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/* Declarations for math functions. Copyright (C) 1991-2018 Free Software Foundation, Inc. This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License along with the GNU C Library; if not, see <http://www.gnu.org/licenses/>. */
/* * ISO C99 Standard: 7.12 Mathematics <math.h> */
#if defined log && defined __GNUC__ # warning A macro called log was already defined when <math.h> was included. # warning This will cause compilation problems. #endif
__BEGIN_DECLS
/* Get definitions of __intmax_t and __uintmax_t. */ #include <bits/types.h>
/* Get machine-dependent vector math functions declarations. */ #include <bits/math-vector.h>
/* Gather machine dependent type support. */ #include <bits/floatn.h>
/* Value returned on overflow. With IEEE 754 floating point, this is +Infinity, otherwise the largest representable positive value. */ #if __GNUC_PREREQ (3, 3) # define HUGE_VAL (__builtin_huge_val ()) #else /* This may provoke compiler warnings, and may not be rounded to +Infinity in all IEEE 754 rounding modes, but is the best that can be done in ISO C while remaining a constant expression. 10,000 is greater than the maximum (decimal) exponent for all supported floating-point formats and widths. */ # define HUGE_VAL 1e10000 #endif #ifdef __USE_ISOC99 # if __GNUC_PREREQ (3, 3) # define HUGE_VALF (__builtin_huge_valf ()) # define HUGE_VALL (__builtin_huge_vall ()) # else # define HUGE_VALF 1e10000f # define HUGE_VALL 1e10000L # endif #endif #if __HAVE_FLOAT16 && __GLIBC_USE (IEC_60559_TYPES_EXT) # define HUGE_VAL_F16 (__builtin_huge_valf16 ()) #endif #if __HAVE_FLOAT32 && __GLIBC_USE (IEC_60559_TYPES_EXT) # define HUGE_VAL_F32 (__builtin_huge_valf32 ()) #endif #if __HAVE_FLOAT64 && __GLIBC_USE (IEC_60559_TYPES_EXT) # define HUGE_VAL_F64 (__builtin_huge_valf64 ()) #endif #if __HAVE_FLOAT128 && __GLIBC_USE (IEC_60559_TYPES_EXT) # define HUGE_VAL_F128 (__builtin_huge_valf128 ()) #endif #if __HAVE_FLOAT32X && __GLIBC_USE (IEC_60559_TYPES_EXT) # define HUGE_VAL_F32X (__builtin_huge_valf32x ()) #endif #if __HAVE_FLOAT64X && __GLIBC_USE (IEC_60559_TYPES_EXT) # define HUGE_VAL_F64X (__builtin_huge_valf64x ()) #endif #if __HAVE_FLOAT128X && __GLIBC_USE (IEC_60559_TYPES_EXT) # define HUGE_VAL_F128X (__builtin_huge_valf128x ()) #endif
/* IEEE Not A Number. */ # if __GNUC_PREREQ (3, 3) # define NAN (__builtin_nanf ("")) # else /* This will raise an "invalid" exception outside static initializers, but is the best that can be done in ISO C while remaining a constant expression. */ # define NAN (0.0f / 0.0f) # endif #endif /* __USE_ISOC99 */
/* Get __GLIBC_FLT_EVAL_METHOD. */ #include <bits/flt-eval-method.h>
#ifdef __USE_ISOC99 /* Define the following typedefs.
float_t floating-point type at least as wide as `float' used to evaluate `float' expressions double_t floating-point type at least as wide as `double' used to evaluate `double' expressions */ # if __GLIBC_FLT_EVAL_METHOD == 0 || __GLIBC_FLT_EVAL_METHOD == 16 typedef float float_t; typedef double double_t; # elif __GLIBC_FLT_EVAL_METHOD == 1 typedef double float_t; typedef double double_t; # elif __GLIBC_FLT_EVAL_METHOD == 2 typedef long double float_t; typedef long double double_t; # elif __GLIBC_FLT_EVAL_METHOD == 32 typedef _Float32 float_t; typedef double double_t; # elif __GLIBC_FLT_EVAL_METHOD == 33 typedef _Float32x float_t; typedef _Float32x double_t; # elif __GLIBC_FLT_EVAL_METHOD == 64 typedef _Float64 float_t; typedef _Float64 double_t; # elif __GLIBC_FLT_EVAL_METHOD == 65 typedef _Float64x float_t; typedef _Float64x double_t; # elif __GLIBC_FLT_EVAL_METHOD == 128 typedef _Float128 float_t; typedef _Float128 double_t; # elif __GLIBC_FLT_EVAL_METHOD == 129 typedef _Float128x float_t; typedef _Float128x double_t; # else # error "Unknown __GLIBC_FLT_EVAL_METHOD" # endif #endif
/* Define macros for the return values of ilogb and llogb, based on __FP_LOGB0_IS_MIN and __FP_LOGBNAN_IS_MIN.
