Caculating 1/d if you have multiply

Thread starter rcgldr
Start date Apr 18, 2007

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SUMMARY

The discussion focuses on calculating the reciprocal of a number (1/D) using assembly code, specifically through an integer multiplication method that involves 32-bit by 32-bit multiplication yielding a 64-bit result. The algorithm utilizes an unsigned approach and begins with an initial estimated quotient derived from a table with 8 bits of precision. The iterative formula q_{n+1} = q_n (2 - q_n X) is employed, requiring only 4 to 5 iterations to achieve 32 bits of precision. The conversation raises the question of whether superior algorithms exist for this calculation.

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Understanding of assembly language programming
Familiarity with integer multiplication techniques
Knowledge of fixed-point arithmetic
Basic grasp of iterative algorithms and convergence

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Apr 18, 2007

rcgldr

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This will be done in assembly code, using an integer multiply, 32 bit by 32 bit producing 64 bit result. Unsigned algorithm is good enough.

Generic algorithm to find 1 / D, eq is initial estimated quotient, from table, say with 8 bits of precision.

[tex]q_0\ =\ eq[/tex]

[tex]q_{n+1}\ =\ q_n\ (2\ -\ q_n\ X)[/tex]

For integer math, pre and post shifting of values will be done. Generally only 4 or 5 interations are required to get 32 bits of precision.

Are there better algorithms?

Last edited: Apr 18, 2007