lib/utils/libquad/qdivrem.c - opensbi - Git at Google

 /*-
  * SPDX-License-Identifier: BSD-3-Clause
  *
  * Copyright (c) 1992, 1993
  *	The Regents of the University of California.  All rights reserved.
  *
  * This software was developed by the Computer Systems Engineering group
  * at Lawrence Berkeley Laboratory under DARPA contract BG 91-66 and
  * contributed to Berkeley.
  *
  * Redistribution and use in source and binary forms, with or without
  * modification, are permitted provided that the following conditions
  * are met:
  * 1. Redistributions of source code must retain the above copyright
  *    notice, this list of conditions and the following disclaimer.
  * 2. Redistributions in binary form must reproduce the above copyright
  *    notice, this list of conditions and the following disclaimer in the
  *    documentation and/or other materials provided with the distribution.
  * 3. Neither the name of the University nor the names of its contributors
  *    may be used to endorse or promote products derived from this software
  *    without specific prior written permission.
  *
  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
  * SUCH DAMAGE.
  */

 #if defined(LIBC_SCCS) && !defined(lint)
 static char sccsid[] = "@(#)qdivrem.c	8.1 (Berkeley) 6/4/93";
 #endif /* LIBC_SCCS and not lint */
 #include <sys/cdefs.h>
 __FBSDID("$FreeBSD$");

 /*
  * Multiprecision divide.  This algorithm is from Knuth vol. 2 (2nd ed),
  * section 4.3.1, pp. 257--259.
  */

 #include "quad.h"

 #define	B	(1L << HALF_BITS)	/* digit base */

 /* Combine two `digits' to make a single two-digit number. */
 #define	COMBINE(a, b) (((u_long)(a) << HALF_BITS) | (b))

 /* select a type for digits in base B: use unsigned short if they fit */
 #if ULONG_MAX == 0xffffffff && USHRT_MAX >= 0xffff
 typedef unsigned short digit;
 #else
 typedef u_long digit;
 #endif

 /*
  * Shift p[0]..p[len] left `sh' bits, ignoring any bits that
  * `fall out' the left (there never will be any such anyway).
  * We may assume len >= 0.  NOTE THAT THIS WRITES len+1 DIGITS.
  */
 static void
 shl(digit *p, int len, int sh)
 {
 	int i;

 	for (i = 0; i < len; i++)
 		p[i] = LHALF(p[i] << sh) | (p[i + 1] >> (HALF_BITS - sh));
 	p[i] = LHALF(p[i] << sh);
 }

 /*
  * __qdivrem(u, v, rem) returns u/v and, optionally, sets *rem to u%v.
  *
  * We do this in base 2-sup-HALF_BITS, so that all intermediate products
  * fit within u_long.  As a consequence, the maximum length dividend and
  * divisor are 4 `digits' in this base (they are shorter if they have
  * leading zeros).
  */
 u_quad_t
 __qdivrem(u_quad_t uq, u_quad_t vq, u_quad_t *arq)
 {
 	union uu tmp;
 	digit *u, *v, *q;
 	digit v1, v2;
 	u_long qhat, rhat, t;
 	int m, n, d, j, i;
 	digit uspace[5], vspace[5], qspace[5];

 	/*
 	 * Take care of special cases: divide by zero, and u < v.
 	 */
 	if (vq == 0) {
 		/* divide by zero. */
 		static volatile const unsigned int zero = 0;

 		tmp.ul[H] = tmp.ul[L] = 1 / zero;
 		if (arq)
 			*arq = uq;
 		return (tmp.q);
 	}
 	if (uq < vq) {
 		if (arq)
 			*arq = uq;
 		return (0);
 	}
 	u = &uspace[0];
 	v = &vspace[0];
 	q = &qspace[0];

