/** @file * IPRT - Assembly Routines for Optimizing some Integers Math Operations. */ /* * Copyright (C) 2006-2022 Oracle Corporation * * This file is part of VirtualBox Open Source Edition (OSE), as * available from http://www.virtualbox.org. This file is free software; * you can redistribute it and/or modify it under the terms of the GNU * General Public License (GPL) as published by the Free Software * Foundation, in version 2 as it comes in the "COPYING" file of the * VirtualBox OSE distribution. VirtualBox OSE is distributed in the * hope that it will be useful, but WITHOUT ANY WARRANTY of any kind. * * The contents of this file may alternatively be used under the terms * of the Common Development and Distribution License Version 1.0 * (CDDL) only, as it comes in the "COPYING.CDDL" file of the * VirtualBox OSE distribution, in which case the provisions of the * CDDL are applicable instead of those of the GPL. * * You may elect to license modified versions of this file under the * terms and conditions of either the GPL or the CDDL or both. */ #ifndef IPRT_INCLUDED_asm_math_h #define IPRT_INCLUDED_asm_math_h #ifndef RT_WITHOUT_PRAGMA_ONCE # pragma once #endif #include #if defined(_MSC_VER) && RT_INLINE_ASM_USES_INTRIN /* Emit the intrinsics at all optimization levels. */ # include # pragma intrinsic(__emul) # pragma intrinsic(__emulu) # ifdef RT_ARCH_AMD64 # pragma intrinsic(_mul128) # pragma intrinsic(_umul128) # endif #endif /** @defgroup grp_rt_asm_math Interger Math Optimizations * @ingroup grp_rt_asm * @{ */ /** * Multiplies two unsigned 32-bit values returning an unsigned 64-bit result. * * @returns u32F1 * u32F2. */ #if RT_INLINE_ASM_EXTERNAL && !RT_INLINE_ASM_USES_INTRIN && defined(RT_ARCH_X86) DECLASM(uint64_t) ASMMult2xU32RetU64(uint32_t u32F1, uint32_t u32F2); #else DECLINLINE(uint64_t) ASMMult2xU32RetU64(uint32_t u32F1, uint32_t u32F2) { # ifdef RT_ARCH_X86 uint64_t u64; # if RT_INLINE_ASM_GNU_STYLE __asm__ __volatile__("mull %%edx" : "=A" (u64) : "a" (u32F2), "d" (u32F1)); # elif RT_INLINE_ASM_USES_INTRIN u64 = __emulu(u32F1, u32F2); # else __asm { mov edx, [u32F1] mov eax, [u32F2] mul edx mov dword ptr [u64], eax mov dword ptr [u64 + 4], edx } # endif return u64; # else /* generic: */ return (uint64_t)u32F1 * u32F2; # endif } #endif /** * Multiplies two signed 32-bit values returning a signed 64-bit result. * * @returns u32F1 * u32F2. */ #if RT_INLINE_ASM_EXTERNAL && !RT_INLINE_ASM_USES_INTRIN && defined(RT_ARCH_X86) DECLASM(int64_t) ASMMult2xS32RetS64(int32_t i32F1, int32_t i32F2); #else DECLINLINE(int64_t) ASMMult2xS32RetS64(int32_t i32F1, int32_t i32F2) { # ifdef RT_ARCH_X86 int64_t i64; # if RT_INLINE_ASM_GNU_STYLE __asm__ __volatile__("imull %%edx" : "=A" (i64) : "a" (i32F2), "d" (i32F1)); # elif RT_INLINE_ASM_USES_INTRIN i64 = __emul(i32F1, i32F2); # else __asm { mov edx, [i32F1] mov eax, [i32F2] imul edx mov dword ptr [i64], eax mov dword ptr [i64 + 4], edx } # endif return i64; # else /* generic: */ return (int64_t)i32F1 * i32F2; # endif } #endif DECLINLINE(uint64_t) ASMMult2xU64Ret2xU64(uint64_t u64F1, uint64_t u64F2, uint64_t *pu64ProdHi) { #if defined(RT_ARCH_AMD64) && (RT_INLINE_ASM_GNU_STYLE || RT_INLINE_ASM_USES_INTRIN) # if RT_INLINE_ASM_GNU_STYLE uint64_t u64Low, u64High; __asm__ __volatile__("mulq %%rdx" : "=a" (u64Low), "=d" (u64High) : "0" (u64F1), "1" (u64F2)); *pu64ProdHi = u64High; return u64Low; # elif RT_INLINE_ASM_USES_INTRIN return _umul128(u64F1, u64F2, pu64ProdHi); # else # error "hmm" # endif #else /* generic: */ /* * F1 * F2 = Prod * -- -- * ab * cd = b*d + a*d*10 + b*c*10 + a*c*100 * * Where a, b, c and d are 'digits', and 10 is max digit + 1. * * Our digits are 32-bit wide, so instead of 10 we multiply by 4G. * Prod = F1.s.Lo*F2.s.Lo + F1.s.Hi*F2.s.Lo*4G * + F1.s.Lo*F2.s.Hi*4G + F1.s.Hi*F2.s.Hi*4G*4G */ RTUINT128U Prod; RTUINT64U Tmp1; uint64_t u64Tmp; RTUINT64U F1, F2; F1.u = u64F1; F2.u = u64F2; Prod.s.Lo = ASMMult2xU32RetU64(F1.s.Lo, F2.s.Lo); Tmp1.u = ASMMult2xU32RetU64(F1.s.Hi, F2.s.Lo); u64Tmp = (uint64_t)Prod.DWords.dw1 + Tmp1.s.Lo; Prod.DWords.dw1 = (uint32_t)u64Tmp; Prod.s.Hi = Tmp1.s.Hi; Prod.s.Hi += u64Tmp >> 32; /* carry */ Tmp1.u = ASMMult2xU32RetU64(F1.s.Lo, F2.s.Hi); u64Tmp = (uint64_t)Prod.DWords.dw1 + Tmp1.s.Lo; Prod.DWords.dw1 = (uint32_t)u64Tmp; u64Tmp >>= 32; /* carry */ u64Tmp += Prod.DWords.dw2; u64Tmp += Tmp1.s.Hi; Prod.DWords.dw2 = (uint32_t)u64Tmp; Prod.DWords.dw3 += u64Tmp >> 32; /* carry */ Prod.s.Hi += ASMMult2xU32RetU64(F1.s.Hi, F2.s.Hi); *pu64ProdHi = Prod.s.Hi; return Prod.s.Lo; #endif } /** * Divides a 64-bit unsigned by a 32-bit unsigned returning an unsigned 32-bit result. * * @returns u64 / u32. */ #if RT_INLINE_ASM_EXTERNAL && defined(RT_ARCH_X86) DECLASM(uint32_t) ASMDivU64ByU32RetU32(uint64_t u64, uint32_t u32); #else DECLINLINE(uint32_t) ASMDivU64ByU32RetU32(uint64_t u64, uint32_t u32) { # ifdef RT_ARCH_X86 # if RT_INLINE_ASM_GNU_STYLE RTCCUINTREG uDummy; __asm__ __volatile__("divl %3" : "=a" (u32), "=d"(uDummy) : "A" (u64), "r" (u32)); # else __asm { mov eax, dword ptr [u64] mov edx, dword ptr [u64 + 4] mov ecx, [u32] div ecx mov [u32], eax } # endif return u32; # else /* generic: */ return (uint32_t)(u64 / u32); # endif } #endif /** * Divides a 64-bit signed by a 32-bit signed returning a signed 32-bit result. * * @returns u64 / u32. */ #if RT_INLINE_ASM_EXTERNAL && defined(RT_ARCH_X86) DECLASM(int32_t) ASMDivS64ByS32RetS32(int64_t i64, int32_t i32); #else