| Index: fusl/src/math/erf.c
|
| diff --git a/fusl/src/math/erf.c b/fusl/src/math/erf.c
|
| index 2f30a298f997cde0316af8681bb1447f085de54d..aff8bd054d341eb350f9c206d3f58b648720cc24 100644
|
| --- a/fusl/src/math/erf.c
|
| +++ b/fusl/src/math/erf.c
|
| @@ -105,169 +105,173 @@
|
|
|
| #include "libm.h"
|
|
|
| -static const double
|
| -erx = 8.45062911510467529297e-01, /* 0x3FEB0AC1, 0x60000000 */
|
| -/*
|
| - * Coefficients for approximation to erf on [0,0.84375]
|
| - */
|
| -efx8 = 1.02703333676410069053e+00, /* 0x3FF06EBA, 0x8214DB69 */
|
| -pp0 = 1.28379167095512558561e-01, /* 0x3FC06EBA, 0x8214DB68 */
|
| -pp1 = -3.25042107247001499370e-01, /* 0xBFD4CD7D, 0x691CB913 */
|
| -pp2 = -2.84817495755985104766e-02, /* 0xBF9D2A51, 0xDBD7194F */
|
| -pp3 = -5.77027029648944159157e-03, /* 0xBF77A291, 0x236668E4 */
|
| -pp4 = -2.37630166566501626084e-05, /* 0xBEF8EAD6, 0x120016AC */
|
| -qq1 = 3.97917223959155352819e-01, /* 0x3FD97779, 0xCDDADC09 */
|
| -qq2 = 6.50222499887672944485e-02, /* 0x3FB0A54C, 0x5536CEBA */
|
| -qq3 = 5.08130628187576562776e-03, /* 0x3F74D022, 0xC4D36B0F */
|
| -qq4 = 1.32494738004321644526e-04, /* 0x3F215DC9, 0x221C1A10 */
|
| -qq5 = -3.96022827877536812320e-06, /* 0xBED09C43, 0x42A26120 */
|
| -/*
|
| - * Coefficients for approximation to erf in [0.84375,1.25]
|
| - */
|
| -pa0 = -2.36211856075265944077e-03, /* 0xBF6359B8, 0xBEF77538 */
|
| -pa1 = 4.14856118683748331666e-01, /* 0x3FDA8D00, 0xAD92B34D */
|
| -pa2 = -3.72207876035701323847e-01, /* 0xBFD7D240, 0xFBB8C3F1 */
|
| -pa3 = 3.18346619901161753674e-01, /* 0x3FD45FCA, 0x805120E4 */
|
| -pa4 = -1.10894694282396677476e-01, /* 0xBFBC6398, 0x3D3E28EC */
|
| -pa5 = 3.54783043256182359371e-02, /* 0x3FA22A36, 0x599795EB */
|
| -pa6 = -2.16637559486879084300e-03, /* 0xBF61BF38, 0x0A96073F */
|
| -qa1 = 1.06420880400844228286e-01, /* 0x3FBB3E66, 0x18EEE323 */
|
| -qa2 = 5.40397917702171048937e-01, /* 0x3FE14AF0, 0x92EB6F33 */
|
| -qa3 = 7.18286544141962662868e-02, /* 0x3FB2635C, 0xD99FE9A7 */
|
| -qa4 = 1.26171219808761642112e-01, /* 0x3FC02660, 0xE763351F */
|
| -qa5 = 1.36370839120290507362e-02, /* 0x3F8BEDC2, 0x6B51DD1C */
|
| -qa6 = 1.19844998467991074170e-02, /* 0x3F888B54, 0x5735151D */
|
| -/*
|
| - * Coefficients for approximation to erfc in [1.25,1/0.35]
|
| - */
|
| -ra0 = -9.86494403484714822705e-03, /* 0xBF843412, 0x600D6435 */
|
| -ra1 = -6.93858572707181764372e-01, /* 0xBFE63416, 0xE4BA7360 */
|
| -ra2 = -1.05586262253232909814e+01, /* 0xC0251E04, 0x41B0E726 */
|
| -ra3 = -6.23753324503260060396e+01, /* 0xC04F300A, 0xE4CBA38D */
|
| -ra4 = -1.62396669462573470355e+02, /* 0xC0644CB1, 0x84282266 */
|
| -ra5 = -1.84605092906711035994e+02, /* 0xC067135C, 0xEBCCABB2 */
|
| -ra6 = -8.12874355063065934246e+01, /* 0xC0545265, 0x57E4D2F2 */
|
| -ra7 = -9.81432934416914548592e+00, /* 0xC023A0EF, 0xC69AC25C */
