math64.h

  1/* SPDX-License-Identifier: GPL-2.0 */
  2#ifndef _LINUX_MATH64_H
  3#define _LINUX_MATH64_H
  4
  5#include <linux/types.h>
  6#include <linux/math.h>
  7#include <asm/div64.h>
  8#include <vdso/math64.h>
  9
 10#if BITS_PER_LONG == 64
 11
 12#define div64_long(x, y) div64_s64((x), (y))
 13#define div64_ul(x, y)   div64_u64((x), (y))
 14
 15/**
 16 * div_u64_rem - unsigned 64bit divide with 32bit divisor with remainder
 17 * @dividend: unsigned 64bit dividend
 18 * @divisor: unsigned 32bit divisor
 19 * @remainder: pointer to unsigned 32bit remainder
 20 *
 21 * Return: sets ``*remainder``, then returns dividend / divisor
 22 *
 23 * This is commonly provided by 32bit archs to provide an optimized 64bit
 24 * divide.
 25 */
 26static inline u64 div_u64_rem(u64 dividend, u32 divisor, u32 *remainder)
 27{
 28	*remainder = dividend % divisor;
 29	return dividend / divisor;
 30}
 31
 32/**
 33 * div_s64_rem - signed 64bit divide with 32bit divisor with remainder
 34 * @dividend: signed 64bit dividend
 35 * @divisor: signed 32bit divisor
 36 * @remainder: pointer to signed 32bit remainder
 37 *
 38 * Return: sets ``*remainder``, then returns dividend / divisor
 39 */
 40static inline s64 div_s64_rem(s64 dividend, s32 divisor, s32 *remainder)
 41{
 42	*remainder = dividend % divisor;
 43	return dividend / divisor;
 44}
 45
 46/**
 47 * div64_u64_rem - unsigned 64bit divide with 64bit divisor and remainder
 48 * @dividend: unsigned 64bit dividend
 49 * @divisor: unsigned 64bit divisor
 50 * @remainder: pointer to unsigned 64bit remainder
 51 *
 52 * Return: sets ``*remainder``, then returns dividend / divisor
 53 */
 54static inline u64 div64_u64_rem(u64 dividend, u64 divisor, u64 *remainder)
 55{
 56	*remainder = dividend % divisor;
 57	return dividend / divisor;
 58}
 59
 60/**
 61 * div64_u64 - unsigned 64bit divide with 64bit divisor
 62 * @dividend: unsigned 64bit dividend
 63 * @divisor: unsigned 64bit divisor
 64 *
 65 * Return: dividend / divisor
 66 */
 67static inline u64 div64_u64(u64 dividend, u64 divisor)
 68{
 69	return dividend / divisor;
 70}
 71
 72/**
 73 * div64_s64 - signed 64bit divide with 64bit divisor
 74 * @dividend: signed 64bit dividend
 75 * @divisor: signed 64bit divisor
 76 *
 77 * Return: dividend / divisor
 78 */
 79static inline s64 div64_s64(s64 dividend, s64 divisor)
 80{
 81	return dividend / divisor;
 82}
 83
 84#elif BITS_PER_LONG == 32
 85
 86#define div64_long(x, y) div_s64((x), (y))
 87#define div64_ul(x, y)   div_u64((x), (y))
 88
 89#ifndef div_u64_rem
 90static inline u64 div_u64_rem(u64 dividend, u32 divisor, u32 *remainder)
 91{
 92	*remainder = do_div(dividend, divisor);
 93	return dividend;
 94}
 95#endif
 96
 97#ifndef div_s64_rem
 98extern s64 div_s64_rem(s64 dividend, s32 divisor, s32 *remainder);
 99#endif
100
101#ifndef div64_u64_rem
102extern u64 div64_u64_rem(u64 dividend, u64 divisor, u64 *remainder);
103#endif
104
105#ifndef div64_u64
106extern u64 div64_u64(u64 dividend, u64 divisor);
107#endif
108
109#ifndef div64_s64
110extern s64 div64_s64(s64 dividend, s64 divisor);
111#endif
112
113#endif /* BITS_PER_LONG */
114
115/**
116 * div_u64 - unsigned 64bit divide with 32bit divisor
117 * @dividend: unsigned 64bit dividend
118 * @divisor: unsigned 32bit divisor
119 *
120 * This is the most common 64bit divide and should be used if possible,
121 * as many 32bit archs can optimize this variant better than a full 64bit
122 * divide.
