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11210 libm should be cstyle(1ONBLD) clean
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--- old/usr/src/lib/libm/common/complex/k_atan2l.c
+++ new/usr/src/lib/libm/common/complex/k_atan2l.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
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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.
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 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
23 24 */
25 +
24 26 /*
25 27 * Copyright 2005 Sun Microsystems, Inc. All rights reserved.
26 28 * Use is subject to license terms.
27 29 */
28 30
29 -#include "libm.h" /* __k_atan2l */
31 +#include "libm.h" /* __k_atan2l */
30 32 #include "complex_wrapper.h"
31 33
32 34 #if defined(__sparc)
33 -#define HALF(x) ((int *) &x)[3] = 0; ((int *) &x)[2] &= 0xfe000000
35 +#define HALF(x) ((int *)&x)[3] = 0; ((int *)&x)[2] &= 0xfe000000
34 36 #elif defined(__x86)
35 -#define HALF(x) ((int *) &x)[0] = 0
37 +#define HALF(x) ((int *)&x)[0] = 0
36 38 #endif
37 39
38 40 /*
39 41 * long double __k_atan2l(long double y, long double x, long double *e)
40 42 *
41 43 * Compute atan2l with error terms.
42 44 *
43 45 * Important formula:
44 46 * 3 5
45 47 * x x
46 48 * atan(x) = x - ----- + ----- - ... (for x <= 1)
47 49 * 3 5
48 50 *
49 51 * pi 1 1
50 52 * = --- - --- + --- - ... (for x > 1)
51 53 * 3
52 54 * 2 x 3x
53 55 *
54 56 * Arg(x + y i) = sign(y) * atan2(|y|, x)
55 57 * = sign(y) * atan(|y|/x) (for x > 0)
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56 58 * sign(y) * (PI - atan(|y|/|x|)) (for x < 0)
57 59 * Thus if x >> y (IEEE double: EXP(x) - EXP(y) >= 60):
58 60 * 1. (x > 0): atan2(y,x) ~ y/x
59 61 * 2. (x < 0): atan2(y,x) ~ sign(y) (PI - |y/x|))
60 62 * Otherwise if x << y:
61 63 * atan2(y,x) ~ sign(y)*PI/2 - x/y
62 64 *
63 65 * __k_atan2l call static functions mx_polyl, mx_atanl
64 66 */
65 67
66 -
67 68 /*
68 69 * (void) mx_polyl (long double *z, long double *a, long double *e, int n)
69 70 * return
70 71 * e = a + z*(a + z*(a + ... z*(a + e)...))
71 72 * 0 2 4 2n
72 73 * Note:
73 74 * 1. e and coefficient ai are represented by two long double numbers.
74 75 * For e, the first one contain the leading 53 bits (30 for x86 exteneded)
75 76 * and the second one contain the remaining 113 bits (64 for x86 extended).
76 77 * For ai, the first one contian the leading 53 bits (or 30 for x86)
77 78 * rounded, and the second is the remaining 113 bits (or 64 for x86).
78 79 * 2. z is an array of three doubles.
79 - * z[0] : the rounded value of Z (the intended value of z)
80 - * z[1] : the leading 32 (or 56) bits of Z rounded
81 - * z[2] : the remaining 113 (or 64) bits of Z
80 + * z[0] : the rounded value of Z (the intended value of z)
81 + * z[1] : the leading 32 (or 56) bits of Z rounded
82 + * z[2] : the remaining 113 (or 64) bits of Z
82 83 * Note that z[0] = z[1]+z[2] rounded.
83 84 *
84 85 */
85 -
86 86 static void
87 -mx_polyl(const long double *z, const long double *a, long double *e, int n) {
87 +mx_polyl(const long double *z, const long double *a, long double *e, int n)
88 +{
88 89 long double r, s, t, p_h, p_l, z_h, z_l, p, w;
89 90 int i;
91 +
90 92 n = n + n;
91 93 p = e[0] + a[n];
92 94 p_l = a[n + 1];
93 - w = p; HALF(w);
95 + w = p;
96 + HALF(w);
94 97 p_h = w;
95 - p = a[n - 2] + z[0] * p;
96 - z_h = z[1]; z_l = z[2];
98 + p = a[n - 2] + z[0] * p;
99 + z_h = z[1];
100 + z_l = z[2];
97 101 p_l += e[0] - (p_h - a[n]);
98 102
99 103 for (i = n - 2; i >= 2; i -= 2) {
100 -
101 - /* compute p = ai + z * p */
104 + /* compute p = ai + z * p */
102 105 t = z_h * p_h;
103 106 s = z[0] * p_l + p_h * z_l;
104 - w = p; HALF(w);
107 + w = p;
108 + HALF(w);
105 109 p_h = w;
106 - s += a[i + 1];
107 - r = t - (p_h - a[i]);
108 - p = a[i - 2] + z[0] * p;
110 + s += a[i + 1];
111 + r = t - (p_h - a[i]);
112 + p = a[i - 2] + z[0] * p;
109 113 p_l = r + s;
110 114 }
111 - w = p; HALF(w);
115 +
116 + w = p;
117 + HALF(w);
112 118 e[0] = w;
113 - t = z_h * p_h;
114 - s = z[0] * p_l + p_h * z_l;
115 - r = t - (e[0] - a[0]);
119 + t = z_h * p_h;
120 + s = z[0] * p_l + p_h * z_l;
121 + r = t - (e[0] - a[0]);
116 122 e[1] = r + s;
117 123 }
118 124
119 125 /*
120 126 * Table of constants for atan from 0.125 to 8
121 127 * 0.125 -- 0x3ffc0000 --- (increment at bit 12)
122 128 * 0x3ffc1000
123 129 * 0x3ffc2000
124 130 * ... ...
