Faster remainder by direct computation: Applications to compilers and software libraries

@article{Lemire2019FasterRB,
  title={Faster remainder by direct computation: Applications to compilers and software libraries},
  author={D. Lemire and Owen Kaser and Nathan Kurz},
  journal={Software: Practice and Experience},
  year={2019},
  volume={49},
  pages={953 - 970}
}
On common processors, integer multiplication is many times faster than integer division. Dividing a numerator n by a divisor d is mathematically equivalent to multiplication by the inverse of the divisor (n/d=n∗1/d). If the divisor is known in advance, or if repeated integer divisions will be performed with the same divisor, it can be beneficial to substitute a less costly multiplication for an expensive division. Currently, the remainder of the division by a constant is computed from the… Expand
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References

SHOWING 1-10 OF 19 REFERENCES
Efficient Algorithms for Integer Division by Constants Using Multiplication
TLDR
This analysis leads to the discovery of a limit to the straightforward application of this method in the form of a critical dividend, which fortunately associates with a minority of the possible divisors and defines only a small upper part of the available dividend space. Expand
Improved Division by Invariant Integers
TLDR
An algorithm is described that produces a quotient and remainder using one umul and one umullo, which is an improvement over earlier methods, since the new method uses cheaper multiplication operations. Expand
Hardware Division by Small Integer Constants
TLDR
The article studies whether the division by the product of two constants is better implemented as two successive dividers or as one atomic divider, and considers the case when only a quotient or only a remainder is needed. Expand
Division by invariant integers using multiplication
TLDR
This paper presents code sequences for division by arbitrary nonzero integer constants and run-time invariants using integer multiplication using a two's complement architecture, and treats unsigned division, signed division, and division where the result is known a priori. Expand
Efficient and formally proven reduction of large integers by small moduli
TLDR
This work presents a modular reduction algorithm implementing division by a modulus through multiplication by a reciprocal of that modulus, a well-known method for moduli larger than 2w-1, and shows that application of this method to smaller moduli makes it possible to express certain modular sums and differences without having to compensate for word overflows. Expand
Constant-division algorithms
There exist many types of special-purpose systems that require rapid and repeated division by a set of known constant divisors. Numerous solutions have been proposed in response to the deficiencies… Expand
A Combinatoric Division Algorithm for Fixed-Integer Divisors
A procedure is presented for performing a combinatoric fixed-integer division that satisfies the division algorithm in regard to both quotient and remainder. In this procedure, division is performed… Expand
Special Cases of Division
This surveys algorithms and circuits for integer division in special cases. These include division by constants, small divisors, exact divisors, and cases where the divisor and the number base have a… Expand
IBM POWER8 processor core microarchitecture
TLDR
The core microarchitecture innovations made in the POWER8 processor, designed to significantly improve both single-thread performance and single-core throughput over its predecessor, the POWER7® processor, are described. Expand
Hacker's Delight
TLDR
The term "hacker" in the title is meant in the originalsense of an aficionado of computers—someone who enjoys making computers do new things, or do old things in a new and clever way. Expand
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