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