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]
18 lines
456 B
C
18 lines
456 B
C
#include "libm.h"
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/* acosh(x) = log(x + sqrt(x*x-1)) */
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float acoshf(float x)
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{
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union {float f; int32_t i;} u = {.f = x};
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if (u.i < 0x3f800000+(1<<23))
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/* x < 2, invalid if x < 1 or nan */
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/* up to 2ulp error in [1,1.125] */
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return log1pf(x-1 + sqrtf((x-1)*(x-1)+2*(x-1)));
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if (u.i < 0x3f800000+(12<<23))
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/* x < 0x1p12 */
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return logf(2*x - 1/(x+sqrtf(x*x-1)));
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/* x >= 0x1p12 */
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return logf(x) + 0.693147180559945309417232121458176568f;
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}
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