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pi is an irrational number, and sin(pi) is 0. 1pi is floating number.
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Fang Liu 2023-03-30 08:47:47 +00:00 committed by GitHub
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@ -80,7 +80,7 @@ As floating point numbers may be approximations, some values are not quite what
```{julia}
sqrt(2) * sqrt(2) - 2, sin(pi), 1/10 + 1/5 - 3/10
sqrt(2) * sqrt(2) - 2, sin(1pi), 1/10 + 1/5 - 3/10
```
These values are *very* small numbers, but not exactly $0$, as they are mathematically.
@ -163,7 +163,7 @@ Integers are often used casually, as they come about from parsing. As with a cal
[Floating point](http://en.wikipedia.org/wiki/Floating_point) numbers are a computational model for the real numbers. For floating point numbers, $64$ bits are used by default for both $32$- and $64$-bit systems, though other storage sizes can be requested. This gives a large ranging - but still finite - set of real numbers that can be represented. However, there are infinitely many real numbers just between $0$ and $1$, so there is no chance that all can be represented exactly on the computer with a floating point value. Floating point then is *necessarily* an approximation for all but a subset of the real numbers. Floating point values can be viewed in normalized [scientific notation](http://en.wikipedia.org/wiki/Scientific_notation) as $a\cdot 2^b$ where $a$ is the *significand* and $b$ is the *exponent*. Save for special values, the significand $a$ is normalized to satisfy $1 \leq \lvert a\rvert < 2$, the exponent can be taken to be an integer, possibly negative.
As per IEEE Standard 754, the `Float64` type gives 52 bits to the precision (with an additional implied one), 11 bits to the exponent and the other bit is used to represent the sign. Positive, finite, floating point numbers have a range approximately between $10^{-308}$ and $10^{308}$, as 308 is about $\log_{10}\cdot 2^{1023}$. The numbers are not evenly spread out over this range, but, rather, are much more concentrated closer to $0$.
As per IEEE Standard 754, the `Float64` type gives 52 bits to the precision (with an additional implied one), 11 bits to the exponent and the other bit is used to represent the sign. Positive, finite, floating point numbers have a range approximately between $10^{-308}$ and $10^{308}$, as 308 is about $\log_{10} 2^{1023}$. The numbers are not evenly spread out over this range, but, rather, are much more concentrated closer to $0$.
:::{.callout-warning}