libsimbody-dev 3.5.4+dfsg-1ubuntu2 / usr / include / simbody / SimTKcommon / Constants.h

#ifndef SimTK_SimTKCOMMON_CONSTANTS_H_
#define SimTK_SimTKCOMMON_CONSTANTS_H_

/* -------------------------------------------------------------------------- *
 *                       Simbody(tm): SimTKcommon                             *
 * -------------------------------------------------------------------------- *
 * This is part of the SimTK biosimulation toolkit originating from           *
 * Simbios, the NIH National Center for Physics-Based Simulation of           *
 * Biological Structures at Stanford, funded under the NIH Roadmap for        *
 * Medical Research, grant U54 GM072970. See https://simtk.org/home/simbody.  *
 *                                                                            *
 * Portions copyright (c) 2006-12 Stanford University and the Authors.        *
 * Authors: Michael Sherman                                                   *
 * Contributors:                                                              *
 *                                                                            *
 * Licensed under the Apache License, Version 2.0 (the "License"); you may    *
 * not use this file except in compliance with the License. You may obtain a  *
 * copy of the License at http://www.apache.org/licenses/LICENSE-2.0.         *
 *                                                                            *
 * Unless required by applicable law or agreed to in writing, software        *
 * distributed under the License is distributed on an "AS IS" BASIS,          *
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.   *
 * See the License for the specific language governing permissions and        *
 * limitations under the License.                                             *
 * -------------------------------------------------------------------------- */

/**@file
High precision mathematical and physical constants. This file is self-contained
and can be included in ANSI C programs as well as C++.**/

/** @defgroup PredefinedConstants      Predefined Constants

There are two kinds of numerical constants predefined by %SimTK: (1) a set
of typed, const, in-memory values in the SimTK namespace, at the default Real 
precision or with other specific types, and (2) a set of preprocessor
(\#define) macros containing extremely high-precision precalculated numerical 
values in long double precision.

You should use the typed constants whenever possible in your code since they
are very compact and well-behaved in C++. They have memory addresses so can
be returned as references. Because they are filled in at startup, they can
include machine- and precision-specific values like NaN, Infinity, machine
roundoff error, number of digits in a float, etc. that are very useful for 
writing robust, precision-independent numerical algorithms.

The macro values must be cast to the appropriate type before use, and are 
mostly useful as raw material for making \e typed constants. These macros
contain <em>machine-independent</em> constants, including unitless mathematical 
constants like pi, as well as physical constants and unit conversion factors.
These constants are provided at extremely high precision as compile-time 
macros in long double precision. By using very high precision we ensure 
sufficient accuracy for any IEEE long double precision implementation (they 
can be 64, 80, or 128 bits). These constants can be used as raw material for
providing nicer templatized constants in appropriate precisions and unit 
systems.

<h2>Naming conventions</h2>
Note that the %SimTK convention for typed constants is to name them
like ordinary variables except with an initial capital letter (like a
class name). This is distinct from the widely-used convention for 
constants that are defined via the presprocessor as macros (that is, 
using \#define). Those are written entirely in 
\c UPPER_CASE_WITH_UNDERSCORES, after an initial \c SimTK_. Typed constants
are processed instead by the compiler itself and do not require any
special treatment when used; they behave just like variables of the
same type and value would behave so there is no need to shout when 
using them. **/

/** @defgroup MacroConstants      Preprocessor Macro Constants
    @ingroup  PredefinedConstants

These are preprocessor (\#define) macros providing constants values at very
high precision.\ See the discussion under the main \ref PredefinedConstants
module heading.

<h2>Units</h2>
Our most common unit systems are the "SI" (MKS) system, and the "MD" system 
used for molecular dynamics. SI units are meters, kg, seconds, coulombs 
(ampere-s), kelvins and moles. MD units are nanometers, atomic mass units
(Daltons, g/mol), picoseconds, proton charge e, kelvins, and moles. Many
molecular dynamicists and chemists prefer kcals for energy and angstroms for
length. This does not constitute a consistent set of units, however, so
we provide for it by conversion from the MD units, which are consistent.
(By consistent, we mean that force units = mass-length/time^2, so f=ma!)

