Libraries: Math Utils (MT4)

[Automated-Trading]

Math Utils (MT4):

Handy functions for comparison and rounding of floating-point numbers (prices, lots and money).

Author: amrali

[amrali]

Update 19 May 2021

Added functions for debugging 

// Converting numeric value into the exact decimal text string.
string DoubleToStringExact(double value);

// Converting numeric value into the raw hexadecimal text string.
string DoubleToHexadecimal(double value);

[amrali]

Update 21 May 2021

Added miscellaneous functions

// Convert x in range [min, max] to y in another range [new_min, new_max]. 
// This can be used to rescale indicator values or graphic objects.
double map_range(double x, double min, double max, double new_min, double new_max);

// Get number of digits after the decimal point.
int GetDigits(double number);

[Mohammad Hossein Sadeghi]

Please look at this library, it's great:

https://www.mql5.com/en/code/19727

[amrali]

Mohammad Hossein Sadeghi:
Please look at this library, it's great:

https://www.mql5.com/en/code/19727

I consider the CDouble written by nicholish a good library.

However, I found that some calculations from CDouble are not correct.

My library has very accurate calculations.

Here is a test script to demonstrate the found issues.

#include <Double.mqh>
#include <math_utils.mqh>  // for RoundToStepDown() and GetDigits()

#define PRINT(A) Print(#A + " = ", (A))
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
void OnStart()
{
//--- rounding issues in CDouble library
   double lotstep = 0.01;

   PRINT( CDouble::RoundToStepDown(1.15, lotstep) );   // 1.14  incorrect result!
   PRINT( RoundToStepDown(1.15, lotstep) );            // 1.15  correct (value is already rounded)


//--- operator overloading issues in CDouble library
   double  lot1 = 0.1,
           sum1 = lot1 + 0.2;

   CDouble lot2 = 0.1,
           sum2 = lot2 + 0.2;

   PRINT( lot1 == lot2.AsRawDouble() );   // true
   PRINT( sum1 == sum2.AsRawDouble() );   // false


//--- GetDigits() function issues in CDouble library
   PRINT( CDouble::GetDigits(1.12) );     // 16  incorrect result!
   PRINT( CDouble::GetDigits(90.268) );   // 14  incorrect result!
   PRINT( CDouble::GetDigits(1.0954) );   // 16  incorrect result!
   PRINT( CDouble::GetDigits(1.27481) );  // 16  incorrect result!

   PRINT( GetDigits(1.12) );              // 2
   PRINT( GetDigits(90.268) );            // 3
   PRINT( GetDigits(1.0954) );            // 4
   PRINT( GetDigits(1.27481) );           // 5
  }

[Mohammad Hossein Sadeghi]

amrali:

I consider the CDouble written by nicholish a good library.

However, I found that some calculations from CDouble are not correct.

My library has very accurate calculations.

Here is a test script to demonstrate the found issues.

You're right, thanks for sharing.

[Mohammad Hossein Sadeghi]

Any solution to get digits of the price when there is only zero after decimal, for example GetDigits to return 2 for 3850.00?

[amrali]

Mohammad Hossein Sadeghi:
Any solution to get digits of the price when there is only zero after decimal, for example GetDigits to return 2 for 3850.00?

GetDigits work on numeric values (i.e., 3850), your value 3850.00 is string.

Note that:

 GetDigits(1.1200) == 2;  // not 4

[amrali]

Update 27 May 2021

Added functions for debugging

// Returns int diff between two floats expressed in epsilon (ulps).
long UlpDiff(const double num1, const double num2);

// Returns the next representable value after x
double nextafter(double num);

Added miscellaneous functions

bool IsRound(const double number, const int digits);

bool IsRoundToStep(const double number, const double step);

Added 'dotnet_cross_check.mq5' script and 'RoundSharp.dll' written in C#.

[amrali]

Update 30 May 2021

Added miscellaneous functions

//Get number of integer digits to the left of decimal point.
int    IntegerDigits(double number);

//map x on a scale [min, max] to normalized scale [0, 1].
double normalize(double x, double min, double max);

Handy functions for the binary representation of doubles

//Returns the double value corresponding to a bit representation.
double LongBitsToDouble(long bits);

//Returns the bit representation corresponding to a double value .
long   DoubleToLongBits(double value);

//Returns the unbiased exponent used in the bit representation.
int    GetExponent(double value);

//Returns the mantissa used in the bit representation.
long   GetMantissa(double value);

//Returns the size of an ulp of the argument.
double Ulp(double value);

Handy functions for the string representation of doubles

// Converting numeric value into the shortest string representation
// that round-trips into the same numeric value.
string Repr(double value);

[amrali]

Update 1 June 2021

Added new functions:

// Returns the raw encoding of exponent in the bit representation.
int    RawExponent(double value);

// Returns raw encoding of significand in the bit representation.
long   RawSignificand(double value);

// Returns the unbiased (adjusted) exponent of a double value.
int    Exponent(double value);

// Returns the significand of a double value.
double Significand(double value);

// Determine whether number is exactly representable in double.
bool   IsExactDouble(double value);

// Formats number with thousands separator.
string FormatNumber(const double number,const string separator=",");