DECLINLINE(int32_t) ASMDivS64ByS32RetS32(int64_t i64, int32_t i32) { # ifdef RT_ARCH_X86 # if RT_INLINE_ASM_GNU_STYLE RTCCUINTREG iDummy; __asm__ __volatile__("idivl %3" : "=a" (i32), "=d"(iDummy) : "A" (i64), "r" (i32)); # else __asm { mov eax, dword ptr [i64] mov edx, dword ptr [i64 + 4] mov ecx, [i32] idiv ecx mov [i32], eax } # endif return i32; # else /* generic: */ return (int32_t)(i64 / i32); # endif } #endif /** * Performs 64-bit unsigned by a 32-bit unsigned division with a 32-bit unsigned result, * returning the rest. * * @returns u64 % u32. * * @remarks It is important that the result is <= UINT32_MAX or we'll overflow and crash. */ #if RT_INLINE_ASM_EXTERNAL && defined(RT_ARCH_X86) DECLASM(uint32_t) ASMModU64ByU32RetU32(uint64_t u64, uint32_t u32); #else DECLINLINE(uint32_t) ASMModU64ByU32RetU32(uint64_t u64, uint32_t u32) { # ifdef RT_ARCH_X86 # if RT_INLINE_ASM_GNU_STYLE RTCCUINTREG uDummy; __asm__ __volatile__("divl %3" : "=a" (uDummy), "=d"(u32) : "A" (u64), "r" (u32)); # else __asm { mov eax, dword ptr [u64] mov edx, dword ptr [u64 + 4] mov ecx, [u32] div ecx mov [u32], edx } # endif return u32; # else /* generic: */ return (uint32_t)(u64 % u32); # endif } #endif /** * Performs 64-bit signed by a 32-bit signed division with a 32-bit signed result, * returning the rest. * * @returns u64 % u32. * * @remarks It is important that the result is <= UINT32_MAX or we'll overflow and crash. */ #if RT_INLINE_ASM_EXTERNAL && defined(RT_ARCH_X86) DECLASM(int32_t) ASMModS64ByS32RetS32(int64_t i64, int32_t i32); #else DECLINLINE(int32_t) ASMModS64ByS32RetS32(int64_t i64, int32_t i32) { # ifdef RT_ARCH_X86 # if RT_INLINE_ASM_GNU_STYLE RTCCUINTREG iDummy; __asm__ __volatile__("idivl %3" : "=a" (iDummy), "=d"(i32) : "A" (i64), "r" (i32)); # else __asm { mov eax, dword ptr [i64] mov edx, dword ptr [i64 + 4] mov ecx, [i32] idiv ecx mov [i32], edx } # endif return i32; # else /* generic: */ return (int32_t)(i64 % i32); # endif } #endif /** * Multiple a 32-bit by a 32-bit integer and divide the result by a 32-bit integer * using a 64 bit intermediate result. * * @returns (u32A * u32B) / u32C. * @param u32A The 32-bit value (A). * @param u32B The 32-bit value to multiple by A. * @param u32C The 32-bit value to divide A*B by. * * @remarks Architecture specific. * @remarks Make sure the result won't ever exceed 32-bit, because hardware * exception may be raised if it does. * @remarks On x86 this may be used to avoid dragging in 64-bit builtin * arithmetics functions. */ #if RT_INLINE_ASM_EXTERNAL && (defined(RT_ARCH_AMD64) || defined(RT_ARCH_X86)) DECLASM(uint32_t) ASMMultU32ByU32DivByU32(uint32_t u32A, uint32_t u32B, uint32_t u32C); #else DECLINLINE(uint32_t) ASMMultU32ByU32DivByU32(uint32_t