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| 1 #include "libm.h" |
| 2 |
| 3 /* sinh(x) = (exp(x) - 1/exp(x))/2 |
| 4 * = (exp(x)-1 + (exp(x)-1)/exp(x))/2 |
| 5 * = x + x^3/6 + o(x^5) |
| 6 */ |
| 7 double sinh(double x) |
| 8 { |
| 9 union {double f; uint64_t i;} u = {.f = x}; |
| 10 uint32_t w; |
| 11 double t, h, absx; |
| 12 |
| 13 h = 0.5; |
| 14 if (u.i >> 63) |
| 15 h = -h; |
| 16 /* |x| */ |
| 17 u.i &= (uint64_t)-1/2; |
| 18 absx = u.f; |
| 19 w = u.i >> 32; |
| 20 |
| 21 /* |x| < log(DBL_MAX) */ |
| 22 if (w < 0x40862e42) { |
| 23 t = expm1(absx); |
| 24 if (w < 0x3ff00000) { |
| 25 if (w < 0x3ff00000 - (26<<20)) |
| 26 /* note: inexact and underflow are raised by exp
m1 */ |
| 27 /* note: this branch avoids spurious underflow *
/ |
| 28 return x; |
| 29 return h*(2*t - t*t/(t+1)); |
| 30 } |
| 31 /* note: |x|>log(0x1p26)+eps could be just h*exp(x) */ |
| 32 return h*(t + t/(t+1)); |
| 33 } |
| 34 |
| 35 /* |x| > log(DBL_MAX) or nan */ |
| 36 /* note: the result is stored to handle overflow */ |
| 37 t = 2*h*__expo2(absx); |
| 38 return t; |
| 39 } |
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