fluencelabs/musl
1
0
Fork 0
mirror of https://github.com/fluencelabs/musl synced 2025-06-28 06:02:04 +00:00
Code Issues Projects Releases Wiki Activity

math: erf and erfc cleanup

Browse Source 
common part of erf and erfc was put in a separate function which
saved some space and the new code is using unsigned arithmetics

erfcf had a bug: for some inputs in [7.95,8] the result had
more than 60ulp error: in expf(-z*z - 0.5625f) the argument
must be exact but not enough lowbits of z were zeroed,
-SET_FLOAT_WORD(z, ix&0xfffff000);
+SET_FLOAT_WORD(z, ix&0xffffe000);
fixed the issue
This commit is contained in:
Szabolcs Nagy
2013-01-07 23:54:13 +01:00
parent d84923d89e
commit 121e3a38a1
3 changed files with 208 additions and 298 deletions
Download Patch File Download Diff File Expand all files Collapse all files

197
src/math/erfl.c
View File

@ -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] = {
@ -239,26 +235,80 @@ sc[] = {
/* 1.000000000000000000000000000000000000000E0 */
};
static long double erfc1(long double x)
{
long double s,P,Q;
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;
}
static long double erfc2(uint32_t ix, long double x)
{
long double s,z,R,S;
uint32_t i0,i1;
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))))));
}
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 */
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(ix, i0, i1, z);
i1 = 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 erfl(long double x)
{
long double R, S, P, Q, s, y, z, r;
int32_t ix, i;
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) { /* erf(nan)=nan */
i = ((se & 0xffff) >> 15) << 1;
return (long double)(1 - i) + 1.0 / x; /* erf(+-inf)=+-1 */
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 */
if (ix < 0x00080000)
return 0.125 * (8.0 * x + efx8 * x); /* avoid underflow */
return x + efx * x;
return 0.125 * (8 * x + efx8 * x); /* avoid underflow */
}
z = x * x;
r = pp[0] + z * (pp[1] +
@ -268,55 +318,25 @@ long double erfl(long double x)
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;
}
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 */
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))))));
}
z = x;
GET_LDOUBLE_WORDS(i, 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;
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)
{
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)
/* 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;
return 0.5 - (x - 0.5 + 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) {
z = 1.0 - erx;
return z - P / Q;
}
z = erx + P / Q;
return 1.0 + z;
}
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