ESM Math Library

Welcome

to the Stage Function Repository! The goal of the Repository is, to create a huge database of available functions all using the method described in the article Simulating new functions. If you've written such a function and you think it might be helpful to others, don't hesitate to contribute to this repository.

First Steps

To get this up and running follow there simple setup steps:

• Open any Plugin you wish or create a new one with the Construction Set
• Create a new Quest called "f" (yes, just the letter "f", nothing more)
• Activate the Checkbox "Allow repeated stages". (This is VERY important!!)
• Create a new Quest Script and copy the whole content of the "Quest Script" section from this article into this script. Don't forget to attach it to your f-Quest!
• Create a new stage in this quest for each function you want to use from this repository and copy all code from it's section in this article to the related Result Script textbox. Make sure to select the right stage number for the function.
• That's it! You should be able to use them now!

Quest Script

ScriptName FunctionQuestScript

; Internals
short doOnce
float fQuestDelayTime

; Constants
float pi
float rad

; Function In- and Output
float fin1
float fin2
float fin3
float fout
float fout2
float fout3

;S5 FUNCTION sqrt
float sqr

;S10 FUNCTION Hypotenuse
;float sqr
float n

;S15 FUNCTION SinCosTan 1
float ang
float sin
float cos
float tan
float exp

;S16 FUNCTION SinCodTan 2
;float ang
;float sin
;float cos
float t1
float t2
float t5
float t6

;S20 FUNCTION Arcsine 1
;float sin
;float ang
;float n

;S21 FUNCTION Arcsine 2
float t3
;float t5
float t7

;S22 FUNCTION Arccosine 1

;S23 FUNCTION Arccosine 2

;S24 FUNCTION Arctan
;float t3
;float t5
;float t7

;S30 FUNCTION getAngle
float tan
;float ang

; Set constants first
Begin Gamemode
  if doOnce == 0
    set pi to 3.1415927
    set rad to 180.0/pi

    set fQuestDelayTime to 30
    set doOnce to 1
  endif
End

Stage 5: Square Root

Based on Square Root Article

;FUNCTION float sqrt(float input)
if (f.fin1 <= 0)
  set f.fout to 0
else
  set f.sqr to f.fin1/2
  set f.sqr to (f.sqr+(f.fin1/f.sqr))/2
  set f.sqr to (f.sqr+(f.fin1/f.sqr))/2
  set f.sqr to (f.sqr+(f.fin1/f.sqr))/2
  set f.sqr to (f.sqr+(f.fin1/f.sqr))/2
  set f.sqr to (f.sqr+(f.fin1/f.sqr))/2
  set f.fout to f.sqr
endif

Stage 10: Hypotenuse

;FUNCTION float Hypotenuse(float CathetusA, float CathetusB)

set f.n to ((f.fin1 * f.fin1) + (f.fin2 * f.fin2))
;FUNCTION float sqrt(float input)
set f.fin1 to f.n
setStage f 5
;fout is already the result

Stage 15: Sin Cos Tan

Based on Trigonometry Functions Article

;FUNCTION float,float,float SinCosTan(float Angle)
;Taylor Series Variant 1 - script by Galerion

set f.ang to f.fin1

if f.ang < -180
  set f.ang to (f.ang + 360)
elseif f.ang > 180
  set f.ang to (f.ang - 360)
endif

;approximate
set f.ang to (f.ang/f.rad)
set f.cos to 1
set f.exp to f.ang
set f.sin to f.exp
set f.exp to (f.exp * f.ang)
set f.cos to (f.cos - f.exp / 2)
set f.exp to (f.exp * f.ang)
set f.sin to (f.sin - f.exp / 6)
set f.exp to (f.exp * f.ang)
set f.cos to (f.cos + f.exp / 24)
set f.exp to (f.exp * f.ang)
set f.sin to (f.sin + f.exp / 120)
set f.exp to (f.exp * f.ang)
set f.cos to (f.cos - f.exp / 720)
set f.exp to (f.exp * f.ang)
set f.sin to (f.sin - f.exp / 5040)
set f.exp to (f.exp * f.ang)
set f.cos to (f.cos + f.exp / 40320)
set f.exp to (f.exp * f.ang)
set f.sin to (f.sin + f.exp / 362880)

