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11210 libm should be cstyle(1ONBLD) clean
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--- old/usr/src/lib/libm/common/Q/j1l.c
+++ new/usr/src/lib/libm/common/Q/j1l.c
1 1 /*
2 2 * CDDL HEADER START
3 3 *
4 4 * The contents of this file are subject to the terms of the
5 5 * Common Development and Distribution License (the "License").
6 6 * You may not use this file except in compliance with the License.
7 7 *
8 8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
9 9 * or http://www.opensolaris.org/os/licensing.
10 10 * See the License for the specific language governing permissions
11 11 * and limitations under the License.
12 12 *
13 13 * When distributing Covered Code, include this CDDL HEADER in each
14 14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
|
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14 lines elided |
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15 15 * If applicable, add the following below this CDDL HEADER, with the
16 16 * fields enclosed by brackets "[]" replaced with your own identifying
17 17 * information: Portions Copyright [yyyy] [name of copyright owner]
18 18 *
19 19 * CDDL HEADER END
20 20 */
21 21
22 22 /*
23 23 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
24 24 */
25 +
25 26 /*
26 27 * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
27 28 * Use is subject to license terms.
28 29 */
29 30
30 31 /*
31 32 * floating point Bessel's function of the first and second kinds
32 33 * of order zero: j1(x),y1(x);
33 34 *
34 35 * Special cases:
35 36 * y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal;
36 37 * y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal.
37 38 */
38 39
39 40 #pragma weak __j1l = j1l
40 41 #pragma weak __y1l = y1l
41 42
42 43 #include "libm.h"
43 44 #include "longdouble.h"
44 45
45 -#define GENERIC long double
46 -static const GENERIC
47 -zero = 0.0L,
48 -small = 1.0e-9L,
49 -tiny = 1.0e-38L,
50 -one = 1.0L,
51 -five = 5.0L,
52 -invsqrtpi= 5.641895835477562869480794515607725858441e-0001L,
53 -tpi = 0.636619772367581343075535053490057448L;
46 +#define GENERIC long double
47 +
48 +static const GENERIC zero = 0.0L,
49 + small = 1.0e-9L,
50 + tiny = 1.0e-38L,
51 + one = 1.0L,
52 + five = 5.0L,
53 + invsqrtpi = 5.641895835477562869480794515607725858441e-0001L,
54 + tpi = 0.636619772367581343075535053490057448L;
54 55
55 56 static GENERIC pone(GENERIC);
56 57 static GENERIC qone(GENERIC);
57 58
58 59 static const GENERIC r0[7] = {
59 - -6.249999999999999999999999999999999627320e-0002L,
60 - 1.940606727194041716205384618494641565464e-0003L,
61 - -3.005630423155733701856481469986459043883e-0005L,
62 - 2.345586219403918667468341047369572169358e-0007L,
63 - -9.976809285885253587529010109133336669724e-0010L,
64 - 2.218743258363623946078958783775107473381e-0012L,
65 - -2.071079656218700604767650924103578046280e-0015L,
60 + -6.249999999999999999999999999999999627320e-0002L,
61 + 1.940606727194041716205384618494641565464e-0003L,
62 + -3.005630423155733701856481469986459043883e-0005L,
63 + 2.345586219403918667468341047369572169358e-0007L,
64 + -9.976809285885253587529010109133336669724e-0010L,
65 + 2.218743258363623946078958783775107473381e-0012L,
66 + -2.071079656218700604767650924103578046280e-0015L,
66 67 };
68 +
67 69 static const GENERIC s0[7] = {
68 - 1.0e0L,
69 - 1.061695903156199920738051277075003059555e-0002L,
70 - 5.521860513111180371566951179398862692060e-0005L,
71 - 1.824214367413754193524107877084979441407e-0007L,
72 - 4.098957778439576834818838198039029353925e-0010L,
73 - 6.047735079699666389853240090925264056197e-0013L,
74 - 4.679044728878836197247923279512047035041e-0016L,
70 + 1.0e0L,
71 + 1.061695903156199920738051277075003059555e-0002L,
72 + 5.521860513111180371566951179398862692060e-0005L,
73 + 1.824214367413754193524107877084979441407e-0007L,
74 + 4.098957778439576834818838198039029353925e-0010L,
75 + 6.047735079699666389853240090925264056197e-0013L,
76 + 4.679044728878836197247923279512047035041e-0016L,
75 77 };
76 78
77 79 GENERIC
78 -j1l(x) GENERIC x;{
79 - GENERIC z, d, s,c,ss,cc,r;
80 +j1l(GENERIC x)
81 +{
82 + GENERIC z, d, s, c, ss, cc, r;
80 83 int i, sgn;
81 84
82 - if (!finitel(x)) return one/x;
85 + if (!finitel(x))
86 + return (one / x);
87 +
83 88 sgn = signbitl(x);
84 89 x = fabsl(x);
90 +
85 91 if (x > 1.28L) {
86 92 s = sinl(x);
87 93 c = cosl(x);
88 - /*
89 - * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x0)-q1(x)*sin(x0))
90 - * where x0 = x-3pi/4
91 - * Better formula:
92 - * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
93 - * = 1/sqrt(2) * (sin(x) - cos(x))
94 - * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
95 - * = -1/sqrt(2) * (cos(x) + sin(x))
96 - * To avoid cancellation, use
97 - * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
98 - * to compute the worse one.
99 - */
100 - if (x>1.0e2450L) { /* x+x may overflow */
101 - ss = -s-c;
102 - cc = s-c;
94 +
95 + /* BEGIN CSTYLED */
96 + /*
97 + * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x0)-q1(x)*sin(x0))
98 + * where x0 = x-3pi/4
99 + * Better formula:
100 + * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
101 + * = 1/sqrt(2) * (sin(x) - cos(x))
102 + * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
103 + * = -1/sqrt(2) * (cos(x) + sin(x))
104 + * To avoid cancellation, use
105 + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
106 + * to compute the worse one.
107 + */
108 + /* END CSTYLED */
109 + if (x > 1.0e2450L) { /* x+x may overflow */
110 + ss = -s - c;
111 + cc = s - c;
103 112 } else if (signbitl(s) != signbitl(c)) {
104 113 cc = s - c;
105 - ss = cosl(x+x)/cc;
114 + ss = cosl(x + x) / cc;
106 115 } else {
107 - ss = -s-c;
108 - cc = cosl(x+x)/ss;
116 + ss = -s - c;
117 + cc = cosl(x + x) / ss;
109 118 }
110 - /*
111 - * j1(x) = 1/sqrt(pi*x) * (P(1,x)*cc - Q(1,x)*ss)
112 - * y1(x) = 1/sqrt(pi*x) * (P(1,x)*ss + Q(1,x)*cc)
113 - */
114 - if (x>1.0e120L) return (invsqrtpi*cc)/sqrtl(x);
115 - d = invsqrtpi*(pone(x)*cc-qone(x)*ss)/sqrtl(x);
116 - if (sgn == 0) return d; else return -d;
119 +
120 + /*
121 + * j1(x) = 1/sqrt(pi*x) * (P(1,x)*cc - Q(1,x)*ss)
122 + * y1(x) = 1/sqrt(pi*x) * (P(1,x)*ss + Q(1,x)*cc)
123 + */
124 + if (x > 1.0e120L)
125 + return ((invsqrtpi * cc) / sqrtl(x));
126 +
127 + d = invsqrtpi * (pone(x) * cc - qone(x) * ss) / sqrtl(x);
128 +
129 + if (sgn == 0)
130 + return (d);
131 + else
132 + return (-d);
133 + }
134 +
135 + if (x <= small) {
136 + if (x <= tiny)
137 + d = 0.5L * x;
138 + else
139 + d = x * (0.5L - x * x * 0.125L);
140 +
141 + if (sgn == 0)
142 + return (d);
143 + else
144 + return (-d);
117 145 }
118 - if (x<=small) {
119 - if (x<=tiny) d = 0.5L*x;
120 - else d = x*(0.5L-x*x*0.125L);
121 - if (sgn == 0) return d; else return -d;
122 - }
123 - z = x*x;
124 - r = r0[6];
125 - s = s0[6];
126 - for (i=5;i>=0;i--) {
127 - r = r*z + r0[i];
128 - s = s*z + s0[i];
129 - }
130 - d = x*0.5L+x*(z*(r/s));
131 - if (sgn == 0) return d; else return -d;
146 +
147 + z = x * x;
148 + r = r0[6];
149 + s = s0[6];
150 +
151 + for (i = 5; i >= 0; i--) {
152 + r = r * z + r0[i];
153 + s = s * z + s0[i];
154 + }
155 +
156 + d = x * 0.5L + x * (z * (r / s));
157 +
158 + if (sgn == 0)
159 + return (d);
160 + else
161 + return (-d);
132 162 }
133 163
