Chapter 12: Utilities

constant

Returns the value of various mathematical and physical constants.

Synopsis

#include <imsl.h>

float imsl_f_constant (char name, char unit)

The type double function is imsl_d_constant.

Required Arguments

char *name   (Input)
Character string containing the name of the desired constant. The case of the character string name does not matter. The names “PI”, “Pi”, “pI”, and “pi” are equivalent. Spaces and underscores are allowed and ignored.

char *unit   (Input)
Character string containing the units of the desired constant. If NULL, then Systθme International d’Unitιs (SI) units are assumed. The case of the character string unit does not matter. The names “METER”, “Meter” and “meter” are equivalent. unit has the form U1*U2*... *Um/V1/.../Vn, where Ui and Vi are the names of basic units or are the names of basic units raised to a power. Basic units must be separated by * or /. Powers are indicated by ^, as in “m^2” for m2. Examples are, “METER*KILOGRAM/SECOND”, “M*KG/S”, “METER”, or “M/KG^2”.

Return Value

By default, imsl_f_constant returns the desired constant. If no value can be computed, NaN is returned.

Description

The names allowed are listed in the following table. Values marked with a ‡ are exact (to machine precision). The references in the right-hand column are indicated by the code numbers: [1] for Cohen and Taylor (1986), [2] for Liepman (1964), and [3] for precomputed mathematical constants.

Name

Description

Value

Reference

Amu

Atomic mass unit

1.6605655 ΄ 10-27 kg

1

ATM

Standard atm pressure

1.01325 ΄ 105 N/m2 ‡

2

AU

Astronomical unit

1.496 ΄ 1011 m

 

Avogadro

Avogadro's number, N

6.022045 ΄ 1023 1/mole

1

Boltzman

Boltzman's constant, k

1.380662 ΄ 10-23 J/K

1

C

Speed of light, c

2.997924580 ΄ 108 m/s

1

Catalan

Catalan's constant

0.915965Ό ‡

3

E

Base of natural logs, e

2.718Ό ‡

3

ElectronCharge

Electron charge, e

1.6021892 ΄ 10-19 C

1

ElectronMass

Electron mass, me

9.109534 ΄ 10-31 kg

1

ElectronVolt

Euler

ElectronVolt, ev

Euler's constant, g

1.6021892 x10 -19J

0.577Ό ‡

1

3

Faraday

Faraday constant, F

9.648456 ΄ 104 C/mole

1

FineStructure

Fine structure, a

7.2973506 ΄ 10-3

1

Gamma

Euler's constant, g

0.577Ό ‡

3

Gas

Gas constant, R0

8.31441 J/mole/K

1

Gravity

Gravitational constant, G

6.6720 ΄ 10-11 N m2/kg2

1

Hbar

Planck's constant/2p

1.0545887 ΄ 10-34 J s

1

PerfectGasVolume

Std vol ideal gas

2.241383 ΄ 10-2 m3/mole

1

Pi

Pi, p

3.141Ό ‡

3

Planck

Planck's constant, h

6.626176 ΄ 10-34 J s

1

ProtonMass

Proton mass, Mp

1.6726485 ΄ 10-27 kg

1

Rydberg

Rydberg's constant, R΅

1.097373177 ΄ 107/m

1

Speedlight

Speed of light, c

2.997924580 ΄ 108 m/s

1

StandardGravity

Standard g

9.80665 m/s2 ‡

2

StandardPressure

Standard atm pressure

1.01325 ΄ 105 N/m2 ‡

2

StefanBoltzman

Stefan-Boltzman, s

5.67032 ΄ 10-8W/K4/m2

1

WaterTriple

Triple point of water

2.7316 ΄ 102 K

2

The units allowed are as follows:

 

Unit

Description

Time

day, hour = hr, min, minute, s = sec = second, year

Frequency

Hertz = Hz

Mass

AMU, g = gram, lb = pound, ounce = oz, slug

Distance

Angstrom, AU, feet = foot, in = inch, m = meter = metre, micron, mile, mill, parsec, yard

Area

acre

Volume

1 = liter=litre

Force

dyne, N = Newton

Energy

BTU, Erg, J = Joule

Work

W = watt

Pressure

ATM = atmosphere, bar

Temperature

degC = Celsius, degF = Fahrenheit, degK = Kelvin

Viscosity

poise, stoke

Charge

Abcoulomb, C = Coulomb, statcoulomb

Current

A = ampere, abampere, statampere

Voltage

Abvolt, V = volt

Magnetic induction

T = Telsa, Wb = Weber

Other units

I, farad, mole, Gauss, Henry, Maxwell, Ohm

 

The following metric prefixes may be used with the above units. The one or two letter prefixes may only be used with one letter unit abbreviations.

 

a

atto

10-18

 

d

deci

10-1

f

femto

10-15

 

dk

deca

102

p

pico

10-12

 

k

kilo

103

n

nano

10-9

 

 

myria

104

u

micro

10-6

 

 

mega

106

m

milli

10-3

 

g

giga

109

c

centi

10-2

 

t

tera

1012

There is no one letter unit abbreviation for myria or mega since m means milli.

Examples

Example 1

In this example, Euler’s constant γ is obtained and printed. Euler’s constant is defined to be

#include <stdio.h>
#include <imsl.h>

main()
{
    float       gamma;
                                /* Get gamma */
    gamma = imsl_f_constant("gamma", 0);
                                /* Print gamma */
    printf("gamma = %f\n", gamma);
}

Output

gamma = 0.577216

Example 2

In this example, the speed of light is obtained using several different units.

#include <stdio.h>
#include <imsl.h>

main()
{
    float       speed_light;
                           /* Get speed of light in meters/second */
    speed_light = imsl_f_constant("Speed Light", "meter/second");
    printf("speed of light = %g meter/second\n", speed_light);
                           /* Get speed of light in miles/second */
    speed_light = imsl_f_constant("Speed Light", "mile/second");
    printf("speed of light = %g mile/second\n", speed_light);
                           /* Get speed of light in */
                           /* centimeters/nanosecond */
    speed_light = imsl_f_constant("Speed Light", "cm/ns");
    printf("speed of light = %g cm/ns\n", speed_light);
}

Output

speed of light = 2.99792e+08 meter/second
speed of light = 186282 mile/second
speed of light = 29.9793 cm/ns

Warning Errors

IMSL_MASS_TO_FORCE                              A conversion of units of mass to units of force was required for consistency.

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