lots to go on

dlib/mutil.js

@@ -83,8 +83,8 @@ bench = function (meth, bentime, meth_nm, meth_arg) {
   }
 
   ops=Math.floor(((ra+rb)*qqtlen*1000)/2)/1000000
-  console.log(meth_nm+" "+ops+" Mop/s "+donereps+
-    "  am  "+retvsum/donereps);
+  console.log(meth_nm+" "+ops+" Mtest/s "+
+    "  avg : "+retvsum/donereps);
   if ((retvsum/donereps)>0.5){ globav+=1; }
   gdone++;
 };

drafts/atanminer.js

@@ -0,0 +1,243 @@
+require ('../dlib/mutil.js')
+Fdrandom=require ('../dlib/Fdrandom.js')
+TRG=require('../trigfills.js')
+
+Fdrandom=Fdrandom.hot()
+
+var tau=Math.PI*2   ,pi=Math.PI 
+   ,hpi=Math.PI*0.5 ,qpi=Math.PI*0.25 ,epi=Math.PI*0.125 
+   ,sq3=1.7320508075688772 //sqrt(3)
+
+function modp(a,b){
+  return a-Math.floor(a/b)*b //removes neg
+}
+
+
+//tweaked factors give atan some extra accuracy
+
+function atan(x,ff3,ff5,ff7,ff9,ff11){
+
+  var pos=1, mut=0, mut2=0
+
+  if(x<0){ pos=0,x=0-x }
+  if(x>1){ x=1/x , mut=1  }
+
+  if(x>0.26794919){
+    x=(sq3*x-1)/(sq3+x) 
+    mut2=1;
+  }
+
+  var x2=x*x ,x4=x2*x2 ,x8=x4*x4
+
+  x=x- x*x2*ff3 +x4*x*ff5 -x4*x2*x*ff7 +x8*x*ff9 -x8*x2*x*ff11
+
+  if(mut2){ x+= hpi*f3 }
+  if(mut) { x = hpi-x  }
+
+  if(pos) return x
+  return -0-x
+}
+
+
+function atanw(x){
+
+  var pos=1, mut=0, mut2=0
+
+  if(x<0){ pos=0,x=0-x }
+  if(x>1){ x=1/x , mut=1  }
+
+  if(x>0.26794919){
+    x=(sq3*x-1)/(sq3+x) 
+    mut2=1;
+  }
+
+  var x2=x*x ,x4=x2*x2 ,x8=x4*x4
+
+  x=x- x*x2/3 +x4*x/5 -x4*x2*x/7 +x8*x/9 -x8*x2*x/11 +x8*x4*x/13-x8*x4*x*x2/15+x8*x8*x/17-x8*x8*x*x2/19
+
+  if(mut2){ x+= hpi*f3  }
+  if(mut) {x = hpi-x }
+
+  if(pos) return x
+  return -x
+}
+
+//~ x - 1/3 x^3 + 1/5 x^5 - 1/7 x^7 + 1/9 x^9 - 1/11 x^11 + 1/13 x^13 - 1/15 x^15 + 1/17 x^17 - 1/19 x^19 + 1/21 x^21 - 1/23 x^23 + 1/25 x^25 - 1/27 x^27 + 1/29 x^29 - 1/31 x^31 + 1/33 x^33 - 1/35 x^35
+
+
+function funcomp(fna,fnb,s,e,d){
+
+  var tt=0, mx=0 , ttv=0, mxv=0//, cntt=0, 
+     ,st=(e-s)*0.9999999999/(d-1) 
+  for(var i=s;i<=e;i=i+st){ 
+    var x=fna(i),y=fnb(i)
+    //~ console.log(i.toPrecision(2),x,y,x-y)
+    var uu=Math.abs(x-y)
+    tt+=(x-y)*(x-y)
+    if(uu>mx) mx=uu
+
+    var uv, ax=Math.abs(x),ay=Math.abs(y)
+    uv=Math.abs(x-y)/(ax+ay+0.0001)
+    ttv+=(uv)*(uv)
+    if(uv>mxv) mxv=uv
+
+    //~ cnt++
+  }
+  //~ console.log("tot",tt)
+  //~ console.log("mx",mx)
+  return {t:tt,m:mx,tv:ttv,mv:mxv}
+}
+
+
+var tal=100000000000, max=tal, talv=tal, maxv=max,ocount=0
+
+///1- x2*ff2 + x4*f24 - x2*x4*f720 + x4*x4*f40k
+///costay  f2=1/2, f24=1/24,f720=1/720,f40k=1/40580 
+var dz=[100000000000, 10000000, 100000, 10000, 1000]
+var tz=[300000000000, 50000000, 700000, 90000,11000]
+var tz=[299999999180, 50000090, 700010, 90010,11770]
+
+/*
+finals for:
+299999999497,500001,7001,8988,10960
+abs pres 2.797721373020903e-18 3.110341428858021e-10
+rel pres 1.3736299797925403e-17 6.680824194513865e-10
+abs impv 4.9880406991317673e-17 2.3468899046363845e-9
+rel impv 1.9209020330666428e-16 4.407209347755503e-9
+
+finals for:
+29999999908,5000048,70021,8983,10854
+abs pres 7.857765678061745e-19 2.087385819748988e-10
+rel pres 5.0643991460008675e-18 3.9858520510724077e-10
+abs impv 5.1892351796532406e-17 2.4491854655472878e-9
