Wave3b
Diff polynomial Wavetable with phase modulation. Experimental. Note: - hard coded pre integrated table (see Local Data) - optimizations (more or less dirty) - should be oversampled x2 or x4 - tried 2nd order with 32bits ->KO
Inlets
frac32.bipolar pitch
frac32buffer.bipolar m
frac32.positive mEnv
Outlets
frac32buffer.bipolar selfPM wave
Parameters
frac32.s.map.pitch pitch
frac32.u.map I1
frac32.u.map I0
Declaration
// _____________________________________________________________________
const int32_t *table_dv_q20(void) {
static const int32_t dv[] = {
341270, 293052, 214566, 130383, 59189, 8646, -22360, -38891,
-46224, -48113, -46441, -41505, -32547, -18451, 1347, 25778,
51101, 70452, 74881, 56674, 14201, -44947, -106115, -154580,
-182276, -189636, -182696, -168813, -153723, -140485, -129654, -119973,
-109280, -95565, -77974, -57272, -35219, -12971, 10392, 37737,
71697, 111739, 152890, 187564, 209394, 216147, 209859, 194666,
174201, 149890, 120490, 82761, 33197, -29238, -100133, -168374,
-218951, -239722, -227925, -191189, -142375, -92968, -49664, -14725,
12158, 32437, 48089, 61406, 74779, 90374, 109670, 132828,
157819, 179489, 189315, 177198, 136199, 68565, -11773, -84294,
-132125, -149526, -141598, -118530, -89908, -61992, -37601, -17067,
743, 17689, 35835, 56951, 81818, 109192, 134493, 148901,
140401, 98459, 21648, -76927, -172884, -242400, -273781, -270153,
-243551, -206983, -169647, -135977, -106831, -81204, -57761, -35991,
-16840, -2516, 4697, 4268, -1128, -5620, -2111, 14378,
43709, 80157, 115241, 142015, 157859, 164394, 165468, 164886,
164886, 165468, 164394, 157859, 142015, 115241, 80157, 43709,
14378, -2111, -5620, -1128, 4268, 4697, -2516, -16840,
-35991, -57761, -81204, -106831, -135977, -169647, -206983, -243551,
-270153, -273781, -242400, -172884, -76927, 21648, 98459, 140401,
148901, 134493, 109192, 81818, 56951, 35835, 17689, 743,
-17067, -37601, -61992, -89908, -118530, -141598, -149526, -132125,
-84294, -11773, 68565, 136199, 177198, 189315, 179489, 157819,
132828, 109670, 90374, 74779, 61406, 48089, 32437, 12158,
-14725, -49664, -92968, -142375, -191189, -227925, -239722, -218951,
-168374, -100133, -29238, 33197, 82761, 120490, 149890, 174201,
194666, 209859, 216147, 209394, 187564, 152890, 111739, 71697,
37737, 10392, -12971, -35219, -57272, -77974, -95565, -109280,
-119973, -129654, -140485, -153723, -168813, -182696, -189636, -182276,
-154580, -106115, -44947, 14201, 56674, 74881, 70452, 51101,
25778, 1347, -18451, -32547, -41505, -46441, -48113, -46224,
-38891, -22360, 8646, 59189, 130383, 214566, 293052, 341270};
return dv;
}
// _____________________________________________________________________
// Info: max/MAX_VALUE=0.015891638%
const int32_t *table_v_q20(void) {
static const int32_t v[] = {
0, 341270, 634322, 848888, 979271, 1038460, 1047106,
1024746, 985854, 939630, 891517, 845075, 803570, 771023,
752572, 753919, 779697, 830799, 901251, 976132, 1032806,
1047007, 1002059, 895944, 741363, 559088, 369452, 186756,
17943, -135780, -276265, -405918, -525891, -635171, -730736,
-808710, -865982, -901201, -914172, -903780, -866043, -794347,
-682607, -529718, -342153, -132759, 83388, 293247, 487912,
662113, 812003, 932493, 1015253, 1048450, 1019212, 919079,
750705, 531755, 292033, 64108, -127081, -269456, -362424,
-412088, -426813, -414655, -382218, -334128, -272723, -197943,
-107569, 2101, 134929, 292748, 472236, 661551, 838750,
