Binary floating-level math is complicated and subtle. I’ve silent here about a of my licensed oddball info about IEEE floating-level math, in step with the articles to this level in my floating-level series. The level of hobby in this list is on scurry collectively with the float nonetheless the identical ideas all observe to double.
These oddities don’t create floating-level math imperfect, and in lots of cases these oddities would possibly maybe also furthermore be neglected. However while you strive to simulate the limitless expanse of the precise-number line with 32-bit or 64-bit numbers then there will inevitably be locations where the abstraction breaks down, and it’s valid to be taught about them.
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- Adjoining floats (of the identical sign) comprise adjacent integer representations, which makes producing the following (or all) floats trivial
- FLT_MIN is no longer the smallest certain scurry collectively with the float (FLT_MIN is the smallest certain normalized scurry collectively with the float)
- The smallest certain scurry collectively with the float – assuming denormals are supported, as they would possibly maybe also silent be – is 8,388,608 times smaller than FLT_MIN
- FLT_MAX is no longer the largest certain scurry collectively with the float (it’s the largest finite scurry collectively with the float, nonetheless the particular imprint infinity is bigger)
- 0.1 can’t be exactly represented in a scurry collectively with the float
- All floats would possibly maybe also furthermore be exactly represented in decimal
- Over a hundred decimal digits of mantissa are required to precisely level to the imprint of some floats
- 9 decimal digits of mantissa (plus sign and exponent) are enough to uniquely title any scurry collectively with the float
- The Visible C++ 2010 debugger shows floats with edifying 8 mantissa digits
- The integer representation of a scurry collectively with the float is a piecewise linear approximation of the base-2 logarithm of that scurry collectively with the float
- You would possibly per chance calculate the base-2 log of an integer by assigning it to a scurry collectively with the float
- Most scurry collectively with the float math offers inexact results attributable to rounding
- The elemental IEEE math operations guarantee edifying rounding
- Subtraction of floats with a connected values (f2 0.5
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