trigfills.js

//     ~         trigfills - trig function pollyfills        ~      + 
/*           Copyright 2017 by Andrew Strain. No warranty           * 
 *  This program can be redistributed and modified under the terms  * 
 *  of the Apache License Version 2.0 - see LICENSE for details     * 
 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * **/ 

// www.mathonweb.com/help_ebook/html/algorithms.htm
// web.mit.edu/kenta/www/three/taylor.html

var trigfillfactory = function(){ 
  
  var pi=Math.PI, tau=pi*2 ,hpi=pi/2 ,qpi=pi/4 
     ,spi=pi/6 ,epi=pi/8 ,sq3=1.7320508075688772 //sqrt(3)

  function version(){ return "0.9.5" } 
      
  function modp(a,b){
    return a-Math.floor(a/b)*b //removes neg
  }

  function modn(a,b){
    return a-Math.floor(a/b + 0.5)*b //creates neg (math.round is slow)
  }

  function cos(x){
    
    x=x-Math.floor(x/tau)*tau
    
    if(x>pi) x=tau-x
    if(x>=hpi) { var pol=-1; x=pi-x }else{ pol=1 }
    
    if(x>qpi) return pol*sintay(hpi-x) 
    return pol*costay(x)
  }

  function sin(x){
    
    x=x-Math.floor(x/tau)*tau
    
    if(x>pi){ var pol=-1; x-=pi }else{ pol=1 }
    if(x>=hpi) x=pi-x 
    
    if(x>qpi) return pol*costay(hpi-x) 
    return pol*sintay(x) 
  }
                                                                                          
  var f24=100000/2399999,f720=100000/71998376,f40k=1000/40578583 
  function costay(x){
    var x2=x*x,x4=x2*x2
    return 1 - x2*0.5 + x4*f24 - x4*x2*f720 + x4*x4*f40k 
  }

  var fh6=100000000/600000005,f120=1/120,f5k=1000/5039680,f362k=10/3628880
  function sintay(x){
    var x3=x*x*x,x6=x3*x3
    return x - x3*fh6 + x3*x*x*f120 - x6*x*f5k + x6*x3*f362k 
  }

  var ff3=100000000000/299999999177
     ,ff5=10000000/50000082
     ,ff7=100000/700011 ,ff9=10000/90019 ,ff11 =1000/11768
  
  function atan(x){
    
    var pos=1, mut=false, mut2=false
    
    if(x<0){ pos=-1, x=-x }
    if(x>1){ x=1/x , mut=true  }
    if(x>0.26794919){
      x=(sq3*x-1)/(sq3+x) 
      mut2=true
    }

    var x2=x*x ,x4=x2*x2 ,x9=x4*x4*x
    x=x -x*x2*ff3 +x4*x*ff5 -x4*x2*x*ff7 +x9*ff9 -x9*x2*ff11

    if(mut2) x+= spi
    if(mut)  x = hpi-x
    return x*pos
  }
  
  function atan2(y,x){
        
    if(x===0){
      if(y===0) return 0
      if(y < 0) return -hpi; else return hpi 
    }
    var r=atan(y/x) 
    if(x>0) return r 
    if(y<0) r-=pi; else r+=pi 
    
    return r-Math.floor(r/tau + 0.5)*tau
  }
  
  var fg3=1000000000/2999999887,f15=200000000/1500000678
     ,f315=170000/3150457,f2k=6200/282874,f155k=1382/146286
  
  function tan(x){

    var pos=1 ,mut=false ,mut2=false
    x = modp(x,pi)*0.99999999999999993

    if(x>hpi) x= pi-x ,pos=-1 
    if(x>qpi) x=hpi-x ,mut=true
    if(x>epi) x=x*0.5 ,mut2=true 
    
    var x2=x*x ,x4=x2*x2 ,x9=x4*x4*x
    x=x +x*x2*fg3 +x4*x*f15 +x4*x2*x*f315 +x9*f2k +x9*x2*f155k
      
    if(mut2) x=2*x/(1-x*x)
    if(mut)  x=1/x 
    
    return x*pos
  }

  function acos(x){
   if(x==-1) return Math.PI
   return modp( atan( Math.sqrt(1-x*x)/x),Math.PI )
  }

  function asin(x){ return atan( x/Math.sqrt(1-x*x) ) }

  function setmaths(){
    Math.sin=sin, Math.cos=cos, Math.tan=tan 
   ,Math.acos=acos ,Math.asin=asin ,Math.atan=atan ,Math.atan2=atan2 
   ,Math.hasTrigfills=version()
  }
  
  return {
    sin:sin     ,cos:cos    ,tan:tan 
   ,acos:acos  ,asin:asin  ,atan:atan  ,atan2:atan2
   ,modp:modp  ,modn:modn
   ,setmaths:setmaths
   ,version:version
  }
    
}
 
if(typeof module!=='undefined' && module.exports) module.exports = trigfillfactory()
else if(typeof window!=='undefined') window.trigfills = trigfillfactory()
else console.log("trigfills.js did not import")