125 131 * 0x4001f000
126 132 * 8.000 -- 0x40020000 (total: 97)
127 133 */
128 134
129 135 static const long double TBL_atan_hil[] = {
130 136 #if defined(__sparc)
131 -1.2435499454676143503135484916387102416568e-01L,
132 -1.3203976161463874927468440652656953226250e-01L,
133 -1.3970887428916364518336777673909505681607e-01L,
134 -1.4736148108865163560980276039684551821066e-01L,
135 -1.5499674192394098230371437493349219133371e-01L,
136 -1.6261382859794857537364156376155780062019e-01L,
137 -1.7021192528547440449049660709976171369543e-01L,
138 -1.7779022899267607079662479921582468899456e-01L,
139 -1.8534794999569476488602596122854464667261e-01L,
140 -1.9288431225797466419705871069022730349878e-01L,
141 -2.0039855382587851465394578503437838446153e-01L,
142 -2.0788992720226299360533498310299432475629e-01L,
143 -2.1535769969773804802445962716648964165745e-01L,
144 -2.2280115375939451577103212214043255525024e-01L,
145 -2.3021958727684373024017095967980299065551e-01L,
146 -2.3761231386547125247388363432563777919892e-01L,
147 -2.4497866312686415417208248121127580641959e-01L,
148 -2.5962962940825753102994644318397190560106e-01L,
149 -2.7416745111965879759937189834217578592444e-01L,
150 -2.8858736189407739562361141995821834504332e-01L,
151 -3.0288486837497140556055609450555821812277e-01L,
152 -3.1705575320914700980901557667446732975852e-01L,
153 -3.3109607670413209494433878775694455421259e-01L,
154 -3.4500217720710510886768128690005168408290e-01L,
155 -3.5877067027057222039592006392646052215363e-01L,
156 -3.7239844667675422192365503828370182641413e-01L,
157 -3.8588266939807377589769548460723139638186e-01L,
158 -3.9922076957525256561471669615886476491104e-01L,
159 -4.1241044159738730689979128966712694260920e-01L,
160 -4.2544963737004228954226360518079233013817e-01L,
161 -4.3833655985795780544561604921477130895882e-01L,
162 -4.5106965598852347637563925728219344073798e-01L,
163 -4.6364760900080611621425623146121439713344e-01L,
164 -4.8833395105640552386716496074706484459644e-01L,
165 -5.1238946031073770666660102058425923805558e-01L,
166 -5.3581123796046370026908506870769144698471e-01L,
167 -5.5859931534356243597150821640166122875873e-01L,
168 -5.8075635356767039920327447500150082375122e-01L,
169 -6.0228734613496418168212269420423291922459e-01L,
170 -6.2319932993406593099247534906037459367793e-01L,
171 -6.4350110879328438680280922871732260447265e-01L,
172 -6.6320299270609325536325431023827583417226e-01L,
173 -6.8231655487474807825642998171115298784729e-01L,
174 -7.0085440788445017245795128178675127318623e-01L,
175 -7.1882999962162450541701415152590469891043e-01L,
176 -7.3625742898142813174283527108914662479274e-01L,
177 -7.5315128096219438952473937026902888600575e-01L,
178 -7.6952648040565826040682003598565401726598e-01L,
179 -7.8539816339744830961566084581987569936977e-01L,
180 -8.1569192331622341102146083874564582672284e-01L,
181 -8.4415398611317100251784414827164746738632e-01L,
182 -8.7090345707565295314017311259781407291650e-01L,
183 -8.9605538457134395617480071802993779546602e-01L,
184 -9.1971960535041681722860345482108940969311e-01L,
185 -9.4200004037946366473793717053459362115891e-01L,
186 -9.6299433068093620181519583599709989677298e-01L,
187 -9.8279372324732906798571061101466603762572e-01L,
188 -1.0014831356942347329183295953014374896343e+00L,
189 -1.0191413442663497346383429170230636212354e+00L,
190 -1.0358412530088001765846944703254440735476e+00L,
191 -1.0516502125483736674598673120862999026920e+00L,
192 -1.0666303653157435630791763474202799086015e+00L,
193 -1.0808390005411683108871567292171997859003e+00L,
194 -1.0943289073211899198927883146102352763033e+00L,
195 -1.1071487177940905030170654601785370497543e+00L,
196 -1.1309537439791604464709335155363277560026e+00L,
197 -1.1525719972156675180401498626127514672834e+00L,
198 -1.1722738811284763866005949441337046006865e+00L,
199 -1.1902899496825317329277337748293182803384e+00L,
200 -1.2068173702852525303955115800565576625682e+00L,
201 -1.2220253232109896370417417439225704120294e+00L,
202 -1.2360594894780819419094519711090786146210e+00L,
