| /* Declarations for math functions. |
| Copyright (C) 1991-2016 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> |
| */ |
| |
| #ifndef _MATH_H |
| #define _MATH_H 1 |
| |
| #include <features.h> |
| |
| __BEGIN_DECLS |
| |
| /* Get machine-dependent vector math functions declarations. */ |
| #include <bits/math-vector.h> |
| |
| /* Get machine-dependent HUGE_VAL value (returned on overflow). |
| On all IEEE754 machines, this is +Infinity. */ |
| #include <bits/huge_val.h> |
| #ifdef __USE_ISOC99 |
| # include <bits/huge_valf.h> |
| # include <bits/huge_vall.h> |
| |
| /* Get machine-dependent INFINITY value. */ |
| # include <bits/inf.h> |
| |
| /* Get machine-dependent NAN value (returned for some domain errors). */ |
| # include <bits/nan.h> |
| #endif /* __USE_ISOC99 */ |
| |
| /* Get general and ISO C99 specific information. */ |
| #include <bits/mathdef.h> |
| |
| /* 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'. */ |
| |
| #define __SIMD_DECL(function) __CONCAT (__DECL_SIMD_, function) |
| |
| #define __MATHCALL_VEC(function, suffix, args) \ |
| __SIMD_DECL (__MATH_PRECNAME (function, suffix)) \ |
| __MATHCALL (function, suffix, args) |
| |
| #define __MATHDECL_VEC(type, function,suffix, args) \ |
| __SIMD_DECL (__MATH_PRECNAME (function, suffix)) \ |
| __MATHDECL(type, function,suffix, args) |
| |
| #define __MATHCALL(function,suffix, args) \ |
| __MATHDECL (_Mdouble_,function,suffix, args) |
| #define __MATHDECL(type, function,suffix, args) \ |
| __MATHDECL_1(type, function,suffix, args); \ |
| __MATHDECL_1(type, __CONCAT(__,function),suffix, args) |
| #define __MATHCALLX(function,suffix, args, attrib) \ |
| __MATHDECLX (_Mdouble_,function,suffix, args, attrib) |
| #define __MATHDECLX(type, function,suffix, args, attrib) \ |
| __MATHDECL_1(type, function,suffix, args) __attribute__ (attrib); \ |
| __MATHDECL_1(type, __CONCAT(__,function),suffix, args) __attribute__ (attrib) |
| #define __MATHDECL_1(type, function,suffix, args) \ |
| extern type __MATH_PRECNAME(function,suffix) args __THROW |
| |
| #define _Mdouble_ double |
| #define __MATH_PRECNAME(name,r) __CONCAT(name,r) |
| #define __MATH_DECLARING_DOUBLE 1 |
| #define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_STD |
| #define _Mdouble_END_NAMESPACE __END_NAMESPACE_STD |
| #include <bits/mathcalls.h> |
| #undef _Mdouble_ |
| #undef _Mdouble_BEGIN_NAMESPACE |
| #undef _Mdouble_END_NAMESPACE |
| #undef __MATH_PRECNAME |
| #undef __MATH_DECLARING_DOUBLE |
| |
| #ifdef __USE_ISOC99 |
| |
| |
| /* Include the file of declarations again, this time using `float' |
| instead of `double' and appending f to each function name. */ |
| |
| # ifndef _Mfloat_ |
| # define _Mfloat_ float |
| # endif |
| # define _Mdouble_ _Mfloat_ |
| # define __MATH_PRECNAME(name,r) name##f##r |
| # define __MATH_DECLARING_DOUBLE 0 |
| # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99 |
| # define _Mdouble_END_NAMESPACE __END_NAMESPACE_C99 |
| # include <bits/mathcalls.h> |
| # undef _Mdouble_ |
| # undef _Mdouble_BEGIN_NAMESPACE |
| # undef _Mdouble_END_NAMESPACE |
| # undef __MATH_PRECNAME |
| # undef __MATH_DECLARING_DOUBLE |
| |
| # if !(defined __NO_LONG_DOUBLE_MATH && defined _LIBC) \ |
| || defined __LDBL_COMPAT \ |
| || defined _LIBC_TEST |
| # ifdef __LDBL_COMPAT |
| |
| # ifdef __USE_ISOC99 |
| extern float __nldbl_nexttowardf (float __x, long double __y) |
| __THROW __attribute__ ((__const__)); |
| # ifdef __REDIRECT_NTH |
| extern float __REDIRECT_NTH (nexttowardf, (float __x, long double __y), |
| __nldbl_nexttowardf) |
| __attribute__ ((__const__)); |
| extern double __REDIRECT_NTH (nexttoward, (double __x, long double __y), |
| nextafter) __attribute__ ((__const__)); |
| extern long double __REDIRECT_NTH (nexttowardl, |
| (long double __x, long double __y), |
| nextafter) __attribute__ ((__const__)); |
| # endif |
| # endif |
| |
| # undef __MATHDECL_1 |
| # define __MATHDECL_2(type, function,suffix, args, alias) \ |
