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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/log2.h>
26
27/* Not needed on 64bit architectures */
28#if BITS_PER_LONG == 32
29
30#ifndef __div64_32
31uint32_t __attribute__((weak)) __div64_32(uint64_t *n, uint32_t base)
32{
33 uint64_t rem = *n;
34 uint64_t b = base;
35 uint64_t res, d = 1;
36 uint32_t high = rem >> 32;
37
38 /* Reduce the thing a bit first */
39 res = 0;
40 if (high >= base) {
41 high /= base;
42 res = (uint64_t) high << 32;
43 rem -= (uint64_t) (high*base) << 32;
44 }
45
46 while ((int64_t)b > 0 && b < rem) {
47 b = b+b;
48 d = d+d;
49 }
50
51 do {
52 if (rem >= b) {
53 rem -= b;
54 res += d;
55 }
56 b >>= 1;
57 d >>= 1;
58 } while (d);
59
60 *n = res;
61 return rem;
62}
63EXPORT_SYMBOL(__div64_32);
64#endif
65
66/**
67 * div_s64_rem - signed 64bit divide with 64bit divisor and remainder
68 * @dividend: 64bit dividend
69 * @divisor: 64bit divisor
70 * @remainder: 64bit remainder
71 */
72#ifndef div_s64_rem
73s64 div_s64_rem(s64 dividend, s32 divisor, s32 *remainder)
74{
75 u64 quotient;
76
77 if (dividend < 0) {
78 quotient = div_u64_rem(-dividend, abs(divisor), (u32 *)remainder);
79 *remainder = -*remainder;
80 if (divisor > 0)
81 quotient = -quotient;
82 } else {
83 quotient = div_u64_rem(dividend, abs(divisor), (u32 *)remainder);
84 if (divisor < 0)
85 quotient = -quotient;
86 }
87 return quotient;
88}
89EXPORT_SYMBOL(div_s64_rem);
90#endif
91
92/**
93 * div64_u64_rem - unsigned 64bit divide with 64bit divisor and remainder
94 * @dividend: 64bit dividend
95 * @divisor: 64bit divisor
96 * @remainder: 64bit remainder
97 *
98 * This implementation is a comparable to algorithm used by div64_u64.
99 * But this operation, which includes math for calculating the remainder,
100 * is kept distinct to avoid slowing down the div64_u64 operation on 32bit
101 * systems.
102 */
103#ifndef div64_u64_rem
104u64 div64_u64_rem(u64 dividend, u64 divisor, u64 *remainder)
105{
106 u32 high = divisor >> 32;
107 u64 quot;
108
109 if (high == 0) {
110 u32 rem32;
111 quot = div_u64_rem(dividend, divisor, &rem32);
112 *remainder = rem32;
113 } else {
114 int n = fls(high);
115 quot = div_u64(dividend >> n, divisor >> n);
116
117 if (quot != 0)
118 quot--;
119
120 *remainder = dividend - quot * divisor;
121 if (*remainder >= divisor) {
122 quot++;
123 *remainder -= divisor;
124 }
125 }
126
127 return quot;
128}
129EXPORT_SYMBOL(div64_u64_rem);
130#endif
131
132/**
133 * div64_u64 - unsigned 64bit divide with 64bit divisor
134 * @dividend: 64bit dividend
135 * @divisor: 64bit divisor
136 *
137 * This implementation is a modified version of the algorithm proposed
138 * by the book 'Hacker's Delight'. The original source and full proof
139 * can be found here and is available for use without restriction.
140 *
141 * 'http://www.hackersdelight.org/hdcodetxt/divDouble.c.txt'
142 */
143#ifndef div64_u64
144u64 div64_u64(u64 dividend, u64 divisor)
145{
146 u32 high = divisor >> 32;
147 u64 quot;
148
149 if (high == 0) {
150 quot = div_u64(dividend, divisor);
151 } else {
152 int n = fls(high);
153 quot = div_u64(dividend >> n, divisor >> n);
154
155 if (quot != 0)
156 quot--;
157 if ((dividend - quot * divisor) >= divisor)
158 quot++;
159 }
160
161 return quot;
162}
163EXPORT_SYMBOL(div64_u64);
164#endif
165
166/**
167 * div64_s64 - signed 64bit divide with 64bit divisor
168 * @dividend: 64bit dividend
169 * @divisor: 64bit divisor
170 */
171#ifndef div64_s64
172s64 div64_s64(s64 dividend, s64 divisor)
173{
174 s64 quot, t;
175
176 quot = div64_u64(abs(dividend), abs(divisor));
177 t = (dividend ^ divisor) >> 63;
178
179 return (quot ^ t) - t;
180}
181EXPORT_SYMBOL(div64_s64);
182#endif
183
184#endif /* BITS_PER_LONG == 32 */
185
186/*
187 * Iterative div/mod for use when dividend is not expected to be much
188 * bigger than divisor.
189 */
190u32 iter_div_u64_rem(u64 dividend, u32 divisor, u64 *remainder)
191{
192 return __iter_div_u64_rem(dividend, divisor, remainder);
193}
194EXPORT_SYMBOL(iter_div_u64_rem);
195
196#ifndef mul_u64_u64_div_u64
197u64 mul_u64_u64_div_u64(u64 a, u64 b, u64 c)
198{
199 u64 res = 0, div, rem;
200 int shift;
201
202 /* can a * b overflow ? */
203 if (ilog2(a) + ilog2(b) > 62) {
204 /*
205 * (b * a) / c is equal to
206 *
207 * (b / c) * a +
208 * (b % c) * a / c
209 *
210 * if nothing overflows. Can the 1st multiplication
211 * overflow? Yes, but we do not care: this can only
212 * happen if the end result can't fit in u64 anyway.
213 *
214 * So the code below does
215 *
216 * res = (b / c) * a;
217 * b = b % c;
218 */
219 div = div64_u64_rem(b, c, &rem);
220 res = div * a;
221 b = rem;
222
223 shift = ilog2(a) + ilog2(b) - 62;
224 if (shift > 0) {
225 /* drop precision */
226 b >>= shift;
227 c >>= shift;
228 if (!c)
229 return res;
230 }
231 }
232
233 return res + div64_u64(a * b, c);
234}
235EXPORT_SYMBOL(mul_u64_u64_div_u64);
236#endif
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