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> 25 #include <linux/minmax.h>
26 #include <linux/log2.h> 26 #include <linux/log2.h>
27 27
28 /* Not needed on 64bit architectures */ 28 /* Not needed on 64bit architectures */
29 #if BITS_PER_LONG == 32 29 #if BITS_PER_LONG == 32
30 30
31 #ifndef __div64_32 31 #ifndef __div64_32
32 uint32_t __attribute__((weak)) __div64_32(uint 32 uint32_t __attribute__((weak)) __div64_32(uint64_t *n, uint32_t base)
33 { 33 {
34 uint64_t rem = *n; 34 uint64_t rem = *n;
35 uint64_t b = base; 35 uint64_t b = base;
36 uint64_t res, d = 1; 36 uint64_t res, d = 1;
37 uint32_t high = rem >> 32; 37 uint32_t high = rem >> 32;
38 38
39 /* Reduce the thing a bit first */ 39 /* Reduce the thing a bit first */
40 res = 0; 40 res = 0;
41 if (high >= base) { 41 if (high >= base) {
42 high /= base; 42 high /= base;
43 res = (uint64_t) high << 32; 43 res = (uint64_t) high << 32;
44 rem -= (uint64_t) (high*base) 44 rem -= (uint64_t) (high*base) << 32;
45 } 45 }
46 46
47 while ((int64_t)b > 0 && b < rem) { 47 while ((int64_t)b > 0 && b < rem) {
48 b = b+b; 48 b = b+b;
49 d = d+d; 49 d = d+d;
50 } 50 }
51 51
52 do { 52 do {
53 if (rem >= b) { 53 if (rem >= b) {
54 rem -= b; 54 rem -= b;
55 res += d; 55 res += d;
56 } 56 }
57 b >>= 1; 57 b >>= 1;
58 d >>= 1; 58 d >>= 1;
59 } while (d); 59 } while (d);
60 60
61 *n = res; 61 *n = res;
62 return rem; 62 return rem;
63 } 63 }
64 EXPORT_SYMBOL(__div64_32); 64 EXPORT_SYMBOL(__div64_32);
65 #endif 65 #endif
66 66
67 #ifndef div_s64_rem 67 #ifndef div_s64_rem
68 s64 div_s64_rem(s64 dividend, s32 divisor, s32 68 s64 div_s64_rem(s64 dividend, s32 divisor, s32 *remainder)
69 { 69 {
70 u64 quotient; 70 u64 quotient;
71 71
72 if (dividend < 0) { 72 if (dividend < 0) {
73 quotient = div_u64_rem(-divide 73 quotient = div_u64_rem(-dividend, abs(divisor), (u32 *)remainder);
74 *remainder = -*remainder; 74 *remainder = -*remainder;
75 if (divisor > 0) 75 if (divisor > 0)
76 quotient = -quotient; 76 quotient = -quotient;
77 } else { 77 } else {
78 quotient = div_u64_rem(dividen 78 quotient = div_u64_rem(dividend, abs(divisor), (u32 *)remainder);
79 if (divisor < 0) 79 if (divisor < 0)
80 quotient = -quotient; 80 quotient = -quotient;
81 } 81 }
82 return quotient; 82 return quotient;
83 } 83 }
84 EXPORT_SYMBOL(div_s64_rem); 84 EXPORT_SYMBOL(div_s64_rem);
85 #endif 85 #endif
86 86
87 /* 87 /*
88 * div64_u64_rem - unsigned 64bit divide with 88 * div64_u64_rem - unsigned 64bit divide with 64bit divisor and remainder
89 * @dividend: 64bit dividend 89 * @dividend: 64bit dividend
90 * @divisor: 64bit divisor 90 * @divisor: 64bit divisor
91 * @remainder: 64bit remainder 91 * @remainder: 64bit remainder
92 * 92 *
93 * This implementation is a comparable to algo 93 * This implementation is a comparable to algorithm used by div64_u64.
94 * But this operation, which includes math for 94 * But this operation, which includes math for calculating the remainder,
95 * is kept distinct to avoid slowing down the 95 * is kept distinct to avoid slowing down the div64_u64 operation on 32bit
96 * systems. 96 * systems.
