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An implementation of Unix dc and POSIX bc with GNU and BSD extensions
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/*
* *****************************************************************************
*
* SPDX-License-Identifier: BSD-2-Clause
*
* Copyright (c) 2018-2020 Gavin D. Howard and contributors.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* * Redistributions of source code must retain the above copyright notice, this
* list of conditions and the following disclaimer.
*
* * Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
* LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
* *****************************************************************************
*
* 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+.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;++i){
p*=x
f*=i
v=p/f
r+=v
}
while(d--)r*=r
scale=s
ibase=b
if(n)return(1/r)
return(r/1)
}
define l(x){
auto b,s,r,p,a,q,i,v
if(x<=0)return((1-A^scale)/1)
b=ibase
ibase=A
s=scale
scale+=6
p=2
while(x>=2){
p*=2
x=sqrt(x)
}
while(x<=.5){
p*=2
x=sqrt(x)
}
r=a=(x-1)/(x+1)
q=a*a
v=1
for(i=3;v;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,a,q,i
if(x<0)return(-s(-x))
b=ibase
ibase=A
s=scale
4 years ago
scale=1.1*s+2
a=a(1)
scale=0
q=(x/a+2)/4
x-=4*q*a
if(q%2)x=-x
4 years ago
scale=s+2
r=a=x
q=-x*x
for(i=3;a;i+=2){
a*=q/(i*(i-1))
r+=a
}
scale=s
ibase=b
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(scale<65){
if(x==1){
r=.7853981633974483096156608458198757210492923498437764552437361480/n
ibase=b
return(r)
}
if(x==.2){
r=.1973955598498807583700497651947902934475851037878521015176889402/n
ibase=b
return(r)
}
}
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;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
o=n%2
}
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+=length(a)-scale(a)
for(i=1;v;++i){
v=v*f/i/(n+i)
r+=v
}
scale=s
ibase=b
if(o)a=-a
return(a*r/1)
}