In my analysis of decimal to floating-point conversion I noted an example that was converted incorrectly by the Microsoft Visual C++ compiler. I’ve found more examples — including a class of examples — that it converts incorrectly. I will analyze those examples in this article.
In my article “Quick and Dirty Decimal to Floating-Point Conversion” I presented a small C program that converts a decimal string to a double-precision binary floating-point number. The number it produces, however, is not necessarily the closest — or so-called correctly rounded — double-precision binary floating-point number. This is not a failing of the algorithm; mathematically speaking, the algorithm is correct. The flaw comes in its implementation in limited precision binary floating-point arithmetic.
The quick and dirty program is implemented in native C, so it’s limited to double-precision floating-point arithmetic (although on some systems, extended precision may be used). Higher precision arithmetic — in fact, arbitrary precision arithmetic — is needed to ensure that all decimal inputs are converted correctly. I will demonstrate the need for high precision by analyzing three examples, all taken from Vern Paxson’s paper “A Program for Testing IEEE Decimal–Binary Conversion”.
