1*c9945492SAndroid Build Coastguard Worker #include "libm.h" 2*c9945492SAndroid Build Coastguard Worker 3*c9945492SAndroid Build Coastguard Worker /* asinh(x) = sign(x)*log(|x|+sqrt(x*x+1)) ~= x - x^3/6 + o(x^5) */ asinh(double x)4*c9945492SAndroid Build Coastguard Workerdouble asinh(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 10*c9945492SAndroid Build Coastguard Worker /* |x| */ 11*c9945492SAndroid Build Coastguard Worker u.i &= (uint64_t)-1/2; 12*c9945492SAndroid Build Coastguard Worker x = u.f; 13*c9945492SAndroid Build Coastguard Worker 14*c9945492SAndroid Build Coastguard Worker if (e >= 0x3ff + 26) { 15*c9945492SAndroid Build Coastguard Worker /* |x| >= 0x1p26 or inf or nan */ 16*c9945492SAndroid Build Coastguard Worker x = log(x) + 0.693147180559945309417232121458176568; 17*c9945492SAndroid Build Coastguard Worker } else if (e >= 0x3ff + 1) { 18*c9945492SAndroid Build Coastguard Worker /* |x| >= 2 */ 19*c9945492SAndroid Build Coastguard Worker x = log(2*x + 1/(sqrt(x*x+1)+x)); 20*c9945492SAndroid Build Coastguard Worker } else if (e >= 0x3ff - 26) { 21*c9945492SAndroid Build Coastguard Worker /* |x| >= 0x1p-26, up to 1.6ulp error in [0.125,0.5] */ 22*c9945492SAndroid Build Coastguard Worker x = log1p(x + x*x/(sqrt(x*x+1)+1)); 23*c9945492SAndroid Build Coastguard Worker } else { 24*c9945492SAndroid Build Coastguard Worker /* |x| < 0x1p-26, raise inexact if x != 0 */ 25*c9945492SAndroid Build Coastguard Worker FORCE_EVAL(x + 0x1p120f); 26*c9945492SAndroid Build Coastguard Worker } 27*c9945492SAndroid Build Coastguard Worker return s ? -x : x; 28*c9945492SAndroid Build Coastguard Worker } 29