134 164 static const GENERIC u0[7] = {
135 - -1.960570906462389484060557273467558703503e-0001L,
136 - 5.166389353148318460304315890665450006495e-0002L,
137 - -2.229699464105910913337190798743451115604e-0003L,
138 - 3.625437034548863342715657067759078267158e-0005L,
139 - -2.689902826993117212255524537353883987171e-0007L,
140 - 9.304570592456930912969387719010256018466e-0010L,
141 - -1.234878126794286643318321347997500346131e-0012L,
165 + -1.960570906462389484060557273467558703503e-0001L,
166 + 5.166389353148318460304315890665450006495e-0002L,
167 + -2.229699464105910913337190798743451115604e-0003L,
168 + 3.625437034548863342715657067759078267158e-0005L,
169 + -2.689902826993117212255524537353883987171e-0007L,
170 + 9.304570592456930912969387719010256018466e-0010L,
171 + -1.234878126794286643318321347997500346131e-0012L,
142 172 };
173 +
143 174 static const GENERIC v0[8] = {
144 - 1.0e0L,
145 - 1.369394302535807332517110204820556695644e-0002L,
146 - 9.508438148097659501433367062605935379588e-0005L,
147 - 4.399007309420092056052714797296467565655e-0007L,
148 - 1.488083087443756398305819693177715000787e-0009L,
149 - 3.751609832625793536245746965768587624922e-0012L,
150 - 6.680926434086257291872903276124244131448e-0015L,
151 - 6.676602383908906988160099057991121446058e-0018L,
175 + 1.0e0L,
176 + 1.369394302535807332517110204820556695644e-0002L,
177 + 9.508438148097659501433367062605935379588e-0005L,
178 + 4.399007309420092056052714797296467565655e-0007L,
179 + 1.488083087443756398305819693177715000787e-0009L,
180 + 3.751609832625793536245746965768587624922e-0012L,
181 + 6.680926434086257291872903276124244131448e-0015L,
182 + 6.676602383908906988160099057991121446058e-0018L,
152 183 };
153 184
154 185 GENERIC
155 -y1l(x) GENERIC x;{
156 - GENERIC z, s,c,ss,cc,u,v;
186 +y1l(GENERIC x)
187 +{
188 + GENERIC z, s, c, ss, cc, u, v;
157 189 int i;
158 190
159 - if (isnanl(x)) return x+x;
191 + if (isnanl(x))
192 + return (x + x);
193 +
160 194 if (x <= zero) {
161 195 if (x == zero)
162 - return -one/zero;
196 + return (-one / zero);
163 197 else
164 - return zero/zero;
198 + return (zero / zero);
165 199 }
200 +
166 201 if (x > 1.28L) {
167 - if (!finitel(x)) return zero;
202 + if (!finitel(x))
203 + return (zero);
204 +
168 205 s = sinl(x);
169 206 c = cosl(x);
170 - /*
171 - * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x0)-q1(x)*sin(x0))
172 - * where x0 = x-3pi/4
173 - * Better formula:
174 - * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
175 - * = 1/sqrt(2) * (sin(x) - cos(x))
176 - * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
177 - * = -1/sqrt(2) * (cos(x) + sin(x))
178 - * To avoid cancellation, use
179 - * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
180 - * to compute the worse one.
181 - */
182 - if (x>1.0e2450L) { /* x+x may overflow */
183 - ss = -s-c;
184 - cc = s-c;
207 +
208 + /* BEGIN CSTYLED */
209 + /*
210 + * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x0)-q1(x)*sin(x0))
211 + * where x0 = x-3pi/4
212 + * Better formula:
213 + * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
214 + * = 1/sqrt(2) * (sin(x) - cos(x))
215 + * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
216 + * = -1/sqrt(2) * (cos(x) + sin(x))
217 + * To avoid cancellation, use
218 + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
219 + * to compute the worse one.
220 + */
221 + /* END CSTYLED */
222 + if (x > 1.0e2450L) { /* x+x may overflow */
223 + ss = -s - c;
224 + cc = s - c;
185 225 } else if (signbitl(s) != signbitl(c)) {
186 226 cc = s - c;
187 - ss = cosl(x+x)/cc;
227 + ss = cosl(x + x) / cc;
188 228 } else {
189 - ss = -s-c;
190 - cc = cosl(x+x)/ss;
229 + ss = -s - c;
230 + cc = cosl(x + x) / ss;
191 231 }
192 - /*
193 - * j1(x) = 1/sqrt(pi*x) * (P(1,x)*cc - Q(1,x)*ss)
194 - * y1(x) = 1/sqrt(pi*x) * (P(1,x)*ss + Q(1,x)*cc)
195 - */
196 - if (x>1.0e91L) return (invsqrtpi*ss)/sqrtl(x);
197 - return invsqrtpi*(pone(x)*ss+qone(x)*cc)/sqrtl(x);
232 +
233 + /*
234 + * j1(x) = 1/sqrt(pi*x) * (P(1,x)*cc - Q(1,x)*ss)
235 + * y1(x) = 1/sqrt(pi*x) * (P(1,x)*ss + Q(1,x)*cc)
236 + */
237 + if (x > 1.0e91L)
238 + return ((invsqrtpi * ss) / sqrtl(x));
239 +
240 + return (invsqrtpi * (pone(x) * ss + qone(x) * cc) / sqrtl(x));
241 + }
242 +
243 + if (x <= tiny)
244 + return (-tpi / x);
245 +
246 + z = x * x;
247 + u = u0[6];
248 + v = v0[6] + z * v0[7];
249 +
250 + for (i = 5; i >= 0; i--) {
251 + u = u * z + u0[i];
252 + v = v * z + v0[i];
198 253 }
199 - if (x<=tiny) {
200 - return (-tpi/x);
201 - }
202 - z = x*x;
203 - u = u0[6]; v = v0[6]+z*v0[7];
204 - for (i=5;i>=0;i--) {
205 - u = u*z + u0[i];
206 - v = v*z + v0[i];
207 - }
208 - return(x*(u/v) + tpi*(j1l(x)*logl(x)-one/x));
254 +
255 + return (x * (u / v) + tpi * (j1l(x) * logl(x) - one / x));
209 256 }
210 257
211 258 static const GENERIC pr0[12] = {
212 - 1.000000000000000000000000000000000000267e+0000L,
213 - 1.060717875045891455602180843276758003035e+0003L,
214 - 4.344347542892127024446687712181105852335e+0005L,
215 - 8.915680220724007016377924252717410457094e+0007L,
216 - 9.969502259938406062809873257569171272819e+0009L,
217 - 6.200290193138613035646510338707386316595e+0011L,
218 - 2.105978548788015119851815854422247330118e+0013L,
219 - 3.696635772784601239371730810311998368948e+0014L,
220 - 3.015913097920694682057958412534134515156e+0015L,
221 - 9.370298471339353098123277427328592725921e+0015L,
222 - 7.190349005196335967340799265074029443057e+0015L,
223 - 2.736097786240689996880391074927552517982e+0014L,
259 + 1.000000000000000000000000000000000000267e+0000L,
260 + 1.060717875045891455602180843276758003035e+0003L,
261 + 4.344347542892127024446687712181105852335e+0005L,
262 + 8.915680220724007016377924252717410457094e+0007L,
263 + 9.969502259938406062809873257569171272819e+0009L,
264 + 6.200290193138613035646510338707386316595e+0011L,
265 + 2.105978548788015119851815854422247330118e+0013L,
266 + 3.696635772784601239371730810311998368948e+0014L,
267 + 3.015913097920694682057958412534134515156e+0015L,
268 + 9.370298471339353098123277427328592725921e+0015L,
269 + 7.190349005196335967340799265074029443057e+0015L,
270 + 2.736097786240689996880391074927552517982e+0014L,
224 271 };
272 +
225 273 static const GENERIC ps0[11] = {
226 - 1.0e0L,
227 - 1.060600687545891455602180843276758095107e+0003L,
228 - 4.343106093416975589147153906505338900961e+0005L,
229 - 8.910605869002176566582072242244353399059e+0007L,
230 - 9.959122058635087888690713917622056540190e+0009L,
231 - 6.188744967234948231792482949171041843894e+0011L,
232 - 2.098863976953783506401759873801990304907e+0013L,
233 - 3.672870357018063196746729751479938908450e+0014L,
234 - 2.975538419246824921049011529574385888420e+0015L,
235 - 9.063657659995043205018686029284479837091e+0015L,
236 - 6.401953344314747916729366441508892711691e+0015L,
274 + 1.0e0L,
275 + 1.060600687545891455602180843276758095107e+0003L,
276 + 4.343106093416975589147153906505338900961e+0005L,
277 + 8.910605869002176566582072242244353399059e+0007L,
278 + 9.959122058635087888690713917622056540190e+0009L,
279 + 6.188744967234948231792482949171041843894e+0011L,
280 + 2.098863976953783506401759873801990304907e+0013L,
281 + 3.672870357018063196746729751479938908450e+0014L,
282 + 2.975538419246824921049011529574385888420e+0015L,
283 + 9.063657659995043205018686029284479837091e+0015L,