203 -1.2490457723982544258299170772810900483550e+00L,
204 -1.2610933822524404193139408812473357640124e+00L,
205 -1.2722973952087173412961937498224805746463e+00L,
206 -1.2827408797442707473628852511364955164072e+00L,
207 -1.2924966677897852679030914214070816723528e+00L,
208 -1.3016288340091961438047858503666855024453e+00L,
209 -1.3101939350475556342564376891719053437537e+00L,
210 -1.3182420510168370498593302023271363040427e+00L,
211 -1.3258176636680324650592392104284756886164e+00L,
212 -1.3397056595989995393283037525895557850243e+00L,
213 -1.3521273809209546571891479413898127598774e+00L,
214 -1.3633001003596939542892985278250991560269e+00L,
215 -1.3734007669450158608612719264449610604836e+00L,
216 -1.3825748214901258580599674177685685163955e+00L,
217 -1.3909428270024183486427686943836432395486e+00L,
218 -1.3986055122719575950126700816114282727858e+00L,
219 -1.4056476493802697809521934019958080664406e+00L,
220 -1.4121410646084952153676136718584890852820e+00L,
221 -1.4181469983996314594038603039700988632607e+00L,
222 -1.4237179714064941189018190466107297108905e+00L,
223 -1.4288992721907326964184700745371984001389e+00L,
224 -1.4337301524847089866404719096698873880264e+00L,
225 -1.4382447944982225979614042479354816039669e+00L,
226 -1.4424730991091018200252920599377291810352e+00L,
227 -1.4464413322481351841999668424758803866109e+00L,
137 + 1.2435499454676143503135484916387102416568e-01L,
138 + 1.3203976161463874927468440652656953226250e-01L,
139 + 1.3970887428916364518336777673909505681607e-01L,
140 + 1.4736148108865163560980276039684551821066e-01L,
141 + 1.5499674192394098230371437493349219133371e-01L,
142 + 1.6261382859794857537364156376155780062019e-01L,
143 + 1.7021192528547440449049660709976171369543e-01L,
144 + 1.7779022899267607079662479921582468899456e-01L,
145 + 1.8534794999569476488602596122854464667261e-01L,
146 + 1.9288431225797466419705871069022730349878e-01L,
147 + 2.0039855382587851465394578503437838446153e-01L,
148 + 2.0788992720226299360533498310299432475629e-01L,
149 + 2.1535769969773804802445962716648964165745e-01L,
150 + 2.2280115375939451577103212214043255525024e-01L,
151 + 2.3021958727684373024017095967980299065551e-01L,
152 + 2.3761231386547125247388363432563777919892e-01L,
153 + 2.4497866312686415417208248121127580641959e-01L,
154 + 2.5962962940825753102994644318397190560106e-01L,
155 + 2.7416745111965879759937189834217578592444e-01L,
156 + 2.8858736189407739562361141995821834504332e-01L,
157 + 3.0288486837497140556055609450555821812277e-01L,
158 + 3.1705575320914700980901557667446732975852e-01L,
159 + 3.3109607670413209494433878775694455421259e-01L,
160 + 3.4500217720710510886768128690005168408290e-01L,
161 + 3.5877067027057222039592006392646052215363e-01L,
162 + 3.7239844667675422192365503828370182641413e-01L,
163 + 3.8588266939807377589769548460723139638186e-01L,
164 + 3.9922076957525256561471669615886476491104e-01L,
165 + 4.1241044159738730689979128966712694260920e-01L,
166 + 4.2544963737004228954226360518079233013817e-01L,
167 + 4.3833655985795780544561604921477130895882e-01L,
168 + 4.5106965598852347637563925728219344073798e-01L,
169 + 4.6364760900080611621425623146121439713344e-01L,
170 + 4.8833395105640552386716496074706484459644e-01L,
171 + 5.1238946031073770666660102058425923805558e-01L,
172 + 5.3581123796046370026908506870769144698471e-01L,
173 + 5.5859931534356243597150821640166122875873e-01L,
174 + 5.8075635356767039920327447500150082375122e-01L,
175 + 6.0228734613496418168212269420423291922459e-01L,
176 + 6.2319932993406593099247534906037459367793e-01L,
177 + 6.4350110879328438680280922871732260447265e-01L,
178 + 6.6320299270609325536325431023827583417226e-01L,
179 + 6.8231655487474807825642998171115298784729e-01L,
180 + 7.0085440788445017245795128178675127318623e-01L,
181 + 7.1882999962162450541701415152590469891043e-01L,
182 + 7.3625742898142813174283527108914662479274e-01L,
183 + 7.5315128096219438952473937026902888600575e-01L,
184 + 7.6952648040565826040682003598565401726598e-01L,
185 + 7.8539816339744830961566084581987569936977e-01L,
