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24 lines
569 B
24 lines
569 B
#include "libm.h"
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#if FLT_EVAL_METHOD==2
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#undef sqrt
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#define sqrt sqrtl
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#endif
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/* acosh(x) = log(x + sqrt(x*x-1)) */
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double acosh(double x)
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{
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union {double f; uint64_t i;} u = {.f = x};
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unsigned e = u.i >> 52 & 0x7ff;
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/* x < 1 domain error is handled in the called functions */
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if (e < 0x3ff + 1)
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/* |x| < 2, up to 2ulp error in [1,1.125] */
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return log1p(x-1 + sqrt((x-1)*(x-1)+2*(x-1)));
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if (e < 0x3ff + 26)
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/* |x| < 0x1p26 */
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return log(2*x - 1/(x+sqrt(x*x-1)));
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/* |x| >= 0x1p26 or nan */
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return log(x) + 0.693147180559945309417232121458176568;
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}
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