Error Functions and Normal Distribution.
License:
BSD style: see license.txt
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
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