One-step-one-step write algorithm (large number calculation)

Original: One-step-one-step write algorithm (large number calculation)

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We know that on the x86 32-bit CPU, int represents 32 bits, and if it is accounted for as an integer, it is about more than 4 billion. Similarly, if you are on a 64-bit CPU, the largest integer that can be represented is the 64-bit binary, which represents a much larger number. So what if you want to represent a large integer in 32 digits? It's only on our own.

First, let's look back at how the addition and subtraction of our hand-counted integers, the multiplication method, is done:

(1) Remember the multiplication formula between 9*9

(2) Remember the addition and subtraction between single and single digits

(3) All multiplication is represented by addition and left shift, and all subtraction is expressed by subtraction and right shift

After understanding the above, we can manually write the addition of a large integer:

int* big_int_add (int src1[], int length1, int src2[], int length2) {int* dest = null;int length;int index;int smaller;int p Refix = 0;if (NULL = = Src1 | | 0 >= LENGTH1 | | NULL = = Src2 | | 0 >= length2) return null;length = length1 > length2?  (Length1 + 1): (length2 + 1);d est = (int*) malloc (sizeof (int) * length); assert (NULL! = dest); memset (dest, 0, sizeof (int) * length); smaller = (Length2 < length1)? Length2:length1;for (index = 0; index < smaller; index + +) Dest[index] = Src1[index] + src2[index];if (length1 > Leng Th2) {for (; index < length1; index++) Dest[index] = Src1[index];} Else{for (; index < length2; index++) Dest[index] = Src2[index];} for (index = 0; index < length; index + +) {Dest[index] + = prefix; prefix = dest[index]/10;dest[index]%= 10;} return dest;}

The most important feature of the algorithm above is: When the calculation is not considered 10 binary, wait until all the results come out after the start of each of the binary processing.

Discuss:

After seeing the algorithm above, you can consider:

(1) How should subtraction be written?

(2) How about multiplication? What about division?

One-step-one-step write algorithm (large number calculation)