1 #include "libm.h" 2 3 /* k is such that k*ln2 has minimal relative error and x - kln2 > log(DBL_MIN) */ 4 static const int k = 2043; 5 static 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) */ 8 double __expo2(double x) 9 { 10 double scale; 11 12 /* note that k is odd and scale*scale overflows */ 13 INSERT_WORDS(scale, (uint32_t)(0x3ff + k/2) << 20, 0); 14 /* exp(x - k ln2) * 2**(k-1) */ 15 return exp(x - kln2) * scale * scale; 16 } 17