gmp_lib.mpn_divexact_by3c Method

public static mp_limb_t mpn_divexact_by3c(
	mp_ptr rp,
	mp_ptr sp,
	mp_size_t n,
	mp_limb_t carry
)

Public Shared Function mpn_divexact_by3c ( 
	rp As mp_ptr,
	sp As mp_ptr,
	n As mp_size_t,
	carry As mp_limb_t
) As mp_limb_t

public:
static mp_limb_t mpn_divexact_by3c(
	mp_ptr^ rp, 
	mp_ptr^ sp, 
	mp_size_t n, 
	mp_limb_t carry
)

static member mpn_divexact_by3c : 
        rp : mp_ptr * 
        sp : mp_ptr * 
        n : mp_size_t * 
        carry : mp_limb_t -> mp_limb_t 

Parameters

rp

Type: Math.Gmp.Nativemp_ptr
The result integer.

sp

Type: Math.Gmp.Nativemp_ptr
The operand integer.

n

Type: Math.Gmp.Nativemp_size_t
The number of limbs in sp.

carry

Type: Math.Gmp.Nativemp_limb_t
The initial carry.

Return Value

mpn_divexact_by3c takes an initial carry parameter, which can be the return value from a previous call, so a large calculation can be done piece by piece from low to high. mpn_divexact_by3 is simply a macro calling mpn_divexact_by3c with a 0 carry parameter.

These routines use a multiply-by-inverse and will be faster than mpn_divrem_1 on CPUs with fast multiplication but slow division.

The source a, result q, size n, initial carry i, and return value c satisfy c * b^n + a - i = 3 * q, where b = 2^mp_bits_per_limb. The return c is always 0, 1 or 2, and the initial carry i must also be 0, 1 or 2 (these are both borrows really). When c = 0 clearly q = (a - i) / 3. When c != 0, the remainder (a - i) mod 3 is given by 3 - c, because b ≡ 1 mod 3 (when mp_bits_per_limb is even, which is always so currently).

Reference