Fixed-point arithmetic: Difference between revisions

Revision as of 01:43, 18 June 2025

Revision as of 01:45, 18 June 2025

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===Multiplication===

To multiply two fixed-point numbers, it suffices to multiply the two underlying integers, and assume that the scaling factor of the result is the product of their scaling factors. The result will be exact, with no rounding, provided that it does not overflow the receiving variable. (Specifically, with integer multiplication, the product is up to twice the width of the two factors. Overflow behaviour follows a [[finite ring]], which is not very useful after scaling.)

For example, multiplying the numbers 123 scaled by 1/1000 (0.123) and 25 scaled by 1/10 (2.5) yields the integer 123×25 = 3075 scaled by (1/1000)×(1/10) = 1/10000, that is 3075/10000 = 0.3075. As another example, multiplying the first number by 155 implicitly scaled by 1/32 (155/32 = 4.84375) yields the integer 123×155 = 19065 with implicit scaling factor (1/1000)×(1/32) = 1/32000, that is 19065/32000 = 0.59578125.