// This file is part of OpenCV project.
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// It is subject to the license terms in the LICENSE file found in the top-level directory
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// of this distribution and at http://opencv.org/license.html
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// This file is based on files from package issued with the following license:
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/*============================================================================
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This C header file is part of the SoftFloat IEEE Floating-Point Arithmetic
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Package, Release 3c, by John R. Hauser.
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Copyright 2011, 2012, 2013, 2014, 2015, 2016, 2017 The Regents of the
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University of California. All rights reserved.
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Redistribution and use in source and binary forms, with or without
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modification, are permitted provided that the following conditions are met:
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1. Redistributions of source code must retain the above copyright notice,
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this list of conditions, and the following disclaimer.
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2. Redistributions in binary form must reproduce the above copyright notice,
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this list of conditions, and the following disclaimer in the documentation
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and/or other materials provided with the distribution.
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3. Neither the name of the University nor the names of its contributors may
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be used to endorse or promote products derived from this software without
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specific prior written permission.
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THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS "AS IS", AND ANY
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EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
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WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, ARE
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DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY
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DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
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(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
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ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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=============================================================================*/
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#pragma once
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#ifndef softfloat_h
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#define softfloat_h 1
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#include "cvdef.h"
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namespace cv
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{
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/** @addtogroup core_utils_softfloat
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[SoftFloat](http://www.jhauser.us/arithmetic/SoftFloat.html) is a software implementation
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of floating-point calculations according to IEEE 754 standard.
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All calculations are done in integers, that's why they are machine-independent and bit-exact.
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This library can be useful in accuracy-critical parts like look-up tables generation, tests, etc.
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OpenCV contains a subset of SoftFloat partially rewritten to C++.
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### Types
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There are two basic types: @ref softfloat and @ref softdouble.
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These types are binary compatible with float and double types respectively
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and support conversions to/from them.
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Other types from original SoftFloat library like fp16 or fp128 were thrown away
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as well as quiet/signaling NaN support, on-the-fly rounding mode switch
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and exception flags (though exceptions can be implemented in the future).
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### Operations
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Both types support the following:
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- Construction from signed and unsigned 32-bit and 64 integers,
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float/double or raw binary representation
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- Conversions between each other, to float or double and to int
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using @ref cvRound, @ref cvTrunc, @ref cvFloor, @ref cvCeil or a bunch of
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saturate_cast functions
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- Add, subtract, multiply, divide, remainder, square root, FMA with absolute precision
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- Comparison operations
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- Explicit sign, exponent and significand manipulation through get/set methods,
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number state indicators (isInf, isNan, isSubnormal)
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- Type-specific constants like eps, minimum/maximum value, best pi approximation, etc.
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- min(), max(), abs(), exp(), log() and pow() functions
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*/
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//! @{
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struct softfloat;
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struct softdouble;
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struct CV_EXPORTS softfloat
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{
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public:
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/** @brief Default constructor */
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softfloat() { v = 0; }
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/** @brief Copy constructor */
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softfloat( const softfloat& c) { v = c.v; }
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/** @brief Assign constructor */
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softfloat& operator=( const softfloat& c )
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{
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if(&c != this) v = c.v;
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return *this;
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}
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/** @brief Construct from raw
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Builds new value from raw binary representation
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*/
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static const softfloat fromRaw( const uint32_t a ) { softfloat x; x.v = a; return x; }
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/** @brief Construct from integer */
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explicit softfloat( const uint32_t );
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explicit softfloat( const uint64_t );
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explicit softfloat( const int32_t );
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explicit softfloat( const int64_t );
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#ifdef CV_INT32_T_IS_LONG_INT
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// for platforms with int32_t = long int
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explicit softfloat( const int a ) { *this = softfloat(static_cast<int32_t>(a)); }
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#endif
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/** @brief Construct from float */
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explicit softfloat( const float a ) { Cv32suf s; s.f = a; v = s.u; }
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/** @brief Type casts */
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operator softdouble() const;
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operator float() const { Cv32suf s; s.u = v; return s.f; }
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/** @brief Basic arithmetics */
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softfloat operator + (const softfloat&) const;
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softfloat operator - (const softfloat&) const;
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softfloat operator * (const softfloat&) const;
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softfloat operator / (const softfloat&) const;
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softfloat operator - () const { softfloat x; x.v = v ^ (1U << 31); return x; }
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/** @brief Remainder operator
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A quote from original SoftFloat manual:
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> The IEEE Standard remainder operation computes the value
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> a - n * b, where n is the integer closest to a / b.
