CODEWITHSUNDEEP
iosobjective-cmacosfloating-point
hpique
hpique

Reputation: 120364

Incrementing or decrementing a float

What is the minimum value d such that...

f - d != f
f + d != f

...for any CGFloat f (except infinity)?

For example, it's not 1.

CGFloat f = CGFLOAT_MAX;
CGFloat d = 1;
NSLog(@"%d", f - d != f); // Prints 0

Upvotes: 0

Views: 372

Answers (4)

rmaddy
rmaddy

Reputation: 318955

The minimum value for d depends on the value of f.

The problem is that CGFloat only supports a certain number of significant digits and not all floating point number are represented exactly.

The following is not exact results but meant to illustrate the problem.

If f is 1.0 then d might need to be something like 0.0000001. But if f is 1000000.0 (one million) then d would need to be 0.1.

Basically the value of d must be within the significant digits of f for the result to be noticeable.

Consider using NSDecimalNumber to be able to fully represent large numbers eliminating this problem.

Upvotes: 0

Klas Lindbäck
Klas Lindbäck

Reputation: 33283

That would depend on the the definition of CGFLOAT on your platform.

Current platforms use either float (typically when compiling for 32-bit platforms) or double (typically when compiling for 64-bit platforms).

32 bit floats use 23 bits for the fraction, which means that d would probably be around CGFLOAT_MAX/2^23

64 bit doubles use 52 bits for the fraction, which means that d would probably be around CGFLOAT_MAX/2^52

Upvotes: 0

Eric Postpischil
Eric Postpischil

Reputation: 224556

If “any CGFLOAT” truly means any value that a CGFLOAT can take, then the answer is infinity. Otherwise, f could be infinity (a legal value), and f-d would equal f for any finite value of d.

If f is limited to finite values, then d is 2970 if CGFLOAT_IS_DOUBLE is set and 2103 otherwise. This is because those are the smallest values required to cause a change when d is added to the largest finite values that a CGFLOAT could have.

These are undoubtedly not the values you are looking for. As Stephen Canon notes, what are you really trying to do?

Upvotes: 3

Merlevede
Merlevede

Reputation: 8180

The value such that 

f - d != f
f + d != f

is not fixed for all possible floating point numbers. You've probably came to this conclusion your own because you can clearly see that for d=1 and f=5.0, f-d=4.0... but this doesn' work for CGFLOAT_MAX.

This is because of how floating point numbers are stored in memory, they are stored with a base and an exponent, so not all digits are being represented.

Upvotes: 0

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