如果我正确解释你的问题(特别是这部分Factor is in 32b integer
),您想要将 64 位被除数除以 32 位除数并得到 64 位商。
如果这种解释是正确的,那么实际上用 32 位代码很容易做到。
这个想法是,将被除数的“一半”除以除数,并将第一次除法的余数重新用于第二次除法。
说明如何执行此操作的 C 代码:
#include <stdio.h>
#include <limits.h>
#define C_ASSERT(expr) extern char CAssertExtern[(expr)?1:-1]
#if UINT_MAX >= 0xFFFFFFFF
typedef unsigned int uint32;
#else
typedef unsigned long uint32;
#endif
typedef unsigned long long uint64;
typedef unsigned long ulong;
// Make sure uint32=32 bits and uint64=64 bits
C_ASSERT(sizeof(uint32) * CHAR_BIT == 32);
C_ASSERT(sizeof(uint64) * CHAR_BIT == 64);
int div64by32eq64(uint64* dividend, uint32 divisor)
{
uint32 dividendHi = (uint32)(*dividend >> 32);
uint32 dividendLo = (uint32)*dividend;
uint32 quotientHi;
uint32 quotientLo;
if (divisor == 0)
return 0;
// This can be done as one 32-bit DIV, e.g. "div ecx"
quotientHi = dividendHi / divisor;
dividendHi = dividendHi % divisor;
// This can be done as another 32-bit DIV, e.g. "div ecx"
quotientLo = (uint32)((((uint64)dividendHi << 32) + dividendLo) / divisor);
*dividend = ((uint64)quotientHi << 32) + quotientLo;
return 1;
}
int main(void)
{
static const struct
{
uint64 dividend;
uint32 divisor;
} testData[] =
{
{ 1 , 0 },
{ 0xFFFFFFFFFFFFFFFFULL, 1 },
{ 0xFFFFFFFFFFFFFFFFULL, 2 },
{ 0xFFFFFFFF00000000ULL, 0xFFFFFFFFUL },
{ 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFUL },
};
int i;
for (i = 0; i < sizeof(testData)/sizeof(testData[0]); i++)
{
uint64 dividend = testData[i].dividend;
uint32 divisor = testData[i].divisor;
printf("0x%016llX / 0x%08lX = ", dividend, (ulong)divisor);
if (div64by32eq64(÷nd, divisor))
printf("0x%016llX\n", dividend);
else
printf("division by 0 error\n");
}
return 0;
}
Output (ideone http://ideone.com/aVoNoh):
0x0000000000000001 / 0x00000000 = division by 0 error
0xFFFFFFFFFFFFFFFF / 0x00000001 = 0xFFFFFFFFFFFFFFFF
0xFFFFFFFFFFFFFFFF / 0x00000002 = 0x7FFFFFFFFFFFFFFF
0xFFFFFFFF00000000 / 0xFFFFFFFF = 0x0000000100000000
0xFFFFFFFFFFFFFFFF / 0xFFFFFFFF = 0x0000000100000001
现在汇编中的等效除法代码(NASM 语法)无需检查是否被 0 除:
; 64-bit dividend
mov edx, 0xFFFFFFFF
mov eax, 0xFFFFFFFF
; 32-bit divisor
mov ecx, 0xFFFFFFFF
push eax
mov eax, edx
xor edx, edx
div ecx ; get high 32 bits of quotient
xchg eax, [esp] ; store them on stack, get low 32 bits of dividend
div ecx ; get low 32 bits of quotient
pop edx ; 64-bit quotient in edx:eax now
; edx:eax should now be equal 0x0000000100000001