|
| -sa1 = 1.96512716674392571292e+01, /* 0x4033A6B9, 0xBD707687 */
|
| -sa2 = 1.37657754143519042600e+02, /* 0x4061350C, 0x526AE721 */
|
| -sa3 = 4.34565877475229228821e+02, /* 0x407B290D, 0xD58A1A71 */
|
| -sa4 = 6.45387271733267880336e+02, /* 0x40842B19, 0x21EC2868 */
|
| -sa5 = 4.29008140027567833386e+02, /* 0x407AD021, 0x57700314 */
|
| -sa6 = 1.08635005541779435134e+02, /* 0x405B28A3, 0xEE48AE2C */
|
| -sa7 = 6.57024977031928170135e+00, /* 0x401A47EF, 0x8E484A93 */
|
| -sa8 = -6.04244152148580987438e-02, /* 0xBFAEEFF2, 0xEE749A62 */
|
| -/*
|
| - * Coefficients for approximation to erfc in [1/.35,28]
|
| - */
|
| -rb0 = -9.86494292470009928597e-03, /* 0xBF843412, 0x39E86F4A */
|
| -rb1 = -7.99283237680523006574e-01, /* 0xBFE993BA, 0x70C285DE */
|
| -rb2 = -1.77579549177547519889e+01, /* 0xC031C209, 0x555F995A */
|
| -rb3 = -1.60636384855821916062e+02, /* 0xC064145D, 0x43C5ED98 */
|
| -rb4 = -6.37566443368389627722e+02, /* 0xC083EC88, 0x1375F228 */
|
| -rb5 = -1.02509513161107724954e+03, /* 0xC0900461, 0x6A2E5992 */
|
| -rb6 = -4.83519191608651397019e+02, /* 0xC07E384E, 0x9BDC383F */
|
| -sb1 = 3.03380607434824582924e+01, /* 0x403E568B, 0x261D5190 */
|
| -sb2 = 3.25792512996573918826e+02, /* 0x40745CAE, 0x221B9F0A */
|
| -sb3 = 1.53672958608443695994e+03, /* 0x409802EB, 0x189D5118 */
|
| -sb4 = 3.19985821950859553908e+03, /* 0x40A8FFB7, 0x688C246A */
|
| -sb5 = 2.55305040643316442583e+03, /* 0x40A3F219, 0xCEDF3BE6 */
|
| -sb6 = 4.74528541206955367215e+02, /* 0x407DA874, 0xE79FE763 */
|
| -sb7 = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */
|
| +static const double erx =
|
| + 8.45062911510467529297e-01, /* 0x3FEB0AC1, 0x60000000 */
|
| + /*
|
| + * Coefficients for approximation to erf on [0,0.84375]
|
| + */
|
| + efx8 = 1.02703333676410069053e+00, /* 0x3FF06EBA, 0x8214DB69 */
|
| + pp0 = 1.28379167095512558561e-01, /* 0x3FC06EBA, 0x8214DB68 */
|
| + pp1 = -3.25042107247001499370e-01, /* 0xBFD4CD7D, 0x691CB913 */
|
| + pp2 = -2.84817495755985104766e-02, /* 0xBF9D2A51, 0xDBD7194F */
|
| + pp3 = -5.77027029648944159157e-03, /* 0xBF77A291, 0x236668E4 */
|
| + pp4 = -2.37630166566501626084e-05, /* 0xBEF8EAD6, 0x120016AC */
|
| + qq1 = 3.97917223959155352819e-01, /* 0x3FD97779, 0xCDDADC09 */
|
| + qq2 = 6.50222499887672944485e-02, /* 0x3FB0A54C, 0x5536CEBA */
|
| + qq3 = 5.08130628187576562776e-03, /* 0x3F74D022, 0xC4D36B0F */
|
| + qq4 = 1.32494738004321644526e-04, /* 0x3F215DC9, 0x221C1A10 */
|
| + qq5 = -3.96022827877536812320e-06, /* 0xBED09C43, 0x42A26120 */
|
| + /*
|
| + * Coefficients for approximation to erf in [0.84375,1.25]
|
| + */
|
| + pa0 = -2.36211856075265944077e-03, /* 0xBF6359B8, 0xBEF77538 */
|
| + pa1 = 4.14856118683748331666e-01, /* 0x3FDA8D00, 0xAD92B34D */
|
| + pa2 = -3.72207876035701323847e-01, /* 0xBFD7D240, 0xFBB8C3F1 */
