/* Inline math functions for i387 and SSE.

[0] Fix | Delete

Copyright (C) 1995-2018 Free Software Foundation, Inc.

[1] Fix | Delete

This file is part of the GNU C Library.

[2] Fix | Delete

[3] Fix | Delete

The GNU C Library is free software; you can redistribute it and/or

[4] Fix | Delete

modify it under the terms of the GNU Lesser General Public

[5] Fix | Delete

License as published by the Free Software Foundation; either

[6] Fix | Delete

version 2.1 of the License, or (at your option) any later version.

[7] Fix | Delete

[8] Fix | Delete

The GNU C Library is distributed in the hope that it will be useful,

[9] Fix | Delete

but WITHOUT ANY WARRANTY; without even the implied warranty of

[10] Fix | Delete

MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU

[11] Fix | Delete

Lesser General Public License for more details.

[12] Fix | Delete

[13] Fix | Delete

You should have received a copy of the GNU Lesser General Public

[14] Fix | Delete

License along with the GNU C Library; if not, see

[15] Fix | Delete

<http://www.gnu.org/licenses/>. */

[16] Fix | Delete

[17] Fix | Delete

#ifndef _MATH_H

[18] Fix | Delete

# error "Never use <bits/mathinline.h> directly; include <math.h> instead."

[19] Fix | Delete

#endif

[20] Fix | Delete

[21] Fix | Delete

#ifndef __extern_always_inline

[22] Fix | Delete

# define __MATH_INLINE __inline

[23] Fix | Delete

#else

[24] Fix | Delete

# define __MATH_INLINE __extern_always_inline

[25] Fix | Delete

#endif

[26] Fix | Delete

[27] Fix | Delete

/* Disable x87 inlines when -fpmath=sse is passed and also when we're building

[28] Fix | Delete

on x86_64. Older gcc (gcc-3.2 for example) does not define __SSE2_MATH__

[29] Fix | Delete

for x86_64. */

[30] Fix | Delete

#if !defined __SSE2_MATH__ && !defined __x86_64__

[31] Fix | Delete

# if ((!defined __NO_MATH_INLINES || defined __LIBC_INTERNAL_MATH_INLINES) \

[32] Fix | Delete

&& defined __OPTIMIZE__)

[33] Fix | Delete

[34] Fix | Delete

/* The inline functions do not set errno or raise necessarily the

[35] Fix | Delete

correct exceptions. */

[36] Fix | Delete

# undef math_errhandling

[37] Fix | Delete

[38] Fix | Delete

/* A macro to define float, double, and long double versions of various

[39] Fix | Delete

math functions for the ix87 FPU. FUNC is the function name (which will

[40] Fix | Delete

be suffixed with f and l for the float and long double version,

[41] Fix | Delete

respectively). OP is the name of the FPU operation.

