/************************************************************************ ************************************************************************ FAUST library file Copyright (C) 2003-2011 GRAME, Centre National de Creation Musicale --------------------------------------------------------------------- This program is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with the GNU C Library; if not, write to the Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA. ************************************************************************ ************************************************************************/ declare name "Math Library"; declare author "GRAME"; declare copyright "GRAME"; declare version "1.0"; declare license "LGPL"; //-------------------------------------------------------------------------------- // Mathematic library for Faust // Implementation of the math.h file as Faust foreign functions // // History // ---------- // 28/06/2005 [YO] postfixed functions with 'f' to force float version // instead of double // [YO] removed 'modf' because it requires a pointer as argument //--------------------------------------------------------------------------------- // -- Utilities and constants SR = min(192000, max(1, fconstant(int fSamplingFreq, ))); BS = fvariable(int count, ); PI = 3.1415926535897932385; // -- neg and inv functions neg(x) = -x; inv(x) = 1/x; // -- Trigonometric Functions //acos = ffunction(float acosf (float), , ""); //asin = ffunction(float asinf (float), , ""); //atan = ffunction(float atanf (float), , ""); //atan2 = ffunction(float atan2f (float, float), , ""); //sin = ffunction(float sinf (float), , ""); //cos = ffunction(float cosf (float), , ""); //tan = ffunction(float tanf (float), ,""); // -- Exponential Functions //exp = ffunction(float expf (float), ,""); //log = ffunction(float logf (float), ,""); //log10 = ffunction(float log10f (float), ,""); //pow = ffunction(float powf (float, float), ,""); //sqrt = ffunction(float sqrtf (float), ,""); cbrt = ffunction(float cbrtf (float), ,""); hypot = ffunction(float hypotf (float, float), ,""); ldexp = ffunction(float ldexpf (float, int), ,""); scalb = ffunction(float scalbf (float, float), ,""); log1p = ffunction(float log1pf (float), ,""); logb = ffunction(float logbf (float), ,""); ilogb = ffunction(int ilogbf (float), ,""); expm1 = ffunction(float expm1f (float), ,""); // -- Hyperbolic Functions acosh = ffunction(float acoshf (float), , ""); asinh = ffunction(float asinhf (float), , ""); atanh = ffunction(float atanhf (float), , ""); sinh = ffunction(float sinhf (float), , ""); cosh = ffunction(float coshf (float), , ""); tanh = ffunction(float tanhf (float), ,""); // -- Remainder Functions //fmod = ffunction(float fmodf (float, float),,""); //remainder = ffunction(float remainderf (float, float),,""); // -- Nearest Integer Functions //floor = ffunction(float floorf (float), ,""); //ceil = ffunction(float ceilf (float), ,""); //rint = ffunction(float rintf (float), ,""); // -- Special Functions erf = ffunction(float erff(float), ,""); erfc = ffunction(float erfcf(float), ,""); gamma = ffunction(float gammaf(float), ,""); J0 = ffunction(float j0f(float), ,""); J1 = ffunction(float j1f(float), ,""); Jn = ffunction(float jnf(int, float), ,""); lgamma = ffunction(float lgammaf(float), ,""); Y0 = ffunction(float y0f(float), ,""); Y1 = ffunction(float y1f(float), ,""); Yn = ffunction(float ynf(int, float), ,""); // -- Miscellaneous Functions //fabs = ffunction(float fabsf (float), ,""); //fmax = ffunction(float max (float, float),,""); //fmin = ffunction(float min (float, float),,""); fabs = abs; fmax = max; fmin = min; isnan = ffunction(int isnan (float),,""); nextafter = ffunction(float nextafter(float, float),,""); // Pattern matching functions to count and access the elements of a list // USAGE : count ((10,20,30,40)) -> 4 // take (3,(10,20,30,40)) -> 30 // count ((xs, xxs)) = 1 + count(xxs); count (xx) = 1; take (1, (xs, xxs)) = xs; take (1, xs) = xs; take (nn, (xs, xxs)) = take (nn-1, xxs); // linear interpolation between two signals interpolate(i) = *(1.0-i),*(i) : +; // if-then-else implemented with a select2. if(cond,thn,els) = select2(cond,els,thn); //----------------------------------------------------------------- // countdown(count,trig) // start counting down from count, count-1,...,0 when trig > 0 //----------------------------------------------------------------- countdown(count, trig) = \(c).(if(trig>0, count, max(0, c-1))) ~_; //----------------------------------------------------------------- // countup(count,trig) // start counting down from 0, 1, ... count-1, count when trig > 0 //----------------------------------------------------------------- countup(count, trig) = \(c).(if(trig>0, 0, min(count, c+1))) ~_; /****************************************************************** * Hadamard matrix function * Implementation contributed by Remy Muller *****************************************************************/ // bus(n) : n parallel cables bus(2) = _,_; // avoids a lot of "bus(1)" labels in block diagrams bus(n) = par(i, n, _); // selector(i,n) : select ith cable among n selector(i,n) = par(j, n, S(i, j)) with { S(i,i) = _; S(i,j) = !; }; // interleave(m,n) : interleave m*n cables : x(0), x(m), x(2m), ..., x(1),x(1+m), x(1+2m)... //interleave(m,n) = bus(m*n) <: par(i, m, par(j, n, selector(i+j*m,m*n))); // interleave(row,col) : interleave row*col cables from column order to row order. // input : x(0), x(1), x(2) ..., x(row*col-1) // output: x(0+0*row), x(0+1*row), x(0+2*row), ..., x(1+0*row), x(1+1*row), x(1+2*row), ... interleave(row,col) = bus(row*col) <: par(r, row, par(c, col, selector(r+c*row,row*col))); // butterfly(n) : addition then substraction of interleaved signals : butterfly(n) = bus(n) <: interleave(n/2,2), interleave(n/2,2) : par(i, n/2, +), par(i, n/2, -); // hadamard(n) : hadamard matrix function of size n = 2^k hadamard(2) = butterfly(2); hadamard(n) = butterfly(n) : (hadamard(n/2) , hadamard(n/2));