1 /* SPDX-License-Identifier: GPL-2.0 */
2 #ifndef _ASM_GENERIC_DIV64_H
3 #define _ASM_GENERIC_DIV64_H
5 * Copyright (C) 2003 Bernardo Innocenti <bernie@develer.com>
6 * Based on former asm-ppc/div64.h and asm-m68knommu/div64.h
8 * Optimization for constant divisors on 32-bit machines:
9 * Copyright (C) 2006-2015 Nicolas Pitre
11 * The semantics of do_div() are:
13 * uint32_t do_div(uint64_t *n, uint32_t base)
15 * uint32_t remainder = *n % base;
20 * NOTE: macro parameter n is evaluated multiple times,
21 * beware of side effects!
24 #include <linux/types.h>
25 #include <linux/compiler.h>
27 #if BITS_PER_LONG == 64
29 # define do_div(n,base) ({ \
30 uint32_t __base = (base); \
32 __rem = ((uint64_t)(n)) % __base; \
33 (n) = ((uint64_t)(n)) / __base; \
37 #elif BITS_PER_LONG == 32
39 #include <linux/log2.h>
42 * If the divisor happens to be constant, we determine the appropriate
43 * inverse at compile time to turn the division into a few inline
44 * multiplications which ought to be much faster. And yet only if compiling
45 * with a sufficiently recent gcc version to perform proper 64-bit constant
48 * (It is unfortunate that gcc doesn't perform all this internally.)
51 #ifndef __div64_const32_is_OK
52 #define __div64_const32_is_OK (__GNUC__ >= 4)
55 #define __div64_const32(n, ___b) \
58 * Multiplication by reciprocal of b: n / b = n * (p / b) / p \
60 * We rely on the fact that most of this code gets optimized \
61 * away at compile time due to constant propagation and only \
62 * a few multiplication instructions should remain. \
63 * Hence this monstrous macro (static inline doesn't always \
64 * do the trick here). \
66 uint64_t ___res, ___x, ___t, ___m, ___n = (n); \
67 uint32_t ___p, ___bias; \
69 /* determine MSB of b */ \
70 ___p = 1 << ilog2(___b); \
72 /* compute m = ((p << 64) + b - 1) / b */ \
73 ___m = (~0ULL / ___b) * ___p; \
74 ___m += (((~0ULL % ___b + 1) * ___p) + ___b - 1) / ___b; \
76 /* one less than the dividend with highest result */ \
77 ___x = ~0ULL / ___b * ___b - 1; \
79 /* test our ___m with res = m * x / (p << 64) */ \
80 ___res = ((___m & 0xffffffff) * (___x & 0xffffffff)) >> 32; \
81 ___t = ___res += (___m & 0xffffffff) * (___x >> 32); \
82 ___res += (___x & 0xffffffff) * (___m >> 32); \
83 ___t = (___res < ___t) ? (1ULL << 32) : 0; \
84 ___res = (___res >> 32) + ___t; \
85 ___res += (___m >> 32) * (___x >> 32); \
88 /* Now sanitize and optimize what we've got. */ \
89 if (~0ULL % (___b / (___b & -___b)) == 0) { \
90 /* special case, can be simplified to ... */ \
91 ___n /= (___b & -___b); \
92 ___m = ~0ULL / (___b / (___b & -___b)); \
95 } else if (___res != ___x / ___b) { \
97 * We can't get away without a bias to compensate \
98 * for bit truncation errors. To avoid it we'd need an \
99 * additional bit to represent m which would overflow \
100 * a 64-bit variable. \
102 * Instead we do m = p / b and n / b = (n * m + m) / p. \
105 /* Compute m = (p << 64) / b */ \
106 ___m = (~0ULL / ___b) * ___p; \
107 ___m += ((~0ULL % ___b + 1) * ___p) / ___b; \
110 * Reduce m / p, and try to clear bit 31 of m when \
