Interface to the BigDigits "bd" functions using BIGD objects with automatic memory allocation. More...

Typedefs
typedef int(*	BD_RANDFUNC )(unsigned char buf, size_t nbytes, const unsigned char seed, size_t seedlen)
	TYPEDEF for user-defined random byte generator function. More...

typedef uint32_t	bdigit_t
	A synonym for a single digit (DIGIT_T is not exposed) More...

Functions
int	bdAdd (BIGD w, BIGD u, BIGD v)
	Compute sum w = u + v. More...

int	bdAdd_s (BIGD w, BIGD u, BIGD v)
	Compute w = u + v without restrictions on overlap of bdAdd() More...

void	bdAndBits (BIGD a, BIGD b, BIGD c)
	Computes bitwise operation a = b AND c. More...

size_t	bdBitLength (BIGD b)
	Returns number of significant bits in b. More...

int	bdCompare (BIGD a, BIGD b)
	Returns sign of `(a-b)` in `{0,1,-1}` More...

int	bdCompare_ct (BIGD a, BIGD b)
	Returns sign of `(a-b)` as `{-1,0,+1}` using constant-time algorithm. More...

const char *	bdCompileTime (void)
	Returns a pointer to a static string containing the time of compilation. More...

size_t	bdConvFromDecimal (BIGD b, const char *s)
	Convert string of decimal characters into a BIGD object. More...

size_t	bdConvFromHex (BIGD b, const char *s)
	Convert string of hexadecimal characters into a BIGD object. More...

size_t	bdConvFromOctets (BIGD b, const unsigned char *octets, size_t nbytes)
	Converts a byte array into a BIGD object. More...

size_t	bdConvToDecimal (BIGD b, char *s, size_t smax)
	Convert BIGD object into a string of decimal characters. More...

size_t	bdConvToHex (BIGD b, char *s, size_t smax)
	Convert BIGD object into a string of hexadecimal characters. More...

size_t	bdConvToOctets (BIGD b, unsigned char *octets, size_t nbytes)
	Converts a BIGD into an array of bytes, in big-endian order. More...

int	bdCubeRoot (BIGD s, BIGD x)
	Computes integer cube root s = floor(cuberoot(x)) More...

int	bdDecrement (BIGD a)
	Sets a = a - 1. More...

int	bdDivide (BIGD q, BIGD r, BIGD u, BIGD v)
	Compute integer division of u by v such that u=qv+r. More...

int	bdDivide_s (BIGD q, BIGD r, BIGD u, BIGD v)
	Compute u div v without restrictions on overlap of bdDivide() More...

void	bdFree (BIGD *bd)
	Destroy BIGD object: zeroise contents and free allocated memory. More...

void	bdFreeVars (BIGD *pb1,...)
	Destroy a set of BIGD objects. More...

int	bdGcd (BIGD g, BIGD x, BIGD y)
	Computes g = gcd(x, y), the greatest common divisor of x and y. More...

int	bdGeneratePrime (BIGD a, size_t nbits, size_t ntests, const unsigned char *seed, size_t seedlen, BD_RANDFUNC RandFunc)
	Generate a prime number. More...

int	bdGetBit (BIGD a, size_t ibit)
	Returns value 1 or 0 of bit n of a (0..nbits-1) More...

int	bdIncrement (BIGD a)
	Sets a = a + 1. More...

int	bdIsEqual (BIGD a, BIGD b)
	Returns true (1) if a == b, else false (0) More...

int	bdIsEqual_ct (BIGD a, BIGD b)
	Returns true if a == b, else false, using constant-time algorithm. More...

int	bdIsEven (BIGD a)
	Returns true (1) if a is even, else false (0) More...

int	bdIsOdd (BIGD a)
	Returns true (1) if a is odd, else false (0) More...

int	bdIsPrime (BIGD b, size_t ntests)
	Returns true (1) if `b` is probably prime. More...

int	bdIsZero (BIGD a)
	Returns true (1) if a is zero, else false (0) More...

int	bdIsZero_ct (BIGD a)
	Returns true if a is zero, else false, using constant-time algorithm. More...

int	bdJacobi (BIGD a, BIGD n)
	Returns the Jacobi symbol (a/n) = {-1, 0, +1}. More...