 	/*
 	 * Break dividend and divisor into digits in base B, then
 	 * count leading zeros to determine m and n.  When done, we
 	 * will have:
 	 *	u = (u[1]u[2]...u[m+n]) sub B
 	 *	v = (v[1]v[2]...v[n]) sub B
 	 *	v[1] != 0
 	 *	1 < n <= 4 (if n = 1, we use a different division algorithm)
 	 *	m >= 0 (otherwise u < v, which we already checked)
 	 *	m + n = 4
 	 * and thus
 	 *	m = 4 - n <= 2
 	 */
 	tmp.uq = uq;
 	u[0] = 0;
 	u[1] = HHALF(tmp.ul[H]);
 	u[2] = LHALF(tmp.ul[H]);
 	u[3] = HHALF(tmp.ul[L]);
 	u[4] = LHALF(tmp.ul[L]);
 	tmp.uq = vq;
 	v[1] = HHALF(tmp.ul[H]);
 	v[2] = LHALF(tmp.ul[H]);
 	v[3] = HHALF(tmp.ul[L]);
 	v[4] = LHALF(tmp.ul[L]);
 	for (n = 4; v[1] == 0; v++) {
 		if (--n == 1) {
 			u_long rbj;	/* r*B+u[j] (not root boy jim) */
 			digit q1, q2, q3, q4;

 			/*
 			 * Change of plan, per exercise 16.
 			 *	r = 0;
 			 *	for j = 1..4:
 			 *		q[j] = floor((r*B + u[j]) / v),
 			 *		r = (r*B + u[j]) % v;
 			 * We unroll this completely here.
 			 */
 			t = v[2];	/* nonzero, by definition */
 			q1 = u[1] / t;
 			rbj = COMBINE(u[1] % t, u[2]);
 			q2 = rbj / t;
 			rbj = COMBINE(rbj % t, u[3]);
 			q3 = rbj / t;
 			rbj = COMBINE(rbj % t, u[4]);
 			q4 = rbj / t;
 			if (arq)
 				*arq = rbj % t;
 			tmp.ul[H] = COMBINE(q1, q2);
 			tmp.ul[L] = COMBINE(q3, q4);
 			return (tmp.q);
 		}
 	}

 	/*
 	 * By adjusting q once we determine m, we can guarantee that
 	 * there is a complete four-digit quotient at &qspace[1] when
 	 * we finally stop.
 	 */
 	for (m = 4 - n; u[1] == 0; u++)
 		m--;
 	for (i = 4 - m; --i >= 0;)
 		q[i] = 0;
 	q += 4 - m;

 	/*
 	 * Here we run Program D, translated from MIX to C and acquiring
 	 * a few minor changes.
 	 *
 	 * D1: choose multiplier 1 << d to ensure v[1] >= B/2.
 	 */
 	d = 0;
 	for (t = v[1]; t < B / 2; t <<= 1)
 		d++;
 	if (d > 0) {
 		shl(&u[0], m + n, d);		/* u <<= d */
 		shl(&v[1], n - 1, d);		/* v <<= d */
 	}
 	/*
 	 * D2: j = 0.
 	 */
 	j = 0;
 	v1 = v[1];	/* for D3 -- note that v[1..n] are constant */
 	v2 = v[2];	/* for D3 */
 	do {
 		digit uj0, uj1, uj2;

