1#include "libm.h" 2 3/* k is such that k*ln2 has minimal relative error and x - kln2 > log(DBL_MIN) */ 4static const int k = 2043; 5static const double kln2 = 0x1.62066151add8bp+10; 6 7/* exp(x)/2 for x >= log(DBL_MAX), slightly better than 0.5*exp(x/2)*exp(x/2) */ 8double __expo2(double x) { 9 double scale; 10 11 /* note that k is odd and scale*scale overflows */ 12 INSERT_WORDS(scale, (uint32_t)(0x3ff + k / 2) << 20, 0); 13 /* exp(x - k ln2) * 2**(k-1) */ 14 return exp(x - kln2) * scale * scale; 15} 16