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Diffstat (limited to 'winsup/mingw/mingwex/math/erfl.c')
| -rwxr-xr-x | winsup/mingw/mingwex/math/erfl.c | 296 |
1 files changed, 0 insertions, 296 deletions
diff --git a/winsup/mingw/mingwex/math/erfl.c b/winsup/mingw/mingwex/math/erfl.c deleted file mode 100755 index 3f9b2b9f3..000000000 --- a/winsup/mingw/mingwex/math/erfl.c +++ /dev/null @@ -1,296 +0,0 @@ -/* erfl.c - * - * Error function - * - * - * - * SYNOPSIS: - * - * long double x, y, erfl(); - * - * y = erfl( x ); - * - * - * - * DESCRIPTION: - * - * The integral is - * - * x - * - - * 2 | | 2 - * erf(x) = -------- | exp( - t ) dt. - * sqrt(pi) | | - * - - * 0 - * - * The magnitude of x is limited to about 106.56 for IEEE - * arithmetic; 1 or -1 is returned outside this range. - * - * For 0 <= |x| < 1, erf(x) = x * P6(x^2)/Q6(x^2); - * Otherwise: erf(x) = 1 - erfc(x). - * - * - * - * ACCURACY: - * - * Relative error: - * arithmetic domain # trials peak rms - * IEEE 0,1 50000 2.0e-19 5.7e-20 - * - */ - -/* erfcl.c - * - * Complementary error function - * - * - * - * SYNOPSIS: - * - * long double x, y, erfcl(); - * - * y = erfcl( x ); - * - * - * - * DESCRIPTION: - * - * - * 1 - erf(x) = - * - * inf. - * - - * 2 | | 2 - * erfc(x) = -------- | exp( - t ) dt - * sqrt(pi) | | - * - - * x - * - * - * For small x, erfc(x) = 1 - erf(x); otherwise rational - * approximations are computed. - * - * A special function expx2l.c is used to suppress error amplification - * in computing exp(-x^2). - * - * - * ACCURACY: - * - * Relative error: - * arithmetic domain # trials peak rms - * IEEE 0,13 50000 8.4e-19 9.7e-20 - * IEEE 6,106.56 20000 2.9e-19 7.1e-20 - * - * - * ERROR MESSAGES: - * - * message condition value returned - * erfcl underflow x^2 > MAXLOGL 0.0 - * - * - */ - - -/* -Modified from file ndtrl.c -Cephes Math Library Release 2.3: January, 1995 -Copyright 1984, 1995 by Stephen L. Moshier -*/ - -#include <math.h> -#include "cephes_mconf.h" - -/* erfc(x) = exp(-x^2) P(1/x)/Q(1/x) - 1/8 <= 1/x <= 1 - Peak relative error 5.8e-21 */ - -static const uLD P[] = { -{ { 0x4bf0,0x9ad8,0x7a03,0x86c7,0x401d, XPD } }, -{ { 0xdf23,0xd843,0x4032,0x8881,0x401e, XPD } }, -{ { 0xd025,0xcfd5,0x8494,0x88d3,0x401e, XPD } }, -{ { 0xb6d0,0xc92b,0x5417,0xacb1,0x401d, XPD } }, -{ { 0xada8,0x356a,0x4982,0x94a6,0x401c, XPD } }, -{ { 0x4e13,0xcaee,0x9e31,0xb258,0x401a, XPD } }, -{ { 0x5840,0x554d,0x37a3,0x9239,0x4018, XPD } }, -{ { 0x3b58,0x3da2,0xaf02,0x9780,0x4015, XPD } }, -{ { 0x0144,0x489e,0xbe68,0x9c31,0x4011, XPD } }, -{ { 0x333b,0xd9e6,0xd404,0x986f,0xbfee, XPD } } -}; -static const uLD Q[] = { -{ { 0X0e43,0x302d,0x79ed,0x86c7,0x401d, XPD } }, -{ { 0xf817,0x9128,0xc0f8,0xd48b,0x401e, XPD } }, -{ { 0x8eae,0x8dad,0x6eb4,0x9aa2,0x401f, XPD } }, -{ { 0x00e7,0x7595,0xcd06,0x88bb,0x401f, XPD } }, -{ { 0x4991,0xcfda,0x52f1,0xa2a9,0x401e, XPD } }, -{ { 0xc39d,0xe415,0xc43d,0x87c0,0x401d, XPD } }, -{ { 0xa75d,0x436f,0x30dd,0xa027,0x401b, XPD } }, -{ { 0xc4cb,0x305a,0xbf78,0x8220,0x4019, XPD } }, -{ { 0x3708,0x33b1,0x07fa,0x8644,0x4016, XPD } }, -{ { 0x24fa,0x96f6,0x7153,0x8a6c,0x4012, XPD } } -}; - -/* erfc(x) = exp(-x^2) 1/x R(1/x^2) / S(1/x^2) - 1/128 <= 1/x < 1/8 - Peak relative error 1.9e-21 */ - -static const uLD R[] = { -{ { 