# When is double rounding innocuous?

@article{Figueroa1995WhenID, title={When is double rounding innocuous?}, author={Samuel Figueroa}, journal={ACM Signum Newsletter}, year={1995}, volume={30}, pages={21-26} }

Double rounding is the phenomenon that occurs when the result of an operation is rounded to fit some intermediate destination, and then again when delivered to its final destination. This can be a common occurrence when using some floating-point arithmetic engines which lack single precision registers: results of operations are typically rounded to fit in a register, whose width may be double precision or wider, before being stored in some memory location possibly in a format narrower than that…

## 22 Citations

### Innocuous Double Rounding of Basic Arithmetic Operations

- Computer ScienceJ. Formaliz. Reason.
- 2014

The formal proof of the folklore in the floating-point arithmetic community that double rounding is innocuous for the basic arithmetic operations as soon as the final precision is about twice larger than the intermediate one is addressed.

### Some issues related to double rounding

- Computer Science
- 2013

The potential influence of double rounding on the Fast2Sum and 2Sum algorithms, on some summation algorithms, and Veltkamp’s splitting is analyzed.

### Emulation of a FMA and Correctly Rounded Sums: Proved Algorithms Using Rounding to Odd

- Computer Science, MathematicsIEEE Transactions on Computers
- 2008

An algorithm for emulating the fused multiply-and-add operator and an iterative algorithm for computing the correctly rounded sum of a set of floating-point numbers under mild assumptions are presented.

### Some issues related to double roundings

- Computer Science
- 2018

The potential inﬂuence of double rounding on the Fast2Sum and 2Sum algorithms, on some summation algorithms, and Veltkamp’s splitting is analyzed.

### Verified Compilation of Floating-Point Computations

- Computer ScienceJournal of Automated Reasoning
- 2014

This paper reports on the recent success in formally specifying and proving correct CompCert’s compilation of floating-point arithmetic and obtains the first formally verified compiler that provably preserves the semantics offloating-point programs.

### A Formally-Verified C Compiler Supporting Floating-Point Arithmetic

- Computer Science2013 IEEE 21st Symposium on Computer Arithmetic
- 2013

This paper reports on the recent success in formally specifying and proving correct Comp Cert's compilation of floating-point arithmetic, and obtains the first formally verified compiler that provably preserves the semantics of float-point programs.

### A Bibliography of Publications on Floating-Point Arithmetic

- Computer Science
- 1999

This is a bibliography of material on floating-point arithmetic that I came up with while doing research on a floating-point package of my own. I don’t claim it to be anywhere near complete. The…

### A Software Implementation of the IEEE 754R Decimal Floating-Point Arithmetic Using the Binary Encoding Format

- Computer Science, Engineering18th IEEE Symposium on Computer Arithmetic (ARITH '07)
- 2007

New algorithms and properties are presented in this paper which are used in a software implementation of the IEEE 754R decimal floatingpoint arithmetic, with emphasis on using binary operations efficiently.

### Efficient Multibyte Floating Point Data Formats Using Vectorization

- Computer ScienceIEEE Transactions on Computers
- 2017

It is demonstrated that supporting reduced precision by exploiting native vector instructions can yield a low overhead custom-precision floating point solution that does not require specialized hardware support.

### SIMULATING LOW PRECISION FLOATING-POINT ARITHMETIC Higham, Nicholas J. and Pranesh, Srikara 2019

- Computer Science
- 2019

This work provides a MATLAB function chop that can be used to efficiently simulate fp16, bfloat16, and other low precision arithmetics, with or without the representation of subnormal numbers and with the options of round to nearest, directed rounding, stochastic rounding, and random bit flips in the significand.

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