Simbody
3.7
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This is a set of predefined constants in the form of Real (SimTK default precision) symbols that are important for writing precision-independent numerical algorithms. More...
Variables | |
const Real | SimTK::NaN |
This is the IEEE "not a number" constant for this implementation of the default-precision Real type; be very careful using this because it has many strange properties such as not comparing equal to itself. More... | |
const Real | SimTK::Infinity |
This is the IEEE positive infinity constant for this implementation of the default-precision Real type; -Infinity will produce the negative infinity constant. More... | |
const Real | SimTK::Eps |
Epsilon is the size of roundoff noise; it is the smallest positive number of default-precision type Real such that 1+Eps != 1. More... | |
const Real | SimTK::SqrtEps |
This is the square root of Eps, ~1e-8 if Real is double, ~3e-4 if Real is float. More... | |
const Real | SimTK::TinyReal |
TinyReal is a floating point value smaller than the floating point precision; it is defined as Eps^(5/4) which is ~1e-20 for Real==double and ~1e-9 for float. More... | |
const Real | SimTK::SignificantReal |
SignificantReal is the smallest value that we consider to be clearly distinct from roundoff error when it is the result of a computation; it is defined as Eps^(7/8) which is ~1e-14 when Real==double, ~1e-6 when Real==float. More... | |
const Real | SimTK::LeastPositiveReal |
This is the smallest positive real number that can be expressed in the type Real; it is ~1e-308 when Real==double, ~1e-38 when Real==float. More... | |
const Real | SimTK::MostPositiveReal |
This is the largest finite positive real number that can be expressed in the Real type; ~1e+308 when Real==double, ~1e+38 when Real==float. Note that there is also a value Infinity that will test larger than this one. More... | |
const Real | SimTK::LeastNegativeReal |
This is the largest negative real number (that is, closest to zero) that can be expressed in values of type Real. More... | |
const Real | SimTK::MostNegativeReal |
This is the smallest finite negative real number that can be expressed in values of type Real. Note that -Infinity is a value that will still test smaller than this one. More... | |
const int | SimTK::NumDigitsReal |
This is the number of decimal digits that can be reliably stored and retrieved in the default Real precision (typically log10(1/eps)-1), that is, about 15 digits when Real==double and 6 digits when Real==float. More... | |
const int | SimTK::LosslessNumDigitsReal |
This is the smallest number of decimal digits you should store in a text file if you want to be able to get exactly the same bit pattern back when you read it back in and convert the text to a Real value. More... | |
const Real | SimTK::Zero |
Real(0) More... | |
const Real | SimTK::One |
Real(1) More... | |
const Real | SimTK::MinusOne |
Real(-1) More... | |
const Real | SimTK::Two |
Real(2) More... | |
const Real | SimTK::Three |
Real(3) More... | |
const Real | SimTK::OneHalf |
Real(1)/2. More... | |
const Real | SimTK::OneThird |
Real(1)/3. More... | |
const Real | SimTK::OneFourth |
Real(1)/4. More... | |
const Real | SimTK::OneFifth |
Real(1)/5. More... | |
const Real | SimTK::OneSixth |
Real(1)/6. More... | |
const Real | SimTK::OneSeventh |
Real(1)/7. More... | |
const Real | SimTK::OneEighth |
Real(1)/8. More... | |
const Real | SimTK::OneNinth |
Real(1)/9. More... | |
const Real | SimTK::Pi |
Real(pi) More... | |
const Real | SimTK::OneOverPi |
1/Real(pi) More... | |
const Real | SimTK::E |
e = Real(exp(1)) More... | |
const Real | SimTK::Log2E |
Real(log2(e)) (log base 2) More... | |
const Real | SimTK::Log10E |
Real(log10(e)) (log base 10) More... | |
const Real | SimTK::Sqrt2 |
Real(sqrt(2)) More... | |
const Real | SimTK::OneOverSqrt2 |
1/sqrt(2)==sqrt(2)/2 as Real More... | |
const Real | SimTK::Sqrt3 |
Real(sqrt(3)) More... | |
const Real | SimTK::OneOverSqrt3 |
Real(1/sqrt(3)) More... | |
const Real | SimTK::CubeRoot2 |
Real(2^(1/3)) (cube root of 2) More... | |
const Real | SimTK::CubeRoot3 |
Real(3^(1/3)) (cube root of 3) More... | |
const Real | SimTK::Ln2 |
Real(ln(2)) (natural log of 2) More... | |
const Real | SimTK::Ln10 |
Real(ln(10)) (natural log of 10) More... | |
const Complex | SimTK::I |
We only need one complex constant, i = sqrt(-1). For the rest just multiply the real constant by i, or convert with Complex(the Real constant), or if you need an address you can use NTraits<Complex>::getPi(), etc. More... | |
This is a set of predefined constants in the form of Real (SimTK default precision) symbols that are important for writing precision-independent numerical algorithms.
These constants have memory addresses (that is, they are not macros), so you can return references to them. These are global external symbols rather than static members to avoid problems with static initialization order.
