/* Copyright (C) 1997-2016 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
. */
/*
* ISO C99 Standard: 7.22 Type-generic math
*/
#ifndef _TGMATH_H
#define _TGMATH_H 1
/* Include the needed headers. */
#include
#include
/* Since `complex' is currently not really implemented in most C compilers
and if it is implemented, the implementations differ. This makes it
quite difficult to write a generic implementation of this header. We
do not try this for now and instead concentrate only on GNU CC. Once
we have more information support for other compilers might follow. */
#if __GNUC_PREREQ (2, 7)
# ifdef __NO_LONG_DOUBLE_MATH
# define __tgml(fct) fct
# else
# define __tgml(fct) fct ## l
# endif
/* This is ugly but unless gcc gets appropriate builtins we have to do
something like this. Don't ask how it works. */
/* 1 if 'type' is a floating type, 0 if 'type' is an integer type.
Allows for _Bool. Expands to an integer constant expression. */
# if __GNUC_PREREQ (3, 1)
# define __floating_type(type) \
(__builtin_classify_type ((type) 0) == 8 \
|| (__builtin_classify_type ((type) 0) == 9 \
&& __builtin_classify_type (__real__ ((type) 0)) == 8))
# else
# define __floating_type(type) (((type) 0.25) && ((type) 0.25 - 1))
# endif
/* The tgmath real type for T, where E is 0 if T is an integer type and
1 for a floating type. */
# define __tgmath_real_type_sub(T, E) \
__typeof__ (*(0 ? (__typeof__ (0 ? (double *) 0 : (void *) (E))) 0 \
: (__typeof__ (0 ? (T *) 0 : (void *) (!(E)))) 0))
/* The tgmath real type of EXPR. */
# define __tgmath_real_type(expr) \
__tgmath_real_type_sub (__typeof__ ((__typeof__ (expr)) 0), \
__floating_type (__typeof__ (expr)))
/* We have two kinds of generic macros: to support functions which are
only defined on real valued parameters and those which are defined
for complex functions as well. */
# define __TGMATH_UNARY_REAL_ONLY(Val, Fct) \
(__extension__ ((sizeof (Val) == sizeof (double) \
|| __builtin_classify_type (Val) != 8) \
? (__tgmath_real_type (Val)) Fct (Val) \
: (sizeof (Val) == sizeof (float)) \
? (__tgmath_real_type (Val)) Fct##f (Val) \
: (__tgmath_real_type (Val)) __tgml(Fct) (Val)))
# define __TGMATH_UNARY_REAL_RET_ONLY(Val, RetType, Fct) \
(__extension__ ((sizeof (Val) == sizeof (double) \
|| __builtin_classify_type (Val) != 8) \
? (RetType) Fct (Val) \
: (sizeof (Val) == sizeof (float)) \
? (RetType) Fct##f (Val) \
: (RetType) __tgml(Fct) (Val)))
# define __TGMATH_BINARY_FIRST_REAL_ONLY(Val1, Val2, Fct) \
(__extension__ ((sizeof (Val1) == sizeof (double) \
|| __builtin_classify_type (Val1) != 8) \
? (__tgmath_real_type (Val1)) Fct (Val1, Val2) \
: (sizeof (Val1) == sizeof (float)) \
? (__tgmath_real_type (Val1)) Fct##f (Val1, Val2) \
: (__tgmath_real_type (Val1)) __tgml(Fct) (Val1, Val2)))
# define __TGMATH_BINARY_REAL_ONLY(Val1, Val2, Fct) \
(__extension__ (((sizeof (Val1) > sizeof (double) \
|| sizeof (Val2) > sizeof (double)) \
&& __builtin_classify_type ((Val1) + (Val2)) == 8) \
? (__typeof ((__tgmath_real_type (Val1)) 0 \
+ (__tgmath_real_type (Val2)) 0)) \
__tgml(Fct) (Val1, Val2) \
: (sizeof (Val1) == sizeof (double) \
|| sizeof (Val2) == sizeof (double) \
|| __builtin_classify_type (Val1) != 8 \
|| __builtin_classify_type (Val2) != 8) \
? (__typeof ((__tgmath_real_type (Val1)) 0 \
+ (__tgmath_real_type (Val2)) 0)) \
Fct (Val1, Val2) \
: (__typeof ((__tgmath_real_type (Val1)) 0 \
