float_math.hpp File Reference

#include <cmath>
#include <climits>
#include <type_traits>
#include <algorithm>
#include <jau/base_math.hpp>
#include <jau/string_util.hpp>

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Namespaces
namespace	jau
	__pack(...): Produces MSVC, clang and gcc compatible lead-in and -out macros.

Typedefs
typedef jau::uint_bytes< sizeof(double)>::type	jau::double_uint_t
typedef jau::uint_bytes< sizeof(float)>::type	jau::float_uint_t

Functions
template<typename T , std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr T	jau::adeg_to_rad (const T arc_degree) noexcept
	Converts arc-degree to radians. More...
template<class T >
std::enable_if< std::is_floating_point_v< T >, bool >::type	jau::almost_equal (const T &a, const T &b, int ulp=1, const T &epsilon=std::numeric_limits< T >::epsilon()) noexcept
	Returns true, if both floating point values are equal in the sense that their potential difference is less or equal epsilon * |a+b| * ulp, where |a+b| scales epsilon to the magnitude of used values. More...
constexpr uint64_t	jau::bit_value (const double a) noexcept
	Returns the unsigned integer representation according to IEEE 754 (IEC 559) double floating-point bit layout. More...
constexpr uint32_t	jau::bit_value (const float a) noexcept
	Returns the unsigned integer representation according to IEEE 754 (IEC 559) single floating-point bit layout. More...
constexpr uint64_t	jau::bit_value_raw (const double a) noexcept
	Returns the unsigned integer representation according to IEEE 754 (IEC 559) double floating-point bit layout. More...
constexpr uint32_t	jau::bit_value_raw (const float a) noexcept
	Returns the unsigned integer representation according to IEEE 754 (IEC 559) single floating-point bit layout. More...
template<class T , std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
jau::uint_bytes< sizeof(T)>::type	jau::bit_value_raw (const T a) noexcept
	Returns the unsigned integer representation according to IEEE 754 (IEC 559) floating-point bit layout. More...
template<class T , std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr int	jau::compare (const T a, const T b) noexcept
	Returns -1, 0 or 1 if a is less, equal or greater than b, disregarding epsilon but considering NaN, -Inf and +Inf. More...
template<class T , std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr int	jau::compare (const T a, const T b, const T epsilon) noexcept
	Returns -1, 0 or 1 if a is less, equal or greater than b, considering epsilon and NaN, -Inf and +Inf. More...
constexpr double	jau::double_value (const uint64_t a) noexcept
	Converting IEEE 754 (IEC 559) double floating-point bit layout to double, see bit_value() More...
template<class T >
std::enable_if< std::is_floating_point_v< T >, bool >::type constexpr	jau::equals (const T &a, const T &b, const T &epsilon=std::numeric_limits< T >::epsilon()) noexcept
	Returns true if both values are equal, i.e. More...
template<class T >
std::enable_if< std::is_floating_point_v< T >, bool >::type constexpr	jau::equals (const T &a, const T &b, int ulp, const T &epsilon=std::numeric_limits< T >::epsilon()) noexcept
	Returns true, if both floating point values are equal in the sense that their potential difference is less or equal epsilon * ulp. More...
template<class T >
std::enable_if< std::is_floating_point_v< T >, bool >::type constexpr	jau::equals2 (const T &a, const T &b, const T &epsilon=std::numeric_limits< T >::epsilon()) noexcept
	Returns true if both values are equal, i.e. More...
template<class T >
std::enable_if< std::is_floating_point_v< T >, bool >::type constexpr	jau::equals_raw (const T &a, const T &b) noexcept
	Returns true if both values are equal disregarding epsilon but considering NaN, -Inf and +Inf. More...
constexpr float	jau::float_value (const uint32_t a) noexcept
	Converting IEEE 754 (IEC 559) single floating-point bit layout to float, see bit_value() More...
template<class T >
std::enable_if< std::is_floating_point_v< T >, bool >::type constexpr	jau::is_zero (const T &a, const T &epsilon=std::numeric_limits< T >::epsilon()) noexcept
	Returns true if the given value is less than epsilon, w/ epsilon > 0. More...
template<class T >
std::enable_if< std::is_floating_point_v< T >, bool >::type constexpr	jau::is_zero2f (const T &a, const T &b, const T &epsilon=std::numeric_limits< T >::epsilon()) noexcept
	Returns true if all given values a and b are less than epsilon, w/ epsilon > 0. More...
template<class T >
std::enable_if< std::is_floating_point_v< T >, bool >::type constexpr	jau::is_zero3f (const T &a, const T &b, const T &c, const T &epsilon=std::numeric_limits< T >::epsilon()) noexcept
	Returns true if all given values a, b and c are less than epsilon, w/ epsilon > 0. More...
template<class T >
std::enable_if< std::is_floating_point_v< T >, bool >::type constexpr	jau::is_zero4f (const T &a, const T &b, const T &c, const T &d, const T &epsilon=std::numeric_limits< T >::epsilon()) noexcept
	Returns true if all given values a, b, c and d are less than epsilon, w/ epsilon > 0. More...
template<class T >
std::enable_if< std::is_floating_point_v< T >, bool >::type constexpr	jau::is_zero_raw (const T &a) noexcept
	Returns true if the given value is zero, disregarding epsilon but considering NaN, -Inf and +Inf. More...
template<class T >
std::enable_if< std::is_floating_point_v< T >, T >::type	jau::machineEpsilon () noexcept
	Calculates the smallest floating point value approximation the given type T can represent, the machine epsilon of T. More...
template<typename T , std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
std::string &	jau::mat_to_string (std::string &sb, const std::string &rowPrefix, const std::string &f, const T a[], const jau::nsize_t rows, const jau::nsize_t columns, const bool rowMajorOrder) noexcept
	Appends a matrix of floating points to the given string sb More...
template<typename T , std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr T	jau::rad_to_adeg (const T rad) noexcept
	Converts radians to arc-degree. More...
template<class T , std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr jau::sint_bytes< sizeof(T)>::type	jau::round_to_int (const T v) noexcept
	Returns the rounded value cast to int. More...
template<typename T , std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
std::string &	jau::row_to_string (std::string &sb, const std::string &f, const T a[], const jau::nsize_t rows, const jau::nsize_t columns, const bool rowMajorOrder, const jau::nsize_t row) noexcept
	Appends a row of floating points to the given string sb More...

