Module malachite_base::num::arithmetic::div_mod

Traits for simultaneously finding the quotient and remainder of two numbers, subject to various rounding rules.

These are the traits:

rounding	by value or reference	by mutable reference (assignment)
towards $-\infty$	DivMod	DivAssignMod
towards 0	DivRem	DivAssignRem
towards $\infty$	CeilingDivMod	CeilingDivAssignMod
towards $\infty$	CeilingDivNegMod	CeilingDivAssignNegMod

CeilingDivMod and CeilingDivNegMod are similar. The difference is that CeilingDivMod returns a remainder less than or equal to 0, so that the usual relation $x = qy + r$ is satisfied, while CeilingDivNegMod returns a remainder greater than or equal to zero. This allows the remainder to have an unsigned type, but modifies the relation to $x = qy

• r$.

div_mod

use malachite_base::num::arithmetic::traits::DivMod;

// 2 * 10 + 3 = 23
assert_eq!(23u8.div_mod(10), (2, 3));

// 9 * 5 + 0 = 45
assert_eq!(45u32.div_mod(5), (9, 0));

// 2 * 10 + 3 = 23
assert_eq!(23i8.div_mod(10), (2, 3));

// -3 * -10 + -7 = 23
assert_eq!(23i16.div_mod(-10), (-3, -7));

// -3 * 10 + 7 = -23
assert_eq!((-23i32).div_mod(10), (-3, 7));

// 2 * -10 + -3 = -23
assert_eq!((-23i64).div_mod(-10), (2, -3));

div_assign_mod

use malachite_base::num::arithmetic::traits::DivAssignMod;

// 2 * 10 + 3 = 23
let mut x = 23u8;
assert_eq!(x.div_assign_mod(10), 3);
assert_eq!(x, 2);

// 9 * 5 + 0 = 45
let mut x = 45u32;
assert_eq!(x.div_assign_mod(5), 0);
assert_eq!(x, 9);

// 2 * 10 + 3 = 23
let mut x = 23i8;
assert_eq!(x.div_assign_mod(10), 3);
assert_eq!(x, 2);

// -3 * -10 + -7 = 23
let mut x = 23i16;
assert_eq!(x.div_assign_mod(-10), -7);
assert_eq!(x, -3);

// -3 * 10 + 7 = -23
let mut x = -23i32;
assert_eq!(x.div_assign_mod(10), 7);
assert_eq!(x, -3);

// 2 * -10 + -3 = -23
let mut x = -23i64;
assert_eq!(x.div_assign_mod(-10), -3);
assert_eq!(x, 2);

div_rem

use malachite_base::num::arithmetic::traits::DivRem;

// 2 * 10 + 3 = 23
assert_eq!(23u8.div_rem(10), (2, 3));

// 9 * 5 + 0 = 45
assert_eq!(45u32.div_rem(5), (9, 0));

// 2 * 10 + 3 = 23
assert_eq!(23i8.div_rem(10), (2, 3));

// -2 * -10 + 3 = 23
assert_eq!(23i16.div_rem(-10), (-2, 3));

// -2 * 10 + -3 = -23
assert_eq!((-23i32).div_rem(10), (-2, -3));

// 2 * -10 + -3 = -23
assert_eq!((-23i64).div_rem(-10), (2, -3));

div_assign_rem

use malachite_base::num::arithmetic::traits::DivAssignRem;

// 2 * 10 + 3 = 23
let mut x = 23u8;
assert_eq!(x.div_assign_rem(10), 3);
assert_eq!(x, 2);

// 9 * 5 + 0 = 45
let mut x = 45u32;
assert_eq!(x.div_assign_rem(5), 0);
assert_eq!(x, 9);

// 2 * 10 + 3 = 23
let mut x = 23i8;
assert_eq!(x.div_assign_rem(10), 3);
assert_eq!(x, 2);

// -2 * -10 + 3 = 23
let mut x = 23i16;
assert_eq!(x.div_assign_rem(-10), 3);
assert_eq!(x, -2);

// -2 * 10 + -3 = -23
let mut x = -23i32;
assert_eq!(x.div_assign_rem(10), -3);
assert_eq!(x, -2);

// 2 * -10 + -3 = -23
let mut x = -23i64;
assert_eq!(x.div_assign_rem(-10), -3);
assert_eq!(x, 2);

ceiling_div_neg_mod

use malachite_base::num::arithmetic::traits::CeilingDivNegMod;

// 3 * 10 - 7 = 23
assert_eq!(23u8.ceiling_div_neg_mod(10), (3, 7));

// 9 * 5 + 0 = 45
assert_eq!(45u32.ceiling_div_neg_mod(5), (9, 0));

ceiling_div_assign_neg_mod

use malachite_base::num::arithmetic::traits::CeilingDivAssignNegMod;

// 3 * 10 - 7 = 23
let mut x = 23u8;
assert_eq!(x.ceiling_div_assign_neg_mod(10), 7);
assert_eq!(x, 3);

// 9 * 5 + 0 = 45
let mut x = 45u32;
assert_eq!(x.ceiling_div_assign_neg_mod(5), 0);
assert_eq!(x, 9);

ceiling_div_mod

use malachite_base::num::arithmetic::traits::CeilingDivMod;

// 3 * 10 + -7 = 23
assert_eq!(23i8.ceiling_div_mod(10), (3, -7));

// -2 * -10 + 3 = 23
assert_eq!(23i16.ceiling_div_mod(-10), (-2, 3));

// -2 * 10 + -3 = -23
assert_eq!((-23i32).ceiling_div_mod(10), (-2, -3));

// 3 * -10 + 7 = -23
assert_eq!((-23i64).ceiling_div_mod(-10), (3, 7));

ceiling_div_assign_mod

use malachite_base::num::arithmetic::traits::CeilingDivAssignMod;

// 3 * 10 + -7 = 23
let mut x = 23i8;
assert_eq!(x.ceiling_div_assign_mod(10), -7);
assert_eq!(x, 3);

// -2 * -10 + 3 = 23
let mut x = 23i16;
assert_eq!(x.ceiling_div_assign_mod(-10), 3);
assert_eq!(x, -2);

// -2 * 10 + -3 = -23
let mut x = -23i32;
assert_eq!(x.ceiling_div_assign_mod(10), -3);
assert_eq!(x, -2);

// 3 * -10 + 7 = -23
let mut x = -23i64;
assert_eq!(x.ceiling_div_assign_mod(-10), 7);
assert_eq!(x, 3);