gen/lib.bc

/*
 * *****************************************************************************
 *
 * Copyright 2018 Gavin D. Howard
 *
 * Permission to use, copy, modify, and/or distribute this software for any
 * purpose with or without fee is hereby granted.
 *
 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES WITH
 * REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY
 * AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT,
 * INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM
 * LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR
 * OTHER TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR
 * PERFORMANCE OF THIS SOFTWARE.
 *
 * *****************************************************************************
 *
 * The bc math library.
 *
 */

scale=20
define e(x){
	auto b,s,n,r,d,i,p,f,v
	b=ibase
	ibase=A
	if(x<0){
		n=1
		x=-x
	}
	s=scale
	r=6+s+0.44*x
	scale=scale(x)+1
	while(x>1){
		d+=1
		x/=2
		scale+=1
	}
	scale=r
	r=x+1
	p=x
	f=v=1
	for(i=2;v!=0;++i){
		p*=x
		f*=i
		v=p/f
		r+=v
	}
	while((d--)!=0)r*=r
	scale=s
	ibase=b
	if(n!=0)return(1/r)
	return(r/1)
}
define l(x){
	auto b,s,r,p,a,q,i,v
	b=ibase
	ibase=A
	if(x<=0){
		r=(1-10^scale)/1
		ibase=b
		return(r)
	}
	s=scale
	scale+=6
	p=2
	while(x>=2){
		p*=2
		x=sqrt(x)
	}
	while(x<=0.5){
		p*=2
		x=sqrt(x)
	}
	r=a=(x-1)/(x+1)
	q=a*a
	v=1
	for(i=3;v!=0;i+=2){
		a*=q
		v=a/i
		r+=v
	}
	r*=p
	scale=s
	ibase=b
	return(r/1)
}
define s(x){
	auto b,s,r,n,a,q,i
	b=ibase
	ibase=A
	s=scale
	scale=1.1*s+2
	a=a(1)
	if(x<0){
		n=1
		x=-x
	}
	scale=0
	q=(x/a+2)/4
	x=x-4*q*a
	if(q%2!=0)x=-x
	scale=s+2
	r=a=x
	q=-x*x
	for(i=3;a!=0;i+=2){
		a*=q/(i*(i-1))
		r+=a
	}
	scale=s
	ibase=b
	if(n!=0)return(-r/1)
	return(r/1)
}
define c(x){
	auto b,s
	b=ibase
	ibase=A
	s=scale
	scale*=1.2
	x=s(2*a(1)+x)
	scale=s
	ibase=b
	return(x/1)
}
define a(x){
	auto b,s,r,n,a,m,t,f,i,u
	b=ibase
	ibase=A
	n=1
	if(x<0){
		n=-1
		x=-x
	}
	if(x==1){
		if(scale<65){
			return(.7853981633974483096156608458198757210492923498437764552437361480/n)
		}
	}
	if(x==.2){
		if(scale<65){
			return(.1973955598498807583700497651947902934475851037878521015176889402/n)
		}
	}
	s=scale
	if(x>.2){
		scale+=5
		a=a(.2)
	}
	scale=s+3
	while(x>.2){
		m+=1
		x=(x-.2)/(1+.2*x)
	}
	r=u=x
	f=-x*x
	t=1
	for(i=3;t!=0;i+=2){
		u*=f
		t=u/i
		r+=t
	}
	scale=s
	ibase=b
	return((m*a+r)/n)
}
define j(n,x){
	auto b,s,o,a,i,v,f
	b=ibase
	ibase=A
	s=scale
	scale=0
	n/=1
	if(n<0){
		n=-n
		if(n%2==1)o=1
	}
	a=1
	for(i=2;i<=n;++i)a*=i
	scale=1.5*s
	a=(x^n)/2^n/a
	r=v=1
	f=-x*x/4
	scale=scale+length(a)-scale(a)
	for(i=1;v!=0;++i){
		v=v*f/i/(n+i)
		r+=v
	}
	scale=s
	ibase=b
	if(o!=0)a=-a
	return(a*r/1)
}