diff options
Diffstat (limited to 'src/math/erf.c')
| -rw-r--r-- | src/math/erf.c | 155 |
1 files changed, 62 insertions, 93 deletions
diff --git a/src/math/erf.c b/src/math/erf.c index dd8c3a77..c0fc41db 100644 --- a/src/math/erf.c +++ b/src/math/erf.c @@ -106,13 +106,10 @@ #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 */ @@ -177,52 +174,31 @@ sb5 = 2.55305040643316442583e+03, /* 0x40A3F219, 0xCEDF3BE6 */ 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*( @@ -230,22 +206,52 @@ double erf(double x) } 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 */ @@ -254,50 +260,13 @@ double erfc(double 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 (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; } |