PositionalNumeralSystem Class Reference

Base class for all numeral systems with a positional notation. More...

#include <ntextp.h>

Inheritance diagram for PositionalNumeralSystem:

Collaboration diagram for PositionalNumeralSystem:

Public Member Functions
	PositionalNumeralSystem (unsigned int base, unsigned int digits, const char fractionPoint)
	~PositionalNumeralSystem ()
virtual const char *	GetName ()
virtual const char *	GetPrefix ()
virtual unsigned int	GetDigits ()
virtual void	SetDigits (unsigned int digits)
virtual const char	GetFractionPoint ()
virtual void	SetFractionPoint (const char fractionPoint)
virtual const char *	GetText (Number *number)
virtual Number *	Parse (const char *text, unsigned int *length, char **end)
Public Member Functions inherited from NumeralSystem
	NumeralSystem ()
virtual	~NumeralSystem ()
virtual Number *	Parse (const char *text)

Protected Member Functions
const char *	GetSpecialCase (Number *number)
void	IntegerToBuffer (double value, unsigned int digits, int *outdigits) const

Protected Attributes
double	baseDouble
unsigned int	digits
char	fractionPoint
Protected Attributes inherited from NumeralSystem
CharBuffer *	buf

Private Member Functions
const char *	GetText (double number) const
bool	IsDigit (char *digit)

Private Attributes
unsigned int	baseInteger
char	maxNumeric
char	maxAlphaLower
char	maxAlphaUpper

Detailed Description

Base class for all numeral systems with a positional notation.

More info on positional notation is available at Wikipedia: https://wikipedia.org/wiki/Positional_notation

Definition at line 41 of file ntextp.h.

Constructor & Destructor Documentation

PositionalNumeralSystem()

PositionalNumeralSystem::PositionalNumeralSystem	(	unsigned int	base,
		unsigned int	digits,
		const char	fractionPoint
	)

Definition at line 40 of file ntextp.cpp.

References baseDouble, baseInteger, digits, fractionPoint, maxAlphaLower, maxAlphaUpper, and maxNumeric.

Referenced by DecimalSystem::DecimalSystem(), Program::NewPositionalInput(), and Program::NewPositionalOutput().

                              : digits(digits)
{
    this->fractionPoint = fractionPoint;
    this->baseInteger = base;
    this->baseDouble = base * 1.0;
    this->maxNumeric = (base > 10 ? 10 : base) + '0' - 1;
    this->maxAlphaLower = base > 10 ? base + 'a' - 11 : 0;
    this->maxAlphaUpper = base > 10 ? base + 'A' - 11 : 0;
}

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~PositionalNumeralSystem()

PositionalNumeralSystem::~PositionalNumeralSystem

(

)

Definition at line 53 of file ntextp.cpp.

{
}

Member Function Documentation

GetDigits()

unsigned int PositionalNumeralSystem::GetDigits ( )

virtual

Implements NumeralSystem.

Definition at line 97 of file ntextp.cpp.

References digits.

{
    return digits;
}

GetFractionPoint()

const char PositionalNumeralSystem::GetFractionPoint ( )

virtual

Implements NumeralSystem.

Definition at line 107 of file ntextp.cpp.

References fractionPoint.

{
    return static_cast<const char>(this->fractionPoint);
}

GetName()

const char * PositionalNumeralSystem::GetName ( )

virtual

Implements NumeralSystem.

Definition at line 62 of file ntextp.cpp.

References CharBuffer::Append(), baseInteger, NumeralSystem::buf, DecimalSystem::DecimalSystem(), CharBuffer::Empty(), CharBuffer::EnsureSize(), CharBuffer::GetString(), NumeralSystem::GetText(), RealNumber::RealNumber(), and StrLen().

{
    switch (baseInteger)
    {
    case 2:
        return "binary";
    case 8:
        return "octal";
    case 10:
        return "decimal";
    case 16:
        return "hexadecimal";
    }

    const char *text = "base ";
    Number *n = new RealNumber(baseInteger);
    NumeralSystem *ns = new DecimalSystem(2);
    const char *numtext = ns->GetText(n);

    buf->EnsureSize(StrLen(text) + StrLen(numtext) + 1);
    buf->Empty();
    buf->Append(text);
    buf->Append(numtext);

    delete ns;
    delete n;
    return buf->GetString();
}

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GetPrefix()

const char * PositionalNumeralSystem::GetPrefix ( )

virtual

Implements NumeralSystem.