[42] Fix | Delete

We define two sets of macros. The set with the additional NP

[43] Fix | Delete

doesn't add a prototype declaration. */

[44] Fix | Delete

[45] Fix | Delete

# ifdef __USE_ISOC99

[46] Fix | Delete

# define __inline_mathop(func, op) \

[47] Fix | Delete

__inline_mathop_ (double, func, op) \

[48] Fix | Delete

__inline_mathop_ (float, __CONCAT(func,f), op) \

[49] Fix | Delete

__inline_mathop_ (long double, __CONCAT(func,l), op)

[50] Fix | Delete

# define __inline_mathopNP(func, op) \

[51] Fix | Delete

__inline_mathopNP_ (double, func, op) \

[52] Fix | Delete

__inline_mathopNP_ (float, __CONCAT(func,f), op) \

[53] Fix | Delete

__inline_mathopNP_ (long double, __CONCAT(func,l), op)

[54] Fix | Delete

# else

[55] Fix | Delete

# define __inline_mathop(func, op) \

[56] Fix | Delete

__inline_mathop_ (double, func, op)

[57] Fix | Delete

# define __inline_mathopNP(func, op) \

[58] Fix | Delete

__inline_mathopNP_ (double, func, op)

[59] Fix | Delete

# endif

[60] Fix | Delete

[61] Fix | Delete

# define __inline_mathop_(float_type, func, op) \

[62] Fix | Delete

__inline_mathop_decl_ (float_type, func, op, "0" (__x))

[63] Fix | Delete

# define __inline_mathopNP_(float_type, func, op) \

[64] Fix | Delete

__inline_mathop_declNP_ (float_type, func, op, "0" (__x))

[65] Fix | Delete

[66] Fix | Delete

[67] Fix | Delete

# ifdef __USE_ISOC99

[68] Fix | Delete

# define __inline_mathop_decl(func, op, params...) \

[69] Fix | Delete

__inline_mathop_decl_ (double, func, op, params) \

[70] Fix | Delete

__inline_mathop_decl_ (float, __CONCAT(func,f), op, params) \

[71] Fix | Delete

__inline_mathop_decl_ (long double, __CONCAT(func,l), op, params)

[72] Fix | Delete

# define __inline_mathop_declNP(func, op, params...) \

[73] Fix | Delete

__inline_mathop_declNP_ (double, func, op, params) \

[74] Fix | Delete

__inline_mathop_declNP_ (float, __CONCAT(func,f), op, params) \

[75] Fix | Delete

__inline_mathop_declNP_ (long double, __CONCAT(func,l), op, params)

[76] Fix | Delete

# else

[77] Fix | Delete

# define __inline_mathop_decl(func, op, params...) \

[78] Fix | Delete

__inline_mathop_decl_ (double, func, op, params)

[79] Fix | Delete

# define __inline_mathop_declNP(func, op, params...) \

[80] Fix | Delete

__inline_mathop_declNP_ (double, func, op, params)

[81] Fix | Delete

# endif

[82] Fix | Delete

[83] Fix | Delete

# define __inline_mathop_decl_(float_type, func, op, params...) \

[84] Fix | Delete

__MATH_INLINE float_type func (float_type) __THROW; \

[85] Fix | Delete

__inline_mathop_declNP_ (float_type, func, op, params)

[86] Fix | Delete

[87] Fix | Delete

# define __inline_mathop_declNP_(float_type, func, op, params...) \

[88] Fix | Delete

__MATH_INLINE float_type __NTH (func (float_type __x)) \

[89] Fix | Delete

{ \

[90] Fix | Delete

register float_type __result; \

[91] Fix | Delete

__asm __volatile__ (op : "=t" (__result) : params); \

[92] Fix | Delete

return __result; \

[93] Fix | Delete

}

[94] Fix | Delete

[95] Fix | Delete

[96] Fix | Delete

# ifdef __USE_ISOC99

[97] Fix | Delete

# define __inline_mathcode(func, arg, code) \

[98] Fix | Delete

__inline_mathcode_ (double, func, arg, code) \

[99] Fix | Delete

