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lfos)\r\nParam\t cutoffsmooth(20, min=0, max=1000);\t\t// default 20 ms\r\nParam\t resonancesmooth(10, min=0, max=1000);\t// default 10 ms\r\n// mono cutoff modulation or seperate left/right ?\r\nParam\t modulation(0, min=0, max=1);\t\t\t// mod mono (0) or stereo (1)\r\n\r\n// mono/stereo only uses required cpu\r\nParam\t stereo(1, min=0, max=1);\t\t\t\t// mono (0) or stereo (1) operation\r\n// slope 12/24 only uses required cpu\r\nParam\t slope(0, min=0, max=1);\t\t\t\t// 12dB (0) or 24dB (1) filter slope\r\n// (0) = bypass entire filter section & do not use the cpu\r\nParam\t filter(1, min=0, max=3);\t\t\t\t// choose lowpass (1), bandpass (2), highpass (3)\r\n// nonlinearity choice only uses required cpu\r\nParam\t nonlinear(1, min=0, max=1);\t\t\t// nonlinear (tanh) filters (1), pure linear filter sections (0)\r\n\r\n// (oversampled) nonlinearity is pre filter (0) or post filter (1) ?\r\nParam\t order(1, min=0, max=1);\r\n// for final nonlinearity\r\nParam\t drive(0, min=0, max=1);\t\t\t\t// % 0..1 (0 does not mean none !)\r\n// (0) = bypass entire nonlinearity section & do not use the cpu\r\nParam\t oversampling(2, min=0, max=2);\t\t\t// 1x (1) or 4x (2) oversampling for final nonlinearity\r\n\r\n//\t//\t//\tsetup\r\n\r\ncfm\t\t = int(cutoffmode);\r\nmod\t\t = int(modulation);\r\n\r\nms\t\t = int(stereo);\r\nslp\t\t = int(slope);\r\natten\t = expsmooth((1 / (slp + 2)), 0.015111);\r\nfilt\t = int(filter);\r\nft\t\t = maximum(filt, 1);\r\nnl\t\t = int(nonlinear);\r\n\r\n// clip and scale at param rate, then smooth\r\ndrv\t\t = logsmooth((((drive * 0.9) + 0.1) * pi), 0.022666);\r\nover\t = int(oversampling);\r\nord\t\t = int(order);\r\n\r\n//\t//\t//\tinputs\r\n\r\nxL\t\t = in1;\r\nxR\t\t = in2;\t\t\t\t\t\t\t\t\t// xR only used if 'stereo == 1'\r\n\r\ncfL\t\t = in3;\r\ncfR\t\t = in4;\t\t\t\t\t\t\t\t\t// cutoffR only used if 'stereo == 1'\r\n\r\nres\t\t = in5;\r\n\r\n//\t//\t//\tK scale\r\n\r\nK\t\t \t= clip(res, 0, 1) * 2;\r\n\r\nkitten\t\t= 1;\t\t\t\t\t\t\t\t// must be '1' if unused\r\nif ((K > 1) && (drive >= 0.5)) {\r\n\r\n\tkitten\t= (((clip(drive, 0.5, 1) - 0.5) * 0.1997) * ((slp * 0.92) + 1.07)) + ((over != 2) * 0.07053);\r\n\tkitten\t= 1 - (kitten * kitten);\r\n\r\n}\r\n\r\nyL, yR\t = 0;\r\n\r\nif (filt > 0) {\t\t\t\t\t\t\t\t\t// if entire filter chain not bypassed\r\n\r\n//\t//\t//\tparse modulation\r\n\r\nif (cfm > 0) {\t\t\t\t\t\t\t\t\t// if midi pitch input chosen for 'cutoff's\r\n\tcfL\t = mtofApprox(cfL);\r\n}\r\ncfLmod\t = clip(cfL, 10, (samplerate / 2.25));\t// clip at hz level\r\n\r\n// optional smoothing (turn off for modulated inputs)\r\ncs\t\t\t= 0;\r\nif (cutoffsmooth > 0) {\r\n\tcs\t\t= cutoffsmooth * 0.001;\t\t\t\t// ..secs\r\n\tcfLmod\t= logsmooth(cfLmod, cs);\r\n}\r\n\r\nif (resonancesmooth > 0) {\r\n\trs\t\t= resonancesmooth * 0.001;\t\t\t// ...secs\r\n\tK\t\t= interp((clip(K, 1, 2) - 1), K, (K * kitten), mode=\"linear\");\t// mode=\"cosine\"\r\n\tK\t\t= expsmooth(K * 0.95, rs);\r\n} else {\r\n\tkitten\t= expsmooth(kitten, 0.015111);\r\n\tK\t\t= interp((clip(K, 1, 2) - 1), K, (K * kitten), mode=\"linear\");\t// mode=\"cosine\"\r\n\tK\t\t= K * 0.95;\r\n}\r\n\r\n//\t//\t//\tprocessing\r\n\r\noverpre\t\t = ((over == 0) || (ord == 1)) ? 0 : over;\r\nxL\t\t\t = rsinNonlin(xL, drv, overpre);\t// only processes pre filter if (ord == 0) ...\r\nif (ms > 0) {\r\n\txR\t\t = rsinNonlin(xR, drv, overpre);\t// ...\r\n}\r\n\r\na1_L, a2_L, a3_L, a4_L, a5_L\t\t\t\t\t= skfTanCoef(cfLmod, K);\r\n\r\nif (ms > 0) {\t\t\t\t\t\t\t\t\t// if signal chain stereo\r\n\r\n\tcfRmod\t\t\t= 0;\r\n\tif (mod > 0) {\t\t\t\t\t\t\t\t// if modulation stereo\r\n\r\n\t\tif (cfm > 0) {\t\t\t\t\t\t\t// if midi pitch input chosen for 'cutoff's\r\n\t\t\tcfR\t \t= mtofApprox(cfR);\r\n\t\t}\r\n\t\tcfRmod\t \t= clip(cfR, 10, (samplerate / 2.25));// clip at hz level\r\n\r\n\t\t// optional smoothing (turn off for modulated inputs)\r\n\t\tif (cutoffsmooth > 0) {\r\n\t\t\tcfRmod\t= logsmooth(cfRmod, cs);\r\n\t\t}\r\n\r\n\t} else {\t\t\t\t\t\t\t\t\t// if modulation mono\r\n\r\n\t\tcfRmod\t \t= cfLmod;\r\n\r\n\t}\r\n\r\n\ta1_R, a2_R, a3_R, a4_R, a5_R\t\t\t\t= skfTanCoef(cfRmod, K);\r\n\r\n\tif (slp >= 0) {\r\n\t\tyL\t = skfTanNlto((xL * sqrt1_2), a1_L, a2_L, a3_L, a4_L, a5_L, K, nl, ft);\r\n\t\tyR\t = skfTanNlto((xR * sqrt1_2), a1_R, a2_R, a3_R, a4_R, a5_R, K, nl, ft);\r\n\t}\r\n\t// this is wrong, we should really recompute the coefficients for second filter in the\r\n\t// cascade, but trying to save cpu here; fixing this is on my 'todo' list\r\n\tif (slp >= 1) {\r\n\t\tyL\t = skfTanNlto((yL * sqrt1_2), a1_L, a2_L, a3_L, a4_L, a5_L, K, nl, ft);\r\n\t\tyR\t = skfTanNlto((yR * sqrt1_2), a1_R, a2_R, a3_R, a4_R, a5_R, K, nl, ft);\r\n\t}\r\n\r\n\tyL\t\t = yL * atten;\r\n\tyR\t\t = yR * atten;\r\n\r\n} else {\t\t\t\t\t\t\t\t\t\t// if signal chain mono\r\n\r\n\tif (slp >= 0) {\r\n\t\tyL\t = skfTanNlto((xL * sqrt1_2), a1_L, a2_L, a3_L, a4_L, a5_L, K, nl, ft);\r\n\t}\r\n\t// this is wrong, 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'fastexp()') { x = 0.999996 + (0.031261316 + (0.00048274797 + 0.000006 * x0) * x0) * x0; x *= x; x *= x; x *= x; x *= x; x *= x; return x; } dbtoaApprox(db) // i know this is shit, will fix one day, ok for +/- 12 dB input { return fastpow(10, (db * 0.05)) + 0.028652; // 0 dB == 1 amplitude } // cheaper than library 'mtof()' mtofApprox(pitch) // using 'expA()' for approximated accuracy { mtofA = 440 * expA(0.057762265 * (pitch - 69)); return mtofA + 0.120906; // + offset = accurate (exact) for input 48..69 } // cheaper tan approx tnA(x) // tan approximation (0..1 input) { x2 = (x * x); x3 = (x2 * x); x5 = (x2 * x3); return ((x5 * 0.133333) + (x3 * 0.333333)) + x; } tanO14(x) // tan approx octant { c1 = -34287.4662577359568109624; c2 = 2566.7175462315050423295; c3 = -26.5366371951731325438; c4 = -43656.1579281292375769579; c5 = 12244.4839556747426927793; c6 = -336.611376245464339493; x2 = x * x; return (x * (c1 + x2 * (c2 + x2 * c3))) / (c4 + x2 * (c5 + x2 * (c6 + x2))); } // good tan approx tan_14(x) // tan approx { four_over_pi = 1.27323954473516; // 4 / pi threehalfpi = 4.7123889803847; // 3 * halfpi octant = int(x * four_over_pi); // get octant # (0 to 7) tanreturn = 0; if (octant == 0) { tanreturn = tanO14(x * four_over_pi); } else if (octant == 1) { tanreturn = 1 / tanO14((halfpi - x) * four_over_pi); } else if (octant == 2) { tanreturn = -1 / tanO14((x - halfpi) * four_over_pi); } else if (octant == 3) { tanreturn = -tanO14((pi - x) * four_over_pi); } else if (octant == 4) { tanreturn = tanO14((x - pi) * four_over_pi); } else if (octant == 5) { tanreturn = 1 / tanO14((threehalfpi - x) * four_over_pi); } else if (octant == 6) { tanreturn = -1 / tanO14((x - threehalfpi) * four_over_pi); } else { // (octant == 7) tanreturn = -tanO14((twopi - x) * four_over_pi); } return tanreturn; } cosQ32(x) { c1 = 0.99940307; c2 = -0.49558072; c3 = 0.03679168; x2 = x * x; return (c1 + x2 * (c2 + c3 * x2)); } cos_32(x) { two_over_pi = 0.63661977236758; // 2 / pi quad = int(x * two_over_pi); // get quadrant # (0 to 3) we're in cosreturn = 0; if (quad == 0) { cosreturn = cosQ32(x); } else if (quad == 1) { cosreturn = -cosQ32(pi - x); } else if (quad == 2) { cosreturn = -cosQ32(x - pi); } else { // (quad == 3) cosreturn = cosQ32(twopi - x); } return cosreturn; } sin_32(x) { return cos_32(halfpi - x); } cosQ231(x) { c1 = 0.9999999999999999999999914771; c2 = -0.4999999999999999999991637437; c3 = 0.04166666666666666665319411988; c4 = -0.00138888888888888880310186415; c5 = 0.00002480158730158702330045157; c6 = -0.000000275573192239332256421489; c7 = 0.000000002087675698165412591559; c8 = -0.0000000000114707451267755432394; c9 = 0.0000000000000477945439406649917; c10 = -0.00000000000000015612263428827781; c11 = 0.00000000000000000039912654507924; x2 = x * x; return c1 + x2 * (c2 + x2 * (c3 + x2 * (c4 + x2 * (c5 + x2 * (c6 + x2 * (c7 + x2 * (c8 + x2 * (c9 + x2 * (c10 + x2 * c11))))))))); } cos_231(x) { two_over_pi = 