diff options
Diffstat (limited to 'txr.1')
| -rw-r--r-- | txr.1 | 75 |
1 files changed, 50 insertions, 25 deletions
@@ -17745,7 +17745,7 @@ and tests for termination with .codn nil . .SS* Math Library -.coNP Arithmetic functions @ + and @ - +.coNP Functions @ + and @ - .synb .mets (+ << number *) .mets (- < number << number *) @@ -17910,44 +17910,69 @@ then generalized into the floating point domain. For instance the expression yields a residue of 0.25 because 0.5 "goes into" 0.75 only once, with a "remainder" of 0.25. -.coNP Function @ gcd +.coNP Functions @ gcd and @ lcm .synb -.mods (gcd < left << right ) +.mets (gcd << number *) +.mets (lcm << number *) .syne .desc The .code gcd function computes the greatest common divisor: the largest positive -integer which divides both arguments. +integer which divides each +.metn number . -Operands -.meta left -and -.meta right -must be integers, or else an exception is thrown. +The +.code lcm +function computes the lowest common multiple: the smallest positive +integer which is a multiple of +each +.metn number . + +Each +.meta number +must be an integer. + +Negative integers are replaced by their absolute values, so +.code (lcm -3 -4) +is +.code 12 +and +.code (gcd -12 -9) +yields +.codn 3 . The value of -.code (gcd 0 x) -is 0 for all -.codn x , -including 0. +.code (gcd) +is +.code 0 +and that of +.code (lcm) +is 1 . The value of -.code (gcd x 123) +.code (gcd x) +and +.code (lcm x) is -.code (abs x) -for all -.codn x . +.codn (abs x) . -Negative operands are permitted; this operation effectively ignores sign, so -that the value of -.code (gcd x y) -is the same as -.code (gcd (abs x) (abs y)) -for all -.code x +Any arguments of +.code gcd +which are zero are effectively ignored so that +.code (gcd 0) and -.codn y . +.code (gcd 0 0 0) +are both the same as +.code (gcd) +and +.code (gcd 1 0 2 0 3) +is the same as +.codn (gcd 1 2 3) . + +If +.code lcm +has any argument which is zero, it yields zero. .coNP Function @ abs .synb |