__inline_mathcode_ (float, __CONCAT(func,f), arg, code) \

[100] Fix | Delete

__inline_mathcode_ (long double, __CONCAT(func,l), arg, code)

[101] Fix | Delete

# define __inline_mathcodeNP(func, arg, code) \

[102] Fix | Delete

__inline_mathcodeNP_ (double, func, arg, code) \

[103] Fix | Delete

__inline_mathcodeNP_ (float, __CONCAT(func,f), arg, code) \

[104] Fix | Delete

__inline_mathcodeNP_ (long double, __CONCAT(func,l), arg, code)

[105] Fix | Delete

# define __inline_mathcode2(func, arg1, arg2, code) \

[106] Fix | Delete

__inline_mathcode2_ (double, func, arg1, arg2, code) \

[107] Fix | Delete

__inline_mathcode2_ (float, __CONCAT(func,f), arg1, arg2, code) \

[108] Fix | Delete

__inline_mathcode2_ (long double, __CONCAT(func,l), arg1, arg2, code)

[109] Fix | Delete

# define __inline_mathcodeNP2(func, arg1, arg2, code) \

[110] Fix | Delete

__inline_mathcodeNP2_ (double, func, arg1, arg2, code) \

[111] Fix | Delete

__inline_mathcodeNP2_ (float, __CONCAT(func,f), arg1, arg2, code) \

[112] Fix | Delete

__inline_mathcodeNP2_ (long double, __CONCAT(func,l), arg1, arg2, code)

[113] Fix | Delete

# define __inline_mathcode3(func, arg1, arg2, arg3, code) \

[114] Fix | Delete

__inline_mathcode3_ (double, func, arg1, arg2, arg3, code) \

[115] Fix | Delete

__inline_mathcode3_ (float, __CONCAT(func,f), arg1, arg2, arg3, code) \

[116] Fix | Delete

__inline_mathcode3_ (long double, __CONCAT(func,l), arg1, arg2, arg3, code)

[117] Fix | Delete

# define __inline_mathcodeNP3(func, arg1, arg2, arg3, code) \

[118] Fix | Delete

__inline_mathcodeNP3_ (double, func, arg1, arg2, arg3, code) \

[119] Fix | Delete

__inline_mathcodeNP3_ (float, __CONCAT(func,f), arg1, arg2, arg3, code) \

[120] Fix | Delete

__inline_mathcodeNP3_ (long double, __CONCAT(func,l), arg1, arg2, arg3, code)

[121] Fix | Delete

# else

[122] Fix | Delete

# define __inline_mathcode(func, arg, code) \

[123] Fix | Delete

__inline_mathcode_ (double, func, (arg), code)

[124] Fix | Delete

# define __inline_mathcodeNP(func, arg, code) \

[125] Fix | Delete

__inline_mathcodeNP_ (double, func, (arg), code)

[126] Fix | Delete

# define __inline_mathcode2(func, arg1, arg2, code) \

[127] Fix | Delete

__inline_mathcode2_ (double, func, arg1, arg2, code)

[128] Fix | Delete

# define __inline_mathcodeNP2(func, arg1, arg2, code) \

[129] Fix | Delete

__inline_mathcodeNP2_ (double, func, arg1, arg2, code)

[130] Fix | Delete

# define __inline_mathcode3(func, arg1, arg2, arg3, code) \

[131] Fix | Delete

__inline_mathcode3_ (double, func, arg1, arg2, arg3, code)

[132] Fix | Delete

# define __inline_mathcodeNP3(func, arg1, arg2, arg3, code) \

[133] Fix | Delete

__inline_mathcodeNP3_ (double, func, arg1, arg2, arg3, code)

[134] Fix | Delete

# endif

[135] Fix | Delete

[136] Fix | Delete

# define __inline_mathcode_(float_type, func, arg, code) \

[137] Fix | Delete

__MATH_INLINE float_type func (float_type) __THROW; \

[138] Fix | Delete

__inline_mathcodeNP_(float_type, func, arg, code)

[139] Fix | Delete

[140] Fix | Delete

# define __inline_mathcodeNP_(float_type, func, arg, code) \

[141] Fix | Delete

__MATH_INLINE float_type __NTH (func (float_type arg)) \

[142] Fix | Delete

{ \

