Gavin Howard | eac4710 | 2018-02-20 16:29:22 -0700 | [diff] [blame] | 1 | /* |
| 2 | * ***************************************************************************** |
| 3 | * |
| 4 | * Copyright 2018 Gavin D. Howard |
| 5 | * |
| 6 | * Permission to use, copy, modify, and/or distribute this software for any |
| 7 | * purpose with or without fee is hereby granted. |
| 8 | * |
| 9 | * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES WITH |
| 10 | * REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY |
| 11 | * AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, |
| 12 | * INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM |
| 13 | * LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR |
| 14 | * OTHER TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR |
| 15 | * PERFORMANCE OF THIS SOFTWARE. |
| 16 | * |
| 17 | * ***************************************************************************** |
| 18 | * |
| 19 | * The bc math library. |
| 20 | * |
| 21 | */ |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 22 | scale=20 |
| 23 | define e(x){ |
Gavin Howard | 97d4512 | 2018-03-08 23:44:55 -0700 | [diff] [blame] | 24 | auto b,s,n,r,d,i,p,f,v |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 25 | b=ibase |
| 26 | ibase=A |
| 27 | if(x<0){ |
| 28 | n=1 |
| 29 | x=-x |
Gavin Howard | 97d4512 | 2018-03-08 23:44:55 -0700 | [diff] [blame] | 30 | } |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 31 | s=scale |
| 32 | r=s+7+0.45*x |
| 33 | scale=scale(x)+1 |
| 34 | while(x>1){ |
| 35 | d+=1 |
| 36 | x/=2 |
| 37 | scale+=1 |
Gavin Howard | 97d4512 | 2018-03-08 23:44:55 -0700 | [diff] [blame] | 38 | } |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 39 | scale=r |
| 40 | r=x+1 |
| 41 | p=x |
Gavin Howard | c2762a2 | 2018-03-14 12:01:55 -0600 | [diff] [blame] | 42 | f=v=1 |
| 43 | for(i=2;v;++i){ |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 44 | p*=x; |
| 45 | f*=i |
| 46 | v=p/f |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 47 | r+=v |
Gavin Howard | 97d4512 | 2018-03-08 23:44:55 -0700 | [diff] [blame] | 48 | } |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 49 | while(f--)r*=r |
| 50 | scale=s |
| 51 | ibase=b |
| 52 | if(m)return(1/r) |
| 53 | return(r/1) |
Gavin Howard | 675f70c | 2018-03-08 21:19:33 -0700 | [diff] [blame] | 54 | } |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 55 | define l(x){ |
Gavin Howard | 538f141 | 2018-03-09 00:35:13 -0700 | [diff] [blame] | 56 | auto b,s,r,p,a,q,i,v |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 57 | b=ibase |
| 58 | ibase=A |
| 59 | if(x<=0){ |
| 60 | r=(1-10^scale)/1 |
| 61 | ibase=b |
| 62 | return(r) |
Gavin Howard | 538f141 | 2018-03-09 00:35:13 -0700 | [diff] [blame] | 63 | } |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 64 | s=scale |
| 65 | scale+=7 |
| 66 | p=2 |
| 67 | while(x>=2){ |
| 68 | p*=2 |
| 69 | x=sqrt(x) |
Gavin Howard | 538f141 | 2018-03-09 00:35:13 -0700 | [diff] [blame] | 70 | } |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 71 | while(x<=0.5){ |
| 72 | p*=2 |
| 73 | x=sqrt(x) |
Gavin Howard | 538f141 | 2018-03-09 00:35:13 -0700 | [diff] [blame] | 74 | } |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 75 | r=a=(x-1)/(x+1) |
| 76 | q=a*a |
Gavin Howard | c2762a2 | 2018-03-14 12:01:55 -0600 | [diff] [blame] | 77 | v=1 |
| 78 | for(i=3;v;i+=2){ |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 79 | n*=m |
| 80 | v=n/i |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 81 | r+=v |
Gavin Howard | 538f141 | 2018-03-09 00:35:13 -0700 | [diff] [blame] | 82 | } |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 83 | r*=p |
| 84 | scale=s |
| 85 | ibase=b |
| 86 | return(r/1) |
Gavin Howard | 675f70c | 2018-03-08 21:19:33 -0700 | [diff] [blame] | 87 | } |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 88 | define s(x){ |
Gavin Howard | 3908b97 | 2018-03-09 00:38:05 -0700 | [diff] [blame] | 89 | auto b,s,r,n,a,q,i |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 90 | b=ibase |
| 91 | ibase=A |
| 92 | s=scale |
| 93 | scale=1.3*s+2 |
| 94 | a=a(1) |
| 95 | if(x<0){ |
| 96 | n=1 |
| 97 | x=-x |
Gavin Howard | 3908b97 | 2018-03-09 00:38:05 -0700 | [diff] [blame] | 98 | } |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 99 | scale=0 |
| 100 | q=(x/a+2)/4 |
