Hi Juraj, I think this would be a very useful addition to the `math' module.
The gating issue is probably C compiler support. The most important non-C99 C compiler for Python is probably MS Visual Studio. And that one appears to support it: https://msdn.microsoft.com/en-us/library/mt720715.aspx So +1 on the proposal. Stephan 2017-01-15 18:25 GMT+01:00 Juraj Sukop <juraj.su...@gmail.com>: > Hello! > > Fused multiply-add (henceforth FMA) is an operation which calculates the > product of two numbers and then the sum of the product and a third number > with just one floating-point rounding. More concretely: > > r = x*y + z > > The value of `r` is the same as if the RHS was calculated with infinite > precision and the rounded to a 32-bit single-precision or 64-bit > double-precision floating-point number [1]. > > Even though one FMA CPU instruction might be calculated faster than the > two separate instructions for multiply and add, its main advantage comes > from the increased precision of numerical computations that involve the > accumulation of products. Examples which benefit from using FMA are: dot > product [2], compensated arithmetic [3], polynomial evaluation [4], matrix > multiplication, Newton's method and many more [5]. > > C99 includes `fma` function to `math.h` [6] and emulates the calculation > if the FMA instruction is not present on the host CPU [7]. PEP 7 states > that "Python versions greater than or equal to 3.6 use C89 with several > select C99 features" and that "Future C99 features may be added to this > list in the future depending on compiler support" [8]. > > This proposal is then about adding new `fma` function with the following > signature to `math` module: > > math.fma(x, y, z) > > '''Return a float representing the result of the operation `x*y + z` with > single rounding error, as defined by the platform C library. The result is > the same as if the operation was carried with infinite precision and > rounded to a floating-point number.''' > > There is a simple module for Python 3 demonstrating the fused multiply-add > operation which was build with simple `python3 setup.py build` under Linux > [9]. > > Any feedback is greatly appreciated! > > Juraj Sukop > > [1] https://en.wikipedia.org/wiki/Multiply%E2%80%93accumulate_operation > [2] S. Graillat, P. Langlois, N. Louvet. Accurate dot products with FMA. > 2006 > [3] S. Graillat, Accurate Floating Point Product and Exponentiation. 2007. > [4] S. Graillat, P. Langlois, N. Louvet. Improving the compensated Horner > scheme with a Fused Multiply and Add. 2006 > [5] J.-M. Muller, N. Brisebarre, F. de Dinechin, C.-P. Jeannerod, V. > Lefèvre, G. Melquiond, N. Revol, D. Stehlé, S. Torres. Handbook of > Floating-Point Arithmetic. 2010. Chapter 5 > [6] ISO/IEC 9899:TC3, "7.12.13.1 The fma functions", Committee Draft - > Septermber 7, 2007 > [7] https://git.musl-libc.org/cgit/musl/tree/src/math/fma.c > [8] https://www.python.org/dev/peps/pep-0007/ > [9] https://github.com/sukop/fma > > _______________________________________________ > Python-ideas mailing list > Python-ideas@python.org > https://mail.python.org/mailman/listinfo/python-ideas > Code of Conduct: http://python.org/psf/codeofconduct/ >
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