PreVerify/lib/opencv480/include/opencv2/core/softfloat.hpp

// This file is part of OpenCV project.
// It is subject to the license terms in the LICENSE file found in the top-level directory
// of this distribution and at http://opencv.org/license.html

// This file is based on files from package issued with the following license:

/*============================================================================

This C header file is part of the SoftFloat IEEE Floating-Point Arithmetic
Package, Release 3c, by John R. Hauser.

Copyright 2011, 2012, 2013, 2014, 2015, 2016, 2017 The Regents of the
University of California.  All rights reserved.

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    be used to endorse or promote products derived from this software without
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=============================================================================*/

#pragma once
#ifndef softfloat_h
#define softfloat_h 1

#include "cvdef.h"

namespace cv
{

/** @addtogroup core_utils_softfloat

  [SoftFloat](http://www.jhauser.us/arithmetic/SoftFloat.html) is a software implementation
  of floating-point calculations according to IEEE 754 standard.
  All calculations are done in integers, that's why they are machine-independent and bit-exact.
  This library can be useful in accuracy-critical parts like look-up tables generation, tests, etc.
  OpenCV contains a subset of SoftFloat partially rewritten to C++.

  ### Types

  There are two basic types: @ref softfloat and @ref softdouble.
  These types are binary compatible with float and double types respectively
  and support conversions to/from them.
  Other types from original SoftFloat library like fp16 or fp128 were thrown away
  as well as quiet/signaling NaN support, on-the-fly rounding mode switch
  and exception flags (though exceptions can be implemented in the future).

  ### Operations

  Both types support the following:
  - Construction from signed and unsigned 32-bit and 64 integers,
  float/double or raw binary representation
  - Conversions between each other, to float or double and to int
  using @ref cvRound, @ref cvTrunc, @ref cvFloor, @ref cvCeil or a bunch of
  saturate_cast functions
  - Add, subtract, multiply, divide, remainder, square root, FMA with absolute precision
  - Comparison operations
  - Explicit sign, exponent and significand manipulation through get/set methods,
 number state indicators (isInf, isNan, isSubnormal)
  - Type-specific constants like eps, minimum/maximum value, best pi approximation, etc.
  - min(), max(), abs(), exp(), log() and pow() functions

*/
//! @{

struct softfloat;
struct softdouble;

struct CV_EXPORTS softfloat
{
public:
    /** @brief Default constructor */
    softfloat() { v = 0; }
    /** @brief Copy constructor */
    softfloat( const softfloat& c) { v = c.v; }
    /** @brief Assign constructor */
    softfloat& operator=( const softfloat& c )
    {
        if(&c != this) v = c.v;
        return *this;
    }
    /** @brief Construct from raw

    Builds new value from raw binary representation
    */
    static const softfloat fromRaw( const uint32_t a ) { softfloat x; x.v = a; return x; }

    /** @brief Construct from integer */
    explicit softfloat( const uint32_t );
    explicit softfloat( const uint64_t );
    explicit softfloat( const int32_t );
    explicit softfloat( const int64_t );

#ifdef CV_INT32_T_IS_LONG_INT
    // for platforms with int32_t = long int
    explicit softfloat( const int a ) { *this = softfloat(static_cast<int32_t>(a)); }
#endif

    /** @brief Construct from float */
    explicit softfloat( const float a ) { Cv32suf s; s.f = a; v = s.u; }

    /** @brief Type casts  */
    operator softdouble() const;
    operator float() const { Cv32suf s; s.u = v; return s.f; }

    /** @brief Basic arithmetics */
    softfloat operator + (const softfloat&) const;
    softfloat operator - (const softfloat&) const;
    softfloat operator * (const softfloat&) const;
    softfloat operator / (const softfloat&) const;
    softfloat operator - () const { softfloat x; x.v = v ^ (1U << 31); return x; }

    /** @brief Remainder operator

    A quote from original SoftFloat manual:

