1// SPDX-License-Identifier: GPL-2.0
  2/*
  3 * Copyright (C) 2003 Bernardo Innocenti <bernie@develer.com>
  4 *
  5 * Based on former do_div() implementation from asm-parisc/div64.h:
  6 *	Copyright (C) 1999 Hewlett-Packard Co
  7 *	Copyright (C) 1999 David Mosberger-Tang <davidm@hpl.hp.com>
  8 *
  9 *
 10 * Generic C version of 64bit/32bit division and modulo, with
 11 * 64bit result and 32bit remainder.
 12 *
 13 * The fast case for (n>>32 == 0) is handled inline by do_div().
 14 *
 15 * Code generated for this function might be very inefficient
 16 * for some CPUs. __div64_32() can be overridden by linking arch-specific
 17 * assembly versions such as arch/ppc/lib/div64.S and arch/sh/lib/div64.S
 18 * or by defining a preprocessor macro in arch/include/asm/div64.h.
 19 */
 20
 21#include <linux/bitops.h>
 22#include <linux/export.h>
 23#include <linux/math.h>
 24#include <linux/math64.h>
 25#include <linux/minmax.h>
 26#include <linux/log2.h>
 27
 28/* Not needed on 64bit architectures */
 29#if BITS_PER_LONG == 32
 30
 31#ifndef __div64_32
 32uint32_t __attribute__((weak)) __div64_32(uint64_t *n, uint32_t base)
 33{
 34	uint64_t rem = *n;
 35	uint64_t b = base;
 36	uint64_t res, d = 1;
 37	uint32_t high = rem >> 32;
 38
 39	/* Reduce the thing a bit first */
 40	res = 0;
 41	if (high >= base) {
 42		high /= base;
 43		res = (uint64_t) high << 32;
 44		rem -= (uint64_t) (high*base) << 32;
 45	}
 46
 47	while ((int64_t)b > 0 && b < rem) {
 48		b = b+b;
 49		d = d+d;
 50	}
 51
 52	do {
 53		if (rem >= b) {
 54			rem -= b;
 55			res += d;
 56		}
 57		b >>= 1;
 58		d >>= 1;
 59	} while (d);
 60
 61	*n = res;
 62	return rem;
 63}
 64EXPORT_SYMBOL(__div64_32);
 65#endif
 66
 67#ifndef div_s64_rem
 68s64 div_s64_rem(s64 dividend, s32 divisor, s32 *remainder)
 69{
 70	u64 quotient;
 71
 72	if (dividend < 0) {
 73		quotient = div_u64_rem(-dividend, abs(divisor), (u32 *)remainder);
 74		*remainder = -*remainder;
 75		if (divisor > 0)
 76			quotient = -quotient;
 77	} else {
 78		quotient = div_u64_rem(dividend, abs(divisor), (u32 *)remainder);
 79		if (divisor < 0)
 80			quotient = -quotient;
 81	}
 82	return quotient;
 83}
 84EXPORT_SYMBOL(div_s64_rem);
 85#endif
 86
 87/*
 88 * div64_u64_rem - unsigned 64bit divide with 64bit divisor and remainder
 89 * @dividend:	64bit dividend
 90 * @divisor:	64bit divisor
 91 * @remainder:  64bit remainder
 92 *
 93 * This implementation is a comparable to algorithm used by div64_u64.
 94 * But this operation, which includes math for calculating the remainder,
 95 * is kept distinct to avoid slowing down the div64_u64 operation on 32bit
 96 * systems.
