1 // SPDX-License-Identifier: GPL-2.0 1 // SPDX-License-Identifier: GPL-2.0
2 /* 2 /*
3 * Copyright (C) 2003 Bernardo Innocenti <bern 3 * Copyright (C) 2003 Bernardo Innocenti <bernie@develer.com>
4 * 4 *
5 * Based on former do_div() implementation fro 5 * Based on former do_div() implementation from asm-parisc/div64.h:
6 * Copyright (C) 1999 Hewlett-Packard Co 6 * Copyright (C) 1999 Hewlett-Packard Co
7 * Copyright (C) 1999 David Mosberger-Tan 7 * Copyright (C) 1999 David Mosberger-Tang <davidm@hpl.hp.com>
8 * 8 *
9 * 9 *
10 * Generic C version of 64bit/32bit division a 10 * Generic C version of 64bit/32bit division and modulo, with
11 * 64bit result and 32bit remainder. 11 * 64bit result and 32bit remainder.
12 * 12 *
13 * The fast case for (n>>32 == 0) is handled i 13 * The fast case for (n>>32 == 0) is handled inline by do_div().
14 * 14 *
15 * Code generated for this function might be v 15 * Code generated for this function might be very inefficient
16 * for some CPUs. __div64_32() can be overridd 16 * for some CPUs. __div64_32() can be overridden by linking arch-specific
17 * assembly versions such as arch/ppc/lib/div6 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 18 * or by defining a preprocessor macro in arch/include/asm/div64.h.
19 */ 19 */
20 20
21 #include <linux/bitops.h> 21 #include <linux/bitops.h>
22 #include <linux/export.h> 22 #include <linux/export.h>
23 #include <linux/math.h> 23 #include <linux/math.h>
24 #include <linux/math64.h> 24 #include <linux/math64.h>
25 #include <linux/minmax.h> <<
26 #include <linux/log2.h> 25 #include <linux/log2.h>
27 26
28 /* Not needed on 64bit architectures */ 27 /* Not needed on 64bit architectures */
29 #if BITS_PER_LONG == 32 28 #if BITS_PER_LONG == 32
30 29
31 #ifndef __div64_32 30 #ifndef __div64_32
32 uint32_t __attribute__((weak)) __div64_32(uint 31 uint32_t __attribute__((weak)) __div64_32(uint64_t *n, uint32_t base)
33 { 32 {
34 uint64_t rem = *n; 33 uint64_t rem = *n;
35 uint64_t b = base; 34 uint64_t b = base;
36 uint64_t res, d = 1; 35 uint64_t res, d = 1;
37 uint32_t high = rem >> 32; 36 uint32_t high = rem >> 32;
38 37
39 /* Reduce the thing a bit first */ 38 /* Reduce the thing a bit first */
40 res = 0; 39 res = 0;
41 if (high >= base) { 40 if (high >= base) {
42 high /= base; 41 high /= base;
43 res = (uint64_t) high << 32; 42 res = (uint64_t) high << 32;
44 rem -= (uint64_t) (high*base) 43 rem -= (uint64_t) (high*base) << 32;
45 } 44 }
46 45
47 while ((int64_t)b > 0 && b < rem) { 46 while ((int64_t)b > 0 && b < rem) {
48 b = b+b; 47 b = b+b;
49 d = d+d; 48 d = d+d;
50 } 49 }
51 50
52 do { 51 do {
53 if (rem >= b) { 52 if (rem >= b) {
54 rem -= b; 53 rem -= b;
55 res += d; 54 res += d;
56 } 55 }
57 b >>= 1; 56 b >>= 1;
58 d >>= 1; 57 d >>= 1;
59 } while (d); 58 } while (d);
60 59
61 *n = res; 60 *n = res;
62 return rem; 61 return rem;
63 } 62 }
64 EXPORT_SYMBOL(__div64_32); 63 EXPORT_SYMBOL(__div64_32);
65 #endif 64 #endif
66 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 */
67 #ifndef div_s64_rem 72 #ifndef div_s64_rem
68 s64 div_s64_rem(s64 dividend, s32 divisor, s32 73 s64 div_s64_rem(s64 dividend, s32 divisor, s32 *remainder)
69 { 74 {
70 u64 quotient; 75 u64 quotient;
71 76
72 if (dividend < 0) { 77 if (dividend < 0) {
73 quotient = div_u64_rem(-divide 78 quotient = div_u64_rem(-dividend, abs(divisor), (u32 *)remainder);
74 *remainder = -*remainder; 79 *remainder = -*remainder;
75 if (divisor > 0) 80 if (divisor > 0)
76 quotient = -quotient; 81 quotient = -quotient;
77 } else { 82 } else {
78 quotient = div_u64_rem(dividen 83 quotient = div_u64_rem(dividend, abs(divisor), (u32 *)remainder);
79 if (divisor < 0) 84 if (divisor < 0)
80 quotient = -quotient; 85 quotient = -quotient;
81 } 86 }
82 return quotient; 87 return quotient;
83 } 88 }
84 EXPORT_SYMBOL(div_s64_rem); 89 EXPORT_SYMBOL(div_s64_rem);
85 #endif 90 #endif
86 91
87 /* !! 92 /**
88 * div64_u64_rem - unsigned 64bit divide with 93 * div64_u64_rem - unsigned 64bit divide with 64bit divisor and remainder
89 * @dividend: 64bit dividend 94 * @dividend: 64bit dividend
90 * @divisor: 64bit divisor 95 * @divisor: 64bit divisor
91 * @remainder: 64bit remainder 96 * @remainder: 64bit remainder
92 * 97 *
93 * This implementation is a comparable to algo 98 * This implementation is a comparable to algorithm used by div64_u64.