186 + 8.1569192331622341102146083874564582672284e-01L,
187 + 8.4415398611317100251784414827164746738632e-01L,
188 + 8.7090345707565295314017311259781407291650e-01L,
189 + 8.9605538457134395617480071802993779546602e-01L,
190 + 9.1971960535041681722860345482108940969311e-01L,
191 + 9.4200004037946366473793717053459362115891e-01L,
192 + 9.6299433068093620181519583599709989677298e-01L,
193 + 9.8279372324732906798571061101466603762572e-01L,
194 + 1.0014831356942347329183295953014374896343e+00L,
195 + 1.0191413442663497346383429170230636212354e+00L,
196 + 1.0358412530088001765846944703254440735476e+00L,
197 + 1.0516502125483736674598673120862999026920e+00L,
198 + 1.0666303653157435630791763474202799086015e+00L,
199 + 1.0808390005411683108871567292171997859003e+00L,
200 + 1.0943289073211899198927883146102352763033e+00L,
201 + 1.1071487177940905030170654601785370497543e+00L,
202 + 1.1309537439791604464709335155363277560026e+00L,
203 + 1.1525719972156675180401498626127514672834e+00L,
204 + 1.1722738811284763866005949441337046006865e+00L,
205 + 1.1902899496825317329277337748293182803384e+00L,
206 + 1.2068173702852525303955115800565576625682e+00L,
207 + 1.2220253232109896370417417439225704120294e+00L,
208 + 1.2360594894780819419094519711090786146210e+00L,
209 + 1.2490457723982544258299170772810900483550e+00L,
210 + 1.2610933822524404193139408812473357640124e+00L,
211 + 1.2722973952087173412961937498224805746463e+00L,
212 + 1.2827408797442707473628852511364955164072e+00L,
213 + 1.2924966677897852679030914214070816723528e+00L,
214 + 1.3016288340091961438047858503666855024453e+00L,
215 + 1.3101939350475556342564376891719053437537e+00L,
216 + 1.3182420510168370498593302023271363040427e+00L,
217 + 1.3258176636680324650592392104284756886164e+00L,
218 + 1.3397056595989995393283037525895557850243e+00L,
219 + 1.3521273809209546571891479413898127598774e+00L,
220 + 1.3633001003596939542892985278250991560269e+00L,
221 + 1.3734007669450158608612719264449610604836e+00L,
222 + 1.3825748214901258580599674177685685163955e+00L,
223 + 1.3909428270024183486427686943836432395486e+00L,
224 + 1.3986055122719575950126700816114282727858e+00L,
225 + 1.4056476493802697809521934019958080664406e+00L,
226 + 1.4121410646084952153676136718584890852820e+00L,
227 + 1.4181469983996314594038603039700988632607e+00L,
228 + 1.4237179714064941189018190466107297108905e+00L,
229 + 1.4288992721907326964184700745371984001389e+00L,
230 + 1.4337301524847089866404719096698873880264e+00L,
231 + 1.4382447944982225979614042479354816039669e+00L,
232 + 1.4424730991091018200252920599377291810352e+00L,
233 + 1.4464413322481351841999668424758803866109e+00L,
228 234 #elif defined(__x86)
229 -1.243549945356789976358413696289e-01L, 1.320397615781985223293304443359e-01L,
230 -1.397088742814958095550537109375e-01L, 1.473614810383878648281097412109e-01L,
231 -1.549967419123277068138122558594e-01L, 1.626138285500928759574890136719e-01L,
232 -1.702119252295233309268951416016e-01L, 1.777902289759367704391479492188e-01L,
233 -1.853479499695822596549987792969e-01L, 1.928843122441321611404418945312e-01L,
234 -2.003985538030974566936492919922e-01L, 2.078899272019043564796447753906e-01L,
235 -2.153576996643096208572387695312e-01L, 2.228011537226848304271697998047e-01L,
236 -2.302195872762240469455718994141e-01L, 2.376123138237744569778442382812e-01L,
237 -2.449786631041206419467926025391e-01L, 2.596296293195337057113647460938e-01L,
238 -2.741674510762095451354980468750e-01L, 2.885873618070036172866821289062e-01L,
239 -3.028848683461546897888183593750e-01L, 3.170557531993836164474487304688e-01L,
240 -3.310960766393691301345825195312e-01L, 3.450021771714091300964355468750e-01L,
241 -3.587706702528521418571472167969e-01L, 3.723984466632828116416931152344e-01L,
242 -3.858826693613082170486450195312e-01L, 3.992207695264369249343872070312e-01L,
243 -4.124104415532201528549194335938e-01L, 4.254496373469009995460510253906e-01L,
244 -4.383365598041564226150512695312e-01L, 4.510696559445932507514953613281e-01L,
245 -4.636476089945062994956970214844e-01L, 4.883339509833604097366333007812e-01L,
