Math functions
- Contract / Module:
free.util-math
- Dependencies:
free.util-lists
Constants
PI
decimal
pact> PI
3.141592653589793
E
decimal
Euler’s number
pact> E 2.718281828459045
GOLDEN-RATIO
decimal
Golden Ratio (Phi)
pact> GOLDEN-RATIO
1.6180339887498949025257388711906969547271728515625
General functions
dec*
x <a[integer,decimal]> → decimal
Starred version of (*dec). Convert an integer to a decimal, but does not fail
if x is already a decimal.
pact> (dec* 3)
3.0
pact> (dec* 3.0)
3.0
between
a decimal b decimal x decimal → bool
Return true is a <= x <= b.
pact> (between -1.0 1.0 0.2)
true
pact> (between -1.0 1.0 1.2)
false
sign
x
decimal→decimal
pact> (sign 2.0)
1.0
pact> (sign -2.0)
-1.0
pact> (sign 0.0)
0.0
Integers functions
is-even
y integer → bool
Return true if x is even.
pact> (is-even 4)
true
pact> (is-even 5)
false
is-odd
y integer → bool
Return true if x is odd.
pact> (is-odd 4)
false
pact> (is-odd 5)
true
sizeof
y integer → integer
Returns the storage size of a positive integer in bytes
pact> (sizeof 1)
1
pact> (sizeof 255)
1
pact> (sizeof 256)
2
pact> (sizeof 65536)
3
++
x integer → integer
Increment an integer
pact> (++ 1)
2
- -
x integer → integer
Decrement an integer
pact> (-- 1)
0
gcd
a integer b integer → integer
Return the greatest common divisor of a and b.
Zeros are allowed for a or b or both.
(gcd 0 0) returns 0.
Negative numbers are allowed.
pact> (gcd 8 0)
8
pact> (gcd 0 0)
0
pact> (gcd 21 9)
3
pact> (gcd -9 21)
3
lcm
a integer b integer → integer
Return the least common multiple of a and b.
Zeros are not allowed for any of the arguments.
Negative numbers are allowed.
pact> (lcm 6 16)
48
pact> (lcm 16 -6)
48
pact> (lcm 3 5)
15
pact> (lcm 3 0)
util-math.pact:185:4: Arguments can't be 0
Min/Max functions
min
x decimal y decimal → decimal
Return the min of 2 values.
pact> (min 1.1 5.1)
1.1
max
x decimal y decimal → decimal
Return the max of 2 values.
pact> (max 1.1 5.1)
5.1
min3
x decimal y decimal z decimal → decimal
Return the min of 3 values.
pact> (min3 1.1 8.2 5.1)
1.1
max3
x decimal y decimal z decimal → decimal
Return the max of 3 values.
pact> (max3 1.1 8.2 5.1)
8.2
min4
x decimal y decimal z decimal zz decimal → decimal
Return the min of 4 values.
pact> (min4 1.1 8.2 -1.0 5.1)
1.1
max4
x decimal y decimal z decimal zz decimal → decimal
Return the max of 4 values.
pact> (max4 1.1 8.2 -1.0 5.1)
8.2
min-list
x [decimal] → decimal
Return the min of a list.
pact> (min-list [1.1 8.2 -1.0 5.1])
1.1
max-list
x [decimal] → decimal
Return the max of a list.
pact> (max-list [1.1 8.2 -1.0 5.1])
8.2
amin
x [decimal] → integer
Return the min index of a list.
pact> (amin [1.1 8.2 -1.0 5.1])
2
amax
x [decimal] → integer
Return the max index of a list.
pact> (amax [1.1 8.2 -1.0 5.1])
1
clamp
low-limit decimal up-limit decimal x decimal → decimal
Clamp x between low-limit and up-limit:
if x > up-limit => Return up-limit
if x < low-limit => Return low-limit
if x is between low-limit and up-limit => Return x
Equivalent to MAX(low-limit, MIN(up-limit, x))
pact> (clamp 10.0 20.0 12.0)
12.0
pact> (clamp 10.0 20.0 8.0)
10.0
pact> (clamp 10.0 20.0 25.0)
20.0
Sum functions
- Remarks:
There is no function to add 2 decimals here. Indeed the native (+ x y) can be used.
