29 lines
668 B
C
29 lines
668 B
C
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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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/* asinh(x) = copysign(log(fabs(x) + sqrt(x * x + 1.0)), x) */
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long double asinhl(long double x)
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{
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long double z;
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if (!isfinite (x))
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return x;
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z = fabsl (x);
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/* Avoid setting FPU underflow exception flag in x * x. */
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#if 0
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if ( z < 0x1p-32)
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return x;
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#endif
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/* Use log1p to avoid cancellation with small x. Put
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x * x in denom, so overflow is harmless.
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asinh(x) = log1p (x + sqrt (x * x + 1.0) - 1.0)
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= log1p (x + x * x / (sqrt (x * x + 1.0) + 1.0)) */
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z = __fast_log1pl (z + z * z / (__fast_sqrtl (z * z + 1.0L) + 1.0L));
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return ( x > 0.0 ? z : -z);
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}
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