284 + 6.401953344314747916729366441508892711691e+0015L,
237 285 };
286 +
238 287 static const GENERIC pr1[12] = {
239 - 1.000000000000000000000023667524130660984e+0000L,
240 - 6.746154419979618754354803488126452971204e+0002L,
241 - 1.811210781083390154857018330296145970502e+0005L,
242 - 2.533098390379924268038005329095287842244e+0007L,
243 - 2.029683619805342145252338570875424600729e+0009L,
244 - 9.660859662192711465301069401598929980319e+0010L,
245 - 2.743396238644831519934098967716621316316e+0012L,
246 - 4.553097354140854377931023170263455246288e+0013L,
247 - 4.210245069852219757476169864974870720374e+0014L,
248 - 1.987334056229596485076645967176169801727e+0015L,
249 - 4.067120052787096893838970455751338930462e+0015L,
250 - 2.486539606380406398310845264910691398133e+0015L,
288 + 1.000000000000000000000023667524130660984e+0000L,
289 + 6.746154419979618754354803488126452971204e+0002L,
290 + 1.811210781083390154857018330296145970502e+0005L,
291 + 2.533098390379924268038005329095287842244e+0007L,
292 + 2.029683619805342145252338570875424600729e+0009L,
293 + 9.660859662192711465301069401598929980319e+0010L,
294 + 2.743396238644831519934098967716621316316e+0012L,
295 + 4.553097354140854377931023170263455246288e+0013L,
296 + 4.210245069852219757476169864974870720374e+0014L,
297 + 1.987334056229596485076645967176169801727e+0015L,
298 + 4.067120052787096893838970455751338930462e+0015L,
299 + 2.486539606380406398310845264910691398133e+0015L,
251 300 };
301 +
252 302 static const GENERIC ps1[14] = {
253 - 1.0e0L,
254 - 6.744982544979618754355808680196859521782e+0002L,
255 - 1.810421795396966762032155290441364740350e+0005L,
256 - 2.530986460644310651529583759699988435573e+0007L,
257 - 2.026743276048023121360249288818290224145e+0009L,
258 - 9.637461924407405935245269407052641341836e+0010L,
259 - 2.732378628423766417402292797028314160831e+0012L,
260 - 4.522345274960527124354844364012184278488e+0013L,
261 - 4.160650668341743132685335758415469856545e+0014L,
262 - 1.943730242988858208243492424892435901211e+0015L,
263 - 3.880228532692127989901131618598067450001e+0015L,
264 - 2.178020816161154615841000173683302999728e+0015L,
265 - -8.994062666842225551554346698171600634173e+0013L,
266 - 1.368520368508851253495764806934619574990e+0013L,
303 + 1.0e0L,
304 + 6.744982544979618754355808680196859521782e+0002L,
305 + 1.810421795396966762032155290441364740350e+0005L,
306 + 2.530986460644310651529583759699988435573e+0007L,
307 + 2.026743276048023121360249288818290224145e+0009L,
308 + 9.637461924407405935245269407052641341836e+0010L,
309 + 2.732378628423766417402292797028314160831e+0012L,
310 + 4.522345274960527124354844364012184278488e+0013L,
311 + 4.160650668341743132685335758415469856545e+0014L,
312 + 1.943730242988858208243492424892435901211e+0015L,
313 + 3.880228532692127989901131618598067450001e+0015L,
314 + 2.178020816161154615841000173683302999728e+0015L,
315 + -8.994062666842225551554346698171600634173e+0013L,
316 + 1.368520368508851253495764806934619574990e+0013L,
267 317 };
318 +
268 319 static const GENERIC pr2[12] = {
269 - 1.000000000000000006938651621840396237282e+0000L,
270 - 3.658416291850404981407101077037948144698e+0002L,
271 - 5.267073772170356547709794670602812447537e+0004L,
272 - 3.912012101226837463014925210735894620442e+0006L,
273 - 1.651295648974103957193874928714180765625e+0008L,
274 - 4.114901144480797609972484998142146783499e+0009L,
275 - 6.092524309766036681542980572526335147672e+0010L,
276 - 5.263913178071282616719249969074134570577e+0011L,
277 - 2.538408581124324223367341020538081330994e+0012L,
278 - 6.288607929360291027895126983015365677648e+0012L,
279 - 6.848330048211148419047055075386525945280e+0012L,
280 - 2.290309646838867941423178163991423244690e+0012L,
320 + 1.000000000000000006938651621840396237282e+0000L,
321 + 3.658416291850404981407101077037948144698e+0002L,
322 + 5.267073772170356547709794670602812447537e+0004L,
323 + 3.912012101226837463014925210735894620442e+0006L,
324 + 1.651295648974103957193874928714180765625e+0008L,
325 + 4.114901144480797609972484998142146783499e+0009L,
326 + 6.092524309766036681542980572526335147672e+0010L,
327 + 5.263913178071282616719249969074134570577e+0011L,
328 + 2.538408581124324223367341020538081330994e+0012L,
329 + 6.288607929360291027895126983015365677648e+0012L,
330 + 6.848330048211148419047055075386525945280e+0012L,
331 + 2.290309646838867941423178163991423244690e+0012L,
281 332 };
333 +
282 334 static const GENERIC ps2[14] = {
283 - 1.0e0L,
284 - 3.657244416850405086459410165762319861856e+0002L,
285 - 5.262802358425023243992387075861237306312e+0004L,
286 - 3.905896813959919648136295861661483848364e+0006L,
287 - 1.646791907791461220742694842108202772763e+0008L,
288 - 4.096132803064256022224954120208201437344e+0009L,
289 - 6.046665195915950447544429445730680236759e+0010L,
290 - 5.198061739781991313414052212328653295168e+0011L,
291 - 2.484233851814333966401527626421254279796e+0012L,
292 - 6.047868806925315879339651539434315255940e+0012L,
293 - 6.333103831254091652501642567294101813354e+0012L,
294 - 1.875143098754284994467609936924685024968e+0012L,
295 - -5.238330920563392692965412762508813601534e+0010L,
296 - 4.656888609439364725427789198383779259957e+0009L,
335 + 1.0e0L,
336 + 3.657244416850405086459410165762319861856e+0002L,
337 + 5.262802358425023243992387075861237306312e+0004L,
338 + 3.905896813959919648136295861661483848364e+0006L,
339 + 1.646791907791461220742694842108202772763e+0008L,
340 + 4.096132803064256022224954120208201437344e+0009L,
341 + 6.046665195915950447544429445730680236759e+0010L,
342 + 5.198061739781991313414052212328653295168e+0011L,
343 + 2.484233851814333966401527626421254279796e+0012L,
344 + 6.047868806925315879339651539434315255940e+0012L,
345 + 6.333103831254091652501642567294101813354e+0012L,
346 + 1.875143098754284994467609936924685024968e+0012L,
347 + -5.238330920563392692965412762508813601534e+0010L,
348 + 4.656888609439364725427789198383779259957e+0009L,
297 349 };
350 +
298 351 static const GENERIC pr3[13] = {
299 - 1.000000000000009336887318068056137842897e+0000L,
300 - 2.242719942728459588488051572002835729183e+0002L,
301 - 1.955450611382026550266257737331095691092e+0004L,
302 - 8.707143293993619899395400562409175590739e+0005L,
303 - 2.186267894487004565948324289010954505316e+0007L,
304 - 3.224328510541957792360691585667502864688e+0008L,
305 - 2.821057355151380597331792896882741364897e+0009L,
306 - 1.445371387295422404365584793796028979840e+0010L,
307 - 4.181743160669891357783011002656658107864e+0010L,
308 - 6.387371088767993119325536137794535513922e+0010L,
309 - 4.575619999412716078064070587767416436396e+0010L,
310 - 1.228415651211639160620284441690503550842e+0010L,
311 - 7.242170349875563053436050532153112882072e+0008L,
352 + 1.000000000000009336887318068056137842897e+0000L,
353 + 2.242719942728459588488051572002835729183e+0002L,
354 + 1.955450611382026550266257737331095691092e+0004L,
355 + 8.707143293993619899395400562409175590739e+0005L,
356 + 2.186267894487004565948324289010954505316e+0007L,
357 + 3.224328510541957792360691585667502864688e+0008L,
358 + 2.821057355151380597331792896882741364897e+0009L,
359 + 1.445371387295422404365584793796028979840e+0010L,
360 + 4.181743160669891357783011002656658107864e+0010L,
361 + 6.387371088767993119325536137794535513922e+0010L,
