tango.math.ErrorFunction

Error Functions and Normal Distribution.

License:
BSD style:

Authors:
Stephen L. Moshier, ported to D by Don Clugston

real erfc(real a);
Complementary error function

erfc(x) = 1 - erf(x), and has high relative accuracy for values of x far from zero. (For values near zero, use erf(x)).

1 - erf(x) = 2/ (π) ∫ exp( - t2) dt



For small x, erfc(x) = 1 - erf(x); otherwise rational approximations are computed.

A special function expx2(x) is used to suppress error amplification in computing exp(-x^2).

real erf(real x);
Error function

The integral is

erf(x) = 2/ (π) ∫ exp( - t2) dt

The magnitude of x is limited to about 106.56 for IEEE 80-bit arithmetic; 1 or -1 is returned outside this range.

For 0 <= |x| < 1, a rational polynomials are used; otherwise erf(x) = 1 - erfc(x).

ACCURACY:
Relative error: arithmetic domain # trials peak rms IEEE 0,1 50000 2.0e-19 5.7e-20


Page generated by Ddoc. Copyright (C) 1984, 1995, 2000 Stephen L. Moshier Code taken from the Cephes Math Library Release 2.3: January, 1995