1 3940506b 2005-01-13 devnull scale = 50
  2 3940506b 2005-01-13 devnull define e(x) {
  3 3940506b 2005-01-13 devnull 	auto a, b, c, d, e, g, w, y, t, r
  4 3940506b 2005-01-13 devnull 
  5 3940506b 2005-01-13 devnull 	r = ibase
  6 3940506b 2005-01-13 devnull 	ibase = A
  7 3940506b 2005-01-13 devnull 
  8 3940506b 2005-01-13 devnull 	t = scale
  9 3940506b 2005-01-13 devnull 	scale = t + .434*x + 1
 10 3940506b 2005-01-13 devnull 
 11 3940506b 2005-01-13 devnull 	w = 0
 12 3940506b 2005-01-13 devnull 	if(x<0) {
 13 3940506b 2005-01-13 devnull 		x = -x
 14 3940506b 2005-01-13 devnull 		w = 1
 15 3940506b 2005-01-13 devnull 	}
 16 3940506b 2005-01-13 devnull 	y = 0
 17 3940506b 2005-01-13 devnull 	while(x>2) {
 18 3940506b 2005-01-13 devnull 		x /= 2
 19 3940506b 2005-01-13 devnull 		y++
 20 3940506b 2005-01-13 devnull 	}
 21 3940506b 2005-01-13 devnull 
 22 3940506b 2005-01-13 devnull 	a = 1
 23 3940506b 2005-01-13 devnull 	b = 1
 24 3940506b 2005-01-13 devnull 	c = b
 25 3940506b 2005-01-13 devnull 	d = 1
 26 3940506b 2005-01-13 devnull 	e = 1
 27 3940506b 2005-01-13 devnull 	for(a=1; 1; a++) {
 28 3940506b 2005-01-13 devnull 		b *= x
 29 3940506b 2005-01-13 devnull 		c = c*a+b
 30 3940506b 2005-01-13 devnull 		d *= a
 31 3940506b 2005-01-13 devnull 		g = c/d
 32 3940506b 2005-01-13 devnull 		if(g == e) {
 33 3940506b 2005-01-13 devnull 			g = g/1
 34 3940506b 2005-01-13 devnull 			while(y--) {
 35 3940506b 2005-01-13 devnull 				g *= g
 36 3940506b 2005-01-13 devnull 			}
 37 3940506b 2005-01-13 devnull 			scale = t
 38 3940506b 2005-01-13 devnull 			if(w==1) {
 39 3940506b 2005-01-13 devnull 				ibase = r
 40 3940506b 2005-01-13 devnull 				return 1/g
 41 3940506b 2005-01-13 devnull 			}
 42 3940506b 2005-01-13 devnull 			ibase = r
 43 3940506b 2005-01-13 devnull 			return g/1
 44 3940506b 2005-01-13 devnull 		}
 45 3940506b 2005-01-13 devnull 		e = g
 46 3940506b 2005-01-13 devnull 	}
 47 3940506b 2005-01-13 devnull }
 48 3940506b 2005-01-13 devnull 
 49 3940506b 2005-01-13 devnull define l(x) {
 50 3940506b 2005-01-13 devnull 	auto a, b, c, d, e, f, g, u, s, t, r, z
 51 3940506b 2005-01-13 devnull 
 52 3940506b 2005-01-13 devnull 	r = ibase
 53 3940506b 2005-01-13 devnull 	ibase = A
 54 3940506b 2005-01-13 devnull 	if(x <= 0) {
 55 3940506b 2005-01-13 devnull 		z = 1-10^scale
 56 3940506b 2005-01-13 devnull 		ibase = r
 57 3940506b 2005-01-13 devnull 		return z
 58 3940506b 2005-01-13 devnull 	}
 59 3940506b 2005-01-13 devnull 	t = scale
 60 3940506b 2005-01-13 devnull 
 61 3940506b 2005-01-13 devnull 	f = 1
 62 3940506b 2005-01-13 devnull 	scale += scale(x) - length(x) + 1
 63 3940506b 2005-01-13 devnull 	s = scale