0.63661977236758; // 2 / pi quad = int(x * two_over_pi); // get quadrant # (0 to 3) we're in cosreturn = 0; if (quad == 0) { cosreturn = cosQ231(x); } else if (quad == 1) { cosreturn = -cosQ231(pi - x); } else if (quad == 2) { cosreturn = -cosQ231(x - pi); } else { // (quad == 3) cosreturn = cosQ231(twopi - x); } return cosreturn; } sin_231(x) { return cos_231(halfpi - x); } // smoothing tauA(t) // approximate 'exp(-1 / (t * samplerate))' { y = expA(-1 / (t * samplerate)); return y + 0.000128; // approximation has excellent accuracy above... } // ...0.01 seconds (10 milliseconds) input // more 'exact' than 'logsmooth()' expsmooth(x, t) // t is smooth time in seconds { History w(0); z = tauA(t); y = (z * w) + (x * (1 - z)); w = y; return y; } logsmooth(x, s) // s = time to drop 6dB (in seconds) { History z(0); // ad = 0.693147 / maximum((s * samplerate), 1); // incl. maximum check ad = 0.693147 / (s * samplerate); y = ((x - z) * ad) + z; z = y; return y; } // nonlinearaties tnhL(x) // HQ tanh Lambert approx { x2 = x * x; a = (((x2 + 378) * x2 + 17325) * x2 + 135135) * x; b = ((28 * x2 + 3150) * x2 + 62370) * x2 + 135135; return clamp((a / b), -1, 1); } rsindrive(xin, scaledrive) // 'scaledrive' clipped and scaled before smoothing, for example, if initial 'drive' param 0..1: // scaledrive = logsmooth((((drive * 0.9) + 0.1) * pi), 0.022666); // must be 0..pi for our purposes { pidiv10 = 0.31415926535897932384626433832795; outdrive = 1 / sin_32(clip(scaledrive, pidiv10, halfpi)) - 0.000597; x = sin_231(clip(xin, -1, 1) * scaledrive); // sin_231 phase -pi..pi & not clipped return x * outdrive; } // fixed 4x cheap oversampling, plus voodoo for GenExpr rsin4x(XIN, w) { History umTm1_0(0), umT0_0(0), umT1_0(0); History dmT2_1(0), dmT1_1(0), dmT0_1(0); History dmT2_2(0), dmT1_2(0), dmT0_2(0); History dmT2_3(0), dmT1_3(0), dmT0_3(0); History doX0(0); x0_0_a = XIN + 0; x1_0 = interp(0.25, umTm1_0, umT0_0, umT1_0, x0_0_a, mode="spline"); x3_0 = interp(0.75, umTm1_0, umT0_0, umT1_0, x0_0_a, mode="spline"); x2_0 = interp(0.5, umTm1_0, umT0_0, umT1_0, x0_0_a, mode="spline"); // process 4x y1_0 = rsindrive(x1_0, w); y2_0 = rsindrive(x2_0, w); y3_0 = rsindrive(x3_0, w); y4_0 = rsindrive(umT1_0, w); y4_0_a = y4_0 + 0; y4_1 = interp(0.75, y4_0_a, dmT0_3, dmT1_3, dmT2_3, mode="spline"); y3_0_a = y3_0 + 0; y3_1 = interp(0.5, y3_0_a, dmT0_2, dmT1_2, dmT2_2, mode="spline"); y2_0_a = y2_0 + 0; y2_1 = interp(0.25, y2_0_a, dmT0_1, dmT1_1, dmT2_1, mode="spline"); y0_0 = (((doX0 + y2_1) + y3_1) + y4_1) * 0.25; umTm1_0 = umT0_0; umT0_0 = umT1_0; umT1_0 = XIN; dmT1_1 = dmT0_1; dmT0_1 = y2_0; dmT2_1 = dmT1_1; dmT1_2 = dmT0_2; dmT0_2 = y3_0; dmT2_2 = dmT1_2; dmT1_3 = dmT0_3; dmT0_3 = y4_0; dmT2_3 = dmT1_3; doX0 = y1_0; return dcblock(y0_0); } // make oversampling choice on nonlinearity rsinNonlin(xin, drive, oversampling) { History rsindummy(0); // for embedding y = 0; if (oversampling == 1) { // use 1x oversampling y = rsindrive(xin, drive); } else if (oversampling == 2) { // use 4x oversampling y = rsin4x(xin, drive); } else { // BYPASSED y = xin; } return y; } // for master filter skfTanCoef(cf, k) { // setup g0 = tan_14(pi * (cf / samplerate)); // cutoff g1 = 1 + g0; // k = 2 * res; // multiply before a0 = 1 / ((g1 * g1) - (g0 * k)); // coefficients a1 = k * a0; a2 = g1 * a0; a3 = g0 * a2; a4 = 1 / g1; a5 = g0 * a4; // coefficients to filter return a1, a2, a3, a4, a5; } skfTanNlto(v0, a1, a2, a3, a4, a5, k, sat, ft) { History ic1eq(0), ic2eq(0); // tick v1, v2 = 0; if (sat > 0) { v1 = (a1 * ic2eq) + (a2 * ic1eq) + tnhL(a3 * v0); v2 = (a4 * ic2eq) + tnhL(a5 * v1); } else { v1 = (a1 * ic2eq) + (a2 * ic1eq) + (a3 * v0); v2 = (a4 * ic2eq) + (a5 * v1); } // filters // (could be simultaneous outs, but not needed here) yv = 0; if (ft == 2) { // bandpass yv = v1 - v2; } else if (ft == 3) { // highpass yv = v0 - v2; } else { // (ft == 1) // lowpass, default yv = v2; } // updates ic1eq = (2 * (v1 - (k * v2))) - ic1eq; ic2eq = (2 * v2) - ic2eq; // out return dcblock(yv); } skfTanNltoMulti(v0, a1, a2, a3, a4, a5, k, sat) { History ic1eq(0), ic2eq(0); // tick v1, v2 = 0; if (sat > 0) { v1 = (a1 * ic2eq) + (a2 * ic1eq) + tnhL(a3 * v0); v2 = (a4 * ic2eq) + tnhL(a5 * v1); } else { v1 = (a1 * ic2eq) + (a2 * ic1eq) + (a3 * v0); v2 = (a4 * ic2eq) + (a5 * v1); } // filters hp = v0 - v2; // highpass bp = v1 - v2; // bandpass lp = v2; // lowpass // updates ic1eq = (2 * (v1 - (k * v2))) - ic1eq; ic2eq = (2 * v2) - ic2eq; // out return lp, bp, hp; } skfTanNltoCoef(v0, cf, res, sat, ft) { History ic1eq(0), ic2eq(0); // setup g0 = tnA(pi * (cf / samplerate)); // cutoff g1 = 1 + g0; k = 2 * res; // // coefficients a0 = 1 / ((g1 * g1) - (g0 * k)); // a1 = k * a0; a2 = g1 * a0; a3 = g0 * a2; a4 = 1 / g1; a5 = g0 * a4; // tick v1, v2 = 0; if (sat > 0) { v1 = (a1 * ic2eq) + (a2 * ic1eq) + (a3 * tnhL(v0)); v2 = (a4 * ic2eq) + tnhL(a5 * v1); } else { v1 = (a1 * ic2eq) + (a2 * ic1eq) + (a3 * v0); v2 = (a4 * ic2eq) + (a5 * v1); } // filters // (could be simultaneous outs, but not needed here) yv = 0; if (ft == 1) { // bandpass yv = v1 - v2; } else if (ft == 2) { // highpass yv = v0 - v2; } else { // (ft == 0) // lowpass, default yv = v2; } // updates ic1eq = (2 * (v1 - (k * v2))) - ic1eq; ic2eq = (2 * v2) - ic2eq; // out return dcblock(yv); // } skfTanNltoCoefMulti(v0, cf, res, sat) { History ic1eq(0), ic2eq(0); // setup g0 = tnA(pi * (cf / samplerate)); // cutoff g1 = 1 + g0; k = 2 * res; // // coefficients a0 = 1 / ((g1 * g1) - (g0 * k)); // a1 = k * a0; a2 = g1 * a0; a3 = g0 * a2; a4 = 1 / g1; a5 = g0 * a4; // tick v1, v2 = 0; if (sat > 0) { v1 = (a1 * ic2eq) + (a2 * ic1eq) + (a3 * tnhL(v0)); v2 = (a4 * ic2eq) + tnhL(a5 * v1); } else { v1 = (a1 * ic2eq) + (a2 * ic1eq) + (a3 * v0); v2 = (a4 * ic2eq) + (a5 * v1); } // filters hp = v0 - v2; // highpass bp = v1 - v2; // bandpass lp = v2; // lowpass // updates ic1eq = (2 * (v1 - (k * v2))) - ic1eq; ic2eq = (2 * v2) - ic2eq; // out return lp, bp, hp; } { "patcher" : { "fileversion" : 1, "appversion" : { "major" : 7, "minor" : 1, 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10.0, "id" : "obj-32", "linecount" : 3, "maxclass" : "comment", "numinlets" : 1, "numoutlets" : 0, "patching_rect" : [ 370.931641, 160.0, 184.000015, 40.0 ], "style" : "", "text" : "cutoff smooth time in milliseconds; choose 0 (off, default) for signal rate modulation input" } } , { "box" : { "fontname" : "Arial Bold", "fontsize" : 10.0, "id" : "obj-15", "maxclass" : "comment", "numinlets" : 1, "numoutlets" : 0, "patching_rect" : [ 379.421631, 97.0, 225.000015, 18.0 ], "style" : "", "text" : "flag, 0 = hz input, 1 = pitch input (default)" } } , { "box" : { "fontname" : "Arial Bold", "fontsize" : 10.0, "id" : "obj-27", "linecount" : 3, "maxclass" : "comment", "numinlets" : 1, "numoutlets" : 0, "patching_rect" : [ 349.931641, 493.0, 266.0, 40.0 ], "style" : "", "text" : "'saturate' ('shape') is a special feature which boosts/attenuates pre/post main nonlinearity in the filter; 0.5 (default) = off; smoothed internally" } } , { "box" : { "fontname" : "Arial Bold", "fontsize" : 10.0, "hidden" : 1, "id" : "obj-8", "maxclass" : "comment", "numinlets" : 1, "numoutlets" : 0, "patching_rect" : [ 417.931641, 467.0, 198.000015, 18.0 ], "style" : "" } } , { "box" : { "fontname" : "Arial Bold", "fontsize" : 10.0, "id" : "obj-25", "linecount" : 3, "maxclass" : "comment", "numinlets" : 1, "numoutlets" : 0, "patching_rect" : [ 453.931641, 345.0, 162.000015, 40.0 ], "style" : "", "text" : "resonance smooth time in milliseconds; choose 0 (off) for signal rate modulation input" } } , { "box" : { "background" : 1, "fontname" : "Arial Bold", "fontsize" : 10.0, "id" : "obj-38", "maxclass" : "comment", "numinlets" : 1, "numoutlets" : 0, "patching_rect" : [ 10.931656, 63.0, 577.325012, 18.0 ], "style" : "", "text" : "gen~ realisation by Pete Dowling & Matt Jackson @Surreal Machines, thanks to Graham Wakefield" } } , { "box" : { "background" : 1, "fontname" : "Arial Bold", "fontsize" : 10.0, "id" : "obj-3", "maxclass" : "comment", "numinlets" : 