+ (__tgmath_real_type (Val2)) 0)) \
Fct##f (Val1, Val2)))
# define __TGMATH_TERNARY_FIRST_SECOND_REAL_ONLY(Val1, Val2, Val3, Fct) \
(__extension__ (((sizeof (Val1) > sizeof (double) \
|| sizeof (Val2) > sizeof (double)) \
&& __builtin_classify_type ((Val1) + (Val2)) == 8) \
? (__typeof ((__tgmath_real_type (Val1)) 0 \
+ (__tgmath_real_type (Val2)) 0)) \
__tgml(Fct) (Val1, Val2, Val3) \
: (sizeof (Val1) == sizeof (double) \
|| sizeof (Val2) == sizeof (double) \
|| __builtin_classify_type (Val1) != 8 \
|| __builtin_classify_type (Val2) != 8) \
? (__typeof ((__tgmath_real_type (Val1)) 0 \
+ (__tgmath_real_type (Val2)) 0)) \
Fct (Val1, Val2, Val3) \
: (__typeof ((__tgmath_real_type (Val1)) 0 \
+ (__tgmath_real_type (Val2)) 0)) \
Fct##f (Val1, Val2, Val3)))
# define __TGMATH_TERNARY_REAL_ONLY(Val1, Val2, Val3, Fct) \
(__extension__ (((sizeof (Val1) > sizeof (double) \
|| sizeof (Val2) > sizeof (double) \
|| sizeof (Val3) > sizeof (double)) \
&& __builtin_classify_type ((Val1) + (Val2) + (Val3)) \
== 8) \
? (__typeof ((__tgmath_real_type (Val1)) 0 \
+ (__tgmath_real_type (Val2)) 0 \
+ (__tgmath_real_type (Val3)) 0)) \
__tgml(Fct) (Val1, Val2, Val3) \
: (sizeof (Val1) == sizeof (double) \
|| sizeof (Val2) == sizeof (double) \
|| sizeof (Val3) == sizeof (double) \
|| __builtin_classify_type (Val1) != 8 \
|| __builtin_classify_type (Val2) != 8 \
|| __builtin_classify_type (Val3) != 8) \
? (__typeof ((__tgmath_real_type (Val1)) 0 \
+ (__tgmath_real_type (Val2)) 0 \
+ (__tgmath_real_type (Val3)) 0)) \
Fct (Val1, Val2, Val3) \
: (__typeof ((__tgmath_real_type (Val1)) 0 \
+ (__tgmath_real_type (Val2)) 0 \
+ (__tgmath_real_type (Val3)) 0)) \
Fct##f (Val1, Val2, Val3)))
/* XXX This definition has to be changed as soon as the compiler understands
the imaginary keyword. */
# define __TGMATH_UNARY_REAL_IMAG(Val, Fct, Cfct) \
(__extension__ ((sizeof (__real__ (Val)) == sizeof (double) \
|| __builtin_classify_type (__real__ (Val)) != 8) \
? ((sizeof (__real__ (Val)) == sizeof (Val)) \
? (__tgmath_real_type (Val)) Fct (Val) \
: (__tgmath_real_type (Val)) Cfct (Val)) \
: (sizeof (__real__ (Val)) == sizeof (float)) \
? ((sizeof (__real__ (Val)) == sizeof (Val)) \
? (__tgmath_real_type (Val)) Fct##f (Val) \
: (__tgmath_real_type (Val)) Cfct##f (Val)) \
: ((sizeof (__real__ (Val)) == sizeof (Val)) \
? (__tgmath_real_type (Val)) __tgml(Fct) (Val) \
: (__tgmath_real_type (Val)) __tgml(Cfct) (Val))))
# define __TGMATH_UNARY_IMAG(Val, Cfct) \
(__extension__ ((sizeof (__real__ (Val)) == sizeof (double) \
|| __builtin_classify_type (__real__ (Val)) != 8) \
? (__typeof__ ((__tgmath_real_type (Val)) 0 \
+ _Complex_I)) Cfct (Val) \
: (sizeof (__real__ (Val)) == sizeof (float)) \
? (__typeof__ ((__tgmath_real_type (Val)) 0 \
+ _Complex_I)) Cfct##f (Val) \
: (__typeof__ ((__tgmath_real_type (Val)) 0 \
+ _Complex_I)) __tgml(Cfct) (Val)))
/* XXX This definition has to be changed as soon as the compiler understands
the imaginary keyword. */
# define __TGMATH_UNARY_REAL_IMAG_RET_REAL(Val, Fct, Cfct) \
(__extension__ ((sizeof (__real__ (Val)) == sizeof (double) \
|| __builtin_classify_type (__real__ (Val)) != 8) \
? ((sizeof (__real__ (Val)) == sizeof (Val)) \
? (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\
Fct (Val) \
: (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\
Cfct (Val)) \
: (sizeof (__real__ (Val)) == sizeof (float)) \
