mirror of git://git.musl-libc.org/musl
math: erf and erfc cleanup
common part of erf and erfc was put in a separate function which saved some space and the new code is using unsigned arithmetics erfcf had a bug: for some inputs in [7.95,8] the result had more than 60ulp error: in expf(-z*z - 0.5625f) the argument must be exact but not enough lowbits of z were zeroed, -SET_FLOAT_WORD(z, ix&0xfffff000); +SET_FLOAT_WORD(z, ix&0xffffe000); fixed the issue
This commit is contained in:
Szabolcs Nagy
parent
d84923d89e
commit
121e3a38a1
153
src/math/erf.c
153
src/math/erf.c
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@ -106,13 +106,10 @@
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#include "libm.h"
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static const double
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tiny = 1e-300,
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/* c = (float)0.84506291151 */
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erx = 8.45062911510467529297e-01, /* 0x3FEB0AC1, 0x60000000 */
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/*
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* Coefficients for approximation to erf on [0,0.84375]
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*/
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efx = 1.28379167095512586316e-01, /* 0x3FC06EBA, 0x8214DB69 */
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efx8 = 1.02703333676410069053e+00, /* 0x3FF06EBA, 0x8214DB69 */
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pp0 = 1.28379167095512558561e-01, /* 0x3FC06EBA, 0x8214DB68 */
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pp1 = -3.25042107247001499370e-01, /* 0xBFD4CD7D, 0x691CB913 */
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@ -177,52 +174,31 @@ sb5 = 2.55305040643316442583e+03, /* 0x40A3F219, 0xCEDF3BE6 */
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sb6 = 4.74528541206955367215e+02, /* 0x407DA874, 0xE79FE763 */
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sb7 = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */
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double erf(double x)
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static double erfc1(double x)
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{
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int32_t hx,ix,i;
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double R,S,P,Q,s,y,z,r;
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double s,P,Q;
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GET_HIGH_WORD(hx, x);
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ix = hx & 0x7fffffff;
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if (ix >= 0x7ff00000) {
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/* erf(nan)=nan, erf(+-inf)=+-1 */
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i = ((uint32_t)hx>>31)<<1;
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return (double)(1-i) + 1.0/x;
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}
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if (ix < 0x3feb0000) { /* |x|<0.84375 */
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if (ix < 0x3e300000) { /* |x|<2**-28 */
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if (ix < 0x00800000)
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/* avoid underflow */
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return 0.125*(8.0*x + efx8*x);
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return x + efx*x;
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}
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z = x*x;
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r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
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s = 1.0+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
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y = r/s;
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return x + x*y;
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}
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if (ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */
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s = fabs(x)-1.0;
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s = fabs(x) - 1;
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P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
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Q = 1.0+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
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if (hx >= 0)
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return erx + P/Q;
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return -erx - P/Q;
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}
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if (ix >= 0x40180000) { /* inf > |x| >= 6 */
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if (hx >= 0)
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return 1.0 - tiny;
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return tiny - 1.0;
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}
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Q = 1+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
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return 1 - erx - P/Q;
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}
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static double erfc2(uint32_t ix, double x)