1, "numoutlets" : 0, "patching_rect" : [ 10.931656, 49.0, 577.325012, 18.0 ], "style" : "", "text" : "theory by Vadim Zavalishin, Native Instruments GmbH" } } , { "box" : { "background" : 1, "fontname" : "Arial Bold", "fontsize" : 10.0, "id" : "obj-16", "maxclass" : "comment", "numinlets" : 1, "numoutlets" : 0, "patching_rect" : [ 10.931656, 7.0, 577.325012, 18.0 ], "style" : "", "text" : "Zero Delay Feedback 24dB Lowpass Ladder filter, Newton-Raphson model" } } , { "box" : { "background" : 1, "fontname" : "Arial Bold", "fontsize" : 10.0, "id" : "obj-17", "maxclass" : "comment", "numinlets" : 1, "numoutlets" : 0, "patching_rect" : [ 10.931656, 21.0, 577.325012, 18.0 ], "style" : "", "text" : "based on: \"Computational optimization of nonlinear zero-delay feedback by second-order piecewise approximation\"" } } , { "box" : { "background" : 1, "fontname" : "Arial Bold", "fontsize" : 10.0, "id" : "obj-6", "maxclass" : "comment", "numinlets" : 1, "numoutlets" : 0, "patching_rect" : [ 10.931656, 35.0, 577.325012, 18.0 ], "style" : "", "text" : "and: “Preserving the LTI system topology in s- to z-plane transforms”" } } , { "box" : { "background" : 1, "fontname" : "Arial Bold", "fontsize" : 10.0, "id" : "obj-22", "maxclass" : "comment", "numinlets" : 1, "numoutlets" : 0, "patching_rect" : [ 217.931671, 546.5, 347.48999, 18.0 ], "style" : "", "text" : "Surreal Machines ZDF Ladder core abstraction" } } , { "box" : { "background" : 1, "fontface" : 2, "fontname" : "Arial Bold", "fontsize" : 10.0, "id" : "obj-2", "maxclass" : "comment", "numinlets" : 1, "numoutlets" : 0, "patching_rect" : [ 232.931671, 560.5, 382.999969, 18.0 ], "style" : "", "text" : "this can be instantiated in either gen~ (as it is here), or in GenExpr code..." } } , { "box" : { "background" : 1, "fontface" : 2, "fontname" : "Arial Bold", "fontsize" : 10.0, "id" : "obj-5", "maxclass" : "comment", "numinlets" : 1, "numoutlets" : 0, "patching_rect" : [ 232.931671, 574.5, 332.48999, 18.0 ], "style" : "", "text" : "...for example: y = sm_ladder(x, hz, 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s)\t\t\t\t\t\t\t\t// s = time to drop 6dB (in seconds)\r\n{\n\tHistory z(0);\n//\tad = 0.693147 / maximum((s * samplerate), 1);// maximum check not required here\n\tad = 0.693147 / (s * samplerate);\n\ty = ((x - z) * ad) + z;\n\tz = y;\n\treturn y;\n}\r\n\r\n// cheaper than library 'mtof()'\nmtofApprox(pitch)\t\t\t\t\t\t\t// using 'expA()' for approx with good accuracy\r\n{\r\n\tmtofA = 440 * expA(0.057762265 * (pitch - 69));\n\treturn mtofA + 0.120906;\t\t\t\t// + offset = accurate (exact) for input 48..69\n}\n\r\n//\t//\t//\tdeclare\r\n\r\n// choose cutoff input in Hz (0) or pitch (1, default)\r\nParam\tcutoffmode(1, min=0, max=1);\r\n// cutoff & resonance smooth times in ms; if == 0 then no cpu used\r\n// for smoothing and inputs can be signal rate modulators (e.g. lfos)\r\nParam\tcutoffsmooth(0, min=0, max=1000);\t\t// default off\r\nParam\tresonancesmooth(10, min=0, max=1000);\t// default 10 ms\r\n\r\n//\t//\t//\tinputs\r\n\r\ncfm\t\t\t= int(cutoffmode);\r\n\r\ncutoff\t\t= 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2566.7175462315050423295; c3 = -26.5366371951731325438; c4 = -43656.1579281292375769579; c5 = 12244.4839556747426927793; c6 = -336.611376245464339493; x2 = x * x; return (x * (c1 + x2 * (c2 + x2 * c3))) / (c4 + x2 * (c5 + x2 * (c6 + x2))); } // good tan approx tan_14(x) // tan approx { four_over_pi = 1.27323954473516; // 4 / pi threehalfpi = 4.7123889803847; // 3 * halfpi octant = int(x * four_over_pi); // get octant # (0 to 7) tanreturn = 0; if (octant == 0) { tanreturn = tanO14(x * four_over_pi); } else if (octant == 1) { tanreturn = 1 / tanO14((halfpi - x) * four_over_pi); } else if (octant == 2) { tanreturn = -1 / tanO14((x - halfpi) * four_over_pi); } else if (octant == 3) { tanreturn = -tanO14((pi - x) * four_over_pi); } else if (octant == 4) { tanreturn = tanO14((x - pi) * four_over_pi); } else if (octant == 5) { tanreturn = 1 / tanO14((threehalfpi - x) * four_over_pi); } else if (octant == 6) { tanreturn = -1 / tanO14((x - threehalfpi) * four_over_pi); } else { // (octant == 7) tanreturn = -tanO14((twopi - x) * four_over_pi); } return tanreturn; } cosQ32(x) { c1 = 0.99940307; c2 = -0.49558072; c3 = 0.03679168; x2 = x * x; return (c1 + x2 * (c2 + c3 * x2)); } cos_32(x) { two_over_pi = 0.63661977236758; // 2 / pi quad = int(x * two_over_pi); // get quadrant # (0 to 3) we're in cosreturn = 0; if (quad == 0) { cosreturn = cosQ32(x); } else if (quad == 1) { cosreturn = -cosQ32(pi - x); } else if (quad == 2) { cosreturn = -cosQ32(x - pi); } else { // (quad == 3) cosreturn = cosQ32(twopi - x); } return cosreturn; } sin_32(x) { return cos_32(halfpi - x); } cosQ231(x) { c1 = 0.9999999999999999999999914771; c2 = -0.4999999999999999999991637437; c3 = 0.04166666666666666665319411988; c4 = -0.00138888888888888880310186415; c5 = 0.00002480158730158702330045157; c6 = -0.000000275573192239332256421489; c7 = 0.000000002087675698165412591559; c8 = -0.0000000000114707451267755432394; c9 = 0.0000000000000477945439406649917; c10 = -0.00000000000000015612263428827781; c11 = 0.00000000000000000039912654507924; x2 = x * x; return c1 + x2 * (c2 + x2 * (c3 + x2 * (c4 + x2 * (c5 + x2 * (c6 + x2 * (c7 + x2 * (c8 + x2 * (c9 + x2 * (c10 + x2 * c11))))))))); } cos_231(x) { two_over_pi = 0.63661977236758; // 2 / pi quad = int(x * two_over_pi); // get quadrant # (0 to 3) we're in cosreturn = 0; if (quad == 0) { cosreturn = cosQ231(x); } else if (quad == 1) { cosreturn = -cosQ231(pi - x); } else if (quad == 2) { cosreturn = -cosQ231(x - pi); } else { // (quad == 3) cosreturn = cosQ231(twopi - x); } return cosreturn; } sin_231(x) { return cos_231(halfpi - x); } // smoothing tauA(t) // approximate 'exp(-1 / (t * samplerate))' { y = expA(-1 / (t * samplerate)); return y + 0.000128; // approximation has excellent accuracy above... } // ...0.01 seconds (10 milliseconds) input // more 'exact' than 'logsmooth()' expsmooth(x, t) // t is smooth time in seconds { History w(0); z = tauA(t); y = (z * w) + (x * (1 - z)); w = y; return y; } logsmooth(x, s) // s = time to drop 6dB (in seconds) { History z(0); // ad = 0.693147 / maximum((s * samplerate), 1); // incl. maximum check ad = 0.693147 / (s * samplerate); y = ((x - z) * ad) + z; z = y; return y; } // nonlinearaties tnhL(x) // HQ tanh Lambert approx { x2 = x * x; a = (((x2 + 378) * x2 + 17325) * x2 + 135135) * x; b = ((28 * x2 + 3150) * x2 + 62370) * x2 + 135135; return clamp((a / b), -1, 1); } rsindrive(xin, scaledrive) // 'scaledrive' clipped and scaled before smoothing, for example, if initial 'drive' param 0..1: // scaledrive = logsmooth((((drive * 0.9) + 0.1) * pi), 0.022666); // must be 0..pi for our purposes { pidiv10 = 0.31415926535897932384626433832795; outdrive = 1 / sin_32(clip(scaledrive, pidiv10, halfpi)) - 0.000597; x = sin_231(clip(xin, -1, 1) * scaledrive); // sin_231 phase -pi..pi & not clipped return x * outdrive; } // fixed 4x cheap oversampling, plus voodoo for GenExpr rsin4x(XIN, w) { History umTm1_0(0), umT0_0(0), umT1_0(0); History dmT2_1(0), dmT1_1(0), dmT0_1(0); History dmT2_2(0), dmT1_2(0), dmT0_2(0); History dmT2_3(0), dmT1_3(0), dmT0_3(0); History doX0(0); x0_0_a = XIN + 0; x1_0 = interp(0.25, umTm1_0, umT0_0, umT1_0, x0_0_a, mode="spline"); x3_0 = interp(0.75, umTm1_0, umT0_0, umT1_0, x0_0_a, mode="spline"); x2_0 = interp(0.5, umTm1_0, umT0_0, umT1_0, x0_0_a, mode="spline"); // process 4x y1_0 = rsindrive(x1_0, w); y2_0 = rsindrive(x2_0, w); y3_0 = rsindrive(x3_0, w); y4_0 = rsindrive(umT1_0, w); y4_0_a = y4_0 + 0; y4_1 = interp(0.75, y4_0_a, dmT0_3, dmT1_3, dmT2_3, mode="spline"); y3_0_a = y3_0 + 0; y3_1 = interp(0.5, y3_0_a, dmT0_2, dmT1_2, dmT2_2, mode="spline"); y2_0_a = y2_0 + 0; y2_1 = interp(0.25, y2_0_a, dmT0_1, dmT1_1, dmT2_1, mode="spline"); y0_0 = (((doX0 + y2_1) + y3_1) + y4_1) * 0.25; umTm1_0 = umT0_0; umT0_0 = umT1_0; umT1_0 = XIN; dmT1_1 = dmT0_1; dmT0_1 = y2_0; dmT2_1 = dmT1_1; dmT1_2 = dmT0_2; dmT0_2 = y3_0; dmT2_2 = dmT1_2; dmT1_3 = dmT0_3; dmT0_3 = y4_0; dmT2_3 = dmT1_3; doX0 = y1_0; return dcblock(y0_0); } // make oversampling choice on nonlinearity rsinNonlin(xin, drive, oversampling) { History rsindummy(0); // for embedding y = 0; if (oversampling == 1) { // use 1x oversampling y = rsindrive(xin, drive); } else if (oversampling == 2) { // use 4x oversampling y = rsin4x(xin, drive); } else { // BYPASSED y = xin; } return y; } // for master filter skfTanCoef(cf, k) { // setup g0 = tan_14(pi * (cf / samplerate)); // cutoff g1 = 1 + g0; // k = 2 * res; // multiply before a0 = 1 / ((g1 * g1) - (g0 * k)); // coefficients a1 = k * a0; a2 = g1 * a0; a3 = g0 * a2; a4 = 1 / g1; a5 = g0 * a4; // coefficients to filter return a1, a2, a3, a4, a5; } skfTanNlto(v0, a1, a2, a3, a4, a5, k, sat, ft) { History ic1eq(0), ic2eq(0); // tick v1, v2 = 0; if (sat > 0) { v1 = (a1 * ic2eq) + (a2 * ic1eq) + tnhL(a3 * v0); v2 = (a4 * ic2eq) + tnhL(a5 * v1); } else { v1 = (a1 * ic2eq) + (a2 * ic1eq) + (a3 * v0); v2 = (a4 * ic2eq) + (a5 * v1); } // filters // (could be simultaneous outs, but not needed here) yv = 0; if (ft == 2) { // bandpass yv = v1 - v2; } else if (ft == 3) { // highpass yv = v0 - v2; } else { // (ft == 1) // lowpass, default yv = v2; } // updates ic1eq = (2 * (v1 - (k * v2))) - ic1eq; ic2eq = (2 * v2) - ic2eq; // out return dcblock(yv); } skfTanNltoMulti(v0, a1, a2, a3, a4, a5, k, sat) { History ic1eq(0), ic2eq(0); // tick v1, v2 = 0; if (sat > 0) { v1 = (a1 * ic2eq) + (a2 * ic1eq) + tnhL(a3 * v0); v2 = (a4 * ic2eq) + tnhL(a5 * v1); } else { v1 = (a1 * ic2eq) + (a2 * ic1eq) + (a3 * v0); v2 = (a4 * ic2eq) + (a5 * v1); } // filters hp = v0 - v2; // highpass bp = v1 - v2; // bandpass lp = v2; // lowpass // updates ic1eq = (2 * (v1 - (k * v2))) - ic1eq; ic2eq = (2 * v2) - ic2eq; // out return lp, bp, hp; } skfTanNltoCoef(v0, cf, res, sat, ft) { History ic1eq(0), ic2eq(0); // setup g0 = tnA(pi * (cf / samplerate)); // cutoff g1 = 1 + g0; k = 2 * res; // // coefficients a0 = 1 / ((g1 * g1) - (g0 * k)); // a1 = k * a0; a2 = g1 * a0; a3 = g0 * a2; a4 = 1 / g1; a5 = g0 * a4; // tick v1, v2 = 0; if (sat > 0) { v1 = (a1 * ic2eq) + (a2 * ic1eq) + (a3 * tnhL(v0)); v2 = (a4 * ic2eq) + tnhL(a5 * v1); } else { v1 = (a1 * ic2eq) + (a2 * ic1eq) + (a3 * v0); v2 = (a4 * ic2eq) + (a5 * v1); } // filters // (could be simultaneous outs, but not needed here) yv = 0; if (ft == 1) { // bandpass yv = v1 - v2; } else if (ft == 2) { // highpass yv = v0 - v2; } else { // (ft == 0) // lowpass, default yv = v2; } // updates ic1eq = (2 * (v1 - (k * v2))) - ic1eq; ic2eq = (2 * v2) - ic2eq; // out return dcblock(yv); // } skfTanNltoCoefMulti(v0, cf, res, sat) { History ic1eq(0), ic2eq(0); // setup g0 = tnA(pi * (cf / samplerate)); // cutoff g1 = 1 + g0; k = 2 * res; // // coefficients a0 = 1 / ((g1 * g1) - (g0 * k)); // a1 = k * a0; a2 = g1 * a0; a3 = g0 * a2; a4 = 1 / g1; a5 = g0 * a4; // tick v1, v2 = 0; if (sat > 0) { v1 = (a1 * ic2eq) + (a2 * ic1eq) + (a3 * tnhL(v0)); v2 = (a4 * ic2eq) + tnhL(a5 * v1); } else { v1 = (a1 * ic2eq) + (a2 * ic1eq) + (a3 * v0); v2 = (a4 * ic2eq) + (a5 * v1); } // filters hp = v0 - v2; // highpass bp = v1 - v2; // bandpass lp = v2; // lowpass // updates ic1eq = (2 * (v1 - (k * v2))) - ic1eq; ic2eq = (2 * v2) - ic2eq; // out return lp, bp, hp; } /* 'require' for sm_sallenkey filter abstractions Pete Dowling @Surreal Machines, 2015 for 'smFilterPack' package, available from Cycling '74 */ // approximations expA(x0) // approx exp(x) (more accurate than 'fastexp()') { x = 0.999996 + (0.031261316 + (0.00048274797 + 0.000006 * x0) * x0) * x0; x *= x; x *= x; x *= x; x *= x; x *= x; return x; } dbtoaApprox(db) // i know this is shit, will fix one day, ok for +/- 12 dB input { return fastpow(10, (db * 0.05)) + 0.028652; // 0 dB == 1 amplitude } // cheaper than library 'mtof()' mtofApprox(pitch) // using 'expA()' for approximated accuracy { mtofA = 440 * expA(0.057762265 * (pitch - 69)); return mtofA + 0.120906; // + offset = accurate (exact) for input 48..69 } // cheaper tan approx tnA(x) // tan approximation (0..1 input) { x2 = (x * x); x3 = (x2 * x); x5 = (x2 * x3); return ((x5 * 0.133333) + (x3 * 0.333333)) + x; } tanO14(x) // tan approx octant { c1 = -34287.4662577359568109624; c2 = 2566.7175462315050423295; c3 = -26.5366371951731325438; c4 = -43656.1579281292375769579; c5 = 12244.4839556747426927793; c6 = -336.611376245464339493; x2 = x * x; return (x * (c1 + x2 * (c2 + x2 * c3))) / (c4 + x2 * (c5 + x2 * (c6 + x2))); } // good tan approx tan_14(x) // tan approx { four_over_pi = 1.27323954473516; // 4 / pi threehalfpi = 4.7123889803847; // 3 * halfpi octant = int(x * four_over_pi); // get octant # (0 to 7) tanreturn = 0; if (octant == 0) { tanreturn = tanO14(x * four_over_pi); } else if (octant == 1) { tanreturn = 1 / tanO14((halfpi - x) * four_over_pi); } else if (octant == 2) { tanreturn = -1 / tanO14((x - halfpi) * four_over_pi); } else if (octant == 3) { tanreturn = -tanO14((pi - x) * four_over_pi); } else if (octant == 4) { tanreturn = tanO14((x - pi) * four_over_pi); } else if (octant == 5) { tanreturn = 1 / tanO14((threehalfpi - x) * four_over_pi); } else if (octant == 6) { tanreturn = -1 / tanO14((x - threehalfpi) * four_over_pi); } else { // (octant == 7) tanreturn = -tanO14((twopi - x) * four_over_pi); } return tanreturn; } cosQ32(x) { c1 = 0.99940307; c2 = -0.49558072; c3 = 0.03679168; x2 = x * x; return (c1 + x2 * (c2 + c3 * x2)); } cos_32(x) { two_over_pi = 0.63661977236758; // 2 / pi quad = int(x * two_over_pi); // get quadrant # (0 to 3) we're in cosreturn = 0; if (quad == 0) { cosreturn = cosQ32(x); } else if (quad == 1) { cosreturn = -cosQ32(pi - x); } else if (quad == 2) { cosreturn = -cosQ32(x - pi); } else { // (quad == 3) cosreturn = cosQ32(twopi - x); } return cosreturn; } sin_32(x) { return cos_32(halfpi - x); } cosQ231(x) { c1 = 0.9999999999999999999999914771; c2 = -0.4999999999999999999991637437; c3 = 0.04166666666666666665319411988; c4 = -0.00138888888888888880310186415; c5 = 0.00002480158730158702330045157; c6 = -0.000000275573192239332256421489; c7 = 0.000000002087675698165412591559; c8 = -0.0000000000114707451267755432394; c9 = 0.0000000000000477945439406649917; c10 = -0.00000000000000015612263428827781; c11 = 0.00000000000000000039912654507924; x2 = x * x; return c1 + x2 * (c2 + x2 * (c3 + x2 * (c4 + x2 * (c5 + x2 * (c6 + x2 * (c7 + x2 * (c8 + x2 * (c9 + x2 * (c10 + x2 * c11))))))))); } cos_231(x) { two_over_pi = 0.63661977236758; // 2 / pi quad = int(x * two_over_pi); // get quadrant # (0 to 3) we're in cosreturn = 0; if (quad == 0) { cosreturn = cosQ231(x); } else if (quad == 1) { cosreturn = -cosQ231(pi - x); } else if (quad == 2) { cosreturn = -cosQ231(x - pi); } else { // (quad == 3) cosreturn = cosQ231(twopi - x); } return cosreturn; } sin_231(x) { return cos_231(halfpi - x); } // smoothing tauA(t) // approximate 'exp(-1 / (t * samplerate))' { y = expA(-1 / (t * samplerate)); return y + 0.000128; // approximation has excellent accuracy above... } // ...0.01 seconds (10 milliseconds) input // more 'exact' than 'logsmooth()' expsmooth(x, t) // t is smooth time in seconds { History w(0); z = tauA(t); y = (z * w) + (x * (1 - z)); w = y; return y; } logsmooth(x, s) // s = time to drop 6dB (in seconds) { History z(0); // ad = 0.693147 / maximum((s * samplerate), 1); // incl. maximum check ad = 0.693147 / (s * samplerate); y = ((x - z) * ad) + z; z = y; return y; } // nonlinearaties tnhL(x) // HQ tanh Lambert approx { x2 = x * x; a = (((x2 + 378) * x2 + 17325) * x2 + 135135) * x; b = ((28 * x2 + 3150) * x2 + 62370) * x2 + 135135; return clamp((a / b), -1, 1); } rsindrive(xin, scaledrive) // 'scaledrive' clipped and scaled before smoothing, for example, if initial 'drive' param 0..1: // scaledrive = logsmooth((((drive * 0.9) + 0.1) * pi), 0.022666); // must be 0..pi for our purposes { pidiv10 = 0.31415926535897932384626433832795; outdrive = 1 / sin_32(clip(scaledrive, pidiv10, halfpi)) - 0.000597; x = sin_231(clip(xin, -1, 