246 -5.123894601128995418548583984375e-01L, 5.358112377580255270004272460938e-01L,
247 -5.585993151180446147918701171875e-01L, 5.807563534472137689590454101562e-01L,
248 -6.022873460315167903900146484375e-01L, 6.231993297114968299865722656250e-01L,
249 -6.435011087451130151748657226562e-01L, 6.632029926404356956481933593750e-01L,
250 -6.823165547102689743041992187500e-01L, 7.008544078562408685684204101562e-01L,
251 -7.188299994450062513351440429688e-01L, 7.362574287690222263336181640625e-01L,
252 -7.531512808054685592651367187500e-01L, 7.695264802314341068267822265625e-01L,
253 -7.853981633670628070831298828125e-01L, 8.156919232569634914398193359375e-01L,
254 -8.441539860796183347702026367188e-01L, 8.709034570492804050445556640625e-01L,
255 -8.960553845390677452087402343750e-01L, 9.197196052409708499908447265625e-01L,
256 -9.420000403188169002532958984375e-01L, 9.629943305626511573791503906250e-01L,
257 -9.827937232330441474914550781250e-01L, 1.001483135391026735305786132812e+00L,
258 -1.019141343887895345687866210938e+00L, 1.035841252654790878295898437500e+00L,
259 -1.051650212146341800689697265625e+00L, 1.066630364861339330673217773438e+00L,
260 -1.080839000176638364791870117188e+00L, 1.094328907318413257598876953125e+00L,
261 -1.107148717623203992843627929688e+00L, 1.130953743588179349899291992188e+00L,
262 -1.152571997139602899551391601562e+00L, 1.172273880802094936370849609375e+00L,
263 -1.190289949532598257064819335938e+00L, 1.206817369908094406127929687500e+00L,
264 -1.222025323193520307540893554688e+00L, 1.236059489194303750991821289062e+00L,
265 -1.249045772012323141098022460938e+00L, 1.261093381792306900024414062500e+00L,
266 -1.272297394927591085433959960938e+00L, 1.282740879338234663009643554688e+00L,
267 -1.292496667709201574325561523438e+00L, 1.301628833636641502380371093750e+00L,
268 -1.310193934943526983261108398438e+00L, 1.318242050707340240478515625000e+00L,
269 -1.325817663222551345825195312500e+00L, 1.339705659542232751846313476562e+00L,
270 -1.352127380669116973876953125000e+00L, 1.363300099968910217285156250000e+00L,
271 -1.373400766868144273757934570312e+00L, 1.382574821356683969497680664062e+00L,
272 -1.390942826867103576660156250000e+00L, 1.398605511989444494247436523438e+00L,
273 -1.405647648964077234268188476562e+00L, 1.412141064181923866271972656250e+00L,
274 -1.418146998155862092971801757812e+00L, 1.423717970959842205047607421875e+00L,
275 -1.428899271879345178604125976562e+00L, 1.433730152435600757598876953125e+00L,
276 -1.438244794495403766632080078125e+00L, 1.442473099101334810256958007812e+00L,
277 -1.446441331878304481506347656250e+00L,
235 + 1.243549945356789976358413696289e-01L,
236 + 1.320397615781985223293304443359e-01L,
237 + 1.397088742814958095550537109375e-01L,
238 + 1.473614810383878648281097412109e-01L,
239 + 1.549967419123277068138122558594e-01L,
240 + 1.626138285500928759574890136719e-01L,
241 + 1.702119252295233309268951416016e-01L,
242 + 1.777902289759367704391479492188e-01L,
243 + 1.853479499695822596549987792969e-01L,
244 + 1.928843122441321611404418945312e-01L,
245 + 2.003985538030974566936492919922e-01L,
246 + 2.078899272019043564796447753906e-01L,
247 + 2.153576996643096208572387695312e-01L,
248 + 2.228011537226848304271697998047e-01L,
249 + 2.302195872762240469455718994141e-01L,
250 + 2.376123138237744569778442382812e-01L,
251 + 2.449786631041206419467926025391e-01L,
252 + 2.596296293195337057113647460938e-01L,
253 + 2.741674510762095451354980468750e-01L,
254 + 2.885873618070036172866821289062e-01L,
255 + 3.028848683461546897888183593750e-01L,
256 + 3.170557531993836164474487304688e-01L,
257 + 3.310960766393691301345825195312e-01L,
258 + 3.450021771714091300964355468750e-01L,
259 + 3.587706702528521418571472167969e-01L,
260 + 3.723984466632828116416931152344e-01L,
261 + 3.858826693613082170486450195312e-01L,
262 + 3.992207695264369249343872070312e-01L,
263 + 4.124104415532201528549194335938e-01L,
264 + 4.254496373469009995460510253906e-01L,
265 + 4.383365598041564226150512695312e-01L,
266 + 4.510696559445932507514953613281e-01L,