[143] Fix | Delete

code; \

[144] Fix | Delete

}

[145] Fix | Delete

[146] Fix | Delete

[147] Fix | Delete

# define __inline_mathcode2_(float_type, func, arg1, arg2, code) \

[148] Fix | Delete

__MATH_INLINE float_type func (float_type, float_type) __THROW; \

[149] Fix | Delete

__inline_mathcodeNP2_ (float_type, func, arg1, arg2, code)

[150] Fix | Delete

[151] Fix | Delete

# define __inline_mathcodeNP2_(float_type, func, arg1, arg2, code) \

[152] Fix | Delete

__MATH_INLINE float_type __NTH (func (float_type arg1, float_type arg2)) \

[153] Fix | Delete

{ \

[154] Fix | Delete

code; \

[155] Fix | Delete

}

[156] Fix | Delete

[157] Fix | Delete

# define __inline_mathcode3_(float_type, func, arg1, arg2, arg3, code) \

[158] Fix | Delete

__MATH_INLINE float_type func (float_type, float_type, float_type) __THROW; \

[159] Fix | Delete

__inline_mathcodeNP3_(float_type, func, arg1, arg2, arg3, code)

[160] Fix | Delete

[161] Fix | Delete

# define __inline_mathcodeNP3_(float_type, func, arg1, arg2, arg3, code) \

[162] Fix | Delete

__MATH_INLINE float_type __NTH (func (float_type arg1, float_type arg2, \

[163] Fix | Delete

float_type arg3)) \

[164] Fix | Delete

{ \

[165] Fix | Delete

code; \

[166] Fix | Delete

}

[167] Fix | Delete

# endif

[168] Fix | Delete

[169] Fix | Delete

[170] Fix | Delete

# if !defined __NO_MATH_INLINES && defined __OPTIMIZE__

[171] Fix | Delete

/* Miscellaneous functions */

[172] Fix | Delete

[173] Fix | Delete

/* __FAST_MATH__ is defined by gcc -ffast-math. */

[174] Fix | Delete

# ifdef __FAST_MATH__

[175] Fix | Delete

/* Optimized inline implementation, sometimes with reduced precision

[176] Fix | Delete

and/or argument range. */

[177] Fix | Delete

[178] Fix | Delete

# if __GNUC_PREREQ (3, 5)

[179] Fix | Delete

# define __expm1_code \

[180] Fix | Delete

register long double __temp; \

[181] Fix | Delete

__temp = __builtin_expm1l (__x); \

[182] Fix | Delete

return __temp ? __temp : __x

[183] Fix | Delete

# else

[184] Fix | Delete

# define __expm1_code \

[185] Fix | Delete

register long double __value; \

[186] Fix | Delete

register long double __exponent; \

[187] Fix | Delete

register long double __temp; \

[188] Fix | Delete

__asm __volatile__ \

[189] Fix | Delete

("fldl2e # e^x - 1 = 2^(x * log2(e)) - 1\n\t" \

[190] Fix | Delete

"fmul %%st(1) # x * log2(e)\n\t" \

[191] Fix | Delete

"fst %%st(1)\n\t" \

[192] Fix | Delete

"frndint # int(x * log2(e))\n\t" \

[193] Fix | Delete

"fxch\n\t" \

[194] Fix | Delete

"fsub %%st(1) # fract(x * log2(e))\n\t" \

[195] Fix | Delete

"f2xm1 # 2^(fract(x * log2(e))) - 1\n\t" \

[196] Fix | Delete

"fscale # 2^(x * log2(e)) - 2^(int(x * log2(e)))\n\t" \

[197] Fix | Delete

: "=t" (__value), "=u" (__exponent) : "0" (__x)); \

[198] Fix | Delete

__asm __volatile__ \

[199] Fix | Delete

("fscale # 2^int(x * log2(e))\n\t" \

[200] Fix | Delete

: "=t" (__temp) : "0" (1.0), "u" (__exponent)); \

[201] Fix | Delete

__temp -= 1.0; \

[202] Fix | Delete

__temp += __value; \

[203] Fix | Delete

return __temp ? __temp : __x

[204] Fix | Delete

# endif

[205] Fix | Delete

__inline_mathcodeNP_ (long double, __expm1l, __x, __expm1_code)

[206] Fix | Delete