 		/*
 		 * D3: Calculate qhat (\^q, in TeX notation).
 		 * Let qhat = min((u[j]*B + u[j+1])/v[1], B-1), and
 		 * let rhat = (u[j]*B + u[j+1]) mod v[1].
 		 * While rhat < B and v[2]*qhat > rhat*B+u[j+2],
 		 * decrement qhat and increase rhat correspondingly.
 		 * Note that if rhat >= B, v[2]*qhat < rhat*B.
 		 */
 		uj0 = u[j + 0];	/* for D3 only -- note that u[j+...] change */
 		uj1 = u[j + 1];	/* for D3 only */
 		uj2 = u[j + 2];	/* for D3 only */
 		if (uj0 == v1) {
 			qhat = B;
 			rhat = uj1;
 			goto qhat_too_big;
 		} else {
 			u_long n = COMBINE(uj0, uj1);
 			qhat = n / v1;
 			rhat = n % v1;
 		}
 		while (v2 * qhat > COMBINE(rhat, uj2)) {
 	qhat_too_big:
 			qhat--;
 			if ((rhat += v1) >= B)
 				break;
 		}
 		/*
 		 * D4: Multiply and subtract.
 		 * The variable `t' holds any borrows across the loop.
 		 * We split this up so that we do not require v[0] = 0,
 		 * and to eliminate a final special case.
 		 */
 		for (t = 0, i = n; i > 0; i--) {
 			t = u[i + j] - v[i] * qhat - t;
 			u[i + j] = LHALF(t);
 			t = (B - HHALF(t)) & (B - 1);
 		}
 		t = u[j] - t;
 		u[j] = LHALF(t);
 		/*
 		 * D5: test remainder.
 		 * There is a borrow if and only if HHALF(t) is nonzero;
 		 * in that (rare) case, qhat was too large (by exactly 1).
 		 * Fix it by adding v[1..n] to u[j..j+n].
 		 */
 		if (HHALF(t)) {
 			qhat--;
 			for (t = 0, i = n; i > 0; i--) { /* D6: add back. */
 				t += u[i + j] + v[i];
 				u[i + j] = LHALF(t);
 				t = HHALF(t);
 			}
 			u[j] = LHALF(u[j] + t);
 		}
 		q[j] = qhat;
 	} while (++j <= m);		/* D7: loop on j. */

 	/*
 	 * If caller wants the remainder, we have to calculate it as
 	 * u[m..m+n] >> d (this is at most n digits and thus fits in
 	 * u[m+1..m+n], but we may need more source digits).
 	 */
 	if (arq) {
 		if (d) {
 			for (i = m + n; i > m; --i)
 				u[i] = (u[i] >> d) |
 				    LHALF(u[i - 1] << (HALF_BITS - d));
 			u[i] = 0;
 		}
 		tmp.ul[H] = COMBINE(uspace[1], uspace[2]);
 		tmp.ul[L] = COMBINE(uspace[3], uspace[4]);
 		*arq = tmp.q;
 	}

 	tmp.ul[H] = COMBINE(qspace[1], qspace[2]);
 	tmp.ul[L] = COMBINE(qspace[3], qspace[4]);
 	return (tmp.q);
 }
	/*-
	* SPDX-License-Identifier: BSD-3-Clause
	*
	* Copyright (c) 1992, 1993
	* The Regents of the University of California. All rights reserved.
	*
	* This software was developed by the Computer Systems Engineering group
	* at Lawrence Berkeley Laboratory under DARPA contract BG 91-66 and
	* contributed to Berkeley.
	*
	* Redistribution and use in source and binary forms, with or without
	* modification, are permitted provided that the following conditions
	* are met:
	* 1. Redistributions of source code must retain the above copyright
	* notice, this list of conditions and the following disclaimer.
	* 2. Redistributions in binary form must reproduce the above copyright
	* notice, this list of conditions and the following disclaimer in the
	* documentation and/or other materials provided with the distribution.
	* 3. Neither the name of the University nor the names of its contributors
	* may be used to endorse or promote products derived from this software
	* without specific prior written permission.
	*
	* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
	* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
	* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
	* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
	* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
	* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
	* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
	* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
	* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
	* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
	* SUCH DAMAGE.
	*/

	#if defined(LIBC_SCCS) && !defined(lint)
	static char sccsid[] = "@(#)qdivrem.c 8.1 (Berkeley) 6/4/93";
	#endif /* LIBC_SCCS and not lint */
	#include <sys/cdefs.h>
	__FBSDID("$FreeBSD$");

	/*
	* Multiprecision divide. This algorithm is from Knuth vol. 2 (2nd ed),
	* section 4.3.1, pp. 257--259.
	*/

	#include "quad.h"

	#define B (1L << HALF_BITS) /* digit base */

	/* Combine two `digits' to make a single two-digit number. */
	#define COMBINE(a, b) (((u_long)(a) << HALF_BITS) \| (b))

