#include "libm.h"
static const double
-tiny = 1e-300,
-/* c = (float)0.84506291151 */
erx = 8.45062911510467529297e-01, /* 0x3FEB0AC1, 0x60000000 */
/*
* Coefficients for approximation to erf on [0,0.84375]
*/
-efx = 1.28379167095512586316e-01, /* 0x3FC06EBA, 0x8214DB69 */
efx8 = 1.02703333676410069053e+00, /* 0x3FF06EBA, 0x8214DB69 */
pp0 = 1.28379167095512558561e-01, /* 0x3FC06EBA, 0x8214DB68 */
pp1 = -3.25042107247001499370e-01, /* 0xBFD4CD7D, 0x691CB913 */
sb6 = 4.74528541206955367215e+02, /* 0x407DA874, 0xE79FE763 */
sb7 = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */
-double erf(double x)
+static double erfc1(double x)
{
- int32_t hx,ix,i;
- double R,S,P,Q,s,y,z,r;
+ double 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;
+}
+
+static double erfc2(uint32_t ix, double x)
+{
+ double s,z,R,S;
+
+ if (ix < 0x3ff40000) /* |x| < 1.25 */
+ return erfc1(x);
- GET_HIGH_WORD(hx, x);
- ix = hx & 0x7fffffff;
- if (ix >= 0x7ff00000) {
- /* erf(nan)=nan, erf(+-inf)=+-1 */
- i = ((uint32_t)hx>>31)<<1;
- return (double)(1-i) + 1.0/x;
- }
- if (ix < 0x3feb0000) { /* |x|<0.84375 */
- if (ix < 0x3e300000) { /* |x|<2**-28 */
- if (ix < 0x00800000)
- /* avoid underflow */
- return 0.125*(8.0*x + efx8*x);
- return x + efx*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 < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */
- s = fabs(x)-1.0;
- P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
- Q = 1.0+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
- if (hx >= 0)
- return erx + P/Q;
- return -erx - P/Q;
- }
- if (ix >= 0x40180000) { /* inf > |x| >= 6 */
- if (hx >= 0)
- return 1.0 - tiny;
- return tiny - 1.0;
- }
x = fabs(x);
- s = 1.0/(x*x);
- if (ix < 0x4006DB6E) { /* |x| < 1/0.35 */
+ 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| >= 1/0.35 */
+ } 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*(
}
z = x;
SET_LOW_WORD(z,0);
- r = exp(-z*z-0.5625)*exp((z-x)*(z+x)+R/S);
- if (hx >= 0)
- return 1.0 - r/x;
- return r/x - 1.0;
+ 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;
+
+ 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)
{
- int32_t hx,ix;
- double R,S,P,Q,s,y,z,r;
+ double r,s,z,y;
+ uint32_t ix;
+ int sign;
- GET_HIGH_WORD(hx, x);
- ix = hx & 0x7fffffff;
+ GET_HIGH_WORD(ix, x);
+ sign = ix>>31;
+ ix &= 0x7fffffff;
if (ix >= 0x7ff00000) {
/* erfc(nan)=nan, erfc(+-inf)=0,2 */
- return (double)(((uint32_t)hx>>31)<<1) + 1.0/x;
+ return 2*sign + 1/x;
}
if (ix < 0x3feb0000) { /* |x| < 0.84375 */
if (ix < 0x3c700000) /* |x| < 2**-56 */
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 (hx < 0x3fd00000) { /* x < 1/4 */
+ if (sign || ix < 0x3fd00000) { /* x < 1/4 */
return 1.0 - (x+x*y);
- } else {
- r = x*y;
- r += x - 0.5;
- return 0.5 - r ;
- }
- }
- if (ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */
- s = fabs(x)-1.0;
- P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
- Q = 1.0+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
- if (hx >= 0) {
- z = 1.0-erx;
- return z - P/Q;
- } else {
- z = erx+P/Q;
- return 1.0 + z;
}
+ return 0.5 - (x - 0.5 + x*y);
}
- if (ix < 0x403c0000) { /* |x| < 28 */
- x = fabs(x);
- s = 1.0/(x*x);
- if (ix < 0x4006DB6D) { /* |x| < 1/.35 ~ 2.857143*/
- 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 ~ 2.857143 */
- if (hx < 0 && ix >= 0x40180000) /* x < -6 */
- return 2.0 - tiny;
- 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);
- r = exp(-z*z-0.5625)*exp((z-x)*(z+x)+R/S);
- if (hx > 0)
- return r/x;
- return 2.0 - r/x;
+ if (ix < 0x403c0000) { /* 0.84375 <= |x| < 28 */
+ return sign ? 2 - erfc2(ix,x) : erfc2(ix,x);
}
- if (hx > 0)
- return tiny*tiny;
- return 2.0 - tiny;
+ return sign ? 2 - 0x1p-1022 : 0x1p-1022*0x1p-1022;
}
projects / musl / blobdiff