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Simbody
3.3
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Simbody
3.3
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These are some common unitless numerical constants evaluated to 64 digits and written here in maximal (long double) precision. More...
Macros | |
| #define | SimTK_PI 3.141592653589793238462643383279502884197169399375105820974944592L |
| The ratio pi of a circle's circumference to its diameter in Euclidean geometry. More... | |
| #define | SimTK_E 2.718281828459045235360287471352662497757247093699959574966967628L |
| e, or exp(1). More... | |
| #define | SimTK_LN2 6.931471805599453094172321214581765680755001343602552541206800095e-1L |
| The natural (base e) logarithm of 2. More... | |
| #define | SimTK_LN10 2.302585092994045684017991454684364207601101488628772976033327901L |
| The natural (base e) logarithm of 10. More... | |
| #define | SimTK_LOG2E 1.442695040888963407359924681001892137426645954152985934135449407L |
| log2(e). More... | |
| #define | SimTK_LOG10E 4.342944819032518276511289189166050822943970058036665661144537832e-1L |
| log10(e). More... | |
| #define | SimTK_SQRT2 1.414213562373095048801688724209698078569671875376948073176679738L |
| The square root of 2. More... | |
| #define | SimTK_OOSQRT2 .7071067811865475244008443621048490392848359376884740365883398690L |
| One over the square root of 2; also half the square root of 2 since 1/sqrt(2) == 2^(-1/2) == sqrt(2)/2. More... | |
| #define | SimTK_CBRT2 1.259921049894873164767210607278228350570251464701507980081975112L |
| The cube root of 2, 2^(1/3). More... | |
| #define | SimTK_OOCBRT2 .7937005259840997373758528196361541301957466639499265049041428810L |
| One over the cube root of 2, 2^(-1/3). More... | |
| #define | SimTK_SIXRT2 1.122462048309372981433533049679179516232411110613986753440409546L |
| The sixth root of 2, 2^(1/6). More... | |
| #define | SimTK_OOSIXRT2 .8908987181403393047402262055905125079872126158781604033837569922L |
| One over the sixth root of 2, 2^(-1/6). More... | |
| #define | SimTK_SQRT3 1.732050807568877293527446341505872366942805253810380628055806979L |
| The square root of 3. More... | |
| #define | SimTK_CBRT3 1.442249570307408382321638310780109588391869253499350577546416195L |
| The cube root of 3. More... | |
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.
| #define SimTK_PI 3.141592653589793238462643383279502884197169399375105820974944592L |
The ratio pi of a circle's circumference to its diameter in Euclidean geometry.
| #define SimTK_E 2.718281828459045235360287471352662497757247093699959574966967628L |
e, or exp(1).
| #define SimTK_LN2 6.931471805599453094172321214581765680755001343602552541206800095e-1L |
| #define SimTK_LN10 2.302585092994045684017991454684364207601101488628772976033327901L |
| #define SimTK_LOG2E 1.442695040888963407359924681001892137426645954152985934135449407L |
log2(e).
| #define SimTK_LOG10E 4.342944819032518276511289189166050822943970058036665661144537832e-1L |
log10(e).
| #define SimTK_SQRT2 1.414213562373095048801688724209698078569671875376948073176679738L |
The square root of 2.
| #define SimTK_OOSQRT2 .7071067811865475244008443621048490392848359376884740365883398690L |
One over the square root of 2; also half the square root of 2 since 1/sqrt(2) == 2^(-1/2) == sqrt(2)/2.
| #define SimTK_CBRT2 1.259921049894873164767210607278228350570251464701507980081975112L |
The cube root of 2, 2^(1/3).
| #define SimTK_OOCBRT2 .7937005259840997373758528196361541301957466639499265049041428810L |
One over the cube root of 2, 2^(-1/3).
| #define SimTK_SIXRT2 1.122462048309372981433533049679179516232411110613986753440409546L |
The sixth root of 2, 2^(1/6).
| #define SimTK_OOSIXRT2 .8908987181403393047402262055905125079872126158781604033837569922L |
One over the sixth root of 2, 2^(-1/6).
| #define SimTK_SQRT3 1.732050807568877293527446341505872366942805253810380628055806979L |
The square root of 3.
| #define SimTK_CBRT3 1.442249570307408382321638310780109588391869253499350577546416195L |
The cube root of 3.
1.8.6 