|
| + pa3 = 3.18346619901161753674e-01, /* 0x3FD45FCA, 0x805120E4 */
|
| + pa4 = -1.10894694282396677476e-01, /* 0xBFBC6398, 0x3D3E28EC */
|
| + pa5 = 3.54783043256182359371e-02, /* 0x3FA22A36, 0x599795EB */
|
| + pa6 = -2.16637559486879084300e-03, /* 0xBF61BF38, 0x0A96073F */
|
| + qa1 = 1.06420880400844228286e-01, /* 0x3FBB3E66, 0x18EEE323 */
|
| + qa2 = 5.40397917702171048937e-01, /* 0x3FE14AF0, 0x92EB6F33 */
|
| + qa3 = 7.18286544141962662868e-02, /* 0x3FB2635C, 0xD99FE9A7 */
|
| + qa4 = 1.26171219808761642112e-01, /* 0x3FC02660, 0xE763351F */
|
| + qa5 = 1.36370839120290507362e-02, /* 0x3F8BEDC2, 0x6B51DD1C */
|
| + qa6 = 1.19844998467991074170e-02, /* 0x3F888B54, 0x5735151D */
|
| + /*
|
| + * Coefficients for approximation to erfc in [1.25,1/0.35]
|
| + */
|
| + ra0 = -9.86494403484714822705e-03, /* 0xBF843412, 0x600D6435 */
|
| + ra1 = -6.93858572707181764372e-01, /* 0xBFE63416, 0xE4BA7360 */
|
| + ra2 = -1.05586262253232909814e+01, /* 0xC0251E04, 0x41B0E726 */
|
| + ra3 = -6.23753324503260060396e+01, /* 0xC04F300A, 0xE4CBA38D */
|
| + ra4 = -1.62396669462573470355e+02, /* 0xC0644CB1, 0x84282266 */
|
| + ra5 = -1.84605092906711035994e+02, /* 0xC067135C, 0xEBCCABB2 */
|
| + ra6 = -8.12874355063065934246e+01, /* 0xC0545265, 0x57E4D2F2 */
|
| + ra7 = -9.81432934416914548592e+00, /* 0xC023A0EF, 0xC69AC25C */
|
| + sa1 = 1.96512716674392571292e+01, /* 0x4033A6B9, 0xBD707687 */
|
| + sa2 = 1.37657754143519042600e+02, /* 0x4061350C, 0x526AE721 */
|
| + sa3 = 4.34565877475229228821e+02, /* 0x407B290D, 0xD58A1A71 */
|
| + sa4 = 6.45387271733267880336e+02, /* 0x40842B19, 0x21EC2868 */
|
| + sa5 = 4.29008140027567833386e+02, /* 0x407AD021, 0x57700314 */
|
| + sa6 = 1.08635005541779435134e+02, /* 0x405B28A3, 0xEE48AE2C */
|
| + sa7 = 6.57024977031928170135e+00, /* 0x401A47EF, 0x8E484A93 */
|
| + sa8 = -6.04244152148580987438e-02, /* 0xBFAEEFF2, 0xEE749A62 */
|
| + /*
|
| + * Coefficients for approximation to erfc in [1/.35,28]
|
| + */
|
| + rb0 = -9.86494292470009928597e-03, /* 0xBF843412, 0x39E86F4A */
|
| + rb1 = -7.99283237680523006574e-01, /* 0xBFE993BA, 0x70C285DE */
|
| + rb2 = -1.77579549177547519889e+01, /* 0xC031C209, 0x555F995A */
|
| + rb3 = -1.60636384855821916062e+02, /* 0xC064145D, 0x43C5ED98 */
|
| + rb4 = -6.37566443368389627722e+02, /* 0xC083EC88, 0x1375F228 */
|
| + rb5 = -1.02509513161107724954e+03, /* 0xC0900461, 0x6A2E5992 */
|
| + rb6 = -4.83519191608651397019e+02, /* 0xC07E384E, 0x9BDC383F */
|
| + sb1 = 3.03380607434824582924e+01, /* 0x403E568B, 0x261D5190 */
|
| + sb2 = 3.25792512996573918826e+02, /* 0x40745CAE, 0x221B9F0A */
|
| + sb3 = 1.53672958608443695994e+03, /* 0x409802EB, 0x189D5118 */
|
| + sb4 = 3.19985821950859553908e+03, /* 0x40A8FFB7, 0x688C246A */
|
| + sb5 = 2.55305040643316442583e+03, /* 0x40A3F219, 0xCEDF3BE6 */
|
