tango.math.ErrorFunction

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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