Optimizing loop by using floating point value as loop counter -

i need execute loop

while (x) y 

for n times, large number. while y, loop body, rather quick, test x takes 70% of runtime.

i can calculate number of loop iterations n beforehand instead of using x condition, simple for-loop possible.

for (i=1 n) y 

however, n might exceed maximum value integer can store on machine, not option. alternative, proposed use floating point variable f instead. n large, f cannot equal n. thus, calculate f largest floating point number smaller n. allows me run

for (i=1 f) y while (x) y 

most of iterations not need test x everytime, last n-f do.

the question is: how implement for-loop 1 f? increasing counter or decreasing f 1 in each step not work, numerical error grow large. current solution is:

for (while f > maxint)     (i=1 maxint)         y     f -= maxint while (x) y 

is there better way solve problem?

what mean numerical error? floating point counting exact within precision. here maximum values representable integers using following data types:

uint32max     = 4294967295 uint64max     = 18446744073709551615 float32intmax = 16777216 float64intmax = 9007199254740992 

every integer 0 max representable without numerical error.

as can see, largest count available uint64. next comes float64, uint32 , float32.

what happens when increment uint32=4294967295 ? 0.

what happens when increment float32=16777216 ? 16777216.

which better behavior?

have thought using 2-dimensional loop? if n ism maximum count 1-dimensional loop, n x n maximum 2-dimensional loop, etc. if maximum count less maxuint x maxuint, decompose number n such that:

n == m * maxuint + r; 

where

m = n / maxuint; r = n - m * maxuint; 

then

for (i = m; i--;) (j = maxuint; j--;) dostuff(); (i = r; i--;) dostuff(); 

if maxuint*maxuint not large enough count you, can add 3-, 4-, ... -dimensional loops.