Integer and Floating points - Julia Taiwan study group

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# Integer and Floating points

### Julia Study Group

#### Yueh-Hua Tu

#### 2020.10.17

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# Outline

* Integer
  * Floating points

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# Integer

* `Int8`
  * `Int16`
  * `Int32`
  * `Int64`

### Default integer

* `Int`
  * `Sys.WORD_SIZE`

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# Binary representation of integer

* `7` => `0000 0111`
  * range: $-2^7 \sim 2^7 - 1$ for 8-bit

### Binary representation in Julia

* `bitstring`

### Try (in 8-bit)

* -1
  * 127
  * 128
  * -127
  * -128

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# Complements (補數)

Complement system is a representation for signed integer. There are two ways:

### Two's complement (8 bits)

* `1`: `0000 0001`
  * `0`: `0000 0000`
  * `-1`: `1111 1111`

### One's complement (8 bits)

* `1`: `0000 0001`
  * `0`: `0000 0000`
  * `-1`: `1111 1110`

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# Unsigned integer

* `UInt8`
  * `UInt16`
  * `UInt32`
  * `UInt64`

### Binary representation

### Try

* `0x123`

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# Overflow

* `Int8(127) + Int8(1)`

```
julia> bitstring(Int8(127))
"01111111"

julia> bitstring(Int8(1))
"00000001"
```

```
julia> bitstring(Int8(-128))
"10000000"
```

### Another example

* `Int(-128) - Int(1)`

```
julia> bitstring(Int8(-128))
"10000000"

julia> bitstring(Int8(1))
"00000001"
```

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# Floating point

* `Float16`
  * `Float32`
  * `Float64`

### Size of value in memory

* `sizeof`

### Try

* `1.`
  * `.1`
  * `1e5`
  * `1e-5`
  * `2.5f0`
  * `typeof(2.5f0)`
  * `2.5f-4`
  * `sizeof(2.5f-4)`

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# Binary representation of floating point

* `bitstring(1.0)`
  * `bitstring(-1.0)`
  * `bitstring(Float16(2.0))`
  * `bitstring(Float16(1024.))`
  * `bitstring(Float16(2048.))`
  * `bitstring(Float16(4096.))`

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# Machine epsilon

The relative error due to rounding in floating point arithmetic.

* `eps`

### Try

* `eps(Float64)`
  * `eps(Float32)`
  * `eps()`
  * `eps(1.0)`

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# Extreme value for types

* `typemax`
  * `typemin`

### Try

* `typemax(Int64)`
  * `typemax(Int32)`
  * `typemax(Int16)`

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# Arithmatic operations

* `+`
  * `-`
  * `*`
  * `/`
  * `%` or `rem`
  * `div`
  * `^`
  * `sqrt`
  * `abs2`
  * `abs`

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# Comparison operations

* `>`
  * `=`
  * `<`
  * `≤` or `<=`
  * `≥` or `>=`
  * `≠` or `!=`

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# Conversion between integer and floating point

* `Integer(1.0)`
  * `Int(1.0)`
  * `Int(1.1)`
  * `Float64(1)`

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# Transcendental function (超越函數)

* `sin`
  * `cos`
  * `tan`
  * `exp`
  * `log`
  * `log2`
  * `log10`
  * `log1p`

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# Round, ceiling and floor

* `round`
  * `ceil`
  * `floor`

### Try

* `round(7.321, digits=2)`
  * `ceil(7.321, digits=1)`
  * `floor(7.321, digits=2)`
  * `ceil(7, base=8)`

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# Infinity and not a number

* `Inf`, `Inf32`, `Inf16`
  * `NaN`, `NaN32`, `NaN16`

### Arithmetic operations

* `Inf + 1`
  * `Inf - Inf`
  * `1/Inf`
  * `1/0`
  * `Inf == Inf`
  * `0/0`
  * `NaN + 1`
  * `0*Inf`
  * `Inf/Inf`

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# Standard input and parsing

* `readline()`
  * `parse`

### Practice: BMI calculator

$$ bmi = \frac{weight (kg)}{height^2 (m)} $$

### Practice: Compound interest

$$ interest = base(1 + \frac{r}{n})^{nt} $$

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# If-else

```
if <condition>
    <do something>
elseif <condition>
    <do another thing>
else
    <do other thing>
end
```

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# Random numbers

* `rand()`
  * `rand(10)`
  * `rand(3, 4)`
  * `rand([0, 1])`

### Try

* generate a uniform-distributed random number from 1.23 ~ 5.67

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# Thank you for attention