    > The IEEE Standard remainder operation computes the value
    > a - n * b, where n is the integer closest to a / b.
    > If a / b is exactly halfway between two integers, n is the even integer
    > closest to a / b. The IEEE Standard’s remainder operation is always exact and so requires no rounding.
    > Depending on the relative magnitudes of the operands, the remainder functions
    > can take considerably longer to execute than the other SoftFloat functions.
    > This is an inherent characteristic of the remainder operation itself and is not a flaw
    > in the SoftFloat implementation.
    */
    softfloat operator % (const softfloat&) const;

    softfloat& operator += (const softfloat& a) { *this = *this + a; return *this; }
    softfloat& operator -= (const softfloat& a) { *this = *this - a; return *this; }
    softfloat& operator *= (const softfloat& a) { *this = *this * a; return *this; }
    softfloat& operator /= (const softfloat& a) { *this = *this / a; return *this; }
    softfloat& operator %= (const softfloat& a) { *this = *this % a; return *this; }

    /** @brief Comparison operations

     - Any operation with NaN produces false
       + The only exception is when x is NaN: x != y for any y.
     - Positive and negative zeros are equal
    */
    bool operator == ( const softfloat& ) const;
    bool operator != ( const softfloat& ) const;
    bool operator >  ( const softfloat& ) const;
    bool operator >= ( const softfloat& ) const;
    bool operator <  ( const softfloat& ) const;
    bool operator <= ( const softfloat& ) const;

    /** @brief NaN state indicator */
    inline bool isNaN() const { return (v & 0x7fffffff)  > 0x7f800000; }
    /** @brief Inf state indicator */
    inline bool isInf() const { return (v & 0x7fffffff) == 0x7f800000; }
    /** @brief Subnormal number indicator */
    inline bool isSubnormal() const { return ((v >> 23) & 0xFF) == 0; }

    /** @brief Get sign bit */
    inline bool getSign() const { return (v >> 31) != 0; }
    /** @brief Construct a copy with new sign bit */
    inline softfloat setSign(bool sign) const { softfloat x; x.v = (v & ((1U << 31) - 1)) | ((uint32_t)sign << 31); return x; }
    /** @brief Get 0-based exponent */
    inline int getExp() const { return ((v >> 23) & 0xFF) - 127; }
    /** @brief Construct a copy with new 0-based exponent */
    inline softfloat setExp(int e) const { softfloat x; x.v = (v & 0x807fffff) | (((e + 127) & 0xFF) << 23 ); return x; }

    /** @brief Get a fraction part

    Returns a number 1 <= x < 2 with the same significand
    */
    inline softfloat getFrac() const
    {
        uint_fast32_t vv = (v & 0x007fffff) | (127 << 23);
        return softfloat::fromRaw(vv);
    }
    /** @brief Construct a copy with provided significand

    Constructs a copy of a number with significand taken from parameter
    */
    inline softfloat setFrac(const softfloat& s) const
    {
        softfloat x;
        x.v = (v & 0xff800000) | (s.v & 0x007fffff);
        return x;
    }

    /** @brief Zero constant */
    static softfloat zero() { return softfloat::fromRaw( 0 ); }
    /** @brief Positive infinity constant */
    static softfloat  inf() { return softfloat::fromRaw( 0xFF << 23 ); }
    /** @brief Default NaN constant */
    static softfloat  nan() { return softfloat::fromRaw( 0x7fffffff ); }
    /** @brief One constant */
    static softfloat  one() { return softfloat::fromRaw(  127 << 23 ); }
    /** @brief Smallest normalized value */
    static softfloat  min() { return softfloat::fromRaw( 0x01 << 23 ); }
    /** @brief Difference between 1 and next representable value */
    static softfloat  eps() { return softfloat::fromRaw( (127 - 23) << 23 ); }
    /** @brief Biggest finite value */
    static softfloat  max() { return softfloat::fromRaw( (0xFF << 23) - 1 ); }
    /** @brief Correct pi approximation */
    static softfloat   pi() { return softfloat::fromRaw( 0x40490fdb ); }

    uint32_t v;
};

/*----------------------------------------------------------------------------
*----------------------------------------------------------------------------*/

struct CV_EXPORTS softdouble
{
public:
    /** @brief Default constructor */
    softdouble() : v(0) { }
    /** @brief Copy constructor */
    softdouble( const softdouble& c) { v = c.v; }
    /** @brief Assign constructor */
    softdouble& operator=( const softdouble& c )
    {
        if(&c != this) v = c.v;
        return *this;
    }
    /** @brief Construct from raw

