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The variant's value must decrease during each loop iteration but must never become negative during the correct execution of the loop. Loop variants are used to guarantee that loops will terminate. A loop invariant is an assertion which must be true before the first loop iteration and remain true after each iteration.
Some loops can be shown to always terminate or never terminate through human inspection. For example, the following loop will, in theory, never stop. However, it may halt when executed on a physical machine due to arithmetic overflow : either leading to an exception or causing the counter to wrap to a negative value and enabling the loop ...
The loop counter is used to decide when the loop should terminate and for the program flow to continue to the next instruction after the loop. A common identifier naming convention is for the loop counter to use the variable names i , j , and k (and so on if needed), where i would be the most outer loop, j the next inner loop, etc.
[16] [17] And with certain programs the number of steps may be much smaller, for example a specific family of lambda terms using Church numerals take an infinite amount of steps with call-by-value (i.e. never complete), an exponential number of steps with call-by-name, but only a polynomial number with call-by-need.
The goal of loop unwinding is to increase a program's speed by reducing or eliminating instructions that control the loop, such as pointer arithmetic and "end of loop" tests on each iteration; [2] reducing branch penalties; as well as hiding latencies, including the delay in reading data from memory. [3]
On some systems, this loop will execute ten times as expected, but on other systems it will never terminate. The problem is that the loop terminating condition (x != 1.1) tests for exact equality of two floating point values, and the way floating point values are represented in many computers will make this test fail, because they cannot ...
A more efficient implementation would allocate a single array for y, and compute y in a single loop. To optimize this, a C++ compiler would need to: Inline the sin and operator+ function calls. Fuse the loops into a single loop. Remove the unused stores into the temporary arrays (can use a register or stack variable instead).
The test for i < len is still present, but it has been moved outside the loop, which now contains only a single test (for the value), and is guaranteed to terminate due to the sentinel value. There is a single check on termination if the sentinel value has been hit, which replaces a test for each iteration.