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41 lines
764 B
41 lines
764 B
7 years ago
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#include "libm.h"
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/* cosh(x) = (exp(x) + 1/exp(x))/2
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* = 1 + 0.5*(exp(x)-1)*(exp(x)-1)/exp(x)
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* = 1 + x*x/2 + o(x^4)
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*/
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double cosh(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;
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/* |x| */
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u.i &= (uint64_t)-1/2;
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x = u.f;
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w = u.i >> 32;
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/* |x| < log(2) */
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if (w < 0x3fe62e42) {
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if (w < 0x3ff00000 - (26<<20)) {
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/* raise inexact if x!=0 */
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FORCE_EVAL(x + 0x1p120f);
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return 1;
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}
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t = expm1(x);
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return 1 + t*t/(2*(1+t));
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}
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/* |x| < log(DBL_MAX) */
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if (w < 0x40862e42) {
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t = exp(x);
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/* note: if x>log(0x1p26) then the 1/t is not needed */
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return 0.5*(t + 1/t);
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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 = __expo2(x);
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return t;
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}
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