1*c9945492SAndroid Build Coastguard Worker #include "libm.h" 2*c9945492SAndroid Build Coastguard Worker 3*c9945492SAndroid Build Coastguard Worker /* atanh(x) = log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2 ~= x + x^3/3 + o(x^5) */ atanh(double x)4*c9945492SAndroid Build Coastguard Workerdouble atanh(double x) 5*c9945492SAndroid Build Coastguard Worker { 6*c9945492SAndroid Build Coastguard Worker union {double f; uint64_t i;} u = {.f = x}; 7*c9945492SAndroid Build Coastguard Worker unsigned e = u.i >> 52 & 0x7ff; 8*c9945492SAndroid Build Coastguard Worker unsigned s = u.i >> 63; 9*c9945492SAndroid Build Coastguard Worker double_t y; 10*c9945492SAndroid Build Coastguard Worker 11*c9945492SAndroid Build Coastguard Worker /* |x| */ 12*c9945492SAndroid Build Coastguard Worker u.i &= (uint64_t)-1/2; 13*c9945492SAndroid Build Coastguard Worker y = u.f; 14*c9945492SAndroid Build Coastguard Worker 15*c9945492SAndroid Build Coastguard Worker if (e < 0x3ff - 1) { 16*c9945492SAndroid Build Coastguard Worker if (e < 0x3ff - 32) { 17*c9945492SAndroid Build Coastguard Worker /* handle underflow */ 18*c9945492SAndroid Build Coastguard Worker if (e == 0) 19*c9945492SAndroid Build Coastguard Worker FORCE_EVAL((float)y); 20*c9945492SAndroid Build Coastguard Worker } else { 21*c9945492SAndroid Build Coastguard Worker /* |x| < 0.5, up to 1.7ulp error */ 22*c9945492SAndroid Build Coastguard Worker y = 0.5*log1p(2*y + 2*y*y/(1-y)); 23*c9945492SAndroid Build Coastguard Worker } 24*c9945492SAndroid Build Coastguard Worker } else { 25*c9945492SAndroid Build Coastguard Worker /* avoid overflow */ 26*c9945492SAndroid Build Coastguard Worker y = 0.5*log1p(2*(y/(1-y))); 27*c9945492SAndroid Build Coastguard Worker } 28*c9945492SAndroid Build Coastguard Worker return s ? -y : y; 29*c9945492SAndroid Build Coastguard Worker } 30