 64 3940506b 2005-01-13 devnull 	while(x > 2) {
 65 3940506b 2005-01-13 devnull 		s += (length(x)-scale(x))/2 + 1
 66 3940506b 2005-01-13 devnull 		if(s>0) {
 67 3940506b 2005-01-13 devnull 			scale = s
 68 3940506b 2005-01-13 devnull 		}
 69 3940506b 2005-01-13 devnull 		x = sqrt(x)
 70 3940506b 2005-01-13 devnull 		f *= 2
 71 3940506b 2005-01-13 devnull 	}
 72 3940506b 2005-01-13 devnull 	while(x < .5) {
 73 3940506b 2005-01-13 devnull 		s += (length(x)-scale(x))/2 + 1
 74 3940506b 2005-01-13 devnull 		if(s>0) {
 75 3940506b 2005-01-13 devnull 			scale = s
 76 3940506b 2005-01-13 devnull 		}
 77 3940506b 2005-01-13 devnull 		x = sqrt(x)
 78 3940506b 2005-01-13 devnull 		f *= 2
 79 3940506b 2005-01-13 devnull 	}
 80 3940506b 2005-01-13 devnull 
 81 3940506b 2005-01-13 devnull 	scale = t + length(f) - scale(f) + 1
 82 3940506b 2005-01-13 devnull 	u = (x-1)/(x+1)
 83 3940506b 2005-01-13 devnull 
 84 3940506b 2005-01-13 devnull 	scale += 1.1*length(t) - 1.1*scale(t)
 85 3940506b 2005-01-13 devnull 	s = u*u
 86 3940506b 2005-01-13 devnull 	b = 2*f
 87 3940506b 2005-01-13 devnull 	c = b
 88 3940506b 2005-01-13 devnull 	d = 1
 89 3940506b 2005-01-13 devnull 	e = 1
 90 3940506b 2005-01-13 devnull 	for(a=3; 1; a=a+2){
 91 3940506b 2005-01-13 devnull 		b *= s
 92 3940506b 2005-01-13 devnull 		c = c*a + d*b
 93 3940506b 2005-01-13 devnull 		d *= a
 94 3940506b 2005-01-13 devnull 		g = c/d
 95 3940506b 2005-01-13 devnull 		if(g==e) {
 96 3940506b 2005-01-13 devnull 			scale = t
 97 3940506b 2005-01-13 devnull 			ibase = r
 98 3940506b 2005-01-13 devnull 			return u*c/d
 99 3940506b 2005-01-13 devnull 		}
100 3940506b 2005-01-13 devnull 		e = g
101 3940506b 2005-01-13 devnull 	}
102 3940506b 2005-01-13 devnull }
103 3940506b 2005-01-13 devnull 
104 3940506b 2005-01-13 devnull define s(x) {
105 3940506b 2005-01-13 devnull 	auto a, b, c, s, t, y, p, n, i, r
106 3940506b 2005-01-13 devnull 
107 3940506b 2005-01-13 devnull 	r = ibase
108 3940506b 2005-01-13 devnull 	ibase = A
109 3940506b 2005-01-13 devnull 	t = scale
110 3940506b 2005-01-13 devnull 	y = x/.7853
111 3940506b 2005-01-13 devnull 	s = t + length(y) - scale(y)
112 3940506b 2005-01-13 devnull 	if(s<t) {
113 3940506b 2005-01-13 devnull 		s = t
114 3940506b 2005-01-13 devnull 	}
115 3940506b 2005-01-13 devnull 	scale = s
116 3940506b 2005-01-13 devnull 	p = a(1)
117 3940506b 2005-01-13 devnull 
118 3940506b 2005-01-13 devnull 	scale = 0
119 3940506b 2005-01-13 devnull 	if(x>=0) {
120 3940506b 2005-01-13 devnull 		n = (x/(2*p)+1)/2
121 3940506b 2005-01-13 devnull 	}
122 3940506b 2005-01-13 devnull 	if(x<0) {
123 3940506b 2005-01-13 devnull 		n = (x/(2*p)-1)/2
