Merge tag 'docs-4.15' of git://git.lwn.net/linux
[muen/linux.git] / include / asm-generic / div64.h
1 /* SPDX-License-Identifier: GPL-2.0 */
2 #ifndef _ASM_GENERIC_DIV64_H
3 #define _ASM_GENERIC_DIV64_H
4 /*
5  * Copyright (C) 2003 Bernardo Innocenti <bernie@develer.com>
6  * Based on former asm-ppc/div64.h and asm-m68knommu/div64.h
7  *
8  * Optimization for constant divisors on 32-bit machines:
9  * Copyright (C) 2006-2015 Nicolas Pitre
10  *
11  * The semantics of do_div() are:
12  *
13  * uint32_t do_div(uint64_t *n, uint32_t base)
14  * {
15  *      uint32_t remainder = *n % base;
16  *      *n = *n / base;
17  *      return remainder;
18  * }
19  *
20  * NOTE: macro parameter n is evaluated multiple times,
21  *       beware of side effects!
22  */
23
24 #include <linux/types.h>
25 #include <linux/compiler.h>
26
27 #if BITS_PER_LONG == 64
28
29 /**
30  * do_div - returns 2 values: calculate remainder and update new dividend
31  * @n: pointer to uint64_t dividend (will be updated)
32  * @base: uint32_t divisor
33  *
34  * Summary:
35  * ``uint32_t remainder = *n % base;``
36  * ``*n = *n / base;``
37  *
38  * Return: (uint32_t)remainder
39  *
40  * NOTE: macro parameter @n is evaluated multiple times,
41  * beware of side effects!
42  */
43 # define do_div(n,base) ({                                      \
44         uint32_t __base = (base);                               \
45         uint32_t __rem;                                         \
46         __rem = ((uint64_t)(n)) % __base;                       \
47         (n) = ((uint64_t)(n)) / __base;                         \
48         __rem;                                                  \
49  })
50
51 #elif BITS_PER_LONG == 32
52
53 #include <linux/log2.h>
54
55 /*
56  * If the divisor happens to be constant, we determine the appropriate
57  * inverse at compile time to turn the division into a few inline
58  * multiplications which ought to be much faster. And yet only if compiling
59  * with a sufficiently recent gcc version to perform proper 64-bit constant
60  * propagation.
61  *
62  * (It is unfortunate that gcc doesn't perform all this internally.)
63  */
64
65 #ifndef __div64_const32_is_OK
66 #define __div64_const32_is_OK (__GNUC__ >= 4)
67 #endif
68
69 #define __div64_const32(n, ___b)                                        \
70 ({                                                                      \
71         /*                                                              \
72          * Multiplication by reciprocal of b: n / b = n * (p / b) / p   \
73          *                                                              \
74          * We rely on the fact that most of this code gets optimized    \
75          * away at compile time due to constant propagation and only    \
76          * a few multiplication instructions should remain.             \
77          * Hence this monstrous macro (static inline doesn't always     \
78          * do the trick here).                                          \
79          */                                                             \
80         uint64_t ___res, ___x, ___t, ___m, ___n = (n);                  \
81         uint32_t ___p, ___bias;                                         \
82                                                                         \
83         /* determine MSB of b */                                        \
84         ___p = 1 << ilog2(___b);                                        \
85                                                                         \
86         /* compute m = ((p << 64) + b - 1) / b */                       \
87         ___m = (~0ULL / ___b) * ___p;                                   \
88         ___m += (((~0ULL % ___b + 1) * ___p) + ___b - 1) / ___b;        \
89                                                                         \
90         /* one less than the dividend with highest result */            \
91         ___x = ~0ULL / ___b * ___b - 1;                                 \
92                                                                         \
93         /* test our ___m with res = m * x / (p << 64) */                \
94         ___res = ((___m & 0xffffffff) * (___x & 0xffffffff)) >> 32;     \
95         ___t = ___res += (___m & 0xffffffff) * (___x >> 32);            \
96         ___res += (___x & 0xffffffff) * (___m >> 32);                   \
97         ___t = (___res < ___t) ? (1ULL << 32) : 0;                      \
98         ___res = (___res >> 32) + ___t;                                 \
99         ___res += (___m >> 32) * (___x >> 32);                          \
100         ___res /= ___p;                                                 \
101                                                                         \
102         /* Now sanitize and optimize what we've got. */                 \
103         if (~0ULL % (___b / (___b & -___b)) == 0) {                     \
104                 /* special case, can be simplified to ... */            \
105                 ___n /= (___b & -___b);                                 \
106                 ___m = ~0ULL / (___b / (___b & -___b));                 \
107                 ___p = 1;                                               \
108                 ___bias = 1;                                            \
109         } else if (___res != ___x / ___b) {                             \
110                 /*                                                      \
111                  * We can't get away without a bias to compensate       \
112                  * for bit truncation errors.  To avoid it we'd need an \
113                  * additional bit to represent m which would overflow   \
114                  * a 64-bit variable.                                   \
115                  *                                                      \
116                  * Instead we do m = p / b and n / b = (n * m + m) / p. \
117                  */                                                     \
118                 ___bias = 1;                                            \
119                 /* Compute m = (p << 64) / b */                         \
120                 ___m = (~0ULL / ___b) * ___p;                           \
121                 ___m += ((~0ULL % ___b + 1) * ___p) / ___b;             \
122         } else {                                                        \
123                 /*                                                      \