362 + 4.575619999412716078064070587767416436396e+0010L,
363 + 1.228415651211639160620284441690503550842e+0010L,
364 + 7.242170349875563053436050532153112882072e+0008L,
312 365 };
366 +
313 367 static const GENERIC ps3[13] = {
314 - 1.0e0L,
315 - 2.241548067728529551049804610486061401070e+0002L,
316 - 1.952838216795552145132137932931237181307e+0004L,
317 - 8.684574926493185744628127341069974575526e+0005L,
318 - 2.176357771067037962940853412819852189164e+0007L,
319 - 3.199958682356132977319258783167122100567e+0008L,
320 - 2.786218931525334687844675219914201872570e+0009L,
321 - 1.416283776951741549631417572317916039767e+0010L,
322 - 4.042962659271567948735676834609348842922e+0010L,
323 - 6.028168462646694510083847222968444402161e+0010L,
324 - 4.118410226794641413833887606580085281111e+0010L,
325 - 9.918735736297038430744161253338202230263e+0009L,
326 - 4.092967198238098023219124487437130332038e+0008L,
368 + 1.0e0L,
369 + 2.241548067728529551049804610486061401070e+0002L,
370 + 1.952838216795552145132137932931237181307e+0004L,
371 + 8.684574926493185744628127341069974575526e+0005L,
372 + 2.176357771067037962940853412819852189164e+0007L,
373 + 3.199958682356132977319258783167122100567e+0008L,
374 + 2.786218931525334687844675219914201872570e+0009L,
375 + 1.416283776951741549631417572317916039767e+0010L,
376 + 4.042962659271567948735676834609348842922e+0010L,
377 + 6.028168462646694510083847222968444402161e+0010L,
378 + 4.118410226794641413833887606580085281111e+0010L,
379 + 9.918735736297038430744161253338202230263e+0009L,
380 + 4.092967198238098023219124487437130332038e+0008L,
327 381 };
382 +
328 383 static const GENERIC pr4[13] = {
329 - 1.000000000001509220978157399042059553390e+0000L,
330 - 1.437551868378147851133499996323782607787e+0002L,
331 - 7.911335537418177296041518061404505428004e+0003L,
332 - 2.193710939115317214716518908935756104804e+0005L,
333 - 3.390662495136730962513489796538274984382e+0006L,
334 - 3.048655347929348891006070609293884274789e+0007L,
335 - 1.613781633489496606354045161527450975195e+0008L,
336 - 4.975089835037230277110156150038482159988e+0008L,
337 - 8.636047087015115403880904418339566323264e+0008L,
338 - 7.918202912328366140110671223076949101509e+0008L,
339 - 3.423294665798984733439650311722794853294e+0008L,
340 - 5.621904953441963961040503934782662613621e+0007L,
341 - 2.086303543310240260758670404509484499793e+0006L,
384 + 1.000000000001509220978157399042059553390e+0000L,
385 + 1.437551868378147851133499996323782607787e+0002L,
386 + 7.911335537418177296041518061404505428004e+0003L,
387 + 2.193710939115317214716518908935756104804e+0005L,
388 + 3.390662495136730962513489796538274984382e+0006L,
389 + 3.048655347929348891006070609293884274789e+0007L,
390 + 1.613781633489496606354045161527450975195e+0008L,
391 + 4.975089835037230277110156150038482159988e+0008L,
392 + 8.636047087015115403880904418339566323264e+0008L,
393 + 7.918202912328366140110671223076949101509e+0008L,
394 + 3.423294665798984733439650311722794853294e+0008L,
395 + 5.621904953441963961040503934782662613621e+0007L,
396 + 2.086303543310240260758670404509484499793e+0006L,
342 397 };
398 +
343 399 static const GENERIC ps4[13] = {
344 - 1.0e0L,
345 - 1.436379993384532371670493319591847362304e+0002L,
346 - 7.894647154785430678061053848847436659499e+0003L,
347 - 2.184659753392097529008981741550878586174e+0005L,
348 - 3.366109083305465176803513738147049499361e+0006L,
349 - 3.011911545968996817697665866587226343186e+0007L,
350 - 1.582262913779689851316760148459414895301e+0008L,
351 - 4.819268809494937919217938589530138201770e+0008L,
352 - 8.201355762990450679702837123432527154830e+0008L,
353 - 7.268232093982510937417446421282341425212e+0008L,
354 - 2.950911909015572933262131323934036480462e+0008L,
355 - 4.242839924305934423010858966540621219396e+0007L,
356 - 1.064387620445090779182117666330405186866e+0006L,
400 + 1.0e0L,
401 + 1.436379993384532371670493319591847362304e+0002L,
402 + 7.894647154785430678061053848847436659499e+0003L,
403 + 2.184659753392097529008981741550878586174e+0005L,
404 + 3.366109083305465176803513738147049499361e+0006L,
405 + 3.011911545968996817697665866587226343186e+0007L,
406 + 1.582262913779689851316760148459414895301e+0008L,
407 + 4.819268809494937919217938589530138201770e+0008L,
408 + 8.201355762990450679702837123432527154830e+0008L,
409 + 7.268232093982510937417446421282341425212e+0008L,
410 + 2.950911909015572933262131323934036480462e+0008L,
411 + 4.242839924305934423010858966540621219396e+0007L,
412 + 1.064387620445090779182117666330405186866e+0006L,
357 413 };
414 +
358 415 static const GENERIC pr5[13] = {
359 - 1.000000000102434805241171427253847353861e+0000L,
360 - 9.129332257083629259060502249025963234821e+0001L,
361 - 3.132238483586953037576119377504557191413e+0003L,
362 - 5.329782528269307971278943122454171107861e+0004L,
363 - 4.988460157184117790692873002103052944145e+0005L,
364 - 2.686602071615786816147010334256047469378e+0006L,
365 - 8.445418526028961197703799808701268301831e+0006L,
366 - 1.536575358646141157475725889907900827390e+0007L,
367 - 1.568405818236523821796862770586544811945e+0007L,
368 - 8.450876239888770102387618667362302173547e+0006L,
369 - 2.154414900139567328424026827163203446077e+0006L,
370 - 2.105656926565043898888460254808062352205e+0005L,
371 - 4.739165011023396507022134303736862812975e+0003L,
416 + 1.000000000102434805241171427253847353861e+0000L,
417 + 9.129332257083629259060502249025963234821e+0001L,
418 + 3.132238483586953037576119377504557191413e+0003L,
419 + 5.329782528269307971278943122454171107861e+0004L,
420 + 4.988460157184117790692873002103052944145e+0005L,
421 + 2.686602071615786816147010334256047469378e+0006L,
422 + 8.445418526028961197703799808701268301831e+0006L,
423 + 1.536575358646141157475725889907900827390e+0007L,
424 + 1.568405818236523821796862770586544811945e+0007L,
425 + 8.450876239888770102387618667362302173547e+0006L,
426 + 2.154414900139567328424026827163203446077e+0006L,
427 + 2.105656926565043898888460254808062352205e+0005L,
428 + 4.739165011023396507022134303736862812975e+0003L,
372 429 };
430 +
373 431 static const GENERIC ps5[13] = {
374 - 1.0e0L,
375 - 9.117613509595327476509152673394703847793e+0001L,
376 - 3.121697972484015639301279229281770795147e+0003L,
377 - 5.294447222735893568040911873834576440255e+0004L,
378 - 4.930368882192772335798256684110887882807e+0005L,
379 - 2.634854685641165298302167435798357437768e+0006L,
380 - 8.185462775400326393555896157031818280918e+0006L,
381 - 1.462417423080215192609668642663030667086e+0007L,
382 - 1.450624993985851675982860844153954896015e+0007L,
383 - 7.460467647561995283219086567162006113864e+0006L,
384 - 1.754210981405612478869227142579056338965e+0006L,
385 - 1.463286721155271971526264914524746699596e+0005L,
386 - 2.155894725796702015341211116579827039459e+0003L,
432 + 1.0e0L,
433 + 9.117613509595327476509152673394703847793e+0001L,
434 + 3.121697972484015639301279229281770795147e+0003L,
435 + 5.294447222735893568040911873834576440255e+0004L,
436 + 4.930368882192772335798256684110887882807e+0005L,
437 + 2.634854685641165298302167435798357437768e+0006L,
438 + 8.185462775400326393555896157031818280918e+0006L,
439 + 1.462417423080215192609668642663030667086e+0007L,
440 + 1.450624993985851675982860844153954896015e+0007L,
