floor/ -- r7rs Definition

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Kind

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procedure;

Implemented by

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• floor/ (from vonuvoli);

Procedure signature

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Procedure variants:

• ((real-not-nan real-not-zero-not-nan) -> (real-not-nan real-not-nan))
  • inputs:
    • a value of type real-not-nan;
    • a value of type real-not-zero-not-nan;
  • outputs:
    • a value of type real-not-nan;
    • a value of type real-not-nan;
• ((real real-not-zero) -> (real-nan real-nan))
  • inputs:
    • a value of type real;
    • a value of type real-not-zero;
  • outputs:
    • a value of type real-nan;
    • a value of type real-nan;

Exports

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• scheme:base -- (scheme base);

Exports recursive

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• scheme -- (scheme);

Description

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(floor/ n_1 n_2)
(floor-quotient n_1 n_2)
(floor-remainder n_1 n_2)
(truncate/ n_1 n_2)
(truncate-quotient n_1 n_2)
(truncate-remainder n_1 n_2)

These procedures implement number-theoretic (integer) division. It is an error if n_2 is zero. The procedures ending in / return two integers; the other procedures return an integer. All the procedures compute a quotient n_q and remainder n_r such that n_1 = n_2 n_q + n_r. For each of the division operators, there are three procedures defined as follows:

(<operator>/ n_1 n_2)             ===>  n_q n_r
(<operator>-quotient n_1 n_2)     ===>  n_q
(<operator>-remainder n_1 n_2)    ===>  n_r

The remainder n_r is determined by the choice of integer n_q: n_r = n_1 - n_2 n_q. Each set of operators uses a different choice of n_q:

• floor -- n_q = floor(n_1 / n_2);
• truncate -- n_q = truncate(n_1 / n_2);

For any of the operators, and for integers n_1 and n_2 with n_2 not equal to 0,

     (= n_1 (+ (* n_2 (<operator>-quotient n_1 n_2))
           (<operator>-remainder n_1 n_2)))
                                 ===>  #t

provided all numbers involved in that computation are exact.

Examples:

(floor/ 5 2)         ===>   2    1
(floor/ -5 2)        ===>  -3    1
(floor/ 5 -2)        ===>  -3   -1
(floor/ -5 -2)       ===>   2   -1
(truncate/ 5 2)      ===>   2    1
(truncate/ -5 2)     ===>  -2   -1
(truncate/ 5 -2)     ===>  -2    1
(truncate/ -5 -2)    ===>   2   -1
(truncate/ -5.0 -2)  ===>   2.0 -1.0

(quotient n_1 n_2)
(remainder n_1 n_2)
(modulo n_1 n_2)

The quotient and remainder procedures are equivalent to truncate-quotient and truncate-remainder, respectively, and modulo is equivalent to floor-remainder.

Note: These procedures are provided for backward compatibility with earlier versions of this report.

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The text herein was sourced and adapted as described in the "R7RS attribution of various text snippets" appendix.

Referenced-types

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• real-not-nan;
• real-not-zero-not-nan;
• real;
• real-not-zero;
• real-nan;