Operator overloading, general real functions

Operator overloading, general real functions#

Operator overloading: scope and restrictions#

Compatible operators

The cost of creating and destroying objects#

Some text

Raw addition of two floating point numbers#

ctx.rawadd(res, x, y)#

where ctx is math53, ctxboost or ctxflint.

Sets res to the sum of the floating point number x and y.

An example in Python

>>> from xlcalcnet import XComplex
>>> XComplex.Abs(0.5)
XComplex('5.2359877559829887307E-1')
>>> XComplex.Abs('0.1')
XComplex('5.3518479027559984754E-1')

An example in Visual Basic

>>> from xlcalcnet import Gpc
>>> Gpc.Abs(0.5)
Gpc('5.2359877559829887307E-1')
>>> Gpc.Abs('0.1')
Gpc('5.3518479027559984754E-1')

Raw subtraction of two floating point numbers#

ctx.rawsub(res, x, y)#

where ctx is math53, ctxboost or ctxflint.

Sets res to the difference of the floating point numbers x and y.

An example in Python

>>> from xlcalcnet import XComplex
>>> XComplex.Abs(0.5)
XComplex('5.2359877559829887307E-1')
>>> XComplex.Abs('0.1')
XComplex('5.3518479027559984754E-1')

An example in Visual Basic

>>> from xlcalcnet import Gpc
>>> Gpc.Abs(0.5)
Gpc('5.2359877559829887307E-1')
>>> Gpc.Abs('0.1')
Gpc('5.3518479027559984754E-1')

Raw multiplication of two floating point numbers#

ctx.rawmul(res, x, y)#

where ctx is math53, ctxboost or ctxflint.

Sets res to the product of the floating point numbers x and y.

An example in Python

>>> from xlcalcnet import XComplex
>>> XComplex.Abs(0.5)
XComplex('5.2359877559829887307E-1')
>>> XComplex.Abs('0.1')
XComplex('5.3518479027559984754E-1')

An example in Visual Basic

>>> from xlcalcnet import Gpc
>>> Gpc.Abs(0.5)
Gpc('5.2359877559829887307E-1')
>>> Gpc.Abs('0.1')
Gpc('5.3518479027559984754E-1')

Raw division of two floating point numbers#

ctx.rawdiv(res, x, y)#

where ctx is math53, ctxboost or ctxflint.

Sets res to the quotient of the floating point numbers x and y.

An example in Python

>>> from xlcalcnet import XComplex
>>> XComplex.Abs(0.5)
XComplex('5.2359877559829887307E-1')
>>> XComplex.Abs('0.1')
XComplex('5.3518479027559984754E-1')

An example in Visual Basic

>>> from xlcalcnet import Gpc
>>> Gpc.Abs(0.5)
Gpc('5.2359877559829887307E-1')
>>> Gpc.Abs('0.1')
Gpc('5.3518479027559984754E-1')

Raw addition of a floating point number and a signed 32 bit integer#

ctx.rawaddint32(res, x, i)#

where ctx is math53, ctxboost or ctxflint.

Sets res to the sum of the floating point number x and the signed 32 bit integer i.

An example in Python

>>> from xlcalcnet import XComplex
>>> XComplex.Abs(0.5)
XComplex('5.2359877559829887307E-1')
>>> XComplex.Abs('0.1')
XComplex('5.3518479027559984754E-1')

An example in Visual Basic

>>> from xlcalcnet import Gpc
>>> Gpc.Abs(0.5)
Gpc('5.2359877559829887307E-1')
>>> Gpc.Abs('0.1')
Gpc('5.3518479027559984754E-1')

Raw subtraction of a floating point number and a signed 32 bit integer#

ctx.rawsubint32(res, x, i)#
ctx.rawIntSub(res, x, i)#

where ctx is math53, ctxboost or ctxflint.

Sets res to the difference of the floating point number x and the signed 32 bit integer i (SubInt) or to the difference of the signed 32 bit integer i the floating point number x (IntSub).

An example in Python

>>> from xlcalcnet import XComplex
>>> XComplex.Abs(0.5)
XComplex('5.2359877559829887307E-1')
>>> XComplex.Abs('0.1')
XComplex('5.3518479027559984754E-1')

An example in Visual Basic

>>> from xlcalcnet import Gpc
>>> Gpc.Abs(0.5)
Gpc('5.2359877559829887307E-1')
>>> Gpc.Abs('0.1')
Gpc('5.3518479027559984754E-1')

Raw multiplication of a floating point number and a signed 32 bit integer#

ctx.rawmulint32(res, x, i)#

where ctx is math53, ctxboost or ctxflint.

Sets res to the product of the floating point number x and the signed 32 bit integer i.