set f.fout to f.sin
set f.fout2 to f.cos
set f.fout3 to (f.sin/f.cos) ;tan

Stage 16: Sin Cos Tan 2

Based on Trigonometry Functions Article

;FUNCTION float,float,float SinCosTan(float Angle)
;Taylor Series Variant 2 - script by JOG

set f.ang to f.fin1

if f.ang < -180
  set f.ang to f.ang + 360
elseif f.ang > 180
  set f.ang to f.ang - 360
endif

set f.t1 to (f.ang/f.rad)
set f.t2 to (f.t1*f.t1)
set f.t5 to (f.t2*f.t2*f.t1)
set f.t6 to (f.t5*f.t1)
set f.sin to (f.t1 - (f.t1*f.t2/6) + (f.t5/120) - (f.t5*f.t2/5040) + (f.t6*f.t2*f.t1/362880))
set f.cos to (1 - (f.t2/2) + (f.t2*f.t2/24) - (f.t6/720) + (f.t6*f.t2/40320))

set f.fout to f.sin
set f.fout2 to f.cos
set f.fout3 to f.sin/f.cos ;tan

Stage 20: Arcsine

Based on Trigonometry Functions Article

;FUNCTION float Arcsine(float sin)
;Abramowitz/Stegun Approximation - script by JOG

set f.sin to f.fin1
set f.n to 1 - f.sin
set f.ang to f.n/2
set f.ang to (f.ang+(f.n/f.ang))/2
set f.ang to (f.ang+(f.n/f.ang))/2
set f.ang to (f.ang+(f.n/f.ang))/2
set f.n to (f.ang+(f.n/f.ang))/2

set f.fout to f.rad*(1.5707963 - f.n*(1.5707288 - 0.2121144*f.sin+0.0742610*f.sin*f.sin - 0.0187293*f.sin*f.sin*f.sin))

Stage 21: Arcsine 2

Based on Trigonometry Functions Article

;FUNCTION float Arcsine(float sin)
;Approximation by Taylor Series - script by DragoonWraith

set f.t3 to (f.fin1 * f.fin1 * f.fin1)
set f.t5 to (f.t3 * f.fin1 * f.fin1)
set f.t7 to (f.t5 * f.fin1 * f.fin1)

set f.fout to (f.fin1 + (1/2)*(f.t3/3) + (3/8)*(f.t5/5) + (15/48)*(f.t7/7) )

Stage 22: Aroccosine

Based on Trigonometry Functions Article

;FUNCTION float Arccosine(float cos)
setStage f 20 ;Call Arcsine with same input
set f.fout to ((f.pi / 2) - f.fout)

Stage 23: Arccosine 2

Based on Trigonometry Functions Article

;FUNCTION float Arccosine(float cos)
setStage f 21 ;Call Arcsine with same input
set f.fout to ((f.pi / 2) - f.fout)

Stage 24: Arctan

Based on Trigonometry Functions Article

;FUNCTION float Arctan(float tan)
;Approximation by Taylor Series - script by DragoonWraith

set f.t3 to (f.fin1 * f.fin1 * f.fin1)
set f.t5 to (f.t3 * f.fin1 * f.fin1)
set f.t7 to (f.t5 * f.fin1 * f.fin1)

set f.fout to (f.fin1 - (f.t3/3) + (f.t5/5) - (f.t7/7))

Stage 30: getAngle

;FUNCTION float getAngle(float x, float y)

set f.tan to (f.fin1/f.fin2)
if f.tan >1 || f.tan < -1
  set f.tan to (f.fin2/ -f.fin1)
  if f.fin1 >= 0
    set f.ang to 90
  else
    set f.ang to -90
  endif
else
  if f.fin2 >= 0
    set f.ang to 0
  else
    set f.ang to 180
  endif
endif

set f.fin1 to f.tan
setStage f 24 ;Call Arctan

if f.fout > (f.pi/2)
  set f.fout to (f.pi/2)
elseif f.fout < (f.pi/ -2)
  set f.fout to (f.pi/ -2)
endif
set f.fout to ((f.fout*f.rad) + f.ang)