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}