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单精度浮点除法的最佳精度

[英]Best possible accuracy for single precision floating point division

原文 2014-07-18 14:06:22 0 1 c/ math/ assembly/ floating-point/ verilog

Is it possible to perform division and obtain IEEE-754 single-precision correct values if one is using single-precision add/sub and multiplication hardware only (no FMA)? 如果只使用单精度加/减和乘法硬件（无FMA），是否可以执行除法并获得IEEE-754单精度正确值？

Specifically if the Newton-Raphson method for carrying out floating-point division is carried out on single-precision hardware, is it possible to achieve a result that is IEEE-754 correct? 具体而言，如果在单精度硬件上执行用于执行浮点除法的Newton-Raphson方法，是否可以实现IEEE-754正确的结果？

1 个解决方案

Is it possible to perform division and obtain IEEE-754 single-precision correct values if one is using single-precision add/sub and multiplication hardware only (no FMA)? 如果只使用单精度加/减和乘法硬件（无FMA），是否可以执行除法并获得IEEE-754单精度正确值？

Yes. 是。

It is always possible to emulate higher precision by representing numbers as the sum of several single-precision floats, either two , three , or four (see the QD library on this page ). 通过将数字表示为几个单精度浮点（两个，三个或四个）的总和，总是可以模拟更高的精度（请参阅本页的QD库）。 You should only need the precision brought by two single-precision numbers for a correctly-rounded single-precision division, and the necessary operations for this representation can be implemented with only single-precision addition, subtraction and multiplication. 对于正确舍入的单精度除法，您应该只需要两个单精度数带来的精度，并且只需要单精度加法，减法和乘法就可以实现该表示的必要操作。