I recently received an update of the Tanh-Sinh Quadrature spreadsheet from Graeme Dennes, which can be downloaded from:  Tanh-Sinh Quadrature (including, as usual, full open source code). – Link fixed 5th April 2011

Here is Graeme’s description of the updates:

The Tanh-Sinh program and the two Double Exponential programs have been revised to improve their robustness when dealing with functions and limits for which overflow can occur. Previously, overflow events were managed by the automatic tolerance feature I introduced, which worked very well – for most situations. This revision takes a different path, in that the abscissas and weights for the interval (-1,1) are generated first, and stored in an array. The abscissas and weights are independent of the integrand and the limits, and are based only on the given tolerance figure (10^-14), Excel’s smallest positive floating point number (10^-305, with just a tad in reserve), and the method itself. The abscissas and weights are different for each program. The programs then access their array data as required. (Previously the abscissas and weights were calculated on the fly by the integration programs themselves.) Thus, overflow should not be possible with this new method.

The core technique (pre-generation of the abscissas and weights and overflow prevention) is by Takuya Ooura.

Consequently, the automatic tolerance feature has been removed from the three programs as being redundant, and all related text has been removed.

As a further change, the optional inputs of tolerance and level/panels/loops have been removed from all five programs, as these are no longer considered necessary or useful. All related text has also been removed.

In summary, overflow should not occur, the results should be at the maximum accuracy possible, and the programs’ use has been simplified.

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