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source: vbox/trunk/include/iprt/asm-math.h@ 103224

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1/** @file
2 * IPRT - Assembly Routines for Optimizing some Integers Math Operations.
3 */
4
5/*
6 * Copyright (C) 2006-2023 Oracle and/or its affiliates.
7 *
8 * This file is part of VirtualBox base platform packages, as
9 * available from https://www.virtualbox.org.
10 *
11 * This program is free software; you can redistribute it and/or
12 * modify it under the terms of the GNU General Public License
13 * as published by the Free Software Foundation, in version 3 of the
14 * License.
15 *
16 * This program is distributed in the hope that it will be useful, but
17 * WITHOUT ANY WARRANTY; without even the implied warranty of
18 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
19 * General Public License for more details.
20 *
21 * You should have received a copy of the GNU General Public License
22 * along with this program; if not, see <https://www.gnu.org/licenses>.
23 *
24 * The contents of this file may alternatively be used under the terms
25 * of the Common Development and Distribution License Version 1.0
26 * (CDDL), a copy of it is provided in the "COPYING.CDDL" file included
27 * in the VirtualBox distribution, in which case the provisions of the
28 * CDDL are applicable instead of those of the GPL.
29 *
30 * You may elect to license modified versions of this file under the
31 * terms and conditions of either the GPL or the CDDL or both.
32 *
33 * SPDX-License-Identifier: GPL-3.0-only OR CDDL-1.0
34 */
35
36#ifndef IPRT_INCLUDED_asm_math_h
37#define IPRT_INCLUDED_asm_math_h
38#ifndef RT_WITHOUT_PRAGMA_ONCE
39# pragma once
40#endif
41
42#include <iprt/types.h>
43
44#if defined(_MSC_VER) && RT_INLINE_ASM_USES_INTRIN
45/* Emit the intrinsics at all optimization levels. */
46# include <iprt/sanitized/intrin.h>
47# pragma intrinsic(__emul)
48# pragma intrinsic(__emulu)
49# ifdef RT_ARCH_AMD64
50# pragma intrinsic(_mul128)
51# pragma intrinsic(_umul128)
52# endif
53#endif
54
55
56/** @defgroup grp_rt_asm_math Interger Math Optimizations
57 * @ingroup grp_rt_asm
58 * @{ */
59
60/**
61 * Multiplies two unsigned 32-bit values returning an unsigned 64-bit result.
62 *
63 * @returns u32F1 * u32F2.
64 */
65
66#if RT_INLINE_ASM_EXTERNAL && !RT_INLINE_ASM_USES_INTRIN && defined(RT_ARCH_X86)
67DECLASM(uint64_t) ASMMult2xU32RetU64(uint32_t u32F1, uint32_t u32F2);
68#else
69DECLINLINE(uint64_t) ASMMult2xU32RetU64(uint32_t u32F1, uint32_t u32F2)
70{
71# ifdef RT_ARCH_X86
72 uint64_t u64;
73# if RT_INLINE_ASM_GNU_STYLE
74 __asm__ __volatile__("mull %%edx"
75 : "=A" (u64)
76 : "a" (u32F2), "d" (u32F1));
77# elif RT_INLINE_ASM_USES_INTRIN
78 u64 = __emulu(u32F1, u32F2);
79# else
80 __asm
81 {
82 mov edx, [u32F1]
83 mov eax, [u32F2]
84 mul edx
85 mov dword ptr [u64], eax
86 mov dword ptr [u64 + 4], edx
87 }
88# endif
89 return u64;
90# else /* generic: */
91 return (uint64_t)u32F1 * u32F2;
92# endif
93}
94#endif
95
96
97/**
98 * Multiplies two signed 32-bit values returning a signed 64-bit result.
99 *
100 * @returns u32F1 * u32F2.