124                  * Reduce m / p, and try to clear bit 31 of m when      \
125                  * possible, otherwise that'll need extra overflow      \
126                  * handling later.                                      \
127                  */                                                     \
128                 uint32_t ___bits = -(___m & -___m);                     \
129                 ___bits |= ___m >> 32;                                  \
130                 ___bits = (~___bits) << 1;                              \
131                 /*                                                      \
132                  * If ___bits == 0 then setting bit 31 is  unavoidable. \
133                  * Simply apply the maximum possible reduction in that  \
134                  * case. Otherwise the MSB of ___bits indicates the     \
135                  * best reduction we should apply.                      \
136                  */                                                     \
137                 if (!___bits) {                                         \
138                         ___p /= (___m & -___m);                         \
139                         ___m /= (___m & -___m);                         \
140                 } else {                                                \
141                         ___p >>= ilog2(___bits);                        \
142                         ___m >>= ilog2(___bits);                        \
143                 }                                                       \
144                 /* No bias needed. */                                   \
145                 ___bias = 0;                                            \
146         }                                                               \
147                                                                         \
148         /*                                                              \
149          * Now we have a combination of 2 conditions:                   \
150          *                                                              \
151          * 1) whether or not we need to apply a bias, and               \
152          *                                                              \
153          * 2) whether or not there might be an overflow in the cross    \
154          *    product determined by (___m & ((1 << 63) | (1 << 31))).   \
155          *                                                              \
156          * Select the best way to do (m_bias + m * n) / (1 << 64).      \
157          * From now on there will be actual runtime code generated.     \
158          */                                                             \
159         ___res = __arch_xprod_64(___m, ___n, ___bias);                  \
160                                                                         \
161         ___res /= ___p;                                                 \
162 })
163
164 #ifndef __arch_xprod_64
165 /*
166  * Default C implementation for __arch_xprod_64()
167  *
168  * Prototype: uint64_t __arch_xprod_64(const uint64_t m, uint64_t n, bool bias)
169  * Semantic:  retval = ((bias ? m : 0) + m * n) >> 64
170  *
171  * The product is a 128-bit value, scaled down to 64 bits.
172  * Assuming constant propagation to optimize away unused conditional code.
173  * Architectures may provide their own optimized assembly implementation.
174  */
175 static inline uint64_t __arch_xprod_64(const uint64_t m, uint64_t n, bool bias)
176 {
177         uint32_t m_lo = m;
178         uint32_t m_hi = m >> 32;
179         uint32_t n_lo = n;
180         uint32_t n_hi = n >> 32;
181         uint64_t res, tmp;
182
183         if (!bias) {
184                 res = ((uint64_t)m_lo * n_lo) >> 32;
185         } else if (!(m & ((1ULL << 63) | (1ULL << 31)))) {
186                 /* there can't be any overflow here */
187                 res = (m + (uint64_t)m_lo * n_lo) >> 32;
188         } else {
189                 res = m + (uint64_t)m_lo * n_lo;
190                 tmp = (res < m) ? (1ULL << 32) : 0;
191                 res = (res >> 32) + tmp;
192         }
193
194         if (!(m & ((1ULL << 63) | (1ULL << 31)))) {
195                 /* there can't be any overflow here */
196                 res += (uint64_t)m_lo * n_hi;
197                 res += (uint64_t)m_hi * n_lo;
198                 res >>= 32;
199         } else {
200                 tmp = res += (uint64_t)m_lo * n_hi;
201                 res += (uint64_t)m_hi * n_lo;
202                 tmp = (res < tmp) ? (1ULL << 32) : 0;
203                 res = (res >> 32) + tmp;
204         }
205
206         res += (uint64_t)m_hi * n_hi;
207
208         return res;
209 }
210 #endif
211
212 #ifndef __div64_32
213 extern uint32_t __div64_32(uint64_t *dividend, uint32_t divisor);
214 #endif
215
216 /* The unnecessary pointer compare is there
217  * to check for type safety (n must be 64bit)
218  */
219 # define do_div(n,base) ({                              \
220         uint32_t __base = (base);                       \
221         uint32_t __rem;                                 \
222         (void)(((typeof((n)) *)0) == ((uint64_t *)0));  \
223         if (__builtin_constant_p(__base) &&             \
224             is_power_of_2(__base)) {                    \
225                 __rem = (n) & (__base - 1);             \
226                 (n) >>= ilog2(__base);                  \
227         } else if (__div64_const32_is_OK &&             \
228                    __builtin_constant_p(__base) &&      \
229                    __base != 0) {                       \
230                 uint32_t __res_lo, __n_lo = (n);        \
231                 (n) = __div64_const32(n, __base);       \
232                 /* the remainder can be computed with 32-bit regs */ \
233                 __res_lo = (n);                         \
234                 __rem = __n_lo - __res_lo * __base;     \
235         } else if (likely(((n) >> 32) == 0)) {          \
236                 __rem = (uint32_t)(n) % __base;         \
237                 (n) = (uint32_t)(n) / __base;           \
238         } else                                          \
239                 __rem = __div64_32(&(n), __base);       \
240         __rem;                                          \
241  })
242
243 #else /* BITS_PER_LONG == ?? */
244
245 # error do_div() does not yet support the C64
246
247 #endif /* BITS_PER_LONG */
248
249 #endif /* _ASM_GENERIC_DIV64_H */