<pre>
Unit systems

           SI (MKS)           MD                     KCAL-ANGSTROM
---------  --------------  ------------------------  ------------------
length     meter           nanometer                 angstrom (A)
mass       kg              amu, dalton               amu, dalton
time       second          picosecond                picosecond
charge     coulomb         e, proton charge          e, proton charge
temp.      kelvin          kelvin                    kelvin
substance  mole            mole                      mole

velocity   m/s             km/s (nm/ps)              100m/s (A/ps)

energy     J (kg-m^2/s^2)  kJ/mol                    kcal/mol 
                             (Da-nm^2/ps^2)            (418.4 Da-A^2/ps^2)
force      N (kg-m/s^2)    kJ/(mol-nm) = TN/mol      kcal/(mol-A)
                             (Da-nm/ps^2) (T=10^12)    (418.4 Da-A/ps^2)

</pre>

We always keep angles in radians internally, which are unitless. However,
most humans prefer degrees where 1 degree = Pi/180 radians so we provide
convenient conversions. **/


    /**************************/
    /* MATHEMATICAL CONSTANTS */
    /**************************/

/** @defgroup MathConstants          Mathematical Constants
    @ingroup  MacroConstants

These are some common unitless numerical constants evaluated to 64 digits and
written here in maximal (long double) precision. (These values were generated 
using the symbolic calculator Maple which is part of Matlab's Symbolic 
Toolbox.) These can be cast to lower precisions when needed, and can be used
in compile-time constant expressions like 2*SimTK_PI or 1/SimTK_SQRT2 for which
the compiler will properly calculate a long double result with no runtime cost.

These constants are also available as type-safe, already-rounded, 
precision-templatized values with static memory addresses as part of our scalar
system (see NTraits<T>). You should use the templatized versions when possible.
The templatized versions also contain more elaborate constants such as NaN, 
Infinity, and "epsilon" (machine precision) which can only be generated for 
specific types. **/

/**@{**/

/** The ratio pi of a circle's circumference to its diameter in Euclidean geometry.
 * @par uncertainty
 *      approximation of an exact value
 */
#define SimTK_PI     3.141592653589793238462643383279502884197169399375105820974944592L

/** e, or exp(1).
 * @par uncertainty
 *      approximation of an exact value
 */
#define SimTK_E      2.718281828459045235360287471352662497757247093699959574966967628L

/** The natural (base e) logarithm of 2.
 * @par uncertainty
 *      approximation of an exact value
 * @see SimTK_E
 */
#define SimTK_LN2    6.931471805599453094172321214581765680755001343602552541206800095e-1L

/** The natural (base e) logarithm of 10.
 * @par uncertainty
 *      approximation of an exact value
 * @see SimTK_E
 */
#define SimTK_LN10   2.302585092994045684017991454684364207601101488628772976033327901L

/** log2(e).
 * @par uncertainty
 *      approximation of an exact value
 */
#define SimTK_LOG2E  1.442695040888963407359924681001892137426645954152985934135449407L

/** log10(e).
 * @par uncertainty
 *      approximation of an exact value
 */
#define SimTK_LOG10E 4.342944819032518276511289189166050822943970058036665661144537832e-1L

/** The square root of 2.
 * @par uncertainty
 *      approximation of an exact value
 */
#define SimTK_SQRT2  1.414213562373095048801688724209698078569671875376948073176679738L

/** One over the square root of 2; also half the square root of 2 since
 * 1/sqrt(2) == 2^(-1/2) == sqrt(2)/2.
 * @par uncertainty
 *      approximation of an exact value
 */
#define SimTK_OOSQRT2 .7071067811865475244008443621048490392848359376884740365883398690L