97 */ 97 */
98 #ifndef div64_u64_rem 98 #ifndef div64_u64_rem
99 u64 div64_u64_rem(u64 dividend, u64 divisor, u 99 u64 div64_u64_rem(u64 dividend, u64 divisor, u64 *remainder)
100 { 100 {
101 u32 high = divisor >> 32; 101 u32 high = divisor >> 32;
102 u64 quot; 102 u64 quot;
103 103
104 if (high == 0) { 104 if (high == 0) {
105 u32 rem32; 105 u32 rem32;
106 quot = div_u64_rem(dividend, d 106 quot = div_u64_rem(dividend, divisor, &rem32);
107 *remainder = rem32; 107 *remainder = rem32;
108 } else { 108 } else {
109 int n = fls(high); 109 int n = fls(high);
110 quot = div_u64(dividend >> n, 110 quot = div_u64(dividend >> n, divisor >> n);
111 111
112 if (quot != 0) 112 if (quot != 0)
113 quot--; 113 quot--;
114 114
115 *remainder = dividend - quot * 115 *remainder = dividend - quot * divisor;
116 if (*remainder >= divisor) { 116 if (*remainder >= divisor) {
117 quot++; 117 quot++;
118 *remainder -= divisor; 118 *remainder -= divisor;
119 } 119 }
120 } 120 }
121 121
122 return quot; 122 return quot;
123 } 123 }
124 EXPORT_SYMBOL(div64_u64_rem); 124 EXPORT_SYMBOL(div64_u64_rem);
125 #endif 125 #endif
126 126
127 /* 127 /*
128 * div64_u64 - unsigned 64bit divide with 64bi 128 * div64_u64 - unsigned 64bit divide with 64bit divisor
129 * @dividend: 64bit dividend 129 * @dividend: 64bit dividend
130 * @divisor: 64bit divisor 130 * @divisor: 64bit divisor
131 * 131 *
132 * This implementation is a modified version o 132 * This implementation is a modified version of the algorithm proposed
133 * by the book 'Hacker's Delight'. The origin 133 * by the book 'Hacker's Delight'. The original source and full proof
134 * can be found here and is available for use 134 * can be found here and is available for use without restriction.
135 * 135 *
136 * 'http://www.hackersdelight.org/hdcodetxt/di 136 * 'http://www.hackersdelight.org/hdcodetxt/divDouble.c.txt'
137 */ 137 */
138 #ifndef div64_u64 138 #ifndef div64_u64
139 u64 div64_u64(u64 dividend, u64 divisor) 139 u64 div64_u64(u64 dividend, u64 divisor)
140 { 140 {
141 u32 high = divisor >> 32; 141 u32 high = divisor >> 32;
142 u64 quot; 142 u64 quot;
143 143
144 if (high == 0) { 144 if (high == 0) {
145 quot = div_u64(dividend, divis 145 quot = div_u64(dividend, divisor);
146 } else { 146 } else {
147 int n = fls(high); 147 int n = fls(high);
148 quot = div_u64(dividend >> n, 148 quot = div_u64(dividend >> n, divisor >> n);
149 149
150 if (quot != 0) 150 if (quot != 0)
151 quot--; 151 quot--;
152 if ((dividend - quot * divisor 152 if ((dividend - quot * divisor) >= divisor)
153 quot++; 153 quot++;
154 } 154 }
155 155
156 return quot; 156 return quot;
157 } 157 }
158 EXPORT_SYMBOL(div64_u64); 158 EXPORT_SYMBOL(div64_u64);
159 #endif 159 #endif
160 160
161 #ifndef div64_s64 161 #ifndef div64_s64
162 s64 div64_s64(s64 dividend, s64 divisor) 162 s64 div64_s64(s64 dividend, s64 divisor)
163 { 163 {
164 s64 quot, t; 164 s64 quot, t;
165 165
166 quot = div64_u64(abs(dividend), abs(di 166 quot = div64_u64(abs(dividend), abs(divisor));
167 t = (dividend ^ divisor) >> 63; 167 t = (dividend ^ divisor) >> 63;
168 168
169 return (quot ^ t) - t; 169 return (quot ^ t) - t;
170 } 170 }
171 EXPORT_SYMBOL(div64_s64); 171 EXPORT_SYMBOL(div64_s64);
172 #endif 172 #endif
173 173
174 #endif /* BITS_PER_LONG == 32 */ 174 #endif /* BITS_PER_LONG == 32 */
175 175
176 /* 176 /*
177 * Iterative div/mod for use when dividend is 177 * Iterative div/mod for use when dividend is not expected to be much
178 * bigger than divisor. 178 * bigger than divisor.