Definition at line 91 of file ntextp.cpp.

{
    // TODO: Consider using prefix with numral systems != base 10
    return EMPTYSTRING;
}

GetSpecialCase()

const char * PositionalNumeralSystem::GetSpecialCase ( Number *  number )

protected

Definition at line 117 of file ntextp.cpp.

References CharBuffer::Append(), NumeralSystem::buf, CharBuffer::Empty(), CharBuffer::GetString(), Number::IsInfinite(), Number::IsNaN(), Number::IsNegative(), Number::IsNotImplemented(), and Number::IsZero().

Referenced by DecimalSystem::GetText(), and GetText().

{
    if (number->IsNaN())
    {
        buf->Empty();
        buf->Append("NaN");
        return buf->GetString();
    }

    if (number->IsNotImplemented())
    {
        buf->Empty();
        buf->Append("NotImplemented");
        return buf->GetString();
    }

    if (number->IsInfinite() && number->IsNegative())
    {
        buf->Empty();
        buf->Append("-Inf");
        return buf->GetString();
    }

    if (number->IsInfinite() && !number->IsNegative())
    {
        buf->Empty();
        buf->Append("Inf");
        return buf->GetString();
    }

    if (number->IsZero())
    {
        buf->Empty();
        buf->Append("0");
        return buf->GetString();
    }

    return nullptr;
}

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GetText() [1/2]

const char * PositionalNumeralSystem::GetText ( Number *  number )

virtual

Implements NumeralSystem.

Reimplemented in DecimalSystem.

Definition at line 157 of file ntextp.cpp.

References CharBuffer::Append(), NumeralSystem::buf, CharBuffer::CharBuffer(), cimag(), CharBuffer::Copy(), creal(), CharBuffer::Empty(), ComplexNumber::GetComplexValue(), Number::GetRealValue(), GetSpecialCase(), CharBuffer::GetString(), GetText(), nsysreal, and Number::system.

{
    const char *sc = GetSpecialCase(number);
    if (sc != nullptr)
    {
        return sc;
    }

    if (number->system == nsysreal)
    {
        return GetText(number->GetRealValue());
    }

    complex w = static_cast<ComplexNumber *>(number)->GetComplexValue();
    double a = creal(w);
    double b = cimag(w);

    if (a == 0.0 && b == 0.0)
    {
        buf->Empty();
        buf->Append('0');
        return buf->GetString();
    }

    CharBuffer *val = new CharBuffer(512);
    val->Empty();

    if (a != 0.0)
    {
        const char *real = GetText(a);
        val->Append(real);
    }

    const char *imag = GetText(b);
    if (a != 0.0 && b > 0.0)
    {
        val->Append('+');
    }

    if (b != 0.0)
    {
        val->Append(imag);
        val->Append('i');
    }

    buf->Copy(val);
    delete val;

    return buf->GetString();
}

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GetText() [2/2]

const char * PositionalNumeralSystem::GetText ( double  number ) const

private

Definition at line 208 of file ntextp.cpp.

References CharBuffer::Append(), baseDouble, NumeralSystem::buf, digits, CharBuffer::Empty(), fabs(), FloatUnion64::floatingPoint, fractionPoint, CharBuffer::GetString(), IntegerToBuffer(), CharBuffer::Is(), FloatUnion64::IsInf(), log2p(), pow(), CharBuffer::RemoveTrailing(), round(), and trunc().

Referenced by GetText().

{
    if (number == 0.0)
    {
        return "0";
    }

    buf->Empty();

    double dnumber = number;
    if (dnumber < 0.0)
    {
        buf->Append('-');
        dnumber = -dnumber;
    }

    double expbor = log2p(baseDouble, dnumber);
    double expacc = expbor > 0.0 ? 4e-14 : -1e-15;
    double expborder = trunc(expbor + expacc);

    int exponent = 0;
    double rounding;

    double bordermax = trunc(9.0 * 10 / baseDouble);
    double bordermin = trunc(-8.0 * 10 / baseDouble);

    // Find exponent
    if (expborder >= bordermax || expborder <= bordermin)
    {
        double dexp = trunc(log2p(baseDouble, dnumber) + expacc);
        dnumber = dnumber * pow(baseDouble, -dexp);

        // pow is inaccurate on small and large numbers
        if (dexp > 15 || dexp < -15)
        {
            dnumber += 2e-15;
        }