123 *
124 * Return: dividend / divisor
125 */
126#ifndef div_u64
127static inline u64 div_u64(u64 dividend, u32 divisor)
128{
129	u32 remainder;
130	return div_u64_rem(dividend, divisor, &remainder);
131}
132#endif
133
134/**
135 * div_s64 - signed 64bit divide with 32bit divisor
136 * @dividend: signed 64bit dividend
137 * @divisor: signed 32bit divisor
138 *
139 * Return: dividend / divisor
140 */
141#ifndef div_s64
142static inline s64 div_s64(s64 dividend, s32 divisor)
143{
144	s32 remainder;
145	return div_s64_rem(dividend, divisor, &remainder);
146}
147#endif
148
149u32 iter_div_u64_rem(u64 dividend, u32 divisor, u64 *remainder);
150
151#ifndef mul_u32_u32
152/*
153 * Many a GCC version messes this up and generates a 64x64 mult :-(
154 */
155static inline u64 mul_u32_u32(u32 a, u32 b)
156{
157	return (u64)a * b;
158}
159#endif
160
161#ifndef add_u64_u32
162/*
163 * Many a GCC version also messes this up.
164 * Zero extending b and then spilling everything to stack.
165 */
166static inline u64 add_u64_u32(u64 a, u32 b)
167{
168	return a + b;
169}
170#endif
171
172#if defined(CONFIG_ARCH_SUPPORTS_INT128) && defined(__SIZEOF_INT128__)
173
174#ifndef mul_u64_u32_shr
175static __always_inline u64 mul_u64_u32_shr(u64 a, u32 mul, unsigned int shift)
176{
177	return (u64)(((unsigned __int128)a * mul) >> shift);
178}
179#endif /* mul_u64_u32_shr */
180
181#ifndef mul_u64_u64_shr
182static __always_inline u64 mul_u64_u64_shr(u64 a, u64 mul, unsigned int shift)
183{
184	return (u64)(((unsigned __int128)a * mul) >> shift);
185}
186#endif /* mul_u64_u64_shr */
187
188#else
189
190#ifndef mul_u64_u32_shr
191static __always_inline u64 mul_u64_u32_shr(u64 a, u32 mul, unsigned int shift)
192{
193	u32 ah = a >> 32, al = a;
194	u64 ret;
195
196	ret = mul_u32_u32(al, mul) >> shift;
197	if (ah)
198		ret += mul_u32_u32(ah, mul) << (32 - shift);
199	return ret;
200}
201#endif /* mul_u64_u32_shr */
202
203#ifndef mul_u64_u64_shr
204static inline u64 mul_u64_u64_shr(u64 a, u64 b, unsigned int shift)
205{
206	union {
207		u64 ll;
208		struct {
209#ifdef __BIG_ENDIAN
210			u32 high, low;
211#else
212			u32 low, high;
213#endif
214		} l;
215	} rl, rm, rn, rh, a0, b0;
216	u64 c;
217
218	a0.ll = a;
219	b0.ll = b;
220
221	rl.ll = mul_u32_u32(a0.l.low, b0.l.low);
222	rm.ll = mul_u32_u32(a0.l.low, b0.l.high);
223	rn.ll = mul_u32_u32(a0.l.high, b0.l.low);
224	rh.ll = mul_u32_u32(a0.l.high, b0.l.high);
225
226	/*
227	 * Each of these lines computes a 64-bit intermediate result into "c",
228	 * starting at bits 32-95.  The low 32-bits go into the result of the
229	 * multiplication, the high 32-bits are carried into the next step.
