Number Class Reference

A number. More...

`#include <Number.h>`

## Public Member Functions

| Number ()
| Number (std::string number, const ParseOptions &po=default_parse_options)
| Number (long int numerator, long int denominator=1, long int exp_10=0)
| Number (const Number &o)
void | set (std::string number, const ParseOptions &po=default_parse_options)
void | set (long int numerator, long int denominator=1, long int exp_10=0, bool keep_precision=false, bool keep_imag=false)
void | setPlusInfinity (bool keep_precision=false, bool keep_imag=false)
void | setMinusInfinity (bool keep_precision=false, bool keep_imag=false)
void | setFloat (long double d_value)
bool | setInterval (const Number &nr_lower, const Number &nr_upper, bool keep_precision=false)
void | setInternal (const mpz_t &mpz_value, bool keep_precision=false, bool keep_imag=false)
void | setInternal (mpz_srcptr mpz_value, bool keep_precision=false, bool keep_imag=false)
void | setInternal (const mpq_t &mpq_value, bool keep_precision=false, bool keep_imag=false)
void | setInternal (const mpz_t &mpz_num, const mpz_t &mpz_den, bool keep_precision=false, bool keep_imag=false)
void | setInternal (const mpfr_t &mpfr_value, bool merge_precision=false, bool keep_imag=false)
void | setImaginaryPart (const Number &o)
void | setImaginaryPart (long int numerator, long int denominator=1, long int exp_10=0)
void | set (const Number &o, bool merge_precision=false, bool keep_imag=false)
void | clear (bool keep_precision=false)
void | clearReal ()
void | clearImaginary ()
const mpq_t & | internalRational () const
const mpfr_t & | internalUpperFloat () const
const mpfr_t & | internalLowerFloat () const
mpq_t & | internalRational ()
mpfr_t & | internalUpperFloat ()
mpfr_t & | internalLowerFloat ()
Number * | internalImaginary () const
void | markAsImaginaryPart (bool is_imag=true)
const NumberType & | internalType () const
bool | setToFloatingPoint ()
void | precisionToInterval ()
bool | intervalToPrecision (long int min_precision=2)
void | intervalToMidValue (bool increase_precision_if_close)
void | intervalToMidValue ()
void | splitInterval (unsigned int nr_of_parts, std::vector< Number > &v) const
bool | getCentralInteger (Number &nr_int, bool *b_multiple=NULL, std::vector< Number > *v=NULL) const
bool | mergeInterval (const Number &o, bool set_to_overlap=false)
void | setUncertainty (const Number &o, bool to_precision=false)
void | setRelativeUncertainty (const Number &o, bool to_precision=false)
Number | uncertainty () const
Number | relativeUncertainty () const
double | floatValue () const
int | intValue (bool *overflow=NULL) const
unsigned int | uintValue (bool *overflow=NULL) const
long int | lintValue (bool *overflow=NULL) const
long long int | llintValue () const
unsigned long int | ulintValue (bool *overflow=NULL) const
bool | isApproximate () const
bool | isFloatingPoint () const
void | setPrecisionAndApproximateFrom (const Number &o)
bool | isInterval (bool ignore_imag=true) const
bool | imaginaryPartIsInterval () const
void | setApproximate (bool is_approximate=true)
int | precision (int calculate_from_interval=0) const
void | setPrecision (int prec)
bool | isUndefined () const
bool | isInfinite (bool ignore_imag=true) const
bool | isPlusInfinity (bool ignore_imag=false) const
bool | isMinusInfinity (bool ignore_imag=false) const
bool | includesInfinity (bool ignore_imag=false) const
bool | includesPlusInfinity () const
bool | includesMinusInfinity () const
Number | realPart () const
Number | imaginaryPart () const
Number | numerator () const
Number | denominator () const
Number | complexNumerator () const
Number | complexDenominator () const
Number | lowerEndPoint (bool include_imag=false) const
Number | upperEndPoint (bool include_imag=false) const
void | operator= (const Number &o)
void | operator= (long int i)
void | operator-- (int)
void | operator++ (int)
Number | operator- () const
Number | operator* (const Number &o) const
Number | operator/ (const Number &o) const
Number | operator+ (const Number &o) const
Number | operator- (const Number &o) const
Number | operator^ (const Number &o) const
Number | operator* (long int i) const
Number | operator/ (long int i) const
Number | operator+ (long int i) const
Number | operator- (long int i) const
Number | operator^ (long int i) const
Number | operator&& (const Number &o) const
Number | operator|| (const Number &o) const
Number | operator! () const
void | operator*= (const Number &o)
void | operator/= (const Number &o)
void | operator+= (const Number &o)
void | operator-= (const Number &o)
void | operator^= (const Number &o)
void | operator*= (long int i)
void | operator/= (long int i)
void | operator+= (long int i)
void | operator-= (long int i)
void | operator^= (long int i)
bool | operator== (const Number &o) const
bool | operator!= (const Number &o) const
bool | operator< (const Number &o) const
bool | operator<= (const Number &o) const
bool | operator> (const Number &o) const
bool | operator>= (const Number &o) const
bool | operator< (long int i) const
bool | operator<= (long int i) const
bool | operator> (long int i) const
bool | operator>= (long int i) const
bool | operator== (long int i) const
bool | operator!= (long int i) const
bool | bitAnd (const Number &o)
bool | bitOr (const Number &o)
bool | bitXor (const Number &o)
bool | bitNot ()
bool | bitCmp (unsigned int bits)
bool | bitSet (unsigned long bit, bool set=true)
int | bitGet (unsigned long bit) const
bool | bitEqv (const Number &o)
bool | shiftLeft (const Number &o)
bool | shiftRight (const Number &o)
bool | shift (const Number &o)
bool | hasRealPart () const
bool | hasImaginaryPart () const
bool | isComplex () const
bool | isInteger (IntegerType integer_type=INTEGER_TYPE_NONE) const
Number | integer () const
bool | isRational () const
bool | isReal () const
bool | isNonInteger () const
