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# std.math.remainder

This is a submodule of std.math.
It contains several versions of remainder calculation.
License:
Boost License 1.0.
Authors:
Walter Bright, Don Clugston, Conversion of CEPHES math library to D by Iain Buclaw and David Nadlinger

Source std/math/remainder.d

nothrow @nogc @trusted real `fmod`(real `x`, real `y`);
  Calculates the remainder from the calculation x/y.
  Returns:
  The value of x - i * y, where i is the number of times that y can be completely subtracted from x. The result has the same sign as x.

  Special Values
  x | y | fmod(x, y) | invalid?
  --- | --- | --- | ---
  ±0.0 | not 0.0 | ±0.0 | no
  ±∞ | anything | NAN | yes
  anything | ±0.0 | NAN | yes
  !=±∞ | ±∞ | x | no

  Examples:

      import std.math.operations : feqrel;
      import std.math.traits : isIdentical, isNaN;

      assert(isIdentical(fmod(0.0, 1.0), 0.0));
      assert(fmod(5.0, 3.0).feqrel(2.0) > 16);
      assert(isNaN(fmod(5.0, 0.0)));

nothrow @nogc @trusted real `modf`(real `x`, ref real `i`);
  Breaks x into an integral part and a fractional part, each of which has the same sign as x. The integral part is stored in i.
  Returns:
  The fractional part of x.

  Special Values
  x | i (on input) | modf(x, i) | i (on return)
  --- | --- | --- | ---
  ±∞ | anything | ±0.0 | ±∞

  Examples:

      import std.math.operations : feqrel;

      real frac;
      real intpart;

      frac = modf(3.14159, intpart);
      assert(intpart.feqrel(3.0) > 16);
      assert(frac.feqrel(0.14159) > 16);

nothrow @nogc @trusted real `remainder`(real `x`, real `y`);
nothrow @nogc @trusted real `remquo`(real `x`, real `y`, out int `n`);
  Calculate the remainder x REM y, following IEC 60559.
  REM is the value of x - y * n, where n is the integer nearest the exact value of x / y. If |n - x / y| == 0.5, n is even. If the result is zero, it has the same sign as x. Otherwise, the sign of the result is the sign of x / y. Precision mode has no effect on the remainder functions.
  remquo returns `n` in the parameter `n`.

  Special Values
  x | y | remainder(x, y) | n | invalid?
  --- | --- | --- | --- | ---
  ±0.0 | not 0.0 | ±0.0 | 0.0 | no
  ±∞ | anything | -NAN | ? | yes
  anything | ±0.0 | ±NAN | ? | yes
  != ±∞ | ±∞ | x | ? | no

  Examples:

      import std.math.operations : feqrel;
      import std.math.traits : isNaN;

      assert(remainder(5.1, 3.0).feqrel(-0.9) > 16);
      assert(remainder(-5.1, 3.0).feqrel(0.9) > 16);
      writeln(remainder(0.0, 3.0)); // 0.0

      assert(isNaN(remainder(1.0, 0.0)));
      assert(isNaN(remainder(-1.0, 0.0)));

  Examples:

      import std.math.operations : feqrel;

      int n;

      assert(remquo(5.1, 3.0, n).feqrel(-0.9) > 16 && n == 2);
      assert(remquo(-5.1, 3.0, n).feqrel(0.9) > 16 && n == -2);
      assert(remquo(0.0, 3.0, n) == 0.0 && n == 0);

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