124 3940506b 2005-01-13 devnull 	}
125 3940506b 2005-01-13 devnull 	x -= 4*n*p
126 3940506b 2005-01-13 devnull 	if(n%2 != 0) {
127 3940506b 2005-01-13 devnull 		x = -x
128 3940506b 2005-01-13 devnull 	}
129 3940506b 2005-01-13 devnull 
130 3940506b 2005-01-13 devnull 	scale = t + length(1.2*t) - scale(1.2*t)
131 3940506b 2005-01-13 devnull 	y = -x*x
132 3940506b 2005-01-13 devnull 	a = x
133 3940506b 2005-01-13 devnull 	b = 1
134 3940506b 2005-01-13 devnull 	s = x
135 3940506b 2005-01-13 devnull 	for(i=3; 1; i+=2) {
136 3940506b 2005-01-13 devnull 		a *= y
137 3940506b 2005-01-13 devnull 		b *= i*(i-1)
138 3940506b 2005-01-13 devnull 		c = a/b
139 3940506b 2005-01-13 devnull 		if(c==0){
140 3940506b 2005-01-13 devnull 			scale = t
141 3940506b 2005-01-13 devnull 			ibase = r
142 3940506b 2005-01-13 devnull 			return s/1
143 3940506b 2005-01-13 devnull 		}
144 3940506b 2005-01-13 devnull 		s += c
145 3940506b 2005-01-13 devnull 	}
146 3940506b 2005-01-13 devnull }
147 3940506b 2005-01-13 devnull 
148 3940506b 2005-01-13 devnull define c(x) {
149 3940506b 2005-01-13 devnull 	auto t, r
150 3940506b 2005-01-13 devnull 
151 3940506b 2005-01-13 devnull 	r = ibase
152 3940506b 2005-01-13 devnull 	ibase = A
153 3940506b 2005-01-13 devnull 	t = scale
154 3940506b 2005-01-13 devnull 	scale = scale+1
155 3940506b 2005-01-13 devnull 	x = s(x + 2*a(1))
156 3940506b 2005-01-13 devnull 	scale = t
157 3940506b 2005-01-13 devnull 	ibase = r
158 3940506b 2005-01-13 devnull 	return x/1
159 3940506b 2005-01-13 devnull }
160 3940506b 2005-01-13 devnull 
161 3940506b 2005-01-13 devnull define a(x) {
162 3940506b 2005-01-13 devnull 	auto a, b, c, d, e, f, g, s, t, r, z
163 3940506b 2005-01-13 devnull 
164 3940506b 2005-01-13 devnull 	r = ibase
165 3940506b 2005-01-13 devnull 	ibase = A
166 3940506b 2005-01-13 devnull 	if(x==0) {
167 3940506b 2005-01-13 devnull 		return 0
168 3940506b 2005-01-13 devnull 	}
169 3940506b 2005-01-13 devnull 	if(x==1) {
170 3940506b 2005-01-13 devnull 		z = .7853981633974483096156608458198757210492923498437764/1
171 3940506b 2005-01-13 devnull 		ibase = r
172 3940506b 2005-01-13 devnull 		if(scale<52) {
173 3940506b 2005-01-13 devnull 			return z
174 3940506b 2005-01-13 devnull 		}
175 3940506b 2005-01-13 devnull 	}
176 3940506b 2005-01-13 devnull 	t = scale
177 3940506b 2005-01-13 devnull 	f = 1
178 3940506b 2005-01-13 devnull 	while(x > .5) {
179 3940506b 2005-01-13 devnull 		scale++
180 3940506b 2005-01-13 devnull 		x = -(1 - sqrt(1.+x*x))/x
181 3940506b 2005-01-13 devnull 		f *= 2
182 3940506b 2005-01-13 devnull 	}
183 3940506b 2005-01-13 devnull 	while(x < -.5) {