FP_ILOGB0 Expands to a value returned by `ilogb (0.0)'. FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'. FP_LLOGB0 Expands to a value returned by `llogb (0.0)'. FP_LLOGBNAN Expands to a value returned by `llogb (NAN)'.
/* Get the architecture specific values describing the floating-point evaluation. The following symbols will get defined:
FP_FAST_FMA FP_FAST_FMAF FP_FAST_FMAL If defined it indicates that the `fma' function generally executes about as fast as a multiply and an add. This macro is defined only iff the `fma' function is implemented directly with a hardware multiply-add instructions. */
/* The file <bits/mathcalls.h> contains the prototypes for all the actual math functions. These macros are used for those prototypes, so we can easily declare each function as both `name' and `__name', and can declare the float versions `namef' and `__namef'. */
/* Depending on the type of TG_ARG, call an appropriately suffixed version of FUNC with arguments (including parentheses) ARGS. Suffixed functions may not exist for long double if it has the same format as double, or for other types with the same format as float, double or long double. The behavior is undefined if the argument does not have a real floating type. The definition may use a conditional expression, so all suffixed versions of FUNC must return the same type (FUNC may include a cast if necessary rather than being a single identifier). */ #ifdef __NO_LONG_DOUBLE_MATH # if __HAVE_DISTINCT_FLOAT128 # error "Distinct _Float128 without distinct long double not supported." # endif # define __MATH_TG(TG_ARG, FUNC, ARGS) \ (sizeof (TG_ARG) == sizeof (float) ? FUNC ## f ARGS : FUNC ARGS) #elif __HAVE_DISTINCT_FLOAT128 # if __HAVE_GENERIC_SELECTION # if __HAVE_FLOATN_NOT_TYPEDEF && __HAVE_FLOAT32 # define __MATH_TG_F32(FUNC, ARGS) _Float32: FUNC ## f ARGS, # else # define __MATH_TG_F32(FUNC, ARGS) # endif # if __HAVE_FLOATN_NOT_TYPEDEF && __HAVE_FLOAT64X # if __HAVE_FLOAT64X_LONG_DOUBLE # define __MATH_TG_F64X(FUNC, ARGS) _Float64x: FUNC ## l ARGS, # else # define __MATH_TG_F64X(FUNC, ARGS) _Float64x: FUNC ## f128 ARGS, # endif # else # define __MATH_TG_F64X(FUNC, ARGS) # endif # define __MATH_TG(TG_ARG, FUNC, ARGS) \ _Generic ((TG_ARG), \ float: FUNC ## f ARGS, \ __MATH_TG_F32 (FUNC, ARGS) \ default: FUNC ARGS, \ long double: FUNC ## l ARGS, \ __MATH_TG_F64X (FUNC, ARGS) \ _Float128: FUNC ## f128 ARGS) # else # if __HAVE_FLOATN_NOT_TYPEDEF # error "Non-typedef _FloatN but no _Generic." # endif # define __MATH_TG(TG_ARG, FUNC, ARGS) \ __builtin_choose_expr \ (__builtin_types_compatible_p (__typeof (TG_ARG), float), \ FUNC ## f ARGS, \ __builtin_choose_expr \ (__builtin_types_compatible_p (__typeof (TG_ARG), double), \ FUNC ARGS, \ __builtin_choose_expr \ (__builtin_types_compatible_p (__typeof (TG_ARG), long double), \ FUNC ## l ARGS, \ FUNC ## f128 ARGS))) # endif #else # define __MATH_TG(TG_ARG, FUNC, ARGS) \ (sizeof (TG_ARG) == sizeof (float) \ ? FUNC ## f ARGS \ : sizeof (TG_ARG) == sizeof (double) \ ? FUNC ARGS \ : FUNC ## l ARGS) #endif
/* ISO C99 defines some generic macros which work on any data type. */ #ifdef __USE_ISOC99
/* All floating-point numbers can be put in one of these categories. */ enum { FP_NAN = # define FP_NAN 0 FP_NAN, FP_INFINITE = # define FP_INFINITE 1 FP_INFINITE, FP_ZERO = # define FP_ZERO 2 FP_ZERO, FP_SUBNORMAL = # define FP_SUBNORMAL 3 FP_SUBNORMAL, FP_NORMAL = # define FP_NORMAL 4 FP_NORMAL };
