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| 1 #include "libm.h" | 1 #include "libm.h" | 
| 2 | 2 | 
| 3 /* asinh(x) = sign(x)*log(|x|+sqrt(x*x+1)) ~= x - x^3/6 + o(x^5) */ | 3 /* asinh(x) = sign(x)*log(|x|+sqrt(x*x+1)) ~= x - x^3/6 + o(x^5) */ | 
| 4 double asinh(double x) | 4 double asinh(double x) { | 
| 5 { | 5   union { | 
| 6 »       union {double f; uint64_t i;} u = {.f = x}; | 6     double f; | 
| 7 »       unsigned e = u.i >> 52 & 0x7ff; | 7     uint64_t i; | 
| 8 »       unsigned s = u.i >> 63; | 8   } u = {.f = x}; | 
|  | 9   unsigned e = u.i >> 52 & 0x7ff; | 
|  | 10   unsigned s = u.i >> 63; | 
| 9 | 11 | 
| 10 »       /* |x| */ | 12   /* |x| */ | 
| 11 »       u.i &= (uint64_t)-1/2; | 13   u.i &= (uint64_t)-1 / 2; | 
| 12 »       x = u.f; | 14   x = u.f; | 
| 13 | 15 | 
| 14 »       if (e >= 0x3ff + 26) { | 16   if (e >= 0x3ff + 26) { | 
| 15 »       »       /* |x| >= 0x1p26 or inf or nan */ | 17     /* |x| >= 0x1p26 or inf or nan */ | 
| 16 »       »       x = log(x) + 0.693147180559945309417232121458176568; | 18     x = log(x) + 0.693147180559945309417232121458176568; | 
| 17 »       } else if (e >= 0x3ff + 1) { | 19   } else if (e >= 0x3ff + 1) { | 
| 18 »       »       /* |x| >= 2 */ | 20     /* |x| >= 2 */ | 
| 19 »       »       x = log(2*x + 1/(sqrt(x*x+1)+x)); | 21     x = log(2 * x + 1 / (sqrt(x * x + 1) + x)); | 
| 20 »       } else if (e >= 0x3ff - 26) { | 22   } else if (e >= 0x3ff - 26) { | 
| 21 »       »       /* |x| >= 0x1p-26, up to 1.6ulp error in [0.125,0.5] */ | 23     /* |x| >= 0x1p-26, up to 1.6ulp error in [0.125,0.5] */ | 
| 22 »       »       x = log1p(x + x*x/(sqrt(x*x+1)+1)); | 24     x = log1p(x + x * x / (sqrt(x * x + 1) + 1)); | 
| 23 »       } else { | 25   } else { | 
| 24 »       »       /* |x| < 0x1p-26, raise inexact if x != 0 */ | 26     /* |x| < 0x1p-26, raise inexact if x != 0 */ | 
| 25 »       »       FORCE_EVAL(x + 0x1p120f); | 27     FORCE_EVAL(x + 0x1p120f); | 
| 26 »       } | 28   } | 
| 27 »       return s ? -x : x; | 29   return s ? -x : x; | 
| 28 } | 30 } | 
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