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> If a / b is exactly halfway between two integers, n is the even integer
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> closest to a / b. The IEEE Standard’s remainder operation is always exact and so requires no rounding.
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> Depending on the relative magnitudes of the operands, the remainder functions
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> can take considerably longer to execute than the other SoftFloat functions.
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> This is an inherent characteristic of the remainder operation itself and is not a flaw
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> in the SoftFloat implementation.
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*/
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softfloat operator % (const softfloat&) const;
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softfloat& operator += (const softfloat& a) { *this = *this + a; return *this; }
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softfloat& operator -= (const softfloat& a) { *this = *this - a; return *this; }
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softfloat& operator *= (const softfloat& a) { *this = *this * a; return *this; }
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softfloat& operator /= (const softfloat& a) { *this = *this / a; return *this; }
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softfloat& operator %= (const softfloat& a) { *this = *this % a; return *this; }
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/** @brief Comparison operations
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- Any operation with NaN produces false
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+ The only exception is when x is NaN: x != y for any y.
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- Positive and negative zeros are equal
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*/
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bool operator == ( const softfloat& ) const;
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bool operator != ( const softfloat& ) const;
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bool operator > ( const softfloat& ) const;
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bool operator >= ( const softfloat& ) const;
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bool operator < ( const softfloat& ) const;
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bool operator <= ( const softfloat& ) const;
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/** @brief NaN state indicator */
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inline bool isNaN() const { return (v & 0x7fffffff) > 0x7f800000; }
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/** @brief Inf state indicator */
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inline bool isInf() const { return (v & 0x7fffffff) == 0x7f800000; }
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/** @brief Subnormal number indicator */
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inline bool isSubnormal() const { return ((v >> 23) & 0xFF) == 0; }
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/** @brief Get sign bit */
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inline bool getSign() const { return (v >> 31) != 0; }
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/** @brief Construct a copy with new sign bit */
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inline softfloat setSign(bool sign) const { softfloat x; x.v = (v & ((1U << 31) - 1)) | ((uint32_t)sign << 31); return x; }
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/** @brief Get 0-based exponent */
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inline int getExp() const { return ((v >> 23) & 0xFF) - 127; }
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/** @brief Construct a copy with new 0-based exponent */
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inline softfloat setExp(int e) const { softfloat x; x.v = (v & 0x807fffff) | (((e + 127) & 0xFF) << 23 ); return x; }
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/** @brief Get a fraction part
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Returns a number 1 <= x < 2 with the same significand
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*/
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inline softfloat getFrac() const
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{
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uint_fast32_t vv = (v & 0x007fffff) | (127 << 23);
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return softfloat::fromRaw(vv);
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}
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/** @brief Construct a copy with provided significand
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Constructs a copy of a number with significand taken from parameter
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*/
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inline softfloat setFrac(const softfloat& s) const
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{
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softfloat x;
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x.v = (v & 0xff800000) | (s.v & 0x007fffff);
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return x;
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}
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/** @brief Zero constant */
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static softfloat zero() { return softfloat::fromRaw( 0 ); }
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/** @brief Positive infinity constant */
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static softfloat inf() { return softfloat::fromRaw( 0xFF << 23 ); }
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/** @brief Default NaN constant */
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static softfloat nan() { return softfloat::fromRaw( 0x7fffffff ); }
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/** @brief One constant */
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static softfloat one() { return softfloat::fromRaw( 127 << 23 ); }
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/** @brief Smallest normalized value */
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static softfloat min() { return softfloat::fromRaw( 0x01 << 23 ); }
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/** @brief Difference between 1 and next representable value */
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static softfloat eps() { return softfloat::fromRaw( (127 - 23) << 23 ); }
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/** @brief Biggest finite value */
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static softfloat max() { return softfloat::fromRaw( (0xFF << 23) - 1 ); }
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/** @brief Correct pi approximation */
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static softfloat pi() { return softfloat::fromRaw( 0x40490fdb ); }
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uint32_t v;
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};
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/*----------------------------------------------------------------------------
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*----------------------------------------------------------------------------*/
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struct CV_EXPORTS softdouble
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{
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public:
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/** @brief Default constructor */
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softdouble() : v(0) { }
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/** @brief Copy constructor */
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softdouble( const softdouble& c) { v = c.v; }
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/** @brief Assign constructor */
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softdouble& operator=( const softdouble& c )