/* GCC bug 66462 means we cannot use the math builtins with -fsignaling-nan, so disable builtins if this is enabled. When fixed in a newer GCC, the __SUPPORT_SNAN__ check may be skipped for those versions. */
/* Return number of classification appropriate for X. */ # if ((__GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__) \ || __glibc_clang_prereq (2,8)) \ && (!defined __OPTIMIZE_SIZE__ || defined __cplusplus) /* The check for __cplusplus allows the use of the builtin, even when optimization for size is on. This is provided for libstdc++, only to let its configure test work when it is built with -Os. No further use of this definition of fpclassify is expected in C++ mode, since libstdc++ provides its own version of fpclassify in cmath (which undefines fpclassify). */ # define fpclassify(x) __builtin_fpclassify (FP_NAN, FP_INFINITE, \ FP_NORMAL, FP_SUBNORMAL, FP_ZERO, x) # else # define fpclassify(x) __MATH_TG ((x), __fpclassify, (x)) # endif
/* Return nonzero value if sign of X is negative. */ # if __GNUC_PREREQ (6,0) || __glibc_clang_prereq (3,3) # define signbit(x) __builtin_signbit (x) # elif defined __cplusplus /* In C++ mode, __MATH_TG cannot be used, because it relies on __builtin_types_compatible_p, which is a C-only builtin. The check for __cplusplus allows the use of the builtin instead of __MATH_TG. This is provided for libstdc++, only to let its configure test work. No further use of this definition of signbit is expected in C++ mode, since libstdc++ provides its own version of signbit in cmath (which undefines signbit). */ # define signbit(x) __builtin_signbitl (x) # elif __GNUC_PREREQ (4,0) # define signbit(x) __MATH_TG ((x), __builtin_signbit, (x)) # else # define signbit(x) __MATH_TG ((x), __signbit, (x)) # endif
/* Return nonzero value if X is not +-Inf or NaN. */ # if (__GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__) \ || __glibc_clang_prereq (2,8) # define isfinite(x) __builtin_isfinite (x) # else # define isfinite(x) __MATH_TG ((x), __finite, (x)) # endif
/* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN. */ # if (__GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__) \ || __glibc_clang_prereq (2,8) # define isnormal(x) __builtin_isnormal (x) # else # define isnormal(x) (fpclassify (x) == FP_NORMAL) # endif
/* Return nonzero value if X is a NaN. We could use `fpclassify' but we already have this functions `__isnan' and it is faster. */ # if (__GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__) \ || __glibc_clang_prereq (2,8) # define isnan(x) __builtin_isnan (x) # else # define isnan(x) __MATH_TG ((x), __isnan, (x)) # endif
/* Return nonzero value if X is positive or negative infinity. */ # if __HAVE_DISTINCT_FLOAT128 && !__GNUC_PREREQ (7,0) \ && !defined __SUPPORT_SNAN__ && !defined __cplusplus /* Since __builtin_isinf_sign is broken for float128 before GCC 7.0, use the helper function, __isinff128, with older compilers. This is only provided for C mode, because in C++ mode, GCC has no support for __builtin_types_compatible_p (and when in C++ mode, this macro is not used anyway, because libstdc++ headers undefine it). */ # define isinf(x) \ (__builtin_types_compatible_p (__typeof (x), _Float128) \ ? __isinff128 (x) : __builtin_isinf_sign (x)) # elif (__GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__) \ || __glibc_clang_prereq (3,7) # define isinf(x) __builtin_isinf_sign (x) # else # define isinf(x) __MATH_TG ((x), __isinf, (x)) # endif