974949, 1043514, 1031741, 947446, 815322, 665795, 524197,
405667, 315759, 253767, 216166, 199100, 199843, 217532,
253367, 310318, 392136, 501327, 635820, 784721, 925122,
1023581, 1045229, 968302, 795418, 553018, 279237, 9084,
-234467, -441450, -611097, -747074, -853905, -935108, -992869,
-1028860, -1045700, -1048216, -1043518, -1039250, -1040378, -1045998,
-1048109, -1033730, -990021, -909864, -794623, -652608, -494749,
-330354, -164886, 0, 164886, 330354, 494749, 652608,
794623, 909864, 990021, 1033730, 1048109, 1045998, 1040378,
1039250, 1043518, 1048216, 1045700, 1028860, 992869, 935108,
853905, 747074, 611097, 441450, 234467, -9084, -279237,
-553018, -795418, -968302, -1045229, -1023581, -925122, -784721,
-635820, -501327, -392136, -310318, -253367, -217532, -199843,
-199100, -216166, -253767, -315759, -405667, -524197, -665795,
-815322, -947446, -1031741, -1043514, -974949, -838750, -661551,
-472236, -292748, -134929, -2101, 107569, 197943, 272723,
334128, 382218, 414655, 426813, 412088, 362424, 269456,
127081, -64108, -292033, -531755, -750705, -919079, -1019212,
-1048450, -1015253, -932493, -812003, -662113, -487912, -293247,
-83388, 132759, 342153, 529718, 682607, 794347, 866043,
903780, 914172, 901201, 865982, 808710, 730736, 635171,
525891, 405918, 276265, 135780, -17943, -186756, -369452,
-559088, -741363, -895944, -1002059, -1047007, -1032806, -976132,
-901251, -830799, -779697, -753919, -752572, -771023, -803570,
-845075, -891517, -939630, -985854, -1024746, -1047106, -1038460,
-979271, -848888, -634322, -341270};
return v;
}
// Info: max/MAX_VALUE=0.048822273%
// _____________________________________________________________________
const int32_t *table_Iv_q20(void) {
static const int32_t Iv[] = {
-19987852, -19817216, -19329420, -18587815, -17673735, -16664869,
-15622086, -14586160, -13580860, -12618118, -11702545, -10834249,
-10009926, -9222630, -8460832, -7707587, -6940778, -6135530,
-5269505, -4330814, -3326345, -2286438, -1261905, -312904,
505750, 1155976, 1620246, 1898350, 2000700, 1941781,
1735759, 1394667, 928763, 348232, -334722, -1104445,
-1941791, -2825383, -3733069, -4642045, -5526957, -6357152,
-7095629, -7701791, -8137727, -8375183, -8399869, -8211552,
-7820972, -7245959, -6508901, -5636653, -4662780, -3630928,
-2597097, -1627952, -793059, -151829, 260065, 438135,
406649, 208381, -107559, -494815, -914266, -1335000,
-1733436, -2091610, -2395035, -2630368, -2783124, -2835859,
-2767344, -2553506, -2171014, -1604120, -853969, 52880,
1062111, 2099738, 3089332, 3970716, 4711274, 5306270,
5771202, 6131916, 6416679, 6651646, 6859279, 7058750,
7267437, 7502887, 7784730, 8135957, 8582688, 9151262,
9861533, 10716454, 11690806, 12725211, 13731976, 14613836,
15288054, 15704181, 15848342, 15735651, 15397693, 14871420,
14192334, 13391845, 12497339, 11533350, 10522486, 9485206,
8438249, 7392382, 6350998, 5311184, 4267997, 3220943,
2180024, 1168148, 218205, -634039, -1357654, -1931332,
-2343884, -2591504, -2673947, -2591504, -2343884, -1931332,
-1357654, -634039, 218205, 1168148, 2180024, 3220943,
4267997, 5311184, 6350998, 7392382, 8438249, 9485206,
10522486, 11533350, 12497339, 13391845, 14192334, 14871420,
15397693, 15735651, 15848342, 15704181, 15288054, 14613836,
13731976, 12725211, 11690806, 10716454, 9861533, 9151262,
8582688, 8135957, 7784730, 7502887, 7267437, 7058750,
6859279, 6651646, 6416679, 6131916, 5771202, 5306270,
4711274, 3970716, 3089332, 2099738, 1062111, 52880,