    Builds new value from raw binary representation
    */
    static softdouble fromRaw( const uint64_t a ) { softdouble x; x.v = a; return x; }

    /** @brief Construct from integer */
    explicit softdouble( const uint32_t );
    explicit softdouble( const uint64_t );
    explicit softdouble( const  int32_t );
    explicit softdouble( const  int64_t );

#ifdef CV_INT32_T_IS_LONG_INT
    // for platforms with int32_t = long int
    explicit softdouble( const int a ) { *this = softdouble(static_cast<int32_t>(a)); }
#endif

    /** @brief Construct from double */
    explicit softdouble( const double a ) { Cv64suf s; s.f = a; v = s.u; }

    /** @brief Type casts  */
    operator softfloat() const;
    operator double() const { Cv64suf s; s.u = v; return s.f; }

    /** @brief Basic arithmetics */
    softdouble operator + (const softdouble&) const;
    softdouble operator - (const softdouble&) const;
    softdouble operator * (const softdouble&) const;
    softdouble operator / (const softdouble&) const;
    softdouble operator - () const { softdouble x; x.v = v ^ (1ULL << 63); return x; }

    /** @brief Remainder operator

    A quote from original SoftFloat manual:

    > The IEEE Standard remainder operation computes the value
    > a - n * b, where n is the integer closest to a / b.
    > If a / b is exactly halfway between two integers, n is the even integer
    > closest to a / b. The IEEE Standard’s remainder operation is always exact and so requires no rounding.
    > Depending on the relative magnitudes of the operands, the remainder functions
    > can take considerably longer to execute than the other SoftFloat functions.
    > This is an inherent characteristic of the remainder operation itself and is not a flaw
    > in the SoftFloat implementation.
    */
    softdouble operator % (const softdouble&) const;

    softdouble& operator += (const softdouble& a) { *this = *this + a; return *this; }
    softdouble& operator -= (const softdouble& a) { *this = *this - a; return *this; }
    softdouble& operator *= (const softdouble& a) { *this = *this * a; return *this; }
    softdouble& operator /= (const softdouble& a) { *this = *this / a; return *this; }
    softdouble& operator %= (const softdouble& a) { *this = *this % a; return *this; }

    /** @brief Comparison operations

     - Any operation with NaN produces false
       + The only exception is when x is NaN: x != y for any y.
     - Positive and negative zeros are equal
    */
    bool operator == ( const softdouble& ) const;
    bool operator != ( const softdouble& ) const;
    bool operator >  ( const softdouble& ) const;
    bool operator >= ( const softdouble& ) const;
    bool operator <  ( const softdouble& ) const;
    bool operator <= ( const softdouble& ) const;

    /** @brief NaN state indicator */
    inline bool isNaN() const { return (v & 0x7fffffffffffffff)  > 0x7ff0000000000000; }
    /** @brief Inf state indicator */
    inline bool isInf() const { return (v & 0x7fffffffffffffff) == 0x7ff0000000000000; }
    /** @brief Subnormal number indicator */
    inline bool isSubnormal() const { return ((v >> 52) & 0x7FF) == 0; }

    /** @brief Get sign bit */
    inline bool getSign() const { return (v >> 63) != 0; }
    /** @brief Construct a copy with new sign bit */
    softdouble setSign(bool sign) const { softdouble x; x.v = (v & ((1ULL << 63) - 1)) | ((uint_fast64_t)(sign) << 63); return x; }
    /** @brief Get 0-based exponent */
    inline int getExp() const { return ((v >> 52) & 0x7FF) - 1023; }
    /** @brief Construct a copy with new 0-based exponent */
    inline softdouble setExp(int e) const
    {
        softdouble x;
        x.v = (v & 0x800FFFFFFFFFFFFF) | ((uint_fast64_t)((e + 1023) & 0x7FF) << 52);
        return x;
    }

    /** @brief Get a fraction part

    Returns a number 1 <= x < 2 with the same significand
    */
    inline softdouble getFrac() const
    {
        uint_fast64_t vv = (v & 0x000FFFFFFFFFFFFF) | ((uint_fast64_t)(1023) << 52);
        return softdouble::fromRaw(vv);
    }
    /** @brief Construct a copy with provided significand

