1131722Sobrien#include "libm.h" 2218822Sdim 3131722Sobrien/* atanh(x) = log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2 ~= x + x^3/3 + o(x^5) */ 4131722Sobriendouble atanh(double x) { 5131722Sobrien union { 6131722Sobrien double f; 7131722Sobrien uint64_t i; 8131722Sobrien } u = {.f = x}; 9131722Sobrien unsigned e = u.i >> 52 & 0x7ff; 10131722Sobrien unsigned s = u.i >> 63; 11131722Sobrien double_t y; 12131722Sobrien 13131722Sobrien /* |x| */ 14131722Sobrien u.i &= (uint64_t)-1 / 2; 15131722Sobrien y = u.f; 16131722Sobrien 17131722Sobrien if (e < 0x3ff - 1) { 18218822Sdim if (e < 0x3ff - 32) { 19131722Sobrien /* handle underflow */ 20218822Sdim if (e == 0) 21218822Sdim FORCE_EVAL((float)y); 22218822Sdim } else { 23218822Sdim /* |x| < 0.5, up to 1.7ulp error */ 24218822Sdim y = 0.5 * log1p(2 * y + 2 * y * y / (1 - y)); 25218822Sdim } 26218822Sdim } else { 27218822Sdim /* avoid overflow */ 28218822Sdim y = 0.5 * log1p(2 * (y / (1 - y))); 29131722Sobrien } 30131722Sobrien return s ? -y : y; 31218822Sdim} 32