184 3940506b 2005-01-13 devnull 		scale++
185 3940506b 2005-01-13 devnull 		x = -(1 - sqrt(1.+x*x))/x
186 3940506b 2005-01-13 devnull 		f *= 2
187 3940506b 2005-01-13 devnull 	}
188 3940506b 2005-01-13 devnull 	s = -x*x
189 3940506b 2005-01-13 devnull 	b = f
190 3940506b 2005-01-13 devnull 	c = f
191 3940506b 2005-01-13 devnull 	d = 1
192 3940506b 2005-01-13 devnull 	e = 1
193 3940506b 2005-01-13 devnull 	for(a=3; 1; a+=2) {
194 3940506b 2005-01-13 devnull 		b *= s
195 3940506b 2005-01-13 devnull 		c = c*a + d*b
196 3940506b 2005-01-13 devnull 		d *= a
197 3940506b 2005-01-13 devnull 		g = c/d
198 3940506b 2005-01-13 devnull 		if(g==e) {
199 3940506b 2005-01-13 devnull 			scale = t
200 3940506b 2005-01-13 devnull 			ibase = r
201 3940506b 2005-01-13 devnull 			return x*c/d
202 3940506b 2005-01-13 devnull 		}
203 3940506b 2005-01-13 devnull 		e = g
204 3940506b 2005-01-13 devnull 	}
205 3940506b 2005-01-13 devnull }
206 3940506b 2005-01-13 devnull 
207 3940506b 2005-01-13 devnull define j(n,x) {
208 3940506b 2005-01-13 devnull 	auto a,b,c,d,e,g,i,s,k,t,r
209 3940506b 2005-01-13 devnull 
210 3940506b 2005-01-13 devnull 	r = ibase
211 3940506b 2005-01-13 devnull 	ibase = A
212 3940506b 2005-01-13 devnull 
213 3940506b 2005-01-13 devnull 	t = scale
214 3940506b 2005-01-13 devnull 	k = 1.36*x + 1.16*t - n
215 3940506b 2005-01-13 devnull 	k = length(k) - scale(k)
216 3940506b 2005-01-13 devnull 	if(k>0) {
217 3940506b 2005-01-13 devnull 		scale += k
218 3940506b 2005-01-13 devnull 	}
219 3940506b 2005-01-13 devnull 
220 3940506b 2005-01-13 devnull 	s = -x*x/4
221 3940506b 2005-01-13 devnull 	if(n<0) {
222 3940506b 2005-01-13 devnull 		n = -n
223 3940506b 2005-01-13 devnull 		x = -x
224 3940506b 2005-01-13 devnull 	}
225 3940506b 2005-01-13 devnull 	a = 1
226 3940506b 2005-01-13 devnull 	c = 1
227 3940506b 2005-01-13 devnull 	for(i=1; i<=n; i++) {
228 3940506b 2005-01-13 devnull 		a *= x
229 3940506b 2005-01-13 devnull 		c *= 2*i
230 3940506b 2005-01-13 devnull 	}
231 3940506b 2005-01-13 devnull 	b = a
232 3940506b 2005-01-13 devnull 	d = 1
233 3940506b 2005-01-13 devnull 	e = 1
234 3940506b 2005-01-13 devnull 	for(i=1; 1; i++) {
235 3940506b 2005-01-13 devnull 		a *= s
236 3940506b 2005-01-13 devnull 		b = b*i*(n+i) + a
237 3940506b 2005-01-13 devnull 		c *= i*(n+i)
238 3940506b 2005-01-13 devnull 		g = b/c
239 3940506b 2005-01-13 devnull 		if(g==e) {
240 3940506b 2005-01-13 devnull 			scale = t
241 3940506b 2005-01-13 devnull 			ibase = r
242 3940506b 2005-01-13 devnull 			return g/1
243 3940506b 2005-01-13 devnull 		}
244 3940506b 2005-01-13 devnull 		e = g
245 3940506b 2005-01-13 devnull 	}
246 3940506b 2005-01-13 devnull }