type_template conversion_factor

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Signature

pqs::conversion_factor<std::ratio<Nm,Dm>,pqs::exponent10<Ne,De> >

Header

#include <pqs/types/conversion_factor.hpp>

Description

An instantiable compile-time numeric constant, used as part of the unit of a quantity, to describe the scaling of the numeric value of the quantity ¹ relative to the numeric value of the quantity in a unit expressed as exponents of base_units of the measurement system in which it is expressed.

In the library, the conversion factor is represented as a rational number, raised to a rational base10 exponent.

let a, b be rational numbers.
let k be the conversion factors value then :

k = a * 10 ^b

Within the conversion_factor type a is known as the multiplier and b is known as the exponent.

Conversion factors can be easily composed using constexpr runtime math operations on them and their exponents and multipliers.

Example

   using namespace pqs;

   auto constexpr pi = std::ratio<314159265358979>() ^ exponent10<-14>();
   static_assert(is_conversion_factor<decltype(pi)> );

   auto constexpr v1 = evaluate(pi);             // object argument form

   std::cout << std::setprecision(16) << "pi = " << v1 << '\n';
 
sample output : pi = 3.14159265358979

Maths is exact, but this means that it is possible for the number to overflow. Overflow will cause a compilation failure rather than a runtime failure.

The exponent and multiplier may be any rational number expressible by std::intmax_t

normal form

In normal form the multiplier of the conversion factor evaluates to a number n , where n <= 1 and n < 10. The exponent is adjusted accordingly.

Notation

value pattern	type	notes
mn[x]	std::intmax_t
md[x]	std::intmax_t
en[x]	std::intmax_t
ed[x]	std::intmax_t

typename pattern	type	notes
M[x]	std::ratio<mn[x],md[x]>	multiplier pattern
E[x]	exponent10<en[x],ed[x]>	exponent pattern
CF[x]	conversion_factor<M[x],E[x]> >	conversion factor pattern

typename	type	notes
CF	conversion_factor<M, E>
CFi	conversion_factor<Mi, Ei>
CFo	conversion_factor<Mo, Eo>	std::ratio_less<Mo,std::ratio<10> > == true std::ratio_greater_equal<Mo,std::ratio<1> > == true

type_expression	result	notes
CF::multiplier	std::ratio< mn , md>
CF::exponent	exponent10< en , ed >
normalise< CFi >	CFo	Cfo is the normalised version of CFi

value	type	notes
i	integer type
f	floating point type
cf	conversion_factor
cfr	conversion_factor	local result
r	std::ratio
e10	pqs::exponent10

expression	result	requires	notes
r * cf	cfr		cf multiplied by r , normalised
cf * r	cfr		cf multiplied by r , normalised
cf / r	cfr		cf divided by r , normalised
r / cf	cfr		r divided by cf , normalised
r ^ e10	cfr		multiplier is r , exponent is e10, normalised
cf ^ e10	cfr		exponent of cf raised by e10, normalised
evaluate< CF >()	i	CF can be evaluated to integer precisely	type argument form
evaluate(cf)	i	CF can be evaluated to integer precisely	object argument form
evaluate< CF >()	f	CF cannot be evaluated to integer precisely	type argument form
evaluate(cf)	f	CF cannot be evaluated to integer precisely	object argument form

Notes

• [1] https://en.wikipedia.org/wiki/Conversion_of_units