1*f504f610SAugustin Cavalier #include "libm.h" 2*f504f610SAugustin Cavalier 3*f504f610SAugustin Cavalier /* k is such that k*ln2 has minimal relative error and x - kln2 > log(FLT_MIN) */ 4*f504f610SAugustin Cavalier static const int k = 235; 5*f504f610SAugustin Cavalier static const float kln2 = 0x1.45c778p+7f; 6*f504f610SAugustin Cavalier 7*f504f610SAugustin Cavalier /* expf(x)/2 for x >= log(FLT_MAX), slightly better than 0.5f*expf(x/2)*expf(x/2) */ __expo2f(float x)8*f504f610SAugustin Cavalierfloat __expo2f(float x) 9*f504f610SAugustin Cavalier { 10*f504f610SAugustin Cavalier float scale; 11*f504f610SAugustin Cavalier 12*f504f610SAugustin Cavalier /* note that k is odd and scale*scale overflows */ 13*f504f610SAugustin Cavalier SET_FLOAT_WORD(scale, (uint32_t)(0x7f + k/2) << 23); 14*f504f610SAugustin Cavalier /* exp(x - k ln2) * 2**(k-1) */ 15*f504f610SAugustin Cavalier return expf(x - kln2) * scale * scale; 16*f504f610SAugustin Cavalier } 17