The functions that implement math operators using only BCD_int objects. More...

comp_t	BCD_int::cmp_bcd (const BCD_int x, const BCD_int y)
	Compare two BCD_ints. More...

BCD_int	BCD_int::sign_bcd (BCD_int x, const bool no_copy, const bool negative)
	Change the sign of a BCD_int without relying on internals. More...

BCD_int	BCD_int::abs_bcd (const BCD_int x, const bool no_copy)
	Get the absolute value of a BCD_int without relying on internals. More...

BCD_int	BCD_int::neg_bcd (const BCD_int x, const bool no_copy)
	Get the negative absolute value of a BCD_int without relying on internals. More...

BCD_int	BCD_int::opp_bcd (const BCD_int x, const bool no_copy)
	Get the opposite value of a BCD_int without relying on internals. More...

BCD_int	BCD_int::add_bcd (const BCD_int x, const BCD_int y)
	Add two BCD_ints. More...

BCD_int	BCD_int::inc_bcd (const BCD_int x)
	Increment a BCD_int. More...

BCD_int	BCD_int::sub_bcd (const BCD_int x, const BCD_int y)
	Subtract two BCD_ints. More...

BCD_int	BCD_int::dec_bcd (const BCD_int x)
	Decrement a BCD_int. More...

BCD_int	BCD_int::mul_bcd (const BCD_int x, const BCD_int y)
	Multiply two BCD_ints. More...

BCD_int	BCD_int::div_bcd (const BCD_int x, const BCD_int y)
	Divide two BCD_ints. More...

BCD_int	BCD_int::mod_bcd (const BCD_int x, const BCD_int y)
	Modulo divide two BCD_ints. More...

BCD_int	BCD_int::divmod_bcd (const BCD_int x, BCD_int y, BCD_int *mod)
	Divide and modulo divide two BCD_ints. More...

BCD_int	BCD_int::pow_bcd (const BCD_int x, const BCD_int y)
	Raise x to the power of y. More...

BCD_int	BCD_int::factorial_bcd (const BCD_int x)
	Get the factorial of x. More...

Detailed Description

The functions that implement math operators using only BCD_int objects.

operators

Function Documentation

BCD_int abs_bcd	(	const BCD_int	x,
		const bool	no_copy
	)

Get the absolute value of a BCD_int without relying on internals.

Parameters

[in]	x	The BCD_int in question
[in]	no_copy	If false, this function returns a modified copy of x instead of a modified version of x

Returns: Either a positive copy of x or a positive version of x

Remarks: This will take \(Θ(1)\) time if no_copy is true, and \(Θ(\log_{100}(x))\) if it is false.

Attention: All operators that return a BCD_int may return NaN with error set to NO_MEM (avoid with no_copy); All operators that return a BCD_int will return NaN if fed NaN, and set error to {OP}_NAN.

See also: sign_bcd

BCD_int add_bcd	(	const BCD_int	x,
		const BCD_int	y
	)

Add two BCD_ints.

Parameters

[in]	x	The left-hand BCD_int
[in]	y	The right-hand BCD_int

Returns: A BCD_int reflecting the sum of the arguments

Remarks: This will take \(O(\log_{100}(max(x, y)))\) time

Note: Implementation details:; This function works closely with sub_bcd. If absolute value would go down from this operation, it is handed off to that method.

Attention: All operators that return a BCD_int may return NaN with error set to NO_MEM; All operators that return a BCD_int will return NaN if fed NaN, and set error to {OP}_NAN.

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comp_t cmp_bcd	(	const BCD_int	x,
		const BCD_int	y
	)

Compare two BCD_ints.

Parameters

[in]	x	The left-hand BCD_int
[in]	y	The right-hand BCD_int

Returns: An comp_t reflecting the comparison

Return values

BCD_int dec_bcd ( const BCD_int x )

Decrement a BCD_int.