Variables
constexpr uint64_t const	jau::double_iec559_exp_mask = 0x7ff0000000000000_u64
	Exponent mask bits 52-62 of IEEE 754 (IEC 559) double double-point bit layout, i.e. More...
constexpr uint64_t const	jau::double_iec559_mant_mask = 0x000fffffffffffff_u64
	Mantissa mask bits 0-51 of IEEE 754 (IEC 559) double double-point bit layout, i.e. More...
constexpr uint64_t const	jau::double_iec559_nan_bitval = 0x7ff8000000000000_u64
	NaN bit-value of IEEE 754 (IEC 559) double double-point bit layout, i.e. More...
constexpr uint64_t const	jau::double_iec559_negative_inf_bitval = 0xfff0000000000000_u64
	Negative infinity bit-value of IEEE 754 (IEC 559) double double-point bit layout, i.e. More...
constexpr uint64_t const	jau::double_iec559_positive_inf_bitval = 0x7ff0000000000000_u64
	Positive infinity bit-value of IEEE 754 (IEC 559) double double-point bit layout, i.e. More...
constexpr uint64_t const	jau::double_iec559_sign_bit = 1_u64 << 63
	Signed bit 63 of IEEE 754 (IEC 559) double double-point bit layout, i.e. More...
constexpr uint32_t const	jau::float_iec559_exp_mask = 0x7f800000_u32
	Exponent mask bits 23-30 of IEEE 754 (IEC 559) single float-point bit layout, i.e. More...
constexpr uint32_t const	jau::float_iec559_mant_mask = 0x007fffff_u32
	Mantissa mask bits 0-22 of IEEE 754 (IEC 559) single float-point bit layout, i.e. More...
constexpr uint32_t const	jau::float_iec559_nan_bitval = 0x7fc00000_u32
	NaN bit-value of IEEE 754 (IEC 559) single float-point bit layout, i.e. More...
constexpr uint32_t const	jau::float_iec559_negative_inf_bitval = 0xff800000_u32
	Negative infinity bit-value of IEEE 754 (IEC 559) single float-point bit layout, i.e. More...
constexpr uint32_t const	jau::float_iec559_positive_inf_bitval = 0x7f800000_u32
	Positive infinity bit-value of IEEE 754 (IEC 559) single float-point bit layout, i.e. More...
constexpr uint32_t const	jau::float_iec559_sign_bit = 1_u32 << 31
	Signed bit 31 of IEEE 754 (IEC 559) single float-point bit layout, i.e. More...