| /* |
| * ***************************************************************************** |
| * |
| * SPDX-License-Identifier: BSD-2-Clause |
| * |
| * Copyright (c) 2018-2021 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=2*A |
| 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 |
| scale=1.1*s+2 |
| a=a(1) |
| scale=0 |
| q=(x/a+2)/4 |
| x-=4*q*a |
| if(q%2)x=-x |
| 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,r,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) |
| } |