A BigInt library in C

My project to build the best BigInt library focused on design (ease of use) and high performance.
Available uint types are uint128_t, uint256_t, uint512_t, uint1024_t and uint2048_t.
All uint types are stored on stack memory by default for the best performance.

Examples ( 4/4 factorial examples from 300! to 100,000! )

1. Calculate 300 factorial using uint2048.

#include "BigInt.h"


int main() {

    BigInt bigint = BigIntModule();

    uint2048_t a = bigint.u2048_from_string("01", 2); // Declare a uint2048 variable initialized to value 1.
    unsigned int N = 300;

    while (N > 1) {
        bigint.multiply_by_n(&a, N, &a, a.type); // bigint.multiply_by_n() method to multiply bigint types with unsigned 32 bit integers.
        N -= 1;
    }
    
    // bigint.print( &bigint_num, truncate_leading_zeros, bigint_num_type);
    bigint.print(&a, true, a.type); // prints the result in hexadecimal (base10 print format yet to be implemented).

    return 0;
}

Output:

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

2. Calculate 536 factorial using 2 uint2048 variables.

#include "BigInt.h"


int main() {

    BigInt bigint = BigIntModule();

    uint2048_t a = bigint.u2048_from_string("01", 2);
    uint2048_t b = bigint.u2048(); // using 2 uint2048 as digits to represent one 4096 bit int as 2 digit uint2048 ints.
    unsigned int N = 536;
    unsigned int carry_a = 0;
    unsigned int carry_b = 0;

    while (N > 1) {
        carry_a = bigint.multiply_by_n(&a, N, &a, a.type); // same as { ba x N } where ba is nothing but one 4096 bit int represented as 2 2048 bit int digits. 
        carry_b = bigint.multiply_by_n(&b, N, &b, b.type); // eg: 98 x 2 .. where 9 and 8 can be thought of as uint2048 ints and 2 as an unsigned 32 bit int.
        bigint.add_by_n(&b, carry_a, &b, b.type); 
        if (carry_b > 0) {
            printf("overflow\n");
        }
        N -= 1;
    }
    // bigint.print(&num, truncate_leading_zeros, num.type)
    bigint.print(&b, true, b.type); // b is MSB and a is LSB. Truncate leading zeros.
    bigint.print(&a, false, a.type); // do not truncate leading zeros.

    return 0;
}

Output:

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

3. Calculate 1000 factorial using 5 uint2048 variables.

#include "BigInt.h"


int main() {

    BigInt bigint = BigIntModule();
    
    // An uint2048 array of length 5.
    uint2048_t a_large_num[5]; // a (5 * 2048 = 10,240) bit integer represented as 5 2048 bit int digits.
    
    a_large_num[4] = bigint.u2048_from_string("01", 2); // Initialize the least significant digit as 1.
    for (int i = 3; i > -1; i--) {
        a_large_num[i] = bigint.u2048(); // Initialize the rest of the digits as zeros.
    }

    unsigned int N = 1000;
    unsigned int carry_a = 0;
    unsigned int carry_b = 0;

    while (N > 1) {
        //                                                                                                       1223 (carry) 
        // Below is same as arithmetic multiplication using carrys for a 5 digit number as 12345 x 6 = 74070 i.e 12345 (uint2048 [5]) x 6 (N)
        //                                                                                                       74070 (Result as in uint2048 [5])
        for (int i = 4; i > -1; i--) {
            carry_b = bigint.multiply_by_n(&a_large_num[i], N, &a_large_num[i], uint2048);
            bigint.add_by_n(&a_large_num[i], carry_a, &a_large_num[i], uint2048);
            carry_a = carry_b;
        }
        if (carry_a > 0) {
            printf("overflow \n");
        }
        N -= 1;
    }
    
    // Printing in reverse from the Most significant digit to Least significant digit.
    bigint.print(&a_large_num[0], true, uint2048); //bigint.print( big integer, truncate leading zeros, big integer type )
    for (int i = 1; i < 5; i++) { 
        bigint.print(&a_large_num[i], false, uint2048); 
    }
    return 0;
}

Output:

0002a2a773338969b740de6e2b291fd8dd6ee62a2b41525ab61cbe52489b6cf344c23231711b6d9f34e0f13a
b50eaf1ad3dd92771ec26b4b9ea80411c866b1ccbd855f8326edab10832755e1682d3e7a91335e3670329bc1571b5208d72f7d6be81483a6e6708abf913b789f41838e9a73c1ba82e3a956570405a660a17e1125838bc810c8d2c63915481914ea202867a563a41b6aefef5feac300a78803a30eb995208842ebeba8729397a8cd9087e28fb155a3de0f18dd90e64a9293af6487a5aabdab855fa254fcbdc9f1116060bc2e2b4410e55e7368b844d9bf0aeca92deb017def69af777e8d4edb1f1b926ae01df3366abb9e4568fc08fe255b68bca0e48382a8e6df1c7b0ba33bc2225cc512b39176a26b13098e733e51417224be36fbd933a8a7d98a08f356cf01
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

4. Calculate 100,000 factorial using 750 uint2048 variables.

Same as the previous code but by replacing the array size of 5 with 750. A massive ( 750 * 2048 ) bit integer.