1) * scaledrive); // sin_231 phase -pi..pi & not clipped return x * outdrive; } // fixed 4x cheap oversampling, plus voodoo for GenExpr rsin4x(XIN, w) { History umTm1_0(0), umT0_0(0), umT1_0(0); History dmT2_1(0), dmT1_1(0), dmT0_1(0); History dmT2_2(0), dmT1_2(0), dmT0_2(0); History dmT2_3(0), dmT1_3(0), dmT0_3(0); History doX0(0); x0_0_a = XIN + 0; x1_0 = interp(0.25, umTm1_0, umT0_0, umT1_0, x0_0_a, mode="spline"); x3_0 = interp(0.75, umTm1_0, umT0_0, umT1_0, x0_0_a, mode="spline"); x2_0 = interp(0.5, umTm1_0, umT0_0, umT1_0, x0_0_a, mode="spline"); // process 4x y1_0 = rsindrive(x1_0, w); y2_0 = rsindrive(x2_0, w); y3_0 = rsindrive(x3_0, w); y4_0 = rsindrive(umT1_0, w); y4_0_a = y4_0 + 0; y4_1 = interp(0.75, y4_0_a, dmT0_3, dmT1_3, dmT2_3, mode="spline"); y3_0_a = y3_0 + 0; y3_1 = interp(0.5, y3_0_a, dmT0_2, dmT1_2, dmT2_2, mode="spline"); y2_0_a = y2_0 + 0; y2_1 = interp(0.25, y2_0_a, dmT0_1, dmT1_1, dmT2_1, mode="spline"); y0_0 = (((doX0 + y2_1) + y3_1) + y4_1) * 0.25; umTm1_0 = umT0_0; umT0_0 = umT1_0; umT1_0 = XIN; dmT1_1 = dmT0_1; dmT0_1 = y2_0; dmT2_1 = dmT1_1; dmT1_2 = dmT0_2; dmT0_2 = y3_0; dmT2_2 = dmT1_2; dmT1_3 = dmT0_3; dmT0_3 = y4_0; dmT2_3 = dmT1_3; doX0 = y1_0; return dcblock(y0_0); } // make oversampling choice on nonlinearity rsinNonlin(xin, drive, oversampling) { History rsindummy(0); // for embedding y = 0; if (oversampling == 1) { // use 1x oversampling y = rsindrive(xin, drive); } else if (oversampling == 2) { // use 4x oversampling y = rsin4x(xin, drive); } else { // BYPASSED y = xin; } return y; } // for master filter skfTanCoef(cf, k) { // setup g0 = tan_14(pi * (cf / samplerate)); // cutoff g1 = 1 + g0; // k = 2 * res; // multiply before a0 = 1 / ((g1 * g1) - (g0 * k)); // coefficients a1 = k * a0; a2 = g1 * a0; a3 = g0 * a2; a4 = 1 / g1; a5 = g0 * a4; // coefficients to filter return a1, a2, a3, a4, a5; } skfTanNlto(v0, a1, a2, a3, a4, a5, k, sat, ft) { History ic1eq(0), ic2eq(0); // tick v1, v2 = 0; if (sat > 0) { v1 = (a1 * ic2eq) + (a2 * ic1eq) + tnhL(a3 * v0); v2 = (a4 * ic2eq) + tnhL(a5 * v1); } else { v1 = (a1 * ic2eq) + (a2 * ic1eq) + (a3 * v0); v2 = (a4 * ic2eq) + (a5 * v1); } // filters // (could be simultaneous outs, but not needed here) yv = 0; if (ft == 2) { // bandpass yv = v1 - v2; } else if (ft == 3) { // highpass yv = v0 - v2; } else { // (ft == 1) // lowpass, default yv = v2; } // updates ic1eq = (2 * (v1 - (k * v2))) - ic1eq; ic2eq = (2 * v2) - ic2eq; // out return dcblock(yv); } skfTanNltoMulti(v0, a1, a2, a3, a4, a5, k, sat) { History ic1eq(0), ic2eq(0); // tick v1, v2 = 0; if (sat > 0) { v1 = (a1 * ic2eq) + (a2 * ic1eq) + tnhL(a3 * v0); v2 = (a4 * ic2eq) + tnhL(a5 * v1); } else { v1 = (a1 * ic2eq) + (a2 * ic1eq) + (a3 * v0); v2 = (a4 * ic2eq) + (a5 * v1); } // filters hp = v0 - v2; // highpass bp = v1 - v2; // bandpass lp = v2; // lowpass // updates ic1eq = (2 * (v1 - (k * v2))) - ic1eq; ic2eq = (2 * v2) - ic2eq; // out return lp, bp, hp; } skfTanNltoCoef(v0, cf, res, sat, ft) { History ic1eq(0), ic2eq(0); // setup g0 = tnA(pi * (cf / samplerate)); // cutoff g1 = 1 + g0; k = 2 * res; // // coefficients a0 = 1 / ((g1 * g1) - (g0 * k)); // a1 = k * a0; a2 = g1 * a0; a3 = g0 * a2; a4 = 1 / g1; a5 = g0 * a4; // tick v1, v2 = 0; if (sat > 0) { v1 = (a1 * ic2eq) + (a2 * ic1eq) + (a3 * tnhL(v0)); v2 = (a4 * ic2eq) + tnhL(a5 * v1); } else { v1 = (a1 * ic2eq) + (a2 * ic1eq) + (a3 * v0); v2 = (a4 * ic2eq) + (a5 * v1); } // filters // (could be simultaneous outs, but not needed here) yv = 0; if (ft == 1) { // bandpass yv = v1 - v2; } else if (ft == 2) { // highpass yv = v0 - v2; } else { // (ft == 0) // lowpass, default yv = v2; } // updates ic1eq = (2 * (v1 - (k * v2))) - ic1eq; ic2eq = (2 * v2) - ic2eq; // out return dcblock(yv); // } skfTanNltoCoefMulti(v0, cf, res, sat) { History ic1eq(0), ic2eq(0); // setup g0 = tnA(pi * (cf / samplerate)); // cutoff g1 = 1 + g0; k = 2 * res; // // coefficients a0 = 1 / ((g1 * g1) - (g0 * k)); // a1 = k * a0; a2 = g1 * a0; a3 = g0 * a2; a4 = 1 / g1; a5 = g0 * a4; // tick v1, v2 = 0; if (sat > 0) { v1 = (a1 * ic2eq) + (a2 * ic1eq) + (a3 * tnhL(v0)); v2 = (a4 * ic2eq) + tnhL(a5 * v1); } else { v1 = (a1 * ic2eq) + (a2 * ic1eq) + (a3 * v0); v2 = (a4 * ic2eq) + (a5 * v1); } // filters hp = v0 - v2; // highpass bp = v1 - v2; // bandpass lp = v2; // lowpass // updates ic1eq = (2 * (v1 - (k * v2))) - ic1eq; ic2eq = (2 * v2) - ic2eq; // out return lp, bp, hp; } /* 'require' for sm_sallenkey filter abstractions Pete Dowling @Surreal Machines, 2015 for 'smFilterPack' package, available from Cycling '74 */ // approximations expA(x0) // approx exp(x) (more accurate than 'fastexp()') { x = 0.999996 + (0.031261316 + (0.00048274797 + 0.000006 * x0) * x0) * x0; x *= x; x *= x; x *= x; x *= x; x *= x; return x; } dbtoaApprox(db) // i know this is shit, will fix one day, ok for +/- 12 dB input { return fastpow(10, (db * 0.05)) + 0.028652; // 0 dB == 1 amplitude } // cheaper than library 'mtof()' mtofApprox(pitch) // using 'expA()' for approximated accuracy { mtofA = 440 * expA(0.057762265 * (pitch - 69)); return mtofA + 0.120906; // + offset = accurate (exact) for input 48..69 } // cheaper tan approx tnA(x) // tan approximation (0..1 input) { x2 = (x * x); x3 = (x2 * x); x5 = (x2 * x3); return ((x5 * 0.133333) + (x3 * 0.333333)) + x; } tanO14(x) // tan approx octant { c1 = -34287.4662577359568109624; c2 = 2566.7175462315050423295; c3 = -26.5366371951731325438; c4 = -43656.1579281292375769579; c5 = 12244.4839556747426927793; c6 = -336.611376245464339493; x2 = x * x; return (x * (c1 + x2 * (c2 + x2 * c3))) / (c4 + x2 * (c5 + x2 * (c6 + x2))); } // good tan approx tan_14(x) // tan approx { four_over_pi = 1.27323954473516; // 4 / pi threehalfpi = 4.7123889803847; // 3 * halfpi octant = int(x * four_over_pi); // get octant # (0 to 7) tanreturn = 0; if (octant == 0) { tanreturn = tanO14(x * four_over_pi); } else if (octant == 1) { tanreturn = 1 / tanO14((halfpi - x) * four_over_pi); } else if (octant == 2) { tanreturn = -1 / tanO14((x - halfpi) * four_over_pi); } else if (octant == 3) { tanreturn = -tanO14((pi - x) * four_over_pi); } else if (octant == 4) { tanreturn = tanO14((x - pi) * four_over_pi); } else if (octant == 5) { tanreturn = 1 / tanO14((threehalfpi - x) * four_over_pi); } else if (octant == 6) { tanreturn = -1 / tanO14((x - threehalfpi) * four_over_pi); } else { // (octant == 7) tanreturn = -tanO14((twopi - x) * four_over_pi); } return tanreturn; } cosQ32(x) { c1 = 0.99940307; c2 = -0.49558072; c3 = 0.03679168; x2 = x * x; return (c1 + x2 * (c2 + c3 * x2)); } cos_32(x) { two_over_pi = 0.63661977236758; // 2 / pi quad = int(x * two_over_pi); // get quadrant # (0 to 3) we're in cosreturn = 0; if (quad == 0) { cosreturn = cosQ32(x); } else if (quad == 1) { cosreturn = -cosQ32(pi - x); } else if (quad == 2) { cosreturn = -cosQ32(x - pi); } else { // (quad == 3) cosreturn = cosQ32(twopi - x); } return cosreturn; } sin_32(x) { return cos_32(halfpi - x); } cosQ231(x) { c1 = 0.9999999999999999999999914771; c2 = -0.4999999999999999999991637437; c3 = 0.04166666666666666665319411988; c4 = -0.00138888888888888880310186415; c5 = 0.00002480158730158702330045157; c6 = -0.000000275573192239332256421489; c7 = 0.000000002087675698165412591559; c8 = -0.0000000000114707451267755432394; c9 = 0.0000000000000477945439406649917; c10 = -0.00000000000000015612263428827781; c11 = 0.00000000000000000039912654507924; x2 = x * x; return c1 + x2 * (c2 + x2 * (c3 + x2 * (c4 + x2 * (c5 + x2 * (c6 + x2 * (c7 + x2 * (c8 + x2 * (c9 + x2 * (c10 + x2 * c11))))))))); } cos_231(x) { two_over_pi = 0.63661977236758; // 2 / pi quad = int(x * two_over_pi); // get quadrant # (0 to 3) we're in cosreturn = 0; if (quad == 0) { cosreturn = cosQ231(x); } else if (quad == 1) { cosreturn = -cosQ231(pi - x); } else if (quad == 2) { cosreturn = -cosQ231(x - pi); } else { // (quad == 3) cosreturn = cosQ231(twopi - x); } return cosreturn; } sin_231(x) { return cos_231(halfpi - x); } // smoothing tauA(t) // approximate 'exp(-1 / (t * samplerate))' { y = expA(-1 / (t * samplerate)); return y + 0.000128; // approximation has excellent accuracy above... } // ...0.01 seconds (10 milliseconds) input // more 'exact' than 'logsmooth()' expsmooth(x, t) // t is smooth time in seconds { History w(0); z = tauA(t); y = (z * w) + (x * (1 - z)); w = y; return y; } logsmooth(x, s) // s = time to drop 6dB (in seconds) { History z(0); // ad = 0.693147 / maximum((s * samplerate), 1); // incl. maximum check ad = 0.693147 / (s * samplerate); y = ((x - z) * ad) + z; z = y; return y; } // nonlinearaties tnhL(x) // HQ tanh Lambert approx { x2 = x * x; a = (((x2 + 378) * x2 + 17325) * x2 + 135135) * x; b = ((28 * x2 + 3150) * x2 + 62370) * x2 + 135135; return clamp((a / b), -1, 1); } rsindrive(xin, scaledrive) // 'scaledrive' clipped and scaled before smoothing, for example, if initial 'drive' param 0..1: // scaledrive = logsmooth((((drive * 0.9) + 0.1) * pi), 0.022666); // must be 0..pi for our purposes { pidiv10 = 0.31415926535897932384626433832795; outdrive = 1 / sin_32(clip(scaledrive, pidiv10, halfpi)) - 0.000597; x = sin_231(clip(xin, -1, 1) * scaledrive); // sin_231 phase -pi..pi & not clipped return x * outdrive; } // fixed 4x cheap oversampling, plus voodoo for GenExpr rsin4x(XIN, w) { History umTm1_0(0), umT0_0(0), umT1_0(0); History dmT2_1(0), dmT1_1(0), dmT0_1(0); History dmT2_2(0), dmT1_2(0), dmT0_2(0); History dmT2_3(0), dmT1_3(0), dmT0_3(0); History doX0(0); x0_0_a = XIN + 0; x1_0 = interp(0.25, umTm1_0, umT0_0, umT1_0, x0_0_a, mode="spline"); x3_0 = interp(0.75, umTm1_0, umT0_0, umT1_0, x0_0_a, mode="spline"); x2_0 = interp(0.5, umTm1_0, umT0_0, umT1_0, x0_0_a, mode="spline"); // process 4x y1_0 = rsindrive(x1_0, w); y2_0 = rsindrive(x2_0, w); y3_0 = rsindrive(x3_0, w); y4_0 = rsindrive(umT1_0, w); y4_0_a = y4_0 + 0; y4_1 = interp(0.75, y4_0_a, dmT0_3, dmT1_3, dmT2_3, mode="spline"); y3_0_a = y3_0 + 0; y3_1 = interp(0.5, y3_0_a, dmT0_2, dmT1_2, dmT2_2, mode="spline"); y2_0_a = y2_0 + 0; y2_1 = interp(0.25, y2_0_a, dmT0_1, dmT1_1, dmT2_1, mode="spline"); y0_0 = (((doX0 + y2_1) + y3_1) + y4_1) * 0.25; umTm1_0 = umT0_0; umT0_0 = umT1_0; umT1_0 = XIN; dmT1_1 = dmT0_1; dmT0_1 = y2_0; dmT2_1 = dmT1_1; dmT1_2 = dmT0_2; dmT0_2 = y3_0; dmT2_2 = dmT1_2; dmT1_3 = dmT0_3; dmT0_3 = y4_0; dmT2_3 = dmT1_3; doX0 = y1_0; return dcblock(y0_0); } // make oversampling choice on nonlinearity rsinNonlin(xin, drive, oversampling) { History rsindummy(0); // for embedding y = 0; if (oversampling == 1) { // use 1x oversampling y = rsindrive(xin, drive); } else if (oversampling == 2) { // use 4x oversampling y = rsin4x(xin, drive); } else { // BYPASSED y = xin; } return y; } // for master filter skfTanCoef(cf, k) { // setup g0 = tan_14(pi * (cf / samplerate)); // cutoff g1 = 1 + g0; // k = 2 * res; // multiply before a0 = 1 / ((g1 * g1) - (g0 * k)); // coefficients a1 = k * a0; a2 = g1 * a0; a3 = g0 * a2; a4 = 1 / g1; a5 = g0 * a4; // coefficients to filter return a1, a2, a3, a4, a5; } skfTanNlto(v0, a1, a2, a3, a4, a5, k, sat, ft) { History ic1eq(0), ic2eq(0); // tick v1, v2 = 0; if (sat > 0) { v1 = (a1 * ic2eq) + (a2 * ic1eq) + tnhL(a3 * v0); v2 = (a4 * ic2eq) + tnhL(a5 * v1); } else { v1 = (a1 * ic2eq) + (a2 * ic1eq) + (a3 * v0); v2 = (a4 * ic2eq) + (a5 * v1); } // filters // (could be simultaneous outs, but not needed here) yv = 0; if (ft == 2) { // bandpass yv = v1 - v2; } else if (ft == 3) { // highpass yv = v0 - v2; } else { // (ft == 1) // lowpass, default yv = v2; } // updates ic1eq = (2 * (v1 - (k * v2))) - ic1eq; ic2eq = (2 * v2) - ic2eq; // out return dcblock(yv); } skfTanNltoMulti(v0, a1, a2, a3, a4, a5, k, sat) { History ic1eq(0), ic2eq(0); // tick v1, v2 = 0; if (sat > 0) { v1 = (a1 * ic2eq) + (a2 * ic1eq) + tnhL(a3 * v0); v2 = (a4 * ic2eq) + tnhL(a5 * v1); } else { v1 = (a1 * ic2eq) + (a2 * ic1eq) + (a3 * v0); v2 = (a4 * ic2eq) + (a5 * v1); } // filters hp = v0 - v2; // highpass bp = v1 - v2; // bandpass lp = v2; // lowpass // updates ic1eq = (2 * (v1 - (k * v2))) - ic1eq; ic2eq = (2 * v2) - ic2eq; // out return lp, bp, hp; } skfTanNltoCoef(v0, cf, res, sat, ft) { History ic1eq(0), ic2eq(0); // setup g0 = tnA(pi * (cf / samplerate)); // cutoff g1 = 1 + g0; k = 2 * res; // // coefficients a0 = 1 / ((g1 * g1) - (g0 * k)); // a1 = k * a0; a2 = g1 * a0; a3 = g0 * a2; a4 = 1 / g1; a5 = g0 * a4; // tick v1, v2 = 0; if (sat > 0) { v1 = (a1 * ic2eq) + (a2 * ic1eq) + (a3 * tnhL(v0)); v2 = (a4 * ic2eq) + tnhL(a5 * v1); } else { v1 = (a1 * ic2eq) + (a2 * ic1eq) + (a3 * v0); v2 = (a4 * ic2eq) + (a5 * v1); } // filters // (could be simultaneous outs, but not needed here) yv = 0; if (ft == 1) { // bandpass yv = v1 - v2; } else if (ft == 2) { // highpass yv = v0 - v2; } else { // (ft == 0) // lowpass, default yv = v2; } // updates ic1eq = (2 * (v1 - (k * v2))) - ic1eq; ic2eq = (2 * v2) - ic2eq; // out return dcblock(yv); // } skfTanNltoCoefMulti(v0, cf, res, sat) { History ic1eq(0), ic2eq(0); // setup g0 = tnA(pi * (cf / samplerate)); // cutoff g1 = 1 + g0; k = 2 * res; // // coefficients a0 = 1 / ((g1 * g1) - (g0 * k)); // a1 = k * a0; a2 = g1 * a0; a3 = g0 * a2; a4 = 1 / g1; a5 = g0 * a4; // tick v1, v2 = 0; if (sat > 0) { v1 = (a1 * ic2eq) + (a2 * ic1eq) + (a3 * tnhL(v0)); v2 = (a4 * ic2eq) + tnhL(a5 * v1); } else { v1 = (a1 * ic2eq) + (a2 * ic1eq) + (a3 * v0); v2 = (a4 * ic2eq) + (a5 * v1); } // filters hp = v0 - v2; // highpass bp = v1 - v2; // bandpass lp = v2; // lowpass // updates ic1eq = (2 * (v1 - (k * v2))) - ic1eq; ic2eq = (2 * v2) - ic2eq; // out return lp, bp, hp; } /* 'require' for sm_sallenkey filter abstractions Pete Dowling @Surreal Machines, 2015 for 'smFilterPack' package, available from Cycling '74 */ // approximations expA(x0) // approx exp(x) (more accurate than 'fastexp()') { x = 0.999996 + (0.031261316 + (0.00048274797 + 0.000006 * x0) * x0) * x0; x *= x; x *= x; x *= x; x *= x; x *= x; return x; } dbtoaApprox(db) // i know this is shit, will fix one day, ok for +/- 12 dB input { return fastpow(10, (db * 0.05)) + 0.028652; // 0 dB == 1 amplitude } // cheaper than library 'mtof()' mtofApprox(pitch) // using 'expA()' for approximated accuracy { mtofA = 440 * expA(0.057762265 * (pitch - 69)); return mtofA + 0.120906; // + offset = accurate (exact) for input 48..69 } // cheaper tan approx tnA(x) // tan approximation (0..1 input) { x2 = (x * x); x3 = (x2 * x); x5 = (x2 * x3); return ((x5 * 0.133333) + (x3 * 0.333333)) + x; } tanO14(x) // tan approx octant { c1 = -34287.4662577359568109624; c2 = 2566.7175462315050423295; c3 = -26.5366371951731325438; c4 = -43656.1579281292375769579; c5 = 12244.4839556747426927793; c6 = -336.611376245464339493; x2 = x * x; return (x * (c1 + x2 * (c2 + x2 * c3))) / (c4 + x2 * (c5 + x2 * (c6 + x2))); } // good tan approx tan_14(x) // tan approx { four_over_pi = 1.27323954473516; // 4 / pi threehalfpi = 4.7123889803847; // 3 * halfpi octant = int(x * four_over_pi); // get octant # (0 to 7) tanreturn = 0; if (octant == 0) { tanreturn = tanO14(x * four_over_pi); } else if (octant == 1) { tanreturn = 1 / tanO14((halfpi - x) * four_over_pi); } else if (octant == 2) { tanreturn = -1 / tanO14((x - halfpi) * four_over_pi); } else if (octant == 3) { tanreturn = -tanO14((pi - x) * four_over_pi); } else if (octant == 4) { tanreturn = tanO14((x - pi) * four_over_pi); } else if (octant == 5) { tanreturn = 1 / tanO14((threehalfpi - x) * four_over_pi); } else if (octant == 6) { tanreturn = -1 / tanO14((x - threehalfpi) * four_over_pi); } else { // (octant == 7) tanreturn = -tanO14((twopi - x) * four_over_pi); } return tanreturn; } cosQ32(x) { c1 = 0.99940307; c2 = -0.49558072; c3 = 0.03679168; x2 = x * x; return (c1 + x2 * (c2 + c3 * x2)); } cos_32(x) { two_over_pi = 0.63661977236758; // 2 / pi quad = int(x * two_over_pi); // get quadrant # (0 to 3) we're in cosreturn = 0; if (quad == 0) { cosreturn = cosQ32(x); } else if (quad == 1) { cosreturn = -cosQ32(pi - x); } else if (quad == 2) { cosreturn = -cosQ32(x - pi); } else { // (quad == 3) cosreturn = cosQ32(twopi - x); } return cosreturn; } sin_32(x) { return