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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/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 if (ilog2(a) + ilog2(b) <= 62)
190 return div64_u64(a * b, c);
191
192#if defined(__SIZEOF_INT128__)
193
194 /* native 64x64=128 bits multiplication */
195 u128 prod = (u128)a * b;
196 u64 n_lo = prod, n_hi = prod >> 64;
197
198#else
199
200 /* perform a 64x64=128 bits multiplication manually */
201 u32 a_lo = a, a_hi = a >> 32, b_lo = b, b_hi = b >> 32;
202 u64 x, y, z;
203
204 x = (u64)a_lo * b_lo;
205 y = (u64)a_lo * b_hi + (u32)(x >> 32);
206 z = (u64)a_hi * b_hi + (u32)(y >> 32);
207 y = (u64)a_hi * b_lo + (u32)y;
208 z += (u32)(y >> 32);
209 x = (y << 32) + (u32)x;
210
211 u64 n_lo = x, n_hi = z;
212
213#endif
214
215 /* make sure c is not zero, trigger exception otherwise */
216#pragma GCC diagnostic push
217#pragma GCC diagnostic ignored "-Wdiv-by-zero"
218 if (unlikely(c == 0))
219 return 1/0;
220#pragma GCC diagnostic pop
221
222 int shift = __builtin_ctzll(c);
223
224 /* try reducing the fraction in case the dividend becomes <= 64 bits */
225 if ((n_hi >> shift) == 0) {
226 u64 n = shift ? (n_lo >> shift) | (n_hi << (64 - shift)) : n_lo;
227
228 return div64_u64(n, c >> shift);
229 /*
230 * The remainder value if needed would be:
231 * res = div64_u64_rem(n, c >> shift, &rem);
232 * rem = (rem << shift) + (n_lo - (n << shift));
233 */
234 }
235
236 if (n_hi >= c) {
237 /* overflow: result is unrepresentable in a u64 */
238 return -1;
239 }
240
241 /* Do the full 128 by 64 bits division */
242
243 shift = __builtin_clzll(c);
244 c <<= shift;
245
246 int p = 64 + shift;
247 u64 res = 0;
248 bool carry;
249
250 do {
251 carry = n_hi >> 63;
252 shift = carry ? 1 : __builtin_clzll(n_hi);
253 if (p < shift)
254 break;
255 p -= shift;
256 n_hi <<= shift;
257 n_hi |= n_lo >> (64 - shift);
258 n_lo <<= shift;
259 if (carry || (n_hi >= c)) {
260 n_hi -= c;
261 res |= 1ULL << p;
262 }
263 } while (n_hi);
264 /* The remainder value if needed would be n_hi << p */
265
266 return res;
267}
268EXPORT_SYMBOL(mul_u64_u64_div_u64);
269#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/export.h>
22#include <linux/kernel.h>
23#include <linux/math64.h>
24
25/* Not needed on 64bit architectures */
26#if BITS_PER_LONG == 32
27
28#ifndef __div64_32
29uint32_t __attribute__((weak)) __div64_32(uint64_t *n, uint32_t base)
30{
31 uint64_t rem = *n;
32 uint64_t b = base;
33 uint64_t res, d = 1;
34 uint32_t high = rem >> 32;
35
36 /* Reduce the thing a bit first */
37 res = 0;
38 if (high >= base) {
39 high /= base;
40 res = (uint64_t) high << 32;
41 rem -= (uint64_t) (high*base) << 32;
42 }
43
44 while ((int64_t)b > 0 && b < rem) {
45 b = b+b;
46 d = d+d;
47 }
48
49 do {
50 if (rem >= b) {
51 rem -= b;
52 res += d;
53 }
54 b >>= 1;
55 d >>= 1;
56 } while (d);
57
58 *n = res;
59 return rem;
60}
61EXPORT_SYMBOL(__div64_32);
62#endif
63
64/**
65 * div_s64_rem - signed 64bit divide with 64bit divisor and remainder
66 * @dividend: 64bit dividend
67 * @divisor: 64bit divisor
68 * @remainder: 64bit remainder
69 */
70#ifndef div_s64_rem
71s64 div_s64_rem(s64 dividend, s32 divisor, s32 *remainder)
72{
73 u64 quotient;
74
75 if (dividend < 0) {
76 quotient = div_u64_rem(-dividend, abs(divisor), (u32 *)remainder);
77 *remainder = -*remainder;
78 if (divisor > 0)
79 quotient = -quotient;
80 } else {
81 quotient = div_u64_rem(dividend, abs(divisor), (u32 *)remainder);
82 if (divisor < 0)
83 quotient = -quotient;
84 }
85 return quotient;
86}
87EXPORT_SYMBOL(div_s64_rem);
88#endif
89
90/**
91 * div64_u64_rem - unsigned 64bit divide with 64bit divisor and remainder
92 * @dividend: 64bit dividend
93 * @divisor: 64bit divisor
94 * @remainder: 64bit remainder
95 *
96 * This implementation is a comparable to algorithm used by div64_u64.