void	bdModAdd (BIGD w, BIGD u, BIGD v, BIGD m)
	Computes w = u + v (mod m) More...

int	bdModExp (BIGD y, BIGD x, BIGD e, BIGD m)
	Computes y = x^e mod m. More...

int	bdModExp_ct (BIGD y, BIGD x, BIGD e, BIGD m)
	Computes y = x^e mod m in constant time. More...

void	bdModHalve (BIGD w, const BIGD u, const BIGD p)
	Computes w = u/2 (mod p) for an odd prime p. More...

int	bdModInv (BIGD x, BIGD a, BIGD m)
	Computes the inverse of `a` modulo `m`, `x = a^{-1} mod m` More...

int	bdModMult (BIGD a, BIGD x, BIGD y, BIGD m)
	Computes a = (x * y) mod m. More...

void	bdModPowerOf2 (BIGD a, size_t L)
	Computes a = a mod 2^L, ie clears all bits greater than L. More...

int	bdModSqrt (BIGD x, BIGD a, BIGD p)
	Computes x = one square root of an integer `a` modulo an odd prime `p` More...

int	bdModSquare (BIGD a, BIGD x, BIGD m)
	Computes a = x^2 mod m. More...

void	bdModSub (BIGD w, BIGD u, BIGD v, BIGD m)
	Computes w = u - v (mod m) More...

int	bdModulo (BIGD r, BIGD u, BIGD v)
	Compute remainder r = u mod v. More...

int	bdModulo_s (BIGD r, BIGD u, BIGD v)
	Compute u mod v without restrictions on overlap of bdModulo() More...

int	bdMultiply (BIGD w, BIGD u, BIGD v)
	Compute product w = u * v. More...

int	bdMultiply_s (BIGD w, BIGD u, BIGD v)
	Compute w = u * v without restrictions on overlap of bdMultiply() More...

BIGD	bdNew (void)
	Create new BIGD object. More...

void	bdNewVars (BIGD *pb1,...)
	Create a set of BIGD objects. More...

void	bdNotBits (BIGD a, BIGD b)
	Computes bitwise a = NOT b. More...

void	bdOrBits (BIGD a, BIGD b, BIGD c)
	Computes bitwise operation a = b OR c. More...

int	bdPower (BIGD y, BIGD g, unsigned short int n)
	Computes y = g^n (up to available memory!) More...

void	bdPrint (BIGD b, size_t flags)
	Print b in hex format to stdout. More...

void	bdPrintBits (const char prefix, BIGD b, const char suffix)
	Print b in bit (0/1) format with optional prefix and suffix strings. More...

void	bdPrintDecimal (const char prefix, BIGD b, const char suffix)
	Print b in decimal format with optional prefix and suffix strings. More...

void	bdPrintHex (const char prefix, BIGD b, const char suffix)
	Print b in hex format with optional prefix and suffix strings. More...

size_t	bdQuickRandBits (BIGD a, size_t nbits)
	Generate a quick-and-dirty random number a of bit length at most `nbits` using plain-old-rand. More...

int	bdRabinMiller (BIGD b, size_t ntests)
	Returns true (1) if `b` is probably prime using just the Rabin-Miller test. More...

int	bdRandomSeeded (BIGD a, size_t nbits, const unsigned char *seed, size_t seedlen, BD_RANDFUNC RandFunc)
	Generate a random number nbits long using RandFunc. More...

int	bdSetBit (BIGD a, size_t n, int value)
	Set bit n of a (0..nbits-1) with value 1 or 0. More...

int	bdSetEqual (BIGD a, BIGD b)
	Sets a = b. More...

size_t	bdSetRandTest (BIGD a, size_t ndigits)
	Set a with a "random" value of random length up to ndigits long suitable for quick tests. More...

int	bdSetShort (BIGD b, bdigit_t d)
	Converts a single digit into a BIGD. More...

int	bdSetZero (BIGD a)
	Sets a = 0. More...

void	bdShiftLeft (BIGD a, BIGD b, size_t n)
	Computes a = b << n. More...

void	bdShiftRight (BIGD a, BIGD b, size_t n)
	Computes a = b >> n. More...

int	bdShortAdd (BIGD w, BIGD u, bdigit_t d)
	Computes w = u + d where d is a single digit. More...