sum3
x decimal y decimal z decimal → decimal
Return the sum of 3 values.
pact> (sum3 1.0 2.0 3.0)
6.0
sum4
x decimal y decimal z decimal zz decimal → decimal
Return the sum of 4 values.
pact> (sum4 1.0 2.0 3.0 4.0)
10.0
sum
x [decimal] → decimal
Return the sum of a list.
pact> (sum [1.0 2.0 3.0 4.0])
10.0
Product functions
prod3
x decimal y decimal z decimal → decimal
Return the product of 3 values.
pact> (prod3 2.0 3.0 4.0)
24.0
prod4
x decimal y decimal z decimal zz decimal → decimal
Return the product of 4 values.
pact> (prod4 2.0 3.0 4.0 1.5)
36.0
prod
x [decimal] → decimal
Return the product of a list.
pact> (prod [2.0 3.0 4.0 1.5])
36.0
square
x decimal → decimal
Return the square of x.
pact> (square 6.0)
36.0
Divide functions
safe-/
x decimal y decimal default decimal → decimal
Divide x by y but returns default if y is 0.0.
As a result safe-/ never fails (Division by 0.0 is not possible anymore).
pact> (safe-/ 3.0 2.0 0.0)
1.5
pact> (safe-/ 3.0 0.0 0.0)
0.0
Average and Median
avg
x [decimal] → decimal
Returns the average of a list.
pact> (avg [3.0 0.0 1.0 2.0])
1.5
med
x [decimal] → decimal
Returns the median of a list: if the length of the list is even return the (n/2 -1)th element.
pact> (med [3.0 0.0 1.0 2.0 4.0])
2.0
pact> (med [3.0 0.0 1.0 2.0])
1.0
med*
x [decimal] → decimal
Returns the median of a list: if the length of the list is even return the average of the (n/2 -1)th and (n/2)th elements.
pact> (med* [3.0 0.0 1.0 2.0 4.0])
2.0
pact> (med* [3.0 0.0 1.0 2.0])
1.5
Power/Log functions
pow10
x integer → decimal
Return 10^x, rounded to 12 decimals (rounding is important when x is negative).
pact> (pow10 2)
100.000000000000
pact> (pow10 -2)
0.010000000000
xEy
x decimal y integer → decimal
Return x.10^y, rounded to 12 decimals.
pact> (xEy 4.0 2)
400.000000000000
pact> (xEy 4.0 -2)
0.040000000000
log10
x <a[integer,decimal]> → decimal
Return the log of x base 10, rounded to 12 decimals.
pact> (log10 100)
2.000000000000
pact> (log10 0.001)
-3.000000000000
safe-log
x <a[integer,decimal]> y <a[integer,decimal]> default <a[integer,decimal]> → <a[integer,decimal]>
Log of y base x, but returns default when y is negative.
As a result safe-log never fails (Log of negative numbers not possible anymore).
pact> (safe-log 2 1024.0 0.0)
10.0
pact> (safe-log 2 -1.0 0.0)
0.0
safe-ln
x decimal default decimal → decimal
Natural log of x, but returns default when x <= 0.0.
As a result safe-ln never fails (Log of negative numbers is not possible anymore).
pact> (safe-ln 2.0 0.0)
0.69314718055994528622676398299518041312694549560546875
pact> (safe-ln -2.0 0.0)
0.0
safe-log10
x <a[integer,decimal]> default decimal → decimal
Returns the log of x base 10, rounded to 12 decimals but returns default when x is negative.
As a result safe-log10 never fails (Log of negative numbers is not possible anymore)
pact> (safe-log10 20.0 0.0)
1.301029995664
pact> (safe-log10 -20.0 0.0)
0.0