+rel impv 2.007621039585888e-16 4.676706562099649e-9
+
+finals for:
+30000000026,5000000,69983,8928,1092
+abs pres 1.3564259622350411e-17 1.331409538174455e-9
+rel pres 5.433287258044456e-17 2.542319392858836e-9
+abs impv 3.911386874198817e-17 1.3265145093477315e-9
+rel impv 1.5149363052414513e-16 2.532972374348054e-9
+
+finals for:
+29999999918,5000009,70001,9001,1177
+abs pres 9.527719480092843e-20 4.3549774897400084e-11
+rel pres 6.771670028603219e-19 1.1571264252138234e-10
+abs impv 5.258285116953765e-17 2.6143742726247865e-9
+rel impv 2.0514933610172936e-16 4.959579124685507e-9
+
+finals for:
+299999999177,50000082,700011,90019,11768
+abs pres 7.307093983568608e-20 7.33657579132796e-11
+rel pres 5.229193774078481e-19 1.400915220439228e-10
+abs impv 2.2206254965242346e-20 -2.981598301587951e-11
+rel impv 1.5424762545247381e-19 -2.4378879522540452e-11
+
+*/
+
+
+var fcomp=funcomp
+var tsn
+tsn=10000000
+tsn=500000
+//~ tsn=20000000
+//~ tsn=10000
+//~ tsn=1
+var mage=30
+/*
+
+
+*/
+
+var fz=[]; fz[0]=tz[0],fz[1]=tz[1],fz[2]=tz[2],fz[3]=tz[3],fz[4]=tz[4]
+
+//~ var df=[0,0,0,0,1,-1,3,-3,9,-9,30,-30] 
+var df=[0,0,0,0,-1,1,-2,2]
+var mulla=2,mope=0
+var zzsteps=187
+var alph=1, alp={}
+
+while(tsn--){
+
+  //~ var ofs=Fdrandom.f48()*0.5
+
+  var sc = fcomp(
+   function(x){ return atanw(x) }
+  ,function(x){ 
+    return atan(x 
+     ,dz[0]/tz[0] 
+     ,dz[1]/tz[1]
+     ,dz[2]/tz[2] 
+     ,dz[3]/tz[3]
+     ,dz[4]/tz[4]
+     ) 
+  }
+,0, 0.26794919, zzsteps
+  )
+
+  //~ console.log(sc)
+  if(alph){ alp.t=sc.t, alp.m=sc.m, alp.mv=sc.mv, alp.tv=sc.tv, alph=0 }
+
+  //~ console.log(sc)
+
+  if((sc.t<=tal&&sc.m<=max&&sc.tv<=talv&&sc.mv<=maxv)
+    &&(sc.t<tal||sc.m<max||sc.tv<talv||sc.mv<maxv)
+    ){
+
+    tal=sc.t, max=sc.m,talv=sc.tv, maxv=sc.mv,
+
+    fz[0]=tz[0]
+    fz[1]=tz[1]
+    fz[2]=tz[2]
+    fz[3]=tz[3]
+    fz[4]=tz[4]
+
+    //~ if(ocount++%1000===1)
+    {
+      console.log(fz.join(" "))
+      console.log("scored:",tal,max)
+    }
+    //~ mulla*=1.1
+  }
+
+  //make test set
+  do{
+    Fdrandom.mixup(df)
+    mulla=Fdrandom.f48()*mage+0.5
+
+    tz[0] = fz[0]+Math.floor(df[0] *mulla)    //*mulla
+    tz[1] = fz[1]+Math.floor(df[1] *mulla)    //*mulla
+    tz[2] = fz[2]+Math.floor(df[2] *mulla)
+    tz[3] = fz[3]+Math.floor(df[3] *mulla)
+    tz[4] = fz[4]+Math.floor(df[4] *mulla)
+  }while((tz[0]!=fz[0])&&(tz[1]!=fz[1])&&(tz[2]!=fz[2])&&(tz[3]!=fz[3])&&(tz[4]!=fz[4]))
+
+}
+
+console.log("finals for:")
+
+sc = funcomp(
+ function(x){ return atanw(x) }
+,function(x){ 
+  return atan(x 
+   ,dz[0]/fz[0] 
+   ,dz[1]/fz[1]
+   ,dz[2]/fz[2] 
+   ,dz[3]/fz[3]
+   ,dz[4]/tz[4]
+   ) 
+}
+,0, 0.26794919, zzsteps
+)
+
+console.log(fz.join(","))
+
+console.log("abs pres",sc.t,sc.m)
+console.log("rel pres",sc.tv,sc.mv)
+
+console.log("abs impv",alp.t-sc.t,alp.m-sc.m)
+console.log("rel impv",alp.tv-sc.tv,alp.mv-sc.mv)
+
+//~ console.log(costay(0.78539811350441,dz[0]/fz[0] ,dz[1]/fz[1],dz[2]/fz[2],dz[3]/fz[3]))
+//~ console.log(Math.cos(0.78539811350441),costay(0.78539811350441,dz[0]/fz[0] ,dz[1]/fz[1],dz[2]/fz[2],dz[3]/fz[3])-Math.cos(0.78539811350441))
+