1#include "libm.h"
2
3/* k is such that k*ln2 has minimal relative error and x - kln2 > log(FLT_MIN) */
4static const int k = 235;
5static const float kln2 = 0x1.45c778p+7f;
6
7/* expf(x)/2 for x >= log(FLT_MAX), slightly better than 0.5f*expf(x/2)*expf(x/2) */
8float __expo2f(float x, float sign)
9{
10 float scale;
11
12 /* note that k is odd and scale*scale overflows */
13 SET_FLOAT_WORD(scale, (uint32_t)(0x7f + k/2) << 23);
14 /* exp(x - k ln2) * 2**(k-1) */
15 /* in directed rounding correct sign before rounding or overflow is important */
16 return expf(x - kln2) * (sign * scale) * scale;
17}