int	bdShortCmp (BIGD a, bdigit_t d)
	Returns sign of (a-d) where d is a single digit. More...

int	bdShortDiv (BIGD q, BIGD r, BIGD u, bdigit_t d)
	Computes integer division of u by single digit d. More...

int	bdShortIsEqual (BIGD a, bdigit_t d)
	Returns true if a == d, else false, where d is a single digit. More...

bdigit_t	bdShortMod (BIGD r, BIGD u, bdigit_t d)
	Computes r = u mod d where d is a single digit. More...

int	bdShortMult (BIGD w, BIGD u, bdigit_t d)
	Computes w = u * d where d is a single digit. More...

int	bdShortSub (BIGD w, BIGD u, bdigit_t d)
	Computes w = u - d where d is a single digit. More...

size_t	bdSizeof (BIGD b)
	Returns number of significant digits in b. More...

int	bdSqrt (BIGD s, BIGD x)
	Computes integer square root s = floor(sqrt(x)) More...

int	bdSquare (BIGD w, BIGD x)
	Compute square w = x^2. More...

int	bdSquare_s (BIGD s, BIGD x)
	Compute s = x * x without restrictions on overlap of bdSquare() More...

int	bdSubtract (BIGD w, BIGD u, BIGD v)
	Compute difference w = u - v. More...

int	bdSubtract_s (BIGD w, BIGD u, BIGD v)
	Compute w = u - v without restrictions on overlap of bdSubtract() More...

bdigit_t	bdToShort (BIGD b)
	Returns the least significant digit in b. More...

int	bdVersion (void)
	Returns version number = major1000+minor100+release*10+PP_OPTIONS. More...

void	bdXorBits (BIGD a, BIGD b, BIGD c)
	Computes bitwise operation a = b XOR c. More...

Detailed Description

Interface to the BigDigits "bd" functions using BIGD objects with automatic memory allocation.

PROGRAMMER'S NOTES: Where the function computes a new BIGD value, the result is returned in the first argument. Some functions do not allow variables to overlap. Functions of type int generally return 0 to denote success but some return True/False (1/0) or borrow (+1) or error (-1). Functions of type size_t (an unsigned int) return a length.

Memory allocation: Memory for each variable is allocated as required and is increased automatically if needed. However, memory for a variable is only released when freed with bdFree(). The standard code for a variable b should be as follows:
BIGD b;

b = bdNew();

// operations using b...

bdFree(&b);

Typedef Documentation

typedef int(* BD_RANDFUNC)(unsigned char *buf, size_t nbytes, const unsigned char *seed, size_t seedlen)

TYPEDEF for user-defined random byte generator function.

typedef uint32_t bdigit_t

A synonym for a single digit (DIGIT_T is not exposed)

Function Documentation

int bdAdd	(	BIGD	w,
		BIGD	u,
		BIGD	v
	)

Compute sum w = u + v.

Returns: carry

Remarks: w and v must be separate variables. Use bdAdd_s() to avoid overlap restriction.

int bdAdd_s	(	BIGD	w,
		BIGD	u,
		BIGD	v
	)

Compute w = u + v without restrictions on overlap of bdAdd()

void bdAndBits	(	BIGD	a,
		BIGD	b,
		BIGD	c
	)

Computes bitwise operation a = b AND c.

size_t bdBitLength ( BIGD b )

Returns number of significant bits in b.

int bdCompare	(	BIGD	a,
		BIGD	b
	)

Returns sign of (a-b) in {0,1,-1}

Remarks: Not constant-time

int bdCompare_ct	(	BIGD	a,
		BIGD	b
	)

Returns sign of (a-b) as {-1,0,+1} using constant-time algorithm.

const char* bdCompileTime ( void )

Returns a pointer to a static string containing the time of compilation.

size_t bdConvFromDecimal	(	BIGD	b,
		const char *	s
	)

Convert string of decimal characters into a BIGD object.

Parameters

[out]	b	To receive the result
[in]	s	Null-terminated string of decimal digits `[0-9]`

Returns: Number of significant digits actually set, which could be 0.

size_t bdConvFromHex	(	BIGD	b,
		const char *	s
	)

Convert string of hexadecimal characters into a BIGD object.

