floating point - Matlab - "0:.1:1" unexpected precision behaviour -

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possible duplicate:
matlab gives wrong answer

can explain me why following happens, when use 0:.1:1-range function?

>> veca = 0:.1:1; >> vecb = [0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1]; >> veca == vecb  ans =       1     1     1     0     1     1     1     1     1     1     1

why veca(4) not equal 0.3? look quite same ;)

veca =    columns 1 through 7           0    0.1000    0.2000    0.3000    0.4000    0.5000    0.6000    columns 8 through 11      0.7000    0.8000    0.9000    1.0000  >> vecb  vecb =    columns 1 through 7           0    0.1000    0.2000    0.3000    0.4000    0.5000    0.6000    columns 8 through 11      0.7000    0.8000    0.9000    1.0000

i think there problem precision here? or have problem in understanding?

computers binary, native floating-point format can't store decimal fractions. (you use ratio type, or fixed-point decimal type, computations using these far slower.)

as consequence, testing floating-point values equality practically useless. check absolute value of difference instead.

you should read what every computer scientist should know floating point arithmetic

(there simpler explanations, such http://floating-point-gui.de/ should use these understand goldberg's paper, not replace it)

what seeing in case 0.2 + 0.1 != 0.3 (the range uses first version, veca(3) = veca(2) + step)


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