? ((sizeof (__real__ (Val)) == sizeof (Val)) \
? (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\
Fct##f (Val) \
: (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\
Cfct##f (Val)) \
: ((sizeof (__real__ (Val)) == sizeof (Val)) \
? (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\
__tgml(Fct) (Val) \
: (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\
__tgml(Cfct) (Val))))
/* XXX This definition has to be changed as soon as the compiler understands
the imaginary keyword. */
# define __TGMATH_BINARY_REAL_IMAG(Val1, Val2, Fct, Cfct) \
(__extension__ (((sizeof (__real__ (Val1)) > sizeof (double) \
|| sizeof (__real__ (Val2)) > sizeof (double)) \
&& __builtin_classify_type (__real__ (Val1) \
+ __real__ (Val2)) == 8) \
? ((sizeof (__real__ (Val1)) == sizeof (Val1) \
&& sizeof (__real__ (Val2)) == sizeof (Val2)) \
? (__typeof ((__tgmath_real_type (Val1)) 0 \
+ (__tgmath_real_type (Val2)) 0)) \
__tgml(Fct) (Val1, Val2) \
: (__typeof ((__tgmath_real_type (Val1)) 0 \
+ (__tgmath_real_type (Val2)) 0)) \
__tgml(Cfct) (Val1, Val2)) \
: (sizeof (__real__ (Val1)) == sizeof (double) \
|| sizeof (__real__ (Val2)) == sizeof (double) \
|| __builtin_classify_type (__real__ (Val1)) != 8 \
|| __builtin_classify_type (__real__ (Val2)) != 8) \
? ((sizeof (__real__ (Val1)) == sizeof (Val1) \
&& sizeof (__real__ (Val2)) == sizeof (Val2)) \
? (__typeof ((__tgmath_real_type (Val1)) 0 \
+ (__tgmath_real_type (Val2)) 0)) \
Fct (Val1, Val2) \
: (__typeof ((__tgmath_real_type (Val1)) 0 \
+ (__tgmath_real_type (Val2)) 0)) \
Cfct (Val1, Val2)) \
: ((sizeof (__real__ (Val1)) == sizeof (Val1) \
&& sizeof (__real__ (Val2)) == sizeof (Val2)) \
? (__typeof ((__tgmath_real_type (Val1)) 0 \
+ (__tgmath_real_type (Val2)) 0)) \
Fct##f (Val1, Val2) \
: (__typeof ((__tgmath_real_type (Val1)) 0 \
+ (__tgmath_real_type (Val2)) 0)) \
Cfct##f (Val1, Val2))))
#else
# error "Unsupported compiler; you cannot use "
#endif
/* Unary functions defined for real and complex values. */
/* Trigonometric functions. */
/* Arc cosine of X. */
#define acos(Val) __TGMATH_UNARY_REAL_IMAG (Val, acos, cacos)
/* Arc sine of X. */
#define asin(Val) __TGMATH_UNARY_REAL_IMAG (Val, asin, casin)
/* Arc tangent of X. */
#define atan(Val) __TGMATH_UNARY_REAL_IMAG (Val, atan, catan)
/* Arc tangent of Y/X. */
#define atan2(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, atan2)
/* Cosine of X. */
#define cos(Val) __TGMATH_UNARY_REAL_IMAG (Val, cos, ccos)
/* Sine of X. */
#define sin(Val) __TGMATH_UNARY_REAL_IMAG (Val, sin, csin)
/* Tangent of X. */
#define tan(Val) __TGMATH_UNARY_REAL_IMAG (Val, tan, ctan)
/* Hyperbolic functions. */
/* Hyperbolic arc cosine of X. */
#define acosh(Val) __TGMATH_UNARY_REAL_IMAG (Val, acosh, cacosh)
/* Hyperbolic arc sine of X. */
#define asinh(Val) __TGMATH_UNARY_REAL_IMAG (Val, asinh, casinh)
/* Hyperbolic arc tangent of X. */
#define atanh(Val) __TGMATH_UNARY_REAL_IMAG (Val, atanh, catanh)
/* Hyperbolic cosine of X. */
#define cosh(Val) __TGMATH_UNARY_REAL_IMAG (Val, cosh, ccosh)
/* Hyperbolic sine of X. */
#define sinh(Val) __TGMATH_UNARY_REAL_IMAG (Val, sinh, csinh)
/* Hyperbolic tangent of X. */
#define tanh(Val) __TGMATH_UNARY_REAL_IMAG (Val, tanh, ctanh)
/* Exponential and logarithmic functions. */
/* Exponential function of X. */
#define exp(Val) __TGMATH_UNARY_REAL_IMAG (Val, exp, cexp)
