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/* Inline math functions for i387 and SSE. Copyright (C) 1995-2018 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/>. */ #ifndef _MATH_H # error "Never use <bits/mathinline.h> directly; include <math.h> instead." #endif #ifndef __extern_always_inline # define __MATH_INLINE __inline #else # define __MATH_INLINE __extern_always_inline #endif /* Disable x87 inlines when -fpmath=sse is passed and also when we're building on x86_64. Older gcc (gcc-3.2 for example) does not define __SSE2_MATH__ for x86_64. */ #if !defined __SSE2_MATH__ && !defined __x86_64__ # if ((!defined __NO_MATH_INLINES || defined __LIBC_INTERNAL_MATH_INLINES) \ && defined __OPTIMIZE__) /* The inline functions do not set errno or raise necessarily the correct exceptions. */ # undef math_errhandling /* A macro to define float, double, and long double versions of various math functions for the ix87 FPU. FUNC is the function name (which will be suffixed with f and l for the float and long double version, respectively). OP is the name of the FPU operation. We define two sets of macros. The set with the additional NP doesn't add a prototype declaration. */ # ifdef __USE_ISOC99 # define __inline_mathop(func, op) \ __inline_mathop_ (double, func, op) \ __inline_mathop_ (float, __CONCAT(func,f), op) \ __inline_mathop_ (long double, __CONCAT(func,l), op) # define __inline_mathopNP(func, op) \ __inline_mathopNP_ (double, func, op) \ __inline_mathopNP_ (float, __CONCAT(func,f), op) \ __inline_mathopNP_ (long double, __CONCAT(func,l), op) # else # define __inline_mathop(func, op) \ __inline_mathop_ (double, func, op) # define __inline_mathopNP(func, op) \ __inline_mathopNP_ (double, func, op) # endif # define __inline_mathop_(float_type, func, op) \ __inline_mathop_decl_ (float_type, func, op, "0" (__x)) # define __inline_mathopNP_(float_type, func, op) \ __inline_mathop_declNP_ (float_type, func, op, "0" (__x)) # ifdef __USE_ISOC99 # define __inline_mathop_decl(func, op, params...) \ __inline_mathop_decl_ (double, func, op, params) \ __inline_mathop_decl_ (float, __CONCAT(func,f), op, params) \ __inline_mathop_decl_ (long double, __CONCAT(func,l), op, params) # define __inline_mathop_declNP(func, op, params...) \ __inline_mathop_declNP_ (double, func, op, params) \ __inline_mathop_declNP_ (float, __CONCAT(func,f), op, params) \ __inline_mathop_declNP_ (long double, __CONCAT(func,l), op, params) # else # define __inline_mathop_decl(func, op, params...) \ __inline_mathop_decl_ (double, func, op, params) # define __inline_mathop_declNP(func, op, params...) \ __inline_mathop_declNP_ (double, func, op, params) # endif # define __inline_mathop_decl_(float_type, func, op, params...) \ __MATH_INLINE float_type func (float_type) __THROW; \ __inline_mathop_declNP_ (float_type, func, op, params) # define __inline_mathop_declNP_(float_type, func, op, params...) \ __MATH_INLINE float_type __NTH (func (float_type __x)) \ { \ register float_type __result; \ __asm __volatile__ (op : "=t" (__result) : params); \ return __result; \ } # ifdef __USE_ISOC99 # define __inline_mathcode(func, arg, code) \ __inline_mathcode_ (double, func, arg, code) \ __inline_mathcode_ (float, __CONCAT(func,f), arg, code) \ __inline_mathcode_ (long double, __CONCAT(func,l), arg, code) # define __inline_mathcodeNP(func, arg, code) \ __inline_mathcodeNP_ (double, func, arg, code) \ __inline_mathcodeNP_ (float, __CONCAT(func,f), arg, code) \ __inline_mathcodeNP_ (long double, __CONCAT(func,l), arg, code) # define __inline_mathcode2(func, arg1, arg2, code) \ __inline_mathcode2_ (double, func, arg1, arg2, code) \ __inline_mathcode2_ (float, __CONCAT(func,f), arg1, arg2, code) \ __inline_mathcode2_ (long double, __CONCAT(func,l), arg1, arg2, code) # define __inline_mathcodeNP2(func, arg1, arg2, code) \ __inline_mathcodeNP2_ (double, func, arg1, arg2, code) \ __inline_mathcodeNP2_ (float, __CONCAT(func,f), arg1, arg2, code) \ __inline_mathcodeNP2_ (long double, __CONCAT(func,l), arg1, arg2, code) # define __inline_mathcode3(func, arg1, arg2, arg3, code) \ __inline_mathcode3_ (double, func, arg1, arg2, arg3, code) \ __inline_mathcode3_ (float, __CONCAT(func,f), arg1, arg2, arg3, code) \ __inline_mathcode3_ (long double, __CONCAT(func,l), arg1, arg2, arg3, code) # define __inline_mathcodeNP3(func, arg1, arg2, arg3, code) \ __inline_mathcodeNP3_ (double, func, arg1, arg2, arg3, code) \ __inline_mathcodeNP3_ (float, __CONCAT(func,f), arg1, arg2, arg3, code) \ __inline_mathcodeNP3_ (long double, __CONCAT(func,l), arg1, arg2, arg3, code) # else # define __inline_mathcode(func, arg, code) \ __inline_mathcode_ (double, func, (arg), code) # define __inline_mathcodeNP(func, arg, code) \ __inline_mathcodeNP_ (double, func, (arg), code) # define __inline_mathcode2(func, arg1, arg2, code) \ __inline_mathcode2_ (double, func, arg1, arg2, code) # define __inline_mathcodeNP2(func, arg1, arg2, code) \ __inline_mathcodeNP2_ (double, func, arg1, arg2, code) # define __inline_mathcode3(func, arg1, arg2, arg3, code) \ __inline_mathcode3_ (double, func, arg1, arg2, arg3, code) # define __inline_mathcodeNP3(func, arg1, arg2, arg3, code) \ __inline_mathcodeNP3_ (double, func, arg1, arg2, arg3, code) # endif # define __inline_mathcode_(float_type, func, arg, code) \ __MATH_INLINE float_type func (float_type) __THROW; \ __inline_mathcodeNP_(float_type, func, arg, code) # define __inline_mathcodeNP_(float_type, func, arg, code) \ __MATH_INLINE float_type __NTH (func (float_type arg)) \ { \ code; \ } # define __inline_mathcode2_(float_type, func, arg1, arg2, code) \ __MATH_INLINE float_type func (float_type, float_type) __THROW; \ __inline_mathcodeNP2_ (float_type, func, arg1, arg2, code) # define __inline_mathcodeNP2_(float_type, func, arg1, arg2, code) \ __MATH_INLINE float_type __NTH (func (float_type arg1, float_type arg2)) \ { \ code; \ } # define __inline_mathcode3_(float_type, func, arg1, arg2, arg3, code) \ __MATH_INLINE float_type func (float_type, float_type, float_type) __THROW; \ __inline_mathcodeNP3_(float_type, func, arg1, arg2, arg3, code) # define __inline_mathcodeNP3_(float_type, func, arg1, arg2, arg3, code) \ __MATH_INLINE float_type __NTH (func (float_type arg1, float_type arg2, \ float_type arg3)) \ { \ code; \ } # endif # if !defined __NO_MATH_INLINES && defined __OPTIMIZE__ /* Miscellaneous functions */ /* __FAST_MATH__ is defined by gcc -ffast-math. */ # ifdef __FAST_MATH__ /* Optimized inline implementation, sometimes with reduced precision and/or argument range. */ # if __GNUC_PREREQ (3, 5) # define __expm1_code \ register long double __temp; \ __temp = __builtin_expm1l (__x); \ return __temp ? __temp : __x # else # define __expm1_code \ register long double __value; \ register long double __exponent; \ register long double __temp; \ __asm __volatile__ \ ("fldl2e # e^x - 1 = 2^(x * log2(e)) - 1\n\t" \ "fmul %%st(1) # x * log2(e)\n\t" \ "fst %%st(1)\n\t" \ "frndint # int(x * log2(e))\n\t" \ "fxch\n\t" \ "fsub %%st(1) # fract(x * log2(e))\n\t" \ "f2xm1 # 2^(fract(x * log2(e))) - 1\n\t" \ "fscale # 2^(x * log2(e)) - 2^(int(x * log2(e)))\n\t" \ : "=t" (__value), "=u" (__exponent) : "0" (__x)); \ __asm __volatile__ \ ("fscale # 2^int(x * log2(e))\n\t" \ : "=t" (__temp) : "0" (1.0), "u" (__exponent)); \ __temp -= 1.0; \ __temp += __value; \ return __temp ? __temp : __x # endif __inline_mathcodeNP_ (long double, __expm1l, __x, __expm1_code) # if __GNUC_PREREQ (3, 4) __inline_mathcodeNP_ (long double, __expl, __x, return __builtin_expl (__x)) # else # define __exp_code \ register long double __value; \ register long double __exponent; \ __asm __volatile__ \ ("fldl2e # e^x = 2^(x * log2(e))\n\t" \ "fmul %%st(1) # x * log2(e)\n\t" \ "fst %%st(1)\n\t" \ "frndint # int(x * log2(e))\n\t" \ "fxch\n\t" \ "fsub %%st(1) # fract(x * log2(e))\n\t" \ "f2xm1 # 2^(fract(x * log2(e))) - 1\n\t" \ : "=t" (__value), "=u" (__exponent) : "0" (__x)); \ __value += 1.0; \ __asm __volatile__ \ ("fscale" \ : "=t" (__value) : "0" (__value), "u" (__exponent)); \ return __value __inline_mathcodeNP (exp, __x, __exp_code) __inline_mathcodeNP_ (long double, __expl, __x, __exp_code) # endif # endif /* __FAST_MATH__ */ # ifdef __FAST_MATH__ # if !__GNUC_PREREQ (3,3) __inline_mathopNP (sqrt, "fsqrt") __inline_mathopNP_ (long double, __sqrtl, "fsqrt") # define __libc_sqrtl(n) __sqrtl (n) # else # define __libc_sqrtl(n) __builtin_sqrtl (n) # endif # endif # if __GNUC_PREREQ (2, 8) __inline_mathcodeNP_ (double, fabs, __x, return __builtin_fabs (__x)) # ifdef __USE_ISOC99 __inline_mathcodeNP_ (float, fabsf, __x, return __builtin_fabsf (__x)) __inline_mathcodeNP_ (long double, fabsl, __x, return __builtin_fabsl (__x)) # endif __inline_mathcodeNP_ (long double, __fabsl, __x, return __builtin_fabsl (__x)) # else __inline_mathop (fabs, "fabs") __inline_mathop_ (long double, __fabsl, "fabs") # endif __inline_mathcode_ (long double, __sgn1l, __x, \ __extension__ union { long double __xld; unsigned int __xi[3]; } __n = \ { __xld: __x }; \ __n.__xi[2] = (__n.__xi[2] & 0x8000) | 0x3fff; \ __n.__xi[1] = 0x80000000; \ __n.__xi[0] = 0; \ return __n.__xld) # ifdef __FAST_MATH__ /* The argument range of the inline version of sinhl is slightly reduced. */ __inline_mathcodeNP (sinh, __x, \ register long double __exm1 = __expm1l (__fabsl (__x)); \ return 0.5 * (__exm1 / (__exm1 + 1.0) + __exm1) * __sgn1l (__x)) __inline_mathcodeNP (cosh, __x, \ register long double __ex = __expl (__x); \ return 0.5 * (__ex + 1.0 / __ex)) __inline_mathcodeNP (tanh, __x, \ register long double __exm1 = __expm1l (-__fabsl (__x + __x)); \ return __exm1 / (__exm1 + 2.0) * __sgn1l (-__x)) # endif /* Optimized versions for some non-standardized functions. */ # ifdef __USE_ISOC99 # ifdef __FAST_MATH__ __inline_mathcodeNP (expm1, __x, __expm1_code) /* The argument range of the inline version of asinhl is slightly reduced. */ __inline_mathcodeNP (asinh, __x, \ register long double __y = __fabsl (__x); \ return (log1pl (__y * __y / (__libc_sqrtl (__y * __y + 1.0) + 1.0) + __y) \ * __sgn1l (__x))) __inline_mathcodeNP (acosh, __x, \ return logl (__x + __libc_sqrtl (__x - 1.0) * __libc_sqrtl (__x + 1.0))) __inline_mathcodeNP (atanh, __x, \ register long double __y = __fabsl (__x); \ return -0.5 * log1pl (-(__y + __y) / (1.0 + __y)) * __sgn1l (__x)) /* The argument range of the inline version of hypotl is slightly reduced. */ __inline_mathcodeNP2 (hypot, __x, __y, return __libc_sqrtl (__x * __x + __y * __y)) # endif # endif /* Undefine some of the large macros which are not used anymore. */ # ifdef __FAST_MATH__ # undef __expm1_code # undef __exp_code # endif /* __FAST_MATH__ */ # endif /* __NO_MATH_INLINES */ /* This code is used internally in the GNU libc. */ # ifdef __LIBC_INTERNAL_MATH_INLINES __inline_mathcode2_ (long double, __ieee754_atan2l, __y, __x, register long double __value; __asm __volatile__ ("fpatan\n\t" : "=t" (__value) : "0" (__x), "u" (__y) : "st(1)"); return __value;) # endif #endif /* !__SSE2_MATH__ && !__x86_64__ */