Index: fusl/src/math/erff.c |
diff --git a/fusl/src/math/erff.c b/fusl/src/math/erff.c |
new file mode 100644 |
index 0000000000000000000000000000000000000000..ed5f3975741595057cbc981d13fd6c43ce11270a |
--- /dev/null |
+++ b/fusl/src/math/erff.c |
@@ -0,0 +1,183 @@ |
+/* origin: FreeBSD /usr/src/lib/msun/src/s_erff.c */ |
+/* |
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. |
+ */ |
+/* |
+ * ==================================================== |
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
+ * |
+ * Developed at SunPro, a Sun Microsystems, Inc. business. |
+ * Permission to use, copy, modify, and distribute this |
+ * software is freely granted, provided that this notice |
+ * is preserved. |
+ * ==================================================== |
+ */ |
+ |
+#include "libm.h" |
+ |
+static const float |
+erx = 8.4506291151e-01, /* 0x3f58560b */ |
+/* |
+ * Coefficients for approximation to erf on [0,0.84375] |
+ */ |
+efx8 = 1.0270333290e+00, /* 0x3f8375d4 */ |
+pp0 = 1.2837916613e-01, /* 0x3e0375d4 */ |
+pp1 = -3.2504209876e-01, /* 0xbea66beb */ |
+pp2 = -2.8481749818e-02, /* 0xbce9528f */ |
+pp3 = -5.7702702470e-03, /* 0xbbbd1489 */ |
+pp4 = -2.3763017452e-05, /* 0xb7c756b1 */ |
+qq1 = 3.9791721106e-01, /* 0x3ecbbbce */ |
+qq2 = 6.5022252500e-02, /* 0x3d852a63 */ |
+qq3 = 5.0813062117e-03, /* 0x3ba68116 */ |
+qq4 = 1.3249473704e-04, /* 0x390aee49 */ |
+qq5 = -3.9602282413e-06, /* 0xb684e21a */ |
+/* |
+ * Coefficients for approximation to erf in [0.84375,1.25] |
+ */ |
+pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */ |
+pa1 = 4.1485610604e-01, /* 0x3ed46805 */ |
+pa2 = -3.7220788002e-01, /* 0xbebe9208 */ |
+pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */ |
+pa4 = -1.1089469492e-01, /* 0xbde31cc2 */ |
+pa5 = 3.5478305072e-02, /* 0x3d1151b3 */ |
+pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */ |
+qa1 = 1.0642088205e-01, /* 0x3dd9f331 */ |
+qa2 = 5.4039794207e-01, /* 0x3f0a5785 */ |
+qa3 = 7.1828655899e-02, /* 0x3d931ae7 */ |
+qa4 = 1.2617121637e-01, /* 0x3e013307 */ |
+qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */ |
+qa6 = 1.1984500103e-02, /* 0x3c445aa3 */ |
+/* |
+ * Coefficients for approximation to erfc in [1.25,1/0.35] |
+ */ |
+ra0 = -9.8649440333e-03, /* 0xbc21a093 */ |
+ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */ |
+ra2 = -1.0558626175e+01, /* 0xc128f022 */ |
+ra3 = -6.2375331879e+01, /* 0xc2798057 */ |
+ra4 = -1.6239666748e+02, /* 0xc322658c */ |
+ra5 = -1.8460508728e+02, /* 0xc3389ae7 */ |
+ra6 = -8.1287437439e+01, /* 0xc2a2932b */ |
+ra7 = -9.8143291473e+00, /* 0xc11d077e */ |
+sa1 = 1.9651271820e+01, /* 0x419d35ce */ |
+sa2 = 1.3765776062e+02, /* 0x4309a863 */ |
+sa3 = 4.3456588745e+02, /* 0x43d9486f */ |
+sa4 = 6.4538726807e+02, /* 0x442158c9 */ |
+sa5 = 4.2900814819e+02, /* 0x43d6810b */ |
+sa6 = 1.0863500214e+02, /* 0x42d9451f */ |
+sa7 = 6.5702495575e+00, /* 0x40d23f7c */ |
+sa8 = -6.0424413532e-02, /* 0xbd777f97 */ |
+/* |
+ * Coefficients for approximation to erfc in [1/.35,28] |
+ */ |
+rb0 = -9.8649431020e-03, /* 0xbc21a092 */ |
+rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */ |
+rb2 = -1.7757955551e+01, /* 0xc18e104b */ |
+rb3 = -1.6063638306e+02, /* 0xc320a2ea */ |
+rb4 = -6.3756646729e+02, /* 0xc41f6441 */ |
+rb5 = -1.0250950928e+03, /* 0xc480230b */ |
+rb6 = -4.8351919556e+02, /* 0xc3f1c275 */ |
+sb1 = 3.0338060379e+01, /* 0x41f2b459 */ |
+sb2 = 3.2579251099e+02, /* 0x43a2e571 */ |
+sb3 = 1.5367296143e+03, /* 0x44c01759 */ |
+sb4 = 3.1998581543e+03, /* 0x4547fdbb */ |
+sb5 = 2.5530502930e+03, /* 0x451f90ce */ |
+sb6 = 4.7452853394e+02, /* 0x43ed43a7 */ |
+sb7 = -2.2440952301e+01; /* 0xc1b38712 */ |
+ |
+static float erfc1(float x) |
+{ |
+ float_t 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_t s,R,S; |
+ float z; |
+ |
+ if (ix < 0x3fa00000) /* |x| < 1.25 */ |
+ return erfc1(x); |
+ |
+ x = fabsf(x); |
+ 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*( |
+ sa5+s*(sa6+s*(sa7+s*sa8))))))); |
+ } else { /* |x| >= 1/0.35 */ |
+ 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&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) |
+{ |
+ float r,s,z,y; |
+ uint32_t ix; |
+ int sign; |
+ |
+ GET_FLOAT_WORD(ix, x); |
+ sign = ix>>31; |
+ ix &= 0x7fffffff; |
+ if (ix >= 0x7f800000) { |
+ /* erfc(nan)=nan, erfc(+-inf)=0,2 */ |
+ return 2*sign + 1/x; |
+ } |
+ |
+ if (ix < 0x3f580000) { /* |x| < 0.84375 */ |
+ if (ix < 0x23800000) /* |x| < 2**-56 */ |
+ return 1.0f - 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; |
+ if (sign || ix < 0x3e800000) /* x < 1/4 */ |
+ return 1.0f - (x+x*y); |
+ return 0.5f - (x - 0.5f + x*y); |
+ } |
+ if (ix < 0x41e00000) { /* |x| < 28 */ |
+ return sign ? 2 - erfc2(ix,x) : erfc2(ix,x); |
+ } |
+ return sign ? 2 - 0x1p-120f : 0x1p-120f*0x1p-120f; |
+} |