问题：BigInt分区的一种优秀而有效的算法？
尝试：多项式长除法，除法除法（溢出余数），二进制长除法（任何好处？不确定，这就是我在下面的帖子中所提到的），商猜测除法（带有大商数的过多减法）。< / p>
我一直试图对BigInt部门进行编码。我的最新算法使用二进制除法，但我不认为这是最好的方法。
所以我正在寻找一些关于那些算法的想法; ）。
我正在使用的语言不支持传递诸如数组之类的项目或各种数据类型。我坚持使用整数和布尔值以及全局数组以及在函数顶部声明的局部数组。
我正在使用32768的字大小来提高速度，恰好是2 ^ 15。因此，我可以快速有效地转换为基数2和返回，这就是我决定尝试二进制除法算法的原因。
我的第一种方法导致其余部分在某些情况下溢出，但速度非常快。我的下一个方法是多项式长除法。我也试过了这个商的想法，虽然它会在极大的数字上失败，因为会涉及太多的减法。总的来说，我认为糟糕的二元分割算法可能是最好的选择; |
数字在除数和余数数组的末尾变小。它们在股息阵列的开头处较小。
最终答案存储在binaryDividendBuffer中，其大小为binaryDividendBufferSize（商），余数的大小为remainingSize（余数）。这个东西适用于0个bug，但我觉得它真的很糟糕：o。
globals
private static integer array binaryDividendBuffer //division binary buffer #1 (to be divided)
private static integer binaryDividendBufferSize //division binary count #1
private static integer array binaryBufferDivisor //division binary buffer #2 (to divide)
private static integer binaryBufferDivisorSize //division binary count #2
endglobals
代码：
local integer currentDividendDigit = binaryDividendBufferSize //to be divided int digit count
local integer tempDigit2 //temp digit 2
local integer tempDigit3 //temp digit 3
local integer array remainder //remainder
local integer remainderSize = 0 //remainder count
local boolean remainderLessThanDividend //is the remainder < divisor?
local integer binaryBufferDividendDigitOffset //subtract -1 or 0 (shift the divisor by 1 bit for extra digit)
local boolean gatheredDigits //were bits gatheredDigits?
loop
//gather bits equal to the length of the divisor only if the current remainder isn't equal to length of divisor and there are bits remaining
set gatheredDigits = false
set gatheredDigits = remainderSize != binaryBufferDivisorSize and 0 != currentDividendDigit
if (gatheredDigits) then
loop
exitwhen remainderSize == binaryBufferDivisorSize or 0 == currentDividendDigit
set currentDividendDigit = currentDividendDigit - 1
set remainder[remainderSize] = binaryDividendBuffer[currentDividendDigit]
set remainderSize = remainderSize + 1
set binaryDividendBuffer[currentDividendDigit] = 0
endloop
endif
//if the remainder is smaller than the divisor and there are no bits left to gather, exit
if (remainderSize < binaryBufferDivisorSize and 0 == currentDividendDigit) then
set binaryDividendBuffer[currentDividendDigit] = 0
exitwhen true
endif
//compare the remainder and the divisor to see which one is greater
set tempDigit2 = 0
set remainderLessThanDividend = false
loop
set remainderLessThanDividend = remainder[tempDigit2] < binaryBufferDivisor[tempDigit2]
set tempDigit2 = tempDigit2 + 1
exitwhen tempDigit2 == binaryBufferDivisorSize or remainderLessThanDividend or remainder[tempDigit2] > binaryBufferDivisor[tempDigit2]
endloop
//if remainderLessThanDividend and there are bits remaining, add an additional bit
//set the dividend's current bit to 0 IF bits were gatheredDigits (division taking place)
//if bits weren't gatheredDigits, then setting it to 0 will set an already divided bit
if (remainderLessThanDividend) then
exitwhen 0 == currentDividendDigit
if (gatheredDigits) then
set binaryDividendBuffer[currentDividendDigit] = 0
endif
set currentDividendDigit = currentDividendDigit - 1
set remainder[remainderSize] = binaryDividendBuffer[currentDividendDigit]
set remainderSize = remainderSize + 1
set binaryBufferDividendDigitOffset = -1 //shift divisor's bits by 1 to account for extra digit in remainder
else
set binaryBufferDividendDigitOffset = 0 //don't shift as there is no extra digit in remainder
endif
//subtract
set binaryDividendBuffer[currentDividendDigit] = 1
set tempDigit2 = remainderSize
loop
set tempDigit2 = tempDigit2 - 1
//if only subtract if the divisor actually has a bit to do subtracting (remainder might have 1 more bit than divisor)
if (tempDigit2 + binaryBufferDividendDigitOffset > -1) then
//if the remainder's current bit is remainderLessThanDividend than the divisor's bit, borrow
if (remainder[tempDigit2] < binaryBufferDivisor[tempDigit2 + binaryBufferDividendDigitOffset]) then
set remainder[tempDigit2 - 1] = remainder[tempDigit2 - 1] - 1
set remainder[tempDigit2] = remainder[tempDigit2] + 2
endif
//subtract them
set remainder[tempDigit2] = remainder[tempDigit2] - binaryBufferDivisor[tempDigit2 + binaryBufferDividendDigitOffset]
endif
exitwhen 0 == tempDigit2
endloop
//cut out all of the 0s in front of the remainder and shift it over
//000033 -> 33
//this first loop goes through all of the 0s
loop
exitwhen 0 != remainder[tempDigit2] or tempDigit2 == remainderSize
set tempDigit2 = tempDigit2 + 1
endloop
//this loop removes the 0s by shifting over
if (0 < tempDigit2) then
if (tempDigit2 == remainderSize) then
set remainderSize = 0
set remainder[0] = 0
else
set tempDigit3 = 0
set remainderSize = remainderSize-tempDigit2
loop
set remainder[tempDigit3] = remainder[tempDigit3+tempDigit2]
set remainder[tempDigit3+tempDigit2] = 0
set tempDigit3 = tempDigit3 + 1
exitwhen tempDigit3 == remainderSize
endloop
endif
endif
exitwhen 0 == currentDividendDigit
endloop
//cut out all of the 0s in front of dividend
loop
exitwhen 0 != binaryDividendBuffer[binaryDividendBufferSize]
set binaryDividendBufferSize = binaryDividendBufferSize - 1
endloop