diff options
Diffstat (limited to 'sysdeps/ieee754')
| -rw-r--r-- | sysdeps/ieee754/ldbl-96/s_erfl.c | 32 |
1 files changed, 16 insertions, 16 deletions
diff --git a/sysdeps/ieee754/ldbl-96/s_erfl.c b/sysdeps/ieee754/ldbl-96/s_erfl.c index 69c0eb805c..9f999bf693 100644 --- a/sysdeps/ieee754/ldbl-96/s_erfl.c +++ b/sysdeps/ieee754/ldbl-96/s_erfl.c @@ -17,7 +17,7 @@ * x * 2 |\ * erf(x) = --------- | exp(-t*t)dt - * sqrt(pi) \| + * sqrt(pi) \| * 0 * * erfc(x) = 1-erf(x) @@ -37,12 +37,12 @@ * is close to one. The interval is chosen because the fix * point of erf(x) is near 0.6174 (i.e., erf(x)=x when x is * near 0.6174), and by some experiment, 0.84375 is chosen to - * guarantee the error is less than one ulp for erf. + * guarantee the error is less than one ulp for erf. * * 2. For |x| in [0.84375,1.25], let s = |x| - 1, and * c = 0.84506291151 rounded to single (24 bits) - * erf(x) = sign(x) * (c + P1(s)/Q1(s)) - * erfc(x) = (1-c) - P1(s)/Q1(s) if x > 0 + * erf(x) = sign(x) * (c + P1(s)/Q1(s)) + * erfc(x) = (1-c) - P1(s)/Q1(s) if x > 0 * 1+(c+P1(s)/Q1(s)) if x < 0 * Remark: here we use the taylor series expansion at x=1. * erf(1+s) = erf(1) + s*Poly(s) @@ -50,18 +50,18 @@ * Note that |P1/Q1|< 0.078 for x in [0.84375,1.25] * * 3. For x in [1.25,1/0.35(~2.857143)], - * erfc(x) = (1/x)*exp(-x*x-0.5625+R1(z)/S1(z)) + * erfc(x) = (1/x)*exp(-x*x-0.5625+R1(z)/S1(z)) * z=1/x^2 - * erf(x) = 1 - erfc(x) + * erf(x) = 1 - erfc(x) * * 4. For x in [1/0.35,107] - * erfc(x) = (1/x)*exp(-x*x-0.5625+R2/S2) if x > 0 + * erfc(x) = (1/x)*exp(-x*x-0.5625+R2/S2) if x > 0 * = 2.0 - (1/x)*exp(-x*x-0.5625+R2(z)/S2(z)) * if -6.666<x<0 * = 2.0 - tiny (if x <= -6.666) * z=1/x^2 - * erf(x) = sign(x)*(1.0 - erfc(x)) if x < 6.666, else - * erf(x) = sign(x)*(1.0 - tiny) + * erf(x) = sign(x)*(1.0 - erfc(x)) if x < 6.666, else + * erf(x) = sign(x)*(1.0 - tiny) * Note1: * To compute exp(-x*x-0.5625+R/S), let s be a single * precision number and s := x; then @@ -75,14 +75,14 @@ * x*sqrt(pi) * * 5. For inf > x >= 107 - * erf(x) = sign(x) *(1 - tiny) (raise inexact) - * erfc(x) = tiny*tiny (raise underflow) if x > 0 + * erf(x) = sign(x) *(1 - tiny) (raise inexact) + * erfc(x) = tiny*tiny (raise underflow) if x > 0 * = 2 - tiny if x<0 * * 7. Special case: - * erf(0) = 0, erf(inf) = 1, erf(-inf) = -1, - * erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2, - * erfc/erf(NaN) is NaN + * erf(0) = 0, erf(inf) = 1, erf(-inf) = -1, + * erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2, + * erfc/erf(NaN) is NaN */ @@ -333,7 +333,7 @@ weak_alias (__erf, erfl) #else long double __erfcl (x) - double + long double x; #endif { @@ -394,7 +394,7 @@ weak_alias (__erf, erfl) x = fabsl (x); s = one / (x * x); if (ix < 0x4000b6db) /* 2.85711669921875 */ - { /* |x| < 1/.35 ~ 2.857143 */ + { /* |x| < 1/.35 ~ 2.857143 */ 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] + |