Components

Library dependency tower for xo-unit:

_images/ditaa-ed4e8993c6a283f4464d316a773873fb22d78dc9.png

Install instructions here

Abstraction tower for xo-unit components:

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  • quantity:

    A quantity with unit checking and conversion done at compile-time

    #include "xo/unit/quantity.hpp"
auto q1 = xo::qty::qty::kilometers(7.5);

  • xquantity:

    A quantity with unit checking and conversion done at run-time. This is useful if unit information isn’t known at compile time, for example if reading units from console input.

    #include "xo/unit/xquantity.hpp"
xquantity qty1(7.5, xo::qty::u::foot)

  • scaled_unit:

    #include "xo/unit/scaled_unit.hpp"
auto u = xo::qty::u::millimeter;

    A unit involving zero or more dimensions, and associated conversion factor.

    • can express result of arithmetic involving multiple scales, by reporting an outer scalefactor

    • a scaled unit is ‘natural’ if its outer scalefactor is 1.

    • quantities are represented by associating a natural scaled_unit instance

    • scaled_units are closed under multiplication and division.

    • multiplication and division commit to a single basis_unit for each dimension.

  • natural_unit

    #include "xo/unit/natural_unit.hpp"
auto u = xo::qty::nu::millimeter;

    A unit involving zero or more dimensions, and at most one scale per dimension. A quantity instance is always represented as a dimensionless multiple of a natural unit

    • natural_units are not closed under multiplication and division. (for example consider xo::qty::qty::foot * xo::qty::qty::meter)

  • bpu

    A rational (usually integer) power of a basis unit. Has a single dimension.

    #include "xo/unit/bpu.hpp"
xo::qty::bpu(xo::qty::detail::bu::millimeter,
             xo::qty::power_ratio_type(2));  // mm^2

  • bu_store

    Associates basis units with abbreviations. Abbreviations used to decorate printed quantities.

    For example bu::kilogram => "kg"

    #include "xo/unit/bu_store.hpp"
xo::qty::bu_abbrev_store.bu_abbrev(xo::qty::detail::bu::picogram); // "pg"

  • basis_unit

    A unit with a single dimension and scale.

    #include "xo/unit/basis_unit.hpp"
auto b = xo::qty::detail::bu::picogram;

  • dimension

    identifies a dimension, such as mass or time.

    #include "xo/unit/dimension.hpp"
auto d = xo::qty::dimension::mass;

Representation

Worked example using xo::qty::quantity.

1#include "xo/unit/quantity.hpp"
2...
3using xo::qty;
4namespace q = xo::qty::qty;
5
6// 7.55km.min^-2
7quantity qty1 = 7.55 * q::kilometer / (q::minute * q::minute);

Note: in diagrams below, components with pale blue background are discarded before runtime

object qty1<<quantity>> qty1 : scale = 7.55 rectangle #e0f0ff { object km_per_min2<<natural_unit>> km_per_min2 : n_bpu = 2 km_per_min2 : bpu[0] = km km_per_min2 : bpu[1] = per_min object km<<bpu>> km : native_dim = dim.mass km : scalefactor = 1000/1 km : power = 1 object per_min2<<bpu>> per_min2 : native_dim = dim.time per_min2 : scalefactor = 60/1 per_min2 : power = -2 qty1 o-- km_per_min2 : s_unit (static constexpr) km_per_min2 *-- km km_per_min2 *-- per_min2 }

representation for quantity 7.55km.min^-2

1// 123ng
2quantity qty2 = q::nanograms(123);

object qty2<<quantity>> qty2 : scale = 123 rectangle #e0f0ff { object ng_unit<<natural_unit>> ng_unit : n_bpu = 1 ng_unit : bpu[0] = ng object ng<<bpu>> ng : native_dim = dim::mass ng : scalefactor = 1/10^9 ng : power = 1 qty2 o-- ng_unit : s_unit (static constexpr) ng_unit *-- ng }

representation for quantity 123 nanograms

1// (123*7.55) ng.km.min^-2
2quantity qty3 = qty2 * qty1;

object qty3<<quantity>> qty3 : scale = 928.65 rectangle #e0f0ff { object ng_km_min2_unit<<natural_unit>> ng_km_min2_unit : n_bpu = 3 ng_km_min2_unit : bpu[0] = ng ng_km_min2_unit : bpu[1] = km ng_km_min2_unit : bpu[2] = per_min2 object ng<<bpu>> ng : native_dim = dim::mass ng : scalefactor = 1/10^9 ng : power = 1 object km<<bpu>> km : native_dim = dim::distance km : scalefactor = 1000/1 km : power = 1 object per_min2<<bpu>> per_min2 : native_dim = dim::time per_min2 : scalefactor = 60/1 per_min2 : power = -2 qty3 o-- ng_km_min2_unit : s_unit (static constexpr) ng_km_min2_unit *-- ng ng_km_min2_unit *-- km ng_km_min2_unit *-- per_min2 }

quantity 928.65 ng.km.min^-2

1namespace u = xo::qty::u;
2
3// (123*7.55) ng.km.min^-2  ==>  2.57958e-10kg.m.s^-2
4
5constexpr auto newton = u::kilogram * u::meter / (u::second * u::second);
6
7quantity<newton> qty3b = qty3;
8
9// quantity qty3b = qty3.rescale_ext<newton>();

object qty3b<<quantity>> qty3b : scale = 2.59758e-10 rectangle #e0f0ff { object kg_m_s2_unit<<natural_unit>> kg_m_s2_unit : n_bpu = 3 kg_m_s2_unit : bpu[0] = kg kg_m_s2_unit : bpu[1] = m kg_m_s2_unit : bpu[2] = per_s2 object kg<<bpu>> kg : native_dim = dim::mass kg : scalefactor = 1000/1 kg : power = 1 object m<<bpu>> m : native_dim = dim::distance m : scalefactor = 1/1 m : power = 1 object per_s2<<bpu>> per_s2 : native_dim = dim::time per_s2 : scalefactor = 1/1 per_s2 : power = -2 qty3b o-- kg_m_s2_unit : s_unit (static constexpr) kg_m_s2_unit *-- kg kg_m_s2_unit *-- m kg_m_s2_unit *-- per_s2 }

quantity 928.65 ng.km.min^-2