[207] Fix | Delete

# if __GNUC_PREREQ (3, 4)

[208] Fix | Delete

__inline_mathcodeNP_ (long double, __expl, __x, return __builtin_expl (__x))

[209] Fix | Delete

# else

[210] Fix | Delete

# define __exp_code \

[211] Fix | Delete

register long double __value; \

[212] Fix | Delete

register long double __exponent; \

[213] Fix | Delete

__asm __volatile__ \

[214] Fix | Delete

("fldl2e # e^x = 2^(x * log2(e))\n\t" \

[215] Fix | Delete

"fmul %%st(1) # x * log2(e)\n\t" \

[216] Fix | Delete

"fst %%st(1)\n\t" \

[217] Fix | Delete

"frndint # int(x * log2(e))\n\t" \

[218] Fix | Delete

"fxch\n\t" \

[219] Fix | Delete

"fsub %%st(1) # fract(x * log2(e))\n\t" \

[220] Fix | Delete

"f2xm1 # 2^(fract(x * log2(e))) - 1\n\t" \

[221] Fix | Delete

: "=t" (__value), "=u" (__exponent) : "0" (__x)); \

[222] Fix | Delete

__value += 1.0; \

[223] Fix | Delete

__asm __volatile__ \

[224] Fix | Delete

("fscale" \

[225] Fix | Delete

: "=t" (__value) : "0" (__value), "u" (__exponent)); \

[226] Fix | Delete

return __value

[227] Fix | Delete

__inline_mathcodeNP (exp, __x, __exp_code)

[228] Fix | Delete

__inline_mathcodeNP_ (long double, __expl, __x, __exp_code)

[229] Fix | Delete

# endif

[230] Fix | Delete

# endif /* __FAST_MATH__ */

[231] Fix | Delete

[232] Fix | Delete

[233] Fix | Delete

# ifdef __FAST_MATH__

[234] Fix | Delete

# if !__GNUC_PREREQ (3,3)

[235] Fix | Delete

__inline_mathopNP (sqrt, "fsqrt")

[236] Fix | Delete

__inline_mathopNP_ (long double, __sqrtl, "fsqrt")

[237] Fix | Delete

# define __libc_sqrtl(n) __sqrtl (n)

[238] Fix | Delete

# else

[239] Fix | Delete

# define __libc_sqrtl(n) __builtin_sqrtl (n)

[240] Fix | Delete

# endif

[241] Fix | Delete

# endif

[242] Fix | Delete

[243] Fix | Delete

# if __GNUC_PREREQ (2, 8)

[244] Fix | Delete

__inline_mathcodeNP_ (double, fabs, __x, return __builtin_fabs (__x))

[245] Fix | Delete

# ifdef __USE_ISOC99

[246] Fix | Delete

__inline_mathcodeNP_ (float, fabsf, __x, return __builtin_fabsf (__x))

[247] Fix | Delete

__inline_mathcodeNP_ (long double, fabsl, __x, return __builtin_fabsl (__x))

[248] Fix | Delete

# endif

[249] Fix | Delete

__inline_mathcodeNP_ (long double, __fabsl, __x, return __builtin_fabsl (__x))

[250] Fix | Delete

# else

[251] Fix | Delete

__inline_mathop (fabs, "fabs")

[252] Fix | Delete

__inline_mathop_ (long double, __fabsl, "fabs")

[253] Fix | Delete

# endif

[254] Fix | Delete

[255] Fix | Delete

__inline_mathcode_ (long double, __sgn1l, __x, \

[256] Fix | Delete

__extension__ union { long double __xld; unsigned int __xi[3]; } __n = \

[257] Fix | Delete

{ __xld: __x }; \

[258] Fix | Delete

__n.__xi[2] = (__n.__xi[2] & 0x8000) | 0x3fff; \

[259] Fix | Delete

__n.__xi[1] = 0x80000000; \

[260] Fix | Delete

__n.__xi[0] = 0; \

[261] Fix | Delete

return __n.__xld)

[262] Fix | Delete

[263] Fix | Delete

[264] Fix | Delete

# ifdef __FAST_MATH__

[265] Fix | Delete

/* The argument range of the inline version of sinhl is slightly reduced. */

[266] Fix | Delete

__inline_mathcodeNP (sinh, __x, \

[267] Fix | Delete

register long double __exm1 = __expm1l (__fabsl (__x)); \

[268] Fix | Delete

return 0.5 * (__exm1 / (__exm1 + 1.0) + __exm1) * __sgn1l (__x))