/* Bitmasks for the math_errhandling macro. */ # define MATH_ERRNO 1 /* errno set by math functions. */ # define MATH_ERREXCEPT 2 /* Exceptions raised by math functions. */
/* By default all math functions support both errno and exception handling (except for soft floating point implementations which may only support errno handling). If errno handling is disabled, exceptions are still supported by GLIBC. Set math_errhandling to 0 with -ffast-math (this is nonconforming but it is more useful than leaving it undefined). */ # ifdef __FAST_MATH__ # define math_errhandling 0 # elif defined __NO_MATH_ERRNO__ # define math_errhandling (MATH_ERREXCEPT) # else # define math_errhandling (MATH_ERRNO | MATH_ERREXCEPT) # endif
#endif /* Use ISO C99. */
#if __GLIBC_USE (IEC_60559_BFP_EXT) # include <bits/iscanonical.h>
/* Return nonzero value if X is a signaling NaN. */ # ifndef __cplusplus # define issignaling(x) __MATH_TG ((x), __issignaling, (x)) # else /* In C++ mode, __MATH_TG cannot be used, because it relies on __builtin_types_compatible_p, which is a C-only builtin. On the other hand, overloading provides the means to distinguish between the floating-point types. The overloading resolution will match the correct parameter (regardless of type qualifiers (i.e.: const and volatile)). */ extern "C++" { inline int issignaling (float __val) { return __issignalingf (__val); } inline int issignaling (double __val) { return __issignaling (__val); } inline int issignaling (long double __val) { # ifdef __NO_LONG_DOUBLE_MATH return __issignaling (__val); # else return __issignalingl (__val); # endif } # if __HAVE_FLOAT128_UNLIKE_LDBL /* When using an IEEE 128-bit long double, _Float128 is defined as long double in C++. */ inline int issignaling (_Float128 __val) { return __issignalingf128 (__val); } # endif } /* extern C++ */ # endif
/* Return nonzero value if X is subnormal. */ # define issubnormal(x) (fpclassify (x) == FP_SUBNORMAL)
/* Return nonzero value if X is zero. */ # ifndef __cplusplus # ifdef __SUPPORT_SNAN__ # define iszero(x) (fpclassify (x) == FP_ZERO) # else # define iszero(x) (((__typeof (x)) (x)) == 0) # endif # else /* __cplusplus */ extern "C++" { # ifdef __SUPPORT_SNAN__ inline int iszero (float __val) { return __fpclassifyf (__val) == FP_ZERO; } inline int iszero (double __val) { return __fpclassify (__val) == FP_ZERO; } inline int iszero (long double __val) { # ifdef __NO_LONG_DOUBLE_MATH return __fpclassify (__val) == FP_ZERO; # else return __fpclassifyl (__val) == FP_ZERO; # endif } # if __HAVE_FLOAT128_UNLIKE_LDBL /* When using an IEEE 128-bit long double, _Float128 is defined as long double in C++. */ inline int iszero (_Float128 __val) { return __fpclassifyf128 (__val) == FP_ZERO; } # endif # else template <class __T> inline bool iszero (__T __val) { return __val == 0; } # endif } /* extern C++ */ # endif /* __cplusplus */ #endif /* Use IEC_60559_BFP_EXT. */
#if __HAVE_FLOAT128X && defined __USE_GNU # error "M_* values needed for _Float128x" #endif
/* When compiling in strict ISO C compatible mode we must not use the inline functions since they, among other things, do not set the `errno' variable correctly. */ #if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES # define __NO_MATH_INLINES 1 #endif