| extern type __REDIRECT_NTH(__MATH_PRECNAME(function,suffix), \ |
| args, alias) |
| # define __MATHDECL_1(type, function,suffix, args) \ |
| __MATHDECL_2(type, function,suffix, args, __CONCAT(function,suffix)) |
| # endif |
| |
| /* Include the file of declarations again, this time using `long double' |
| instead of `double' and appending l to each function name. */ |
| |
| # ifndef _Mlong_double_ |
| # define _Mlong_double_ long double |
| # endif |
| # define _Mdouble_ _Mlong_double_ |
| # define __MATH_PRECNAME(name,r) name##l##r |
| # define __MATH_DECLARING_DOUBLE 0 |
| # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99 |
| # define _Mdouble_END_NAMESPACE __END_NAMESPACE_C99 |
| # define __MATH_DECLARE_LDOUBLE 1 |
| # include <bits/mathcalls.h> |
| # undef _Mdouble_ |
| # undef _Mdouble_BEGIN_NAMESPACE |
| # undef _Mdouble_END_NAMESPACE |
| # undef __MATH_PRECNAME |
| # undef __MATH_DECLARING_DOUBLE |
| |
| # endif /* !(__NO_LONG_DOUBLE_MATH && _LIBC) || __LDBL_COMPAT */ |
| |
| #endif /* Use ISO C99. */ |
| #undef __MATHDECL_1 |
| #undef __MATHDECL |
| #undef __MATHCALL |
| |
| |
| #if defined __USE_MISC || defined __USE_XOPEN |
| /* This variable is used by `gamma' and `lgamma'. */ |
| extern int signgam; |
| #endif |
| |
| |
| /* ISO C99 defines some generic macros which work on any data type. */ |
| #ifdef __USE_ISOC99 |
| |
| /* Get the architecture specific values describing the floating-point |
| evaluation. The following symbols will get defined: |
| |
| 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 |
| |
| FLT_EVAL_METHOD |
| Defined to |
| 0 if `float_t' is `float' and `double_t' is `double' |
| 1 if `float_t' and `double_t' are `double' |
| 2 if `float_t' and `double_t' are `long double' |
| else `float_t' and `double_t' are unspecified |
| |
| INFINITY representation of the infinity value of type `float' |
| |
| 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. |
| |
| FP_ILOGB0 Expands to a value returned by `ilogb (0.0)'. |
| FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'. |
| |
| DECIMAL_DIG Number of decimal digits supported by conversion between |
| decimal and all internal floating-point formats. |
| |
| */ |
| |
| /* 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__ \ |
| && !defined __OPTIMIZE_SIZE__ |
| # define fpclassify(x) __builtin_fpclassify (FP_NAN, FP_INFINITE, \ |
| FP_NORMAL, FP_SUBNORMAL, FP_ZERO, x) |
| # elif defined __NO_LONG_DOUBLE_MATH |
| # define fpclassify(x) \ |
| (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x)) |
| # else |
| # define fpclassify(x) \ |
| (sizeof (x) == sizeof (float) \ |
| ? __fpclassifyf (x) \ |
| : sizeof (x) == sizeof (double) \ |
| ? __fpclassify (x) : __fpclassifyl (x)) |
| # endif |
| |
| /* Return nonzero value if sign of X is negative. */ |
| # if __GNUC_PREREQ (4,0) |
| # define signbit(x) \ |
| (sizeof (x) == sizeof (float) \ |
| ? __builtin_signbitf (x) \ |
| : sizeof (x) == sizeof (double) \ |
| ? __builtin_signbit (x) : __builtin_signbitl (x)) |
| # else |
| # ifdef __NO_LONG_DOUBLE_MATH |
| # define signbit(x) \ |
| (sizeof (x) == sizeof (float) ? __signbitf (x) : __signbit (x)) |
| # else |
| # define signbit(x) \ |
| (sizeof (x) == sizeof (float) \ |
| ? __signbitf (x) \ |
| : sizeof (x) == sizeof (double) \ |
| ? __signbit (x) : __signbitl (x)) |
| # endif |
| # endif |
| |
| /* Return nonzero value if X is not +-Inf or NaN. */ |
| # if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__ |
| # define isfinite(x) __builtin_isfinite (x) |
| # elif defined __NO_LONG_DOUBLE_MATH |
| # define isfinite(x) \ |
| (sizeof (x) == sizeof (float) ? __finitef (x) : __finite (x)) |
| # else |
| # define isfinite(x) \ |
| (sizeof (x) == sizeof (float) \ |
| ? __finitef (x) \ |
| : sizeof (x) == sizeof (double) \ |
| ? __finite (x) : __finitel (x)) |
| # endif |
| |
| /* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN. */ |
