40 lines
837 B
C
40 lines
837 B
C
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#include "libm.h"
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/* sinh(x) = (exp(x) - 1/exp(x))/2
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* = (exp(x)-1 + (exp(x)-1)/exp(x))/2
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* = x + x^3/6 + o(x^5)
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*/
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double sinh(double x)
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{
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union {double f; uint64_t i;} u = {.f = x};
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uint32_t w;
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double t, h, absx;
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h = 0.5;
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if (u.i >> 63)
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h = -h;
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/* |x| */
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u.i &= (uint64_t)-1/2;
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absx = u.f;
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w = u.i >> 32;
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/* |x| < log(DBL_MAX) */
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if (w < 0x40862e42) {
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t = expm1(absx);
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if (w < 0x3ff00000) {
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if (w < 0x3ff00000 - (26<<20))
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/* note: inexact and underflow are raised by expm1 */
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/* note: this branch avoids spurious underflow */
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return x;
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return h*(2*t - t*t/(t+1));
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}
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/* note: |x|>log(0x1p26)+eps could be just h*exp(x) */
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return h*(t + t/(t+1));
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}
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/* |x| > log(DBL_MAX) or nan */
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/* note: the result is stored to handle overflow */
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t = 2*h*__expo2(absx);
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return t;
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}
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