Parameters

[out]	b	To receive the result
[in]	s	Null-terminated string of hex digits `[0-9A-Fa-f]`

Returns: Number of significant digits actually set, which could be 0.

size_t bdConvFromOctets	(	BIGD	b,
		const unsigned char *	octets,
		size_t	nbytes
	)

Converts a byte array into a BIGD object.

Parameters

[out]	b	To receive the result
[in]	octets	Pointer to array of bytes (octets)
[in]	nbytes	Number of bytes in sequence

Returns: Number of digits actually set, which may be larger than bdSizeof(BIGD b).

size_t bdConvToDecimal	(	BIGD	b,
		char *	s,
		size_t	smax
	)

Convert BIGD object into a string of decimal characters.

Parameters

[in]	b	BIGD object to be converted
[out]	s	String buffer to receive output
[in]	smax	Size of buffer including the terminating zero

Returns: Exact number of characters required excluding the terminating zero. If s is NULL or smax is zero then just returns required number.
char *s;

size_t nchars = bdConvToDecimal(b, NULL, 0);

s = malloc(nchars+1); // NB add one extra

nchars = bdConvToDecimal(b, s, nchars+1);

Remarks: Always returns the length of the string it tried to create, even if the actual output was truncated, so remember to check.

size_t bdConvToHex	(	BIGD	b,
		char *	s,
		size_t	smax
	)

Convert BIGD object into a string of hexadecimal characters.

Parameters

[in]	b	BIGD object to be converted
[out]	s	String buffer to receive output
[in]	smax	Size of buffer including the terminating zero

Returns: Exact number of characters required excluding the terminating zero. If s is NULL or smax is zero then just returns required number.
char *s;

size_t nchars = bdConvToHex(b, NULL, 0);

s = malloc(nchars+1); // NB add one extra

nchars = bdConvToHex(b, s, nchars+1);

Remarks: Always returns the length of the string it tried to create, even if the actual output was truncated, so remember to check.

size_t bdConvToOctets	(	BIGD	b,
		unsigned char *	octets,
		size_t	nbytes
	)

Converts a BIGD into an array of bytes, in big-endian order.

Parameters

[in]	b	BIGD object to be converted
[out]	octets	Array of bytes (octets) to receive output
[in]	nbytes	Length of array to receive output

Returns: Exact number of significant bytes in the result. If octets is NULL or nbytes is zero then just returns required size (nsig).

Remarks

Will pad on the left with zeros if nbytes is larger than required, or will truncate from the left if it is too short.

if nbytes = nsig, octets <– mmmnnn;
if nbytes > nsig, octets <– 000mmmnnn;
if nbytes < nsig, octets <– nnn.

int bdCubeRoot	(	BIGD	s,
		BIGD	x
	)

Computes integer cube root s = floor(cuberoot(x))

int bdDecrement ( BIGD a )

Sets a = a - 1.

Returns: borrow

Warning: Behaviour is undefined if a becomes negative.

int bdDivide	(	BIGD	q,
		BIGD	r,
		BIGD	u,
		BIGD	v
	)

Compute integer division of u by v such that u=qv+r.

Parameters

[out]	q	To receive quotient = u div v
[out]	r	To receive remainder = u mod v
[in]	u	Dividend
[in]	v	Divisor

Remarks: Trashes q and r first: q and r must be independent of u and v. Use bdDivide_s() to avoid overlap restriction.

int bdDivide_s	(	BIGD	q,
		BIGD	r,
		BIGD	u,
		BIGD	v
	)

Compute u div v without restrictions on overlap of bdDivide()

void bdFree ( BIGD * bd )

Destroy BIGD object: zeroise contents and free allocated memory.

Remarks: Pass a pointer to the handle

void bdFreeVars	(	BIGD *	pb1,
			...
	)

Destroy a set of BIGD objects.

BIGD a, b, c;
bdNewVars(&a, &b, &c, NULL);
// do stuff with variables a, b, c...
bdFreeVars(&a, &b, &c, NULL);

The bdFreeVars function call above is equivalent to

bdFree(&a);
bdFree(&b);
bdFree(&c);

Warning: The list must finish with NULL

int bdGcd	(	BIGD	g,
		BIGD	x,
		BIGD	y
	)

Computes g = gcd(x, y), the greatest common divisor of x and y.

int bdGeneratePrime	(	BIGD	a,
		size_t	nbits,
		size_t	ntests,
		const unsigned char *	seed,
		size_t	seedlen,
		BD_RANDFUNC	RandFunc
	)

Generate a prime number.