441 + 7.460467647561995283219086567162006113864e+0006L,
442 + 1.754210981405612478869227142579056338965e+0006L,
443 + 1.463286721155271971526264914524746699596e+0005L,
444 + 2.155894725796702015341211116579827039459e+0003L,
387 445 };
446 +
388 447 static const GENERIC pr6[13] = {
389 - 1.000000003564855546741735920315743157129e+0000L,
390 - 5.734003934862540458119423509909510288366e+0001L,
391 - 1.209572491935850486086559692291796887976e+0003L,
392 - 1.243398391422281247933674779163660286838e+0004L,
393 - 6.930996755181437937258220998601708278787e+0004L,
394 - 2.198067659532757598646722249966767620099e+0005L,
395 - 4.033659432712058633933179115820576858455e+0005L,
396 - 4.257759657219008027016047206574574358678e+0005L,
397 - 2.511917395876004349480721277445763916389e+0005L,
398 - 7.813756153070623654178731651381881953552e+0004L,
399 - 1.152069173381127881385588092905864352891e+0004L,
400 - 6.548580782804088553777816037551523398082e+0002L,
401 - 8.668725370116906132327542766127938496880e+0000L,
448 + 1.000000003564855546741735920315743157129e+0000L,
449 + 5.734003934862540458119423509909510288366e+0001L,
450 + 1.209572491935850486086559692291796887976e+0003L,
451 + 1.243398391422281247933674779163660286838e+0004L,
452 + 6.930996755181437937258220998601708278787e+0004L,
453 + 2.198067659532757598646722249966767620099e+0005L,
454 + 4.033659432712058633933179115820576858455e+0005L,
455 + 4.257759657219008027016047206574574358678e+0005L,
456 + 2.511917395876004349480721277445763916389e+0005L,
457 + 7.813756153070623654178731651381881953552e+0004L,
458 + 1.152069173381127881385588092905864352891e+0004L,
459 + 6.548580782804088553777816037551523398082e+0002L,
460 + 8.668725370116906132327542766127938496880e+0000L,
402 461 };
462 +
403 463 static const GENERIC ps6[13] = {
404 - 1.0e0L,
405 - 5.722285236357114566499221525736286205184e+0001L,
406 - 1.203010842878317935444582950620339570506e+0003L,
407 - 1.230058335378583550155825502172435371208e+0004L,
408 - 6.800998550607861288865300438648089894412e+0004L,
409 - 2.130767829599304262987769347536850885921e+0005L,
410 - 3.840483466643916681759936972992155310026e+0005L,
411 - 3.947432373459225542861819148108081160393e+0005L,
412 - 2.237816239393081111481588434457838526738e+0005L,
413 - 6.545820495124419723398946273790921540774e+0004L,
414 - 8.729563630320892741500726213278834737196e+0003L,
415 - 4.130762660291894753450174794196998813709e+0002L,
416 - 3.480368898672684645130335786015075595598e+0000L,
464 + 1.0e0L,
465 + 5.722285236357114566499221525736286205184e+0001L,
466 + 1.203010842878317935444582950620339570506e+0003L,
467 + 1.230058335378583550155825502172435371208e+0004L,
468 + 6.800998550607861288865300438648089894412e+0004L,
469 + 2.130767829599304262987769347536850885921e+0005L,
470 + 3.840483466643916681759936972992155310026e+0005L,
471 + 3.947432373459225542861819148108081160393e+0005L,
472 + 2.237816239393081111481588434457838526738e+0005L,
473 + 6.545820495124419723398946273790921540774e+0004L,
474 + 8.729563630320892741500726213278834737196e+0003L,
475 + 4.130762660291894753450174794196998813709e+0002L,
476 + 3.480368898672684645130335786015075595598e+0000L,
417 477 };
478 +
418 479 static const GENERIC sixteen = 16.0L;
419 -static const GENERIC eight = 8.0L;
420 -static const GENERIC huge = 1.0e30L;
480 +static const GENERIC eight = 8.0L;
481 +static const GENERIC huge = 1.0e30L;
421 482
422 -static GENERIC pone(x)
423 -GENERIC x;
483 +static GENERIC
484 +pone(GENERIC x)
424 485 {
425 - GENERIC s,r,t,z;
486 + GENERIC s, r, t, z;
426 487 int i;
427 - if (x>huge) return one;
428 - t = one/x; z = t*t;
429 - if (x>sixteen) {
430 - r = z*pr0[11]+pr0[10]; s = ps0[10];
431 - for (i=9;i>=0;i--) {
432 - r = z*r + pr0[i];
433 - s = z*s + ps0[i];
434 - }
435 - } else if (x>eight) {
436 - r = pr1[11]; s = ps1[11]+z*(ps1[12]+z*ps1[13]);
437 - for (i=10;i>=0;i--) {
438 - r = z*r + pr1[i];
439 - s = z*s + ps1[i];
440 - }
441 - } else if (x>five) {
442 - r = pr2[11]; s = ps2[11]+z*(ps2[12]+z*ps2[13]);
443 - for (i=10;i>=0;i--) {
444 - r = z*r + pr2[i];
445 - s = z*s + ps2[i];
446 - }
447 - } else if (x>3.5L) {
448 - r = pr3[12]; s = ps3[12];
449 - for (i=11;i>=0;i--) {
450 - r = z*r + pr3[i];
451 - s = z*s + ps3[i];
452 - }
453 - } else if (x>2.5L) {
454 - r = pr4[12]; s = ps4[12];
455 - for (i=11;i>=0;i--) {
456 - r = z*r + pr4[i];
457 - s = z*s + ps4[i];
458 - }
459 - } else if (x> (1.0L/0.5625L)) {
460 - r = pr5[12]; s = ps5[12];
461 - for (i=11;i>=0;i--) {
462 - r = z*r + pr5[i];
463 - s = z*s + ps5[i];
464 - }
465 - } else { /* assume x > 1.28 */
466 - r = pr6[12]; s = ps6[12];
467 - for (i=11;i>=0;i--) {
468 - r = z*r + pr6[i];
469 - s = z*s + ps6[i];
470 - }
471 - }
472 - return r/s;
473 -}
474 488
489 + if (x > huge)
490 + return (one);
491 +
492 + t = one / x;
493 + z = t * t;
494 +
495 + if (x > sixteen) {
496 + r = z * pr0[11] + pr0[10];
497 + s = ps0[10];
498 +
499 + for (i = 9; i >= 0; i--) {
500 + r = z * r + pr0[i];
501 + s = z * s + ps0[i];
502 + }
503 + } else if (x > eight) {
504 + r = pr1[11];
505 + s = ps1[11] + z * (ps1[12] + z * ps1[13]);
506 +
507 + for (i = 10; i >= 0; i--) {
508 + r = z * r + pr1[i];
509 + s = z * s + ps1[i];
510 + }
511 + } else if (x > five) {
512 + r = pr2[11];
513 + s = ps2[11] + z * (ps2[12] + z * ps2[13]);
514 +
515 + for (i = 10; i >= 0; i--) {
516 + r = z * r + pr2[i];
517 + s = z * s + ps2[i];
518 + }
519 + } else if (x > 3.5L) {
520 + r = pr3[12];
521 + s = ps3[12];
522 +
523 + for (i = 11; i >= 0; i--) {
524 + r = z * r + pr3[i];
525 + s = z * s + ps3[i];
526 + }
527 + } else if (x > 2.5L) {
528 + r = pr4[12];
529 + s = ps4[12];
530 +
531 + for (i = 11; i >= 0; i--) {
532 + r = z * r + pr4[i];
533 + s = z * s + ps4[i];
534 + }
535 + } else if (x > (1.0L / 0.5625L)) {
536 + r = pr5[12];
537 + s = ps5[12];
538 +
539 + for (i = 11; i >= 0; i--) {
540 + r = z * r + pr5[i];
541 + s = z * s + ps5[i];
542 + }
543 + } else { /* assume x > 1.28 */
544 + r = pr6[12];
545 + s = ps6[12];
546 +
547 + for (i = 11; i >= 0; i--) {
548 + r = z * r + pr6[i];
549 + s = z * s + ps6[i];
550 + }
551 + }
475 552
553 + return (r / s);
554 +}
476 555 static const GENERIC qr0[12] = {
477 - 3.749999999999999999999999999999999971033e-0001L,
478 - 4.256726035237050601607682277433094262226e+0002L,
479 - 1.875976490812878489192409978945401066066e+0005L,
480 - 4.170314268048041914273603680317745592790e+0007L,
481 - 5.092750132543855817293451118974555746551e+0009L,
482 - 3.494749676278488654103505795794139483404e+0011L,
483 - 1.327062148257437316997667817096694173709e+0013L,
484 - 2.648993138273427226907503742066551150490e+0014L,
485 - 2.511695665909547412222430494473998127684e+0015L,
486 - 9.274694506662289043224310499164702306096e+0015L,
487 - 8.150904170663663829331320302911792892002e+0015L,
488 - -5.001918733707662355772037829620388765122e+0014L,
556 + 3.749999999999999999999999999999999971033e-0001L,
557 + 4.256726035237050601607682277433094262226e+0002L,
558 + 1.875976490812878489192409978945401066066e+0005L,
559 + 4.170314268048041914273603680317745592790e+0007L,
560 + 5.092750132543855817293451118974555746551e+0009L,
561 + 3.494749676278488654103505795794139483404e+0011L,
562 + 1.327062148257437316997667817096694173709e+0013L,
563 + 2.648993138273427226907503742066551150490e+0014L,
564 + 2.511695665909547412222430494473998127684e+0015L,