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{
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if(&c != this) v = c.v;
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return *this;
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}
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/** @brief Construct from raw
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Builds new value from raw binary representation
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*/
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static softdouble fromRaw( const uint64_t a ) { softdouble x; x.v = a; return x; }
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/** @brief Construct from integer */
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explicit softdouble( const uint32_t );
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explicit softdouble( const uint64_t );
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explicit softdouble( const int32_t );
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explicit softdouble( const int64_t );
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#ifdef CV_INT32_T_IS_LONG_INT
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// for platforms with int32_t = long int
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explicit softdouble( const int a ) { *this = softdouble(static_cast<int32_t>(a)); }
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#endif
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/** @brief Construct from double */
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explicit softdouble( const double a ) { Cv64suf s; s.f = a; v = s.u; }
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/** @brief Type casts */
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operator softfloat() const;
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operator double() const { Cv64suf s; s.u = v; return s.f; }
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/** @brief Basic arithmetics */
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softdouble operator + (const softdouble&) const;
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softdouble operator - (const softdouble&) const;
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softdouble operator * (const softdouble&) const;
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softdouble operator / (const softdouble&) const;
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softdouble operator - () const { softdouble x; x.v = v ^ (1ULL << 63); return x; }
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/** @brief Remainder operator
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A quote from original SoftFloat manual:
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> The IEEE Standard remainder operation computes the value
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> a - n * b, where n is the integer closest to a / b.
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> If a / b is exactly halfway between two integers, n is the even integer
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> closest to a / b. The IEEE Standard’s remainder operation is always exact and so requires no rounding.
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> Depending on the relative magnitudes of the operands, the remainder functions
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> can take considerably longer to execute than the other SoftFloat functions.
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> This is an inherent characteristic of the remainder operation itself and is not a flaw
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> in the SoftFloat implementation.
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*/
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softdouble operator % (const softdouble&) const;
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softdouble& operator += (const softdouble& a) { *this = *this + a; return *this; }
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softdouble& operator -= (const softdouble& a) { *this = *this - a; return *this; }
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softdouble& operator *= (const softdouble& a) { *this = *this * a; return *this; }
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softdouble& operator /= (const softdouble& a) { *this = *this / a; return *this; }
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softdouble& operator %= (const softdouble& a) { *this = *this % a; return *this; }
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/** @brief Comparison operations
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- Any operation with NaN produces false
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+ The only exception is when x is NaN: x != y for any y.
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- Positive and negative zeros are equal
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*/
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bool operator == ( const softdouble& ) const;
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bool operator != ( const softdouble& ) const;
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bool operator > ( const softdouble& ) const;
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bool operator >= ( const softdouble& ) const;
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bool operator < ( const softdouble& ) const;
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bool operator <= ( const softdouble& ) const;
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/** @brief NaN state indicator */
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inline bool isNaN() const { return (v & 0x7fffffffffffffff) > 0x7ff0000000000000; }
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/** @brief Inf state indicator */
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inline bool isInf() const { return (v & 0x7fffffffffffffff) == 0x7ff0000000000000; }
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/** @brief Subnormal number indicator */
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inline bool isSubnormal() const { return ((v >> 52) & 0x7FF) == 0; }
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/** @brief Get sign bit */
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inline bool getSign() const { return (v >> 63) != 0; }
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/** @brief Construct a copy with new sign bit */
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softdouble setSign(bool sign) const { softdouble x; x.v = (v & ((1ULL << 63) - 1)) | ((uint_fast64_t)(sign) << 63); return x; }
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/** @brief Get 0-based exponent */
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inline int getExp() const { return ((v >> 52) & 0x7FF) - 1023; }
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/** @brief Construct a copy with new 0-based exponent */
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inline softdouble setExp(int e) const
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{
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softdouble x;
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x.v = (v & 0x800FFFFFFFFFFFFF) | ((uint_fast64_t)((e + 1023) & 0x7FF) << 52);
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return x;
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}
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/** @brief Get a fraction part
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Returns a number 1 <= x < 2 with the same significand
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*/
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inline softdouble getFrac() const
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{
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uint_fast64_t vv = (v & 0x000FFFFFFFFFFFFF) | ((uint_fast64_t)(1023) << 52);
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return softdouble::fromRaw(vv);
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}
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/** @brief Construct a copy with provided significand