97 * But this operation, which includes math for calculating the remainder,
98 * is kept distinct to avoid slowing down the div64_u64 operation on 32bit
99 * systems.
100 */
101#ifndef div64_u64_rem
102u64 div64_u64_rem(u64 dividend, u64 divisor, u64 *remainder)
103{
104 u32 high = divisor >> 32;
105 u64 quot;
106
107 if (high == 0) {
108 u32 rem32;
109 quot = div_u64_rem(dividend, divisor, &rem32);
110 *remainder = rem32;
111 } else {
112 int n = fls(high);
113 quot = div_u64(dividend >> n, divisor >> n);
114
115 if (quot != 0)
116 quot--;
117
118 *remainder = dividend - quot * divisor;
119 if (*remainder >= divisor) {
120 quot++;
121 *remainder -= divisor;
122 }
123 }
124
125 return quot;
126}
127EXPORT_SYMBOL(div64_u64_rem);
128#endif
129
130/**
131 * div64_u64 - unsigned 64bit divide with 64bit divisor
132 * @dividend: 64bit dividend
133 * @divisor: 64bit divisor
134 *
135 * This implementation is a modified version of the algorithm proposed
136 * by the book 'Hacker's Delight'. The original source and full proof
137 * can be found here and is available for use without restriction.
138 *
139 * 'http://www.hackersdelight.org/hdcodetxt/divDouble.c.txt'
140 */
141#ifndef div64_u64
142u64 div64_u64(u64 dividend, u64 divisor)
143{
144 u32 high = divisor >> 32;
145 u64 quot;
146
147 if (high == 0) {
148 quot = div_u64(dividend, divisor);
149 } else {
150 int n = fls(high);
151 quot = div_u64(dividend >> n, divisor >> n);
152
153 if (quot != 0)
154 quot--;
155 if ((dividend - quot * divisor) >= divisor)
156 quot++;
157 }
158
159 return quot;
160}
161EXPORT_SYMBOL(div64_u64);
162#endif
163
164/**
165 * div64_s64 - signed 64bit divide with 64bit divisor
166 * @dividend: 64bit dividend
167 * @divisor: 64bit divisor
168 */
169#ifndef div64_s64
170s64 div64_s64(s64 dividend, s64 divisor)
171{
172 s64 quot, t;
173
174 quot = div64_u64(abs(dividend), abs(divisor));
175 t = (dividend ^ divisor) >> 63;
176
177 return (quot ^ t) - t;
178}
179EXPORT_SYMBOL(div64_s64);
180#endif
181
182#endif /* BITS_PER_LONG == 32 */
183
184/*
185 * Iterative div/mod for use when dividend is not expected to be much
186 * bigger than divisor.
187 */
188u32 iter_div_u64_rem(u64 dividend, u32 divisor, u64 *remainder)
189{
190 return __iter_div_u64_rem(dividend, divisor, remainder);
191}
192EXPORT_SYMBOL(iter_div_u64_rem);
193
194#ifndef mul_u64_u64_div_u64
195u64 mul_u64_u64_div_u64(u64 a, u64 b, u64 c)
196{
197 u64 res = 0, div, rem;
198 int shift;
199
200 /* can a * b overflow ? */
201 if (ilog2(a) + ilog2(b) > 62) {
202 /*
203 * (b * a) / c is equal to
204 *
205 * (b / c) * a +
206 * (b % c) * a / c
207 *
208 * if nothing overflows. Can the 1st multiplication
209 * overflow? Yes, but we do not care: this can only
210 * happen if the end result can't fit in u64 anyway.
211 *
212 * So the code below does
213 *
214 * res = (b / c) * a;
215 * b = b % c;
216 */
217 div = div64_u64_rem(b, c, &rem);
218 res = div * a;
219 b = rem;
220
221 shift = ilog2(a) + ilog2(b) - 62;
222 if (shift > 0) {
223 /* drop precision */
224 b >>= shift;
225 c >>= shift;
226 if (!c)
227 return res;
228 }
229 }
230
231 return res + div64_u64(a * b, c);
232}
233#endif