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| 1 #include "libm.h" |
| 2 |
| 3 /* asinh(x) = sign(x)*log(|x|+sqrt(x*x+1)) ~= x - x^3/6 + o(x^5) */ |
| 4 double asinh(double x) |
| 5 { |
| 6 union {double f; uint64_t i;} u = {.f = x}; |
| 7 unsigned e = u.i >> 52 & 0x7ff; |
| 8 unsigned s = u.i >> 63; |
| 9 |
| 10 /* |x| */ |
| 11 u.i &= (uint64_t)-1/2; |
| 12 x = u.f; |
| 13 |
| 14 if (e >= 0x3ff + 26) { |
| 15 /* |x| >= 0x1p26 or inf or nan */ |
| 16 x = log(x) + 0.693147180559945309417232121458176568; |
| 17 } else if (e >= 0x3ff + 1) { |
| 18 /* |x| >= 2 */ |
| 19 x = log(2*x + 1/(sqrt(x*x+1)+x)); |
| 20 } else if (e >= 0x3ff - 26) { |
| 21 /* |x| >= 0x1p-26, up to 1.6ulp error in [0.125,0.5] */ |
| 22 x = log1p(x + x*x/(sqrt(x*x+1)+1)); |
| 23 } else { |
| 24 /* |x| < 0x1p-26, raise inexact if x != 0 */ |
| 25 FORCE_EVAL(x + 0x1p120f); |
| 26 } |
| 27 return s ? -x : x; |
| 28 } |
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