bool | isFraction () const
bool | isZero () const
bool | isNonZero () const
bool | isOne () const
bool | isTwo () const
bool | isI () const
bool | isMinusI () const
bool | isMinusOne () const
bool | isNegative () const
bool | isNonNegative () const
bool | isPositive () const
bool | isNonPositive () const
bool | realPartIsNegative () const
bool | realPartIsNonNegative () const
bool | realPartIsPositive () const
bool | realPartIsNonZero () const
bool | realPartIsRational () const
bool | imaginaryPartIsNegative () const
bool | imaginaryPartIsPositive () const
bool | imaginaryPartIsNonNegative () const
bool | imaginaryPartIsNonPositive () const
bool | imaginaryPartIsNonZero () const
bool | hasNegativeSign () const
bool | hasPositiveSign () const
bool | equalsZero () const
bool | equals (const Number &o, bool allow_interval=false, bool allow_infinite=false) const
bool | equals (long int i) const
int | equalsApproximately (const Number &o, int prec) const
ComparisonResult | compare (const Number &o, bool ignore_imag=false) const
ComparisonResult | compareAbsolute (const Number &o, bool ignore_imag=false) const
ComparisonResult | compare (long int i) const
ComparisonResult | compareApproximately (const Number &o, int prec=EQUALS_PRECISION_LOWEST) const
ComparisonResult | compareImaginaryParts (const Number &o) const
ComparisonResult | compareRealParts (const Number &o) const
bool | isGreaterThan (const Number &o) const
bool | isLessThan (const Number &o) const
bool | isGreaterThanOrEqualTo (const Number &o) const
bool | isLessThanOrEqualTo (const Number &o) const
bool | isGreaterThan (long int i) const
bool | isLessThan (long int i) const
bool | isGreaterThanOrEqualTo (long int i) const
bool | isLessThanOrEqualTo (long int i) const
bool | isEven () const
bool | numeratorIsGreaterThan (long int i) const
bool | numeratorIsLessThan (long int i) const
bool | numeratorEquals (long int i) const
bool | denominatorIsGreaterThan (long int i) const
bool | denominatorIsLessThan (long int i) const
bool | denominatorEquals (long int i) const
bool | denominatorIsGreater (const Number &o) const
bool | denominatorIsLess (const Number &o) const
bool | denominatorIsEqual (const Number &o) const
bool | denominatorIsEven () const
bool | denominatorIsTwo () const
bool | numeratorIsEven () const
bool | numeratorIsOne () const
bool | numeratorIsMinusOne () const
bool | isOdd () const
int | integerLength () const
bool | add (const Number &o)
bool | add (long int i)
bool | subtract (const Number &o)
bool | subtract (long int i)
bool | multiply (const Number &o)
bool | multiply (long int i)
bool | divide (const Number &o)
bool | divide (long int i)
bool | recip ()
bool | raise (const Number &o, bool try_exact=true)
bool | sqrt ()
bool | cbrt ()
bool | root (const Number &o)
bool | allroots (const Number &o, std::vector< Number > &roots)
bool | exp10 (const Number &o)
bool | exp2 (const Number &o)
bool | exp10 ()
bool | exp2 ()
bool | square ()
bool | negate ()
void | setNegative (bool is_negative)
bool | abs ()
bool | signum ()
bool | round (const Number &o, bool halfway_to_even=true)
bool | floor (const Number &o)
bool | ceil (const Number &o)
bool | trunc (const Number &o)
bool | mod (const Number &o)
bool | isIntegerDivisible (const Number &o) const
bool | isqrt ()
bool | isPerfectSquare () const
bool | round (bool halfway_to_even=true)
bool | round (RoundingMode mode)
bool | floor ()
bool | ceil ()
bool | trunc ()
bool | frac ()
bool | rem (const Number &o)
bool | smod (const Number &o)
bool | irem (const Number &o)
bool | irem (const Number &o, Number &q)
bool | iquo (const Number &o)
bool | iquo (unsigned long int i)
bool | iquo (const Number &o, Number &r)
int | getBoolean () const
void | toBoolean ()
void | setTrue (bool is_true=true)
void | setFalse ()
void | setLogicalNot ()
void | e (bool use_cached_number=true)
void | pi ()
void | catalan ()
void | euler ()
bool | zeta ()
bool | zeta (const Number &o)
| Hurwitz zeta function.
bool | gamma ()
bool | digamma ()
bool | airy ()
bool | erf ()
bool | erfi ()
bool | erfc ()
bool | erfinv ()
bool | besselj (const Number &o)
bool | bessely (const Number &o)
bool | sin ()
bool | asin ()
bool | sinh ()
bool | asinh ()
bool | cos ()
bool | acos ()
bool | cosh ()
bool | acosh ()
bool | tan ()
bool | atan ()
bool | atan2 (const Number &o, bool allow_zero=false)
bool | arg ()
bool | tanh ()
bool | atanh ()
bool | ln ()
bool | log (const Number &o)
bool | exp ()
bool | lambertW ()
bool | lambertW (const Number &k)
bool | gcd (const Number &o)
bool | lcm (const Number &o)
bool | polylog (const Number &o)
bool | igamma (const Number &o)
bool | betainc (const Number &p, const Number &q, bool regularized=true)
bool | fresnels ()
bool | fresnelc ()
bool | expint ()
bool | logint ()
bool | sinint ()
bool | sinhint ()
bool | cosint ()
bool | coshint ()
bool | factorial ()
bool | multiFactorial (const Number &o)
bool | doubleFactorial ()
bool | binomial (const Number &m, const Number &k)
bool | factorize (std::vector< Number > &factors)
bool | bernoulli ()
void | rand ()
void | randn ()
void | intRand (const Number &ceil)
bool | add (const Number &o, MathOperation op)
std::string | printNumerator (int base=10, bool display_sign=true, BaseDisplay base_display=BASE_DISPLAY_NORMAL, bool lower_case=false) const
std::string | printDenominator (int base=10, bool display_sign=true, BaseDisplay base_display=BASE_DISPLAY_NORMAL, bool lower_case=false) const
std::string | printImaginaryNumerator (int base=10, bool display_sign=true, BaseDisplay base_display=BASE_DISPLAY_NORMAL, bool lower_case=false) const
std::string | printImaginaryDenominator (int base=10, bool display_sign=true, BaseDisplay base_display=BASE_DISPLAY_NORMAL, bool lower_case=false) const
std::string | print (const PrintOptions &po=default_print_options, const InternalPrintStruct &ips=top_ips) const