565 + 9.274694506662289043224310499164702306096e+0015L,
566 + 8.150904170663663829331320302911792892002e+0015L,
567 + -5.001918733707662355772037829620388765122e+0014L,
489 568 };
569 +
490 570 static const GENERIC qs0[11] = {
491 - 1.0e0L,
492 - 1.135400380229880160428715273982155760093e+0003L,
493 - 5.005701183877126164326765545516590744360e+0005L,
494 - 1.113444200113712167984337603933040102987e+0008L,
495 - 1.361074819925223062778717565699039471124e+0010L,
496 - 9.355750985802849484438933905325982809653e+0011L,
497 - 3.563462786008988825003965543857998084828e+0013L,
498 - 7.155145113900094163648726863803802910454e+0014L,
499 - 6.871266835834472758055559013851843654113e+0015L,
500 - 2.622030899226736712644974988157345234092e+0016L,
501 - 2.602912729172876330650077021706139707746e+0016L,
571 + 1.0e0L,
572 + 1.135400380229880160428715273982155760093e+0003L,
573 + 5.005701183877126164326765545516590744360e+0005L,
574 + 1.113444200113712167984337603933040102987e+0008L,
575 + 1.361074819925223062778717565699039471124e+0010L,
576 + 9.355750985802849484438933905325982809653e+0011L,
577 + 3.563462786008988825003965543857998084828e+0013L,
578 + 7.155145113900094163648726863803802910454e+0014L,
579 + 6.871266835834472758055559013851843654113e+0015L,
580 + 2.622030899226736712644974988157345234092e+0016L,
581 + 2.602912729172876330650077021706139707746e+0016L,
502 582 };
583 +
503 584 static const GENERIC qr1[12] = {
504 - 3.749999999999999999997762458207284405806e-0001L,
505 - 2.697883998881706839929255517498189980485e+0002L,
506 - 7.755195925781028489386938870473834411019e+0004L,
507 - 1.166777762104017777198211072895528968355e+0007L,
508 - 1.011504772984321168320010084520261069362e+0009L,
509 - 5.246007703574156853577754571720205550010e+0010L,
510 - 1.637692549885592683166116551691266537647e+0012L,
511 - 3.022303623698185669912990310925039382495e+0013L,
512 - 3.154769927290655684846107030265909987946e+0014L,
513 - 1.715819913441554770089730934808123360921e+0015L,
514 - 4.165044355759732622273534445131736188510e+0015L,
515 - 3.151381420874174705643100381708086287596e+0015L,
585 + 3.749999999999999999997762458207284405806e-0001L,
586 + 2.697883998881706839929255517498189980485e+0002L,
587 + 7.755195925781028489386938870473834411019e+0004L,
588 + 1.166777762104017777198211072895528968355e+0007L,
589 + 1.011504772984321168320010084520261069362e+0009L,
590 + 5.246007703574156853577754571720205550010e+0010L,
591 + 1.637692549885592683166116551691266537647e+0012L,
592 + 3.022303623698185669912990310925039382495e+0013L,
593 + 3.154769927290655684846107030265909987946e+0014L,
594 + 1.715819913441554770089730934808123360921e+0015L,
595 + 4.165044355759732622273534445131736188510e+0015L,
596 + 3.151381420874174705643100381708086287596e+0015L,
516 597 };
598 +
517 599 static const GENERIC qs1[14] = {
518 - 1.0e0L,
519 - 7.197091705351218239785633172408276982828e+0002L,
520 - 2.070012799599548685544883041297609861055e+0005L,
521 - 3.117014815317656221871840152778458754516e+0007L,
522 - 2.705719678902554974863325877025902971727e+0009L,
523 - 1.406113614727345726925060648750867264098e+0011L,
524 - 4.403777536067131320363005978631674817359e+0012L,
525 - 8.170725690209322283061499386703167242894e+0013L,
526 - 8.609458844975495289227794126964431210566e+0014L,
527 - 4.766766367015473481257280600694952920204e+0015L,
528 - 1.202286587943342194863557940888115641650e+0016L,
529 - 1.012474328306200909525063936061756024120e+0016L,
530 - 6.183552022678917858273222879615824070703e+0014L,
531 - -9.756731548558226997573737400988225722740e+0013L,
600 + 1.0e0L,
601 + 7.197091705351218239785633172408276982828e+0002L,
602 + 2.070012799599548685544883041297609861055e+0005L,
603 + 3.117014815317656221871840152778458754516e+0007L,
604 + 2.705719678902554974863325877025902971727e+0009L,
605 + 1.406113614727345726925060648750867264098e+0011L,
606 + 4.403777536067131320363005978631674817359e+0012L,
607 + 8.170725690209322283061499386703167242894e+0013L,
608 + 8.609458844975495289227794126964431210566e+0014L,
609 + 4.766766367015473481257280600694952920204e+0015L,
610 + 1.202286587943342194863557940888115641650e+0016L,
611 + 1.012474328306200909525063936061756024120e+0016L,
612 + 6.183552022678917858273222879615824070703e+0014L,
613 + -9.756731548558226997573737400988225722740e+0013L,
532 614 };
615 +
533 616 static const GENERIC qr2[12] = {
534 - 3.749999999999999481245647262226994293189e-0001L,
535 - 1.471366807289771354491181140167359026735e+0002L,
536 - 2.279432486768448220142080962843526951250e+0004L,
537 - 1.828943048523771225163804043356958285893e+0006L,
538 - 8.379828388647823135832220596417725010837e+0007L,
539 - 2.279814029335044024585393671278378022053e+0009L,
540 - 3.711653952257118120832817785271466441420e+0010L,
541 - 3.557650914518554549916730572553105048068e+0011L,
542 - 1.924583483146095896259774329498934160650e+0012L,
543 - 5.424386256063736390759567088291887140278e+0012L,
544 - 6.839325621241776786206509704671746841737e+0012L,
545 - 2.702169563144001166291686452305436313971e+0012L,
617 + 3.749999999999999481245647262226994293189e-0001L,
618 + 1.471366807289771354491181140167359026735e+0002L,
619 + 2.279432486768448220142080962843526951250e+0004L,
620 + 1.828943048523771225163804043356958285893e+0006L,
621 + 8.379828388647823135832220596417725010837e+0007L,
622 + 2.279814029335044024585393671278378022053e+0009L,
623 + 3.711653952257118120832817785271466441420e+0010L,
624 + 3.557650914518554549916730572553105048068e+0011L,
625 + 1.924583483146095896259774329498934160650e+0012L,
626 + 5.424386256063736390759567088291887140278e+0012L,
627 + 6.839325621241776786206509704671746841737e+0012L,
628 + 2.702169563144001166291686452305436313971e+0012L,
546 629 };
630 +
547 631 static const GENERIC qs2[14] = {
548 - 1.0e0L,
549 - 3.926379194439388135703211933895203191089e+0002L,
550 - 6.089148804106598297488336063007609312276e+0004L,
551 - 4.893546162973278583711376356041614150645e+0006L,
552 - 2.247571119114497845046388801813832219404e+0008L,
553 - 6.137635663350177751290469334200757872645e+0009L,
554 - 1.005115019784102856424493519524998953678e+0011L,
555 - 9.725664462014503832860151384604677240620e+0011L,
556 - 5.345525100485511116148634192844434636072e+0012L,
557 - 1.549944007398946691720862738173956994779e+0013L,
558 - 2.067148441178952625710302124163264760362e+0013L,
559 - 9.401565402641963611295119487242595462301e+0012L,
560 - 3.548217088622398274748837287769709374385e+0011L,
561 - -2.934470341719047120076509938432417352365e+0010L,
632 + 1.0e0L,
633 + 3.926379194439388135703211933895203191089e+0002L,
634 + 6.089148804106598297488336063007609312276e+0004L,
635 + 4.893546162973278583711376356041614150645e+0006L,
636 + 2.247571119114497845046388801813832219404e+0008L,
637 + 6.137635663350177751290469334200757872645e+0009L,
638 + 1.005115019784102856424493519524998953678e+0011L,
639 + 9.725664462014503832860151384604677240620e+0011L,
640 + 5.345525100485511116148634192844434636072e+0012L,
641 + 1.549944007398946691720862738173956994779e+0013L,
642 + 2.067148441178952625710302124163264760362e+0013L,
643 + 9.401565402641963611295119487242595462301e+0012L,
644 + 3.548217088622398274748837287769709374385e+0011L,
645 + -2.934470341719047120076509938432417352365e+0010L,
562 646 };
