Integral integer operations in constant time (CT), see also and meta-group Specific Mathematical Operations and Functionality. More...

Functions
template<typename T , std::enable_if_t< std::is_arithmetic_v< T > &&std::is_integral_v< T > &&!std::is_unsigned_v< T >, bool > = true>
constexpr T	jau::ct_abs (const T x) noexcept
	Returns the absolute value of an arithmetic number (w/o branching) in O(1) and constant time (CT), while ct_abs(INT_MIN) is undefined behavior (UB) instead of being mapped correctly to INT_MAX like jau::abs() does, see above. More...

constexpr uint32_t	jau::ct_bit_count (uint32_t n) noexcept
	Returns the number of set bits within given 32bit integer (w/o branching) in O(1) and constant time (CT). More...

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>
constexpr T	jau::ct_clamp (const T x, const T min_val, const T max_val) noexcept
	Returns constrained integral value to lie between given min- and maximum value for `MIN <= x - y <= MAX` (w/o branching) in O(1) and constant time (CT). More...

template<typename T , std::enable_if_t< std::is_integral_v< T > &&std::is_unsigned_v< T >, bool > = true>
constexpr T	jau::ct_expand_top_bit (T x)
	Returns ~0 (2-complement) if top bit of arg is set, otherwise 0 (w/o branching) in O(1) and constant time (CT). More...

template<typename T , std::enable_if_t< std::is_integral_v< T > &&std::is_unsigned_v< T >, bool > = true>
constexpr T	jau::ct_is_zero (T x)
	Returns ~0 (2-complement) if arg is zero, otherwise 0 (w/o branching) in O(1) and constant time (CT). More...

template<typename T , std::enable_if_t< std::is_integral_v< T > &&std::is_unsigned_v< T >, bool > = true>
constexpr T	jau::ct_masked_merge (T mask, T a_if_masked, T b_if_unmasked)
	Returns merged `a_if_masked` bits selected by `mask` `1` bits and `b_if_unmasked` bits selected by `mask` `0` bits (w/o branching) in O(1) and constant time (CT). More...

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>
constexpr T	jau::ct_max (const T x, const T y) noexcept
	Returns the maximum of two integrals for `MIN <= x - y <= MAX` (w/o branching) in O(1) and constant time (CT). More...

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>
constexpr T	jau::ct_min (const T x, const T y) noexcept
	Returns the minimum of two integrals for `MIN <= x - y <= MAX` (w/o branching) in O(1) and constant time (CT). More...

constexpr uint32_t	jau::ct_next_power_of_2 (uint32_t n)
	Returns the next higher power of 2 of given unsigned 32-bit `n` (w/o branching) in O(1) and constant time (CT). More...

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>
constexpr int	jau::ct_sign (const T x) noexcept
	Returns the value of the sign function (w/o branching) in O(1) and constant time (CT) More...

Detailed Description

Integral integer operations in constant time (CT), see also and meta-group Specific Mathematical Operations and Functionality.

Function Documentation

◆ ct_sign()

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>

constexpr int jau::ct_sign ( const T x )

constexprnoexcept

Returns the value of the sign function (w/o branching) in O(1) and constant time (CT)

-1 for x < 0
 0 for x = 0
 1 for x > 0

Implementation is type safe.

Branching may occur due to relational operator.

Template Parameters

T	an integral number type

Parameters

x	the number

Returns: function result

Definition at line 67 of file int_math_ct.hpp.

◆ ct_abs()

template<typename T , std::enable_if_t< std::is_arithmetic_v< T > &&std::is_integral_v< T > &&!std::is_unsigned_v< T >, bool > = true>

constexpr T jau::ct_abs ( const T x )

constexprnoexcept

Returns the absolute value of an arithmetic number (w/o branching) in O(1) and constant time (CT), while ct_abs(INT_MIN) is undefined behavior (UB) instead of being mapped correctly to INT_MAX like jau::abs() does, see above.

This implementation is equivalent to std::abs(), i.e. unsafe

signed integral uses 2-complement branch-less conversion, bithacks Integer-Abs
signed floating-point uses x * sign(x)
unsigned just returns the value

This implementation uses 2-complement branch-less conversion, bithacks Integer-Abs

Note: On an x86_64 architecture abs() w/ branching is of equal speed or even faster.

Template Parameters

T	an arithmetic number type

Parameters

x	the number

Returns: function result

Definition at line 95 of file int_math_ct.hpp.

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◆ ct_min()

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>

constexpr T jau::ct_min	(	const T	x,
		const T	y
	)

constexprnoexcept

Returns the minimum of two integrals for MIN <= x - y <= MAX (w/o branching) in O(1) and constant time (CT).