/* Break VALUE into a normalized fraction and an integral power of 2. */
#define frexp(Val1, Val2) __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, frexp)
/* X times (two to the EXP power). */
#define ldexp(Val1, Val2) __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, ldexp)
/* Natural logarithm of X. */
#define log(Val) __TGMATH_UNARY_REAL_IMAG (Val, log, clog)
/* Base-ten logarithm of X. */
#ifdef __USE_GNU
# define log10(Val) __TGMATH_UNARY_REAL_IMAG (Val, log10, __clog10)
#else
# define log10(Val) __TGMATH_UNARY_REAL_ONLY (Val, log10)
#endif
/* Return exp(X) - 1. */
#define expm1(Val) __TGMATH_UNARY_REAL_ONLY (Val, expm1)
/* Return log(1 + X). */
#define log1p(Val) __TGMATH_UNARY_REAL_ONLY (Val, log1p)
/* Return the base 2 signed integral exponent of X. */
#define logb(Val) __TGMATH_UNARY_REAL_ONLY (Val, logb)
/* Compute base-2 exponential of X. */
#define exp2(Val) __TGMATH_UNARY_REAL_ONLY (Val, exp2)
/* Compute base-2 logarithm of X. */
#define log2(Val) __TGMATH_UNARY_REAL_ONLY (Val, log2)
/* Power functions. */
/* Return X to the Y power. */
#define pow(Val1, Val2) __TGMATH_BINARY_REAL_IMAG (Val1, Val2, pow, cpow)
/* Return the square root of X. */
#define sqrt(Val) __TGMATH_UNARY_REAL_IMAG (Val, sqrt, csqrt)
/* Return `sqrt(X*X + Y*Y)'. */
#define hypot(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, hypot)
/* Return the cube root of X. */
#define cbrt(Val) __TGMATH_UNARY_REAL_ONLY (Val, cbrt)
/* Nearest integer, absolute value, and remainder functions. */
/* Smallest integral value not less than X. */
#define ceil(Val) __TGMATH_UNARY_REAL_ONLY (Val, ceil)
/* Absolute value of X. */
#define fabs(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL (Val, fabs, cabs)
/* Largest integer not greater than X. */
#define floor(Val) __TGMATH_UNARY_REAL_ONLY (Val, floor)
/* Floating-point modulo remainder of X/Y. */
#define fmod(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmod)
/* Round X to integral valuein floating-point format using current
rounding direction, but do not raise inexact exception. */
#define nearbyint(Val) __TGMATH_UNARY_REAL_ONLY (Val, nearbyint)
/* Round X to nearest integral value, rounding halfway cases away from
zero. */
#define round(Val) __TGMATH_UNARY_REAL_ONLY (Val, round)
/* Round X to the integral value in floating-point format nearest but
not larger in magnitude. */
#define trunc(Val) __TGMATH_UNARY_REAL_ONLY (Val, trunc)
/* Compute remainder of X and Y and put in *QUO a value with sign of x/y
and magnitude congruent `mod 2^n' to the magnitude of the integral
quotient x/y, with n >= 3. */
#define remquo(Val1, Val2, Val3) \
__TGMATH_TERNARY_FIRST_SECOND_REAL_ONLY (Val1, Val2, Val3, remquo)
/* Round X to nearest integral value according to current rounding
direction. */
#define lrint(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, long int, lrint)
#define llrint(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, long long int, llrint)
/* Round X to nearest integral value, rounding halfway cases away from
zero. */
#define lround(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, long int, lround)
#define llround(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, long long int, llround)
/* Return X with its signed changed to Y's. */
#define copysign(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, copysign)
/* Error and gamma functions. */