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Constructs a copy of a number with significand taken from parameter
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*/
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inline softdouble setFrac(const softdouble& s) const
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{
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softdouble x;
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x.v = (v & 0xFFF0000000000000) | (s.v & 0x000FFFFFFFFFFFFF);
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return x;
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}
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/** @brief Zero constant */
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static softdouble zero() { return softdouble::fromRaw( 0 ); }
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/** @brief Positive infinity constant */
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static softdouble inf() { return softdouble::fromRaw( (uint_fast64_t)(0x7FF) << 52 ); }
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/** @brief Default NaN constant */
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static softdouble nan() { return softdouble::fromRaw( CV_BIG_INT(0x7FFFFFFFFFFFFFFF) ); }
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/** @brief One constant */
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static softdouble one() { return softdouble::fromRaw( (uint_fast64_t)( 1023) << 52 ); }
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/** @brief Smallest normalized value */
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static softdouble min() { return softdouble::fromRaw( (uint_fast64_t)( 0x01) << 52 ); }
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/** @brief Difference between 1 and next representable value */
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static softdouble eps() { return softdouble::fromRaw( (uint_fast64_t)( 1023 - 52 ) << 52 ); }
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/** @brief Biggest finite value */
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static softdouble max() { return softdouble::fromRaw( ((uint_fast64_t)(0x7FF) << 52) - 1 ); }
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/** @brief Correct pi approximation */
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static softdouble pi() { return softdouble::fromRaw( CV_BIG_INT(0x400921FB54442D18) ); }
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uint64_t v;
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};
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/*----------------------------------------------------------------------------
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*----------------------------------------------------------------------------*/
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/** @brief Fused Multiplication and Addition
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Computes (a*b)+c with single rounding
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*/
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CV_EXPORTS softfloat mulAdd( const softfloat& a, const softfloat& b, const softfloat & c);
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CV_EXPORTS softdouble mulAdd( const softdouble& a, const softdouble& b, const softdouble& c);
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/** @brief Square root */
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CV_EXPORTS softfloat sqrt( const softfloat& a );
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CV_EXPORTS softdouble sqrt( const softdouble& a );
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}
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/*----------------------------------------------------------------------------
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| Ported from OpenCV and added for usability
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*----------------------------------------------------------------------------*/
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/** @brief Truncates number to integer with minimum magnitude */
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CV_EXPORTS int cvTrunc(const cv::softfloat& a);
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CV_EXPORTS int cvTrunc(const cv::softdouble& a);
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/** @brief Rounds a number to nearest even integer */
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CV_EXPORTS int cvRound(const cv::softfloat& a);
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CV_EXPORTS int cvRound(const cv::softdouble& a);
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/** @brief Rounds a number to nearest even long long integer */
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CV_EXPORTS int64_t cvRound64(const cv::softdouble& a);
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/** @brief Rounds a number down to integer */
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CV_EXPORTS int cvFloor(const cv::softfloat& a);
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CV_EXPORTS int cvFloor(const cv::softdouble& a);
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/** @brief Rounds number up to integer */
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CV_EXPORTS int cvCeil(const cv::softfloat& a);
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CV_EXPORTS int cvCeil(const cv::softdouble& a);
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namespace cv
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{
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/** @brief Saturate casts */
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template<typename _Tp> static inline _Tp saturate_cast(softfloat a) { return _Tp(a); }
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template<typename _Tp> static inline _Tp saturate_cast(softdouble a) { return _Tp(a); }
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template<> inline uchar saturate_cast<uchar>(softfloat a) { return (uchar)std::max(std::min(cvRound(a), (int)UCHAR_MAX), 0); }
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template<> inline uchar saturate_cast<uchar>(softdouble a) { return (uchar)std::max(std::min(cvRound(a), (int)UCHAR_MAX), 0); }
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template<> inline schar saturate_cast<schar>(softfloat a) { return (schar)std::min(std::max(cvRound(a), (int)SCHAR_MIN), (int)SCHAR_MAX); }
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template<> inline schar saturate_cast<schar>(softdouble a) { return (schar)std::min(std::max(cvRound(a), (int)SCHAR_MIN), (int)SCHAR_MAX); }
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template<> inline ushort saturate_cast<ushort>(softfloat a) { return (ushort)std::max(std::min(cvRound(a), (int)USHRT_MAX), 0); }
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template<> inline ushort saturate_cast<ushort>(softdouble a) { return (ushort)std::max(std::min(cvRound(a), (int)USHRT_MAX), 0); }
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template<> inline short saturate_cast<short>(softfloat a) { return (short)std::min(std::max(cvRound(a), (int)SHRT_MIN), (int)SHRT_MAX); }
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template<> inline short saturate_cast<short>(softdouble a) { return (short)std::min(std::max(cvRound(a), (int)SHRT_MIN), (int)SHRT_MAX); }
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template<> inline int saturate_cast<int>(softfloat a) { return cvRound(a); }
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template<> inline int saturate_cast<int>(softdouble a) { return cvRound(a); }
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template<> inline int64_t saturate_cast<int64_t>(softfloat a) { return cvRound(a); }
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template<> inline int64_t saturate_cast<int64_t>(softdouble a) { return cvRound64(a); }
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/** @brief Saturate cast to unsigned integer and unsigned long long integer
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We intentionally do not clip negative numbers, to make -1 become 0xffffffff etc.