 97 */
 98#ifndef div64_u64_rem
 99u64 div64_u64_rem(u64 dividend, u64 divisor, u64 *remainder)
100{
101	u32 high = divisor >> 32;
102	u64 quot;
103
104	if (high == 0) {
105		u32 rem32;
106		quot = div_u64_rem(dividend, divisor, &rem32);
107		*remainder = rem32;
108	} else {
109		int n = fls(high);
110		quot = div_u64(dividend >> n, divisor >> n);
111
112		if (quot != 0)
113			quot--;
114
115		*remainder = dividend - quot * divisor;
116		if (*remainder >= divisor) {
117			quot++;
118			*remainder -= divisor;
119		}
120	}
121
122	return quot;
123}
124EXPORT_SYMBOL(div64_u64_rem);
125#endif
126
127/*
128 * div64_u64 - unsigned 64bit divide with 64bit divisor
129 * @dividend:	64bit dividend
130 * @divisor:	64bit divisor
131 *
132 * This implementation is a modified version of the algorithm proposed
133 * by the book 'Hacker's Delight'.  The original source and full proof
134 * can be found here and is available for use without restriction.
135 *
136 * 'http://www.hackersdelight.org/hdcodetxt/divDouble.c.txt'
137 */
138#ifndef div64_u64
139u64 div64_u64(u64 dividend, u64 divisor)
140{
141	u32 high = divisor >> 32;
142	u64 quot;
143
144	if (high == 0) {
145		quot = div_u64(dividend, divisor);
146	} else {
147		int n = fls(high);
148		quot = div_u64(dividend >> n, divisor >> n);
149
150		if (quot != 0)
151			quot--;
152		if ((dividend - quot * divisor) >= divisor)
153			quot++;
154	}
155
156	return quot;
157}
158EXPORT_SYMBOL(div64_u64);
159#endif
160
161#ifndef div64_s64
162s64 div64_s64(s64 dividend, s64 divisor)
163{
164	s64 quot, t;
165
166	quot = div64_u64(abs(dividend), abs(divisor));
167	t = (dividend ^ divisor) >> 63;
168
169	return (quot ^ t) - t;
170}
171EXPORT_SYMBOL(div64_s64);
172#endif
173
174#endif /* BITS_PER_LONG == 32 */
175
176/*
177 * Iterative div/mod for use when dividend is not expected to be much
178 * bigger than divisor.
179 */
180u32 iter_div_u64_rem(u64 dividend, u32 divisor, u64 *remainder)
181{
182	return __iter_div_u64_rem(dividend, divisor, remainder);
183}
184EXPORT_SYMBOL(iter_div_u64_rem);
185
186#ifndef mul_u64_u64_div_u64
187u64 mul_u64_u64_div_u64(u64 a, u64 b, u64 c)
188{
189	u64 res = 0, div, rem;
190	int shift;
191
192	/* can a * b overflow ? */
193	if (ilog2(a) + ilog2(b) > 62) {
194		/*
195		 * Note that the algorithm after the if block below might lose
196		 * some precision and the result is more exact for b > a. So
197		 * exchange a and b if a is bigger than b.
198		 *
199		 * For example with a = 43980465100800, b = 100000000, c = 1000000000
200		 * the below calculation doesn't modify b at all because div == 0
201		 * and then shift becomes 45 + 26 - 62 = 9 and so the result
202		 * becomes 4398035251080. However with a and b swapped the exact
203		 * result is calculated (i.e. 4398046510080).
204		 */
205		if (a > b)
206			swap(a, b);
207
208		/*
209		 * (b * a) / c is equal to
210		 *
211		 *      (b / c) * a +
212		 *      (b % c) * a / c
213		 *
214		 * if nothing overflows. Can the 1st multiplication
215		 * overflow? Yes, but we do not care: this can only
216		 * happen if the end result can't fit in u64 anyway.
217		 *
218		 * So the code below does
219		 *
220		 *      res = (b / c) * a;
221		 *      b = b % c;
222		 */
223		div = div64_u64_rem(b, c, &rem);
224		res = div * a;
225		b = rem;
226
227		shift = ilog2(a) + ilog2(b) - 62;
228		if (shift > 0) {
229			/* drop precision */
230			b >>= shift;
231			c >>= shift;
232			if (!c)
233				return res;
234		}
235	}
236
237	return res + div64_u64(a * b, c);
238}
239EXPORT_SYMBOL(mul_u64_u64_div_u64);
240#endif