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-rw-r--r--src/math/erf.c155
-rw-r--r--src/math/erff.c154
-rw-r--r--src/math/erfl.c195
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
generated by cgit v1.2.3-70-g09d2 (git 2.46.0) at 2024-11-17 18:45:20 +0000