Method for achieving correctly rounded quotients in algorithms based on fused multiply-accumulate without requiring the intermediate calculation of a correctly rounded reciprocal
US6598065B1 · kind B1 · utility
Assignee
Inventor
Key dates
| Filing date | Dec 23, 1999 |
| Grant date | Jul 22, 2003 |
| Priority date | — |
| Expiry date | Dec 23, 2019 |
Classification
- Technology area (CPC G)Physics
- CPC primaryG06F7/49963
- WIPO fieldComputer technology
- WIPO sectorElectrical engineering
Abstract
A method and apparatus for performing a floating point division of a dividend (a) by a divisor (b) to produce a correctly rounded-to-nearest quotient (q′) having a mantissa of P bits in a data processing system is disclosed.In one embodiment, the data processing system computes a current quotient estimate (qm′, where m represents an integer and m>=0) that is within 1 ulp of a true quotient (a/b). Then the data processing system computes a current remainder estimate (rm′) based on the dividend (a), the divisor (b) and the current quotient estimate (qm′). The data processing system also computes a current reciprocal estimate (yn′, where n represents an integer and n>=0) based on a reciprocal intermediate value (E) with a relative error with respect to a true reciprocal of the divisor (1/b) of less than or equal to z/(22P) (where z is an integer derived from error analyses of computations of the current reciprocal estimate (yn′)).Finally, the data processing system obtains the correctly rounded-to-nearest quotient (q′), except possibly when z>=(2P−Mb) (where Mb represents mantissa of the divisor, b), based on the current remainder estima…
Source: USPTO / EPO open patent data. Objective bibliographic and citation counts.