Constants defined here include common mathematical values like pi, e, and sqrt(2) and also numerical constants related to the floating point implementation of the Real type, such as NaN, Infinity, and the machine precision Epsilon. For convenience we also provide several common numerical values for which it is useful to have a precision-independent representation (mostly to avoid warnings or casts to avoid them), and also where it is useful to have a referenceable memory location that contains those values. These include small integers and common small fractions like 1/2 and 1/3.
Note that the Simbody convention for typed constants is to name them like ordinary variables except with an initial capital letter (like a class name). Typed constants are processed by the compiler rather than the preprocessor and do not require any special treatment when used; they behave just like variables of the same type and value would behave. So we don't feel the need to draw attention to them with ALL_CAPS like we do with preprocessor symbols.
const Real SimTK::NaN |
This is the IEEE "not a number" constant for this implementation of the default-precision Real type; be very careful using this because it has many strange properties such as not comparing equal to itself.
You must use the SimTK::isNaN() function instead to determine whether something contains a NaN value.
const Real SimTK::Infinity |
This is the IEEE positive infinity constant for this implementation of the default-precision Real type; -Infinity will produce the negative infinity constant.
Infinity tests larger than any other Real value.
const Real SimTK::Eps |
Epsilon is the size of roundoff noise; it is the smallest positive number of default-precision type Real such that 1+Eps != 1.
If Real is double (the normal case) then Eps ~= 1e-16; if Real is float then Eps ~= 1e-7.
const Real SimTK::SqrtEps |
This is the square root of Eps, ~1e-8 if Real is double, ~3e-4 if Real is float.
Many numerical algorithms are limited to accuracy of sqrt(Eps) so this constant is useful in checking for termination of them.
const Real SimTK::TinyReal |
TinyReal is a floating point value smaller than the floating point precision; it is defined as Eps^(5/4) which is ~1e-20 for Real==double and ~1e-9 for float.
This is commonly used as a number to add to a computation in a denominator (such as a vector length) that might come out zero, just for the purpose of avoiding a divide by zero.
const Real SimTK::SignificantReal |
SignificantReal is the smallest value that we consider to be clearly distinct from roundoff error when it is the result of a computation; it is defined as Eps^(7/8) which is ~1e-14 when Real==double, ~1e-6 when Real==float.
const Real SimTK::LeastPositiveReal |
This is the smallest positive real number that can be expressed in the type Real; it is ~1e-308 when Real==double, ~1e-38 when Real==float.
const Real SimTK::MostPositiveReal |
This is the largest finite positive real number that can be expressed in the Real type; ~1e+308 when Real==double, ~1e+38 when Real==float. Note that there is also a value Infinity that will test larger than this one.
const Real SimTK::LeastNegativeReal |
This is the largest negative real number (that is, closest to zero) that can be expressed in values of type Real.
const Real SimTK::MostNegativeReal |
This is the smallest finite negative real number that can be expressed in values of type Real. Note that -Infinity is a value that will still test smaller than this one.
const int SimTK::NumDigitsReal |
This is the number of decimal digits that can be reliably stored and retrieved in the default Real precision (typically log10(1/eps)-1), that is, about 15 digits when Real==double and 6 digits when Real==float.
const int SimTK::LosslessNumDigitsReal |
This is the smallest number of decimal digits you should store in a text file if you want to be able to get exactly the same bit pattern back when you read it back in and convert the text to a Real value.
Typically, this is about log10(1/tiny), which is about 20 digits when Real==double and 9 digits when Real==float.
const Real SimTK::Zero |
Real(0)
const Real SimTK::One |
Real(1)
const Real SimTK::MinusOne |
Real(-1)
const Real SimTK::Two |
Real(2)
const Real SimTK::Three |
Real(3)
const Real SimTK::OneHalf |
Real(1)/2.
const Real SimTK::OneThird |
Real(1)/3.
const Real SimTK::OneFourth |
Real(1)/4.
const Real SimTK::OneFifth |
Real(1)/5.
const Real SimTK::OneSixth |
Real(1)/6.
const Real SimTK::OneSeventh |
Real(1)/7.
const Real SimTK::OneEighth |
Real(1)/8.
const Real SimTK::OneNinth |
Real(1)/9.
const Real SimTK::Pi |
Real(pi)
const Real SimTK::OneOverPi |
1/Real(pi)
const Real SimTK::E |
e = Real(exp(1))
const Real SimTK::Log2E |
Real(log2(e)) (log base 2)
const Real SimTK::Log10E |
Real(log10(e)) (log base 10)
const Real SimTK::Sqrt2 |
Real(sqrt(2))
const Real SimTK::OneOverSqrt2 |
1/sqrt(2)==sqrt(2)/2 as Real
const Real SimTK::Sqrt3 |
Real(sqrt(3))
const Real SimTK::OneOverSqrt3 |
Real(1/sqrt(3))
const Real SimTK::CubeRoot2 |
Real(2^(1/3)) (cube root of 2)
const Real SimTK::CubeRoot3 |
Real(3^(1/3)) (cube root of 3)
const Real SimTK::Ln2 |
Real(ln(2)) (natural log of 2)
const Real SimTK::Ln10 |
Real(ln(10)) (natural log of 10)