Re: [boost] formal review request : mcs::units

From: Andreas Harnack (ah.boost.03_at_[hidden])
Date: 2007-02-09 15:31:43

james.jones_at_[hidden] wrote:

> I suspect this idea, while clever, does not cover the problem domain sufficiently well to be superior to lists.

Please have a look at the attached list.
(I hope sending attachments  works.)

This is a list of all SI units I could find on a quick search. The first 
two columns are nominator and denominator a corresponding rational 
number would have. Of course, this is not a proof, but the numbers 
suggest that for practical purposes we're not even getting near a range 
that's likely to be dangerous.

By the way, there's no need to worry about growing intermediate results: 
a/b * c/d is equal to a/d * c/b and these two factors can be normalized 
before the multiplication is carried out. If that's done and a/b and c/d 
were in normal form, then so will be the result and there's no 
intermediate result growing larger then the final product.

Andreas

9	1	3^2		m^2		area			square metre	m2
27	1	3^3		m^3		volume			cubic metre	m3
3	2	3/2		m/s		speed, velocity		metre per second	m/s
3	4	3/2^2		m/s^2		acceleration		metre per second squared	m/s2
1	3	1/3		1/m		wavenumber		reciprocal metre	m–1
5	27	5/3^3		kg/m^3		mass density		kilogram per cubic metre	kg/m3
5	9	5/3^2		kg/m^2		surface density		kilogram per square metre	kg/m2	
27	5	3^3/5		m^3/kg		specific volume		cubic metre per kilogram	m3/kg	
7	9	7/3^2		A/m^2		current density		ampere per square metre	A/m2	
7	3	7/3		A/m		magnetic field strength	ampere per metre	A/m	
13	27	13/3^3		mol/m^3		concentration		mole per cubic metre	mol/m3	
5	27	5/3^3		kg/m^3		mass concentration	kilogram per cubic metre	kg/m3	
17	9	17/3^2		cd/m^2		luminance		candela per square metre	cd/m2	

1	2	1/2		1/s		frequency		hertz (d)	Hz	
15	4	5*3/2^2		kg*m/s^2	force			newton	N	
5	12	5/(3*2^2)	kg/m*s^2	pressure, stress	pascal	Pa	N/m2
45	4	5*3^2/2^2	kg*m^2/s^2	energy, work, heat	joule	J	N m
45	8	5*3^2/2^3	kg*m^2/s^3	power, radiant flux	watt	W	J/s
14	1	7*2		A*s		electric charge		coulomb	C	
45	56	5*3^2/(7*2^3)	kg*m^2/A*s^3	electric potential	volt	V	W/A
784	45	7^2*2^4/(5*3^2)	A^2*s^4/kg*m^2	capacitance		farad	F	C/V
45	392	5*3^2/(7^2*2^3)	kg*m^2/A^2*s^3	electric resistance	ohm		V/A
392	45	7^2*2^3/(5*3^2)	A^2*s^3/kg*m^2	electric conductance	siemens	S	A/V
45	28	5*3^2/(7*2^2)	kg*m^2/A*s^2	magnetic flux		weber	Wb	V s
5	28	5/(7*2^2)	kg/A*s^2	magnetic flux density	tesla	T	Wb/m2
45	196	5*3^2/(7^2*2^2)	kg*m^2/A^2*s^2	inductance		henry	H	Wb/A
11	1	11		K		Celsius temperature	degree Celsius (e)	°C	
17	1	17		cd		luminous flux		lumen	lm	cd sr (c)
17	9	17/3^2		cd/m^2		illuminance		lux	lx	lm/m2
1	2	1/2		1/s		activity referred to a radionuclide (f)	becquerel (d)	Bq	
9	4	3^2/2^2		m^2/s^2		absorbed dose, specific energy (imparted), kerma	gray	Gy	J/kg

5	6	5/(3*2)		kg/m*s		dynamic viscosity	pascal second	Pa s	
45	4	5*3^2/2^2	kg*m^2/s^2	moment of force		newton metre	N m	
5	4	5/2^2		kg/s^2		surface tension		newton per metre	N/m	
5	8	5/2^3		kg/s^3		heat flux density,	watt per square metre	W/m2	
45	44	5*3^2/(11*2^2)	kg*m^2/K*s^2	heat capacity, entropy	joule per kelvin	J/K	
9	44	3^2/(11*2^2)	m^2/K*s^2	specific heat capacity,	joule per kilogram kelvin	J/(kg K)	
9	4	3^2/(2^2)	m^2/s^2		specific energy		joule per kilogram	J/kg	
15	88	5*3/(11*2^3)	kg*m/K*s^3	thermal conductivity	watt per metre kelvin	W/(m K)	
5	12	5/(3*2^2)	kg/m*s^2	energy density		joule per cubic metre	J/m3	
15	56	5*3/(7*2^3)	kg*m/A*s^3	electric field strength	volt per metre	V/m	
14	27	7*2/(3^3)	A*s/m^3		electric charge density	coulomb per cubic metre	C/m3	
14	9	7*2/3^2		A*s/m^2		surface charge density	coulomb per square metre	C/m2	
14	9	7*2/3^2		A*s/m^2		electric flux density,	coulomb per square metre	C/m2	
784	135	7^2*2^4/(5*3^3)	A^2*s^4/kg*m^3	permittivity		farad per metre	F/m	
15	196	5*3/(7^2*2^2)	kg*m/A^2*s^2	permeability		henry per metre	H/m	
45	52	5*3^2/(13*2^2)	kg*m^2/mol*s^2	molar energy		joule per mole	J/mol	
45	572	5*3^2/(13*11*2^2)	kg*m^2/mol*K*s^2 molar entropy	joule per mole kelvin	J/(mol K)	
14	5	7*2/5		A*s/kg		exposure		coulomb per kilogram	C/kg	
9	8	3^2/2^3		m^2/s^3		absorbed dose rate	gray per second	Gy/s	
13	54	13/(3^3*2)	mol/m^3*s	catalytic activity	katal per cubic metre	kat/m3