diff options
Diffstat (limited to 'sysdeps/libm-ieee754/s_erf.c')
| -rw-r--r-- | sysdeps/libm-ieee754/s_erf.c | 30 |
1 files changed, 17 insertions, 13 deletions
diff --git a/sysdeps/libm-ieee754/s_erf.c b/sysdeps/libm-ieee754/s_erf.c index d3377a5036..022cf11abe 100644 --- a/sysdeps/libm-ieee754/s_erf.c +++ b/sysdeps/libm-ieee754/s_erf.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -19,11 +19,11 @@ static char rcsid[] = "$NetBSD: s_erf.c,v 1.8 1995/05/10 20:47:05 jtc Exp $"; * x * 2 |\ * erf(x) = --------- | exp(-t*t)dt - * sqrt(pi) \| + * sqrt(pi) \| * 0 * * erfc(x) = 1-erf(x) - * Note that + * Note that * erf(-x) = -erf(x) * erfc(-x) = 2 - erfc(x) * @@ -36,7 +36,7 @@ static char rcsid[] = "$NetBSD: s_erf.c,v 1.8 1995/05/10 20:47:05 jtc Exp $"; * Q is an odd poly of degree 10. * -57.90 * | R - (erf(x)-x)/x | <= 2 - * + * * * Remark. The formula is derived by noting * erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....) @@ -59,14 +59,14 @@ static char rcsid[] = "$NetBSD: s_erf.c,v 1.8 1995/05/10 20:47:05 jtc Exp $"; * That is, we use rational approximation to approximate * erf(1+s) - (c = (single)0.84506291151) * Note that |P1/Q1|< 0.078 for x in [0.84375,1.25] - * where + * where * P1(s) = degree 6 poly in s * Q1(s) = degree 6 poly in s * - * 3. For x in [1.25,1/0.35(~2.857143)], + * 3. For x in [1.25,1/0.35(~2.857143)], * erfc(x) = (1/x)*exp(-x*x-0.5625+R1/S1) * erf(x) = 1 - erfc(x) - * where + * where * R1(z) = degree 7 poly in z, (z=1/x^2) * S1(z) = degree 8 poly in z * @@ -84,7 +84,7 @@ static char rcsid[] = "$NetBSD: s_erf.c,v 1.8 1995/05/10 20:47:05 jtc Exp $"; * To compute exp(-x*x-0.5625+R/S), let s be a single * precision number and s := x; then * -x*x = -s*s + (s-x)*(s+x) - * exp(-x*x-0.5626+R/S) = + * exp(-x*x-0.5626+R/S) = * exp(-s*s-0.5625)*exp((s-x)*(s+x)+R/S); * Note2: * Here 4 and 5 make use of the asymptotic series @@ -104,7 +104,7 @@ static char rcsid[] = "$NetBSD: s_erf.c,v 1.8 1995/05/10 20:47:05 jtc Exp $"; * * 7. Special case: * erf(0) = 0, erf(inf) = 1, erf(-inf) = -1, - * erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2, + * erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2, * erfc/erf(NaN) is NaN */ @@ -139,7 +139,7 @@ qq3 = 5.08130628187576562776e-03, /* 0x3F74D022, 0xC4D36B0F */ qq4 = 1.32494738004321644526e-04, /* 0x3F215DC9, 0x221C1A10 */ qq5 = -3.96022827877536812320e-06, /* 0xBED09C43, 0x42A26120 */ /* - * Coefficients for approximation to erf in [0.84375,1.25] + * Coefficients for approximation to erf in [0.84375,1.25] */ pa0 = -2.36211856075265944077e-03, /* 0xBF6359B8, 0xBEF77538 */ pa1 = 4.14856118683748331666e-01, /* 0x3FDA8D00, 0xAD92B34D */ @@ -209,7 +209,7 @@ sb7 = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */ if(ix < 0x3feb0000) { /* |x|<0.84375 */ if(ix < 0x3e300000) { /* |x|<2**-28 */ - if (ix < 0x00800000) + if (ix < 0x00800000) return 0.125*(8.0*x+efx8*x); /*avoid underflow */ return x + efx*x; } @@ -241,7 +241,7 @@ sb7 = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */ S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( sb5+s*(sb6+s*sb7)))))); } - z = x; + z = x; SET_LOW_WORD(z,0); r = __ieee754_exp(-z*z-0.5625)*__ieee754_exp((z-x)*(z+x)+R/S); if(hx>=0) return one-r/x; else return r/x-one; @@ -284,7 +284,7 @@ weak_alias (__erf, erf) P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); if(hx>=0) { - z = one-erx; return z - P/Q; + z = one-erx; return z - P/Q; } else { z = erx+P/Q; return one+z; } @@ -314,3 +314,7 @@ weak_alias (__erf, erf) } } weak_alias (__erfc, erfc) +#ifdef NO_LONG_DOUBLE +strong_alias (__erfc, __erfcl) +weak_alias (__erfc, erfcl) +#endif |