xref: /linux/include/asm-generic/div64.h (revision 8ca4fc323d2e4ab9dabbdd57633af40b0c7e6af9)
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() is, in C++ notation, observing that the name
12  * is a function-like macro and the n parameter has the semantics of a C++
13  * reference:
14  *
15  * uint32_t do_div(uint64_t &n, uint32_t base)
16  * {
17  * 	uint32_t remainder = n % base;
18  * 	n = n / base;
19  * 	return remainder;
20  * }
21  *
22  * NOTE: macro parameter n is evaluated multiple times,
23  *       beware of side effects!
24  */
25 
26 #include <linux/types.h>
27 #include <linux/compiler.h>
28 
29 #if BITS_PER_LONG == 64
30 
31 /**
32  * do_div - returns 2 values: calculate remainder and update new dividend
33  * @n: uint64_t dividend (will be updated)
34  * @base: uint32_t divisor
35  *
36  * Summary:
37  * ``uint32_t remainder = n % base;``
38  * ``n = n / base;``
39  *
40  * Return: (uint32_t)remainder
41  *
42  * NOTE: macro parameter @n is evaluated multiple times,
43  * beware of side effects!
44  */
45 # define do_div(n,base) ({					\
46 	uint32_t __base = (base);				\
47 	uint32_t __rem;						\
48 	__rem = ((uint64_t)(n)) % __base;			\
49 	(n) = ((uint64_t)(n)) / __base;				\
50 	__rem;							\
51  })
52 
53 #elif BITS_PER_LONG == 32
54 
55 #include <linux/log2.h>
56 
57 /*
58  * If the divisor happens to be constant, we determine the appropriate
59  * inverse at compile time to turn the division into a few inline
60  * multiplications which ought to be much faster.
61  *
62  * (It is unfortunate that gcc doesn't perform all this internally.)
63  */
64 
65 #define __div64_const32(n, ___b)					\
66 ({									\
67 	/*								\
68 	 * Multiplication by reciprocal of b: n / b = n * (p / b) / p	\
69 	 *								\
70 	 * We rely on the fact that most of this code gets optimized	\
71 	 * away at compile time due to constant propagation and only	\
72 	 * a few multiplication instructions should remain.		\
73 	 * Hence this monstrous macro (static inline doesn't always	\
74 	 * do the trick here).						\
75 	 */								\
76 	uint64_t ___res, ___x, ___t, ___m, ___n = (n);			\
77 	uint32_t ___p, ___bias;						\
78 									\
79 	/* determine MSB of b */					\
80 	___p = 1 << ilog2(___b);					\
81 									\
82 	/* compute m = ((p << 64) + b - 1) / b */			\
83 	___m = (~0ULL / ___b) * ___p;					\
84 	___m += (((~0ULL % ___b + 1) * ___p) + ___b - 1) / ___b;	\
85 									\
86 	/* one less than the dividend with highest result */		\
87 	___x = ~0ULL / ___b * ___b - 1;					\
88 									\
89 	/* test our ___m with res = m * x / (p << 64) */		\
90 	___res = ((___m & 0xffffffff) * (___x & 0xffffffff)) >> 32;	\
91 	___t = ___res += (___m & 0xffffffff) * (___x >> 32);		\
92 	___res += (___x & 0xffffffff) * (___m >> 32);			\
93 	___t = (___res < ___t) ? (1ULL << 32) : 0;			\
94 	___res = (___res >> 32) + ___t;					\
95 	___res += (___m >> 32) * (___x >> 32);				\
96 	___res /= ___p;							\
97 									\
98 	/* Now sanitize and optimize what we've got. */			\
99 	if (~0ULL % (___b / (___b & -___b)) == 0) {			\
100 		/* special case, can be simplified to ... */		\
101 		___n /= (___b & -___b);					\
102 		___m = ~0ULL / (___b / (___b & -___b));			\
103 		___p = 1;						\
104 		___bias = 1;						\
105 	} else if (___res != ___x / ___b) {				\
106 		/*							\
107 		 * We can't get away without a bias to compensate	\
108 		 * for bit truncation errors.  To avoid it we'd need an	\
109 		 * additional bit to represent m which would overflow	\
110 		 * a 64-bit variable.					\
111 		 *							\
112 		 * Instead we do m = p / b and n / b = (n * m + m) / p.	\
113 		 */							\
114 		___bias = 1;						\
115 		/* Compute m = (p << 64) / b */				\