        // Adjust if below zero
        if (dnumber < 1.0)
        {
            dexp--;
            dnumber *= baseDouble;
        }

        exponent = static_cast<int>(dexp);
        rounding = 0;
    }
    else
    {
        double acc = exponent > 0 ? 15 : -15;
        rounding = pow(baseDouble, exponent + acc);
    }

    int digitout;
    int intdigits;

    double intvalue = trunc(dnumber + rounding);
    IntegerToBuffer(intvalue, digits, &intdigits);

    int fragdigits = digits - intdigits + (intvalue < 1.0 ? 1 : 0);
    if (fragdigits > 0)
    {
        buf->Append(fractionPoint);

        double fraction = fabs(round((dnumber - intvalue) * pow(baseDouble, fragdigits)));
        double temp1 = log2p(baseDouble, fraction);
        FloatUnion64 temp2;
        temp2.floatingPoint = temp1;
        bool fin = !temp2.IsInf();
        int actualdigits = static_cast<int>(trunc(temp1 + 3e-15));
        int padding = fragdigits - (fin == 1 ? actualdigits : 0) - 1;

        // Pad zeros if needed
        while (padding-- > 0)
        {
            buf->Append('0');
        }

        intvalue = static_cast<int64_t>(trunc(fraction * baseDouble) / baseDouble);
        IntegerToBuffer(intvalue, fragdigits, &digitout);

        // Remove trailing zeros
        // ReSharper disable once CppPossiblyErroneousEmptyStatements
        while (buf->RemoveTrailing('0'))
            ;

        buf->RemoveTrailing(fractionPoint);
    }

    // Add exponent
    if (exponent != 0)
    {
        buf->Append('e');
        buf->Append(exponent > 0 ? '+' : '-');
        IntegerToBuffer(abs(exponent), 3, &digitout);
    }

    // Make sure no rounding error is returned
    if (buf->Is("-0"))
    {
        buf->Empty();
        buf->Append('0');
    }

    return buf->GetString();
}

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IntegerToBuffer()

void PositionalNumeralSystem::IntegerToBuffer ( double  value, unsigned int  digits, int *  outdigits  ) const

protected

Definition at line 316 of file ntextp.cpp.

References CharBuffer::Append(), baseDouble, NumeralSystem::buf, fmod(), and trunc().

Referenced by DecimalSystem::GetText(), and GetText().

{
    static const char *alphaNumerics = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";
    unsigned int count = 0;
    char *chars = new char[128];
    char *start = chars;

    do
    {
        count++;
        unsigned int intremainder = static_cast<unsigned int>(trunc(fmod(value, baseDouble)));
        *chars++ = alphaNumerics[intremainder];
        value /= baseDouble;
    } while (value >= 1.0);

    unsigned int n = count;
    unsigned int q = digits;
    chars--;

    while (n-- != 0 && q-- != 0)
    {
        buf->Append(*chars--);
    }

    n++;
    while (n-- != 0)
    {
        buf->Append('0');
    }

    *outdigits = count;
    delete[] start;
}

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IsDigit()

bool PositionalNumeralSystem::IsDigit ( char *  digit )

private

Definition at line 57 of file ntextp.cpp.

{
    return true;
}

Parse()

Number * PositionalNumeralSystem::Parse ( const char *  text, unsigned int *  length, char **  end  )

virtual

Implements NumeralSystem.

Definition at line 350 of file ntextp.cpp.

References baseDouble, fractionPoint, maxAlphaLower, maxAlphaUpper, maxNumeric, pow(), and RealNumber::RealNumber().

{
    unsigned int pos = 0;
    double integer = 0;
    bool done = false;

    // Parse integer part of number
    do
    {
        double addition;
        if (*text == '\0')
        {
            done = true;
            continue;
        }

        if (*text >= '0' && *text <= maxNumeric)
        {
            addition = (*text - '0') * 1.0;
        }
        else if (maxAlphaUpper != 0 && *text >= 'A' && *text <= maxAlphaUpper)
        {
            addition = (*text - 'A' + 10) * 1.0;
        }
        else if (maxAlphaLower != 0 && *text >= 'a' && *text <= maxAlphaLower)
        {
            addition = (*text - 'a' + 10) * 1.0;
        }
        else
        {
            done = true;
            continue;
        }

        integer = integer * baseDouble + addition;
        text++;
        pos++;
    } while (!done);

    // Digits not found
    if (pos == 0)
    {
        *length = 0;
        *end = const_cast<char *>(text);
        return new RealNumber();
    }

