ICODE-ADC/lammps
4
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

complete documentation of the MathSpecial namespace

Browse Source
This commit is contained in:
Axel Kohlmeyer
2022-04-27 11:55:54 -04:00
parent d857600d9c
commit 6439777406
3 changed files with 72 additions and 10 deletions
Download Patch File Download Diff File Expand all files Collapse all files

59
src/math_special.h
View File

@ -22,7 +22,7 @@ namespace MathSpecial {
/*! Fast tabulated factorial function
*
* This function looks up precomputed factorial values for arguments of n = 0
* This function looks up pre-computed factorial values for arguments of n = 0
* to a maximum of 167, which is the maximal value representable by a double
* precision floating point number. For other values of n a NaN value is returned.
*
@ -53,7 +53,7 @@ namespace MathSpecial {
* The implementation makes assumptions about the layout of double
* precision floating point numbers in memory and thus will only work on little
* endian CPUs. If little endian cannot be safely detected, the result of
* calling the exp(x) implementation in the libm math library will be returned.
* calling the exp(x) implementation in the standard math library will be returned.
*
* \param x argument
* \return value of e^x as double precision number */
@ -64,7 +64,17 @@ namespace MathSpecial {
extern double erfcx_y100(const double y100);
// scaled error function complement exp(x*x)*erfc(x) for coul/long styles
/*! Fast scaled error function complement exp(x*x)*erfc(x) for coul/long styles
*
* This is a portable fast implementation of exp(x*x)*erfc(x) that can be used
* in coul/long pair styles as a replacement for the polynomial expansion that
* is/was widely used. Unlike the polynomial expansion, that is only accurate
* at the level of single precision floating point it provides full double precision
* accuracy, but at comparable speed (unlike the erfc() implementation shipped
* with GNU standard math library).
*
* \param x argument
* \return value of e^(x*x)*erfc(x) */
static inline double my_erfcx(const double x)
{
@ -74,7 +84,15 @@ namespace MathSpecial {
return 2.0 * exp(x * x) - erfcx_y100(400.0 / (4.0 - x));
}
// exp(-x*x) for coul/long styles
/*! Fast implementation of exp(-x*x) for little endian CPUs for coul/long styles
*
* This function implements an optimized version of exp(-x*x) based on exp2_x86()
* for use with little endian CPUs. If little endian cannot be safely detected,
* the result of calling the exp(-x*x) implementation in the standard math
* library will be returned.
*
* \param x argument
* \return value of e^(-x*x) as double precision number */
static inline double expmsq(double x)
{
@ -87,18 +105,34 @@ namespace MathSpecial {
#endif
}
// x**2, use instead of pow(x,2.0)
/*! Fast inline version of pow(x, 2.0)
*
* \param x argument
* \return x*x */
static inline double square(const double &x) { return x * x; }
// x**3, use instead of pow(x,3.0)
/*! Fast inline version of pow(x, 3.0)
*
* \param x argument
* \return x*x */
static inline double cube(const double &x) { return x * x * x; }
// return -1.0 for odd n, 1.0 for even n, like pow(-1.0,n)
/* Fast inline version of pow(-1.0, n)
*
* \param n argument (integer)
* \return -1 if n is odd, 1.0 if n is even */
static inline double powsign(const int n) { return (n & 1) ? -1.0 : 1.0; }
// optimized version of pow(x,n) with n being integer
// up to 10x faster than pow(x,y)
/* Fast inline version of pow(x,n) for integer n
*
* This is a version of pow(x,n) optimized for n being integer.
* Speedups of up to 10x faster than pow(x,y) have been measured.
*
* \param n argument (integer)
* \return value of x^n */
static inline double powint(const double &x, const int n)
{
@ -114,7 +148,12 @@ namespace MathSpecial {
return (n > 0) ? yy : 1.0 / yy;
}
// optimized version of (sin(x)/x)**n with n being a _positive_ integer
/* Fast inline version of (sin(x)/x)^n as used by PPPM kspace styles
*
* This is an optimized function to compute (sin(x)/x)^n as frequently used by PPPM.
*
* \param n argument (integer). Expected to be positive.
* \return value of (sin(x)/x)^n */
static inline double powsinxx(const double &x, int n)
{