101 */
102#if RT_INLINE_ASM_EXTERNAL && !RT_INLINE_ASM_USES_INTRIN && defined(RT_ARCH_X86)
103DECLASM(int64_t) ASMMult2xS32RetS64(int32_t i32F1, int32_t i32F2);
104#else
105DECLINLINE(int64_t) ASMMult2xS32RetS64(int32_t i32F1, int32_t i32F2)
106{
107# ifdef RT_ARCH_X86
108 int64_t i64;
109# if RT_INLINE_ASM_GNU_STYLE
110 __asm__ __volatile__("imull %%edx"
111 : "=A" (i64)
112 : "a" (i32F2), "d" (i32F1));
113# elif RT_INLINE_ASM_USES_INTRIN
114 i64 = __emul(i32F1, i32F2);
115# else
116 __asm
117 {
118 mov edx, [i32F1]
119 mov eax, [i32F2]
120 imul edx
121 mov dword ptr [i64], eax
122 mov dword ptr [i64 + 4], edx
123 }
124# endif
125 return i64;
126# else /* generic: */
127 return (int64_t)i32F1 * i32F2;
128# endif
129}
130#endif
131
132
133DECLINLINE(uint64_t) ASMMult2xU64Ret2xU64(uint64_t u64F1, uint64_t u64F2, uint64_t *pu64ProdHi)
134{
135#if defined(RT_ARCH_AMD64) && (RT_INLINE_ASM_GNU_STYLE || RT_INLINE_ASM_USES_INTRIN)
136# if RT_INLINE_ASM_GNU_STYLE
137 uint64_t u64Low, u64High;
138 __asm__ __volatile__("mulq %%rdx"
139 : "=a" (u64Low), "=d" (u64High)
140 : "0" (u64F1), "1" (u64F2));
141 *pu64ProdHi = u64High;
142 return u64Low;
143# elif RT_INLINE_ASM_USES_INTRIN
144 return _umul128(u64F1, u64F2, pu64ProdHi);
145# else
146# error "hmm"
147# endif
148#else /* generic: */
149 /*
150 * F1 * F2 = Prod
151 * -- --
152 * ab * cd = b*d + a*d*10 + b*c*10 + a*c*100
153 *
154 * Where a, b, c and d are 'digits', and 10 is max digit + 1.
155 *
156 * Our digits are 32-bit wide, so instead of 10 we multiply by 4G.
157 * Prod = F1.s.Lo*F2.s.Lo + F1.s.Hi*F2.s.Lo*4G
158 * + F1.s.Lo*F2.s.Hi*4G + F1.s.Hi*F2.s.Hi*4G*4G
159 */
160 RTUINT128U Prod;
161 RTUINT64U Tmp1;
162 uint64_t u64Tmp;
163 RTUINT64U F1, F2;
164 F1.u = u64F1;
165 F2.u = u64F2;
166
167 Prod.s.Lo = ASMMult2xU32RetU64(F1.s.Lo, F2.s.Lo);
168
169 Tmp1.u = ASMMult2xU32RetU64(F1.s.Hi, F2.s.Lo);
170 u64Tmp = (uint64_t)Prod.DWords.dw1 + Tmp1.s.Lo;
171 Prod.DWords.dw1 = (uint32_t)u64Tmp;
172 Prod.s.Hi = Tmp1.s.Hi;
173 Prod.s.Hi += u64Tmp >> 32; /* carry */
174
175 Tmp1.u = ASMMult2xU32RetU64(F1.s.Lo, F2.s.Hi);
176 u64Tmp = (uint64_t)Prod.DWords.dw1 + Tmp1.s.Lo;
177 Prod.DWords.dw1 = (uint32_t)u64Tmp;
178 u64Tmp >>= 32; /* carry */
179 u64Tmp += Prod.DWords.dw2;
180 u64Tmp += Tmp1.s.Hi;
181 Prod.DWords.dw2 = (uint32_t)u64Tmp;
182 Prod.DWords.dw3 += u64Tmp >> 32; /* carry */
183
184 Prod.s.Hi += ASMMult2xU32RetU64(F1.s.Hi, F2.s.Hi);
185 *pu64ProdHi = Prod.s.Hi;
186 return Prod.s.Lo;
187#endif
188}
189
190
191
192/**
193 * Divides a 64-bit unsigned by a 32-bit unsigned returning an unsigned 32-bit result.
194 *
195 * @returns u64 / u32.
196 */
197#if RT_INLINE_ASM_EXTERNAL && defined(RT_ARCH_X86)
198DECLASM(uint32_t) ASMDivU64ByU32RetU32(uint64_t u64, uint32_t u32);
199#else
200DECLINLINE(uint32_t) ASMDivU64ByU32RetU32(uint64_t u64, uint32_t u32)
201{
202# ifdef RT_ARCH_X86
203# if RT_INLINE_ASM_GNU_STYLE
204 RTCCUINTREG uDummy;
205 __asm__ __volatile__("divl %3"
206 : "=a" (u32), "=d"(uDummy)
207 : "A" (u64), "r" (u32));
208# else
209 __asm
210 {
211 mov eax, dword ptr [u64]
212 mov edx, dword ptr [u64 + 4]
213 mov ecx, [u32]
214 div ecx
215 mov [u32], eax
216 }
217# endif
218 return u32;
219# else /* generic: */
220 return (uint32_t)(u64 / u32);
221# endif
222}
223#endif
224
225
226/**
227 * Divides a 64-bit signed by a 32-bit signed returning a signed 32-bit result.