u32A, uint32_t u32B, uint32_t u32C) { # if RT_INLINE_ASM_GNU_STYLE && (defined(RT_ARCH_AMD64) || defined(RT_ARCH_X86)) uint32_t u32Result, u32Spill; __asm__ __volatile__("mull %2\n\t" "divl %3\n\t" : "=&a" (u32Result), "=&d" (u32Spill) : "r" (u32B), "r" (u32C), "0" (u32A)); return u32Result; # else return (uint32_t)(((uint64_t)u32A * u32B) / u32C); # endif } #endif /** * Multiple a 64-bit by a 32-bit integer and divide the result by a 32-bit integer * using a 96 bit intermediate result. * * @returns (u64A * u32B) / u32C. * @param u64A The 64-bit value. * @param u32B The 32-bit value to multiple by A. * @param u32C The 32-bit value to divide A*B by. * * @remarks Architecture specific. * @remarks Make sure the result won't ever exceed 64-bit, because hardware * exception may be raised if it does. * @remarks On x86 this may be used to avoid dragging in 64-bit builtin * arithmetics function. */ #if RT_INLINE_ASM_EXTERNAL || !defined(__GNUC__) || (!defined(RT_ARCH_AMD64) && !defined(RT_ARCH_X86)) DECLASM(uint64_t) ASMMultU64ByU32DivByU32(uint64_t u64A, uint32_t u32B, uint32_t u32C); #else DECLINLINE(uint64_t) ASMMultU64ByU32DivByU32(uint64_t u64A, uint32_t u32B, uint32_t u32C) { # if RT_INLINE_ASM_GNU_STYLE # ifdef RT_ARCH_AMD64 uint64_t u64Result, u64Spill; __asm__ __volatile__("mulq %2\n\t" "divq %3\n\t" : "=&a" (u64Result), "=&d" (u64Spill) : "r" ((uint64_t)u32B), "r" ((uint64_t)u32C), "0" (u64A)); return u64Result; # else uint32_t u32Dummy; uint64_t u64Result; __asm__ __volatile__("mull %%ecx \n\t" /* eax = u64Lo.lo = (u64A.lo * u32B).lo edx = u64Lo.hi = (u64A.lo * u32B).hi */ "xchg %%eax,%%esi \n\t" /* esi = u64Lo.lo eax = u64A.hi */ "xchg %%edx,%%edi \n\t" /* edi = u64Low.hi edx = u32C */ "xchg %%edx,%%ecx \n\t" /* ecx = u32C edx = u32B */ "mull %%edx \n\t" /* eax = u64Hi.lo = (u64A.hi * u32B).lo edx = u64Hi.hi = (u64A.hi * u32B).hi */ "addl %%edi,%%eax \n\t" /* u64Hi.lo += u64Lo.hi */ "adcl $0,%%edx \n\t" /* u64Hi.hi += carry */ "divl %%ecx \n\t" /* eax = u64Hi / u32C edx = u64Hi % u32C */ "movl %%eax,%%edi \n\t" /* edi = u64Result.hi = u64Hi / u32C */ "movl %%esi,%%eax \n\t" /* eax = u64Lo.lo */ "divl %%ecx \n\t" /* u64Result.lo */ "movl %%edi,%%edx \n\t" /* u64Result.hi */ : "=A"(u64Result), "=c"(u32Dummy), "=S"(u32Dummy), "=D"(u32Dummy) : "a"((uint32_t)u64A), "S"((uint32_t)(u64A >> 32)), "c"(u32B), "D"(u32C)); return u64Result; # endif # else RTUINT64U u; uint64_t u64Lo = (uint64_t)(u64A & 0xffffffff) * u32B; uint64_t u64Hi = (uint64_t)(u64A >> 32) * u32B; u64Hi += (u64Lo >> 32); u.s.Hi = (uint32_t)(u64Hi / u32C); u.s.Lo = (uint32_t)((((u64Hi % u32C) << 32) + (u64Lo & 0xffffffff)) / u32C); return u.u; # endif } #endif /** @} */ #endif /* !IPRT_INCLUDED_asm_math_h */