| + sb6 = 4.74528541206955367215e+02, /* 0x407DA874, 0xE79FE763 */
|
| + sb7 = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */
|
|
|
| -static double erfc1(double x)
|
| -{
|
| - double_t s,P,Q;
|
| +static double erfc1(double x) {
|
| + double_t s, P, Q;
|
|
|
| - s = fabs(x) - 1;
|
| - P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
|
| - Q = 1+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
|
| - return 1 - erx - P/Q;
|
| + s = fabs(x) - 1;
|
| + P = pa0 + s * (pa1 + s * (pa2 + s * (pa3 + s * (pa4 + s * (pa5 + s * pa6)))));
|
| + Q = 1 + s * (qa1 + s * (qa2 + s * (qa3 + s * (qa4 + s * (qa5 + s * qa6)))));
|
| + return 1 - erx - P / Q;
|
| }
|
|
|
| -static double erfc2(uint32_t ix, double x)
|
| -{
|
| - double_t s,R,S;
|
| - double z;
|
| +static double erfc2(uint32_t ix, double x) {
|
| + double_t s, R, S;
|
| + double z;
|
|
|
| - if (ix < 0x3ff40000) /* |x| < 1.25 */
|
| - return erfc1(x);
|
| + if (ix < 0x3ff40000) /* |x| < 1.25 */
|
| + return erfc1(x);
|
|
|
| - x = fabs(x);
|
| - s = 1/(x*x);
|
| - if (ix < 0x4006db6d) { /* |x| < 1/.35 ~ 2.85714 */
|
| - R = ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
|
| - ra5+s*(ra6+s*ra7))))));
|
| - S = 1.0+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
|
| - sa5+s*(sa6+s*(sa7+s*sa8)))))));
|
| - } else { /* |x| > 1/.35 */
|
| - R = rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
|
| - rb5+s*rb6)))));
|
| - S = 1.0+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
|
| - sb5+s*(sb6+s*sb7))))));
|
| - }
|
| - z = x;
|
| - SET_LOW_WORD(z,0);
|
| - return exp(-z*z-0.5625)*exp((z-x)*(z+x)+R/S)/x;
|
| + x = fabs(x);
|
| + s = 1 / (x * x);
|
| + if (ix < 0x4006db6d) { /* |x| < 1/.35 ~ 2.85714 */
|
| + R = ra0 +
|
| + s * (ra1 +
|
| + s * (ra2 +
|
| + s * (ra3 + s * (ra4 + s * (ra5 + s * (ra6 + s * ra7))))));
|
| + S = 1.0 +
|
| + s * (sa1 +
|
| + s * (sa2 +
|
| + s * (sa3 +
|
| + s * (sa4 +
|
| + s * (sa5 + s * (sa6 + s * (sa7 + s * sa8)))))));
|
| + } else { /* |x| > 1/.35 */
|
| + R = rb0 +
|
| + s * (rb1 + s * (rb2 + s * (rb3 + s * (rb4 + s * (rb5 + s * rb6)))));
|
| + S = 1.0 +
|
| + s * (sb1 +
|
| + s * (sb2 +
|
| + s * (sb3 + s * (sb4 + s * (sb5 + s * (sb6 + s * sb7))))));
|
| + }
|
| + z = x;
|
| + SET_LOW_WORD(z, 0);
|
| + return exp(-z * z - 0.5625) * exp((z - x) * (z + x) + R / S) / x;
|
| }
|
|
|
| -double erf(double x)
|
| -{
|
| - double r,s,z,y;
|
| - uint32_t ix;
|
| - int sign;
|
| +double erf(double x) {
|
| + double r, s, z, y;
|
| + uint32_t ix;
|
| + int sign;
|
|
|
| - GET_HIGH_WORD(ix, x);
|
| - sign = ix>>31;
|
| - ix &= 0x7fffffff;
|
| - if (ix >= 0x7ff00000) {
|
| - /* erf(nan)=nan, erf(+-inf)=+-1 */
|
| - return 1-2*sign + 1/x;
|
| - }
|
| - if (ix < 0x3feb0000) { /* |x| < 0.84375 */
|
| - if (ix < 0x3e300000) { /* |x| < 2**-28 */
|
| - /* avoid underflow */
|
