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|newpage| Integer related functions =============================================================================== Integral value nearest `x` (rounding to nearest): `\mathrm{nearbyint}(x), \mathrm{rint}(x)` ------------------------------------------------------------------------------------------------- .. method:: 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 .. code-block:: pycon >>> 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 .. code-block:: pycon >>> from xlcalcnet import Gpr >>> Gpr.Rint(0.5) Gpr('5.2359877559829887307E-1') >>> Gpr.Rint('0.51') Gpr('5.3518479027559984754E-1') .. method:: 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)` ------------------------------------------------------------------------------ .. method:: 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 .. code-block:: pycon >>> 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 .. code-block:: pycon >>> 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)` -------------------------------------------------------------------------------- .. method:: 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 .. code-block:: pycon >>> 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 .. code-block:: pycon >>> 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)` ------------------------------------------------------------------------------- .. method:: 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 .. code-block:: pycon >>> 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 .. code-block:: pycon >>> 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)` ---------------------------------------------------------------------------------------------- .. method:: 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 .. code-block:: pycon >>> 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 .. code-block:: pycon >>> 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)` ------------------------------------------------------------------------------------------------- .. method:: 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 .. code-block:: pycon >>> 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 .. code-block:: pycon >>> 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)` ---------------------------------------------------------------------------------------- .. method:: 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 .. code-block:: pycon >>> 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 .. code-block:: pycon >>> 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)` ------------------------------------------------------------------------------------------ .. method:: 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 .. code-block:: pycon >>> 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 .. code-block:: pycon >>> 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)` ------------------------------------------------------------------------------------------ .. method:: 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 .. code-block:: pycon >>> 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 .. code-block:: pycon >>> from xlcalcnet import Gpr >>> Gpr.Round(0.5) Gpr('5.2359877559829887307E-1') >>> Gpr.Round('0.51') Gpr('5.3518479027559984754E-1')