Division algorithm: Difference between revisions

Revision as of 04:45, 16 July 2025

Revision as of 04:46, 16 July 2025

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The following computes the quotient of {{var|N}} and {{var|D}} with a precision of {{var|P}} binary places:

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<pre>

Express D as M × 2^e where 1 &le; M < 2 (standard floating point representation)<br>

D' := D / 2^e+1 ''// scale between 0.5 and 1, can be performed with bit shift / exponent subtraction''<br>

N' := N / 2^e+1<br>

X := 48/17 − 32/17 × D' ''// precompute constants with same precision as D''<br>

{{nowrap|'''repeat''' <math>\left \lceil \log_2 \frac{P + 1}{\log_2 17} \right \rceil \,</math> '''times'''}} ''// can be precomputed based on fixed P''<br>

X := X + X × (1 - D' × X)<br>

'''end'''<br>

'''return''' N' × X<br>

</prediv>

For example, for a double-precision floating-point division, this method uses 10 multiplies, 9 adds, and 2 shifts.