[269] Fix | Delete

[270] Fix | Delete

__inline_mathcodeNP (cosh, __x, \

[271] Fix | Delete

register long double __ex = __expl (__x); \

[272] Fix | Delete

return 0.5 * (__ex + 1.0 / __ex))

[273] Fix | Delete

[274] Fix | Delete

__inline_mathcodeNP (tanh, __x, \

[275] Fix | Delete

register long double __exm1 = __expm1l (-__fabsl (__x + __x)); \

[276] Fix | Delete

return __exm1 / (__exm1 + 2.0) * __sgn1l (-__x))

[277] Fix | Delete

# endif

[278] Fix | Delete

[279] Fix | Delete

[280] Fix | Delete

/* Optimized versions for some non-standardized functions. */

[281] Fix | Delete

# ifdef __USE_ISOC99

[282] Fix | Delete

[283] Fix | Delete

# ifdef __FAST_MATH__

[284] Fix | Delete

__inline_mathcodeNP (expm1, __x, __expm1_code)

[285] Fix | Delete

[286] Fix | Delete

/* The argument range of the inline version of asinhl is slightly reduced. */

[287] Fix | Delete

__inline_mathcodeNP (asinh, __x, \

[288] Fix | Delete

register long double __y = __fabsl (__x); \

[289] Fix | Delete

return (log1pl (__y * __y / (__libc_sqrtl (__y * __y + 1.0) + 1.0) + __y) \

[290] Fix | Delete

* __sgn1l (__x)))

[291] Fix | Delete

[292] Fix | Delete

__inline_mathcodeNP (acosh, __x, \

[293] Fix | Delete

return logl (__x + __libc_sqrtl (__x - 1.0) * __libc_sqrtl (__x + 1.0)))

[294] Fix | Delete

[295] Fix | Delete

__inline_mathcodeNP (atanh, __x, \

[296] Fix | Delete

register long double __y = __fabsl (__x); \

[297] Fix | Delete

return -0.5 * log1pl (-(__y + __y) / (1.0 + __y)) * __sgn1l (__x))

[298] Fix | Delete

[299] Fix | Delete

/* The argument range of the inline version of hypotl is slightly reduced. */

[300] Fix | Delete

__inline_mathcodeNP2 (hypot, __x, __y,

[301] Fix | Delete

return __libc_sqrtl (__x * __x + __y * __y))

[302] Fix | Delete

[303] Fix | Delete

# endif

[304] Fix | Delete

# endif

[305] Fix | Delete

[306] Fix | Delete

[307] Fix | Delete

/* Undefine some of the large macros which are not used anymore. */

[308] Fix | Delete

# ifdef __FAST_MATH__

[309] Fix | Delete

# undef __expm1_code

[310] Fix | Delete

# undef __exp_code

[311] Fix | Delete

# endif /* __FAST_MATH__ */

[312] Fix | Delete

[313] Fix | Delete

# endif /* __NO_MATH_INLINES */

[314] Fix | Delete

[315] Fix | Delete

[316] Fix | Delete

/* This code is used internally in the GNU libc. */

[317] Fix | Delete

# ifdef __LIBC_INTERNAL_MATH_INLINES

[318] Fix | Delete

__inline_mathcode2_ (long double, __ieee754_atan2l, __y, __x,

[319] Fix | Delete

register long double __value;

[320] Fix | Delete

__asm __volatile__ ("fpatan\n\t"

[321] Fix | Delete

: "=t" (__value)

[322] Fix | Delete

: "0" (__x), "u" (__y) : "st(1)");

[323] Fix | Delete

return __value;)

[324] Fix | Delete

# endif

[325] Fix | Delete

[326] Fix | Delete

#endif /* !__SSE2_MATH__ && !__x86_64__ */

[327] Fix | Delete

[328] Fix | Delete