#define erf(Val) __TGMATH_UNARY_REAL_ONLY (Val, erf)
#define erfc(Val) __TGMATH_UNARY_REAL_ONLY (Val, erfc)
#define tgamma(Val) __TGMATH_UNARY_REAL_ONLY (Val, tgamma)
#define lgamma(Val) __TGMATH_UNARY_REAL_ONLY (Val, lgamma)
/* Return the integer nearest X in the direction of the
prevailing rounding mode. */
#define rint(Val) __TGMATH_UNARY_REAL_ONLY (Val, rint)
#if __GLIBC_USE (IEC_60559_BFP_EXT)
/* Return X - epsilon. */
# define nextdown(Val) __TGMATH_UNARY_REAL_ONLY (Val, nextdown)
/* Return X + epsilon. */
# define nextup(Val) __TGMATH_UNARY_REAL_ONLY (Val, nextup)
#endif
/* Return X + epsilon if X < Y, X - epsilon if X > Y. */
#define nextafter(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, nextafter)
#define nexttoward(Val1, Val2) \
__TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, nexttoward)
/* Return the remainder of integer divison X / Y with infinite precision. */
#define remainder(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, remainder)
/* Return X times (2 to the Nth power). */
#ifdef __USE_MISC
# define scalb(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, scalb)
#endif
/* Return X times (2 to the Nth power). */
#define scalbn(Val1, Val2) __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, scalbn)
/* Return X times (2 to the Nth power). */
#define scalbln(Val1, Val2) \
__TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, scalbln)
/* Return the binary exponent of X, which must be nonzero. */
#define ilogb(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, int, ilogb)
/* Return positive difference between X and Y. */
#define fdim(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fdim)
/* Return maximum numeric value from X and Y. */
#define fmax(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmax)
/* Return minimum numeric value from X and Y. */
#define fmin(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmin)
/* Multiply-add function computed as a ternary operation. */
#define fma(Val1, Val2, Val3) \
__TGMATH_TERNARY_REAL_ONLY (Val1, Val2, Val3, fma)
#if __GLIBC_USE (IEC_60559_BFP_EXT)
/* Like ilogb, but returning long int. */
# define llogb(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, long int, llogb)
/* Return value with maximum magnitude. */
# define fmaxmag(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmaxmag)
/* Return value with minimum magnitude. */
# define fminmag(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fminmag)
/* Total order operation. */
# define totalorder(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, \
totalorder)
/* Total order operation on absolute values. */
# define totalordermag(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, \
totalordermag)
#endif
/* Absolute value, conjugates, and projection. */
/* Argument value of Z. */
#define carg(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL (Val, carg, carg)
/* Complex conjugate of Z. */
#define conj(Val) __TGMATH_UNARY_IMAG (Val, conj)
/* Projection of Z onto the Riemann sphere. */
#define cproj(Val) __TGMATH_UNARY_IMAG (Val, cproj)
/* Decomposing complex values. */
/* Imaginary part of Z. */
#define cimag(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL (Val, cimag, cimag)
/* Real part of Z. */
#define creal(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL (Val, creal, creal)
#endif /* tgmath.h */