# [C++] Counting down for-loop does not reach zero

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I'm having a very strange error. I'm totally puzzled.

These are the two codes:

unSize is always 3.
uint64_t is the standard 64-bit unsigned integer type defined in stdint.h.
I copied the code as is, the other variables are irrelevant.

 for (uint64_t i=unSize-1; i>=0; i--) { k_sum = 0.0; for (uint64_t k=unSize-1; k>i; k--) { k_sum += U(i, k) * x(k, 0); } x(i, 0) = (y(i, 0) - k_sum) / U(i, i); } 
The only difference is, loop ending condition being "[color="#8b0000"]i>=0".
The variable i takes the values: 2, 1, 0, 18446744073709551615 (I believe this is unsigned equivalent of -1)

 for (uint64_t i=unSize-1; i>0; i--) { k_sum = 0.0; for (uint64_t k=unSize-1; k>i; k--) { k_sum += U(i, k) * x(k, 0); } x(i, 0) = (y(i, 0) - k_sum) / U(i, i); } 
The only difference is, loop ending condition being "[color="#8b0000"]i>0".
The variable i takes the values: 2, 1

Why doesn't the loop stop at i=0.
I just want the variable i to take the values 2, 1, 0.
How do I make it so that the final value of i in the final loop will be 0?

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for (uint64_t i=...; i>=0; ...)This code is an infinite loop: an unsigned number is always greater than or equal to zero.

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I found my mistake. I want to write the fixed code for reference for other people.

The problem was that, an unsigned variable always has values equal to or greater than zero. So the ending condition "i>=0" does never happen.
I modified the code as below:
 for (uint64_t i=unSize-1; (i>=0) && (i<unSize); i--) { k_sum = 0.0; for (uint64_t k=unSize-1; k>i; k--) { k_sum += U(i, k) * x(k, 0); } x(i, 0) = (y(i, 0) - k_sum) / U(i, i); } 

This way, if variable i underflows and takes a very large value the loop will stop.

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Just a question about the logic of that for block. What's the difference between starting at zero and going to unSize - 1 vs starting at unSize - 1 and going to zero? I don't know what all those functions are doing, but I can't see why you have to have a decrementing loop rather than an incrementing loop.

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Just a question about the logic of that for block. What's the difference between starting at zero and going to unSize - 1 vs starting at unSize - 1 and going to zero? I don't know what all those functions are doing, but I can't see why you have to have a decrementing loop rather than an incrementing loop.

Because of the algorithm (a part of solution of linear matrix equation Ax=b), the loop must run backwards. Calculation of the matrix element x(i, 0) requires previous elements of x matrix (i.e.; x(i-1, 0), x(i-2, 0), x(i-3, 0), ..., x(0, 0)).

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[quote name='Cornstalks' timestamp='1320195358' post='4879473']
Just a question about the logic of that for block. What's the difference between starting at zero and going to unSize - 1 vs starting at unSize - 1 and going to zero? I don't know what all those functions are doing, but I can't see why you have to have a decrementing loop rather than an incrementing loop.

Because of the algorithm (a part of solution of linear matrix equation Ax=b), the loop must run backwards. Calculation of the matrix element x(i, 0) requires previous elements of x matrix (i.e.; x(i-1, 0), x(i-2, 0), x(i-3, 0), ..., x(0, 0)).
[/quote]
Ah, I see. Good old reverse substitution. Makes sense.

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A proper count-down unsigned loop:
for ( uint64_t i = unSize; i--; ) { }

A proper signed count-down loop:
for ( int64_t i = inSize; --i >= 0; ) { }

Counting down is guaranteed to be at least as fast and often faster than counting up, especially in Java.

L. Spiro

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