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exp
Exponential function.SYNOPSIS:
double x, y, exp();
y = exp(x);
DESCRIPTION:
Returns e (2.71828...) raised to the x power.
Range reduction is accomplished by separating the argument into an integer k and fraction f such that:
x k f
e = 2 e.
A Pade' form
1 + 2x P(x**2)/(Q(x**2) - P(x**2)) of degree 2/3 is used to approximate exp(f) in the basic interval [-0.5, 0.5].
ACCURACY:
Relative error:
arithmetic domain # trials peak rms
DEC +- 88 50000 2.8e-17 7.0e-18
IEEE +- 708 40000 2.0e-16 5.6e-17
Error amplification in the exponential function can be a serious matter. The error propagation involves:
exp(X(1+delta)) = exp(X) (1 + X*delta + ...)
This shows that a 1 lsb error in representing X produces a relative error of X times 1 lsb in the function. While the routine gives an accurate result for arguments that are exactly represented by a double precision computer number, the result contains an amplified roundoff error for large arguments not exactly represented.
ERROR MESSAGES:
message condition value returned
underflow x < MINLOG 0.0
overflow x > MAXLOG INFINITY