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pow
Power functionSYNOPSIS:
double x, y, z, pow();
z = pow(x, y);
DESCRIPTION:
Computes x raised to the yth power. Analytically:
x**y = exp(y log(x)).
Following Cody and Waite, this program uses a lookup table of 2**-i/16 and pseudo extended precision arithmetic to obtain an extra three bits of accuracy in both the logarithm and the exponential.
ACCURACY:
Relative error:
arithmetic domain # trials peak rms
IEEE -26,26 30000 4.2e-16 7.7e-17
DEC -26,26 60000 4.8e-17 9.1e-18
1/26 < x < 26, with log(x) uniformly distributed.
-26 < y < 26, y uniformly distributed.
IEEE 0,8700 30000 1.5e-14 2.1e-15
0.99 < x < 1.01, 0 < y < 8700, uniformly distributed.
ERROR MESSAGES:
message condition value returned
overflow x**y > MAXNUM INFINITY
underflow x**y < 1/MAXNUM 0.0
domain x<0 and y noninteger 0.0