/** The cube root of 2, 2^(1/3).
 * @par uncertainty
 *      approximation of an exact value
 */
#define SimTK_CBRT2  1.259921049894873164767210607278228350570251464701507980081975112L

/** One over the cube root of 2, 2^(-1/3).
 * @par uncertainty
 *      approximation of an exact value
 */
#define SimTK_OOCBRT2 .7937005259840997373758528196361541301957466639499265049041428810L

/** The sixth root of 2, 2^(1/6).
 * @par uncertainty
 *      approximation of an exact value
 */
#define SimTK_SIXRT2 1.122462048309372981433533049679179516232411110613986753440409546L

/** One over the sixth root of 2, 2^(-1/6).
 * @par uncertainty
 *      approximation of an exact value
 */
#define SimTK_OOSIXRT2 .8908987181403393047402262055905125079872126158781604033837569922L

/** The square root of 3.
 * @par uncertainty
 *      approximation of an exact value
 */
#define SimTK_SQRT3  1.732050807568877293527446341505872366942805253810380628055806979L

/** The cube root of 3.
 * @par uncertainty
 *      approximation of an exact value
 */
#define SimTK_CBRT3  1.442249570307408382321638310780109588391869253499350577546416195L


/**@}**/    /*end of Mathematical Constants*/

    /**********************/
    /* PHYSICAL CONSTANTS */
    /**********************/

/** @defgroup PhysConstants      Physical Constants
    @ingroup  MacroConstants

These constants are from the CODATA 2002 set from the NIST Physics Laboratory 
web site http://physics.nist.gov/constants (NIST SP 961 Dec 2005).
Ref: P.J. Mohr and B.N. Taylor, Rev. Mod. Phys. 77(1) (2005).

@par Uncertainty
Uncertainties are given in the CODATA set as the one-std-deviation uncertainty 
in the last 2 digits of the given value. That means that there is about a 68% 
chance that the last two digits are as shown +/- the uncertainty.

How to combine uncertainties (extracted from
http://physics.nist.gov/cuu/Uncertainty/combination.html):
Assume measured quantities are x1, y1 with u1=uncertainty(x1), 
u2=uncertainty(x2). We want to combine them into a new quantity y and calculate
u=uncertainty(y).
<pre>
    Addition rule: y    = a1*x1 + a2*x2 for factors a1,a2.
     then          u^2  = a1*u1^2 + a2*u2^2
    Multiplication rule y = a*x1^e1*x2^e2 for factor a and exponents e1,e2.
    Let ur1=u1/|x1|, ur2=u2/|x2| be the relative uncertainties, ur is u/|y|.
     then          ur^2 = e1^2*ur1^2 + e2^2*ur2^2, u = ur*|y|
</pre>
**/

/**@{**/

/** 
 * Avogadro's number (NA) is defined as the number of atoms in 12g of pure Carbon-12 in
 * its unbound, rest state. The number is 1 mole (mol).
 * @par uncertainty
 *      10e16
 */
#define SimTK_AVOGADROS_NUMBER 6.0221415e23L

/**
 * Mass of a proton in MD units.
 *
 * The atomic mass unit u (or amu) is defined as 1/12 of the mass of a Carbon-12 atom,
 * unbound and in its rest state. This definition matched to Avogadro's number's definition
 * ensures that 1 mole of particles of mass 1u each has total mass exactly 1g. This is
 * synonymous with the dalton (Da), with units of g/mole, so 1u = 1Dalton = 1g/mole.
 * We will use Da for this mass unit, with kDa being a common mass measure for 
 * large biomolecules.
 *
 * @par uncertainty
 *      13e-11
 * @see SimTK_AVOGADROS_NUMBER
 */
#define SimTK_MASS_OF_PROTON_IN_MD 1.00727646688L

/**
 * Mass of a neutron in MD units.
 * @par uncertainty
 *      55e-11
 * @see SimTK_MASS_OF_PROTON_IN_MD
 */
#define SimTK_MASS_OF_NEUTRON_IN_MD 1.00866491560L

