Module pico8lib.math
Mathematical operations, mostly on numbers
| gcd_recursive (a, b) |
Return the greatest common divisor of two numbers
This implementation uses recursion |
| gcd (a, b) |
Return the greatest common divisor of two numbers
This implementation is iterative |
| lcm (a, b) |
Return the least common multiple of two numbers |
| nthroot (n, x) |
Calculate the nth root of x
nthroot(3,8)==2 because 2^3==8
All versions start with a guess based on the built in ^ operator
This version performs newton's method until a convergent result or short loop is found
Very accurate |
| nthroot_short (n, x) |
Calculate the nth root of x
This version performs newton's method exactly 4 times
Relatively accurate |
| nthroot_fast (n, x) |
Calculate the nth root of x
This version performs newton's method exactly once, only for positive x
Least accurate, still much better than built in ^ operator alone |
| dist (x, y) |
Distance to a point
Uses dist_naive for small values, dist_trig for large
tokens: 46 |
| dist_naive (x, y) |
Distance to a point
Naive distance calculation
Overflows for dist^2>=32768
tokens: 15
cycles: 9 + 28 = 37 (lua+sys) |
| dist_trig (x, y) |
Distance to a point
Uses trigonometry
Error in range (0,0)-(127,127): max 0.0017, avg 0.0004
tokens: 23
cycles: 21 + 0 = 21 (lua+sys) |
| dist_squared (x, y) |
Distance squared to a point |
| asin_octant (d) |
Arithmetic approximation of arcsin
Intended for 0<=d<=.7071
Exact at d==0, d==sin(1/16), d==sin(1/8)
Max error .0021 at d==sin(3/32) in given range
asin() is the inverse of sin(); a=asin(d) when d=sin(a) |
| interp_linear (a, b, f) |
Linear interpolation between two values
(a,b,0) == a
(a,b,1) == b
(a,b,0.25) is 1/4 of the way from a to b |
| interp_linear_inverse (a, b, v) |
Inverse Linear Interpolation
"How far along the way from a to b is v?"
(a,b,a) == 0
(a,b,b) == 1
(a,b,(a+b)/2) == 0.5 |
| interp_sine (a, b, f) |
Sine interpolation
(a,b,0) == a
(a,b,1) == b
(a,b,0.5) == 70.71% of the way from a to b |
-
gcd_recursive (a, b)
-
Return the greatest common divisor of two numbers
This implementation uses recursion
Parameters:
- a
number
The first number
- b
number
The second number
Returns:
number
The greatest common divisor, or zero
See also:
-
gcd (a, b)
-
Return the greatest common divisor of two numbers
This implementation is iterative
Parameters:
- a
number
The first number
- b
number
The second number
Returns:
number
The greatest common divisor, or zero
See also:
-
lcm (a, b)
-
Return the least common multiple of two numbers
Parameters:
- a
number
The first number
- b
number
The second number
Returns:
number
The least common multiple
-
nthroot (n, x)
-
Calculate the nth root of x
nthroot(3,8)==2 because 2^3==8
All versions start with a guess based on the built in ^ operator
This version performs newton's method until a convergent result or short loop is found
Very accurate
Parameters:
- n
- x
if (n * x == 0) return x * 0 -- preserves non-number type of x, such as rational or complex class
-
nthroot_short (n, x)
-
Calculate the nth root of x
This version performs newton's method exactly 4 times
Relatively accurate
Parameters:
-
nthroot_fast (n, x)
-
Calculate the nth root of x
This version performs newton's method exactly once, only for positive x
Least accurate, still much better than built in ^ operator alone
Parameters:
-
dist (x, y)
-
Distance to a point
Uses dist_naive for small values, dist_trig for large
tokens: 46
Parameters:
- x
number
X coordinate of the point
- y
number
Y coordinate of the point
Returns:
number
Distance from 0,0 to x,y
-
dist_naive (x, y)
-
Distance to a point
Naive distance calculation
Overflows for dist^2>=32768
tokens: 15
cycles: 9 + 28 = 37 (lua+sys)
Parameters:
- x
number
X coordinate of the point
- y
number
Y coordinate of the point
Returns:
number
Distance from 0,0 to x,y
-
dist_trig (x, y)
-
Distance to a point
Uses trigonometry
Error in range (0,0)-(127,127): max 0.0017, avg 0.0004
tokens: 23
cycles: 21 + 0 = 21 (lua+sys)
Parameters:
- x
number
X coordinate of the point
- y
number
Y coordinate of the point
Returns:
number
Distance from 0,0 to x,y
-
dist_squared (x, y)
-
Distance squared to a point
Parameters:
- x
number
X coordinate of the point
- y
number
Y coordinate of the point
Returns:
number
Distance from 0,0 to x,y
-
asin_octant (d)
-
Arithmetic approximation of arcsin
Intended for 0<=d<=.7071
Exact at d==0, d==sin(1/16), d==sin(1/8)
Max error .0021 at d==sin(3/32) in given range
asin() is the inverse of sin(); a=asin(d) when d=sin(a)
Parameters:
Returns:
arcsin of d
-
interp_linear (a, b, f)
-
Linear interpolation between two values
(a,b,0) == a
(a,b,1) == b
(a,b,0.25) is 1/4 of the way from a to b
Parameters:
- a
number
Starting value
- b
number
Ending value
- f
number
[0-1] from a to b
Returns:
number
value between a and b
-
interp_linear_inverse (a, b, v)
-
Inverse Linear Interpolation
"How far along the way from a to b is v?"
(a,b,a) == 0
(a,b,b) == 1
(a,b,(a+b)/2) == 0.5
Parameters:
- a
number
Starting value
- b
number
Ending value
- v
number
Value between a and b, inclusive
Returns:
number
[0-1] from a to b
-
interp_sine (a, b, f)
-
Sine interpolation
(a,b,0) == a
(a,b,1) == b
(a,b,0.5) == 70.71% of the way from a to b
Parameters:
- a
number
Starting value
- b
number
Ending value
- f
number
[0-1] from a to b
Returns:
number
value between a and b