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Nasal-Interpreter
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Improve math lib: ln & asin

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Valk Richard Li 2019-11-19 21:59:27 +08:00 committed by GitHub
parent 9882ab20b4
commit 0b17340bce
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1 changed files with 14 additions and 10 deletions
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balloon/lib/math.nas
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@ -10,13 +10,15 @@ var abs=func(__x)
var ln=func(_x) var ln=func(_x)
{ {
var __balloon_lib_ln_asr=func(__x,__y) var __balloon_lib_ln_asr=func(__left,__right,__total,eps)
{ {
if(abs(__y-__x)<=0.1){return (1/__x+8/(__x+__y)+1/__y)*(__y-__x)/6;} var __mid=(__left+__right)/2;
var __mid=(__x+__y)/2; var L=(1/__left+8/(__left+__mid)+1/__mid)*(__mid-__left)/6;
return __balloon_lib_ln_asr(__x,__mid)+__balloon_lib_ln_asr(__mid,__y); var R=(1/__mid+8/(__mid+__right)+1/__right)*(__right-__mid)/6;
if(abs(L+R-__total)<=15*eps){return L+R+(L+R-__total)/15.0;}
return __balloon_lib_ln_asr(__left,__mid,L,eps/2)+__balloon_lib_ln_asr(__mid,__right,R,eps/2);
}; };
return __balloon_lib_ln_asr(1,_x); return __balloon_lib_ln_asr(1,_x,(1+8/(1+_x)+1/_x)*(_x-1)/6,0.000001);
}; };
var log=func(__a,__x) var log=func(__a,__x)
@ -114,17 +116,19 @@ var sqrt=func(__x)
var asin=func(_x) var asin=func(_x)
{ {
var __balloon_lib_asin_asr=func(__x,__y) var __balloon_lib_asin_asr=func(__left,__right,__total,eps)
{ {
var __mid=(__x+__y)/2; var __mid=(__left+__right)/2;
if(abs(__y-__x)<=0.01){return (1/sqrt(1-__x*__x)+4/sqrt(1-__mid*__mid)+1/sqrt(1-__y*__y))*(__y-__x)/6;} var L=(1/sqrt(1-__left*__left)+4/sqrt(1-(__left+__mid)*(__left+__mid)/4)+1/sqrt(1-__mid*__mid))*(__mid-__left)/6;
return __balloon_lib_asin_asr(__x,__mid)+__balloon_lib_asin_asr(__mid,__y); var R=(1/sqrt(1-__mid*__mid)+4/sqrt(1-(__right+__mid)*(__right+__mid)/4)+1/sqrt(1-__right*__right))*(__right-__mid)/6;
if(abs(L+R-__total)<=15*eps){return L+R+(L+R-__total)/15;}
return __balloon_lib_asin_asr(__left,__mid,L,eps/2)+__balloon_lib_asin_asr(__mid,__right,R,eps/2);
}; };
if(abs(_x)>1){return -1;} if(abs(_x)>1){return -1;}
var fl=1; var fl=1;
if(_x<0){fl=-fl;_x=-_x;} if(_x<0){fl=-fl;_x=-_x;}
if(abs(_x-1)<0.001){return pi/2;} if(abs(_x-1)<0.001){return pi/2;}
return fl*__balloon_lib_asin_asr(0,_x); return fl*__balloon_lib_asin_asr(0,_x,(1+4/sqrt(1-_x*_x/4)+1/sqrt(1-_x*_x))*_x/6,0.000001);
}; };
var acos=func(__x) var acos=func(__x)