/**
 * Mass of an electron in MD units.
 * @par uncertainty
 *      24e-14
 * @see SimTK_MASS_OF_PROTON_IN_MD
 */
#define SimTK_MASS_OF_ELECTRON_IN_MD 5.4857990945e-4L

/**
 * Atomic charge unit e expressed in MKS unit of Coulombs.
 * The charge on an electron is just the negative of this value.
 * @par uncertainty
 *      14e-27
 */
#define SimTK_CHARGE_OF_PROTON_IN_SI 1.60217653e-19L

/**
 * Atomic charge unit e expressed in MD units, which uses e as its charge unit!
 * The charge on an electron is just the negative of this value.
 * @par uncertainty
 *      exact (duh!)
 */
#define SimTK_CHARGE_OF_PROTON_IN_MD 1.L

/**
 * The charge of 1 mole of protons, expressed in Coulombs.
 * <pre>
 *    1.60217653(14)e-19 C/e * 6.0221415(10)e23 = 9.6485338(18)e+4
 * </pre>
 * @par uncertainty
 *      18e-3 
 */
#define SimTK_MOLAR_CHARGE_IN_SI 9.6485338e+4L

/**
 * The charge of 1 mole of protons, expressed in MD units where the unit
 * of charge is just the charge on one proton. So in MD units this is just
 * Avogadro's number.
 * @see SimTK_AVOGADROS_NUMBER
 */
#define SimTK_MOLAR_CHARGE_IN_MD SimTK_AVOGADROS_NUMBER

/**
 * Speed of light c is exact in MKS units of m/s.
 * @par uncertainty
 *      exact
 * @see SimTK_LIGHTSPEED_IN_MD
 */
#define SimTK_LIGHTSPEED_IN_SI 2.99792458e+8L

/**
 * Speed of light c is exact in MD units of nm/ps.
 * @par uncertainty
 *      exact
 * @see SimTK_LIGHTSPEED_IN_SI
 */
#define SimTK_LIGHTSPEED_IN_MD 2.99792458e+5L

/** 
 * Newton's gravitational constant G in N-m^2/kg^2 = m^3 kg^-1 s^-2.
 * The force between two point masses m1,m2 separated by a distance d is
 *     <pre> F = -G m1*m2/d^2 </pre> 
 * (with the "-" indicating an attractive force).
 * @par uncertainty
 *      10e-15
 * @see SimTK_GRAVITATIONAL_CONSTANT_IN_MD
 */
#define SimTK_GRAVITATIONAL_CONSTANT_IN_SI 6.6742e-11L   

/**
 * Newton's gravitational constant G in (kJ/mol)-nm^2/u^2 = nm^3 u^-1 ps^-2.
 * <pre>
 * Conversion is (nm/m)^3 (u/kg)^-1 (ps/s)^-2
 *          = 1.66053886(28)e-24L     (uncertainty: 28e-32)
 * </pre>
 * This is why gravity doesn't matter in molecular systems. Don't try
 * this in single precision -- you'll run out of exponent!
 * @par uncertainty
 *      17e-39
 * @see SimTK_GRAVITATIONAL_CONSTANT_IN_SI
 */
#define SimTK_GRAVITATIONAL_CONSTANT_IN_MD 1.10827e-34L

/**
 * Free space magnetic permeability constant mu0 in SI units (exact).
 * <pre>
 *   = 4*pi * 1e-7 exactly in N/A^2 (Newtons/Ampere^2) = kg-m/C^2
 * </pre>
 * @par uncertainty
 *      approximation of an exact quantity
 * @see SimTK_ELECTRIC_PERMITTIVITY_IN_SI
 */
#define SimTK_MAGNETIC_PERMEABILITY_IN_SI  \
    1.256637061435917295385057353311801153678867759750042328389977837e-6L