    Constructs a copy of a number with significand taken from parameter
    */
    inline softdouble setFrac(const softdouble& s) const
    {
        softdouble x;
        x.v = (v & 0xFFF0000000000000) | (s.v & 0x000FFFFFFFFFFFFF);
        return x;
    }

    /** @brief Zero constant */
    static softdouble zero() { return softdouble::fromRaw( 0 ); }
    /** @brief Positive infinity constant */
    static softdouble  inf() { return softdouble::fromRaw( (uint_fast64_t)(0x7FF) << 52 ); }
    /** @brief Default NaN constant */
    static softdouble  nan() { return softdouble::fromRaw( CV_BIG_INT(0x7FFFFFFFFFFFFFFF) ); }
    /** @brief One constant */
    static softdouble  one() { return softdouble::fromRaw( (uint_fast64_t)( 1023) << 52 ); }
    /** @brief Smallest normalized value */
    static softdouble  min() { return softdouble::fromRaw( (uint_fast64_t)( 0x01) << 52 ); }
    /** @brief Difference between 1 and next representable value */
    static softdouble  eps() { return softdouble::fromRaw( (uint_fast64_t)( 1023 - 52 ) << 52 ); }
    /** @brief Biggest finite value */
    static softdouble  max() { return softdouble::fromRaw( ((uint_fast64_t)(0x7FF) << 52) - 1 ); }
    /** @brief Correct pi approximation */
    static softdouble   pi() { return softdouble::fromRaw( CV_BIG_INT(0x400921FB54442D18) ); }

    uint64_t v;
};

/*----------------------------------------------------------------------------
*----------------------------------------------------------------------------*/

/** @brief Fused Multiplication and Addition

Computes (a*b)+c with single rounding
*/
CV_EXPORTS softfloat  mulAdd( const softfloat&  a, const softfloat&  b, const softfloat & c);
CV_EXPORTS softdouble mulAdd( const softdouble& a, const softdouble& b, const softdouble& c);

/** @brief Square root */
CV_EXPORTS softfloat  sqrt( const softfloat&  a );
CV_EXPORTS softdouble sqrt( const softdouble& a );
}

/*----------------------------------------------------------------------------
| Ported from OpenCV and added for usability
*----------------------------------------------------------------------------*/

/** @brief Truncates number to integer with minimum magnitude */
CV_EXPORTS int cvTrunc(const cv::softfloat&  a);
CV_EXPORTS int cvTrunc(const cv::softdouble& a);

/** @brief Rounds a number to nearest even integer */
CV_EXPORTS int cvRound(const cv::softfloat&  a);
CV_EXPORTS int cvRound(const cv::softdouble& a);

/** @brief Rounds a number to nearest even long long integer */
CV_EXPORTS int64_t cvRound64(const cv::softdouble& a);

/** @brief Rounds a number down to integer */
CV_EXPORTS int cvFloor(const cv::softfloat&  a);
CV_EXPORTS int cvFloor(const cv::softdouble& a);

/** @brief Rounds number up to integer */
CV_EXPORTS int  cvCeil(const cv::softfloat&  a);
CV_EXPORTS int  cvCeil(const cv::softdouble& a);

namespace cv
{
/** @brief Saturate casts */
template<typename _Tp> static inline _Tp saturate_cast(softfloat  a) { return _Tp(a); }
template<typename _Tp> static inline _Tp saturate_cast(softdouble a) { return _Tp(a); }

template<> inline uchar saturate_cast<uchar>(softfloat  a) { return (uchar)std::max(std::min(cvRound(a), (int)UCHAR_MAX), 0); }
template<> inline uchar saturate_cast<uchar>(softdouble a) { return (uchar)std::max(std::min(cvRound(a), (int)UCHAR_MAX), 0); }

template<> inline schar saturate_cast<schar>(softfloat  a) { return (schar)std::min(std::max(cvRound(a), (int)SCHAR_MIN), (int)SCHAR_MAX); }
template<> inline schar saturate_cast<schar>(softdouble a) { return (schar)std::min(std::max(cvRound(a), (int)SCHAR_MIN), (int)SCHAR_MAX); }

template<> inline ushort saturate_cast<ushort>(softfloat  a) { return (ushort)std::max(std::min(cvRound(a), (int)USHRT_MAX), 0); }
template<> inline ushort saturate_cast<ushort>(softdouble a) { return (ushort)std::max(std::min(cvRound(a), (int)USHRT_MAX), 0); }