228 *
229 * @returns u64 / u32.
230 */
231#if RT_INLINE_ASM_EXTERNAL && defined(RT_ARCH_X86)
232DECLASM(int32_t) ASMDivS64ByS32RetS32(int64_t i64, int32_t i32);
233#else
234DECLINLINE(int32_t) ASMDivS64ByS32RetS32(int64_t i64, int32_t i32)
235{
236# ifdef RT_ARCH_X86
237# if RT_INLINE_ASM_GNU_STYLE
238 RTCCUINTREG iDummy;
239 __asm__ __volatile__("idivl %3"
240 : "=a" (i32), "=d"(iDummy)
241 : "A" (i64), "r" (i32));
242# else
243 __asm
244 {
245 mov eax, dword ptr [i64]
246 mov edx, dword ptr [i64 + 4]
247 mov ecx, [i32]
248 idiv ecx
249 mov [i32], eax
250 }
251# endif
252 return i32;
253# else /* generic: */
254 return (int32_t)(i64 / i32);
255# endif
256}
257#endif
258
259
260/**
261 * Performs 64-bit unsigned by a 32-bit unsigned division with a 32-bit unsigned result,
262 * returning the rest.
263 *
264 * @returns u64 % u32.
265 *
266 * @remarks It is important that the result is <= UINT32_MAX or we'll overflow and crash.
267 */
268#if RT_INLINE_ASM_EXTERNAL && defined(RT_ARCH_X86)
269DECLASM(uint32_t) ASMModU64ByU32RetU32(uint64_t u64, uint32_t u32);
270#else
271DECLINLINE(uint32_t) ASMModU64ByU32RetU32(uint64_t u64, uint32_t u32)
272{
273# ifdef RT_ARCH_X86
274# if RT_INLINE_ASM_GNU_STYLE
275 RTCCUINTREG uDummy;
276 __asm__ __volatile__("divl %3"
277 : "=a" (uDummy), "=d"(u32)
278 : "A" (u64), "r" (u32));
279# else
280 __asm
281 {
282 mov eax, dword ptr [u64]
283 mov edx, dword ptr [u64 + 4]
284 mov ecx, [u32]
285 div ecx
286 mov [u32], edx
287 }
288# endif
289 return u32;
290# else /* generic: */
291 return (uint32_t)(u64 % u32);
292# endif
293}
294#endif
295
296
297/**
298 * Performs 64-bit signed by a 32-bit signed division with a 32-bit signed result,
299 * returning the rest.
300 *
301 * @returns u64 % u32.
302 *
303 * @remarks It is important that the result is <= UINT32_MAX or we'll overflow and crash.
304 */
305#if RT_INLINE_ASM_EXTERNAL && defined(RT_ARCH_X86)
306DECLASM(int32_t) ASMModS64ByS32RetS32(int64_t i64, int32_t i32);
307#else
308DECLINLINE(int32_t) ASMModS64ByS32RetS32(int64_t i64, int32_t i32)
309{
310# ifdef RT_ARCH_X86
311# if RT_INLINE_ASM_GNU_STYLE
312 RTCCUINTREG iDummy;
313 __asm__ __volatile__("idivl %3"
314 : "=a" (iDummy), "=d"(i32)
315 : "A" (i64), "r" (i32));
316# else
317 __asm
318 {
319 mov eax, dword ptr [i64]
320 mov edx, dword ptr [i64 + 4]
321 mov ecx, [i32]
322 idiv ecx
323 mov [i32], edx
324 }
325# endif
326 return i32;
327# else /* generic: */
328 return (int32_t)(i64 % i32);
329# endif
330}
331#endif
332
333
334/**
335 * Multiple a 32-bit by a 32-bit integer and divide the result by a 32-bit integer
336 * using a 64 bit intermediate result.
337 *
338 * @returns (u32A * u32B) / u32C.
339 * @param u32A The 32-bit value (A).
340 * @param u32B The 32-bit value to multiple by A.
341 * @param u32C The 32-bit value to divide A*B by.
342 *
343 * @remarks Architecture specific.
344 * @remarks Make sure the result won't ever exceed 32-bit, because hardware
345 * exception may be raised if it does.
346 * @remarks On x86 this may be used to avoid dragging in 64-bit builtin
347 * arithmetics functions.
