# _std/math.dm

eulers | e |
---|---|

pi | π |

ceil2 | ceil, with second argument being the multiple to use for rounding |

nround | rounds down to the nearest integer, note that the built-in round() function alwys roundsd to the lower integer |

posfract | decimal part of a number but always positive. Basically modulo 1 in a way |

fractmodulo | x % y but without rounding x first (i.e. fractmodulo(5.7, 2) = 1.7), also always positive |

sign | Returns the sign of the given number (1 or -1) |

cot | cotangent |

percentmult | Takes a probability 'x' (0-100) and returns the probability (0-100) of seeing at least 1 success were you to test 'x' 'mult' times. Used for lag-compensating prob rolls. |

angledifference | difference in degrees from angle x to angle y |

isnum_safe | NaN isn't a number, damn it. Infinity is a problem too. |

/proc/text2num_safe | Parses a number except for NaNs and infinities |

randfloat | rand() but for floats, returns a random floating point number between L and H |

EXTRACT_BIT | provides the bit at a position (starting from 0) in a binary number
example: `EXTRACT_BIT(9, 1)` |

TOGGLE_BIT | toggles the bit at a position (starting from 0) in a binary number
example: `TOGGLE_BIT(9, 1)` |

CREATE_FULL_BINARY_NUM | creates a binary number that is length bits long. all bits in the number are turned on |

CREATE_EMPTY_BINARY_NUM | creates a binary number that is length bits long. all bits in the number are turned off |

lerp | Linearly interpolates a and b based on t |

/proc/fixed_random | pseudorandom number based on x, y in range 0 to 1 |

## Define Details

### CREATE_EMPTY_BINARY_NUM

creates a binary number that is length bits long. all bits in the number are turned off

### CREATE_FULL_BINARY_NUM

creates a binary number that is length bits long. all bits in the number are turned on

### EXTRACT_BIT

provides the bit at a position (starting from 0) in a binary number
example: `EXTRACT_BIT(9, 1)`

9 in binary is `1001`

if i want to check the value of the 2nd bit in 9, i would use a value of 1 for position
this is because binary numbers start at 0 and bits are counted from right to left
then the << operator shifts that bit a number of bits to the left
in this case, it shifts it 1 bit to the left, turning 1 into 10 (in binary)
so what the macro looks like now (in binary) is `1001 & 0010`

the binary and operator (&) multiplies the values of the bits together
so doing `1001 & 0010`

returns a value of `0000`

this tells us that the 2nd bit of `1001`

is 0 (off)
if we did this with 11 (`1011`

) instead, it would be `1011 & 0010`

, which would return `0010`

, which tells us that the 2nd bit of `1001`

is 1 (on)

### TOGGLE_BIT

toggles the bit at a position (starting from 0) in a binary number
example: `TOGGLE_BIT(9, 1)`

9 in binary is `1001`

if i want to toggle the value of the 2nd bit in 9, i would use a value of 1 for position
this is because binary numbers start at 0 and bits are counted from right to left
then the << operator shifts that bit a number of bits to the left
in this case, it shifts it 1 bit to the left, turning 1 into 10 (in binary)
so what the macro looks like now (in binary) is `1001 ^ 0010`

the binary xor operator (`^`

) sets a bit to 0 if the values of the bits are the same and sets a bit to 1 if the values are different
so doing `1001 & 0010`

returns a value of `1011`

this just toggles the 2nd bit in the number from 0 to 1, or from 1 to 0
if we did this with 11 (`1011`

) instead, it would be `1011 & 0010`

, which would return `1001`

### angledifference

difference in degrees from angle x to angle y

### ceil2

ceil, with second argument being the multiple to use for rounding

### cot

cotangent

### eulers

e

### fractmodulo

x % y but without rounding x first (i.e. fractmodulo(5.7, 2) = 1.7), also always positive

### isnum_safe

NaN isn't a number, damn it. Infinity is a problem too.

### lerp

Linearly interpolates a and b based on t

### nround

rounds down to the nearest integer, note that the built-in round() function alwys roundsd to the lower integer

### percentmult

Takes a probability 'x' (0-100) and returns the probability (0-100) of seeing at least 1 success were you to test 'x' 'mult' times. Used for lag-compensating prob rolls.

### pi

π

### posfract

decimal part of a number but always positive. Basically modulo 1 in a way

### randfloat

rand() but for floats, returns a random floating point number between L and H

### sign

Returns the sign of the given number (1 or -1)