267 + 4.636476089945062994956970214844e-01L,
268 + 4.883339509833604097366333007812e-01L,
269 + 5.123894601128995418548583984375e-01L,
270 + 5.358112377580255270004272460938e-01L,
271 + 5.585993151180446147918701171875e-01L,
272 + 5.807563534472137689590454101562e-01L,
273 + 6.022873460315167903900146484375e-01L,
274 + 6.231993297114968299865722656250e-01L,
275 + 6.435011087451130151748657226562e-01L,
276 + 6.632029926404356956481933593750e-01L,
277 + 6.823165547102689743041992187500e-01L,
278 + 7.008544078562408685684204101562e-01L,
279 + 7.188299994450062513351440429688e-01L,
280 + 7.362574287690222263336181640625e-01L,
281 + 7.531512808054685592651367187500e-01L,
282 + 7.695264802314341068267822265625e-01L,
283 + 7.853981633670628070831298828125e-01L,
284 + 8.156919232569634914398193359375e-01L,
285 + 8.441539860796183347702026367188e-01L,
286 + 8.709034570492804050445556640625e-01L,
287 + 8.960553845390677452087402343750e-01L,
288 + 9.197196052409708499908447265625e-01L,
289 + 9.420000403188169002532958984375e-01L,
290 + 9.629943305626511573791503906250e-01L,
291 + 9.827937232330441474914550781250e-01L,
292 + 1.001483135391026735305786132812e+00L,
293 + 1.019141343887895345687866210938e+00L,
294 + 1.035841252654790878295898437500e+00L,
295 + 1.051650212146341800689697265625e+00L,
296 + 1.066630364861339330673217773438e+00L,
297 + 1.080839000176638364791870117188e+00L,
298 + 1.094328907318413257598876953125e+00L,
299 + 1.107148717623203992843627929688e+00L,
300 + 1.130953743588179349899291992188e+00L,
301 + 1.152571997139602899551391601562e+00L,
302 + 1.172273880802094936370849609375e+00L,
303 + 1.190289949532598257064819335938e+00L,
304 + 1.206817369908094406127929687500e+00L,
305 + 1.222025323193520307540893554688e+00L,
306 + 1.236059489194303750991821289062e+00L,
307 + 1.249045772012323141098022460938e+00L,
308 + 1.261093381792306900024414062500e+00L,
309 + 1.272297394927591085433959960938e+00L,
310 + 1.282740879338234663009643554688e+00L,
311 + 1.292496667709201574325561523438e+00L,
312 + 1.301628833636641502380371093750e+00L,
313 + 1.310193934943526983261108398438e+00L,
314 + 1.318242050707340240478515625000e+00L,
315 + 1.325817663222551345825195312500e+00L,
316 + 1.339705659542232751846313476562e+00L,
317 + 1.352127380669116973876953125000e+00L,
318 + 1.363300099968910217285156250000e+00L,
319 + 1.373400766868144273757934570312e+00L,
320 + 1.382574821356683969497680664062e+00L,
321 + 1.390942826867103576660156250000e+00L,
322 + 1.398605511989444494247436523438e+00L,
323 + 1.405647648964077234268188476562e+00L,
324 + 1.412141064181923866271972656250e+00L,
325 + 1.418146998155862092971801757812e+00L,
326 + 1.423717970959842205047607421875e+00L,
327 + 1.428899271879345178604125976562e+00L,
328 + 1.433730152435600757598876953125e+00L,
329 + 1.438244794495403766632080078125e+00L,
330 + 1.442473099101334810256958007812e+00L,
331 + 1.446441331878304481506347656250e+00L,
278 332 #endif
279 333 };
334 +
280 335 static const long double TBL_atan_lol[] = {
281 336 #if defined(__sparc)
282 -1.4074869197628063802317202820414310039556e-36L,
283 --4.9596961594739925555730439437999675295505e-36L,
284 -8.9527745625194648873931213446361849472788e-36L,
285 -1.1880437423207895718180765843544965589427e-35L,
286 --2.7810278112045145378425375128234365381448e-37L,
287 -1.4797220377023800327295536234315147262387e-36L,
288 --4.2169561400548198732870384801849639863829e-36L,
289 -7.2431229666913484649930323656316023494680e-36L,
290 --2.1573430089839170299895679353790663182462e-36L,
291 --9.9515745405126723554452367298128605186305e-36L,
292 --3.9065558992324838181617569730397882363067e-36L,
293 -5.5260292271793726813211980664661124518807e-36L,
294 -8.8415722215914321807682254318036452043689e-36L,
295 --8.1767728791586179254193323628285599800711e-36L,
296 --1.3344123034656142243797113823028330070762e-36L,
297 --4.4927331207813382908930733924681325892188e-36L,
298 -4.4945511471812490393201824336762495687730e-36L,
299 --1.6688081504279223555776724459648440567274e-35L,
300 -1.5629757586107955769461086568937329684113e-35L,