111 * possible, otherwise that'll need extra overflow \
114 uint32_t ___bits = -(___m & -___m); \
115 ___bits |= ___m >> 32; \
116 ___bits = (~___bits) << 1; \
118 * If ___bits == 0 then setting bit 31 is unavoidable. \
119 * Simply apply the maximum possible reduction in that \
120 * case. Otherwise the MSB of ___bits indicates the \
121 * best reduction we should apply. \
124 ___p /= (___m & -___m); \
125 ___m /= (___m & -___m); \
127 ___p >>= ilog2(___bits); \
128 ___m >>= ilog2(___bits); \
130 /* No bias needed. */ \
135 * Now we have a combination of 2 conditions: \
137 * 1) whether or not we need to apply a bias, and \
139 * 2) whether or not there might be an overflow in the cross \
140 * product determined by (___m & ((1 << 63) | (1 << 31))). \
142 * Select the best way to do (m_bias + m * n) / (1 << 64). \
143 * From now on there will be actual runtime code generated. \
145 ___res = __arch_xprod_64(___m, ___n, ___bias); \
150 #ifndef __arch_xprod_64
152 * Default C implementation for __arch_xprod_64()
154 * Prototype: uint64_t __arch_xprod_64(const uint64_t m, uint64_t n, bool bias)
155 * Semantic: retval = ((bias ? m : 0) + m * n) >> 64
157 * The product is a 128-bit value, scaled down to 64 bits.
158 * Assuming constant propagation to optimize away unused conditional code.
159 * Architectures may provide their own optimized assembly implementation.
161 static inline uint64_t __arch_xprod_64(const uint64_t m, uint64_t n, bool bias)
164 uint32_t m_hi = m >> 32;
166 uint32_t n_hi = n >> 32;
170 res = ((uint64_t)m_lo * n_lo) >> 32;
171 } else if (!(m & ((1ULL << 63) | (1ULL << 31)))) {
172 /* there can't be any overflow here */
173 res = (m + (uint64_t)m_lo * n_lo) >> 32;
175 res = m + (uint64_t)m_lo * n_lo;
176 tmp = (res < m) ? (1ULL << 32) : 0;
177 res = (res >> 32) + tmp;
180 if (!(m & ((1ULL << 63) | (1ULL << 31)))) {
181 /* there can't be any overflow here */
182 res += (uint64_t)m_lo * n_hi;
183 res += (uint64_t)m_hi * n_lo;
186 tmp = res += (uint64_t)m_lo * n_hi;
187 res += (uint64_t)m_hi * n_lo;
188 tmp = (res < tmp) ? (1ULL << 32) : 0;
189 res = (res >> 32) + tmp;
192 res += (uint64_t)m_hi * n_hi;
199 extern uint32_t __div64_32(uint64_t *dividend, uint32_t divisor);
202 /* The unnecessary pointer compare is there
203 * to check for type safety (n must be 64bit)
205 # define do_div(n,base) ({ \
206 uint32_t __base = (base); \
208 (void)(((typeof((n)) *)0) == ((uint64_t *)0)); \
209 if (__builtin_constant_p(__base) && \
210 is_power_of_2(__base)) { \
211 __rem = (n) & (__base - 1); \
212 (n) >>= ilog2(__base); \
213 } else if (__div64_const32_is_OK && \
214 __builtin_constant_p(__base) && \
216 uint32_t __res_lo, __n_lo = (n); \
217 (n) = __div64_const32(n, __base); \
218 /* the remainder can be computed with 32-bit regs */ \
220 __rem = __n_lo - __res_lo * __base; \
221 } else if (likely(((n) >> 32) == 0)) { \
222 __rem = (uint32_t)(n) % __base; \
223 (n) = (uint32_t)(n) / __base; \
225 __rem = __div64_32(&(n), __base); \
229 #else /* BITS_PER_LONG == ?? */
231 # error do_div() does not yet support the C64
233 #endif /* BITS_PER_LONG */
235 #endif /* _ASM_GENERIC_DIV64_H */