94 * But this operation, which includes math for 99 * But this operation, which includes math for calculating the remainder,
95 * is kept distinct to avoid slowing down the 100 * is kept distinct to avoid slowing down the div64_u64 operation on 32bit
96 * systems. 101 * systems.
97 */ 102 */
98 #ifndef div64_u64_rem 103 #ifndef div64_u64_rem
99 u64 div64_u64_rem(u64 dividend, u64 divisor, u 104 u64 div64_u64_rem(u64 dividend, u64 divisor, u64 *remainder)
100 { 105 {
101 u32 high = divisor >> 32; 106 u32 high = divisor >> 32;
102 u64 quot; 107 u64 quot;
103 108
104 if (high == 0) { 109 if (high == 0) {
105 u32 rem32; 110 u32 rem32;
106 quot = div_u64_rem(dividend, d 111 quot = div_u64_rem(dividend, divisor, &rem32);
107 *remainder = rem32; 112 *remainder = rem32;
108 } else { 113 } else {
109 int n = fls(high); 114 int n = fls(high);
110 quot = div_u64(dividend >> n, 115 quot = div_u64(dividend >> n, divisor >> n);
111 116
112 if (quot != 0) 117 if (quot != 0)
113 quot--; 118 quot--;
114 119
115 *remainder = dividend - quot * 120 *remainder = dividend - quot * divisor;
116 if (*remainder >= divisor) { 121 if (*remainder >= divisor) {
117 quot++; 122 quot++;
118 *remainder -= divisor; 123 *remainder -= divisor;
119 } 124 }
120 } 125 }
121 126
122 return quot; 127 return quot;
123 } 128 }
124 EXPORT_SYMBOL(div64_u64_rem); 129 EXPORT_SYMBOL(div64_u64_rem);
125 #endif 130 #endif
126 131
127 /* !! 132 /**
128 * div64_u64 - unsigned 64bit divide with 64bi 133 * div64_u64 - unsigned 64bit divide with 64bit divisor
129 * @dividend: 64bit dividend 134 * @dividend: 64bit dividend
130 * @divisor: 64bit divisor 135 * @divisor: 64bit divisor
131 * 136 *
132 * This implementation is a modified version o 137 * This implementation is a modified version of the algorithm proposed
133 * by the book 'Hacker's Delight'. The origin 138 * by the book 'Hacker's Delight'. The original source and full proof
134 * can be found here and is available for use 139 * can be found here and is available for use without restriction.