301 --2.2389835563308078552507970385331510848109e-35L,
302 --4.8312321745547311551870450671182151367050e-36L,
303 --1.4336172352905832876958926610980698844309e-35L,
304 --8.7440181998899932802989174170960593316080e-36L,
305 -5.9284636008529837445780360785464550143016e-36L,
306 --2.2376651248436241276061055295043514993630e-35L,
307 -6.0745837599336105414280310756677442136480e-36L,
308 -1.5372187110451949677792344762029967023093e-35L,
309 -2.0976068056751156241657121582478790247159e-35L,
310 --5.5623956405495438060726862202622807523700e-36L,
311 -1.9697366707832471841858411934897351901523e-35L,
312 -2.1070311964479488509034733639424887543697e-35L,
313 --2.3027356362982001602256518510854229844561e-35L,
314 -4.8950964225733349266861843522029764772843e-36L,
315 --7.2380143477794458213872723050820253166391e-36L,
316 -1.6365648865703614031637443396049568858105e-35L,
317 --3.9885811958234530793729129919803234197399e-35L,
318 -4.1587722120912613510417783923227421336929e-35L,
319 -3.8347421454556472153684687377337135027394e-35L,
320 --9.2251178933638721723515896465489002497864e-36L,
321 -1.4094619690455989526175736741854656192178e-36L,
322 -3.3568857805472235270612851425810803679451e-35L,
323 -3.9090991055522552395018106803232118803401e-35L,
324 -5.2956416979654208140521862707297033857956e-36L,
325 --5.0960846819945514367847063923662507136721e-36L,
326 --4.4959014425277615858329680393918315204998e-35L,
327 -3.8039226544551634266566857615962609653834e-35L,
328 --4.4056522872895512108308642196611689657618e-36L,
329 -1.6025024192482161076223807753425619076948e-36L,
330 -2.1679525325309452561992610065108380635264e-35L,
331 -1.9844038013515422125715362925736754104066e-35L,
332 -3.9139619471799746834505227353568432457241e-35L,
333 -2.1113443807975453505518453436799561854730e-35L,
334 -3.1558557277444692755039816944392770185432e-35L,
335 -1.6295044520355461408265585619500238335614e-35L,
336 --3.5087245209270305856151230356171213582305e-35L,
337 -2.9041041864282855679591055270946117300088e-35L,
338 --2.3128843453818356590931995209806627233282e-35L,
339 --7.7124923181471578439967973820714857839953e-35L,
340 -2.7539027829886922429092063590445808781462e-35L,
341 --9.4500899453181308951084545990839335972452e-35L,
342 --7.3061755302032092337594946001641651543473e-35L,
343 --4.1736144813953752193952770157406952602798e-35L,
344 -3.4369948356256407045344855262863733571105e-35L,
345 --6.3790243492298090907302084924276831116460e-35L,
346 --9.6842943816353261291004127866079538980649e-36L,
347 -4.8746757539138870909275958326700072821615e-35L,
348 --8.7533886477084190884511601368582548254655e-35L,
349 -1.4284743992327918892692551138086727754845e-35L,
350 -5.7262776211073389542565625693479173445042e-35L,
351 --3.2254883148780411245594822270747948565684e-35L,
352 -7.8853548190609877325965525252380833808405e-35L,
353 -8.4081736739037194097515038365370730251333e-35L,
354 -7.4722870357563683815078242981933587273670e-35L,
355 -7.9977202825793435289434813600890494256112e-36L,
356 --8.0577840773362139054848492346292673645405e-35L,
357 -1.4217746753670583065490040209048757624336e-35L,
358 -1.2232486914221205004109743560319090913328e-35L,
359 -8.9696055070830036447361957217943988339065e-35L,
360 --3.1480394435081884410686066739846269858951e-35L,
361 --5.0927146040715345013240642517608928352977e-35L,
362 --5.7431997715924136568133859432702789493569e-35L,
363 --4.3920451405083770279099766080476485439987e-35L,
364 -9.1106753984907715563018666776308759323326e-35L,
365 --3.7032569014272841009512400773061537538358e-35L,
366 -8.8167419429746714276909825405131416764489e-35L,
367 --3.8389341696028352503752312861740895209678e-36L,
368 --3.3462959341960891546340895508017603408404e-35L,
369 --3.9212626776786074383916188498955828634947e-35L,
370 --7.8340397396377867255864494568594088378648e-35L,
371 -7.4681018632456986520600640340627309824469e-35L,
372 -8.9110918618956918451135594876165314884113e-35L,
373 -3.9418160632271890530431797145664308529115e-35L,
374 --4.1048114088580104820193435638327617443913e-35L,
375 --2.3165419451582153326383944756220900454330e-35L,