-853969, -1604120, -2171014, -2553506, -2767344, -2835859,
-2783124, -2630368, -2395035, -2091610, -1733436, -1335000,
-914266, -494815, -107559, 208381, 406649, 438135,
260065, -151829, -793059, -1627952, -2597097, -3630928,
-4662780, -5636653, -6508901, -7245959, -7820972, -8211552,
-8399869, -8375183, -8137727, -7701791, -7095629, -6357152,
-5526957, -4642045, -3733069, -2825383, -1941791, -1104445,
-334722, 348232, 928763, 1394667, 1735759, 1941781,
2000700, 1898350, 1620246, 1155976, 505750, -312904,
-1261905, -2286438, -3326345, -4330814, -5269505, -6135530,
-6940778, -7707587, -8460832, -9222630, -10009926, -10834249,
-11702545, -12618118, -13580860, -14586160, -15622086, -16664869,
-17673735, -18587815, -19329420, -19817216};
return Iv;
}
// _____________________________________________________________________
// Info: max/MAX_VALUE=0.93075687%
uint32_t p; // phase
int32_t dp; // delta phase aka freq
int32_t x0, x1, I1_0, I1_1;
int32_t kMI; // Modulation Index
int32_t aMI, dMI; // interp Modulation Index
// _____________________________________________________________________
Init
// _____________________________________________________________________
p = 0;
dp = 1;
x0 = 0;
x1 = 1;
I1_0 = I1_1 = 0;
aMI = dMI = kMI = 0;
// _____________________________________________________________________
Control Rate
// _____________________________________________________________________
MTOFEXTENDED(param_pitch + inlet_pitch, dp);
dp >>= 4; // p is uq28 to let room for phase modulation
// (need to calculate x0 - x1 even with over modulation)
// _____________________________________________________________________
// Modulation Index (ie modulation depth)
// mEnv control [0 64] -> [I0 I1]
kMI = ___SMMUL(param_I1 << 2, inlet_mEnv << 4);
kMI = ___SMMLA(param_I0 << 2, (((1 << 27) - 1) - inlet_mEnv) << 4, kMI);
dMI = (kMI - aMI) >> 4; // for arate interpolation
// _____________________________________________________________________
// Audio rate loops
for (int j = 0; j < BUFSIZE; j++) {
p += dp; // phase increment
if (p >= 0x40000000) {
p -= 0x10000000;
x0 -= 0x10000000; // p, xO and x1 must be consistent
}
x1 = x0;
I1_1 = I1_0;
x0 = p + (___SMMUL(inlet_m[j], aMI) << 5);
x1 += (x0 == x1) ? 1 : 0; // avoids ill case
// differentiation part 1/3
// we launch the float div here (14 cycles !!)
// so that integer ops executes in parallel :D
float inv = ((float)(1 << 27)) / ((float)(x0 - x1));
// Now we do as many int ops as we can to fill ~14 cycles
// the interpolation coefficient
int32_t a = (x0 & 0x000FFFFF) << 11; // 0 -> 1 q31
// the segment number
uint32_t i = (x0 & 0x0FF00000) >> 20; // [0 255]
// polynomial calc of the integrand on segment i at position a
// the polynomial is
// I1_0 = Iv + a * v + (a^2/2) dv
// it is the integrand of v + a*dv
// a^2/2 q31
int32_t a2_2 = ___SMMUL(a, a);
I1_0 = ___SMMUL(table_v_q20()[i], a);
I1_0 = ___SMMLA(table_dv_q20()[i], a2_2, I1_0);
I1_0 = table_Iv_q20()[i] + (I1_0 << 1);
// we differentiate the integrand in the interval
// x0 x1: ie in the interval between now and the preceding
// input.
// differentiation part 2/3
int32_t diff = I1_0 - I1_1;
aMI += dMI; // Modulation Index interpolation for next iteration
// now, the result of our float division should be available.
// we haven't wasted our time waiting for it.
// differentiation part 3/3
outlet_wave[j] = (int32_t)(diff * inv);
}
// _____________________________________________________________________