135 * 140 *
136 * 'http://www.hackersdelight.org/hdcodetxt/di 141 * 'http://www.hackersdelight.org/hdcodetxt/divDouble.c.txt'
137 */ 142 */
138 #ifndef div64_u64 143 #ifndef div64_u64
139 u64 div64_u64(u64 dividend, u64 divisor) 144 u64 div64_u64(u64 dividend, u64 divisor)
140 { 145 {
141 u32 high = divisor >> 32; 146 u32 high = divisor >> 32;
142 u64 quot; 147 u64 quot;
143 148
144 if (high == 0) { 149 if (high == 0) {
145 quot = div_u64(dividend, divis 150 quot = div_u64(dividend, divisor);
146 } else { 151 } else {
147 int n = fls(high); 152 int n = fls(high);
148 quot = div_u64(dividend >> n, 153 quot = div_u64(dividend >> n, divisor >> n);
149 154
150 if (quot != 0) 155 if (quot != 0)
151 quot--; 156 quot--;
152 if ((dividend - quot * divisor 157 if ((dividend - quot * divisor) >= divisor)
153 quot++; 158 quot++;
154 } 159 }
155 160
156 return quot; 161 return quot;
157 } 162 }
158 EXPORT_SYMBOL(div64_u64); 163 EXPORT_SYMBOL(div64_u64);
159 #endif 164 #endif
160 165
>> 166 /**
>> 167 * div64_s64 - signed 64bit divide with 64bit divisor
>> 168 * @dividend: 64bit dividend
>> 169 * @divisor: 64bit divisor
>> 170 */
161 #ifndef div64_s64 171 #ifndef div64_s64
162 s64 div64_s64(s64 dividend, s64 divisor) 172 s64 div64_s64(s64 dividend, s64 divisor)
163 { 173 {
164 s64 quot, t; 174 s64 quot, t;
165 175
166 quot = div64_u64(abs(dividend), abs(di 176 quot = div64_u64(abs(dividend), abs(divisor));
167 t = (dividend ^ divisor) >> 63; 177 t = (dividend ^ divisor) >> 63;
168 178
169 return (quot ^ t) - t; 179 return (quot ^ t) - t;
170 } 180 }
171 EXPORT_SYMBOL(div64_s64); 181 EXPORT_SYMBOL(div64_s64);
172 #endif 182 #endif
173 183
174 #endif /* BITS_PER_LONG == 32 */ 184 #endif /* BITS_PER_LONG == 32 */
175 185
176 /* 186 /*
177 * Iterative div/mod for use when dividend is 187 * Iterative div/mod for use when dividend is not expected to be much
178 * bigger than divisor. 188 * bigger than divisor.
179 */ 189 */
180 u32 iter_div_u64_rem(u64 dividend, u32 divisor 190 u32 iter_div_u64_rem(u64 dividend, u32 divisor, u64 *remainder)
181 { 191 {
182 return __iter_div_u64_rem(dividend, di 192 return __iter_div_u64_rem(dividend, divisor, remainder);
183 } 193 }
184 EXPORT_SYMBOL(iter_div_u64_rem); 194 EXPORT_SYMBOL(iter_div_u64_rem);
185 195
186 #ifndef mul_u64_u64_div_u64 196 #ifndef mul_u64_u64_div_u64
187 u64 mul_u64_u64_div_u64(u64 a, u64 b, u64 c) 197 u64 mul_u64_u64_div_u64(u64 a, u64 b, u64 c)
188 { 198 {
189 u64 res = 0, div, rem; 199 u64 res = 0, div, rem;
190 int shift; 200 int shift;
191 201
192 /* can a * b overflow ? */ 202 /* can a * b overflow ? */
193 if (ilog2(a) + ilog2(b) > 62) { 203 if (ilog2(a) + ilog2(b) > 62) {
194 /* <<
195 * Note that the algorithm aft <<
196 * some precision and the resu <<
197 * exchange a and b if a is bi <<
198 * <<
199 * For example with a = 439804 <<
200 * the below calculation doesn <<
201 * and then shift becomes 45 + <<
202 * becomes 4398035251080. Howe <<
203 * result is calculated (i.e. <<
204 */ <<
205 if (a > b) <<
206 swap(a, b); <<
207 <<
208 /* 204 /*
209 * (b * a) / c is equal to 205 * (b * a) / c is equal to
210 * 206 *
211 * (b / c) * a + 207 * (b / c) * a +
212 * (b % c) * a / c 208 * (b % c) * a / c
213 * 209 *
214 * if nothing overflows. Can t 210 * if nothing overflows. Can the 1st multiplication
215 * overflow? Yes, but we do no 211 * overflow? Yes, but we do not care: this can only
216 * happen if the end result ca 212 * happen if the end result can't fit in u64 anyway.
217 * 213 *
218 * So the code below does 214 * So the code below does
219 * 215 *
220 * res = (b / c) * a; 216 * res = (b / c) * a;
221 * b = b % c; 217 * b = b % c;
222 */ 218 */
223 div = div64_u64_rem(b, c, &rem 219 div = div64_u64_rem(b, c, &rem);
224 res = div * a; 220 res = div * a;
225 b = rem; 221 b = rem;
226 222
227 shift = ilog2(a) + ilog2(b) - 223 shift = ilog2(a) + ilog2(b) - 62;
228 if (shift > 0) { 224 if (shift > 0) {
229 /* drop precision */ 225 /* drop precision */
230 b >>= shift; 226 b >>= shift;
231 c >>= shift; 227 c >>= shift;
232 if (!c) 228 if (!c)
233 return res; 229 return res;
234 } 230 }
235 } 231 }
236 232
237 return res + div64_u64(a * b, c); 233 return res + div64_u64(a * b, c);
238 } 234 }
239 EXPORT_SYMBOL(mul_u64_u64_div_u64); 235 EXPORT_SYMBOL(mul_u64_u64_div_u64);
240 #endif 236 #endif
241 237
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