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{
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double s,z,R,S;
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if (ix < 0x3ff40000) /* |x| < 1.25 */
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return erfc1(x);
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x = fabs(x);
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s = 1.0/(x*x);
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if (ix < 0x4006DB6E) { /* |x| < 1/0.35 */
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s = 1/(x*x);
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if (ix < 0x4006db6d) { /* |x| < 1/.35 ~ 2.85714 */
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R = ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
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ra5+s*(ra6+s*ra7))))));
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S = 1.0+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
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sa5+s*(sa6+s*(sa7+s*sa8)))))));
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} else { /* |x| >= 1/0.35 */
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} else { /* |x| > 1/.35 */
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R = rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
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rb5+s*rb6)))));
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S = 1.0+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
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@ -230,22 +206,52 @@ double erf(double x)
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}
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z = x;
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SET_LOW_WORD(z,0);
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r = exp(-z*z-0.5625)*exp((z-x)*(z+x)+R/S);
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if (hx >= 0)
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return 1.0 - r/x;
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return r/x - 1.0;
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return exp(-z*z-0.5625)*exp((z-x)*(z+x)+R/S)/x;
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}
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double erf(double x)
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{
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double r,s,z,y;
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uint32_t ix;
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int sign;
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GET_HIGH_WORD(ix, x);
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sign = ix>>31;
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ix &= 0x7fffffff;
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if (ix >= 0x7ff00000) {
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/* erf(nan)=nan, erf(+-inf)=+-1 */
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return 1-2*sign + 1/x;
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}
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if (ix < 0x3feb0000) { /* |x| < 0.84375 */
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if (ix < 0x3e300000) { /* |x| < 2**-28 */
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/* avoid underflow */
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return 0.125*(8*x + efx8*x);
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}
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z = x*x;
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r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
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s = 1.0+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
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y = r/s;
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return x + x*y;
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}
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if (ix < 0x40180000) /* 0.84375 <= |x| < 6 */
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y = 1 - erfc2(ix,x);
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else
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y = 1 - 0x1p-1022;
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return sign ? -y : y;
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}
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double erfc(double x)
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{
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int32_t hx,ix;
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double R,S,P,Q,s,y,z,r;
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double r,s,z,y;
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uint32_t ix;
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int sign;
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GET_HIGH_WORD(hx, x);
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ix = hx & 0x7fffffff;
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GET_HIGH_WORD(ix, x);
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sign = ix>>31;
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ix &= 0x7fffffff;
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if (ix >= 0x7ff00000) {
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/* erfc(nan)=nan, erfc(+-inf)=0,2 */