| - return 0.125*(8*x + efx8*x);
|
| - }
|
| - z = x*x;
|
| - r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
|
| - s = 1.0+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
|
| - y = r/s;
|
| - return x + x*y;
|
| - }
|
| - if (ix < 0x40180000) /* 0.84375 <= |x| < 6 */
|
| - y = 1 - erfc2(ix,x);
|
| - else
|
| - y = 1 - 0x1p-1022;
|
| - return sign ? -y : y;
|
| + GET_HIGH_WORD(ix, x);
|
| + sign = ix >> 31;
|
| + ix &= 0x7fffffff;
|
| + if (ix >= 0x7ff00000) {
|
| + /* erf(nan)=nan, erf(+-inf)=+-1 */
|
| + return 1 - 2 * sign + 1 / x;
|
| + }
|
| + if (ix < 0x3feb0000) { /* |x| < 0.84375 */
|
| + if (ix < 0x3e300000) { /* |x| < 2**-28 */
|
| + /* avoid underflow */
|
| + return 0.125 * (8 * x + efx8 * x);
|
| + }
|
| + z = x * x;
|
| + r = pp0 + z * (pp1 + z * (pp2 + z * (pp3 + z * pp4)));
|
| + s = 1.0 + z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5))));
|
| + y = r / s;
|
| + return x + x * y;
|
| + }
|
| + if (ix < 0x40180000) /* 0.84375 <= |x| < 6 */
|
| + y = 1 - erfc2(ix, x);
|
| + else
|
| + y = 1 - 0x1p-1022;
|
| + return sign ? -y : y;
|
| }
|
|
|
| -double erfc(double x)
|
| -{
|
| - double r,s,z,y;
|
| - uint32_t ix;
|
| - int sign;
|
| +double erfc(double x) {
|
| + double r, s, z, y;
|
| + uint32_t ix;
|
| + int sign;
|
|
|
| - GET_HIGH_WORD(ix, x);
|
| - sign = ix>>31;
|
| - ix &= 0x7fffffff;
|
| - if (ix >= 0x7ff00000) {
|
| - /* erfc(nan)=nan, erfc(+-inf)=0,2 */
|
| - return 2*sign + 1/x;
|
| - }
|
| - if (ix < 0x3feb0000) { /* |x| < 0.84375 */
|
| - if (ix < 0x3c700000) /* |x| < 2**-56 */
|
| - return 1.0 - x;
|
| - z = x*x;
|
| - r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
|
| - s = 1.0+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
|
| - y = r/s;
|
| - if (sign || ix < 0x3fd00000) { /* x < 1/4 */
|
| - return 1.0 - (x+x*y);
|
| - }
|
| - return 0.5 - (x - 0.5 + x*y);
|
| - }
|
| - if (ix < 0x403c0000) { /* 0.84375 <= |x| < 28 */
|
| - return sign ? 2 - erfc2(ix,x) : erfc2(ix,x);
|
| - }
|
| - return sign ? 2 - 0x1p-1022 : 0x1p-1022*0x1p-1022;
|
| + GET_HIGH_WORD(ix, x);
|
| + sign = ix >> 31;
|
| + ix &= 0x7fffffff;
|
| + if (ix >= 0x7ff00000) {
|
| + /* erfc(nan)=nan, erfc(+-inf)=0,2 */
|
| + return 2 * sign + 1 / x;
|
| + }
|
| + if (ix < 0x3feb0000) { /* |x| < 0.84375 */
|
| + if (ix < 0x3c700000) /* |x| < 2**-56 */
|
| + return 1.0 - x;
|
| + z = x * x;
|
| + r = pp0 + z * (pp1 + z * (pp2 + z * (pp3 + z * pp4)));
|
| + s = 1.0 + z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5))));
|
| + y = r / s;
|
| + if (sign || ix < 0x3fd00000) { /* x < 1/4 */
|
| + return 1.0 - (x + x * y);
|
| + }
|
| + return 0.5 - (x - 0.5 + x * y);
|
| + }
|
| + if (ix < 0x403c0000) { /* 0.84375 <= |x| < 28 */
|
| + return sign ? 2 - erfc2(ix, x) : erfc2(ix, x);
|
| + }
|
| + return sign ? 2 - 0x1p-1022 : 0x1p-1022 * 0x1p-1022;
|
| }
|
|
|