Integer related functions

Integral value nearest \(x\) (rounding to nearest): \(\mathrm{nearbyint}(x), \mathrm{rint}(x)\)

ctx.rint(x)

where ctx is math53, ctxboost or ctxflint.

Returns the integral value (in floating-point format) nearest \(x\), using the rounding-to-nearest rounding mode.

For the std::rint function:

• If num is ±∞, it is returned, unmodified.

• If num is ±0, it is returned, unmodified.

• If num is NaN, NaN is returned.

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

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

An example in Python

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

An example in Visual Basic

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

ctx.nearbyint(x)

Is an alias for ctx.rint(x) in this implementation. The only difference between std::rint and std::nearbyint is that std::nearbyint never raises FE_INEXACT.

32 bit integer nearest \(x\) (rounding to nearest): \(\mathrm{lrint}(x)\)

ctx.lrint(x)

where ctx is math53, ctxboost or ctxflint.

Returns an 32 bit signed integer nearest \(x\), using the rounding-to-nearest rounding mode.

If the result is outside the range representable by an 32 bit signed integer, a domain error or a range error may occur.

An example in Python

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

An example in Visual Basic

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

64 bit integer nearest \(x\) (rounding to nearest): \(\mathrm{llrint}(x)\)

ctx.llrint(x)

where ctx is math53, ctxboost or ctxflint.

Returns an 64 bit signed integer nearest \(x\), using the rounding-to-nearest rounding mode.

If the result is outside the range representable by an 64 bit signed integer, a domain error or a range error may occur.

An example in Python

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

An example in Visual Basic

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

Smallest integral value not less than \(x: \mathrm{ceil}(x)\)

ctx.ceil(x)

where ctx is math53, ctxboost or ctxflint.

Returns the smallest integer \(> x; |x| \le\) MaxLongint.

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

An example in Python

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

An example in Visual Basic

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

Largest integral value not greater than \(x: \mathrm{floor}(x)\)

ctx.floor(x)

where ctx is math53, ctxboost or ctxflint.

Returns the largest integer \(< x; |x| \le\) MaxLongint.

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

An example in Python

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

An example in Visual Basic

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

Nearest integral value not greater in magnitude than \(x: \mathrm{trunc}(x)\)

ctx.trunc(x)

where ctx is math53, ctxboost or ctxflint.

Returns the truncated value of \(x\).

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

An example in Python

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

An example in Visual Basic

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

Nearest integral value, rounding halfway cases away from zero: \(\mathrm{round}(x)\)

ctx.round(x)

where ctx is math53, ctxboost or ctxflint.

Computes the nearest integer (in floating-point format), rounding halfway cases away from zero, regardless of the current rounding mode.

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

An example in Python

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

An example in Visual Basic

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

Nearest 32 bit integer, rounding halfway cases away from zero: \(\mathrm{lround}(x)\)

ctx.lround(x)

where ctx is math53, ctxboost or ctxflint.

Returns the nearest 32 bit signed integer, rounding halfway cases away from zero.

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

An example in Python

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

An example in Visual Basic

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

Nearest 64 bit integer, rounding halfway cases away from zero: \(\mathrm{llround}(x)\)

ctx.llround(x)

where ctx is math53, ctxboost or ctxflint.

Returns the nearest 64 bit signed integer, rounding halfway cases away from zero.

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

An example in Python

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

An example in Visual Basic

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