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return (double)(((uint32_t)hx>>31)<<1) + 1.0/x;
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return 2*sign + 1/x;
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}
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if (ix < 0x3feb0000) { /* |x| < 0.84375 */
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if (ix < 0x3c700000) /* |x| < 2**-56 */
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@ -254,50 +260,13 @@ double erfc(double x)
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r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
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s = 1.0+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
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y = r/s;
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if (hx < 0x3fd00000) { /* x < 1/4 */
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if (sign || ix < 0x3fd00000) { /* x < 1/4 */
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return 1.0 - (x+x*y);
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} else {
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r = x*y;
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r += x - 0.5;
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return 0.5 - r ;
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}
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return 0.5 - (x - 0.5 + x*y);
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}
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if (ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */
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s = fabs(x)-1.0;
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P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
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Q = 1.0+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
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if (hx >= 0) {
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z = 1.0-erx;
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return z - P/Q;
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} else {
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z = erx+P/Q;
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return 1.0 + z;
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if (ix < 0x403c0000) { /* 0.84375 <= |x| < 28 */
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return sign ? 2 - erfc2(ix,x) : erfc2(ix,x);
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}
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}
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if (ix < 0x403c0000) { /* |x| < 28 */
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x = fabs(x);
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s = 1.0/(x*x);
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if (ix < 0x4006DB6D) { /* |x| < 1/.35 ~ 2.857143*/
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R = ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
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ra5+s*(ra6+s*ra7))))));
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S = 1.0+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
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sa5+s*(sa6+s*(sa7+s*sa8)))))));
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} else { /* |x| >= 1/.35 ~ 2.857143 */
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if (hx < 0 && ix >= 0x40180000) /* x < -6 */
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return 2.0 - tiny;
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R = rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
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rb5+s*rb6)))));
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S = 1.0+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
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sb5+s*(sb6+s*sb7))))));
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}
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z = x;
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SET_LOW_WORD(z, 0);
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r = exp(-z*z-0.5625)*exp((z-x)*(z+x)+R/S);
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if (hx > 0)
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return r/x;
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return 2.0 - r/x;
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}
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if (hx > 0)
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return tiny*tiny;
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return 2.0 - tiny;
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return sign ? 2 - 0x1p-1022 : 0x1p-1022*0x1p-1022;
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}
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152
src/math/erff.c
152
src/math/erff.c
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@ -16,13 +16,10 @@
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#include "libm.h"
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static const float
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tiny = 1e-30,
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/* c = (subfloat)0.84506291151 */
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erx = 8.4506291151e-01, /* 0x3f58560b */
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/*
