Szabolcs Nagy
482ccd2f74
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]
29 lines
717 B
C
29 lines
717 B
C
#include "libm.h"
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/* asinh(x) = sign(x)*log(|x|+sqrt(x*x+1)) ~= x - x^3/6 + o(x^5) */
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float asinhf(float x)
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{
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union {float f; uint32_t i;} u = {.f = x};
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uint32_t i = u.i & 0x7fffffff;
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unsigned s = u.i >> 31;
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/* |x| */
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u.i = i;
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x = u.f;
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if (i >= 0x3f800000 + (12<<23)) {
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/* |x| >= 0x1p12 or inf or nan */
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x = logf(x) + 0.693147180559945309417232121458176568f;
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} else if (i >= 0x3f800000 + (1<<23)) {
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/* |x| >= 2 */
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x = logf(2*x + 1/(sqrtf(x*x+1)+x));
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} else if (i >= 0x3f800000 - (12<<23)) {
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/* |x| >= 0x1p-12, up to 1.6ulp error in [0.125,0.5] */
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x = log1pf(x + x*x/(sqrtf(x*x+1)+1));
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} else {
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/* |x| < 0x1p-12, raise inexact if x!=0 */
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FORCE_EVAL(x + 0x1p120f);
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}
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return s ? -x : x;
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}
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