/**
 * Free space magnetic permeability constant mu0 in MD units (not exact).
 * <pre>
 * Convert kg->g/mole, m->nm, C->e = (4*pi*1e5)*1.60217653e-19^2*6.0221415e23
 *      (exact in SI units, but not exact here)
 * </pre>
 * @par uncertainty
 *      47e-16
 * @see SimTK_ELECTRIC_PERMITTIVITY_IN_MD
 */
#define SimTK_MAGNETIC_PERMEABILITY_IN_MD   1.94259179e-8L

/**
 * Free space permittivity constant e0 = 1/(mu0*c^2) Farad/m = Coulomb^2/(N-m^2) (exact in SI units).
 * @par uncertainty
 *      approximation of an exact quantity
 * @see SimTK_MAGNETIC_PERMEABILITY_IN_SI
 */
#define SimTK_ELECTRIC_PERMITTIVITY_IN_SI  \
    8.854187817620389850536563031710750260608370166599449808102417149e-12L  /* approx of exact */

/**
 * Free space permittivity constant e0=1/(mu0*c^2) e^2/(kN-nm^2) using MD permeability and
 * MD lightspeed.
 * @par uncertainty
 *      14e-11
 * @see SimTK_MAGNETIC_PERMEABILITY_IN_MD
 */
#define SimTK_ELECTRIC_PERMITTIVITY_IN_MD 5.7276575e-4L

/**
 * Coulomb's constant kappa = 1/(4pi*e0)=1e-7*c^2 N-m^2/Coulomb^2 (exact in SI units).
 * This is the constant that appears in Coulomb's law f(r)= kappa*q1*q2/r^2.
 * @par uncertainty
 *      exact
 */
#define SimTK_COULOMB_CONSTANT_IN_SI 8.9875517873681764e+9L

/**
 * Coulomb's constant kappa = 1/(4*pi*e0) in MD units.
 * This is the constant that appears in Coulomb's law f(r)= kappa*q1*q2/r^2.
 * <pre>
 * Coulomb's consant in MD units uses MD e0 & c: 
 *   1/(4*pi*e0)=1e5*1.60217653e-19^2*6.0221415e23*c^2 kN-nm^2/e^2 (=kJ-nm/e^2)
 *     (exact in SI units but not exact in MD)
 * </pre>
 * @par uncertainty
 *      33e-6
 */
#define SimTK_COULOMB_CONSTANT_IN_MD 1.38935456e+2L

/**
 * Coulomb's constant kappa = 1/(4*pi*e0) in kcal-Angstroms/e^2.
 * This is the constant that appears in Coulomb's law f(r)= kappa*q1*q2/r^2.
 * This is an exact conversion from MD units (which are inexact).
 * @par uncertainty
 *      80e-6
 */
#define SimTK_COULOMB_CONSTANT_IN_KCAL_ANGSTROM 3.32063711e+2L

/**
 * This is the gas constant R in (J/mol)/K. 
 * @par uncertainty
 *      15e-6
 */
#define SimTK_MOLAR_GAS_CONSTANT_SI 8.314472L

/**
 * This is the gas constant R in (kJ/mol)/K. 
 * This is an exact conversion from SI units, differing only in the use of kJ 
 * here vs. J in SI.
 * @par uncertainty
 *      15e-9
 */
#define SimTK_MOLAR_GAS_CONSTANT_MD 8.314472e-3L

/**
 * This is the gas constant R in (kcal/mol)/K. 
 * This is an exact conversion from MD units, differing only in the use of kcal 
 * here vs. kJ in MD.
 * @par uncertainty
 *      36e-10
 */
#define SimTK_MOLAR_GAS_CONSTANT_KCAL_ANGSTROM 1.9872065e-3L

/**
 * Boltzmann's constant in SI units of joules/kelvin; just divide R by NA.
 * @par uncertainty
 *      24e-30
 */
#define SimTK_BOLTZMANN_CONSTANT_SI  1.3806505e-23L

