15.6: Chapter Summary
- Page ID
- 43755
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)
Floats are approximation of a real number by being able to support a wide range of decimal values. This chapters has reviewed the following points
- Never use = to compare floats (e.g., \( (0.1 + 0.2) = 0.3 \) returns
false) - Use
closeTo:instead (e.g.,(0.1 + 0.2) closeTo: 0.3returnstrue) - A float number is represented in base as \( \mathit{sign} \times \mathit{mantissa} \times 2^{\mathit{exponent}} \) (e.g., \( 1.2345 = 12345 \times 10^{-4} \))
truncateTo:androundTo:do not always work when truncating or rounding up float (e.g.,2.8 roundTo: 0.01returns2.800...003)
There are much more things to know about floats, and if you are advanced enough, it would be a good idea to check this link from the Wikipedia page "What Every Computer Scientist Should Know About Floating-Point Arithmetic" (http://www.validlab.com/goldberg/paper.pdf).