What does "Unsigned modulo 256" mean in the context of image decoding - c

Question

Because I'm masochistic I'm trying to write something in C to decode an 8-bit PNG file (it's a learning thing, I'm not trying to reinvent libpng...)
I've got to the point when the stuff in my deflated, unfiltered data buffer unmistakably resembles the source image (see below), but it's still quite, erm, wrong, and I'm pretty sure there's something askew with my implementation of the filtering algorithms. Most of them are quite simple, but there's one major thing I don't understand in the docs, not being good at maths or ever having taken a comp-sci course:
Unsigned arithmetic modulo 256 is used, so that both the inputs and outputs fit into bytes.
What does that mean?
If someone can tell me that I'd be very grateful!
For reference, (and I apologise for the crappy C) my noddy implementation of the filtering algorithms described in the docs look like:
unsigned char paeth_predictor (unsigned char a, unsigned char b, unsigned char c) {
// a = left, b = above, c = upper left
char p = a + b - c; // initial estimate
char pa = abs(p - a); // distances to a, b, c
char pb = abs(p - b);
char pc = abs(p - c);
// return nearest of a,b,c,
// breaking ties in order a,b,c.
if (pa <= pb && pa <= pc) return a;
else if (pb <= pc) return b;
else return c;
}
void unfilter_sub(char* out, char* in, int bpp, int row, int rowlen) {
for (int i = 0; i < rowlen; i++)
out[i] = in[i] + (i < bpp ? 0 : out[i-bpp]);
}
void unfilter_up(char* out, char* in, int bpp, int row, int rowlen) {
for (int i = 0; i < rowlen; i++)
out[i] = in[i] + (row == 0 ? 0 : out[i-rowlen]);
}
void unfilter_paeth(char* out, char* in, int bpp, int row, int rowlen) {
char a, b, c;
for (int i = 0; i < rowlen; i++) {
a = i < bpp ? 0 : out[i - bpp];
b = row < 1 ? 0 : out[i - rowlen];
c = i < bpp ? 0 : (row == 0 ? 0 : out[i - rowlen - bpp]);
out[i] = in[i] + paeth_predictor(a, b, c);
}
}
And the images I'm seeing:
Source
Source http://img220.imageshack.us/img220/8111/testdn.png
Output
Output http://img862.imageshack.us/img862/2963/helloworld.png

Answer 1

It means that, in the algorithm, whenever an arithmetic operation is performed, it is performed modulo 256, i.e. if the result is greater than 256 then it "wraps" around. The result is that all values will always fit into 8 bits and not overflow.
Unsigned types already behave this way by mandate, and if you use unsigned char (and a byte on your system is 8 bits, which it probably is), then your calculation results will naturally just never overflow beyond 8 bits.

Answer 2

It means only the last 8 bits of the result is used. 2^8=256, the last 8 bits of unsigned value v is the same as (v%256).
For example, 2+255=257, or 100000001, last 8 bits of 257 is 1, and 257%256 is also 1.

Answer 3

In 'simple language' it means that you never go "out" of your byte size.
For example in C# if you try this it will fail:
byte test = 255 + 255;
(1,13): error CS0031: Constant value '510' cannot be converted to a
'byte'
byte test = (byte)(255 + 255);
(1,13): error CS0221: Constant value '510' cannot be converted to a
'byte' (use 'unchecked' syntax to override)
For every calculation you have to do modulo 256 (C#: % 256).
Instead of writing % 256 you can also do AND 255:
(175 + 205) mod 256 = (175 + 205) AND 255
Some C# samples:
byte test = ((255 + 255) % 256);
// test: 254
byte test = ((255 + 255) & 255);
// test: 254
byte test = ((1 + 379) % 256);
// test: 124
byte test = ((1 + 379) & 0xFF);
// test: 124
Note that you sometimes can simplify a byte-series:
(byteVal1 + byteVal2 + byteVal3) % 256
= (((byteVal1 % 256) + (byteVal2 % 256)) % 256 + (byteVal3 % 256)) % 256