348 */
349#if RT_INLINE_ASM_EXTERNAL && (defined(RT_ARCH_AMD64) || defined(RT_ARCH_X86))
350DECLASM(uint32_t) ASMMultU32ByU32DivByU32(uint32_t u32A, uint32_t u32B, uint32_t u32C);
351#else
352DECLINLINE(uint32_t) ASMMultU32ByU32DivByU32(uint32_t u32A, uint32_t u32B, uint32_t u32C)
353{
354# if RT_INLINE_ASM_GNU_STYLE && (defined(RT_ARCH_AMD64) || defined(RT_ARCH_X86))
355 uint32_t u32Result, u32Spill;
356 __asm__ __volatile__("mull %2\n\t"
357 "divl %3\n\t"
358 : "=&a" (u32Result),
359 "=&d" (u32Spill)
360 : "r" (u32B),
361 "r" (u32C),
362 "0" (u32A));
363 return u32Result;
364# else
365 return (uint32_t)(((uint64_t)u32A * u32B) / u32C);
366# endif
367}
368#endif
369
370
371/**
372 * Multiple a 64-bit by a 32-bit integer and divide the result by a 32-bit integer
373 * using a 96 bit intermediate result.
374 *
375 * @returns (u64A * u32B) / u32C.
376 * @param u64A The 64-bit value.
377 * @param u32B The 32-bit value to multiple by A.
378 * @param u32C The 32-bit value to divide A*B by.
379 *
380 * @remarks Architecture specific.
381 * @remarks Make sure the result won't ever exceed 64-bit, because hardware
382 * exception may be raised if it does.
383 * @remarks On x86 this may be used to avoid dragging in 64-bit builtin
384 * arithmetics function.
385 */
386#if RT_INLINE_ASM_EXTERNAL || !defined(__GNUC__) || (!defined(RT_ARCH_AMD64) && !defined(RT_ARCH_X86))
387DECLASM(uint64_t) ASMMultU64ByU32DivByU32(uint64_t u64A, uint32_t u32B, uint32_t u32C);
388#else
389DECLINLINE(uint64_t) ASMMultU64ByU32DivByU32(uint64_t u64A, uint32_t u32B, uint32_t u32C)
390{
391# if RT_INLINE_ASM_GNU_STYLE
392# ifdef RT_ARCH_AMD64
393 uint64_t u64Result, u64Spill;
394 __asm__ __volatile__("mulq %2\n\t"
395 "divq %3\n\t"
396 : "=&a" (u64Result),
397 "=&d" (u64Spill)
398 : "r" ((uint64_t)u32B),
399 "r" ((uint64_t)u32C),
400 "0" (u64A));
401 return u64Result;
402# else
403 uint32_t u32Dummy;
404 uint64_t u64Result;
405 __asm__ __volatile__("mull %%ecx \n\t" /* eax = u64Lo.lo = (u64A.lo * u32B).lo
406 edx = u64Lo.hi = (u64A.lo * u32B).hi */
407 "xchg %%eax,%%esi \n\t" /* esi = u64Lo.lo
408 eax = u64A.hi */
409 "xchg %%edx,%%edi \n\t" /* edi = u64Low.hi
410 edx = u32C */
411 "xchg %%edx,%%ecx \n\t" /* ecx = u32C
412 edx = u32B */
413 "mull %%edx \n\t" /* eax = u64Hi.lo = (u64A.hi * u32B).lo
414 edx = u64Hi.hi = (u64A.hi * u32B).hi */
415 "addl %%edi,%%eax \n\t" /* u64Hi.lo += u64Lo.hi */
416 "adcl $0,%%edx \n\t" /* u64Hi.hi += carry */
417 "divl %%ecx \n\t" /* eax = u64Hi / u32C
418 edx = u64Hi % u32C */
419 "movl %%eax,%%edi \n\t" /* edi = u64Result.hi = u64Hi / u32C */
420 "movl %%esi,%%eax \n\t" /* eax = u64Lo.lo */
421 "divl %%ecx \n\t" /* u64Result.lo */
422 "movl %%edi,%%edx \n\t" /* u64Result.hi */
423 : "=A"(u64Result), "=c"(u32Dummy),
424 "=S"(u32Dummy), "=D"(u32Dummy)
425 : "a"((uint32_t)u64A),
426 "S"((uint32_t)(u64A >> 32)),
427 "c"(u32B),
428 "D"(u32C));
429 return u64Result;
430# endif
431# else
432 RTUINT64U u;
433 uint64_t u64Lo = (uint64_t)(u64A & 0xffffffff) * u32B;
434 uint64_t u64Hi = (uint64_t)(u64A >> 32) * u32B;
435 u64Hi += (u64Lo >> 32);
436 u.s.Hi = (uint32_t)(u64Hi / u32C);
437 u.s.Lo = (uint32_t)((((u64Hi % u32C) << 32) + (u64Lo & 0xffffffff)) / u32C);
438 return u.u;
439# endif
440}
441#endif
442
443/** @} */
444#endif /* !IPRT_INCLUDED_asm_math_h */
445
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