lib/mpi/mpih-div.c

// SPDX-License-Identifier: GPL-2.0-or-later
/* mpihelp-div.c  -  MPI helper functions
 *	Copyright (C) 1994, 1996 Free Software Foundation, Inc.
 *	Copyright (C) 1998, 1999 Free Software Foundation, Inc.
 *
 * This file is part of GnuPG.
 *
 * Note: This code is heavily based on the GNU MP Library.
 *	 Actually it's the same code with only minor changes in the
 *	 way the data is stored; this is to support the abstraction
 *	 of an optional secure memory allocation which may be used
 *	 to avoid revealing of sensitive data due to paging etc.
 *	 The GNU MP Library itself is published under the LGPL;
 *	 however I decided to publish this code under the plain GPL.
 */

#include "mpi-internal.h"
#include "longlong.h"

#ifndef UMUL_TIME
#define UMUL_TIME 1
#endif
#ifndef UDIV_TIME
#define UDIV_TIME UMUL_TIME
#endif

/* Divide num (NP/NSIZE) by den (DP/DSIZE) and write
 * the NSIZE-DSIZE least significant quotient limbs at QP
 * and the DSIZE long remainder at NP.	If QEXTRA_LIMBS is
 * non-zero, generate that many fraction bits and append them after the
 * other quotient limbs.
 * Return the most significant limb of the quotient, this is always 0 or 1.
 *
 * Preconditions:
 * 0. NSIZE >= DSIZE.
 * 1. The most significant bit of the divisor must be set.
 * 2. QP must either not overlap with the input operands at all, or
 *    QP + DSIZE >= NP must hold true.	(This means that it's
 *    possible to put the quotient in the high part of NUM, right after the
 *    remainder in NUM.
 * 3. NSIZE >= DSIZE, even if QEXTRA_LIMBS is non-zero.
 */

mpi_limb_t
mpihelp_divrem(mpi_ptr_t qp, mpi_size_t qextra_limbs,
	       mpi_ptr_t np, mpi_size_t nsize, mpi_ptr_t dp, mpi_size_t dsize)
{
	mpi_limb_t most_significant_q_limb = 0;

	switch (dsize) {
	case 0:
		/* We are asked to divide by zero, so go ahead and do it!  (To make
		   the compiler not remove this statement, return the value.)  */
		/*
		 * existing clients of this function have been modified
		 * not to call it with dsize == 0, so this should not happen
		 */
		return 1 / dsize;

	case 1:
		{
			mpi_size_t i;
			mpi_limb_t n1;
			mpi_limb_t d;

			d = dp[0];
			n1 = np[nsize - 1];

			if (n1 >= d) {
				n1 -= d;
				most_significant_q_limb = 1;
			}

			qp += qextra_limbs;
			for (i = nsize - 2; i >= 0; i--)
				udiv_qrnnd(qp[i], n1, n1, np[i], d);
			qp -= qextra_limbs;

			for (i = qextra_limbs - 1; i >= 0; i--)
				udiv_qrnnd(qp[i], n1, n1, 0, d);

			np[0] = n1;
		}
		break;

	case 2:
		{
			mpi_size_t i;
			mpi_limb_t n1, n0, n2;
			mpi_limb_t d1, d0;

			np += nsize - 2;
			d1 = dp[1];
			d0 = dp[0];
			n1 = np[1];
			n0 = np[0];

			if (n1 >= d1 && (n1 > d1 || n0 >= d0)) {
				sub_ddmmss(n1, n0, n1, n0, d1, d0);
				most_significant_q_limb = 1;
			}

			for (i = qextra_limbs + nsize - 2 - 1; i >= 0; i--) {
				mpi_limb_t q;
				mpi_limb_t r;

				if (i >= qextra_limbs)
					np--;
				else
					np[0] = 0;

				if (n1 == d1) {
					/* Q should be either 111..111 or 111..110.  Need special
					 * treatment of this rare case as normal division would
					 * give overflow.  */
					q = ~(mpi_limb_t) 0;

					r = n0 + d1;
					if (r < d1) {	/* Carry in the addition? */
						add_ssaaaa(n1, n0, r - d0,
							   np[0], 0, d0);
						qp[i] = q;
						continue;
					}
					n1 = d0 - (d0 != 0 ? 1 : 0);
					n0 = -d0;
				} else {
					udiv_qrnnd(q, r, n1, n0, d1);
					umul_ppmm(n1, n0, d0, q);
				}

				n2 = np[0];
q_test:
				if (n1 > r || (n1 == r && n0 > n2)) {
					/* The estimated Q was too large.  */
					q--;
					sub_ddmmss(n1, n0, n1, n0, 0, d0);
					r += d1;
					if (r >= d1)	/* If not carry, test Q again.  */
						goto q_test;
				}

				qp[i] = q;
				sub_ddmmss(n1, n0, r, n2, n1, n0);
			}
			np[1] = n1;
			np[0] = n0;
		}
		break;

	default:
		{
			mpi_size_t i;
			mpi_limb_t dX, d1, n0;

			np += nsize - dsize;
			dX = dp[dsize - 1];
			d1 = dp[dsize - 2];
			n0 = np[dsize - 1];

			if (n0 >= dX) {
				if (n0 > dX
				    || mpihelp_cmp(np, dp, dsize - 1) >= 0) {
					mpihelp_sub_n(np, np, dp, dsize);
					n0 = np[dsize - 1];
					most_significant_q_limb = 1;
				}
			}

			for (i = qextra_limbs + nsize - dsize - 1; i >= 0; i--) {
				mpi_limb_t q;
				mpi_limb_t n1, n2;
				mpi_limb_t cy_limb;

				if (i >= qextra_limbs) {
					np--;
					n2 = np[dsize];
				} else {
					n2 = np[dsize - 1];
					MPN_COPY_DECR(np + 1, np, dsize - 1);
					np[0] = 0;
				}

				if (n0 == dX) {
					/* This might over-estimate q, but it's probably not worth
					 * the extra code here to find out.  */
					q = ~(mpi_limb_t) 0;
				} else {
					mpi_limb_t r;

					udiv_qrnnd(q, r, n0, np[dsize - 1], dX);
					umul_ppmm(n1, n0, d1, q);

					while (n1 > r
					       || (n1 == r
						   && n0 > np[dsize - 2])) {
						q--;
						r += dX;
						if (r < dX)	/* I.e. "carry in previous addition?" */
							break;
						n1 -= n0 < d1;
						n0 -= d1;
					}
				}

				/* Possible optimization: We already have (q * n0) and (1 * n1)
				 * after the calculation of q.  Taking advantage of that, we
				 * could make this loop make two iterations less.  */
				cy_limb = mpihelp_submul_1(np, dp, dsize, q);

				if (n2 != cy_limb) {
					mpihelp_add_n(np, np, dp, dsize);
					q--;
				}

				qp[i] = q;
				n0 = np[dsize - 1];
			}
		}
	}

	return most_significant_q_limb;
}