Types

COMPLEX, LONGCOMPLEX

Syntax

The EBNF for the textual representation of values of types that represent complex numbers is

Values and Value Lists

complexNumberValue :
    compactNotation | expandedNotation | pairNotation ;

complexNumberValueList :
    complexNumberValue ( listSeparator complexNumberValue )* ;

listSeparator :
    defaultListSeparator | userDefinedListSeparator | newline ;

defaultListSeparator :
    defaultListSeparatorForValuesWithCommas |
    defaultListSeparatorForValuesWithoutCommas ;

defaultListSeparatorForValuesWithCommas :
    ';' whitespace ;

defaultListSeparatorForValuesWithoutCommas :
    ',' whitespace ;

userDefinedListSeparator :
    character whitespace? ;

Arrays and Array Lists

complexNumberArray :
     openingArrayDelimiter complexNumberValueList closingArrayDelimiter ;

complexNumberArrayList :
    complexNumberArray ( listSeparator complexNumberArray )* ;

openingArrayDelimiter :
    ( defaultOpeningArrayDelimiter | userDefinedOpeningArrayDelimiter ) whitespace ;

closingArrayDelimiter :
    whitespace ( defaultClosingArrayDelimiter | userDefinedOpeningArrayDelimiter ) ;

defaultOpeningArrayDelimiter :
    '{' ;

defaultClosingArrayDelimiter :
    '}' ;

userDefinedOpeningArrayDelimiter :
    '(' | '[' ;

userDefinedClosingArrayDelimiter :
    ')' | ']' ;

Mathematical Notation

compactNotation :
    compactNotationAllPartsZero | compactNotationImaginaryPartZero |
    compactNotationRealPartZero | compactNotationAllPartsNonZero ;

compactNotationAllPartsZero :
    '0' ;

compactNotationImaginaryPartZero :
    compactRealPart ;

compactNotationRealPartZero ;
    simpleSign? compactImaginaryPart ;

compactNotationAllPartsNonZero :
    compactRealPart simpleSign compactImaginaryPart ;

compactRealPart :
    simpleSign? simpleNonZeroDecimalRealNumber ;

compactImaginaryPart :
    simpleNonZeroDecimalRealNumber imaginaryPartDesignator;

simpleSign :
    '+' | '-' ;

imaginaryPartDesignator :
    'i' | 'j' ;

simpleNonZeroDecimalRealNumber :
    decimalDigit+ ( decimalPoint | decimalComma ) decimalDigit+ ;

expandedNotation :
    expandedRealPart simpleSign expandedImaginaryPart ;

expandedRealPart :
    '0' | simpleNonZeroDecimalRealNumber ;

expandedImaginaryPart :
   ( '0' | simpleNonZeroDecimalRealNumber ) imaginaryPartDesignator ;

Pair Notation

pairNotation :
    unpaddedComplexPair | leftPaddedComplexPair | rightPaddedComplexPair ;

leftPaddedComplexPair :
    whitespace+ unpaddedComplexPair ;

rightPaddedComplexPair :
    unpaddedComplexPair whitespace+ ;

whitespace :
    ' ' ;

unpaddedComplexPair :
    '(' realPart partSeparator imaginaryPart ')' ;

realPart :
    formattedRealNumber ;

imaginaryPart :
    formattedRealNumber ;

partSeparator :
    decimalPointModePartSeparator | decimalCommaModePartSeparator ;

decimalPointModePartSeparator :
    ',' whitespace ;

decimalCommaModePartSeparator :
    ';' whitespace ;

formattedRealNumber :
    realNumberSimpleFormat | realNumberOtherFormats ;

realNumberSimpleFormat :
    negativeSign? decimalDigit decimalPoint decimalDigit+ exponent ;

realNumberOtherFormats :
    sign? fillChar* ( fixedFmtDecimal | engFmtDecimal | expFmtDecimal ) ;

fixedFmtDecimal :
    integralPart ( decimalPoint | decimalComma ) fractionalPart ;

engFmtDecimal :
    engIntegralPart ( decimalPoint | decimalComma ) fractionalPart engExponent ;

expFmtDecimal :
    fixedFmtDecimal exponent ;

sign :
    whitespace | '+' | '-' ;

negativeSign :
    '-' ;

fillChar :
    whitespace | '*' | '0' ;

integralPart :
    decimalDigit decimalDigit? decimalDigit? ( digitSeparator? digitGroup )* ;

engIntegralPart :
    ( ( ( decimalDigit digitSeparator? )? decimalDigit )? decimalDigit )? decimalDigit ;

fractionalPart :
    ( decimalDigit ( decimalDigit ( decimalDigit digitSeparator )? )? )* decimalDigit ;

exponent :
    'E' ( '+' | '-' ) decimalDigit decimalDigit+ ;

engExponent :
    exponent ;

digitSeparator :
    decimalPointModeDigitSeparator | decimalCommaModeDigitSeparator ;

decimalPointModeDigitSeparator :
    whitespace | ',' ;

decimalCommaModeDigitSeparator :
    whitespace | '.' ;

digitGroup :
    decimalDigit decimalDigit decimalDigit ;

decimalPoint :
    '.' ;

decimalComma :
    ',' ;

decimalDigit  :
    '0' .. '9' ;

character :
    <any printable ASCII character> ;

newline :
    <runtime host dependent ASCII control sequence for new line> ;

Static Semantics

• all values in a list are shown in the same notation.
• all values in a list are shown with identical formatting.
• all values in a list are shown with identical imaginary part designators.
• real and imaginary parts are shown with identical formatting.
• the numeric value represented by engExponent is always divisible by three.
• the numeric value represented by simpleNonZeroDecimalRealNumber is never zero.
• in decimal point mode, decimalPoint is shown instead of decimalComma, decimalPointModePartSeparator is shown instead of decimalCommaModePartSeparator and decimalPointModeDigitSeparator is shown instead of decimalCommaModeDigitSeparator.
• in decimal comma mode, decimalComma is shown instead of decimalPoint, decimalCommaModePartSeparator is shown instead of decimalPointModePartSeparator and decimalCommaModeDigitSeparator is shown instead of decimalPointModeDigitSeparator.