## Protected Member Functions

void | testInteger ()
bool | testErrors (int error_level=1) const
bool | testFloatResult (bool allow_infinite_result=true, int error_level=1, bool test_integer=true)

## Protected Attributes

mpq_t | r_value
mpfr_t | fu_value
mpfr_t | fl_value
Number * | i_value
NumberType | n_type
bool | b_approx
bool | b_imag
int | i_precision

## Detailed Description

A number.

Can be rational, floating point, complex or infinite. Has arbitrary precision (uses Calculator::precision()) and infinitely large rational numbers. Implimented using GNU MP and MPFR.

## Constructor & Destructor Documentation

## Number() [1/4]

Number::Number | ( |  | ) |

Constructs a number initialized as zero.

Referenced by add(), divide(), exp10(), exp2(), imaginaryPart(), isFloatingPoint(), multiply(), negate(), Number(), raise(), realPart(), subtract(), and zeta().

## Number() [2/4]

Number::Number | ( | std::string | number,
|  | const ParseOptions & | po = default_parse_options )

Constructs a number parsing a text string.

Parameters

  number | Text string to read number from.
  po | Options for parsing the text string.

## Number() [3/4]

Number::Number | ( | long int | numerator,
|  | long int | denominator = 1,
|  | long int | exp_10 = 0 )

Constructs a rational number (numerator/denominator * 10^exp_10).

Parameters

  numerator | Numerator of rational number
  denominator | Denominator of rational number
  exp_10 | Base-10 exponent

## Number() [4/4]

Number::Number | ( | const Number & | o | ) |

Constructs a copy of a number.

References Number().

## Member Function Documentation

## add()

bool Number::add | ( | const Number & | o | ) |

Add to the number (x+o).

Parameters

  o | Number to add.

Returns
  true if the operation was successful.

References Number().

