITS]; |
| #endif |
| } __log2_data HIDDEN; |
| |
| #define POW_LOG_TABLE_BITS 7 |
| #define POW_LOG_POLY_ORDER 8 |
| extern const struct pow_log_data |
| { |
| double ln2hi; |
| double ln2lo; |
| double poly[POW_LOG_POLY_ORDER - 1]; /* First coefficient is 1. */ |
| /* Note: the pad field is unused, but allows slightly faster indexing. */ |
| struct {double invc, pad, logc, logctail;} tab[1 << POW_LOG_TABLE_BITS]; |
| } __pow_log_data HIDDEN; |
| |
| #endif |