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| 1 #include "libm.h" |
| 2 |
| 3 /* tanh(x) = (exp(x) - exp(-x))/(exp(x) + exp(-x)) |
| 4 * = (exp(2*x) - 1)/(exp(2*x) - 1 + 2) |
| 5 * = (1 - exp(-2*x))/(exp(-2*x) - 1 + 2) |
| 6 */ |
| 7 double tanh(double x) |
| 8 { |
| 9 union {double f; uint64_t i;} u = {.f = x}; |
| 10 uint32_t w; |
| 11 int sign; |
| 12 double_t t; |
| 13 |
| 14 /* x = |x| */ |
| 15 sign = u.i >> 63; |
| 16 u.i &= (uint64_t)-1/2; |
| 17 x = u.f; |
| 18 w = u.i >> 32; |
| 19 |
| 20 if (w > 0x3fe193ea) { |
| 21 /* |x| > log(3)/2 ~= 0.5493 or nan */ |
| 22 if (w > 0x40340000) { |
| 23 /* |x| > 20 or nan */ |
| 24 /* note: this branch avoids raising overflow */ |
| 25 t = 1 - 0/x; |
| 26 } else { |
| 27 t = expm1(2*x); |
| 28 t = 1 - 2/(t+2); |
| 29 } |
| 30 } else if (w > 0x3fd058ae) { |
| 31 /* |x| > log(5/3)/2 ~= 0.2554 */ |
| 32 t = expm1(2*x); |
| 33 t = t/(t+2); |
| 34 } else if (w >= 0x00100000) { |
| 35 /* |x| >= 0x1p-1022, up to 2ulp error in [0.1,0.2554] */ |
| 36 t = expm1(-2*x); |
| 37 t = -t/(t+2); |
| 38 } else { |
| 39 /* |x| is subnormal */ |
| 40 /* note: the branch above would not raise underflow in [0x1p-102
3,0x1p-1022) */ |
| 41 FORCE_EVAL((float)x); |
| 42 t = x; |
| 43 } |
| 44 return sign ? -t : t; |
| 45 } |
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