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
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