| 1 | scale = 20 |
| 2 | define e(x){ |
| 3 | auto a, b, c, d, e, g, w, y |
| 4 | |
| 5 | t = scale |
| 6 | scale = t + .434*x + 1 |
| 7 | |
| 8 | w = 0 |
| 9 | if(x<0){ |
| 10 | x = -x |
| 11 | w = 1 |
| 12 | } |
| 13 | y = 0 |
| 14 | while(x>2){ |
| 15 | x = x/2 |
| 16 | y = y + 1 |
| 17 | } |
| 18 | |
| 19 | a=1 |
| 20 | b=1 |
| 21 | c=b |
| 22 | d=1 |
| 23 | e=1 |
| 24 | for(a=1;1==1;a++){ |
| 25 | b=b*x |
| 26 | c=c*a+b |
| 27 | d=d*a |
| 28 | g = c/d |
| 29 | if(g == e){ |
| 30 | g = g/1 |
| 31 | while(y--){ |
| 32 | g = g*g |
| 33 | } |
| 34 | scale = t |
| 35 | if(w==1) return(1/g) |
| 36 | return(g/1) |
| 37 | } |
| 38 | e=g |
| 39 | } |
| 40 | } |
| 41 | |
| 42 | define l(x){ |
| 43 | auto a, b, c, d, e, f, g, u, s, t |
| 44 | if(x <=0) return(1-10^scale) |
| 45 | t = scale |
| 46 | |
| 47 | f=1 |
| 48 | scale = scale + scale(x) - length(x) + 1 |
| 49 | s=scale |
| 50 | while(x > 2){ |
| 51 | s = s + (length(x)-scale(x))/2 + 1 |
| 52 | if(s>0) scale = s |
| 53 | x = sqrt(x) |
| 54 | f=f*2 |
| 55 | } |
| 56 | while(x < .5){ |
| 57 | s = s + (length(x)-scale(x))/2 + 1 |
| 58 | if(s>0) scale = s |
| 59 | x = sqrt(x) |
| 60 | f=f*2 |
| 61 | } |
| 62 | |
| 63 | scale = t + length(f) - scale(f) + 1 |
| 64 | u = (x-1)/(x+1) |
| 65 | |
| 66 | scale = scale + 1.1*length(t) - 1.1*scale(t) |
| 67 | s = u*u |
| 68 | b = 2*f |
| 69 | c = b |
| 70 | d = 1 |
| 71 | e = 1 |
| 72 | for(a=3;1==1;a=a+2){ |
| 73 | b=b*s |
| 74 | c=c*a+d*b |
| 75 | d=d*a |
| 76 | g=c/d |
| 77 | if(g==e){ |
| 78 | scale = t |
| 79 | return(u*c/d) |
| 80 | } |
| 81 | e=g |
| 82 | } |
| 83 | } |
| 84 | |
| 85 | define s(x){ |
| 86 | auto a, b, c, s, t, y, p, n, i |
| 87 | t = scale |
| 88 | y = x/.7853 |
| 89 | s = t + length(y) - scale(y) |
| 90 | if(s<t) s=t |
| 91 | scale = s |
| 92 | p = a(1) |
| 93 | |
| 94 | scale = 0 |
| 95 | if(x>=0) n = (x/(2*p)+1)/2 |
| 96 | if(x<0) n = (x/(2*p)-1)/2 |
| 97 | x = x - 4*n*p |
| 98 | if(n%2!=0) x = -x |
| 99 | |
| 100 | scale = t + length(1.2*t) - scale(1.2*t) |
| 101 | y = -x*x |
| 102 | a = x |
| 103 | b = 1 |
| 104 | s = x |
| 105 | for(i=3; 1==1; i=i+2){ |
| 106 | a = a*y |
| 107 | b = b*i*(i-1) |
| 108 | c = a/b |
| 109 | if(c==0){scale=t; return(s/1)} |
| 110 | s = s+c |
| 111 | } |
| 112 | } |
| 113 | |
| 114 | define c(x){ |
| 115 | auto t |
| 116 | t = scale |
| 117 | scale = scale+1 |
| 118 | x = s(x+2*a(1)) |
| 119 | scale = t |
| 120 | return(x/1) |
| 121 | } |
| 122 | |
| 123 | define a(x){ |
| 124 | auto a, b, c, d, e, f, g, s, t |
| 125 | if(x==0) return(0) |
| 126 | if(x==1) |
| 127 | if(scale<52) |
| 128 | return(.7853981633974483096156608458198757210492923498437764/1) |
| 129 | t = scale |
| 130 | f=1 |
| 131 | while(x > .5){ |
| 132 | scale = scale + 1 |
| 133 | x= -(1-sqrt(1.+x*x))/x |
| 134 | f=f*2 |
| 135 | } |
| 136 | while(x < -.5){ |
| 137 | scale = scale + 1 |
| 138 | x = -(1-sqrt(1.+x*x))/x |
| 139 | f=f*2 |
| 140 | } |
| 141 | s = -x*x |
| 142 | b = f |
| 143 | c = f |
| 144 | d = 1 |
| 145 | e = 1 |
| 146 | for(a=3;1==1;a=a+2){ |
| 147 | b=b*s |
| 148 | c=c*a+d*b |
| 149 | d=d*a |
| 150 | g=c/d |
| 151 | if(g==e){ |
| 152 | scale = t |
| 153 | return(x*c/d) |
| 154 | } |
| 155 | e=g |
| 156 | } |
| 157 | } |
| 158 | |
| 159 | define j(n,x){ |
| 160 | auto a,b,c,d,e,g,i,s,k,t |
| 161 | |
| 162 | t = scale |
| 163 | k = 1.36*x + 1.16*t - n |
| 164 | k = length(k) - scale(k) |
| 165 | if(k>0) scale = scale + k |
| 166 | |
| 167 | s= -x*x/4 |
| 168 | if(n<0){ |
| 169 | n= -n |
| 170 | x= -x |
| 171 | } |
| 172 | a=1 |
| 173 | c=1 |
| 174 | for(i=1;i<=n;i++){ |
| 175 | a=a*x |
| 176 | c = c*2*i |
| 177 | } |
| 178 | b=a |
| 179 | d=1 |
| 180 | e=1 |
| 181 | for(i=1;1;i++){ |
| 182 | a=a*s |
| 183 | b=b*i*(n+i) + a |
| 184 | c=c*i*(n+i) |
| 185 | g=b/c |
| 186 | if(g==e){ |
| 187 | scale = t |
| 188 | return(g/1) |
| 189 | } |
| 190 | e=g |
| 191 | } |
| 192 | } |