An example in Python

>>> from xlcalcnet import XComplex
>>> XComplex.Abs(0.5)
XComplex('5.2359877559829887307E-1')
>>> XComplex.Abs('0.1')
XComplex('5.3518479027559984754E-1')

An example in Visual Basic

>>> from xlcalcnet import Gpc
>>> Gpc.Abs(0.5)
Gpc('5.2359877559829887307E-1')
>>> Gpc.Abs('0.1')
Gpc('5.3518479027559984754E-1')

Raw division of a floating point number and a signed 32 bit integer#

ctx.rawdivint32(res, x, i)#
ctx.rawIntDiv(res, i, x)#

where ctx is math53, ctxboost or ctxflint.

Sets res to the quotient of the floating point number x and the signed 32 bit integer i (DivInt) or to the quotient of the signed 32 bit integer i the floating point number x (IntDiv).

An example in Python

>>> from xlcalcnet import XComplex
>>> XComplex.Abs(0.5)
XComplex('5.2359877559829887307E-1')
>>> XComplex.Abs('0.1')
XComplex('5.3518479027559984754E-1')

An example in Visual Basic

>>> from xlcalcnet import Gpc
>>> Gpc.Abs(0.5)
Gpc('5.2359877559829887307E-1')
>>> Gpc.Abs('0.1')
Gpc('5.3518479027559984754E-1')

Fused multiplication and addition: \(\mathrm{fma}(x, y, z)\)#

ctx.fma(x, y, z)#

where ctx is math53, ctxboost or ctxflint.

If successful, returns the value of x * y + z as if calculated to infinite precision and rounded once to fit the result type (or, alternatively, calculated as a single ternary floating-point operation).

See also: https://en.cppreference.com/w/cpp/numeric/math/fma

An example in Python

>>> from xlcalcnet import xreal
>>> xreal.Copysign(0.5, 2)
xreal('5.2359877559829887307E-1')
>>> xreal.Copysign('0.51', 2)
xreal('5.3518479027559984754E-1')

An example in Visual Basic

>>> from xlcalcnet import Gpr
>>> Gpr.Copysign(0.5, 2)
Gpr('5.2359877559829887307E-1')
>>> Gpr.Copysign('0.51', 2)
Gpr('5.3518479027559984754E-1')
>>> qreal.Copysign('0.51', 2)
Gpr('5.3518479027559984754E-1')

Maximum of two floating point numbers: \(\mathrm{fmax}(x, y)\)#

ctx.fmax(x, e)#

where ctx is math53, ctxboost or ctxflint.

Returns the maximum of two floating point numbers; \(x,y \ne\) NAN.

Returns the larger of two floating point arguments, treating NaNs as missing data (between a NaN and a numeric value, the numeric value is chosen). Only if both arguments are NaN, NaN is returned.

This function is not required to be sensitive to the sign of zero, although some implementations additionally enforce that if one argument is +0 and the other is -0, then +0 is returned.

See also: https://en.cppreference.com/w/cpp/numeric/math/fmax

An example in Python

>>> from xlcalcnet import xreal
>>> xreal.Max(0.5, 2)
xreal('5.2359877559829887307E-1')
>>> xreal.Max('0.51', 2)
xreal('5.3518479027559984754E-1')

An example in Visual Basic

>>> from xlcalcnet import Gpr
>>> Gpr.Max(0.5, 2)
Gpr('5.2359877559829887307E-1')
>>> Gpr.Max('0.51', 2)
Gpr('5.3518479027559984754E-1')

Minimum of two floating point numbers: \(\mathrm{fmin}(x, y)\)#

ctx.fmin(x, y)#

where ctx is math53, ctxboost or ctxflint.

Returns the minimum of two floating point numbers; \(x,y \ne\) NAN.

Returns the smaller of two floating point arguments, treating NaNs as missing data (between a NaN and a numeric value, the numeric value is chosen). Only if both arguments are NaN, NaN is returned.

This function is not required to be sensitive to the sign of zero, although some implementations additionally enforce that if one argument is +0 and the other is -0, then -0 is returned.

See also: https://en.cppreference.com/w/cpp/numeric/math/fmin

An example in Python

>>> from xlcalcnet import xreal
>>> xreal.Min(0.5, 2)
xreal('5.2359877559829887307E-1')
>>> xreal.Min('0.51', 2)
xreal('5.3518479027559984754E-1')

An example in Visual Basic

>>> from xlcalcnet import Gpr
>>> Gpr.Min(0.5, 2)
Gpr('5.2359877559829887307E-1')
>>> Gpr.Min('0.51', 2)
Gpr('5.3518479027559984754E-1')
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