#!/usr/bin/env python3
"""Verify the article's finite examples, independent of its illustration code."""
from fractions import Fraction as F
from functools import reduce
from operator import xor
from pathlib import Path
import json, math

ROOT = Path(__file__).resolve().parents[1]
out = {}
assert sum(2**k for k in range(4)) == 15 < 16
assert 2**8 == 256 and 2**16 == 65536
out['counting'] = {'four_bit_inputs': 16, 'shorter_strings': 15}
h = lambda p: -sum(q*math.log2(q) for q in [p, 1-p] if q)
assert h(.5) == 1 and h(0) == 0 and h(1) == 0
out['binary_entropy_p_0_9'] = h(.9)
codes = {'A':'0', 'B':'10', 'C':'110', 'D':'111'}
assert all(not b.startswith(a) for a in codes.values() for b in codes.values() if a != b)
message = 'ABACABAD'
encoded = ''.join(codes[c] for c in message)
assert encoded == '01001100100111' and len(encoded) == 14
pending = ''; decoded = ''; inverse = {v:k for k,v in codes.items()}
for bit in encoded:
    pending += bit
    if pending in inverse:
        decoded += inverse[pending]; pending = ''
assert decoded == message and not pending
assert sum(p*len(codes[c]) for c,p in zip('ABCD',[F(1,2),F(1,4),F(1,8),F(1,8)])) == F(7,4)
out['prefix_code'] = {'message': message, 'encoded': encoded, 'bits': len(encoded), 'expected_bits': 1.75}
lo, hi = F(0), F(1); intervals = []
for symbol in '001':
    split = lo + (hi-lo)*F(3,4)
    if symbol == '0': hi = split
    else: lo = split
    intervals.append([str(lo),str(hi)])
assert (lo,hi) == (F(27,64), F(9,16))
assert lo <= F(8,16) < F(9,16) <= hi
value = F(17,32); lo, hi = F(0), F(1); decoded = ''
for _ in range(3):
    split = lo+(hi-lo)*F(3,4)
    if value < split: decoded += '0'; hi = split
    else: decoded += '1'; lo = split
assert decoded == '001'
out['arithmetic_intervals'] = intervals
lz = list('101')
for _ in range(9): lz.append(lz[-3])
assert ''.join(lz) == '101101101101'
assert all((v >> 2) == 25 and ((v >> 2) << 2) == 100 for v in range(100,104))
out['quantization'] = {str(v): {'kept':f'{v>>2:06b}', 'decoded':(v>>2)<<2} for v in range(100,104)}
for a in range(16):
    for b in range(16):
        parity = a ^ b
        assert a ^ parity == b and b ^ parity == a
assert 0b1011 ^ 0b0110 == 0b1101
out['parity_pairs_checked'] = 256
def syndrome(bits):
    return reduce(xor, (i for i,b in enumerate(bits,1) if b == '1'), 0)
count = 0
for n in range(128):
    x = f'{n:07b}'
    for error_position in range(8):
        y = list(x)
        if error_position: y[error_position-1] = str(1-int(y[error_position-1]))
        location = syndrome(x) ^ syndrome(y)
        assert location == error_position
        if location: y[location-1] = str(1-int(y[location-1]))
        assert ''.join(y) == x
        count += 1
assert syndrome('1011001') == 1 and syndrome('1011101') == 4
out['syndrome'] = {'cases_checked':count,'X':'1011001','Y':'1011101','sX':'001','sY':'100','difference':'101','position':5}
for position in range(1,9):
    for amplitude in range(1,256):
        data = [amplitude if i == position else 0 for i in range(1,9)]
        m0 = sum(data); m1 = sum(i*v for i,v in enumerate(data,1))
        assert m0 == amplitude and F(m1,m0) == position
out['one_spike_measurement_cases_checked'] = 8*255
assert F(2,5)*10 == F(3,10)*10+1
out['hypothetical_model_break_even_GiB'] = 10
measurements = json.loads((ROOT/'evidence/measurements.json').read_text())
assert measurements['samples']['periodic']['byte_histogram_entropy'] == 8
assert all(v['round_trip_exact'] for s in measurements['samples'].values() for v in s['compressed'].values())
out['codec_round_trips_recorded'] = 12
(ROOT/'evidence/calculations.json').write_text(json.dumps(out,indent=2)+'\n')
print(f'All worked examples verified, including {count} syndrome cases.')