divMod

simultaneous div and mod. WARNING: This function is partial (because it throws when 0 is passed as the divisor) for all the integer types in base.

simultaneous div and mod WARNING: This function is partial (because it throws when 0 is passed as the divisor) for all the integer types in base.

simultaneous div and mod

\n (QC.NonZero m) -> let (q,r) = divMod n m in n == (q*m+r :: Integer)

\x y -> case (PolyCore.normalize x, PolyCore.normalize y) of (nx, ny) -> not (null (ratioPoly ny)) ==> mapSnd PolyCore.normalize (PolyCore.divMod nx ny) == mapPair (PolyCore.normalize, PolyCore.normalize) (PolyCore.divMod x y)

\x y -> not (isZero (ratioPoly y)) ==> let z = fst $ PolyCore.divMod (Poly.coeffs x) y in  PolyCore.normalize z == z

\x y -> case PolyCore.normalize $ ratioPoly y of ny -> not (null ny) ==> List.length (snd $ PolyCore.divMod x y) < List.length ny

Simultaneous div and mod.

simultaneous div and mod

Type-level divMod

The quotient and remainder of a type-level integer and a natural number. For a negative dividend, the remainder part is positive such that x = q*y + r @since 0.1.4

Generalisation of divMod to any instance of Real

Used to implement divMod for the Integral typeclass. This gives a tuple equivalent to

(div x y, mod x y)

Example

>>> divModInt 10 2
(5,0)

>>> divMod 10 2
(5,0)

Used to implement divMod for the Integral typeclass. This gives a tuple equivalent to

(div x y, mod x y)

Example

>>> divModInteger 10 2
(5,0)

>>> divMod 10 2
(5,0)

Simultaneous divInteger and modInteger. Divisor must be non-zero otherwise the GHC runtime will terminate with a division-by-zero fault.

Allows division by zero. If the divisor is zero, then the dividend is returned as remainder.

The modulus will always have one element less than the divisor. This means that the modulus will be denormalized in some cases, e.g. mod [2,1,1] [1,1,1] == [1,0] instead of [1].