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Timur Gordon
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Numeric Functions
=================
{{#title Numeric Functions}}
Integer Functions
-----------------
The following standard functions operate on integers only.
| Function | Description |
| ----------------------------- | ---------------------------------------------------------------- |
| `is_odd` method and property | returns `true` if the value is an odd number, otherwise `false` |
| `is_even` method and property | returns `true` if the value is an even number, otherwise `false` |
| `min` | returns the smaller of two numbers, the first number if equal |
| `max` | returns the larger of two numbers, the first number if equal |
| `to_float` | convert the value into `f64` (`f32` under 32-bit) |
| `to_decimal` | convert the value into decimal |
Signed Numeric Functions
------------------------
The following standard functions operate on signed numbers (including floating-point and decimal) only.
| Function | Description |
| ----------------------------- | ------------------------------------------------------ |
| `abs` | absolute value |
| `sign` | returns 1 if negative, +1 if positive, 0 if zero |
| `is_zero` method and property | returns `true` if the value is zero, otherwise `false` |
Floating-Point Functions
------------------------
The following standard functions operate on floating-point and decimal numbers only.
| Category | Decimal? | Functions |
| ---------------- | :------: | ---------------------------------------------------------------------------------------- |
| Trigonometry | yes | `sin`, `cos`, `tan` |
| Trigonometry | **no** | `sinh`, `cosh`, `tanh` in radians, `hypot(`_x_`,`_y_`)` |
| Arc-trigonometry | **no** | `asin`, `acos`, `atan(`_v_`)`, `atan(`_x_`,`_y_`)`, `asinh`, `acosh`, `atanh` in radians |
| Square root | yes | `sqrt` |
| Exponential | yes | `exp` (base _e_) |
| Logarithmic | yes | `ln` (base _e_), `log` (base 10) |
| Logarithmic | **no** | `log(`_x_`,`_base_`)` |
| Rounding | yes | `floor`, `ceiling`, `round`, `int`, `fraction` methods and properties |
| Conversion | yes | [`to_int`](convert.md), [`to_decimal`](convert.md), [`to_float`](convert.md) |
| Conversion | **no** | `to_degrees`, `to_radians` |
| Comparison | yes | `min`, `max` (also inter-operates with integers) |
| Testing | **no** | `is_nan`, `is_finite`, `is_infinite` methods and properties |
Decimal Rounding Functions
--------------------------
The following rounding methods operate on decimal numbers only.
| Rounding type | Behavior | Methods |
| ----------------- | ------------------------------------------- | ------------------------------------------------------------ |
| None | | `floor`, `ceiling`, `int`, `fraction` methods and properties |
| Banker's rounding | round to integer | `round` method and property |
| Banker's rounding | round to specified number of decimal points | `round(`_decimal points_`)` |
| Round up | away from zero | `round_up(`_decimal points_`)` |
| Round down | towards zero | `round_down(`_decimal points_`)` |
| Round half-up | mid-point away from zero | `round_half_up(`_decimal points_`)` |
| Round half-down | mid-point towards zero | `round_half_down(`_decimal points_`)` |
Parsing Functions
-----------------
The following standard functions parse numbers.
| Function | Description |
| ----------------------------- | ----------------------------------------------------------------------- |
| [`parse_int`](convert.md) | converts a [string](strings-chars.md) to integer with an optional radix |
| [`parse_float`](convert.md) | converts a [string](strings-chars.md) to floating-point |
| [`parse_decimal`](convert.md) | converts a [string](strings-chars.md) to decimal |
Formatting Functions
--------------------
The following standard functions convert integer numbers into a [string](strings-chars.md) of hex,
octal or binary representations.
| Function | Description |
| ------------------------- | ------------------------------------ |
| [`to_binary`](convert.md) | converts an integer number to binary |
| [`to_octal`](convert.md) | converts an integer number to octal |
| [`to_hex`](convert.md) | converts an integer number to hex |
Floating-point Constants
------------------------
The following functions return standard mathematical constants.
| Function | Description |
| -------- | ------------------------- |
| `PI` | returns the value of π |
| `E` | returns the value of _e_ |