35 lines
941 B
C
35 lines
941 B
C
/**
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* This file has no copyright assigned and is placed in the Public Domain.
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* This file is part of the mingw-w64 runtime package.
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* No warranty is given; refer to the file DISCLAIMER.PD within this package.
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*/
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#include <math.h>
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#include <errno.h>
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#include "fastmath.h"
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/* atanh (x) = 0.5 * log ((1.0 + x)/(1.0 - x)) */
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long double atanhl (long double x)
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{
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long double z;
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if (isnan (x))
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return x;
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z = fabsl (x);
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if (z == 1.0L)
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{
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errno = ERANGE;
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return (x > 0 ? INFINITY : -INFINITY);
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}
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if ( z > 1.0L)
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{
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errno = EDOM;
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return nanl("");
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}
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/* Rearrange formula to avoid precision loss for small x.
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atanh(x) = 0.5 * log ((1.0 + x)/(1.0 - x))
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= 0.5 * log1p ((1.0 + x)/(1.0 - x) - 1.0)
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= 0.5 * log1p ((1.0 + x - 1.0 + x) /(1.0 - x))
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= 0.5 * log1p ((2.0 * x ) / (1.0 - x)) */
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z = 0.5L * __fast_log1pl ((z + z) / (1.0L - z));
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return x >= 0 ? z : -z;
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}
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