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-rw-r--r--src/math/erfl.c195
1 files changed, 84 insertions, 111 deletions
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
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