230	 */
231	rl.l.high = c = (u64)rl.l.high + rm.l.low + rn.l.low;
232	rh.l.low = c = (c >> 32) + rm.l.high + rn.l.high + rh.l.low;
233	rh.l.high = (c >> 32) + rh.l.high;
234
235	/*
236	 * The 128-bit result of the multiplication is in rl.ll and rh.ll,
237	 * shift it right and throw away the high part of the result.
238	 */
239	if (shift == 0)
240		return rl.ll;
241	if (shift < 64)
242		return (rl.ll >> shift) | (rh.ll << (64 - shift));
243	return rh.ll >> (shift & 63);
244}
245#endif /* mul_u64_u64_shr */
246
247#endif
248
249#ifndef mul_s64_u64_shr
250static inline u64 mul_s64_u64_shr(s64 a, u64 b, unsigned int shift)
251{
252	u64 ret;
253
254	/*
255	 * Extract the sign before the multiplication and put it back
256	 * afterwards if needed.
257	 */
258	ret = mul_u64_u64_shr(abs(a), b, shift);
259
260	if (a < 0)
261		ret = -((s64) ret);
262
263	return ret;
264}
265#endif /* mul_s64_u64_shr */
266
267#ifndef mul_u64_u32_div
268static inline u64 mul_u64_u32_div(u64 a, u32 mul, u32 divisor)
269{
270	union {
271		u64 ll;
272		struct {
273#ifdef __BIG_ENDIAN
274			u32 high, low;
275#else
276			u32 low, high;
277#endif
278		} l;
279	} u, rl, rh;
280
281	u.ll = a;
282	rl.ll = mul_u32_u32(u.l.low, mul);
283	rh.ll = mul_u32_u32(u.l.high, mul) + rl.l.high;
284
285	/* Bits 32-63 of the result will be in rh.l.low. */
286	rl.l.high = do_div(rh.ll, divisor);
287
288	/* Bits 0-31 of the result will be in rl.l.low.	*/
289	do_div(rl.ll, divisor);
290
291	rl.l.high = rh.l.low;
292	return rl.ll;
293}
294#endif /* mul_u64_u32_div */
295
296/**
297 * mul_u64_add_u64_div_u64 - unsigned 64bit multiply, add, and divide
298 * @a: first unsigned 64bit multiplicand
299 * @b: second unsigned 64bit multiplicand
300 * @c: unsigned 64bit addend
301 * @d: unsigned 64bit divisor
302 *
303 * Multiply two 64bit values together to generate a 128bit product
304 * add a third value and then divide by a fourth.
305 * The Generic code divides by 0 if @d is zero and returns ~0 on overflow.
306 * Architecture specific code may trap on zero or overflow.
307 *
308 * Return: (@a * @b + @c) / @d
309 */
310u64 mul_u64_add_u64_div_u64(u64 a, u64 b, u64 c, u64 d);
311
312/**
313 * mul_u64_u64_div_u64 - unsigned 64bit multiply and divide
314 * @a: first unsigned 64bit multiplicand
315 * @b: second unsigned 64bit multiplicand
316 * @d: unsigned 64bit divisor
317 *
318 * Multiply two 64bit values together to generate a 128bit product
319 * and then divide by a third value.
320 * The Generic code divides by 0 if @d is zero and returns ~0 on overflow.
321 * Architecture specific code may trap on zero or overflow.
322 *
323 * Return: @a * @b / @d
324 */
325#define mul_u64_u64_div_u64(a, b, d) mul_u64_add_u64_div_u64(a, b, 0, d)
326
327/**
328 * mul_u64_u64_div_u64_roundup - unsigned 64bit multiply and divide rounded up
329 * @a: first unsigned 64bit multiplicand
330 * @b: second unsigned 64bit multiplicand
331 * @d: unsigned 64bit divisor
332 *
333 * Multiply two 64bit values together to generate a 128bit product
334 * and then divide and round up.
335 * The Generic code divides by 0 if @d is zero and returns ~0 on overflow.
336 * Architecture specific code may trap on zero or overflow.