#ifdef __USE_ISOC99 # if __GNUC_PREREQ (3, 1) /* ISO C99 defines some macros to compare number while taking care for unordered numbers. Many FPUs provide special instructions to support these operations. Generic support in GCC for these as builtins went in 2.97, but not all cpus added their patterns until 3.1. Therefore we enable the builtins from 3.1 onwards and use a generic implementation othwerwise. */ # define isgreater(x, y) __builtin_isgreater(x, y) # define isgreaterequal(x, y) __builtin_isgreaterequal(x, y) # define isless(x, y) __builtin_isless(x, y) # define islessequal(x, y) __builtin_islessequal(x, y) # define islessgreater(x, y) __builtin_islessgreater(x, y) # define isunordered(x, y) __builtin_isunordered(x, y) # else # define isgreater(x, y) \ (__extension__ ({ __typeof__ (x) __x = (x); __typeof__ (y) __y = (y); \ !isunordered (__x, __y) && __x > __y; })) # define isgreaterequal(x, y) \ (__extension__ ({ __typeof__ (x) __x = (x); __typeof__ (y) __y = (y); \ !isunordered (__x, __y) && __x >= __y; })) # define isless(x, y) \ (__extension__ ({ __typeof__ (x) __x = (x); __typeof__ (y) __y = (y); \ !isunordered (__x, __y) && __x < __y; })) # define islessequal(x, y) \ (__extension__ ({ __typeof__ (x) __x = (x); __typeof__ (y) __y = (y); \ !isunordered (__x, __y) && __x <= __y; })) # define islessgreater(x, y) \ (__extension__ ({ __typeof__ (x) __x = (x); __typeof__ (y) __y = (y); \ !isunordered (__x, __y) && __x != __y; })) /* isunordered must always check both operands first for signaling NaNs. */ # define isunordered(x, y) \ (__extension__ ({ __typeof__ (x) __u = (x); __typeof__ (y) __v = (y); \ __u != __v && (__u != __u || __v != __v); })) # endif #endif
/* Get machine-dependent inline versions (if there are any). */ #ifdef __USE_EXTERN_INLINES # include <bits/mathinline.h> #endif
/* Define special entry points to use when the compiler got told to only expect finite results. */ #if defined __FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ > 0
#if __GLIBC_USE (IEC_60559_BFP_EXT) /* An expression whose type has the widest of the evaluation formats of X and Y (which are of floating-point types). */ # if __FLT_EVAL_METHOD__ == 2 || __FLT_EVAL_METHOD__ > 64 # define __MATH_EVAL_FMT2(x, y) ((x) + (y) + 0.0L) # elif __FLT_EVAL_METHOD__ == 1 || __FLT_EVAL_METHOD__ > 32 # define __MATH_EVAL_FMT2(x, y) ((x) + (y) + 0.0) # elif __FLT_EVAL_METHOD__ == 0 || __FLT_EVAL_METHOD__ == 32 # define __MATH_EVAL_FMT2(x, y) ((x) + (y) + 0.0f) # else # define __MATH_EVAL_FMT2(x, y) ((x) + (y)) # endif
/* Return X == Y but raising "invalid" and setting errno if X or Y is a NaN. */ # if !defined __cplusplus || (__cplusplus < 201103L && !defined __GNUC__) # define iseqsig(x, y) \ __MATH_TG (__MATH_EVAL_FMT2 (x, y), __iseqsig, ((x), (y))) # else /* In C++ mode, __MATH_TG cannot be used, because it relies on __builtin_types_compatible_p, which is a C-only builtin. Moreover, the comparison macros from ISO C take two floating-point arguments, which need not have the same type. Choosing what underlying function to call requires evaluating the formats of the arguments, then selecting which is wider. The macro __MATH_EVAL_FMT2 provides this information, however, only the type of the macro expansion is relevant (actually evaluating the expression would be incorrect). Thus, the type is used as a template parameter for __iseqsig_type, which calls the appropriate underlying function. */ extern "C++" { template<typename> struct __iseqsig_type;
# if __HAVE_FLOAT128_UNLIKE_LDBL /* When using an IEEE 128-bit long double, _Float128 is defined as long double in C++. */ template<> struct __iseqsig_type<_Float128> { static int __call (_Float128 __x, _Float128 __y) throw () { return __iseqsigf128 (__x, __y); } }; # endif