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* Coefficients for approximation to erf on [0,0.84375]
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*/
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efx = 1.2837916613e-01, /* 0x3e0375d4 */
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efx8 = 1.0270333290e+00, /* 0x3f8375d4 */
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pp0 = 1.2837916613e-01, /* 0x3e0375d4 */
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pp1 = -3.2504209876e-01, /* 0xbea66beb */
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@ -87,47 +84,26 @@ sb5 = 2.5530502930e+03, /* 0x451f90ce */
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sb6 = 4.7452853394e+02, /* 0x43ed43a7 */
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sb7 = -2.2440952301e+01; /* 0xc1b38712 */
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float erff(float x)
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static float erfc1(float x)
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{
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int32_t hx,ix,i;
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float R,S,P,Q,s,y,z,r;
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float s,P,Q;
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GET_FLOAT_WORD(hx, x);
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ix = hx & 0x7fffffff;
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if (ix >= 0x7f800000) {
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/* erf(nan)=nan, erf(+-inf)=+-1 */
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i = ((uint32_t)hx>>31)<<1;
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return (float)(1-i)+1.0f/x;
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}
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if (ix < 0x3f580000) { /* |x| < 0.84375 */
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if (ix < 0x31800000) { /* |x| < 2**-28 */
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if (ix < 0x04000000)
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/*avoid underflow */
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return 0.125f*(8.0f*x + efx8*x);
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return x + efx*x;
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}
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z = x*x;
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r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
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s = 1.0f+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
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y = r/s;
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return x + x*y;
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}
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if (ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
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s = fabsf(x)-1.0f;
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s = fabsf(x) - 1;
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P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
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Q = 1.0f+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
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if (hx >= 0)
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return erx + P/Q;
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return -erx - P/Q;
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}
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if (ix >= 0x40c00000) { /* inf > |x| >= 6 */
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if (hx >= 0)
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return 1.0f - tiny;
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return tiny - 1.0f;
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}
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Q = 1+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
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return 1 - erx - P/Q;
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}
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static float erfc2(uint32_t ix, float x)
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{
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float s,z,R,S;
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if (ix < 0x3fa00000) /* |x| < 1.25 */
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return erfc1(x);
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x = fabsf(x);
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s = 1.0f/(x*x);
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if (ix < 0x4036DB6E) { /* |x| < 1/0.35 */
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s = 1/(x*x);
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if (ix < 0x4036db6d) { /* |x| < 1/0.35 */
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R = ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
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ra5+s*(ra6+s*ra7))))));
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S = 1.0f+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
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@ -139,23 +115,53 @@ float erff(float x)
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sb5+s*(sb6+s*sb7))))));
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}
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GET_FLOAT_WORD(ix, x);