| # if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__ |
| # 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__ |
| # define isnan(x) __builtin_isnan (x) |
| # elif defined __NO_LONG_DOUBLE_MATH |
| # define isnan(x) \ |
| (sizeof (x) == sizeof (float) ? __isnanf (x) : __isnan (x)) |
| # else |
| # define isnan(x) \ |
| (sizeof (x) == sizeof (float) \ |
| ? __isnanf (x) \ |
| : sizeof (x) == sizeof (double) \ |
| ? __isnan (x) : __isnanl (x)) |
| # endif |
| |
| /* Return nonzero value if X is positive or negative infinity. */ |
| # if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__ |
| # define isinf(x) __builtin_isinf_sign (x) |
| # elif defined __NO_LONG_DOUBLE_MATH |
| # define isinf(x) \ |
| (sizeof (x) == sizeof (float) ? __isinff (x) : __isinf (x)) |
| # else |
| # define isinf(x) \ |
| (sizeof (x) == sizeof (float) \ |
| ? __isinff (x) \ |
| : sizeof (x) == sizeof (double) \ |
| ? __isinf (x) : __isinfl (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 functions support both errno and exception handling. |
| In gcc's fast math mode and if inline functions are defined this |
| might not be true. */ |
| # ifndef __FAST_MATH__ |
| # define math_errhandling (MATH_ERRNO | MATH_ERREXCEPT) |
| # endif |
| |
| #endif /* Use ISO C99. */ |
| |
| #ifdef __USE_GNU |
| /* Return nonzero value if X is a signaling NaN. */ |
| # ifdef __NO_LONG_DOUBLE_MATH |
| # define issignaling(x) \ |
| (sizeof (x) == sizeof (float) ? __issignalingf (x) : __issignaling (x)) |
| # else |
| # define issignaling(x) \ |
| (sizeof (x) == sizeof (float) \ |
| ? __issignalingf (x) \ |
| : sizeof (x) == sizeof (double) \ |
| ? __issignaling (x) : __issignalingl (x)) |
| # endif |
| #endif /* Use GNU. */ |
| |
| #ifdef __USE_MISC |
| /* Support for various different standard error handling behaviors. */ |
| typedef enum |
| { |
| _IEEE_ = -1, /* According to IEEE 754/IEEE 854. */ |
| _SVID_, /* According to System V, release 4. */ |
| _XOPEN_, /* Nowadays also Unix98. */ |
| _POSIX_, |
| _ISOC_ /* Actually this is ISO C99. */ |
| } _LIB_VERSION_TYPE; |
| |
| /* This variable can be changed at run-time to any of the values above to |
| affect floating point error handling behavior (it may also be necessary |
| to change the hardware FPU exception settings). */ |
| extern _LIB_VERSION_TYPE _LIB_VERSION; |
| #endif |
| |
| |
| #ifdef __USE_MISC |
| /* In SVID error handling, `matherr' is called with this description |
| of the exceptional condition. |
| |
| We have a problem when using C++ since `exception' is a reserved |
| name in C++. */ |
| # ifdef __cplusplus |
| struct __exception |
| # else |
| struct exception |
| # endif |
| { |
| int type; |
| char *name; |
| double arg1; |
| double arg2; |
| double retval; |
| }; |
| |
| # ifdef __cplusplus |
| extern int matherr (struct __exception *__exc) throw (); |
| # else |
| extern int matherr (struct exception *__exc); |
| # endif |
| |
| # define X_TLOSS 1.41484755040568800000e+16 |
| |
| /* Types of exceptions in the `type' field. */ |
| # define DOMAIN 1 |
| # define SING 2 |
| # define OVERFLOW 3 |
| # define UNDERFLOW 4 |
| # define TLOSS 5 |
| # define PLOSS 6 |
| |
| /* SVID mode specifies returning this large value instead of infinity. */ |
| # define HUGE 3.40282347e+38F |
| |
| #else /* !Misc. */ |
| |
| # ifdef __USE_XOPEN |
| /* X/Open wants another strange constant. */ |
| # define MAXFLOAT 3.40282347e+38F |
| # endif |
| |
| #endif /* Misc. */ |
| |
| |
| /* Some useful constants. */ |
| #if defined __USE_MISC || defined __USE_XOPEN |
| # define M_E 2.7182818284590452354 /* e */ |
| # define M_LOG2E 1.4426950408889634074 /* log_2 e */ |
| # define M_LOG10E 0.43429448190325182765 /* log_10 e */ |
| # define M_LN2 0.69314718055994530942 /* log_e 2 */ |
| # define M_LN10 2.30258509299404568402 /* log_e 10 */ |
| # define M_PI 3.14159265358979323846 /* pi */ |
| # define M_PI_2 1.57079632679489661923 /* pi/2 */ |