#include "BigInt.h"


int main() {

    // (1) import the bigint module.
    BigInt bigint = BigIntModule();

    // (2) create an array of uint2048_t of size 750.
    uint2048_t a_large_num[750];

    // (3) set the least significant bit as 1 & initialize rest of the array with u2048 type.
    a_large_num[749] = bigint.u2048_from_string("01", 2);
    for (int i = 748; i > -1; i--) {
        a_large_num[i] = bigint.u2048();
    }

    // (4) N = 100,000.
    unsigned int N = 100000;
    unsigned int carry_a = 0;
    unsigned int carry_b = 0;
    unsigned int overflow = 0;

    // (5) perform [ bigint_array *= n ] for n from 1 to 100,000 ( Calculate factorial )
    while (N > 1) {
        for (int i = 749; i > -1; i--) {
            carry_b = bigint.multiply_by_n(&a_large_num[i], N, &a_large_num[i], uint2048);
            bigint.add_by_n(&a_large_num[i], carry_a, &a_large_num[i], uint2048);
            carry_a = carry_b;
        }
        N -= 1;
    }
    
    // (6) print the whole array ( result of 100,000 factorial )
    int i = 0;
    // manually truncate leading zeros.
    while (a_large_num[i].len == 1) {
        i += 1;
    }
    // truncate leading zeros in uint2048 for the first digit.
    bigint.print( &a_large_num[i], true, uint2048);
    for (i = i + 1; i < 750; i++) {
        // print rest of the digits without truncating leading zeros.
        bigint.print( &a_large_num[i], false, uint2048);
    }
    
    return 0;

}

Output:

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BigInt Documentation

1. Import the BigInt module :

#include "BigInt.h"

int main() {
  // Import the BigInt module as a "BigInt" variable inside main:
  BigInt bigint = BigIntModule();

  return 0;
}

This is to make sure all bigint functions are easily available under one wrapper.
This will provide better auto suggestions by IDEs and also will be easier to implement user defined custom functions.

2. To create a 128 bit unsigned integer initialized to zero by default use :

The `.u128( void )` method.

uint128_t a = bigint.u128();
uint128_t b = bigint.u128();

bigint.print(&a, a.type);
bigint.print(&b, b.type);

Here we are passing the bigints a and b as references only (ie &a and &b) instead of passing the whole varibales (ie a and b). (passing their addresses only instead of copying the whole variables into the function for better performance and memory management)

Output:

00000000
00000000

3. To create a 128 bit unsigend integer from a string use :

**The `.u128_from_string( char* str , int str_len )` method.**

uint128_t c = bigint.u128_from_string("9037208479874057835479", 22);
uint128_t d = bigint.u128_from_string("0x1e9e8762f43491d13d7", 21);
uint128_t e = bigint.u128_from_string("0b1111010011110100001110110001011110100001101001001000111010001001111010111", 75);

bigint.print(&c, uint128); // can also be written as "bigint.print(&c, c.type)".
bigint.print(&d, uint128); 
bigint.print(&e, e.type); // The e.type, c.type and d.type are nothing by uint128 enums.

The above method supports all three string formats: base10, hexadecimal ( must start with 0x ) and binary ( also must start with 0b ).

Output :

000001e9e8762f43491d13d7
000001e9e8762f43491d13d7
000001e9e8762f43491d13d7

4. To add two bigint integers use :

**The `.add( uint128_t* a, uint128_t* b, uint128_t* output, BigIntType type )` method.**

uint128_t output = bigint.u128();
uint32_t carry = bigint.add(&c, &d, &output, uint128); // OR can also be written as "bigint.add(&c, &d, &output, output.type)".

bigint.print(&output, output.type);

Output :

000003d3d0ec5e86923a27ae

Name		Name	Last commit message	Last commit date
Latest commit History 72 Commits
depreciated		depreciated
.gitattributes		.gitattributes
.gitignore		.gitignore
BigInt.c		BigInt.c
BigInt.h		BigInt.h
BigInt_b.c		BigInt_b.c
BigInt_b.h		BigInt_b.h
BigInt_c.c		BigInt_c.c
BigInt_c.h		BigInt_c.h
BigInt_cache.c		BigInt_cache.c
BigInt_cache.h		BigInt_cache.h
ByteQueue.c		ByteQueue.c
ByteQueue.h		ByteQueue.h
LICENSE		LICENSE
README.md		README.md
bigint_parser.c		bigint_parser.c
bigint_parser.h		bigint_parser.h
log_for_c.c		log_for_c.c
log_for_c.h		log_for_c.h
main.c		main.c
makefile		makefile
run.sh		run.sh
test.c		test.c
tests.c		tests.c
tests.h		tests.h
unittest.c		unittest.c
unittest.h		unittest.h
utils.c		utils.c
utils.h		utils.h

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A BigInt library in C

Examples ( 4/4 factorial examples from 300! to 100,000! )

1. Calculate 300 factorial using uint2048.

2. Calculate 536 factorial using 2 uint2048 variables.

3. Calculate 1000 factorial using 5 uint2048 variables.

4. Calculate 100,000 factorial using 750 uint2048 variables.

Same as the previous code but by replacing the array size of 5 with 750. A massive ( 750 * 2048 ) bit integer.

BigInt Documentation

1. Import the BigInt module :

2. To create a 128 bit unsigned integer initialized to zero by default use :

The .u128( void ) method.

3. To create a 128 bit unsigend integer from a string use :

The .u128_from_string( char* str , int str_len ) method.

4. To add two bigint integers use :

The .add( uint128_t* a, uint128_t* b, uint128_t* output, BigIntType type ) method.

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The `.u128( void )` method.

**The `.u128_from_string( char* str , int str_len )` method.**

**The `.add( uint128_t* a, uint128_t* b, uint128_t* output, BigIntType type )` method.**