Parameters

[out]	a	To receive the result
[in]	nbits	Maximum number of bits in number
[in]	ntests	Number of primality tests to carry out (recommended at least 80)
[in]	seed	Optional seed to add extra entropy
[in]	seedlen	Number of bytes in seed
[in]	RandFunc	User function to generate random bytes

int bdGetBit	(	BIGD	a,
		size_t	ibit
	)

Returns value 1 or 0 of bit n of a (0..nbits-1)

int bdIncrement ( BIGD a )

Sets a = a + 1.

Returns: carry

int bdIsEqual	(	BIGD	a,
		BIGD	b
	)

Returns true (1) if a == b, else false (0)

Remarks: Not constant-time

int bdIsEqual_ct	(	BIGD	a,
		BIGD	b
	)

Returns true if a == b, else false, using constant-time algorithm.

int bdIsEven ( BIGD a )

Returns true (1) if a is even, else false (0)

int bdIsOdd ( BIGD a )

Returns true (1) if a is odd, else false (0)

int bdIsPrime	(	BIGD	b,
		size_t	ntests
	)

Returns true (1) if b is probably prime.

Parameters

[in]	b	Number to test
[in]	ntests	The count of Rabin-Miller primality tests to carry out (recommended at least 80)

Returns: true (1) if b is probably prime otherwise false (0)

Remarks: Uses FIPS-186-2/Rabin-Miller with trial division by small primes, which is faster in most cases than bdRabinMiller().

See Also: bdRabinMiller().

int bdIsZero ( BIGD a )

Returns true (1) if a is zero, else false (0)

Remarks: Not constant-time

int bdIsZero_ct ( BIGD a )

Returns true if a is zero, else false, using constant-time algorithm.

int bdJacobi	(	BIGD	a,
		BIGD	n
	)

Returns the Jacobi symbol (a/n) = {-1, 0, +1}.

Remarks

If n is prime then the Jacobi symbol becomes the Legendre symbol (a/p) defined to be

(a/p) = +1 if a is a quadratic residue modulo p
(a/p) = -1 if a is a quadratic non-residue modulo p
(a/p) = 0 if a is divisible by p

void bdModAdd	(	BIGD	w,
		BIGD	u,
		BIGD	v,
		BIGD	m
	)

Computes w = u + v (mod m)

Precondition: Require u and v to be in the range [0, m-1]. The variables w and v must not overlap.

Remarks: Quicker than adding then using mpModulo()

int bdModExp	(	BIGD	y,
		BIGD	x,
		BIGD	e,
		BIGD	m
	)

Computes y = x^e mod m.

int bdModExp_ct	(	BIGD	y,
		BIGD	x,
		BIGD	e,
		BIGD	m
	)

Computes y = x^e mod m in constant time.

Remarks: Resistant to simple power analysis attack on private exponent. Slower than bdModExp().

void bdModHalve	(	BIGD	w,
		const BIGD	u,
		const BIGD	p
	)

Computes w = u/2 (mod p) for an odd prime p.

Precondition: Require u to be in the range [0,p-1]

int bdModInv	(	BIGD	x,
		BIGD	a,
		BIGD	m
	)

Computes the inverse of a modulo m, x = a^{-1} mod m

int bdModMult	(	BIGD	a,
		BIGD	x,
		BIGD	y,
		BIGD	m
	)

Computes a = (x * y) mod m.

void bdModPowerOf2	(	BIGD	a,
		size_t	L
	)

Computes a = a mod 2^L, ie clears all bits greater than L.

int bdModSqrt	(	BIGD	x,
		BIGD	a,
		BIGD	p
	)

Computes x = one square root of an integer a modulo an odd prime p

Parameters

x	To receive the result
a	An integer expected to be a quadratic residue modulo p
p	An odd prime

Returns: 0 if successful, or -1 if square root does not exist

Remarks: More precisely, find an integer x such that x^2 mod p = a. Uses the Tonelli-Shanks algorithm. The other square root is p - x.