647 +
563 648 static const GENERIC qr3[13] = {
564 - 3.749999999999412724084579833297451472091e-0001L,
565 - 9.058478580291706212422978492938435582527e+0001L,
566 - 8.524056033161038750461083666711724381171e+0003L,
567 - 4.105967158629109427753434569223631014730e+0005L,
568 - 1.118326603378531348259783091972623333657e+0007L,
569 - 1.794636683403578918528064904714132329343e+0008L,
570 - 1.714314157463635959556133236004368896724e+0009L,
571 - 9.622092032236084846572067257267661456030e+0009L,
572 - 3.057759524485859159957762858780768355020e+0010L,
573 - 5.129306780754798531609621454415938890020e+0010L,
574 - 3.999122002794961070680636194346316041352e+0010L,
575 - 1.122298454643493485989721564358100345388e+0010L,
576 - 5.603981987645989709668830968522362582221e+0008L,
649 + 3.749999999999412724084579833297451472091e-0001L,
650 + 9.058478580291706212422978492938435582527e+0001L,
651 + 8.524056033161038750461083666711724381171e+0003L,
652 + 4.105967158629109427753434569223631014730e+0005L,
653 + 1.118326603378531348259783091972623333657e+0007L,
654 + 1.794636683403578918528064904714132329343e+0008L,
655 + 1.714314157463635959556133236004368896724e+0009L,
656 + 9.622092032236084846572067257267661456030e+0009L,
657 + 3.057759524485859159957762858780768355020e+0010L,
658 + 5.129306780754798531609621454415938890020e+0010L,
659 + 3.999122002794961070680636194346316041352e+0010L,
660 + 1.122298454643493485989721564358100345388e+0010L,
661 + 5.603981987645989709668830968522362582221e+0008L,
577 662 };
663 +
578 664 static const GENERIC qs3[13] = {
579 - 1.0e0L,
580 - 2.418328663076578169836155170053634419922e+0002L,
581 - 2.279620205900121042587523541281272875520e+0004L,
582 - 1.100984222585729521470129014992217092794e+0006L,
583 - 3.010743223679247091004262516286654516282e+0007L,
584 - 4.860925542827367817289619265215599433996e+0008L,
585 - 4.686668111035348691982715864307839581243e+0009L,
586 - 2.668701788405102017427214705946730894074e+0010L,
587 - 8.677395746106802640390580944836650584903e+0010L,
588 - 1.511936455574951790658498795945106643036e+0011L,
589 - 1.260845604432623478002018696873608353093e+0011L,
590 - 4.052692278419853853911440231600864589805e+0010L,
591 - 2.965516519212226064983267822243329694729e+0009L,
665 + 1.0e0L,
666 + 2.418328663076578169836155170053634419922e+0002L,
667 + 2.279620205900121042587523541281272875520e+0004L,
668 + 1.100984222585729521470129014992217092794e+0006L,
669 + 3.010743223679247091004262516286654516282e+0007L,
670 + 4.860925542827367817289619265215599433996e+0008L,
671 + 4.686668111035348691982715864307839581243e+0009L,
672 + 2.668701788405102017427214705946730894074e+0010L,
673 + 8.677395746106802640390580944836650584903e+0010L,
674 + 1.511936455574951790658498795945106643036e+0011L,
675 + 1.260845604432623478002018696873608353093e+0011L,
676 + 4.052692278419853853911440231600864589805e+0010L,
677 + 2.965516519212226064983267822243329694729e+0009L,
592 678 };
679 +
593 680 static const GENERIC qr4[13] = {
594 - 3.749999999919234164154669754440123072618e-0001L,
595 - 5.844218580776819864791168253485055101858e+0001L,
596 - 3.489273514092912982675669411371435670220e+0003L,
597 - 1.050523637774575684509663430018995479594e+0005L,
598 - 1.764549172059701565500717319792780115289e+0006L,
599 - 1.725532438844133795028063102681497371154e+0007L,
600 - 9.938114847359778539965140247590176334874e+0007L,
601 - 3.331710808184595545396883770200772842314e+0008L,
602 - 6.271970557641881511609560444872797282698e+0008L,
603 - 6.188529798677357075020774923903737913285e+0008L,
604 - 2.821905302742849974509982167877885011629e+0008L,
605 - 4.615467358646911976773290256984329814896e+0007L,
606 - 1.348140608731546467396685802693380693275e+0006L,
681 + 3.749999999919234164154669754440123072618e-0001L,
682 + 5.844218580776819864791168253485055101858e+0001L,
683 + 3.489273514092912982675669411371435670220e+0003L,
684 + 1.050523637774575684509663430018995479594e+0005L,
685 + 1.764549172059701565500717319792780115289e+0006L,
686 + 1.725532438844133795028063102681497371154e+0007L,
687 + 9.938114847359778539965140247590176334874e+0007L,
688 + 3.331710808184595545396883770200772842314e+0008L,
689 + 6.271970557641881511609560444872797282698e+0008L,
690 + 6.188529798677357075020774923903737913285e+0008L,
691 + 2.821905302742849974509982167877885011629e+0008L,
692 + 4.615467358646911976773290256984329814896e+0007L,
693 + 1.348140608731546467396685802693380693275e+0006L,
607 694 };
695 +
608 696 static const GENERIC qs4[13] = {
609 - 1.0e0L,
610 - 1.561192663112345185261418296389902133372e+0002L,
611 - 9.346678031144098270547225423124213083072e+0003L,
612 - 2.825851246482293547838023847601704751590e+0005L,
613 - 4.776572711622156091710902891124911556293e+0006L,
614 - 4.715106953717135402977938048006267859302e+0007L,
615 - 2.753962350894311316439652227611209035193e+0008L,
616 - 9.428501434615463207768964787500411575223e+0008L,
617 - 1.832650858775206787088236896454141572617e+0009L,
618 - 1.901697378939743226948920874296595242257e+0009L,
619 - 9.433322226854293780627188599226380812725e+0008L,
620 - 1.808520540608671608680284520798858587370e+0008L,
621 - 7.983342331736662753157217446919462398008e+0006L,
697 + 1.0e0L,
698 + 1.561192663112345185261418296389902133372e+0002L,
699 + 9.346678031144098270547225423124213083072e+0003L,
700 + 2.825851246482293547838023847601704751590e+0005L,
701 + 4.776572711622156091710902891124911556293e+0006L,
702 + 4.715106953717135402977938048006267859302e+0007L,
703 + 2.753962350894311316439652227611209035193e+0008L,
704 + 9.428501434615463207768964787500411575223e+0008L,
705 + 1.832650858775206787088236896454141572617e+0009L,
706 + 1.901697378939743226948920874296595242257e+0009L,
707 + 9.433322226854293780627188599226380812725e+0008L,
708 + 1.808520540608671608680284520798858587370e+0008L,
709 + 7.983342331736662753157217446919462398008e+0006L,
622 710 };
711 +
623 712 static const GENERIC qr5[13] = {
624 - 3.749999995331364437028988850515190446719e-0001L,
625 - 3.739356381766559882677514593041627547911e+0001L,
626 - 1.399562500629413529355265462912819802551e+0003L,
627 - 2.594154053098947925345332218062210111753e+0004L,
628 - 2.640149879297408640394163979394594318371e+0005L,
629 - 1.542471854873199142031889093591449397995e+0006L,
630 - 5.242272868972053374067572098992335425895e+0006L,
631 - 1.025834487769410221329633071426044839935e+0007L,
632 - 1.116553924239448940142230579060124209622e+0007L,
633 - 6.318076065595910176374916303525884653514e+0006L,
634 - 1.641218086168640408527639735915512881785e+0006L,
635 - 1.522369793529178644168813882912134706444e+0005L,
636 - 2.526530541062297200914180060208669584055e+0003L,
713 + 3.749999995331364437028988850515190446719e-0001L,
714 + 3.739356381766559882677514593041627547911e+0001L,
715 + 1.399562500629413529355265462912819802551e+0003L,
716 + 2.594154053098947925345332218062210111753e+0004L,
717 + 2.640149879297408640394163979394594318371e+0005L,
718 + 1.542471854873199142031889093591449397995e+0006L,
719 + 5.242272868972053374067572098992335425895e+0006L,
720 + 1.025834487769410221329633071426044839935e+0007L,
721 + 1.116553924239448940142230579060124209622e+0007L,
722 + 6.318076065595910176374916303525884653514e+0006L,
723 + 1.641218086168640408527639735915512881785e+0006L,