/**
 * Boltzmann's constant in MD units of (kJ/mol)/kelvin; same as R.
 * @see SimTK_MOLAR_GAS_CONSTANT_MD
 */
#define SimTK_BOLTZMANN_CONSTANT_MD  SimTK_MOLAR_GAS_CONSTANT_MD

/**
 * Boltzmann's constant in Kcal-Angstrom units of (kcal/mol)/kelvin; same as R.
 * @see SimTK_MOLAR_GAS_CONSTANT_KCAL_ANGSTROM
 */
#define SimTK_BOLTZMANN_CONSTANT_KCAL_ANGSTROM SimTK_MOLAR_GAS_CONSTANT_KCAL_ANGSTROM

/**@}**/   /*end of Physical Constants*/

    /***************************/
    /* UNIT CONVERSION FACTORS */
    /***************************/

/** @defgroup UnitConversionFactors      Unit Conversion Factors
    @ingroup  MacroConstants

In each case here, given a value in the units mentioned first in the name, you
should multiply by the given constant to produce the equivalent quantity 
measured in the units that appear second in the name. You can perform the 
reverse conversion by dividing by the constant, or by using another conversion
constant with the names reversed if one is supplied here.**/

/**@{**/

/** 
 * Convert radians to degrees.
 * @par uncertainty
 *       approximation of an exact quantity
 * @see SimTK_DEGREE_TO_RADIAN
 */
#define SimTK_RADIAN_TO_DEGREE 5.729577951308232087679815481410517033240547246656432154916024386e+1L

/** 
 * Convert degrees to radians.
 * @par uncertainty
 *       approximation of an exact quantity
 * @see SimTK_RADIAN_TO_DEGREE
 */
#define SimTK_DEGREE_TO_RADIAN 1.745329251994329576923690768488612713442871888541725456097191440e-2L

/** 
 * Convert nanoseconds to seconds.
 * @par uncertainty
 *          exact
 * @see SimTK_S_TO_NS
 */
#define SimTK_NS_TO_S 1e-9L

/** 
 * Convert seconds to nanoseconds.
 * @par uncertainty
 *          exact
 * @see SimTK_NS_TO_S
 */
#define SimTK_S_TO_NS 1e9L

/** 
 * Convert Kcal to Kjoule (also Kcal/mol to Kjoule/mol).
 * @par uncertainty
 *         exact
 * @see SimTK_KJOULE_TO_KCAL
 */
#define SimTK_KCAL_TO_KJOULE 4.184L /* exact */

/** 
 * Convert Kjoule to Kcal (also Kjoule/mol to Kcal/mol).
 * @par uncertainty
 *         approximation of an exact quantity
 * @see SimTK_KCAL_TO_KJOULE
 */
#define SimTK_KJOULE_TO_KCAL 2.390057361376673040152963671128107074569789674952198852772466539e-1L

/** 
 * Convert atomic mass unit (amu, Dalton) to g. This is 1/NA (NA=avogadro's number).
 * @par uncertainty
 *         28e-32
 * @see SimTK_AVOGADROS_NUMBER
 */
#define SimTK_DALTON_TO_GRAM     1.66053886e-24L

/** 
 * Convert proton charge units to Coulombs. This is the same as the
 * conversion from electron volts to Joules, and both are just the
 * charge of a proton in SI units.
 * @see SimTK_CHARGE_OF_PROTON_IN_SI
 * @see SimTK_EV_TO_JOULE
 */
#define SimTK_E_TO_COULOMB       SimTK_CHARGE_OF_PROTON_IN_SI

/** 
 * Convert electron volts to Joules. This is the same as the
 * conversion from proton charge units to Coulombs, and both are just the
 * charge of a proton in SI units.
 * @see SimTK_CHARGE_OF_PROTON_IN_SI
 * @see SimTK_E_TO_COULOMB
 */
#define SimTK_EV_TO_JOULE        SimTK_CHARGE_OF_PROTON_IN_SI

/**@}**/    /*end of Unit Conversion Factors*/
    
#endif /* SimTK_SimTKCOMMON_CONSTANTS_H_ */