xref: /openbmc/linux/include/asm-generic/div64.h (revision be709d48)
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 */
250