337 *
338 * Return: (@a * @b + @d - 1) / @d
339 */
340#define mul_u64_u64_div_u64_roundup(a, b, d) \
341	({ u64 _tmp = (d); mul_u64_add_u64_div_u64(a, b, _tmp - 1, _tmp); })
342
343
344/**
345 * DIV64_U64_ROUND_UP - unsigned 64bit divide with 64bit divisor rounded up
346 * @ll: unsigned 64bit dividend
347 * @d: unsigned 64bit divisor
348 *
349 * Divide unsigned 64bit dividend by unsigned 64bit divisor
350 * and round up.
351 *
352 * Return: dividend / divisor rounded up
353 */
354#define DIV64_U64_ROUND_UP(ll, d)	\
355	({ u64 _tmp = (d); div64_u64((ll) + _tmp - 1, _tmp); })
356
357/**
358 * DIV_U64_ROUND_UP - unsigned 64bit divide with 32bit divisor rounded up
359 * @ll: unsigned 64bit dividend
360 * @d: unsigned 32bit divisor
361 *
362 * Divide unsigned 64bit dividend by unsigned 32bit divisor
363 * and round up.
364 *
365 * Return: dividend / divisor rounded up
366 */
367#define DIV_U64_ROUND_UP(ll, d)		\
368	({ u32 _tmp = (d); div_u64((ll) + _tmp - 1, _tmp); })
369
370/**
371 * DIV64_U64_ROUND_CLOSEST - unsigned 64bit divide with 64bit divisor rounded to nearest integer
372 * @dividend: unsigned 64bit dividend
373 * @divisor: unsigned 64bit divisor
374 *
375 * Divide unsigned 64bit dividend by unsigned 64bit divisor
376 * and round to closest integer.
377 *
378 * Return: dividend / divisor rounded to nearest integer
379 */
380#define DIV64_U64_ROUND_CLOSEST(dividend, divisor)	\
381	({ u64 _tmp = (divisor); div64_u64((dividend) + _tmp / 2, _tmp); })
382
383/**
384 * DIV_U64_ROUND_CLOSEST - unsigned 64bit divide with 32bit divisor rounded to nearest integer
385 * @dividend: unsigned 64bit dividend
386 * @divisor: unsigned 32bit divisor
387 *
388 * Divide unsigned 64bit dividend by unsigned 32bit divisor
389 * and round to closest integer.
390 *
391 * Return: dividend / divisor rounded to nearest integer
392 */
393#define DIV_U64_ROUND_CLOSEST(dividend, divisor)	\
394	({ u32 _tmp = (divisor); div_u64((u64)(dividend) + _tmp / 2, _tmp); })
395
396/**
397 * DIV_S64_ROUND_CLOSEST - signed 64bit divide with 32bit divisor rounded to nearest integer
398 * @dividend: signed 64bit dividend
399 * @divisor: signed 32bit divisor
400 *
401 * Divide signed 64bit dividend by signed 32bit divisor
402 * and round to closest integer.
403 *
404 * Return: dividend / divisor rounded to nearest integer
405 */
406#define DIV_S64_ROUND_CLOSEST(dividend, divisor)(	\
407{							\
408	s64 __x = (dividend);				\
409	s32 __d = (divisor);				\
410	((__x > 0) == (__d > 0)) ?			\
411		div_s64((__x + (__d / 2)), __d) :	\
412		div_s64((__x - (__d / 2)), __d);	\
413}							\
414)
415
416/**
417 * roundup_u64 - Round up a 64bit value to the next specified 32bit multiple
418 * @x: the value to up
419 * @y: 32bit multiple to round up to
420 *
421 * Rounds @x to the next multiple of @y. For 32bit @x values, see roundup and
422 * the faster round_up() for powers of 2.
423 *
424 * Return: rounded up value.
425 */
426static inline u64 roundup_u64(u64 x, u32 y)
427{
428	return DIV_U64_ROUND_UP(x, y) * y;
429}
430#endif /* _LINUX_MATH64_H */