libskarnet
skalibs
Software
www.skarnet.org

The biguint library interface

biguint is set of simple primitives performing arithmetical operations on (unsigned) integers of arbitrary length. It is nowhere near as powerful or efficient as specialized, assembly language-optimized libraries such as GMP, but it has the advantages of smallness and simplicity.

Compiling

Programming

You should refer to the skalibs/biguint.h header for the exact function prototypes.

Definitions

Basic operations

Creating a biguint

Just declare uint32_t x[n] ; - n being the length of the biguint. You could also allocate x in the heap, possibly using a uint32_t genalloc. In the following, a biguint is always referred to as a uint32_t * with its unsigned int length ; it must always be pre-allocated.

If an operation fails because a biguint's length n is too small to accommodate the result, the function will write the first (i.e. least significant) n limbs of the result, truncating it, then return 0 with errno set to EOVERFLOW.

Setting it to zero

uint32_t *x ;
unsigned int n ;

 bu_zero(x, n) ;

bu_zero() sets the first n limbs of x to zero.

Copying a biguint

uint32_t const *x ;
unsigned int xn ;
uint32_t *y ;
unsigned int yn ;

  bu_copy(y, yn, x, xn) ;

bu_copy() copies x to y, setting higher limbs of y to zero if needed. It then returns 1. If y is too small to contain x, the function returns 0 EOVERFLOW.

Calculating the order

uint32_t const *x ;
unsigned int n ;
unsigned int r ;

  r = bu_len(x, n) ;

bu_len() outputs the order of x of length n. 0 <= r <= n.

Comparing two biguints

uint32_t const *a ;
unsigned int an ;
uint32_t const *b ;
unsigned int bn ;
int r ;

  r = bu_cmp(a, an, b, bn) ;

bu_cmp() returns -1 if a < b, 1 if a > b, and 0 if a = b.

I/O operations

Writing a biguint as an array of bytes

char *s ;
uint32_t const *x ;
unsigned int n ;

  bu_pack(s, x, n) ;
  bu_pack_big(s, x, n) ;

bu_pack() writes 4*n bytes to s. The bytes are a little-endian representation of x.
bu_pack_big() is the same, with a big-endian representation.

Reading a biguint from an array of bytes

char const *s ;
uint32_t *x ;
unsigned int n ;

  bu_unpack(s, x, n) ;
  bu_unpack_big(s, x, n) ;

bu_unpack() reads 4*n little-endian bytes from s and writes them into the corresponding biguint x.
bu_unpack_big() is the same, but the bytes are interpreted as big-endian.

Formatting a biguint for readable output

char *s ;
uint32_t const *x ;
unsigned int n ;

  bu_fmt(s, x, n) ;

bu_fmt() writes x in s as a standard big-endian hexadecimal number. x is considered of length n, so 8*n bytes will be written to s, even if it x starts with zeros. bu_fmt returns the number of bytes written.

Reading a biguint from readable format

char const *s ;
uint32_t *x ;
unsigned int xn ;
unsigned int z ;
unsigned int len ;

  len = bu_scanlen(s, &z) ;
  bu_scan(s, len, x, xn, z) ;

bu_scanlen() scans s for a biguint written as a hexadecimal number and returns the number of bytes read. The reading stops at the first byte encountered that is not in the 0-9, A-F or a-f range. The z integer then contains the number of bytes excluding leading zeros.

If x has not been allocated yet, you can use xn = bitarray_div8(z) (if you have included the bitarray.h header) and allocate x with length xn.

bu_scan() then reads len bytes from s, assuming there are z significant bytes (i.e. not leading zeros); it writes the resulting biguint into x of length xn. It returns 1, except if xn is too small, in which case it returns 0 EOVERFLOW.

Arithmetic operations

Addition

uint32_t const *a ;
unsigned int an ;
uint32_t const *b ;
unsigned int bn ;
uint32_t *c ;
unsigned int cn ;
unsigned char carrybefore ;
unsigned char carryafter ;

  bu_add(c, cn, a, an, b, bn) ;
  bu_sub(c, cn, a, an, b, bn) ;

bu_add() adds a and b, and puts the result into c. It returns 1 unless it has to truncate it.

bu_sub() substracts b from a, and puts the result into c. If the result should be negative, then it is written as (2^32)^cn - c and the function returns 0 EOVERFLOW.

Multiplication

uint32_t const *a ;
unsigned int an ;
uint32_t const *b ;
unsigned int bn ;
uint32_t *c ;
unsigned int cn ;

 bu_mul(c, cn, a, an, b, bn) ;

bu_mul() computes c=a*b. Make sure that cnbu_len(a, an) + bu_len(b, bn). If it is not the case, the result will be truncated and bu_mul will return 0 EOVERFLOW.

Division

uint32_t const *a ;
unsigned int an ;
uint32_t const *b ;
unsigned int bn ;
uint32_t *q ;
unsigned int qn ;
uint32_t *r ;
unsigned int rn ;

 bu_div(a, an, b, bn, q, qn, r, rn) ;
 bu_mod(r, rn, b, bn) ;

bu_div() computes q, the quotient, and r, the remainder, of a divided by b. If b is zero, it returns 0 EDOM. If qn or rn is to small to store the quotient or the remainder, it returns 0 EOVERFLOW. bu_mod() computes only the remainder, and stores it in-place.

GCD

uint32_t *r ;
unsigned int rn ;
uint32_t const *a ;
unsigned int an ;
uint32_t const *b ;
unsigned int bn ;

 bu_gcd(r, rn, a, an, b, bn) ;

bu_gcd() computes the greatest common divisor between a and b, and stores it into r. It returns 1 if all went well.

Note that this function iterates on divisions, so it might use a non totally negligible amount of CPU time.

Left-shifts and right-shifts

uint32_t *x ;
unsigned int xn ;
unsigned char carryafter ;
unsigned char carrybefore ;

 carryafter = bu_slbc(x, xn, carrybefore) ;
 carryafter = bu_srbc(x, xn, carrybefore) ;

bu_slbc() computes x <<= 1. The least significant bit of x is then set to carrybefore. bu_slbc() returns the previous value of x's most significant bit.
bu_srbc() computes x >>= 1. The most significant bit of x is then set to carrybefore. bu_slbc() returns the previous value of x's least significant bit.
bu_slb(x, n) and bu_srb(x, n) are macros for respectively bu_slbc(x, n, 0) and bu_srbc(x, n, 0).

Modular operations

uint32_t const *a ;
unsigned int an ;
uint32_t const *b ;
unsigned int bn ;
uint32_t *c ;
unsigned int cn ;
uint32_t const *m ;
unsigned int mn ;

 bu_addmod(c, cn, a, an, b, bn, m, mn) ;
 bu_submod(c, cn, a, an, b, bn, m, mn) ;
 bu_mulmod(c, cn, a, an, b, bn, m, mn) ;
 bu_divmod(c, cn, a, an, b, bn, m, mn) ;
 bu_invmod(c, cn, m, mn) ;

bu_addmod() computes c = (a+b) mod m.
bu_submod() computes c = (a-b) mod m.
bu_mulmod() computes c = (a*b) mod m.
a and b must already be numbers modulo m.
The functions return 1 if all went well.

bu_divmod() computes a divided by b modulo m and stores it into c.
bu_invmod() computes the inverse of c modulo m and stores it into c.
The divisor and m must be relatively prime, else those functions return 0 EDOM.