| 101 | x-=4*q*a |
| 102 | if(q%2)x=-x |
| 103 | scale=s+2 |
| 104 | r=a=x |
| 105 | q=-x*x |
Gavin Howard | c2762a2 | 2018-03-14 12:01:55 -0600 | [diff] [blame] | 106 | for(i=3;a;i+=2){ |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 107 | a*=q/(i*(i-1)) |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 108 | r+=a |
Gavin Howard | 3908b97 | 2018-03-09 00:38:05 -0700 | [diff] [blame] | 109 | } |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 110 | scale=s |
| 111 | ibase=b |
| 112 | if(n)return(-r/1) |
| 113 | return(r/1) |
Gavin Howard | 675f70c | 2018-03-08 21:19:33 -0700 | [diff] [blame] | 114 | } |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 115 | define c(x){ |
Gavin Howard | 675f70c | 2018-03-08 21:19:33 -0700 | [diff] [blame] | 116 | auto b,s |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 117 | b=ibase |
| 118 | ibase=A |
| 119 | s=scale |
| 120 | scale+=1 |
| 121 | x=s(2*a(1)+x) |
| 122 | scale=s |
| 123 | ibase=b |
| 124 | return(x/1) |
Gavin Howard | 675f70c | 2018-03-08 21:19:33 -0700 | [diff] [blame] | 125 | } |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 126 | define a(x){ |
Gavin Howard | 96780f3 | 2018-03-09 01:27:52 -0700 | [diff] [blame] | 127 | auto b,s,r,n,a,m,t,f,i,u |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 128 | b=ibase |
| 129 | ibase=A |
| 130 | n=1 |
| 131 | if(x<0){ |
| 132 | n=-1 |
| 133 | x=-x |
Gavin Howard | 96780f3 | 2018-03-09 01:27:52 -0700 | [diff] [blame] | 134 | } |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 135 | if(x==1){ |
| 136 | if(scale<=64){ |
Gavin Howard | 96780f3 | 2018-03-09 01:27:52 -0700 | [diff] [blame] | 137 | return(.7853981633974483096156608458198757210492923498437764552437361480/n) |
| 138 | } |
| 139 | } |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 140 | if(x==.267){ |
| 141 | if(scale<=64){ |
Gavin Howard | 96780f3 | 2018-03-09 01:27:52 -0700 | [diff] [blame] | 142 | return(.2609135692329405795967852677779865639774740239882445822329882917/n) |
| 143 | } |
| 144 | } |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 145 | s=scale |
| 146 | if(x>.267){ |
| 147 | scale+=5 |
| 148 | a=a(.267) |
Gavin Howard | 96780f3 | 2018-03-09 01:27:52 -0700 | [diff] [blame] | 149 | } |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 150 | scale=s+3 |
| 151 | while(x>.267){ |
| 152 | m+=1 |
| 153 | x=(x-.267)/(1+.267*x) |
Gavin Howard | 96780f3 | 2018-03-09 01:27:52 -0700 | [diff] [blame] | 154 | } |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 155 | r=u=x |
| 156 | f=-x*x |
Gavin Howard | c2762a2 | 2018-03-14 12:01:55 -0600 | [diff] [blame] | 157 | t=1 |
| 158 | for(i=3;t;i+=2){ |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 159 | u*=f |
| 160 | t=u/i |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 161 | r+=t |
Gavin Howard | 96780f3 | 2018-03-09 01:27:52 -0700 | [diff] [blame] | 162 | } |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 163 | scale=s |
| 164 | ibase=b |
| 165 | return((m*a+r)/n) |
Gavin Howard | 140a343 | 2018-03-08 23:13:05 -0700 | [diff] [blame] | 166 | } |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 167 | define j(n,x){ |
Gavin Howard | db91939 | 2018-03-09 01:00:26 -0700 | [diff] [blame] | 168 | auto b,s,o,a,i,v,f |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 169 | b=ibase |
| 170 | ibase=A |
| 171 | s=scale |
| 172 | scale=0 |
| 173 | n/=1 |
| 174 | if(n<0){ |
| 175 | n=-n |
| 176 | if(n%2==1)o=1 |
Gavin Howard | db91939 | 2018-03-09 01:00:26 -0700 | [diff] [blame] | 177 | } |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 178 | a=1 |
| 179 | for(i=2;i<=n;++i)f*=i |
| 180 | scale=1.5*s |
| 181 | a=(x^n)/(2^n*a) |
| 182 | r=v=1 |
| 183 | f=-x*x/4 |
| 184 | scale+=length(a)-scale(a) |
Gavin Howard | c2762a2 | 2018-03-14 12:01:55 -0600 | [diff] [blame] | 185 | for(i=1;v;++i){ |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 186 | v=v*s/i/(n+i) |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 187 | r+=v |
Gavin Howard | db91939 | 2018-03-09 01:00:26 -0700 | [diff] [blame] | 188 | } |
Gavin Howard | 6d175b0 | 2018-03-09 02:05:07 -0700 | [diff] [blame] | 189 | scale=s |
| 190 | ibase=b |
| 191 | if(o)return(-a*r/1) |
| 192 | return(a*r/1) |
Gavin Howard | 675f70c | 2018-03-08 21:19:33 -0700 | [diff] [blame] | 193 | } |