0x260a,0xab95,0x2fc7,0xe7c4,0x4000, XPD } }, -{ { 0x4761,0x613e,0xdf6d,0xe58e,0x4001, XPD } }, -{ { 0x0615,0x4b00,0x575f,0xdc7b,0x4000, XPD } }, -{ { 0x521d,0x8527,0x3435,0x8dc2,0x3ffe, XPD } }, -{ { 0x22cf,0xc711,0x6c5b,0xdcfb,0x3ff9, XPD } } -}; -static const uLD S[] = { -{ { 0x5de6,0x17d7,0x54d6,0xaba9,0x4002, XPD } }, -{ { 0x55d5,0xd300,0xe71e,0xf564,0x4002, XPD } }, -{ { 0xb611,0x8f76,0xf020,0xd255,0x4001, XPD } }, -{ { 0x3684,0x3798,0xb793,0x80b0,0x3fff, XPD } }, -{ { 0xf5af,0x2fb2,0x1e57,0xc3d7,0x3ffa, XPD } } -}; - -/* erf(x) = x T(x^2)/U(x^2) - 0 <= x <= 1 - Peak relative error 7.6e-23 */ - -static const uLD T[] = { -{ { 0xfd7a,0x3a1a,0x705b,0xe0c4,0x3ffb, XPD } }, -{ { 0x3128,0xc337,0x3716,0xace5,0x4001, XPD } }, -{ { 0x9517,0x4e93,0x540e,0x8f97,0x4007, XPD } }, -{ { 0x6118,0x6059,0x9093,0xa757,0x400a, XPD } }, -{ { 0xb954,0xa987,0xc60c,0xbc83,0x400e, XPD } }, -{ { 0x7a56,0xe45a,0xa4bd,0x975b,0x4010, XPD } }, -{ { 0xc446,0x6bab,0x0b2a,0x86d0,0x4013, XPD } } -}; - -static const uLD U[] = { -{ { 0x3453,0x1f8e,0xf688,0xb507,0x4004, XPD } }, -{ { 0x71ac,0xb12f,0x21ca,0xf2e2,0x4008, XPD } }, -{ { 0xffe8,0x9cac,0x3b84,0xc2ac,0x400c, XPD } }, -{ { 0x481d,0x445b,0xc807,0xc232,0x400f, XPD } }, -{ { 0x9ad5,0x1aef,0x45b1,0xe25e,0x4011, XPD } }, -{ { 0x71a7,0x1cad,0x012e,0xeef3,0x4012, XPD } } -}; - -/* expx2l.c - * - * Exponential of squared argument - * - * - * - * SYNOPSIS: - * - * long double x, y, expmx2l(); - * int sign; - * - * y = expx2l( x ); - * - * - * - * DESCRIPTION: - * - * Computes y = exp(x*x) while suppressing error amplification - * that would ordinarily arise from the inexactness of the - * exponential argument x*x. - * - * - * - * ACCURACY: - * - * Relative error: - * arithmetic domain # trials peak rms - * IEEE -106.566, 106.566 10^5 1.6e-19 4.4e-20 - * - */ - -#define M 32768.0L -#define MINV 3.0517578125e-5L - -static long double expx2l (long double x) -{ - long double u, u1, m, f; - - x = fabsl (x); - /* Represent x as an exact multiple of M plus a residual. - M is a power of 2 chosen so that exp(m * m) does not overflow - or underflow and so that |x - m| is small. */ - m = MINV * floorl(M * x + 0.5L); - f = x - m; - - /* x^2 = m^2 + 2mf + f^2 */ - u = m * m; - u1 = 2 * m * f + f * f; - - if ((u+u1) > MAXLOGL) - return (INFINITYL); - - /* u is exact, u1 is small. */ - u = expl(u) * expl(u1); - return(u); -} - -long double erfcl(long double a) -{ -long double p,q,x,y,z; - -if (isinf (a)) - return (signbit (a) ? 2.0 : 0.0); - -x = fabsl (a); - -if (x < 1.0L) - return (1.0L - erfl(a)); - -z = a * a; - -if( z > MAXLOGL ) - { -under: - mtherr( "erfcl", UNDERFLOW ); - errno = ERANGE; - return (signbit (a) ? 2.0 : 0.0); - } - -/* Compute z = expl(a * a). */ -z = expx2l (a); -y = 1.0L/x; - -if (x < 8.0L) - { - p = polevll (y, P, 9); - q = p1evll (y, Q, 10); - } -else - { - q = y * y; - p = y * polevll (q, R, 4); - q = p1evll (q, S, 5); - } -y = p/(q * z); - -if (a < 0.0L) - y = 2.0L - y; - -if (y == 0.0L) - goto under; - -return (y); -} - -long double erfl(long double x) -{ -long double y, z; - -if( x == 0.0L ) - return (x); - -if (isinf (x)) - return (signbit (x) ? -1.0L : 1.0L); - -if (fabsl(x) > 1.0L) - return (1.0L - erfcl (x)); - -z = x * x; -y = x * polevll( z, T, 6 ) / p1evll( z, U, 6 ); -return( y ); -} |