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, double sign)
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 /* in directed rounding correct sign before rounding or overflow is important */
16 return exp(x - kln2) * (sign * scale) * scale;
17}