Warning: Check the return value before using the result x.

int bdModSquare	(	BIGD	a,
		BIGD	x,
		BIGD	m
	)

Computes a = x^2 mod m.

void bdModSub	(	BIGD	w,
		BIGD	u,
		BIGD	v,
		BIGD	m
	)

Computes w = u - v (mod m)

Precondition: Require u and v to be in the range [0, m-1]. The variables w and v must not overlap.

Remarks: Quicker than subtracting then using mpModulo()

int bdModulo	(	BIGD	r,
		BIGD	u,
		BIGD	v
	)

Compute remainder r = u mod v.

Remarks: r and u must be separate variables. Use bdModulo_s() to avoid overlap restriction.

int bdModulo_s	(	BIGD	r,
		BIGD	u,
		BIGD	v
	)

Compute u mod v without restrictions on overlap of bdModulo()

int bdMultiply	(	BIGD	w,
		BIGD	u,
		BIGD	v
	)

Compute product w = u * v.

Remarks: w and u must be separate variables. Use bdMultiply_s() to avoid overlap restriction.

int bdMultiply_s	(	BIGD	w,
		BIGD	u,
		BIGD	v
	)

Compute w = u * v without restrictions on overlap of bdMultiply()

BIGD bdNew ( void )

Create new BIGD object.

Returns: Handle to new object

void bdNewVars	(	BIGD *	pb1,
			...
	)

Create a set of BIGD objects.

BIGD a, b, c;
bdNewVars(&a, &b, &c, NULL);
// do stuff with variables a, b, c...
bdFreeVars(&a, &b, &c, NULL);

The bdNewVars function call above is equivalent to

a = bdNew();
b = bdNew();
c = bdNew();

Warning: The list must finish with NULL

void bdNotBits	(	BIGD	a,
		BIGD	b
	)

Computes bitwise a = NOT b.

Remarks: This flips all the bits up to the most significant digit, which may not be exactly what you want.

void bdOrBits	(	BIGD	a,
		BIGD	b,
		BIGD	c
	)

Computes bitwise operation a = b OR c.

int bdPower	(	BIGD	y,
		BIGD	g,
		unsigned short int	n
	)

Computes y = g^n (up to available memory!)

Remarks: Be very careful that n is not too large

void bdPrint	(	BIGD	b,
		size_t	flags
	)

Print b in hex format to stdout.

Parameters

[in]	b	Number to print
[in]	flags	(see below)

Remarks

Flags are

0 default display leading zeros but no newline
BD_PRINT_NL 0x1 append a newline after printing
BD_PRINT_TRIM 0x2 trim leading zero digits

Deprecated:: Use bdPrintHex() or bdPrintDecimal().

void bdPrintBits	(	const char *	prefix,
		BIGD	b,
		const char *	suffix
	)

Print b in bit (0/1) format with optional prefix and suffix strings.

void bdPrintDecimal	(	const char *	prefix,
		BIGD	b,
		const char *	suffix
	)

Print b in decimal format with optional prefix and suffix strings.

void bdPrintHex	(	const char *	prefix,
		BIGD	b,
		const char *	suffix
	)

Print b in hex format with optional prefix and suffix strings.

size_t bdQuickRandBits	(	BIGD	a,
		size_t	nbits
	)

Generate a quick-and-dirty random number a of bit length at most nbits using plain-old-rand.

Returns: Number of digits actually set

Remarks: Not crypto secure. May give same value on repeated calls.

See Also: bdRandomBits() or bdRandomSeeded().

int bdRabinMiller	(	BIGD	b,
		size_t	ntests
	)

Returns true (1) if b is probably prime using just the Rabin-Miller test.

Parameters

[in]	b	Number to test (b > 2)
[in]	ntests	The count of Rabin-Miller primality tests to carry out (recommended at least 80)

Returns: true (1) if b is probably prime otherwise false (0)

Remarks: bdIsPrime() is the recommended function to test for primality. Use this variant if, for some reason, you do not want to do the quicker trial division tests first.

See Also: bdIsPrime()

int bdRandomSeeded	(	BIGD	a,
		size_t	nbits,
		const unsigned char *	seed,
		size_t	seedlen,
		BD_RANDFUNC	RandFunc
	)

Generate a random number nbits long using RandFunc.

