/usr/lib/s9fes/help/quotient is in scheme9 2010.11.13-2.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 | R4RS 6.5.5 (quotient integer1 integer2) ==> integer
(remainder integer1 integer2) ==> integer
(modulo integer1 integer2) ==> integer
These procedures implement number-theoretic (integer) division: For
positive integers n1 and n2, if n3 and n4 are integers such that
n1=n2*n3+n4 and 0<=n4<n2, then
(quotient n1 n2) ==> n3
(remainder n1 n2) ==> n4
(modulo n1 n2) ==> n4
For integers n1 and n2 with n2 not equal to 0,
(= n1 (+ (* n2 (quotient n1 n2))
(remainder n1 n2))) ==> #t.
The value returned by QUOTIENT always has the sign of the product
of its arguments. REMAINDER and MODULO differ on negative arguments--the
remainder is either zero or has the sign of the dividend, while the
modulo always has the sign of the divisor:
(modulo 13 4) ==> 1
(remainder 13 4) ==> 1
(modulo -13 4) ==> 3
(remainder -13 4) ==> -1
(modulo 13 -4) ==> -3
(remainder 13 -4) ==> 1
(modulo -13 -4) ==> -1
(remainder -13 -4) ==> -1
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