◆ memfmsub_BE()

void Chusov::Memory::memfmsub_BE	(	void *restrict	pResult,
		std::size_t	cbResult,
		const void *restrict	pX,
		std::size_t	cbX,
		const void *restrict	pY,
		std::size_t	cbY
	)

noexcept

Performs fused multiplication of two arbitrary-precision integers and a subtraction of the product from another arbitrary-precision integer in place. All integers are specified with vectors of bytes in the Big-Endian order.

Parameters

[in,out]	pResult	A pointer to a buffer which contains an integer whose value is decreased by the product of the values pointed to by `pX` and `pY`.
	cbResult	A byte size of the subtrahend and of the result. Fused multiplication and subtraction is performed by the function modulo `b^cbResult`, where `b = 2^CHAR_BIT` is a number of values that one byte can represent.
[in]	pX	A pointer to the first integral multiplicand.
	cbX	A byte size of the multiplicand pointed to by `pX`.
[in]	pY	A pointer to the second integer multiplicand.
	cbY	A byte size of the multiplicand pointed to by `cbY`.

The function considers the vectors pointed to by pResult, pX and pY to hold bytes of the integers in the Big-Endian byte order. That is, assuming that n_x = cbX - 1, n_y = cbY - 1 and n_R = cbResult - 1, the respective vectors are \(V_R = \{r_0,\dots,r_{n_R}\}\), \(V_X = \{x_0,\dots, x_{n_x}\}\) and \(V_Y = \{y_0,\dots, y_{n_y}\}\), where the bytes \(r_0\), \(x_0\) and \(y_0\) are the first elements within the respective vectors, the function produces the result \(R \gets (R - X \cdot Y)\bmod b^{n_R + 1}\), where on input \(R = \sum_{i=0}^{n_R} r_{n_R-i}\cdot b^i\), \(X = \sum_{i=0}^{n_x} x_{n_x - i}\cdot b^i\), and \(Y = \sum_{i=0}^{n_y} y_{n_y - i}\cdot b^i\) with respect to the Big-Endian order. The result is then written to the buffer pointed to by pResult.

That is, the multiplicands pointed to by pX and pY are firstly zero-extended or contracted in order to produce the \(n_R\)-byte integers \(X' = \sum_{i=0}^{n_R}x'_i\cdot b^i\), where \(x'_i = x_{n_x-i}\), if \(0\le i \le n_x\), and \(x'_i = 0\) otherwise, and \(Y' = \sum_{i=0}^{n_R}y'_{n_y-i}\cdot b^i\), where \(y'_i = y_i\), if \(0\le i\le n_y\), and \(y'_i = 0\) otherwise. Secondly, the integers \(X'\) and \(Y'\) are multiplied modulo \(n_R\). Lastly, the product is subtracted from the integer pointed to by pResult in place of the latter, again modulo \(n_R\).

The buffers pointed to by pResult, pX and pY must not overlap.

The memfmsub_LE function performs the operation over Little-Endian integers.

See also: memfmsub_LE;
memfmadd_BE;
memsub_BE;
memmul_BE.