Parameters

[out]	a	To receive the result
[in]	nbits	Maximum number of bits in number
[in]	seed	Optional seed to add extra entropy
[in]	seedlen	Number of bytes in seed
[in]	RandFunc	User function to generate random bytes

int bdSetBit	(	BIGD	a,
		size_t	n,
		int	value
	)

Set bit n of a (0..nbits-1) with value 1 or 0.

int bdSetEqual	(	BIGD	a,
		BIGD	b
	)

Sets a = b.

size_t bdSetRandTest	(	BIGD	a,
		size_t	ndigits
	)

Set a with a "random" value of random length up to ndigits long suitable for quick tests.

Returns: Number of digits actually set

Remarks: For testing purposes only. Not crypto secure. Not thread safe.

int bdSetShort	(	BIGD	b,
		bdigit_t	d
	)

Converts a single digit into a BIGD.

Parameters

[out]	b	To receive the result
[in]	d	A single digit

Remarks: Use this to set a BIGD variable to a small integer.

int bdSetZero ( BIGD a )

Sets a = 0.

void bdShiftLeft	(	BIGD	a,
		BIGD	b,
		size_t	n
	)

Computes a = b << n.

void bdShiftRight	(	BIGD	a,
		BIGD	b,
		size_t	n
	)

Computes a = b >> n.

int bdShortAdd	(	BIGD	w,
		BIGD	u,
		bdigit_t	d
	)

Computes w = u + d where d is a single digit.

Returns: carry

int bdShortCmp	(	BIGD	a,
		bdigit_t	d
	)

Returns sign of (a-d) where d is a single digit.

int bdShortDiv	(	BIGD	q,
		BIGD	r,
		BIGD	u,
		bdigit_t	d
	)

Computes integer division of u by single digit d.

Parameters

[out]	q	To receive quotient = u div d
[out]	r	To receive remainder = u mod d
[in]	u	Dividend, a BIGD object
[in]	d	Divisor, a single digit

Remarks: A separate BIGD object r must be provided to receive the remainder.

int bdShortIsEqual	(	BIGD	a,
		bdigit_t	d
	)

Returns true if a == d, else false, where d is a single digit.

bdigit_t bdShortMod	(	BIGD	r,
		BIGD	u,
		bdigit_t	d
	)

Computes r = u mod d where d is a single digit.

int bdShortMult	(	BIGD	w,
		BIGD	u,
		bdigit_t	d
	)

Computes w = u * d where d is a single digit.

int bdShortSub	(	BIGD	w,
		BIGD	u,
		bdigit_t	d
	)

Computes w = u - d where d is a single digit.

Returns: borrow

size_t bdSizeof ( BIGD b )

Returns number of significant digits in b.

int bdSqrt	(	BIGD	s,
		BIGD	x
	)

Computes integer square root s = floor(sqrt(x))

int bdSquare	(	BIGD	w,
		BIGD	x
	)

Compute square w = x^2.

Remarks: w and x must be separate variables. Use bdSquare_s() to avoid overlap restriction.

int bdSquare_s	(	BIGD	s,
		BIGD	x
	)

Compute s = x * x without restrictions on overlap of bdSquare()

int bdSubtract	(	BIGD	w,
		BIGD	u,
		BIGD	v
	)

Compute difference w = u - v.

Returns: borrow

Remarks: w and v must be separate variables. Use bdSubtract_s() to avoid overlap restriction.

Warning: Behaviour is undefined for negative numbers.

int bdSubtract_s	(	BIGD	w,
		BIGD	u,
		BIGD	v
	)

Compute w = u - v without restrictions on overlap of bdSubtract()

bdigit_t bdToShort ( BIGD b )

Returns the least significant digit in b.

Returns: A single digit equal to the least significant digit in b

Remarks: Use this to convert (truncate) a BIGD object into a short integer

int bdVersion ( void )

Returns version number = major*1000+minor*100+release*10+PP_OPTIONS.

void bdXorBits	(	BIGD	a,
		BIGD	b,
		BIGD	c
	)

Computes bitwise operation a = b XOR c.

Typedefs

Functions

Detailed Description

Typedef Documentation

Function Documentation