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SET_FLOAT_WORD(z, ix&0xfffff000);
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r = expf(-z*z - 0.5625f) * expf((z-x)*(z+x) + R/S);
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if (hx >= 0)
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return 1.0f - r/x;
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return r/x - 1.0f;
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SET_FLOAT_WORD(z, ix&0xffffe000);
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return expf(-z*z - 0.5625f) * expf((z-x)*(z+x) + R/S)/x;
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}
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float erff(float x)
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{
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float r,s,z,y;
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uint32_t ix;
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int sign;
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GET_FLOAT_WORD(ix, x);
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sign = ix>>31;
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ix &= 0x7fffffff;
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if (ix >= 0x7f800000) {
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/* erf(nan)=nan, erf(+-inf)=+-1 */
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return 1-2*sign + 1/x;
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}
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if (ix < 0x3f580000) { /* |x| < 0.84375 */
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if (ix < 0x31800000) { /* |x| < 2**-28 */
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/*avoid underflow */
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return 0.125f*(8*x + efx8*x);
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}
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z = x*x;
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r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
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s = 1+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
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y = r/s;
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return x + x*y;
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}
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if (ix < 0x40c00000) /* |x| < 6 */
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y = 1 - erfc2(ix,x);
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else
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y = 1 - 0x1p-120f;
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return sign ? -y : y;
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}
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float erfcf(float x)
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{
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int32_t hx,ix;
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float R,S,P,Q,s,y,z,r;
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float r,s,z,y;
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uint32_t ix;
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int sign;
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GET_FLOAT_WORD(hx, x);
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ix = hx & 0x7fffffff;
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GET_FLOAT_WORD(ix, x);
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sign = ix>>31;
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ix &= 0x7fffffff;
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if (ix >= 0x7f800000) {
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/* erfc(nan)=nan, erfc(+-inf)=0,2 */
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return (float)(((uint32_t)hx>>31)<<1) + 1.0f/x;
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return 2*sign + 1/x;
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}
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if (ix < 0x3f580000) { /* |x| < 0.84375 */
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@ -165,50 +171,12 @@ float erfcf(float x)
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r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
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s = 1.0f+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
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y = r/s;
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if (hx < 0x3e800000) { /* x<1/4 */
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if (sign || ix < 0x3e800000) /* x < 1/4 */
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return 1.0f - (x+x*y);
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} else {
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r = x*y;
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r += (x-0.5f);
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return 0.5f - r ;
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}
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}
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if (ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
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s = fabsf(x)-1.0f;
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P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