Parameters

[in] x The BCD_int to decrement

Returns: A BCD_int one less than x

Remarks: This will take \(Θ(\log_{100}(x))\) time

Attention: All operators that return a BCD_int may return NaN with error set to NO_MEM; All operators that return a BCD_int will return NaN if fed NaN, and set error to {OP}_NAN.

See also: sub_bcd

BCD_int div_bcd	(	const BCD_int	x,
		const BCD_int	y
	)

Divide two BCD_ints.

Parameters

[in]	x	The left-hand BCD_int
[in]	y	The right-hand BCD_int

Returns: A BCD_int reflecting the quotient of the arguments

Remarks

See also: divmod_bcd for a performance analysis

Attention: All operators that return a BCD_int may return NaN with error set to NO_MEM; All operators that return a BCD_int will return NaN if fed NaN, and set error to {OP}_NAN.; Returns NaN with error set to DIV_ZERO if y is 0

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BCD_int divmod_bcd	(	const BCD_int	x,
		BCD_int	y,
		BCD_int *	mod
	)

Divide and modulo divide two BCD_ints.

Parameters

[in]	x	The left-hand BCD_int
[in]	y	The right-hand BCD_int
[out]	mod	A pointer to the BCD_int you would like to store the remainder

Returns: A BCD_int reflecting the quotient of the arguments

Remarks

This function has three behaviors for performance analysis

If x or y is NaN, or y is 0, then it will take \(Θ(1)\) time
If y is 1, then it will take \(Θ(\log_{100}(x))\) time
Otherwise it will take \(O(\lceil\frac{x}{y}\rceil \cdot \log_{100}(x))\) time

Attention: All operators that return a BCD_int may return NaN with error set to NO_MEM; All operators that return a BCD_int will return NaN if fed NaN, and set error to {OP}_NAN.; Returns (and assigns to mod) NaN with error set to DIV_ZERO if y is 0

BCD_int factorial_bcd ( const BCD_int x )

Get the factorial of x.

Parameters

[in] x The BCD_int in question

Returns: A BCD_int reflecting the factorial of x

Remarks: This will take \(O(x \cdot \log_{100}(x!)^3)\) time if x is not BCD_nan and is non-negative. Otherwise it takes \(Θ(1)\) time.

Attention: All operators that return a BCD_int may return NaN with error set to NO_MEM; All operators that return a BCD_int will return NaN if fed NaN, and set error to {OP}_NAN.; Returns NaN with error set to FACT_NEG if x < 0

BCD_int inc_bcd ( const BCD_int x )

Increment a BCD_int.

Parameters

[in] x The BCD_int to increment

Returns: A BCD_int one greater than x

Remarks: This will take \(Θ(\log_{100}(x))\) time

Attention: All operators that return a BCD_int may return NaN with error set to NO_MEM; All operators that return a BCD_int will return NaN if fed NaN, and set error to {OP}_NAN.

See also: add_bcd

BCD_int mod_bcd	(	const BCD_int	x,
		const BCD_int	y
	)

Modulo divide two BCD_ints.

Parameters

[in]	x	The left-hand BCD_int
[in]	y	The right-hand BCD_int

Returns: A BCD_int reflecting the remainder of the arguments

Remarks

This function has two behaviors for performance analysis

If x or y is NaN, or y is either 0 or 1, then it will take \(Θ(1)\) time
Otherwise it will take \(O(\lceil\frac{x}{y}\rceil \cdot \log_{100}(x))\) time

Attention: All operators that return a BCD_int may return NaN with error set to NO_MEM; All operators that return a BCD_int will return NaN if fed NaN, and set error to {OP}_NAN.; Returns NaN with error set to DIV_ZERO if y is 0

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BCD_int mul_bcd	(	const BCD_int	x,
		const BCD_int	y
	)

Multiply two BCD_ints.