116 		___m = (~0ULL / ___b) * ___p;				\
117 		___m += ((~0ULL % ___b + 1) * ___p) / ___b;		\
118 	} else {							\
119 		/*							\
120 		 * Reduce m / p, and try to clear bit 31 of m when	\
121 		 * possible, otherwise that'll need extra overflow	\
122 		 * handling later.					\
123 		 */							\
124 		uint32_t ___bits = -(___m & -___m);			\
125 		___bits |= ___m >> 32;					\
126 		___bits = (~___bits) << 1;				\
127 		/*							\
128 		 * If ___bits == 0 then setting bit 31 is  unavoidable.	\
129 		 * Simply apply the maximum possible reduction in that	\
130 		 * case. Otherwise the MSB of ___bits indicates the	\
131 		 * best reduction we should apply.			\
132 		 */							\
133 		if (!___bits) {						\
134 			___p /= (___m & -___m);				\
135 			___m /= (___m & -___m);				\
136 		} else {						\
137 			___p >>= ilog2(___bits);			\
138 			___m >>= ilog2(___bits);			\
139 		}							\
140 		/* No bias needed. */					\
141 		___bias = 0;						\
142 	}								\
143 									\
144 	/*								\
145 	 * Now we have a combination of 2 conditions:			\
146 	 *								\
147 	 * 1) whether or not we need to apply a bias, and		\
148 	 *								\
149 	 * 2) whether or not there might be an overflow in the cross	\
150 	 *    product determined by (___m & ((1 << 63) | (1 << 31))).	\
151 	 *								\
152 	 * Select the best way to do (m_bias + m * n) / (1 << 64).	\
153 	 * From now on there will be actual runtime code generated.	\
154 	 */								\
155 	___res = __arch_xprod_64(___m, ___n, ___bias);			\
156 									\
157 	___res /= ___p;							\
158 })
159 
160 #ifndef __arch_xprod_64
161 /*
162  * Default C implementation for __arch_xprod_64()
163  *
164  * Prototype: uint64_t __arch_xprod_64(const uint64_t m, uint64_t n, bool bias)
165  * Semantic:  retval = ((bias ? m : 0) + m * n) >> 64
166  *
167  * The product is a 128-bit value, scaled down to 64 bits.
168  * Assuming constant propagation to optimize away unused conditional code.
169  * Architectures may provide their own optimized assembly implementation.
170  */
171 static inline uint64_t __arch_xprod_64(const uint64_t m, uint64_t n, bool bias)
172 {
173 	uint32_t m_lo = m;
174 	uint32_t m_hi = m >> 32;
175 	uint32_t n_lo = n;
176 	uint32_t n_hi = n >> 32;
177 	uint64_t res;
178 	uint32_t res_lo, res_hi, tmp;
179 
180 	if (!bias) {
181 		res = ((uint64_t)m_lo * n_lo) >> 32;
182 	} else if (!(m & ((1ULL << 63) | (1ULL << 31)))) {
183 		/* there can't be any overflow here */
184 		res = (m + (uint64_t)m_lo * n_lo) >> 32;
185 	} else {
186 		res = m + (uint64_t)m_lo * n_lo;
187 		res_lo = res >> 32;
188 		res_hi = (res_lo < m_hi);
189 		res = res_lo | ((uint64_t)res_hi << 32);
190 	}
191 
192 	if (!(m & ((1ULL << 63) | (1ULL << 31)))) {
193 		/* there can't be any overflow here */
194 		res += (uint64_t)m_lo * n_hi;
195 		res += (uint64_t)m_hi * n_lo;
196 		res >>= 32;
197 	} else {
198 		res += (uint64_t)m_lo * n_hi;
199 		tmp = res >> 32;
200 		res += (uint64_t)m_hi * n_lo;
201 		res_lo = res >> 32;
202 		res_hi = (res_lo < tmp);
203 		res = res_lo | ((uint64_t)res_hi << 32);
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 (__builtin_constant_p(__base) &&	\
228 		   __base != 0) {			\
229 		uint32_t __res_lo, __n_lo = (n);	\
230 		(n) = __div64_const32(n, __base);	\
231 		/* the remainder can be computed with 32-bit regs */ \
232 		__res_lo = (n);				\
233 		__rem = __n_lo - __res_lo * __base;	\
234 	} else if (likely(((n) >> 32) == 0)) {		\
235 		__rem = (uint32_t)(n) % __base;		\
236 		(n) = (uint32_t)(n) / __base;		\
237 	} else {					\
238 		__rem = __div64_32(&(n), __base);	\
239 	}						\
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 */
250