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Integer Division and Remainder Improved |
initial writing: 2006-10-26 |
The following dyads have been made faster and/or leaner on (machine word) integer arguments, with the largest improvement occurring when the divisor is a positive power of 2 and the dividend is non-negative.
| x <.@% d | integer quotient (also x >.@% d and @: instead of @) | |
| d|x | integer remainder | |
| (0,d)#:x | integer quotient and remainder |
The following benchmarks demonstrate the improvement.
ts=: 6!:2 , 7!:2@] x=: 1e6 ?@$ 2e5 ts 'Expression'
| Expression | J 6.02 | J 6.01 | Ratio | |||||||||
| x <.@% 256 | 0.00557535 | 4.19507e6 | 0.15662585 | 2.09723e7 | 28.09 | 5.00 | ||||||
| x <.@% 17 | 0.02155449 | 4.19507e6 | 0.18823105 | 2.09723e7 | 8.73 | 5.00 | ||||||
| 2 | x | 0.00322822 | 1.04915e6 | 0.02589772 | 4.19488e6 | 8.02 | 4.00 | ||||||
| 256 | x | 0.00610019 | 4.19494e6 | 0.03139283 | 4.19494e6 | 5.15 | 1.00 | ||||||
| 17 | x | 0.02469388 | 4.19494e6 | 0.02866373 | 4.19494e6 | 1.16 | 1.00 | ||||||
| 0 256 #: x | 0.00956875 | 8.38925e6 | 0.06542851 | 8.38925e6 | 6.84 | 1.00 | ||||||
| 0 17 #: x | 0.04244978 | 8.38925e6 | 0.06992786 | 8.38925e6 | 1.65 | 1.00 | ||||||