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Q = 1.0f+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
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if(hx >= 0) {
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z = 1.0f - erx;
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return z - P/Q;
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} else {
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z = erx + P/Q;
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return 1.0f + z;
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}
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return 0.5f - (x - 0.5f + x*y);
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}
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if (ix < 0x41e00000) { /* |x| < 28 */
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x = fabsf(x);
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s = 1.0f/(x*x);
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if (ix < 0x4036DB6D) { /* |x| < 1/.35 ~ 2.857143*/
|
||||
R = ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
|
||||
ra5+s*(ra6+s*ra7))))));
|
||||
S = 1.0f+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
|
||||
sa5+s*(sa6+s*(sa7+s*sa8)))))));
|
||||
} else { /* |x| >= 1/.35 ~ 2.857143 */
|
||||
if (hx < 0 && ix >= 0x40c00000) /* x < -6 */
|
||||
return 2.0f-tiny;
|
||||
R = rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
|
||||
rb5+s*rb6)))));
|
||||
S = 1.0f+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
|
||||
sb5+s*(sb6+s*sb7))))));
|
||||
return sign ? 2 - erfc2(ix,x) : erfc2(ix,x);
|
||||
}
|
||||
GET_FLOAT_WORD(ix, x);
|
||||
SET_FLOAT_WORD(z, ix&0xfffff000);
|
||||
r = expf(-z*z - 0.5625f) * expf((z-x)*(z+x) + R/S);
|
||||
if (hx > 0)
|
||||
return r/x;
|
||||
return 2.0f - r/x;
|
||||
}
|
||||
if (hx > 0)
|
||||
return tiny*tiny;
|
||||
return 2.0f - tiny;
|
||||
return sign ? 2 - 0x1p-120f : 0x1p-120f*0x1p-120f;
|
||||
}
|
||||
|
|
|
|||
197
src/math/erfl.c
197
src/math/erfl.c
|
|
@ -107,15 +107,11 @@ long double erfl(long double x)
|
|||
}
|
||||
#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
|
||||
static const long double
|
||||
tiny = 1e-4931L,
|
||||
/* c = (float)0.84506291151 */
|
||||
erx = 0.845062911510467529296875L,
|
||||
|
||||
/*
|
||||
* Coefficients for approximation to erf on [0,0.84375]
|
||||
*/
|
||||
/* 2/sqrt(pi) - 1 */
|
||||
efx = 1.2837916709551257389615890312154517168810E-1L,
|
||||
/* 8 * (2/sqrt(pi) - 1) */
|
||||
efx8 = 1.0270333367641005911692712249723613735048E0L,
|
||||
pp[6] = {
|
||||
|
|
@ -239,26 +235,80 @@ sc[] = {
|
|||
/* 1.000000000000000000000000000000000000000E0 */
|
||||
};
|
||||
|
||||
static long double erfc1(long double x)
|
||||
{
|
||||
long double s,P,Q;
|
||||
|
||||
s = fabsl(x) - 1;
|
||||
P = pa[0] + s * (pa[1] + s * (pa[2] +
|
||||
s * (pa[3] + s * (pa[4] + s * (pa[5] + s * (pa[6] + s * pa[7]))))));
|
||||
Q = qa[0] + s * (qa[1] + s * (qa[2] +
|
||||
s * (qa[3] + s * (qa[4] + s * (qa[5] + s * (qa[6] + s))))));
|
||||
return 1 - erx - P / Q;
|
||||
}
|
||||
|
||||
static long double erfc2(uint32_t ix, long double x)
|
||||
{
|
||||
long double s,z,R,S;
|
||||
uint32_t i0,i1;
|
||||
|
||||
if (ix < 0x3fffa000) /* 0.84375 <= |x| < 1.25 */
|
||||
return erfc1(x);
|
||||
|
||||
x = fabsl(x);
|
||||
s = 1 / (x * x);
|
||||
if (ix < 0x4000b6db) { /* 1.25 <= |x| < 2.857 ~ 1/.35 */
|
||||
R = ra[0] + s * (ra[1] + s * (ra[2] + s * (ra[3] + s * (ra[4] +
|
||||
s * (ra[5] + s * (ra[6] + s * (ra[7] + s * ra[8])))))));
|
||||
S = sa[0] + s * (sa[1] + s * (sa[2] + s * (sa[3] + s * (sa[4] +
|
||||
s * (sa[5] + s * (sa[6] + s * (sa[7] + s * (sa[8] + s))))))));
|
||||
} else { /* 2.857 <= |x| */
|
||||
R = rb[0] + s * (rb[1] + s * (rb[2] + s * (rb[3] + s * (rb[4] +
|
||||
s * (rb[5] + s * (rb[6] + s * rb[7]))))));
|
||||
S = sb[0] + s * (sb[1] + s * (sb[2] + s * (sb[3] + s * (sb[4] +
|
||||
s * (sb[5] + s * (sb[6] + s))))));
|
||||
}
|
||||
if (ix < 0x4000b6db) { /* 1.25 <= |x| < 2.85711669921875 ~ 1/.35 */
|
||||
R = ra[0] + s * (ra[1] + s * (ra[2] + s * (ra[3] + s * (ra[4] +
|
||||
s * (ra[5] + s * (ra[6] + s * (ra[7] + s * ra[8])))))));
|
||||
S = sa[0] + s * (sa[1] + s * (sa[2] + s * (sa[3] + s * (sa[4] +
|
||||
s * (sa[5] + s * (sa[6] + s * (sa[7] + s * (sa[8] + s))))))));
|
||||
} else if (ix < 0x4001d555) { /* 6.6666259765625 > |x| >= 1/.35 ~ 2.857143 */
|
||||
R = rb[0] + s * (rb[1] + s * (rb[2] + s * (rb[3] + s * (rb[4] +
|
||||
s * (rb[5] + s * (rb[6] + s * rb[7]))))));
|
||||
S = sb[0] + s * (sb[1] + s * (sb[2] + s * (sb[3] + s * (sb[4] +
|
||||
s * (sb[5] + s * (sb[6] + s))))));
|
||||
} else { /* 107 > |x| >= 6.666 */
|
||||
R = rc[0] + s * (rc[1] + s * (rc[2] + s * (rc[3] +
|
||||
s * (rc[4] + s * rc[5]))));
|
||||
S = sc[0] + s * (sc[1] + s * (sc[2] + s * (sc[3] +
|
||||
s * (sc[4] + s))));
|
||||
}
|
||||
z = x;
|
||||
GET_LDOUBLE_WORDS(ix, i0, i1, z);
|
||||
i1 = 0;
|
||||
i0 &= 0xffffff00;
|
||||
SET_LDOUBLE_WORDS(z, ix, i0, i1);
|
||||
return expl(-z*z - 0.5625) * expl((z - x) * (z + x) + R / S) / x;
|
||||
}
|
||||
|
||||
long double erfl(long double x)
|
||||
{
|
||||
long double R, S, P, Q, s, y, z, r;
|
||||
int32_t ix, i;
|
||||
uint32_t se, i0, i1;
|
||||
long double r, s, z, y;
|
||||
uint32_t i0, i1, ix;
|
||||
int sign;
|
||||
|
||||
GET_LDOUBLE_WORDS(se, i0, i1, x);
|
||||
ix = se & 0x7fff;
|
||||
|
||||
if (ix >= 0x7fff) { /* erf(nan)=nan */
|
||||
i = ((se & 0xffff) >> 15) << 1;
|
||||
return (long double)(1 - i) + 1.0 / x; /* erf(+-inf)=+-1 */
|
||||
