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/** @file
* IPRT - Assembly Routines for Optimizing some Integers Math Operations.
*/
/*
* Copyright (C) 2006-2019 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 <iprt/types.h>
#if defined(_MSC_VER) && RT_INLINE_ASM_USES_INTRIN
# pragma warning(push)
# pragma warning(disable:4668) /* Several incorrect __cplusplus uses. */
# pragma warning(disable:4255) /* Incorrect __slwpcb prototype. */
# include <intrin.h>
# pragma warning(pop)
/* Emit the intrinsics at all optimization levels. */
# 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
#if ARCH_BITS == 64
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
}
#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 */
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