	/* select a type for digits in base B: use unsigned short if they fit */
	#if ULONG_MAX == 0xffffffff && USHRT_MAX >= 0xffff
	typedef unsigned short digit;
	#else
	typedef u_long digit;
	#endif

	/*
	* Shift p[0]..p[len] left `sh' bits, ignoring any bits that
	* `fall out' the left (there never will be any such anyway).
	* We may assume len >= 0. NOTE THAT THIS WRITES len+1 DIGITS.
	*/
	static void
	shl(digit *p, int len, int sh)
	{
	int i;

	for (i = 0; i < len; i++)
	p[i] = LHALF(p[i] << sh) \| (p[i + 1] >> (HALF_BITS - sh));
	p[i] = LHALF(p[i] << sh);
	}

	/*
	* __qdivrem(u, v, rem) returns u/v and, optionally, sets *rem to u%v.
	*
	* We do this in base 2-sup-HALF_BITS, so that all intermediate products
	* fit within u_long. As a consequence, the maximum length dividend and
	* divisor are 4 `digits' in this base (they are shorter if they have
	* leading zeros).
	*/
	u_quad_t
	__qdivrem(u_quad_t uq, u_quad_t vq, u_quad_t *arq)
	{
	union uu tmp;
	digit u, v, *q;
	digit v1, v2;
	u_long qhat, rhat, t;
	int m, n, d, j, i;
	digit uspace[5], vspace[5], qspace[5];

	/*
	* Take care of special cases: divide by zero, and u < v.
	*/
	if (vq == 0) {
	/* divide by zero. */
	static volatile const unsigned int zero = 0;

	tmp.ul[H] = tmp.ul[L] = 1 / zero;
	if (arq)
	*arq = uq;
	return (tmp.q);
	}
	if (uq < vq) {
	if (arq)
	*arq = uq;
	return (0);
	}
	u = &uspace[0];
	v = &vspace[0];
	q = &qspace[0];

	/*
	* Break dividend and divisor into digits in base B, then
	* count leading zeros to determine m and n. When done, we
	* will have:
	* u = (u[1]u[2]...u[m+n]) sub B
	* v = (v[1]v[2]...v[n]) sub B
	* v[1] != 0
	* 1 < n <= 4 (if n = 1, we use a different division algorithm)
	* m >= 0 (otherwise u < v, which we already checked)
	* m + n = 4
	* and thus
	* m = 4 - n <= 2
	*/
	tmp.uq = uq;
	u[0] = 0;
	u[1] = HHALF(tmp.ul[H]);
	u[2] = LHALF(tmp.ul[H]);
	u[3] = HHALF(tmp.ul[L]);
	u[4] = LHALF(tmp.ul[L]);
	tmp.uq = vq;
	v[1] = HHALF(tmp.ul[H]);
	v[2] = LHALF(tmp.ul[H]);
	v[3] = HHALF(tmp.ul[L]);
	v[4] = LHALF(tmp.ul[L]);
	for (n = 4; v[1] == 0; v++) {
	if (--n == 1) {
	u_long rbj; /* rB+u[j] (not root boy jim) /
	digit q1, q2, q3, q4;

	/*
	* Change of plan, per exercise 16.
	* r = 0;
	* for j = 1..4:
	* q[j] = floor((r*B + u[j]) / v),
	* r = (r*B + u[j]) % v;
	* We unroll this completely here.
	*/
	t = v[2]; /* nonzero, by definition */
	q1 = u[1] / t;
	rbj = COMBINE(u[1] % t, u[2]);
	q2 = rbj / t;
	rbj = COMBINE(rbj % t, u[3]);
	q3 = rbj / t;
	rbj = COMBINE(rbj % t, u[4]);
	q4 = rbj / t;
	if (arq)
	*arq = rbj % t;
	tmp.ul[H] = COMBINE(q1, q2);
	tmp.ul[L] = COMBINE(q3, q4);
	return (tmp.q);
	}
	}