GET_LDOUBLE_WORDS(ix, i0, i1, x);
|
||||
sign = ix >> 15;
|
||||
ix &= 0x7fff;
|
||||
if (ix == 0x7fff) {
|
||||
/* erf(nan)=nan, erf(+-inf)=+-1 */
|
||||
return 1 - 2*sign + 1/x;
|
||||
}
|
||||
|
||||
ix = (ix << 16) | (i0 >> 16);
|
||||
if (ix < 0x3ffed800) { /* |x| < 0.84375 */
|
||||
if (ix < 0x3fde8000) { /* |x| < 2**-33 */
|
||||
if (ix < 0x00080000)
|
||||
return 0.125 * (8.0 * x + efx8 * x); /* avoid underflow */
|
||||
return x + efx * x;
|
||||
return 0.125 * (8 * x + efx8 * x); /* avoid underflow */
|
||||
}
|
||||
z = x * x;
|
||||
r = pp[0] + z * (pp[1] +
|
||||
|
|
@ -268,55 +318,25 @@ long double erfl(long double x)
|
|||
y = r / s;
|
||||
return x + x * y;
|
||||
}
|
||||
if (ix < 0x3fffa000) { /* 0.84375 <= |x| < 1.25 */
|
||||
s = fabsl(x) - 1.0;
|
||||
P = pa[0] + s * (pa[1] + s * (pa[2] +
|
||||
s * (pa[3] + s * (pa[4] + s * (pa[5] + s * (pa[6] + s * pa[7]))))));
|
||||
Q = qa[0] + s * (qa[1] + s * (qa[2] +
|
||||
s * (qa[3] + s * (qa[4] + s * (qa[5] + s * (qa[6] + s))))));
|
||||
if ((se & 0x8000) == 0)
|
||||
return erx + P / Q;
|
||||
return -erx - P / Q;
|
||||
}
|
||||
if (ix >= 0x4001d555) { /* inf > |x| >= 6.6666259765625 */
|
||||
if ((se & 0x8000) == 0)
|
||||
return 1.0 - tiny;
|
||||
return tiny - 1.0;
|
||||
}
|
||||
x = fabsl (x);
|
||||
s = 1.0 / (x * x);
|
||||
if (ix < 0x4000b6db) { /* 1.25 <= |x| < 2.85711669921875 ~ 1/.35 */
|
||||
R = ra[0] + s * (ra[1] + s * (ra[2] + s * (ra[3] + s * (ra[4] +
|
||||
s * (ra[5] + s * (ra[6] + s * (ra[7] + s * ra[8])))))));
|
||||
S = sa[0] + s * (sa[1] + s * (sa[2] + s * (sa[3] + s * (sa[4] +
|
||||
s * (sa[5] + s * (sa[6] + s * (sa[7] + s * (sa[8] + s))))))));
|
||||
} else { /* 2.857 <= |x| < 6.667 */
|
||||
R = rb[0] + s * (rb[1] + s * (rb[2] + s * (rb[3] + s * (rb[4] +
|
||||
s * (rb[5] + s * (rb[6] + s * rb[7]))))));
|
||||
S = sb[0] + s * (sb[1] + s * (sb[2] + s * (sb[3] + s * (sb[4] +
|
||||
s * (sb[5] + s * (sb[6] + s))))));
|
||||
}
|
||||
z = x;
|
||||
GET_LDOUBLE_WORDS(i, i0, i1, z);
|
||||
i1 = 0;
|
||||
SET_LDOUBLE_WORDS(z, i, i0, i1);
|
||||
r = expl(-z * z - 0.5625) * expl((z - x) * (z + x) + R / S);
|
||||
if ((se & 0x8000) == 0)
|
||||
return 1.0 - r / x;
|
||||
return r / x - 1.0;
|
||||
if (ix < 0x4001d555) /* |x| < 6.6666259765625 */
|
||||
y = 1 - erfc2(ix,x);
|
||||
else
|
||||
y = 1 - 0x1p-16382L;
|
||||
return sign ? -y : y;
|
||||
}
|
||||
|
||||
long double erfcl(long double x)
|
||||
{
|
||||
int32_t hx, ix;
|
||||
long double R, S, P, Q, s, y, z, r;
|
||||
uint32_t se, i0, i1;
|
||||
long double r, s, z, y;
|
||||
uint32_t i0, i1, ix;
|
||||
int sign;
|
||||
|
||||
GET_LDOUBLE_WORDS(se, i0, i1, x);
|
||||
ix = se & 0x7fff;
|
||||
if (ix >= 0x7fff) { /* erfc(nan) = nan, erfc(+-inf) = 0,2 */
|
||||
return (long double)(((se & 0xffff) >> 15) << 1) + 1.0 / x;
|
||||
}
|
||||
GET_LDOUBLE_WORDS(ix, i0, i1, x);
|
||||
sign = ix>>15;
|
||||
ix &= 0x7fff;
|
||||
if (ix == 0x7fff)
|
||||
/* erfc(nan) = nan, erfc(+-inf) = 0,2 */
|
||||
return 2*sign + 1/x;
|
||||
|
||||
ix = (ix << 16) | (i0 >> 16);
|
||||
if (ix < 0x3ffed800) { /* |x| < 0.84375 */
|
||||
|
|
@ -330,57 +350,10 @@ long double erfcl(long double x)
|
|||
y = r / s;
|
||||
if (ix < 0x3ffd8000) /* x < 1/4 */
|
||||
return 1.0 - (x + x * y);
|
||||
r = x * y;
|
||||
r += x - 0.5L;
|
||||
return 0.5L - r;
|
||||
return 0.5 - (x - 0.5 + x * y);
|
||||
}
|
||||
if (ix < 0x3fffa000) { /* 0.84375 <= |x| < 1.25 */
|
||||
s = fabsl(x) - 1.0;
|
||||
P = pa[0] + s * (pa[1] + s * (pa[2] +
|
||||
s * (pa[3] + s * (pa[4] + s * (pa[5] + s * (pa[6] + s * pa[7]))))));
|
||||
Q = qa[0] + s * (qa[1] + s * (qa[2] +
|
||||
s * (qa[3] + s * (qa[4] + s * (qa[5] + s * (qa[6] + s))))));
|
||||
if ((se & 0x8000) == 0) {
|
||||
z = 1.0 - erx;
|
||||
return z - P / Q;
|
||||
}
|
||||
z = erx + P / Q;
|
||||
return 1.0 + z;
|
||||
}
|
||||
if (ix < 0x4005d600) { /* |x| < 107 */
|
||||
x = fabsl(x);
|
||||
s = 1.0 / (x * x);
|
||||
if (ix < 0x4000b6db) { /* 1.25 <= |x| < 2.85711669921875 ~ 1/.35 */
|
||||
R = ra[0] + s * (ra[1] + s * (ra[2] + s * (ra[3] + s * (ra[4] +
|
||||
s * (ra[5] + s * (ra[6] + s * (ra[7] + s * ra[8])))))));
|
||||
S = sa[0] + s * (sa[1] + s * (sa[2] + s * (sa[3] + s * (sa[4] +
|
||||
s * (sa[5] + s * (sa[6] + s * (sa[7] + s * (sa[8] + s))))))));
|
||||
} else if (ix < 0x4001d555) { /* 6.6666259765625 > |x| >= 1/.35 ~ 2.857143 */
|
||||
R = rb[0] + s * (rb[1] + s * (rb[2] + s * (rb[3] + s * (rb[4] +
|
||||
s * (rb[5] + s * (rb[6] + s * rb[7]))))));
|
||||
S = sb[0] + s * (sb[1] + s * (sb[2] + s * (sb[3] + s * (sb[4] +
|
||||
s * (sb[5] + s * (sb[6] + s))))));
|
||||
} else { /* 107 > |x| >= 6.666 */
|
||||
if (se & 0x8000)
|
||||
return 2.0 - tiny;/* x < -6.666 */
|
||||
R = rc[0] + s * (rc[1] + s * (rc[2] + s * (rc[3] +
|
||||
s * (rc[4] + s * rc[5]))));
|
||||
S = sc[0] + s * (sc[1] + s * (sc[2] + s * (sc[3] +
|
||||
s * (sc[4] + s))));
|
||||
}
|
||||
z = x;
|
||||
GET_LDOUBLE_WORDS(hx, i0, i1, z);
|
||||
i1 = 0;
|
||||
i0 &= 0xffffff00;
|
||||
SET_LDOUBLE_WORDS(z, hx, i0, i1);
|
||||
r = expl(-z * z - 0.5625) * expl((z - x) * (z + x) + R / S);
|
||||
if ((se & 0x8000) == 0)
|
||||
return r / x;
|
||||
return 2.0 - r / x;
|
||||
}
|
||||
|
||||
if ((se & 0x8000) == 0)
|
||||
return tiny * tiny;
|
||||
return 2.0 - tiny;
|
||||
if (ix < 0x4005d600) /* |x| < 107 */
|
||||
return sign ? 2 - erfc2(ix,x) : erfc2(ix,x);
|
||||
return sign ? 2 - 0x1p-16382L : 0x1p-16382L*0x1p-16382L;
|
||||
}
|
||||
#endif
|
||||
|
|
|
|||
Loading…
Reference in New Issue