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math: rewrite inverse hyperbolic functions to be simpler/smaller

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modifications:
* avoid unsigned->signed integer conversion
* do not handle special cases when they work correctly anyway
* more strict threshold values (0x1p26 instead of 0x1p28 etc)
* smaller code, cleaner branching logic
* same precision as the old code:
    acosh(x) has up to 2ulp error in [1,1.125]
    asinh(x) has up to 1.6ulp error in [0.125,0.5], [-0.5,-0.125]
    atanh(x) has up to 1.7ulp error in [0.125,0.5], [-0.5,-0.125]
This commit is contained in:
Szabolcs Nagy
2012-12-11 23:06:20 +01:00
parent 64623cd59a
commit 482ccd2f74
9 changed files with 149 additions and 406 deletions
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50
src/math/atanhf.c
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@ -1,42 +1,20 @@
/* origin: FreeBSD /usr/src/lib/msun/src/e_atanhf.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 huge = 1e30;
/* atanh(x) = log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2 ~= x + x^3/3 + o(x^5) */
float atanhf(float x)
{
float t;
int32_t hx,ix;
union {float f; uint32_t i;} u = {.f = x};
unsigned s = u.i >> 31;
GET_FLOAT_WORD(hx, x);
ix = hx & 0x7fffffff;
if (ix > 0x3f800000) /* |x| > 1 */
return (x-x)/(x-x);
if (ix == 0x3f800000)
return x/0.0f;
if (ix < 0x31800000 && huge+x > 0.0f) /* x < 2**-28 */
return x;
SET_FLOAT_WORD(x, ix);
if (ix < 0x3f000000) { /* x < 0.5 */
t = x+x;
t = 0.5f*log1pf(t + t*x/(1.0f-x));
} else
t = 0.5f*log1pf((x+x)/(1.0f-x));
if (hx >= 0)
return t;
return -t;
/* |x| */
u.i &= 0x7fffffff;
x = u.f;
if (u.i < 0x3f800000 - (1<<23)) {
/* |x| < 0.5, up to 1.7ulp error */
x = 0.5f*log1pf(2*x + 2*x*x/(1-x));
} else {
x = 0.5f*log1pf(2*x/(1-x));
}
return s ? -x : x;
}