cos_32(halfpi - x); } cosQ231(x) { c1 = 0.9999999999999999999999914771; c2 = -0.4999999999999999999991637437; c3 = 0.04166666666666666665319411988; c4 = -0.00138888888888888880310186415; c5 = 0.00002480158730158702330045157; c6 = -0.000000275573192239332256421489; c7 = 0.000000002087675698165412591559; c8 = -0.0000000000114707451267755432394; c9 = 0.0000000000000477945439406649917; c10 = -0.00000000000000015612263428827781; c11 = 0.00000000000000000039912654507924; x2 = x * x; return c1 + x2 * (c2 + x2 * (c3 + x2 * (c4 + x2 * (c5 + x2 * (c6 + x2 * (c7 + x2 * (c8 + x2 * (c9 + x2 * (c10 + x2 * c11))))))))); } cos_231(x) { two_over_pi = 0.63661977236758; // 2 / pi quad = int(x * two_over_pi); // get quadrant # (0 to 3) we're in cosreturn = 0; if (quad == 0) { cosreturn = cosQ231(x); } else if (quad == 1) { cosreturn = -cosQ231(pi - x); } else if (quad == 2) { cosreturn = -cosQ231(x - pi); } else { // (quad == 3) cosreturn = cosQ231(twopi - x); } return cosreturn; } sin_231(x) { return cos_231(halfpi - x); } // smoothing tauA(t) // approximate 'exp(-1 / (t * samplerate))' { y = expA(-1 / (t * samplerate)); return y + 0.000128; // approximation has excellent accuracy above... } // ...0.01 seconds (10 milliseconds) input // more 'exact' than 'logsmooth()' expsmooth(x, t) // t is smooth time in seconds { History w(0); z = tauA(t); y = (z * w) + (x * (1 - z)); w = y; return y; } logsmooth(x, s) // s = time to drop 6dB (in seconds) { History z(0); // ad = 0.693147 / maximum((s * samplerate), 1); // incl. maximum check ad = 0.693147 / (s * samplerate); y = ((x - z) * ad) + z; z = y; return y; } // nonlinearaties tnhL(x) // HQ tanh Lambert approx { x2 = x * x; a = (((x2 + 378) * x2 + 17325) * x2 + 135135) * x; b = ((28 * x2 + 3150) * x2 + 62370) * x2 + 135135; return clamp((a / b), -1, 1); } rsindrive(xin, scaledrive) // 'scaledrive' clipped and scaled before smoothing, for example, if initial 'drive' param 0..1: // scaledrive = logsmooth((((drive * 0.9) + 0.1) * pi), 0.022666); // must be 0..pi for our purposes { pidiv10 = 0.31415926535897932384626433832795; outdrive = 1 / sin_32(clip(scaledrive, pidiv10, halfpi)) - 0.000597; x = sin_231(clip(xin, -1, 1) * scaledrive); // sin_231 phase -pi..pi & not clipped return x * outdrive; } // fixed 4x cheap oversampling, plus voodoo for GenExpr rsin4x(XIN, w) { History umTm1_0(0), umT0_0(0), umT1_0(0); History dmT2_1(0), dmT1_1(0), dmT0_1(0); History dmT2_2(0), dmT1_2(0), dmT0_2(0); History dmT2_3(0), dmT1_3(0), dmT0_3(0); History doX0(0); x0_0_a = XIN + 0; x1_0 = interp(0.25, umTm1_0, umT0_0, umT1_0, x0_0_a, mode="spline"); x3_0 = interp(0.75, umTm1_0, umT0_0, umT1_0, x0_0_a, mode="spline"); x2_0 = interp(0.5, umTm1_0, umT0_0, umT1_0, x0_0_a, mode="spline"); // process 4x y1_0 = rsindrive(x1_0, w); y2_0 = rsindrive(x2_0, w); y3_0 = rsindrive(x3_0, w); y4_0 = rsindrive(umT1_0, w); y4_0_a = y4_0 + 0; y4_1 = interp(0.75, y4_0_a, dmT0_3, dmT1_3, dmT2_3, mode="spline"); y3_0_a = y3_0 + 0; y3_1 = interp(0.5, y3_0_a, dmT0_2, dmT1_2, dmT2_2, mode="spline"); y2_0_a = y2_0 + 0; y2_1 = interp(0.25, y2_0_a, dmT0_1, dmT1_1, dmT2_1, mode="spline"); y0_0 = (((doX0 + y2_1) + y3_1) + y4_1) * 0.25; umTm1_0 = umT0_0; umT0_0 = umT1_0; umT1_0 = XIN; dmT1_1 = dmT0_1; dmT0_1 = y2_0; dmT2_1 = dmT1_1; dmT1_2 = dmT0_2; dmT0_2 = y3_0; dmT2_2 = dmT1_2; dmT1_3 = dmT0_3; dmT0_3 = y4_0; dmT2_3 = dmT1_3; doX0 = y1_0; return dcblock(y0_0); } // make oversampling choice on nonlinearity rsinNonlin(xin, drive, oversampling) { History rsindummy(0); // for embedding y = 0; if (oversampling == 1) { // use 1x oversampling y = rsindrive(xin, drive); } else if (oversampling == 2) { // use 4x oversampling y = rsin4x(xin, drive); } else { // BYPASSED y = xin; } return y; } // for master filter skfTanCoef(cf, k) { // setup g0 = tan_14(pi * (cf / samplerate)); // cutoff g1 = 1 + g0; // k = 2 * res; // multiply before a0 = 1 / ((g1 * g1) - (g0 * k)); // coefficients a1 = k * a0; a2 = g1 * a0; a3 = g0 * a2; a4 = 1 / g1; a5 = g0 * a4; // coefficients to filter return a1, a2, a3, a4, a5; } skfTanNlto(v0, a1, a2, a3, a4, a5, k, sat, ft) { History ic1eq(0), ic2eq(0); // tick v1, v2 = 0; if (sat > 0) { v1 = (a1 * ic2eq) + (a2 * ic1eq) + tnhL(a3 * v0); v2 = (a4 * ic2eq) + tnhL(a5 * v1); } else { v1 = (a1 * ic2eq) + (a2 * ic1eq) + (a3 * v0); v2 = (a4 * ic2eq) + (a5 * v1); } // filters // (could be simultaneous outs, but not needed here) yv = 0; if (ft == 2) { // bandpass yv = v1 - v2; } else if (ft == 3) { // highpass yv = v0 - v2; } else { // (ft == 1) // lowpass, default yv = v2; } // updates ic1eq = (2 * (v1 - (k * v2))) - ic1eq; ic2eq = (2 * v2) - ic2eq; // out return dcblock(yv); } skfTanNltoMulti(v0, a1, a2, a3, a4, a5, k, sat) { History ic1eq(0), ic2eq(0); // tick v1, v2 = 0; if (sat > 0) { v1 = (a1 * ic2eq) + (a2 * ic1eq) + tnhL(a3 * v0); v2 = (a4 * ic2eq) + tnhL(a5 * v1); } else { v1 = (a1 * ic2eq) + (a2 * ic1eq) + (a3 * v0); v2 = (a4 * ic2eq) + (a5 * v1); } // filters hp = v0 - v2; // highpass bp = v1 - v2; // bandpass lp = v2; // lowpass // updates ic1eq = (2 * (v1 - (k * v2))) - ic1eq; ic2eq = (2 * v2) - ic2eq; // out return lp, bp, hp; } skfTanNltoCoef(v0, cf, res, sat, ft) { History ic1eq(0), ic2eq(0); // setup g0 = tnA(pi * (cf / samplerate)); // cutoff g1 = 1 + g0; k = 2 * res; // // coefficients a0 = 1 / ((g1 * g1) - (g0 * k)); // a1 = k * a0; a2 = g1 * a0; a3 = g0 * a2; a4 = 1 / g1; a5 = g0 * a4; // tick v1, v2 = 0; if (sat > 0) { v1 = (a1 * ic2eq) + (a2 * ic1eq) + (a3 * tnhL(v0)); v2 = (a4 * ic2eq) + tnhL(a5 * v1); } else { v1 = (a1 * ic2eq) + (a2 * ic1eq) + (a3 * v0); v2 = (a4 * ic2eq) + (a5 * v1); } // filters // (could be simultaneous outs, but not needed here) yv = 0; if (ft == 1) { // bandpass yv = v1 - v2; } else if (ft == 2) { // highpass yv = v0 - v2; } else { // (ft == 0) // lowpass, default yv = v2; } // updates ic1eq = (2 * (v1 - (k * v2))) - ic1eq; ic2eq = (2 * v2) - ic2eq; // out return dcblock(yv); // } skfTanNltoCoefMulti(v0, cf, res, sat) { History ic1eq(0), ic2eq(0); // setup g0 = tnA(pi * (cf / samplerate)); // cutoff g1 = 1 + g0; k = 2 * res; // // coefficients a0 = 1 / ((g1 * g1) - (g0 * k)); // a1 = k * a0; a2 = g1 * a0; a3 = g0 * a2; a4 = 1 / g1; a5 = g0 * a4; // tick v1, v2 = 0; if (sat > 0) { v1 = (a1 * ic2eq) + (a2 * ic1eq) + (a3 * tnhL(v0)); v2 = (a4 * ic2eq) + tnhL(a5 * v1); } else { v1 = (a1 * ic2eq) + (a2 * ic1eq) + (a3 * v0); v2 = (a4 * ic2eq) + (a5 * v1); } // filters hp = v0 - v2; // highpass bp = v1 - v2; // bandpass lp = v2; // lowpass // updates ic1eq = (2 * (v1 - (k * v2))) - ic1eq; ic2eq = (2 * v2) - ic2eq; // out return lp, bp, hp; } /* 'require' for sm_sallenkey filter abstractions Pete Dowling @Surreal Machines, 2015 for 'smFilterPack' package, available from Cycling '74 */ // approximations expA(x0) // approx exp(x) (more accurate than 'fastexp()') { x = 0.999996 + (0.031261316 + (0.00048274797 + 0.000006 * x0) * x0) * x0; x *= x; x *= x; x *= x; x *= x; x *= x; return x; } dbtoaApprox(db) // i know this is shit, will fix one day, ok for +/- 12 dB input { return fastpow(10, (db * 0.05)) + 0.028652; // 0 dB == 1 amplitude } // cheaper than library 'mtof()' mtofApprox(pitch) // using 'expA()' for approximated accuracy { mtofA = 440 * expA(0.057762265 * (pitch - 69)); return mtofA + 0.120906; // + offset = accurate (exact) for input 48..69 } // cheaper tan approx tnA(x) // tan approximation (0..1 input) { x2 = (x * x); x3 = (x2 * x); x5 = (x2 * x3); return ((x5 * 0.133333) + (x3 * 0.333333)) + x; } tanO14(x) // tan approx octant { c1 = -34287.4662577359568109624; c2 = 2566.7175462315050423295; c3 = -26.5366371951731325438; c4 = -43656.1579281292375769579; c5 = 12244.4839556747426927793; c6 = -336.611376245464339493; x2 = x * x; return (x * (c1 + x2 * (c2 + x2 * c3))) / (c4 + x2 * (c5 + x2 * (c6 + x2))); } // good tan approx tan_14(x) // tan approx { four_over_pi = 1.27323954473516; // 4 / pi threehalfpi = 4.7123889803847; // 3 * halfpi octant = int(x * four_over_pi); // get octant # (0 to 7) tanreturn = 0; if (octant == 0) { tanreturn = tanO14(x * four_over_pi); } else if (octant == 1) { tanreturn = 1 / tanO14((halfpi - x) * four_over_pi); } else if (octant == 2) { tanreturn = -1 / tanO14((x - halfpi) * four_over_pi); } else if (octant == 3) { tanreturn = -tanO14((pi - x) * four_over_pi); } else if (octant == 4) { tanreturn = tanO14((x - pi) * four_over_pi); } else if (octant == 5) { tanreturn = 1 / tanO14((threehalfpi - x) * four_over_pi); } else if (octant == 6) { tanreturn = -1 / tanO14((x - threehalfpi) * four_over_pi); } else { // (octant == 7) tanreturn = -tanO14((twopi - x) * four_over_pi); } return tanreturn; } cosQ32(x) { c1 = 0.99940307; c2 = -0.49558072; c3 = 0.03679168; x2 = x * x; return (c1 + x2 * (c2 + c3 * x2)); } cos_32(x) { two_over_pi = 0.63661977236758; // 2 / pi quad = int(x * two_over_pi); // get quadrant # (0 to 3) we're in cosreturn = 0; if (quad == 0) { cosreturn = cosQ32(x); } else if (quad == 1) { cosreturn = -cosQ32(pi - x); } else if (quad == 2) { cosreturn = -cosQ32(x - pi); } else { // (quad == 3) cosreturn = cosQ32(twopi - x); } return cosreturn; } sin_32(x) { return cos_32(halfpi - x); } cosQ231(x) { c1 = 0.9999999999999999999999914771; c2 = -0.4999999999999999999991637437; c3 = 0.04166666666666666665319411988; c4 = -0.00138888888888888880310186415; c5 = 0.00002480158730158702330045157; c6 = -0.000000275573192239332256421489; c7 = 0.000000002087675698165412591559; c8 = -0.0000000000114707451267755432394; c9 = 0.0000000000000477945439406649917; c10 = -0.00000000000000015612263428827781; c11 = 0.00000000000000000039912654507924; x2 = x * x; return c1 + x2 * (c2 + x2 * (c3 + x2 * (c4 + x2 * (c5 + x2 * (c6 + x2 * (c7 + x2 * (c8 + x2 * (c9 + x2 * (c10 + x2 * c11))))))))); } cos_231(x) { two_over_pi = 0.63661977236758; // 2 / pi quad = int(x * two_over_pi); // get quadrant # (0 to 3) we're in cosreturn = 0; if (quad == 0) { cosreturn = cosQ231(x); } else if (quad == 1) { cosreturn = -cosQ231(pi - x); } else if (quad == 2) { cosreturn = -cosQ231(x - pi); } else { // (quad == 3) cosreturn = cosQ231(twopi - x); } return cosreturn; } sin_231(x) { return cos_231(halfpi - x); } // smoothing tauA(t) // approximate 'exp(-1 / (t * samplerate))' { y = expA(-1 / (t * samplerate)); return y + 0.000128; // approximation has excellent accuracy above... } // ...0.01 seconds (10 milliseconds) input // more 'exact' than 'logsmooth()' expsmooth(x, t) // t is smooth time in seconds { History w(0); z = tauA(t); y = (z * w) + (x * (1 - z)); w = y; return y; } logsmooth(x, s) // s = time to drop 6dB (in seconds) { History z(0); // ad = 0.693147 / maximum((s * samplerate), 1); // incl. maximum check ad = 0.693147 / (s * samplerate); y = ((x - z) * ad) + z; z = y; return y; } // nonlinearaties tnhL(x) // HQ tanh Lambert approx { x2 = x * x; a = (((x2 + 378) * x2 + 17325) * x2 + 135135) * x; b = ((28 * x2 + 3150) * x2 + 62370) * x2 + 135135; return clamp((a / b), -1, 1); } rsindrive(xin, scaledrive) // 'scaledrive' clipped and scaled before smoothing, for example, if initial 'drive' param 0..1: // scaledrive = logsmooth((((drive * 0.9) + 0.1) * pi), 0.022666); // must be 0..pi for our purposes { pidiv10 = 0.31415926535897932384626433832795; outdrive = 1 / sin_32(clip(scaledrive, pidiv10, halfpi)) - 0.000597; x = sin_231(clip(xin, -1, 1) * scaledrive); // sin_231 phase -pi..pi & not clipped return x * outdrive; } // fixed 4x cheap oversampling, plus voodoo for GenExpr rsin4x(XIN, w) { History umTm1_0(0), umT0_0(0), umT1_0(0); History dmT2_1(0), dmT1_1(0), dmT0_1(0); History dmT2_2(0), dmT1_2(0), dmT0_2(0); History dmT2_3(0), dmT1_3(0), dmT0_3(0); History doX0(0); x0_0_a = XIN + 0; x1_0 = interp(0.25, umTm1_0, umT0_0, umT1_0, x0_0_a, mode="spline"); x3_0 = interp(0.75, umTm1_0, umT0_0, umT1_0, x0_0_a, mode="spline"); x2_0 = interp(0.5, umTm1_0, umT0_0, umT1_0, x0_0_a, mode="spline"); // process 4x y1_0 = rsindrive(x1_0, w); y2_0 = rsindrive(x2_0, w); y3_0 = rsindrive(x3_0, w); y4_0 = rsindrive(umT1_0, w); y4_0_a = y4_0 + 0; y4_1 = interp(0.75, y4_0_a, dmT0_3, dmT1_3, dmT2_3, mode="spline"); y3_0_a = y3_0 + 0; y3_1 = interp(0.5, y3_0_a, dmT0_2, dmT1_2, dmT2_2, mode="spline"); y2_0_a = y2_0 + 0; y2_1 = interp(0.25, y2_0_a, dmT0_1, dmT1_1, dmT2_1, mode="spline"); y0_0 = (((doX0 + y2_1) + y3_1) + y4_1) * 0.25; umTm1_0 = umT0_0; umT0_0 = umT1_0; umT1_0 = XIN; dmT1_1 = dmT0_1; dmT0_1 = y2_0; dmT2_1 = dmT1_1; dmT1_2 = dmT0_2; dmT0_2 = y3_0; dmT2_2 = dmT1_2; dmT1_3 = dmT0_3; dmT0_3 = y4_0; dmT2_3 = dmT1_3; doX0 = y1_0; return dcblock(y0_0); } // make oversampling choice on nonlinearity rsinNonlin(xin, drive, oversampling) { History rsindummy(0); // for embedding y = 0; if (oversampling == 1) { // use 1x oversampling y = rsindrive(xin, drive); } else if (oversampling == 2) { // use 4x oversampling y = rsin4x(xin, drive); } else { // BYPASSED y = xin; } return y; } // for master filter skfTanCoef(cf, k) { // setup g0 = tan_14(pi * (cf / samplerate)); // cutoff g1 = 1 + g0; // k = 2 * res; // multiply before a0 = 1 / ((g1 * g1) - (g0 * k)); // coefficients a1 = k * a0; a2 = g1 * a0; a3 = g0 * a2; a4 = 1 / g1; a5 = g0 * a4; // coefficients to filter return a1, a2, a3, a4, a5; } skfTanNlto(v0, a1, a2, a3, a4, a5, k, sat, ft) { History ic1eq(0), ic2eq(0); // tick v1, v2 = 0; if (sat > 0) { v1 = (a1 * ic2eq) + (a2 * ic1eq) + tnhL(a3 * v0); v2 = (a4 * ic2eq) + tnhL(a5 * v1); } else { v1 = (a1 * ic2eq) + (a2 * ic1eq) + (a3 * v0); v2 = (a4 * ic2eq) + (a5 * v1); } // filters // (could be simultaneous outs, but not needed here) yv = 0; if (ft == 2) { // bandpass yv = v1 - v2; } else if (ft == 3) { // highpass yv = v0 - v2; } else { // (ft == 1) // lowpass, default yv = v2; } // updates ic1eq = (2 * (v1 - (k * v2))) - ic1eq; ic2eq = (2 * v2) - ic2eq; // out return dcblock(yv); } skfTanNltoMulti(v0, a1, a2, a3, a4, a5, k, sat) { History ic1eq(0), ic2eq(0); // tick v1, v2 = 0; if (sat > 0) { v1 = (a1 * ic2eq) + (a2 * ic1eq) + tnhL(a3 * v0); v2 = (a4 * ic2eq) + tnhL(a5 * v1); } else { v1 = (a1 * ic2eq) + (a2 * ic1eq) + (a3 * v0); v2 = (a4 * ic2eq) + (a5 * v1); } // filters hp = v0 - v2; // highpass bp = v1 - v2; // bandpass lp = v2; // lowpass // updates ic1eq = (2 * (v1 - (k * v2))) - ic1eq; ic2eq = (2 * v2) - ic2eq; // out return lp, bp, hp; } skfTanNltoCoef(v0, cf, res, sat, ft) { History ic1eq(0), ic2eq(0); // setup g0 = tnA(pi * (cf / samplerate)); // cutoff g1 = 1 + g0; k = 2 * res; // // coefficients a0 = 1 / ((g1 * g1) - (g0 * k)); // a1 = k * a0; a2 = g1 * a0; a3 = g0 * a2; a4 = 1 / g1; a5 = g0 * a4; // tick v1, v2 = 0; if (sat > 0) { v1 = (a1 * ic2eq) + (a2 * ic1eq) + (a3 * tnhL(v0)); v2 = (a4 * ic2eq) + tnhL(a5 * v1); } else { v1 = (a1 * ic2eq) + (a2 * ic1eq) + (a3 * v0); v2 = (a4 * ic2eq) + (a5 * v1); } // filters // (could be simultaneous outs, but not needed here) yv = 0; if (ft == 1) { // bandpass yv = v1 - v2; } else if (ft == 2) { // highpass yv = v0 - v2; } else { // (ft == 0) // lowpass, default yv = v2; } // updates ic1eq = (2 * (v1 - (k * v2))) - ic1eq; ic2eq = (2 * v2) - ic2eq; // out return dcblock(yv); // } skfTanNltoCoefMulti(v0, cf, res, sat) { History ic1eq(0), ic2eq(0); // setup g0 = tnA(pi * (cf / samplerate)); // cutoff g1 = 1 + g0; k = 2 * res; // // coefficients a0 = 1 / ((g1 * g1) - (g0 * k)); // a1 = k * a0; a2 = g1 * a0; a3 = g0 * a2; a4 = 1 / g1; a5 = g0 * a4; // tick v1, v2 = 0; if (sat > 0) { v1 = (a1 * ic2eq) + (a2 * ic1eq) + (a3 * tnhL(v0)); v2 = (a4 * ic2eq) + tnhL(a5 * v1); } else { v1 = (a1 * ic2eq) + (a2 * ic1eq) + (a3 * v0); v2 = (a4 * ic2eq) + (a5 * v1); } // filters hp = v0 - v2; // highpass bp = v1 - v2; // bandpass lp = v2; // lowpass // updates ic1eq = (2 * (v1 - (k * v2))) - ic1eq; ic2eq = (2 * v2) - ic2eq; // out return lp, bp, hp; } PNG  IHDRxtEXtSoftwareAdobe ImageReadyqe<(iTXtXML:com.adobe.xmp &cIDATx}`յ٢^nK%r;666B Ix4j#@I@B w `{V\dV׮ IޙYI+7I.%wN)b)ҷjN)b)SL1SL1)b)bSL1SL1b)b L1SL1b)b)&0SL1SL`)b)SL1SL9bw\,b)bJfzL1SL1/ L1SN3#N#S`)rJK8ီ7UyL1֏>e< xԙ&ask!d&sN_=T4t!ڭ#{iǙ5U<` ŧygSmB%t 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