| # define M_PI_4 0.78539816339744830962 /* pi/4 */ |
| # define M_1_PI 0.31830988618379067154 /* 1/pi */ |
| # define M_2_PI 0.63661977236758134308 /* 2/pi */ |
| # define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */ |
| # define M_SQRT2 1.41421356237309504880 /* sqrt(2) */ |
| # define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */ |
| #endif |
| |
| /* The above constants are not adequate for computation using `long double's. |
| Therefore we provide as an extension constants with similar names as a |
| GNU extension. Provide enough digits for the 128-bit IEEE quad. */ |
| #ifdef __USE_GNU |
| # define M_El 2.718281828459045235360287471352662498L /* e */ |
| # define M_LOG2El 1.442695040888963407359924681001892137L /* log_2 e */ |
| # define M_LOG10El 0.434294481903251827651128918916605082L /* log_10 e */ |
| # define M_LN2l 0.693147180559945309417232121458176568L /* log_e 2 */ |
| # define M_LN10l 2.302585092994045684017991454684364208L /* log_e 10 */ |
| # define M_PIl 3.141592653589793238462643383279502884L /* pi */ |
| # define M_PI_2l 1.570796326794896619231321691639751442L /* pi/2 */ |
| # define M_PI_4l 0.785398163397448309615660845819875721L /* pi/4 */ |
| # define M_1_PIl 0.318309886183790671537767526745028724L /* 1/pi */ |
| # define M_2_PIl 0.636619772367581343075535053490057448L /* 2/pi */ |
| # define M_2_SQRTPIl 1.128379167095512573896158903121545172L /* 2/sqrt(pi) */ |
| # define M_SQRT2l 1.414213562373095048801688724209698079L /* sqrt(2) */ |
| # define M_SQRT1_2l 0.707106781186547524400844362104849039L /* 1/sqrt(2) */ |
| #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 |
| |
| #if defined __USE_ISOC99 && __GNUC_PREREQ(2,97) |
| /* 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 before 3.0.0, but not all cpus added their patterns. We define |
| versions that use the builtins here, and <bits/mathinline.h> will |
| undef/redefine as appropriate for the specific GCC version in use. */ |
| # 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(u, v) __builtin_isunordered(u, v) |
| #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 |
| # include <bits/math-finite.h> |
| #endif |
| |
| #ifdef __USE_ISOC99 |
| /* If we've still got undefined comparison macros, provide defaults. */ |
| |
| /* Return nonzero value if X is greater than Y. */ |
| # ifndef isgreater |
| # define isgreater(x, y) \ |
| (__extension__ \ |
| ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ |
| !isunordered (__x, __y) && __x > __y; })) |
| # endif |
| |
| /* Return nonzero value if X is greater than or equal to Y. */ |
| # ifndef isgreaterequal |
| # define isgreaterequal(x, y) \ |
| (__extension__ \ |
| ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ |
| !isunordered (__x, __y) && __x >= __y; })) |
| # endif |
| |
| /* Return nonzero value if X is less than Y. */ |
| # ifndef isless |
| # define isless(x, y) \ |
| (__extension__ \ |
| ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ |
| !isunordered (__x, __y) && __x < __y; })) |
| # endif |
| |
| /* Return nonzero value if X is less than or equal to Y. */ |
| # ifndef islessequal |
| # define islessequal(x, y) \ |
| (__extension__ \ |
| ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ |
| !isunordered (__x, __y) && __x <= __y; })) |
| # endif |
| |
| /* Return nonzero value if either X is less than Y or Y is less than X. */ |
| # ifndef islessgreater |
| # define islessgreater(x, y) \ |
| (__extension__ \ |
| ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ |
| !isunordered (__x, __y) && (__x < __y || __y < __x); })) |
| # endif |
| |
| /* Return nonzero value if arguments are unordered. */ |
| # ifndef isunordered |
| # define isunordered(u, v) \ |
| (__extension__ \ |
| ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v); \ |
| fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; })) |
| # endif |
| |
| #endif |
| |
| __END_DECLS |
| |
| |
| #endif /* math.h */ |