diff options
| -rw-r--r-- | src/math/erf.c | 155 | ||||
| -rw-r--r-- | src/math/erff.c | 154 | ||||
| -rw-r--r-- | src/math/erfl.c | 195 |
3 files changed, 207 insertions, 297 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; } diff --git a/src/math/erff.c b/src/math/erff.c index a0a304e5..e2cfc984 100644 --- a/src/math/erff.c +++ b/src/math/erff.c @@ -16,13 +16,10 @@ #include "libm.h" static const float -tiny = 1e-30, -/* c = (subfloat)0.84506291151 */ erx = 8.4506291151e-01, /* 0x3f58560b */ /* * Coefficients for approximation to erf on [0,0.84375] */ -efx = 1.2837916613e-01, /* 0x3e0375d4 */ efx8 = 1.0270333290e+00, /* 0x3f8375d4 */ pp0 = 1.2837916613e-01, /* 0x3e0375d4 */ pp1 = -3.2504209876e-01, /* 0xbea66beb */ @@ -87,47 +84,26 @@ sb5 = 2.5530502930e+03, /* 0x451f90ce */ sb6 = 4.7452853394e+02, /* 0x43ed43a7 */ sb7 = -2.2440952301e+01; /* 0xc1b38712 */ -float erff(float x) +static float erfc1(float x) { - int32_t hx,ix,i; - float R,S,P,Q,s,y,z,r; + float s,P,Q; + + s = fabsf(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 float erfc2(uint32_t ix, float x) +{ + float s,z,R,S; + + if (ix < 0x3fa00000) /* |x| < 1.25 */ + return erfc1(x); - GET_FLOAT_WORD(hx, x); - ix = hx & 0x7fffffff; - if (ix >= 0x7f800000) { - /* erf(nan)=nan, erf(+-inf)=+-1 */ - i = ((uint32_t)hx>>31)<<1; - return (float)(1-i)+1.0f/x; - } - if (ix < 0x3f580000) { /* |x| < 0.84375 */ - if (ix < 0x31800000) { /* |x| < 2**-28 */ - if (ix < 0x04000000) - /*avoid underflow */ - return 0.125f*(8.0f*x + efx8*x); - return x + efx*x; - } - z = x*x; - r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); - s = 1.0f+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); - y = r/s; - return x + x*y; - } - if (ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */ - s = fabsf(x)-1.0f; - P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); - Q = 1.0f+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 >= 0x40c00000) { /* inf > |x| >= 6 */ - if (hx >= 0) - return 1.0f - tiny; - return tiny - 1.0f; - } x = fabsf(x); - s = 1.0f/(x*x); - if (ix < 0x4036DB6E) { /* |x| < 1/0.35 */ + s = 1/(x*x); + if (ix < 0x4036db6d) { /* |x| < 1/0.35 */ 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*( @@ -139,23 +115,53 @@ float erff(float x) sb5+s*(sb6+s*sb7)))))); } 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 1.0f - r/x; - return r/x - 1.0f; + SET_FLOAT_WORD(z, ix&0xffffe000); + return expf(-z*z - 0.5625f) * expf((z-x)*(z+x) + R/S)/x; +} + +float erff(float x) +{ + float r,s,z,y; + uint32_t ix; + int sign; + + GET_FLOAT_WORD(ix, x); + sign = ix>>31; + ix &= 0x7fffffff; + if (ix >= 0x7f800000) { + /* erf(nan)=nan, erf(+-inf)=+-1 */ + return 1-2*sign + 1/x; + } + if (ix < 0x3f580000) { /* |x| < 0.84375 */ + if (ix < 0x31800000) { /* |x| < 2**-28 */ + /*avoid underflow */ + return 0.125f*(8*x + efx8*x); + } + z = x*x; + r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); + s = 1+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); + y = r/s; + return x + x*y; + } + if (ix < 0x40c00000) /* |x| < 6 */ + y = 1 - erfc2(ix,x); + else + y = 1 - 0x1p-120f; + return sign ? -y : y; } float erfcf(float x) { - int32_t hx,ix; - float R,S,P,Q,s,y,z,r; + float r,s,z,y; + uint32_t ix; + int sign; - GET_FLOAT_WORD(hx, x); - ix = hx & 0x7fffffff; + GET_FLOAT_WORD(ix, x); + sign = ix>>31; + ix &= 0x7fffffff; if (ix >= 0x7f800000) { /* erfc(nan)=nan, erfc(+-inf)=0,2 */ - return (float)(((uint32_t)hx>>31)<<1) + 1.0f/x; + return 2*sign + 1/x; } if (ix < 0x3f580000) { /* |x| < 0.84375 */ @@ -165,50 +171,12 @@ float erfcf(float x) r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); s = 1.0f+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); y = r/s; - if (hx < 0x3e800000) { /* x<1/4 */ + if (sign || ix < 0x3e800000) /* x < 1/4 */ return 1.0f - (x+x*y); - } else { - r = x*y; - r += (x-0.5f); - return 0.5f - r ; - } - } - if (ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */ - s = fabsf(x)-1.0f; - P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); - Q = 1.0f+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); - if(hx >= 0) { - z = 1.0f - erx; - return z - P/Q; - } else { - z = erx + P/Q; - return 1.0f + z; - } + return 0.5f - (x - 0.5f + x*y); } if (ix < 0x41e00000) { /* |x| < 28 */ - x = fabsf(x); - s = 1.0f/(x*x); - 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)))))); - } - 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; + return sign ? 2 - erfc2(ix,x) : erfc2(ix,x); } - if (hx > 0) - return tiny*tiny; - return 2.0f - tiny; + return sign ? 2 - 0x1p-120f : 0x1p-120f*0x1p-120f; } diff --git a/src/math/erfl.c b/src/math/erfl.c index f7449859..fa30d98e 100644 --- a/src/math/erfl.c +++ b/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] = { @@ -239,84 +235,108 @@ sc[] = { /* 1.000000000000000000000000000000000000000E0 */ }; -long double erfl(long double x) +static long double erfc1(long double x) { - long double R, S, P, Q, s, y, z, r; - int32_t ix, i; - uint32_t se, i0, i1; + long double s,P,Q; - GET_LDOUBLE_WORDS(se, i0, i1, x); - ix = se & 0x7fff; + 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; +} - if (ix >= 0x7fff) { /* erf(nan)=nan */ - i = ((se & 0xffff) >> 15) << 1; - return (long double)(1 - i) + 1.0 / x; /* erf(+-inf)=+-1 */ - } +static long double erfc2(uint32_t ix, long double x) +{ + long double s,z,R,S; + uint32_t i0,i1; - 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; - } - z = x * x; - r = pp[0] + z * (pp[1] + - z * (pp[2] + z * (pp[3] + z * (pp[4] + z * pp[5])))); - s = qq[0] + z * (qq[1] + - z * (qq[2] + z * (qq[3] + z * (qq[4] + z * (qq[5] + z))))); - 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; + 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)))))); } - 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 */ + } 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(i, i0, i1, z); + GET_LDOUBLE_WORDS(ix, 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; + 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 erfcl(long double x) +long double erfl(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) { + /* 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 */ + return 0.125 * (8 * x + efx8 * x); /* avoid underflow */ + } + z = x * x; + r = pp[0] + z * (pp[1] + + z * (pp[2] + z * (pp[3] + z * (pp[4] + z * pp[5])))); + s = qq[0] + z * (qq[1] + + z * (qq[2] + z * (qq[3] + z * (qq[4] + z * (qq[5] + z))))); + y = r / s; + return x + x * y; + } + 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) +{ + long double r, s, z, y; + uint32_t i0, i1, ix; + int sign; + + 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; - } - 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; + return 0.5 - (x - 0.5 + x * y); } - 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 |