xref: /linux/lib/math/div64.c (revision 78c3925c048c752334873f56c3a3d1c9d53e0416)
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
32 uint32_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 }
64 EXPORT_SYMBOL(__div64_32);
65 #endif
66 
67 #ifndef div_s64_rem
68 s64 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 }
84 EXPORT_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
99 u64 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 }
124 EXPORT_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
139 u64 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 }
158 EXPORT_SYMBOL(div64_u64);
159 #endif
160 
161 #ifndef div64_s64
162 s64 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 }
171 EXPORT_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  */
180 u32 iter_div_u64_rem(u64 dividend, u32 divisor, u64 *remainder)
181 {
182 	return __iter_div_u64_rem(dividend, divisor, remainder);
183 }
184 EXPORT_SYMBOL(iter_div_u64_rem);
185 
186 #ifndef mul_u64_u64_div_u64
187 u64 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 }
239 EXPORT_SYMBOL(mul_u64_u64_div_u64);
240 #endif
241