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