1#include "libm.h" 2 3/* asinh(x) = sign(x)*log(|x|+sqrt(x*x+1)) ~= x - x^3/6 + o(x^5) */ 4float asinhf(float x) { 5 union { 6 float f; 7 uint32_t i; 8 } u = {.f = x}; 9 uint32_t i = u.i & 0x7fffffff; 10 unsigned s = u.i >> 31; 11 12 /* |x| */ 13 u.i = i; 14 x = u.f; 15 16 if (i >= 0x3f800000 + (12 << 23)) { 17 /* |x| >= 0x1p12 or inf or nan */ 18 x = logf(x) + 0.693147180559945309417232121458176568f; 19 } else if (i >= 0x3f800000 + (1 << 23)) { 20 /* |x| >= 2 */ 21 x = logf(2 * x + 1 / (sqrtf(x * x + 1) + x)); 22 } else if (i >= 0x3f800000 - (12 << 23)) { 23 /* |x| >= 0x1p-12, up to 1.6ulp error in [0.125,0.5] */ 24 x = log1pf(x + x * x / (sqrtf(x * x + 1) + 1)); 25 } else { 26 /* |x| < 0x1p-12, raise inexact if x!=0 */ 27 FORCE_EVAL(x + 0x1p120f); 28 } 29 return s ? -x : x; 30} 31