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precision – as much as you need


dudleybenton

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Sometimes 64-bit floating-point arithmetic just isn't enough, but what else can you do? I solved this problem in 1982 by writing extended precision operations for the HP minicomputer entirely in assembler. I converted these operations to run on Intel processors and published them in 1992. They are available now in C++, which will run on most anything. What can you do with this? How about 4096-point Gauss quadrature? Here are the first 3 abscissas and weights: double A4096[]={0.0003834483770539113, 0.0011503449056439943, 0.0019172407576809915, ...};double W4096[]={0.0007668967165215304, 0.0007668962654860735, 0.0007668953634154251,...}; The differences between what I have developed and what you might find on the web include: 1) the code I've seen on the web is astonishingly messy and will only run on LINUX, not Windows; 2) the format I use is exactly the same as IEEE 754 but with a longer mantissa, which can be ignored or truncated with no impact except diminished precision. The implementation includes: sin, cos, tan, exp, log, pow, etc. You will find this plus many more useful functions for numerical calculus, all free, of course.

Numerical_Calculus_examples.zip

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