## catalan()

void Number::catalan | ( |  | ) |

Set the number to Catalan's constant, calculated with the current default precision.

## divide()

bool Number::divide | ( | const Number & | o | ) |

Divide the number (x/o).

Parameters

  o | Number to divide by.

Returns
  true if the operation was successful.

References Number().

## e()

void Number::e | ( | bool | use_cached_number = true | ) |

Set the number to e, the base of natural logarithm, calculated with the current default precision.

## euler()

void Number::euler | ( |  | ) |

Set the number to Euler's constant, calculated with the current default precision.

## exp10() [1/2]

bool Number::exp10 | ( |  | ) |

Set the number to ten raised by the number (10^x).

Returns
  true if the operation was successful.

## exp10() [2/2]

bool Number::exp10 | ( | const Number & | o | ) |

Multiply the number with a power of ten (x*10^o).

Parameters

  o | Number to raise 10 by.

Returns
  true if the operation was successful.

References Number().

## exp2() [1/2]

bool Number::exp2 | ( |  | ) |

Set the number to two raised by the number (2^x).

Returns
  true if the operation was successful.

## exp2() [2/2]

bool Number::exp2 | ( | const Number & | o | ) |

Multiply the number with a power of two (x*2^o).

Parameters

  o | Number to raise 2 by.

Returns
  true if the operation was successful.

References Number().

## imaginaryPart()

Number Number::imaginaryPart | ( |  | ) | const

Returns the imaginary part as real number of the number if it is complex, or zero if it is real.

Returns
  true if the imaginary part of a complex number.

References Number().

## intValue()

int Number::intValue | ( | bool * | overflow = NULL | ) | const

Converts a number to an integer. If the number does not represent an integer it will rounded using round().

Parameters

  [out] | overflow | If overflow is non-null it will be set to true if the number was to large to fit the return type.

Returns
  Resulting integer.

## isApproximate()

bool Number::isApproximate | ( |  | ) | const

Returns true if the number is approximate.

Returns
  true if the number is approximate.

## isFloatingPoint()

bool Number::isFloatingPoint | ( |  | ) | const

Returns true if the number is a floating point number.

Returns
  true if the number has an approximate representation.

References Number().

## isInfinite()

bool Number::isInfinite | ( | bool | ignore_imag = true | ) | const

Returns true if the number is infinity, plus infinity or minus infinity.

Returns
  true if the number is infinite.

## isMinusInfinity()

bool Number::isMinusInfinity | ( | bool | ignore_imag = false | ) | const

Returns true if the number is minus infinity.

Returns
  true if the number is minus infinity.

## isPlusInfinity()

bool Number::isPlusInfinity | ( | bool | ignore_imag = false | ) | const

Returns true if the number is plus infinity.

Returns
  true if the number is plus infinity.

## multiply()

bool Number::multiply | ( | const Number & | o | ) |

Multiply the number (x*o).

Parameters

  o | Number to multiply with.

Returns
  true if the operation was successful.

References Number().

## negate()

bool Number::negate | ( |  | ) |

Negate the number (-x).

Returns
  true if the operation was successful.

References Number().

## pi()

void Number::pi | ( |  | ) |

Set the number to pi, Archimede's constant, calculated with the current default precision.

## precision()

int Number::precision | ( | int | calculate_from_interval = 0 | ) | const

Returns the.precision of the number.

Returns
  Precision of the number or -1 if the number is exact or the precision has not been set.

## raise()

bool Number::raise | ( | const Number & | o,
|  | bool | try_exact = true )

Raise the number (x^o).

Parameters

  o | Number to raise to.
  try_exact | If an exact solution should be tried first (might be slow).

Returns
  true if the operation was successful.

References Number().

## realPart()

Number Number::realPart | ( |  | ) | const

Returns the real part of the number if it is complex, or a copy if it is real.

Returns
  true if the real part of a complex number.

References Number().

## recip()

bool Number::recip | ( |  | ) |

Invert the number (1/x).

Returns
  true if the operation was successful.

## setApproximate()

void Number::setApproximate | ( | bool | is_approximate = true | ) |

Defines the number as approximate or exact.

Parameters

  is_approximate | If the number shall be regarded as approximate.

## square()

bool Number::square | ( |  | ) |

Raise the number by two (x^2).

Returns
  true if the operation was successful.

## subtract()

bool Number::subtract | ( | const Number & | o | ) |

Subtracts from to the number (x-o).

Parameters

  o | Number to subtract.

Returns
  true if the operation was successful.

References Number().

## zeta()

bool Number::zeta | ( |  | ) |

Set the number to Riemann's zeta with the number as integral point. The number must be an integer greater than one.

Returns
  true if the calculation was successful.

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

- /opt/local/var/macports/build/libqalculate-ce1473f9/work/libqalculate-5.9.0/libqalculate/Number.h