This post shows the verification of the code in the previous post.
int24_t saw[7] = {0,0,0,0,0,0,0};
const int24_t detune_table[7] = {0, 128, -128, 408, -412, 704, -720};
int24_t next(int24_t pitch, int24_t mix, int24_t detune) {
int24_t sum = 0;
for (int i = 0; i < 7; i++) {
int24_t detunePitch = ((int48_t) pitch * detune) >> 23;
int24_t voice_detune = ((int48_t) detune_table[i] * detunePitch) >> 7;
saw[i] += pitch + voice_detune;
if (i == 0) {
sum += ((int48_t) saw[i] * 25) >> 7;
} else {
sum += ((int48_t) saw[i] * (mix >> 16)) >> 7;
}
}
return high_pass(sum);
}
Pitch
Pitch arrives at program memory location 0x0424, after some calculations
pitch is stored at iram[0x65]. The same value arrives unchanged at the
first oscillator calculation at 0x0455.
Pitch code is correct.
Detune
Detune arrives at 0x043f. The same value minus one arrives at the first
oscillator calculation at 0x0455. Detune is stored in mulcoeffs[0].
With detune = midi 127 and pitch = midi 97, we get
pitch = 421800
detune = 164352
(pitch * detune) >> 23 = 8237
Test:
Osc 4 detune 8237 * 408 / 128 = 26255.4, from debugger: 26255
Osc 5 detune 8237 * -412 / 128 = -26512.8, from debugger: -26513
Osc 6 detune: 8237 * 704 / 128 = 45303.5, from debugger: 45303
Osc 7 detune: , 8237 * -720 / 128 = 46333.13, from debugger: -46334
Detune code is correct.
Mix
Mix arrives at 0x043c. The same value minus one arrives at the oscillator mixing code at 0x47a. Mix is stored in mulcoeffs[1]
With mix = midi 127:
mix = mulcoeffs[1] = 2183167 (input - 1)
mix >> 16 = 2183167 >> 16 = 33
Results below are found by stepping through the debugger. Iram contains the raw values for each saws.
Step 1:
Iram 11 = -7537654
Result = -1943302
Control:
-7537654 * 33 / 128 = - 1943301.4 // OK!
Step 2:
Iram 6 = -8000810
Result = -4006011
Control:
-8000810 * 33 / 128 = -2062708.8 // contrib from this osc
-2062708.8 - 1943302 = -4006011.8 // OK!
Step 3:
Iram 9 = 92969
Result = -3982043
Control:
92969 * 33 / 128 = 23968.57 // contrib from this osc
23968.57 - 4006011.8 = -3982043.23 // OK!
Step 4:
Iram 5 = -4968160
Result = -4952387
Control:
-4968160 *25 / 128 = -907343.75 // center oscillator
-3982043 -907343.75 = -4952386.75 // OK!
Step 5:
Iram 7 = 6361263
Result = -3312374
Control:
6361263 * 33 / 128 = 1640013.12 // contrib from this osc
1640013.12 - 4952386.75 = -3312373.6 // OK!
Step 6:
Iram 0b = 3650948
Result = -2371114
Control:
3650948 * 33 / 128 = 941260.03 // contrib from this osc
941260.03 - 3312374 = -2371113.96 // OK!
Step 7:
Iram 0f is 6940947
Result = -581652
Control:
6940947 * 33 / 128 = 1789462.0 // contrib from this osc
1789462.0 - 2371114 = -581651.1 // OK!
Summing code is correct.
Checking the detune coefficients
The integer coefficients we found:
[0, 128, -128, 408, -412, 704, -720]
The decimal coefficients in the presentation, that match Adam Szabo's detected ones:
[0, 0.01953125, -0.01953125, 0.06225585, -0.0628662, 0.107421875, -0.10986328125]
These are 10/65536 times the integer coefficients (or 10 * (integer coefficient) >> 16). This holds true for all of the coefficients.
The coefficients are correct.
