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