The Rise of Mixed Precision Arithmetic

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For the last 30 years, most floating point calculations in scientific computing have been carried out in 64-bit IEEE double precision arithmetic, which provides the elementary operations of additio…
For the last 30 years, most floating point calculations in scientific computing have been carried out in 64-bit IEEE double precision arithmetic, which provides the elementary operations of addition, subtraction, multiplication, and division at a relative accuracy of about . We are now seeing growing use of mixed precision, in which different floating point precisions are combined in order to deliver a result of the required accuracy at minimal cost.

Single precision arithmetic (32 bits) is an attractive alternative to double precision because it halves the costs of storing and transferring data, and on Intel chips the SSE extensions allow single precision arithmetic to run twice as fast as double.

" alt="qd-compare2.jpg" width="300″ height="337″ /> The Mandelbrot set computed in double and quadruple precision. Image taken from https://www.thasler.com/blog/blog/glsl-part5.

Quadruple precision arithmetic, which was included in the 2008 revision of the IEEE standard, is supported by some compilers, and it can be implemented in terms of double precision arithmetic via double-double arithmetic. Arbitrary precision floating point arithmetic is available through, for example, the GNU MPFR library, the mpmath library…
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