179 */ 179 */
180 u32 iter_div_u64_rem(u64 dividend, u32 divisor 180 u32 iter_div_u64_rem(u64 dividend, u32 divisor, u64 *remainder)
181 { 181 {
182 return __iter_div_u64_rem(dividend, di 182 return __iter_div_u64_rem(dividend, divisor, remainder);
183 } 183 }
184 EXPORT_SYMBOL(iter_div_u64_rem); 184 EXPORT_SYMBOL(iter_div_u64_rem);
185 185
186 #ifndef mul_u64_u64_div_u64 186 #ifndef mul_u64_u64_div_u64
187 u64 mul_u64_u64_div_u64(u64 a, u64 b, u64 c) 187 u64 mul_u64_u64_div_u64(u64 a, u64 b, u64 c)
188 { 188 {
189 if (ilog2(a) + ilog2(b) <= 62) !! 189 u64 res = 0, div, rem;
190 return div64_u64(a * b, c); !! 190 int shift;
191 191
192 #if defined(__SIZEOF_INT128__) !! 192 /* can a * b overflow ? */
193 !! 193 if (ilog2(a) + ilog2(b) > 62) {
194 /* native 64x64=128 bits multiplicatio <<
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 multiplica <<
201 u32 a_lo = a, a_hi = a >> 32, b_lo = b <<
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 ex <<
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 t <<
225 if ((n_hi >> shift) == 0) { <<
226 u64 n = shift ? (n_lo >> shift <<
227 <<
228 return div64_u64(n, c >> shift <<
229 /* 194 /*
230 * The remainder value if need !! 195 * Note that the algorithm after the if block below might lose
231 * res = div64_u64_rem(n, c !! 196 * some precision and the result is more exact for b > a. So
232 * rem = (rem << shift) + (n !! 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).
233 */ 204 */
234 } !! 205 if (a > b)
235 !! 206 swap(a, b);
236 if (n_hi >= c) { <<
237 /* overflow: result is unrepre <<
238 return -1; <<
239 } <<
240 <<
241 /* Do the full 128 by 64 bits division <<
242 <<
243 shift = __builtin_clzll(c); <<
244 c <<= shift; <<
245 207
246 int p = 64 + shift; !! 208 /*
247 u64 res = 0; !! 209 * (b * a) / c is equal to
248 bool carry; !! 210 *
249 !! 211 * (b / c) * a +
250 do { !! 212 * (b % c) * a / c
251 carry = n_hi >> 63; !! 213 *
252 shift = carry ? 1 : __builtin_ !! 214 * if nothing overflows. Can the 1st multiplication
253 if (p < shift) !! 215 * overflow? Yes, but we do not care: this can only
254 break; !! 216 * happen if the end result can't fit in u64 anyway.
255 p -= shift; !! 217 *
256 n_hi <<= shift; !! 218 * So the code below does
257 n_hi |= n_lo >> (64 - shift); !! 219 *
258 n_lo <<= shift; !! 220 * res = (b / c) * a;
259 if (carry || (n_hi >= c)) { !! 221 * b = b % c;
260 n_hi -= c; !! 222 */
261 res |= 1ULL << p; !! 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;
262 } 234 }
263 } while (n_hi); !! 235 }
264 /* The remainder value if needed would <<
265 236
266 return res; !! 237 return res + div64_u64(a * b, c);
267 } 238 }
268 EXPORT_SYMBOL(mul_u64_u64_div_u64); 239 EXPORT_SYMBOL(mul_u64_u64_div_u64);
269 #endif 240 #endif
270 241
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