template<> inline short saturate_cast<short>(softfloat  a) { return (short)std::min(std::max(cvRound(a), (int)SHRT_MIN), (int)SHRT_MAX); }
template<> inline short saturate_cast<short>(softdouble a) { return (short)std::min(std::max(cvRound(a), (int)SHRT_MIN), (int)SHRT_MAX); }

template<> inline int saturate_cast<int>(softfloat  a) { return cvRound(a); }
template<> inline int saturate_cast<int>(softdouble a) { return cvRound(a); }

template<> inline int64_t saturate_cast<int64_t>(softfloat  a) { return cvRound(a); }
template<> inline int64_t saturate_cast<int64_t>(softdouble a) { return cvRound64(a); }

/** @brief Saturate cast to unsigned integer and unsigned long long integer
We intentionally do not clip negative numbers, to make -1 become 0xffffffff etc.
*/
template<> inline unsigned saturate_cast<unsigned>(softfloat  a) { return cvRound(a); }
template<> inline unsigned saturate_cast<unsigned>(softdouble a) { return cvRound(a); }

template<> inline uint64_t saturate_cast<uint64_t>(softfloat  a) { return cvRound(a); }
template<> inline uint64_t saturate_cast<uint64_t>(softdouble a) { return cvRound64(a); }

/** @brief Min and Max functions */
inline softfloat  min(const softfloat&  a, const softfloat&  b) { return (a > b) ? b : a; }
inline softdouble min(const softdouble& a, const softdouble& b) { return (a > b) ? b : a; }

inline softfloat  max(const softfloat&  a, const softfloat&  b) { return (a > b) ? a : b; }
inline softdouble max(const softdouble& a, const softdouble& b) { return (a > b) ? a : b; }

/** @brief Absolute value */
inline softfloat  abs( softfloat  a) { softfloat  x; x.v = a.v & ((1U   << 31) - 1); return x; }
inline softdouble abs( softdouble a) { softdouble x; x.v = a.v & ((1ULL << 63) - 1); return x; }

/** @brief Exponent

Special cases:
- exp(NaN) is NaN
- exp(-Inf) == 0
- exp(+Inf) == +Inf
*/
CV_EXPORTS softfloat  exp( const softfloat&  a);
CV_EXPORTS softdouble exp( const softdouble& a);

/** @brief Natural logarithm

Special cases:
- log(NaN), log(x < 0) are NaN
- log(0) == -Inf
*/
CV_EXPORTS softfloat  log( const softfloat&  a );
CV_EXPORTS softdouble log( const softdouble& a );

/** @brief Raising to the power

Special cases:
- x**NaN is NaN for any x
- ( |x| == 1 )**Inf is NaN
- ( |x|  > 1 )**+Inf or ( |x| < 1 )**-Inf is +Inf
- ( |x|  > 1 )**-Inf or ( |x| < 1 )**+Inf is 0
- x ** 0 == 1 for any x
- x ** 1 == 1 for any x
- NaN ** y is NaN for any other y
- Inf**(y < 0) == 0
- Inf ** y is +Inf for any other y
- (x < 0)**y is NaN for any other y if x can't be correctly rounded to integer
- 0 ** 0 == 1
- 0 ** (y < 0) is +Inf
- 0 ** (y > 0) is 0
*/
CV_EXPORTS softfloat  pow( const softfloat&  a, const softfloat&  b);
CV_EXPORTS softdouble pow( const softdouble& a, const softdouble& b);

/** @brief Cube root

Special cases:
- cbrt(NaN) is NaN
- cbrt(+/-Inf) is +/-Inf
*/
CV_EXPORTS softfloat cbrt( const softfloat& a );

/** @brief Sine

Special cases:
- sin(Inf) or sin(NaN) is NaN
- sin(x) == x when sin(x) is close to zero
*/
CV_EXPORTS softdouble sin( const softdouble& a );

/** @brief Cosine
 *
Special cases:
- cos(Inf) or cos(NaN) is NaN
- cos(x) == +/- 1 when cos(x) is close to +/- 1
*/
CV_EXPORTS softdouble cos( const softdouble& a );

//! @} core_utils_softfloat

} // cv::

#endif