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(DBL_MIN) */ 4*f504f610SAugustin Cavalier static const int k = 2043; 5*f504f610SAugustin Cavalier static const double kln2 = 0x1.62066151add8bp+10; 6*f504f610SAugustin Cavalier 7*f504f610SAugustin Cavalier /* exp(x)/2 for x >= log(DBL_MAX), slightly better than 0.5*exp(x/2)*exp(x/2) */ __expo2(double x)8*f504f610SAugustin Cavalierdouble __expo2(double x) 9*f504f610SAugustin Cavalier { 10*f504f610SAugustin Cavalier double scale; 11*f504f610SAugustin Cavalier 12*f504f610SAugustin Cavalier /* note that k is odd and scale*scale overflows */ 13*f504f610SAugustin Cavalier INSERT_WORDS(scale, (uint32_t)(0x3ff + k/2) << 20, 0); 14*f504f610SAugustin Cavalier /* exp(x - k ln2) * 2**(k-1) */ 15*f504f610SAugustin Cavalier return exp(x - kln2) * scale * scale; 16*f504f610SAugustin Cavalier } 17