	/*
	* By adjusting q once we determine m, we can guarantee that
	* there is a complete four-digit quotient at &qspace[1] when
	* we finally stop.
	*/
	for (m = 4 - n; u[1] == 0; u++)
	m--;
	for (i = 4 - m; --i >= 0;)
	q[i] = 0;
	q += 4 - m;

	/*
	* Here we run Program D, translated from MIX to C and acquiring
	* a few minor changes.
	*
	* D1: choose multiplier 1 << d to ensure v[1] >= B/2.
	*/
	d = 0;
	for (t = v[1]; t < B / 2; t <<= 1)
	d++;
	if (d > 0) {
	shl(&u[0], m + n, d); /* u <<= d */
	shl(&v[1], n - 1, d); /* v <<= d */
	}
	/*
	* D2: j = 0.
	*/
	j = 0;
	v1 = v[1]; /* for D3 -- note that v[1..n] are constant */
	v2 = v[2]; /* for D3 */
	do {
	digit uj0, uj1, uj2;

	/*
	* D3: Calculate qhat (\^q, in TeX notation).
	* Let qhat = min((u[j]*B + u[j+1])/v[1], B-1), and
	* let rhat = (u[j]*B + u[j+1]) mod v[1].
	* While rhat < B and v[2]qhat > rhatB+u[j+2],
	* decrement qhat and increase rhat correspondingly.
	* Note that if rhat >= B, v[2]qhat < rhatB.
	*/
	uj0 = u[j + 0]; /* for D3 only -- note that u[j+...] change */
	uj1 = u[j + 1]; /* for D3 only */
	uj2 = u[j + 2]; /* for D3 only */
	if (uj0 == v1) {
	qhat = B;
	rhat = uj1;
	goto qhat_too_big;
	} else {
	u_long n = COMBINE(uj0, uj1);
	qhat = n / v1;
	rhat = n % v1;
	}
	while (v2 * qhat > COMBINE(rhat, uj2)) {
	qhat_too_big:
	qhat--;
	if ((rhat += v1) >= B)
	break;
	}
	/*
	* D4: Multiply and subtract.
	* The variable `t' holds any borrows across the loop.
	* We split this up so that we do not require v[0] = 0,
	* and to eliminate a final special case.
	*/
	for (t = 0, i = n; i > 0; i--) {
	t = u[i + j] - v[i] * qhat - t;
	u[i + j] = LHALF(t);
	t = (B - HHALF(t)) & (B - 1);
	}
	t = u[j] - t;
	u[j] = LHALF(t);
	/*
	* D5: test remainder.
	* There is a borrow if and only if HHALF(t) is nonzero;
	* in that (rare) case, qhat was too large (by exactly 1).
	* Fix it by adding v[1..n] to u[j..j+n].
	*/
	if (HHALF(t)) {
	qhat--;
	for (t = 0, i = n; i > 0; i--) { /* D6: add back. */
	t += u[i + j] + v[i];
	u[i + j] = LHALF(t);
	t = HHALF(t);
	}
	u[j] = LHALF(u[j] + t);
	}
	q[j] = qhat;
	} while (++j <= m); /* D7: loop on j. */

	/*
	* If caller wants the remainder, we have to calculate it as
	* u[m..m+n] >> d (this is at most n digits and thus fits in
	* u[m+1..m+n], but we may need more source digits).
	*/
	if (arq) {
	if (d) {
	for (i = m + n; i > m; --i)
	u[i] = (u[i] >> d) \|
	LHALF(u[i - 1] << (HALF_BITS - d));
	u[i] = 0;
	}
	tmp.ul[H] = COMBINE(uspace[1], uspace[2]);
	tmp.ul[L] = COMBINE(uspace[3], uspace[4]);
	*arq = tmp.q;
	}

	tmp.ul[H] = COMBINE(qspace[1], qspace[2]);
	tmp.ul[L] = COMBINE(qspace[3], qspace[4]);
	return (tmp.q);
	}