lookup_gen.py

#!/usr/bin/env python3
import math

DDS_VALUE_T = 'dds_value_t' # c++ type
DDS_INC_T = 'uint32_t'
DDS_FREQ = 40000 # keep in sync with C++ code

def dds_notes_incs():
    M = 2 ** (1/12)
    LEN = 12*9
    freqs = [440/(M**x) for x in range(57,0,-1)] + [440] + [440*(M**x) for x in range(1,51)]
    r = [round(2**32 * f / DDS_FREQ) for f in freqs]
    assert len(r) == LEN
    for x in r:
        assert x > 0
        assert x < 2**32 / 2
    return r


def sin_points_full(n):
    l = [
        math.floor(math.sin(x*2*math.pi/n)*65535/2 + 65536/2)
        for x in range(0, n)
    ]
    assert len(l) == n
    for x in l:
        assert x >= 0
        assert x < 65536
    return l


def lookup_sin_quarter(i, table_quarter):
    l = len(table_quarter)
    if i < l:
        # first quarter of sine period, just lookup
        r = table_quarter[i]
        return r
    if i == l:
        # maximum value
        return 65535 # FIXME
    if i < l * 2:
        # second quarter of period
        idx = l*2 - i
        r = table_quarter[idx]
        return r
    if i == l * 2:
        # half of period
        return table_quarter[0]
    if i < l * 3:
        # 3rd quarter of period
        r = table_quarter[0] - (table_quarter[i - l*2] - table_quarter[0])
        r -= 1 # remove rounding error to match with "full table" (for tests)
        return r
    if i == l * 3:
        # minimum value
        return 0
    # 4th quarter of period
    assert i < l * 4
    r = table_quarter[0] - (table_quarter[l*4 - i] - table_quarter[0])
    r -= 1
    return r


def sin_points_quarter(n):
    assert n % 4 == 0
    full = sin_points_full(n)
    r = full[:int(n/4)]
    #print(f'F[{len(full)}]: {full}')
    #print(f'Q[{len(r)}]: {r}')
    full_test = [lookup_sin_quarter(i, r) for i in range(0,n)]
    #print(f'Q->F[{len(full_test)}]: {full_test}')
    for i in range(0,n):
        assert lookup_sin_quarter(i, r) == full[i]
    return r


print('// Autogenerated file\n')

print('\nconst std::array<' + DDS_INC_T + ', 12*9> dds_notes_incs = {')
print(" " + ", ".join([str(i) for i in dds_notes_incs()]))
print('};')

# sin tables
for sz in [3, 4, 5, 10, 12]:
    count_full = 2**sz
    print(f'\n// sin{sz}')
    print(f'constexpr std::array<{DDS_VALUE_T}, {int(count_full/4)}> lookup_table_sin{sz} = ' + '{')
    print(f' ' + ", ".join([str(x) for x in sin_points_quarter(count_full)]))
    print('};\n')