/* 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. * * GnuPG is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation; either version 2 of the License, or * (at your option) any later version. * * GnuPG is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License * along with this program; if not, write to the Free Software * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA * * 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 /* FIXME: We should be using invert_limb (or invert_normalized_limb) * here (not udiv_qrnnd). */ mpi_limb_tmpihelp_mod_1(mpi_ptr_t dividend_ptr, mpi_size_t dividend_size,	      mpi_limb_t divisor_limb){	mpi_size_t i;	mpi_limb_t n1, n0, r;	int dummy; 	/* Botch: Should this be handled at all?  Rely on callers?  */	if (!dividend_size)		return 0; 	/* If multiplication is much faster than division, and the	 * dividend is large, pre-invert the divisor, and use	 * only multiplications in the inner loop.	 *	 * This test should be read:	 *   Does it ever help to use udiv_qrnnd_preinv?	 *     && Does what we save compensate for the inversion overhead?	 */	if (UDIV_TIME > (2 * UMUL_TIME + 6)	    && (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME) {		int normalization_steps; 		count_leading_zeros(normalization_steps, divisor_limb);		if (normalization_steps) {			mpi_limb_t divisor_limb_inverted; 			divisor_limb <<= normalization_steps; 			/* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The			 * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the			 * most significant bit (with weight 2**N) implicit.			 *			 * Special case for DIVISOR_LIMB == 100...000.			 */			if (!(divisor_limb << 1))				divisor_limb_inverted = ~(mpi_limb_t) 0;			else				udiv_qrnnd(divisor_limb_inverted, dummy,					   -divisor_limb, 0, divisor_limb); 			n1 = dividend_ptr[dividend_size - 1];			r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps); 			/* Possible optimization:			 * if (r == 0			 * && divisor_limb > ((n1 << normalization_steps)			 *                 | (dividend_ptr[dividend_size - 2] >> ...)))			 * ...one division less...			 */			for (i = dividend_size - 2; i >= 0; i--) {				n0 = dividend_ptr[i];				UDIV_QRNND_PREINV(dummy, r, r,						  ((n1 << normalization_steps)						   | (n0 >>						      (BITS_PER_MPI_LIMB -						       normalization_steps))),						  divisor_limb,						  divisor_limb_inverted);				n1 = n0;			}			UDIV_QRNND_PREINV(dummy, r, r,					  n1 << normalization_steps,					  divisor_limb, divisor_limb_inverted);			return r >> normalization_steps;		} else {			mpi_limb_t divisor_limb_inverted; 			/* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The			 * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the			 * most significant bit (with weight 2**N) implicit.			 *			 * Special case for DIVISOR_LIMB == 100...000.			 */			if (!(divisor_limb << 1))				divisor_limb_inverted = ~(mpi_limb_t) 0;			else				udiv_qrnnd(divisor_limb_inverted, dummy,					   -divisor_limb, 0, divisor_limb); 			i = dividend_size - 1;			r = dividend_ptr[i]; 			if (r >= divisor_limb)				r = 0;			else				i--; 			for (; i >= 0; i--) {				n0 = dividend_ptr[i];				UDIV_QRNND_PREINV(dummy, r, r,						  n0, divisor_limb,						  divisor_limb_inverted);			}			return r;		}	} else {		if (UDIV_NEEDS_NORMALIZATION) {			int normalization_steps; 			count_leading_zeros(normalization_steps, divisor_limb);			if (normalization_steps) {				divisor_limb <<= normalization_steps; 				n1 = dividend_ptr[dividend_size - 1];				r = n1 >> (BITS_PER_MPI_LIMB -					   normalization_steps); 				/* Possible optimization:				 * if (r == 0				 * && divisor_limb > ((n1 << normalization_steps)				 *                 | (dividend_ptr[dividend_size - 2] >> ...)))				 * ...one division less...				 */				for (i = dividend_size - 2; i >= 0; i--) {					n0 = dividend_ptr[i];					udiv_qrnnd(dummy, r, r,						   ((n1 << normalization_steps)						    | (n0 >>						       (BITS_PER_MPI_LIMB -							normalization_steps))),						   divisor_limb);					n1 = n0;				}				udiv_qrnnd(dummy, r, r,					   n1 << normalization_steps,					   divisor_limb);				return r >> normalization_steps;			}		}		/* No normalization needed, either because udiv_qrnnd doesn't require		 * it, or because DIVISOR_LIMB is already normalized.  */		i = dividend_size - 1;		r = dividend_ptr[i]; 		if (r >= divisor_limb)			r = 0;		else			i--; 		for (; i >= 0; i--) {			n0 = dividend_ptr[i];			udiv_qrnnd(dummy, r, r, n0, divisor_limb);		}		return r;	}} /* 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_tmpihelp_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;} /**************** * Divide (DIVIDEND_PTR,,DIVIDEND_SIZE) by DIVISOR_LIMB. * Write DIVIDEND_SIZE limbs of quotient at QUOT_PTR. * Return the single-limb remainder. * There are no constraints on the value of the divisor. * * QUOT_PTR and DIVIDEND_PTR might point to the same limb. */ mpi_limb_tmpihelp_divmod_1(mpi_ptr_t quot_ptr,		 mpi_ptr_t dividend_ptr, mpi_size_t dividend_size,		 mpi_limb_t divisor_limb){	mpi_size_t i;	mpi_limb_t n1, n0, r;	int dummy; 	if (!dividend_size)		return 0; 	/* If multiplication is much faster than division, and the	 * dividend is large, pre-invert the divisor, and use	 * only multiplications in the inner loop.	 *	 * This test should be read:	 * Does it ever help to use udiv_qrnnd_preinv?	 * && Does what we save compensate for the inversion overhead?	 */	if (UDIV_TIME > (2 * UMUL_TIME + 6)	    && (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME) {		int normalization_steps; 		count_leading_zeros(normalization_steps, divisor_limb);		if (normalization_steps) {			mpi_limb_t divisor_limb_inverted; 			divisor_limb <<= normalization_steps; 			/* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The			 * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the			 * most significant bit (with weight 2**N) implicit.			 */			/* Special case for DIVISOR_LIMB == 100...000.  */			if (!(divisor_limb << 1))				divisor_limb_inverted = ~(mpi_limb_t) 0;			else				udiv_qrnnd(divisor_limb_inverted, dummy,					   -divisor_limb, 0, divisor_limb); 			n1 = dividend_ptr[dividend_size - 1];			r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps); 			/* Possible optimization:			 * if (r == 0			 * && divisor_limb > ((n1 << normalization_steps)			 *                 | (dividend_ptr[dividend_size - 2] >> ...)))			 * ...one division less...			 */			for (i = dividend_size - 2; i >= 0; i--) {				n0 = dividend_ptr[i];				UDIV_QRNND_PREINV(quot_ptr[i + 1], r, r,						  ((n1 << normalization_steps)						   | (n0 >>						      (BITS_PER_MPI_LIMB -						       normalization_steps))),						  divisor_limb,						  divisor_limb_inverted);				n1 = n0;			}			UDIV_QRNND_PREINV(quot_ptr[0], r, r,					  n1 << normalization_steps,					  divisor_limb, divisor_limb_inverted);			return r >> normalization_steps;		} else {			mpi_limb_t divisor_limb_inverted; 			/* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The			 * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the			 * most significant bit (with weight 2**N) implicit.			 */			/* Special case for DIVISOR_LIMB == 100...000.  */			if (!(divisor_limb << 1))				divisor_limb_inverted = ~(mpi_limb_t) 0;			else				udiv_qrnnd(divisor_limb_inverted, dummy,					   -divisor_limb, 0, divisor_limb); 			i = dividend_size - 1;			r = dividend_ptr[i]; 			if (r >= divisor_limb)				r = 0;			else				quot_ptr[i--] = 0; 			for (; i >= 0; i--) {				n0 = dividend_ptr[i];				UDIV_QRNND_PREINV(quot_ptr[i], r, r,						  n0, divisor_limb,						  divisor_limb_inverted);			}			return r;		}	} else {		if (UDIV_NEEDS_NORMALIZATION) {			int normalization_steps; 			count_leading_zeros(normalization_steps, divisor_limb);			if (normalization_steps) {

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