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*/
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template<> inline unsigned saturate_cast<unsigned>(softfloat a) { return cvRound(a); }
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template<> inline unsigned saturate_cast<unsigned>(softdouble a) { return cvRound(a); }
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template<> inline uint64_t saturate_cast<uint64_t>(softfloat a) { return cvRound(a); }
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template<> inline uint64_t saturate_cast<uint64_t>(softdouble a) { return cvRound64(a); }
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/** @brief Min and Max functions */
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inline softfloat min(const softfloat& a, const softfloat& b) { return (a > b) ? b : a; }
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inline softdouble min(const softdouble& a, const softdouble& b) { return (a > b) ? b : a; }
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inline softfloat max(const softfloat& a, const softfloat& b) { return (a > b) ? a : b; }
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inline softdouble max(const softdouble& a, const softdouble& b) { return (a > b) ? a : b; }
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/** @brief Absolute value */
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inline softfloat abs( softfloat a) { softfloat x; x.v = a.v & ((1U << 31) - 1); return x; }
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inline softdouble abs( softdouble a) { softdouble x; x.v = a.v & ((1ULL << 63) - 1); return x; }
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/** @brief Exponent
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Special cases:
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- exp(NaN) is NaN
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- exp(-Inf) == 0
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- exp(+Inf) == +Inf
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*/
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CV_EXPORTS softfloat exp( const softfloat& a);
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CV_EXPORTS softdouble exp( const softdouble& a);
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/** @brief Natural logarithm
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Special cases:
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- log(NaN), log(x < 0) are NaN
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- log(0) == -Inf
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*/
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CV_EXPORTS softfloat log( const softfloat& a );
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CV_EXPORTS softdouble log( const softdouble& a );
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/** @brief Raising to the power
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Special cases:
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- x**NaN is NaN for any x
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- ( |x| == 1 )**Inf is NaN
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- ( |x| > 1 )**+Inf or ( |x| < 1 )**-Inf is +Inf
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- ( |x| > 1 )**-Inf or ( |x| < 1 )**+Inf is 0
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- x ** 0 == 1 for any x
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- x ** 1 == 1 for any x
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- NaN ** y is NaN for any other y
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- Inf**(y < 0) == 0
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- Inf ** y is +Inf for any other y
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- (x < 0)**y is NaN for any other y if x can't be correctly rounded to integer
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- 0 ** 0 == 1
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- 0 ** (y < 0) is +Inf
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- 0 ** (y > 0) is 0
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*/
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CV_EXPORTS softfloat pow( const softfloat& a, const softfloat& b);
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CV_EXPORTS softdouble pow( const softdouble& a, const softdouble& b);
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/** @brief Cube root
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Special cases:
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- cbrt(NaN) is NaN
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- cbrt(+/-Inf) is +/-Inf
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*/
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CV_EXPORTS softfloat cbrt( const softfloat& a );
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/** @brief Sine
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Special cases:
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- sin(Inf) or sin(NaN) is NaN
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- sin(x) == x when sin(x) is close to zero
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*/
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CV_EXPORTS softdouble sin( const softdouble& a );
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/** @brief Cosine
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*
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Special cases:
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- cos(Inf) or cos(NaN) is NaN
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- cos(x) == +/- 1 when cos(x) is close to +/- 1
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*/
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CV_EXPORTS softdouble cos( const softdouble& a );
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}
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//! @}
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#endif
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