Source: bithacks Test IntegerMinOrMax

Note: On an x86_64 architecture min() w/ branching is of equal speed or even faster.

Template Parameters

T	an integral number type

Parameters

x	one number
x	the other number

Definition at line 133 of file int_math_ct.hpp.

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◆ ct_max()

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>

constexpr T jau::ct_max	(	const T	x,
		const T	y
	)

constexprnoexcept

Returns the maximum of two integrals for MIN <= x - y <= MAX (w/o branching) in O(1) and constant time (CT).

Source: bithacks Test IntegerMinOrMax

Note: On an x86_64 architecture max() w/ branching is of equal speed or even faster.

Template Parameters

T	an integral number type

Parameters

x	one number
x	the other number

Definition at line 151 of file int_math_ct.hpp.

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◆ ct_clamp()

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>

constexpr T jau::ct_clamp	(	const T	x,
		const T	min_val,
		const T	max_val
	)

constexprnoexcept

Returns constrained integral value to lie between given min- and maximum value for MIN <= x - y <= MAX (w/o branching) in O(1) and constant time (CT).

Implementation returns ct_min(ct_max(x, min_val), max_val), analog to GLSL's clamp()

Note: On an x86_64 architecture clamp() w/ branching is of equal speed or even faster.

Template Parameters

T	an integral number type

Parameters

x	one number
min_val	the minimum limes, inclusive
max_val	the maximum limes, inclusive

Definition at line 171 of file int_math_ct.hpp.

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◆ ct_masked_merge()

template<typename T , std::enable_if_t< std::is_integral_v< T > &&std::is_unsigned_v< T >, bool > = true>

constexpr T jau::ct_masked_merge	(	T	mask,
		T	a_if_masked,
		T	b_if_unmasked
	)

constexpr

Returns merged a_if_masked bits selected by mask 1 bits and b_if_unmasked bits selected by mask 0 bits (w/o branching) in O(1) and constant time (CT).

Source: bithacks MaskedMerge

Template Parameters

T	an unsigned integral number type

Parameters

mask	1 where bits from `a_if_masked` should be selected; 0 where from `b_if_unmasked`.
a_if_masked	value to merge in masked bits
b_if_unmasked	value to merge in non-masked bits

Definition at line 189 of file int_math_ct.hpp.

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◆ ct_next_power_of_2()

constexpr uint32_t jau::ct_next_power_of_2 ( uint32_t n )

constexpr

Returns the next higher power of 2 of given unsigned 32-bit n (w/o branching) in O(1) and constant time (CT).

Source: bithacks RoundUpPowerOf2

Definition at line 200 of file int_math_ct.hpp.

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◆ ct_bit_count()

constexpr uint32_t jau::ct_bit_count ( uint32_t n )

constexprnoexcept

Returns the number of set bits within given 32bit integer (w/o branching) in O(1) and constant time (CT).

Uses a HAKEM 169 Bit Count inspired implementation:

  http://www.inwap.com/pdp10/hbaker/hakmem/hakmem.html
  http://home.pipeline.com/~hbaker1/hakmem/hacks.html#item169
  http://tekpool.wordpress.com/category/bit-count/
  https://github.com/aistrate/HackersDelight/blob/master/Original/HDcode/pop.c.txt
  https://github.com/aistrate/HackersDelight/blob/master/Original/HDcode/newCode/popDiff.c.txt

Definition at line 223 of file int_math_ct.hpp.

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◆ ct_expand_top_bit()

template<typename T , std::enable_if_t< std::is_integral_v< T > &&std::is_unsigned_v< T >, bool > = true>

constexpr T jau::ct_expand_top_bit ( T x )

inlineconstexpr

Returns ~0 (2-complement) if top bit of arg is set, otherwise 0 (w/o branching) in O(1) and constant time (CT).

Template Parameters

T	an unsigned integral number type

Definition at line 252 of file int_math_ct.hpp.

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◆ ct_is_zero()

template<typename T , std::enable_if_t< std::is_integral_v< T > &&std::is_unsigned_v< T >, bool > = true>

constexpr T jau::ct_is_zero ( T x )

inlineconstexpr

Returns ~0 (2-complement) if arg is zero, otherwise 0 (w/o branching) in O(1) and constant time (CT).

Template Parameters

T	an unsigned integral number type

Definition at line 265 of file int_math_ct.hpp.

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Functions

Detailed Description

Function Documentation

◆ ct_sign()

◆ ct_abs()

◆ ct_min()

◆ ct_max()

◆ ct_clamp()

◆ ct_masked_merge()

◆ ct_next_power_of_2()

◆ ct_bit_count()

◆ ct_expand_top_bit()

◆ ct_is_zero()