    // Parse fraction part of number
    double fraction = 0.0;
    double divisor = 1.0;
    if (*text == fractionPoint && fractionPoint != '\0')
    {
        done = false;
        double addition;
        text++;
        pos++;

        do
        {
            if (*text == '\0')
            {
                done = true;
                continue;
            }

            if (*text >= '0' && *text <= maxNumeric)
            {
                addition = (*text - '0') * 1.0;
            }
            else if (maxAlphaUpper != 0 && *text >= 'A' && *text <= maxAlphaUpper)
            {
                addition = (*text - 'A' + 10) * 1.0;
            }
            else if (maxAlphaLower != 0 && *text >= 'a' && *text <= maxAlphaLower)
            {
                addition = (*text - 'a' + 10) * 1.0;
            }
            else
            {
                done = true;
                continue;
            }

            fraction = fraction * baseDouble + addition;
            divisor *= baseDouble;
            text++;
            pos++;
        } while (!done);
    }

    // Parse exponent part of number
    double exp = 0.0;
    if (*text == 'e' || *text == 'E')
    {
        double addition;
        text++;
        pos++;

        double sign = *text == '+' ? 1.0 : *text == '-' ? -1.0 : 0.0;

        if (sign != 0.0)
        {
            done = false;
            text++;
            pos++;

            do
            {
                if (*text == '\0')
                {
                    done = true;
                    continue;
                }

                if (*text >= '0' && *text <= maxNumeric)
                {
                    addition = (*text - '0') * 1.0;
                }
                else if (maxAlphaUpper != 0 && *text >= 'A' && *text <= maxAlphaUpper)
                {
                    addition = (*text - 'A' + 10) * 1.0;
                }
                else if (maxAlphaLower != 0 && *text >= 'a' && *text <= maxAlphaLower)
                {
                    addition = (*text - 'a' + 10) * 1.0;
                }
                else
                {
                    done = true;
                    continue;
                }

                exp = exp * baseDouble + addition;
                text++;
                pos++;
            } while (!done);
            exp *= sign;
        }
        else
        {
            text--;
            pos--;
        }
    }

    *length = pos;
    *end = const_cast<char *>(text);

    double dnumber = (integer + (fraction / divisor));

    if (exp != 0.0)
    {
        // pow seems a bit off
        dnumber *= pow(baseDouble, exp + 4e-15);
    }

    return new RealNumber(dnumber);
}

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SetDigits()

void PositionalNumeralSystem::SetDigits ( unsigned int  digits )

virtual

Implements NumeralSystem.

Definition at line 102 of file ntextp.cpp.

References digits.

{
    this->digits = digits;
}

SetFractionPoint()

void PositionalNumeralSystem::SetFractionPoint ( const char  fractionPoint )

virtual

Implements NumeralSystem.

Definition at line 112 of file ntextp.cpp.

References fractionPoint.

{
    this->fractionPoint = fractionPoint;
}

Member Data Documentation

baseDouble

double PositionalNumeralSystem::baseDouble

protected

Definition at line 60 of file ntextp.h.

Referenced by GetText(), IntegerToBuffer(), Parse(), and PositionalNumeralSystem().

baseInteger

unsigned int PositionalNumeralSystem::baseInteger

private

Definition at line 68 of file ntextp.h.

Referenced by GetName(), and PositionalNumeralSystem().

digits

unsigned int PositionalNumeralSystem::digits

protected

Definition at line 61 of file ntextp.h.

Referenced by GetDigits(), DecimalSystem::GetText(), GetText(), PositionalNumeralSystem(), and SetDigits().

fractionPoint

char PositionalNumeralSystem::fractionPoint

protected

Definition at line 62 of file ntextp.h.

Referenced by GetFractionPoint(), DecimalSystem::GetText(), GetText(), Parse(), PositionalNumeralSystem(), and SetFractionPoint().

maxAlphaLower

char PositionalNumeralSystem::maxAlphaLower

private

Definition at line 70 of file ntextp.h.

Referenced by Parse(), and PositionalNumeralSystem().

maxAlphaUpper

char PositionalNumeralSystem::maxAlphaUpper

private

Definition at line 71 of file ntextp.h.

Referenced by Parse(), and PositionalNumeralSystem().

maxNumeric

char PositionalNumeralSystem::maxNumeric

private

Definition at line 69 of file ntextp.h.

Referenced by Parse(), and PositionalNumeralSystem().

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The documentation for this class was generated from the following files:

• src/lib/ntextp.h
• src/lib/ntextp.cpp