724 + 1.522369793529178644168813882912134706444e+0005L,
725 + 2.526530541062297200914180060208669584055e+0003L,
637 726 };
727 +
638 728 static const GENERIC qs5[13] = {
639 - 1.0e0L,
640 - 9.998960735935075380397545659016287506660e+0001L,
641 - 3.758767417842043742686475060540416737562e+0003L,
642 - 7.013652806952306520121959742519780781653e+0004L,
643 - 7.208949808818615099246529616211730446850e+0005L,
644 - 4.272753927109614455417836186072202009252e+0006L,
645 - 1.482524411356470699336129814111025434703e+0007L,
646 - 2.988750366665678233425279237627700803473e+0007L,
647 - 3.396957890261080492694709150553619185065e+0007L,
648 - 2.050652487738593004111578091156304540386e+0007L,
649 - 5.900504120811732547616511555946279451316e+0006L,
650 - 6.563391409260160897024498082273183468347e+0005L,
651 - 1.692629845012790205348966731477187041419e+0004L,
729 + 1.0e0L,
730 + 9.998960735935075380397545659016287506660e+0001L,
731 + 3.758767417842043742686475060540416737562e+0003L,
732 + 7.013652806952306520121959742519780781653e+0004L,
733 + 7.208949808818615099246529616211730446850e+0005L,
734 + 4.272753927109614455417836186072202009252e+0006L,
735 + 1.482524411356470699336129814111025434703e+0007L,
736 + 2.988750366665678233425279237627700803473e+0007L,
737 + 3.396957890261080492694709150553619185065e+0007L,
738 + 2.050652487738593004111578091156304540386e+0007L,
739 + 5.900504120811732547616511555946279451316e+0006L,
740 + 6.563391409260160897024498082273183468347e+0005L,
741 + 1.692629845012790205348966731477187041419e+0004L,
652 742 };
743 +
653 744 static const GENERIC qr6[13] = {
654 - 3.749999861516664133157566870858975421296e-0001L,
655 - 2.367863756747764863120797431599473468918e+0001L,
656 - 5.476715802114976248882067325630793143777e+0002L,
657 - 6.143190357869842894025012945444096170251e+0003L,
658 - 3.716250534677997850513733595140463851730e+0004L,
659 - 1.270883463823876752138326905022875657430e+0005L,
660 - 2.495301449636814481646371665429083801388e+0005L,
661 - 2.789578988212952248340486296254398601942e+0005L,
662 - 1.718247946911109055931819087137397324634e+0005L,
663 - 5.458973214011665714330326732204106364229e+0004L,
664 - 7.912102686687948786048943339759596652813e+0003L,
665 - 4.077961006160866935722030715149087938091e+0002L,
666 - 3.765206972770245085551057237882528510428e+0000L,
745 + 3.749999861516664133157566870858975421296e-0001L,
746 + 2.367863756747764863120797431599473468918e+0001L,
747 + 5.476715802114976248882067325630793143777e+0002L,
748 + 6.143190357869842894025012945444096170251e+0003L,
749 + 3.716250534677997850513733595140463851730e+0004L,
750 + 1.270883463823876752138326905022875657430e+0005L,
751 + 2.495301449636814481646371665429083801388e+0005L,
752 + 2.789578988212952248340486296254398601942e+0005L,
753 + 1.718247946911109055931819087137397324634e+0005L,
754 + 5.458973214011665714330326732204106364229e+0004L,
755 + 7.912102686687948786048943339759596652813e+0003L,
756 + 4.077961006160866935722030715149087938091e+0002L,
757 + 3.765206972770245085551057237882528510428e+0000L,
667 758 };
759 +
668 760 static const GENERIC qs6[13] = {
669 - 1.0e0L,
670 - 6.341646532940517305641893852673926809601e+0001L,
671 - 1.477058277414040790932597537920671025359e+0003L,
672 - 1.674406564031044491436044253393536487604e+0004L,
673 - 1.028516501369755949895050806908994650768e+0005L,
674 - 3.593620042532885295087463507733285434207e+0005L,
675 - 7.267924991381020915185873399453724799625e+0005L,
676 - 8.462277510768818399961191426205006083088e+0005L,
677 - 5.514399892230892163373611895645500250514e+0005L,
678 - 1.898084241009259353540620272932188102299e+0005L,
679 - 3.102941242117739015721984123081026253068e+0004L,
680 - 1.958971184431466907681440650181421086143e+0003L,
681 - 2.878853357310495087181721613889455121867e+0001L,
761 + 1.0e0L, 6.341646532940517305641893852673926809601e+0001L,
762 + 1.477058277414040790932597537920671025359e+0003L,
763 + 1.674406564031044491436044253393536487604e+0004L,
764 + 1.028516501369755949895050806908994650768e+0005L,
765 + 3.593620042532885295087463507733285434207e+0005L,
766 + 7.267924991381020915185873399453724799625e+0005L,
767 + 8.462277510768818399961191426205006083088e+0005L,
768 + 5.514399892230892163373611895645500250514e+0005L,
769 + 1.898084241009259353540620272932188102299e+0005L,
770 + 3.102941242117739015721984123081026253068e+0004L,
771 + 1.958971184431466907681440650181421086143e+0003L,
772 + 2.878853357310495087181721613889455121867e+0001L,
682 773 };
683 -static GENERIC qone(x)
684 -GENERIC x;
774 +
775 +static GENERIC
776 +qone(GENERIC x)
685 777 {
686 - GENERIC s,r,t,z;
778 + GENERIC s, r, t, z;
687 779 int i;
688 - if (x>huge) return 0.375L/x;
689 - t = one/x; z = t*t;
690 - if (x>sixteen) {
691 - r = z*qr0[11]+qr0[10]; s = qs0[10];
692 - for (i=9;i>=0;i--) {
693 - r = z*r + qr0[i];
694 - s = z*s + qs0[i];
695 - }
696 - } else if (x>eight) {
697 - r = qr1[11]; s = qs1[11]+z*(qs1[12]+z*qs1[13]);
698 - for (i=10;i>=0;i--) {
699 - r = z*r + qr1[i];
700 - s = z*s + qs1[i];
701 - }
702 - } else if (x>five) { /* x > 5.0 */
703 - r = qr2[11]; s = qs2[11]+z*(qs2[12]+z*qs2[13]);
704 - for (i=10;i>=0;i--) {
705 - r = z*r + qr2[i];
706 - s = z*s + qs2[i];
707 - }
708 - } else if (x>3.5L) {
709 - r = qr3[12]; s = qs3[12];
710 - for (i=11;i>=0;i--) {
711 - r = z*r + qr3[i];
712 - s = z*s + qs3[i];
713 - }
714 - } else if (x>2.5L) {
715 - r = qr4[12]; s = qs4[12];
716 - for (i=11;i>=0;i--) {
717 - r = z*r + qr4[i];
718 - s = z*s + qs4[i];
719 - }
720 - } else if (x> (1.0L/0.5625L)) {
721 - r = qr5[12]; s = qs5[12];
722 - for (i=11;i>=0;i--) {
723 - r = z*r + qr5[i];
724 - s = z*s + qs5[i];
725 - }
726 - } else { /* assume x > 1.28 */
727 - r = qr6[12]; s = qs6[12];
728 - for (i=11;i>=0;i--) {
729 - r = z*r + qr6[i];
730 - s = z*s + qs6[i];
731 - }
732 - }
733 - return t*(r/s);
780 +
781 + if (x > huge)
782 + return (0.375L / x);
783 +
784 + t = one / x;
785 + z = t * t;
786 +
787 + if (x > sixteen) {
788 + r = z * qr0[11] + qr0[10];
789 + s = qs0[10];
790 +
791 + for (i = 9; i >= 0; i--) {
792 + r = z * r + qr0[i];
793 + s = z * s + qs0[i];
794 + }
795 + } else if (x > eight) {
796 + r = qr1[11];
797 + s = qs1[11] + z * (qs1[12] + z * qs1[13]);
798 +
799 + for (i = 10; i >= 0; i--) {
800 + r = z * r + qr1[i];
801 + s = z * s + qs1[i];
802 + }
803 + } else if (x > five) { /* x > 5.0 */
804 + r = qr2[11];
805 + s = qs2[11] + z * (qs2[12] + z * qs2[13]);
806 +
807 + for (i = 10; i >= 0; i--) {
808 + r = z * r + qr2[i];
809 + s = z * s + qs2[i];
810 + }
811 + } else if (x > 3.5L) {
812 + r = qr3[12];
813 + s = qs3[12];
814 +
815 + for (i = 11; i >= 0; i--) {
816 + r = z * r + qr3[i];
817 + s = z * s + qs3[i];
818 + }
819 + } else if (x > 2.5L) {
820 + r = qr4[12];
821 + s = qs4[12];
822 +
823 + for (i = 11; i >= 0; i--) {
824 + r = z * r + qr4[i];
825 + s = z * s + qs4[i];
826 + }
827 + } else if (x > (1.0L / 0.5625L)) {
828 + r = qr5[12];
829 + s = qs5[12];
830 +
831 + for (i = 11; i >= 0; i--) {
832 + r = z * r + qr5[i];
833 + s = z * s + qs5[i];
834 + }
835 + } else { /* assume x > 1.28 */
836 + r = qr6[12];
837 + s = qs6[12];
838 +
839 + for (i = 11; i >= 0; i--) {
840 + r = z * r + qr6[i];
841 + s = z * s + qs6[i];
842 + }
843 + }
844 +
845 + return (t * (r / s));
734 846 }
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