Parameters

[in]	x	The left-hand BCD_int
[in]	y	The right-hand BCD_int

Returns: A BCD_int reflecting the product of the arguments

Remarks: This will take \(Θ(\log_{100}(x) \cdot \log_{100}(y) \cdot \log{100}(xy))\) time if x and y are neither BCD_nan nor zero. Otherwise it takes \(Θ(1)\) time. For most purposes this can be simplified to \(O(\log_{100}^3(max(x, y)))\).

Attention: All operators that return a BCD_int may return NaN with error set to NO_MEM; All operators that return a BCD_int will return NaN if fed NaN, and set error to {OP}_NAN.

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BCD_int neg_bcd	(	const BCD_int	x,
		const bool	no_copy
	)

Get the negative absolute value of a BCD_int without relying on internals.

Parameters

[in]	x	The BCD_int in question
[in]	no_copy	If false, this function returns a modified copy of x instead of a modified version of x

Returns: Either a negative copy of x or a negative version of x

Remarks: This will take \(Θ(1)\) time if no_copy is true, and \(Θ(\log_{100}(x))\) if it is false.

Attention: All operators that return a BCD_int may return NaN with error set to NO_MEM (avoid with no_copy); All operators that return a BCD_int will return NaN if fed NaN, and set error to {OP}_NAN.

See also: sign_bcd

BCD_int opp_bcd	(	const BCD_int	x,
		const bool	no_copy
	)

Get the opposite value of a BCD_int without relying on internals.

Parameters

[in]	x	The BCD_int in question
[in]	no_copy	If false, this function returns a modified copy of x instead of a modified version of x

Returns: Either an opposite copy of x or an opposite version of x

Remarks: This will take \(Θ(1)\) time if no_copy is true, and \(Θ(\log_{100}(x))\) if it is false.

Attention: All operators that return a BCD_int may return NaN with error set to NO_MEM (avoid with no_copy); All operators that return a BCD_int will return NaN if fed NaN, and set error to {OP}_NAN.

See also: sign_bcd

BCD_int pow_bcd	(	const BCD_int	x,
		const BCD_int	y
	)

Raise x to the power of y.

Parameters

[in]	x	The left-hand BCD_int
[in]	y	The right-hand BCD_int

Returns: A BCD_int reflecting the yth power of x

Remarks: If x and y are BCD_nan or y is not positive, this takes \(Θ(1)\) time. Otherwise it takes \(O((y \cdot \log_100(x))^3)\) time.

Attention: All operators that return a BCD_int may return NaN with error set to NO_MEM; All operators that return a BCD_int will return NaN if fed NaN, and set error to {OP}_NAN.; Returns NaN with error set to POW_NEG if y < 0 or x = 0

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BCD_int sign_bcd	(	BCD_int	x,
		const bool	no_copy,
		const bool	negative
	)

Change the sign of a BCD_int without relying on internals.

Parameters

[in]	x	The BCD_int in question
[in]	no_copy	If false, this function returns a modified copy of x instead of a modified version of x
[in]	negative	The sign you would like to apply

Returns: Either a modified copy of x or a modified version of x

Remarks: This will take \(Θ(1)\) time if no_copy is true, and \(Θ(\log_{100}(x))\) if it is false.

Attention: All operators that return a BCD_int may return NaN with error set to NO_MEM (avoid with no_copy); All operators that return a BCD_int will return NaN if fed NaN, and set error to {OP}_NAN.

BCD_int sub_bcd	(	const BCD_int	x,
		const BCD_int	y
	)

Subtract two BCD_ints.

Parameters

[in]	x	The left-hand BCD_int
[in]	y	The right-hand BCD_int

Returns: A BCD_int reflecting the difference of the arguments

Remarks: This will take \(O(\log_{100}(max(x, y)))\) time

Note: Implementation details:; This function works closely with add_bcd. If absolute value would go up from this operation, it is handed off to that method.

Attention: All operators that return a BCD_int may return NaN with error set to NO_MEM; All operators that return a BCD_int will return NaN if fed NaN, and set error to {OP}_NAN.

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