The value of an integral

is calculated using the Simpson method. An interval [a,b] is divided into n=2m parts x₀ =a, x₁ =a+h, ..., x_n =b with step h=(b-a)/n. The values y_i  = F(x_i ) in points x_i  are calculated and then the integral value is calculated using the Simpson formula:

where

The number of points of the division is doubled and an accuracy estimation is performed:

If R_n  > e, the number of points of the division is doubled. The value of the sum 2(y₁ +y₂ +...+y_2m-1 ) isn't changed, therefore it is required to calculate the values y_i  only in the new points.

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C#

C# 1.0 source.
simpsonq.csharp.zip - Simpson's method

C++

C++ source.
simpsonq.cpp.zip - Simpson's method
ablas.zip - optimized basic linear algebra subroutines with SSE2 support (for C++ sources only)

Delphi

Delphi source.
Can be compiled under FPC (in Delphi compatibility mode).
simpsonq.delphi.zip - Simpson's method

Visual Basic 6

Visual Basic 6 source.
simpsonq.vb6.zip - Simpson's method

Zonnon ^beta

Zonnon source.
Zonnon is an experimental language developed at ETH Zurich.
See www.zonnon.ethz.ch for more information.
simpsonq.zonnon.zip - Simpson's method