376 --1.8428312581525319409399330203703211113843e-35L,
377 -7.1477316546709482345411712017906842769961e-35L,
378 -2.9914501578435874662153637707016094237004e-35L,
337 + 1.4074869197628063802317202820414310039556e-36L,
338 + -4.9596961594739925555730439437999675295505e-36L,
339 + 8.9527745625194648873931213446361849472788e-36L,
340 + 1.1880437423207895718180765843544965589427e-35L,
341 + -2.7810278112045145378425375128234365381448e-37L,
342 + 1.4797220377023800327295536234315147262387e-36L,
343 + -4.2169561400548198732870384801849639863829e-36L,
344 + 7.2431229666913484649930323656316023494680e-36L,
345 + -2.1573430089839170299895679353790663182462e-36L,
346 + -9.9515745405126723554452367298128605186305e-36L,
347 + -3.9065558992324838181617569730397882363067e-36L,
348 + 5.5260292271793726813211980664661124518807e-36L,
349 + 8.8415722215914321807682254318036452043689e-36L,
350 + -8.1767728791586179254193323628285599800711e-36L,
351 + -1.3344123034656142243797113823028330070762e-36L,
352 + -4.4927331207813382908930733924681325892188e-36L,
353 + 4.4945511471812490393201824336762495687730e-36L,
354 + -1.6688081504279223555776724459648440567274e-35L,
355 + 1.5629757586107955769461086568937329684113e-35L,
356 + -2.2389835563308078552507970385331510848109e-35L,
357 + -4.8312321745547311551870450671182151367050e-36L,
358 + -1.4336172352905832876958926610980698844309e-35L,
359 + -8.7440181998899932802989174170960593316080e-36L,
360 + 5.9284636008529837445780360785464550143016e-36L,
361 + -2.2376651248436241276061055295043514993630e-35L,
362 + 6.0745837599336105414280310756677442136480e-36L,
363 + 1.5372187110451949677792344762029967023093e-35L,
364 + 2.0976068056751156241657121582478790247159e-35L,
365 + -5.5623956405495438060726862202622807523700e-36L,
366 + 1.9697366707832471841858411934897351901523e-35L,
367 + 2.1070311964479488509034733639424887543697e-35L,
368 + -2.3027356362982001602256518510854229844561e-35L,
369 + 4.8950964225733349266861843522029764772843e-36L,
370 + -7.2380143477794458213872723050820253166391e-36L,
371 + 1.6365648865703614031637443396049568858105e-35L,
372 + -3.9885811958234530793729129919803234197399e-35L,
373 + 4.1587722120912613510417783923227421336929e-35L,
374 + 3.8347421454556472153684687377337135027394e-35L,
375 + -9.2251178933638721723515896465489002497864e-36L,
376 + 1.4094619690455989526175736741854656192178e-36L,
377 + 3.3568857805472235270612851425810803679451e-35L,
378 + 3.9090991055522552395018106803232118803401e-35L,
379 + 5.2956416979654208140521862707297033857956e-36L,
380 + -5.0960846819945514367847063923662507136721e-36L,
381 + -4.4959014425277615858329680393918315204998e-35L,
382 + 3.8039226544551634266566857615962609653834e-35L,
383 + -4.4056522872895512108308642196611689657618e-36L,
384 + 1.6025024192482161076223807753425619076948e-36L,
385 + 2.1679525325309452561992610065108380635264e-35L,
386 + 1.9844038013515422125715362925736754104066e-35L,
387 + 3.9139619471799746834505227353568432457241e-35L,
388 + 2.1113443807975453505518453436799561854730e-35L,
389 + 3.1558557277444692755039816944392770185432e-35L,
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391 + -3.5087245209270305856151230356171213582305e-35L,
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398 + -4.1736144813953752193952770157406952602798e-35L,
399 + 3.4369948356256407045344855262863733571105e-35L,
400 + -6.3790243492298090907302084924276831116460e-35L,
401 + -9.6842943816353261291004127866079538980649e-36L,
402 + 4.8746757539138870909275958326700072821615e-35L,
403 + -8.7533886477084190884511601368582548254655e-35L,
404 + 1.4284743992327918892692551138086727754845e-35L,
405 + 5.7262776211073389542565625693479173445042e-35L,
406 + -3.2254883148780411245594822270747948565684e-35L,
407 + 7.8853548190609877325965525252380833808405e-35L,
408 + 8.4081736739037194097515038365370730251333e-35L,
409 + 7.4722870357563683815078242981933587273670e-35L,
410 + 7.9977202825793435289434813600890494256112e-36L,
411 + -8.0577840773362139054848492346292673645405e-35L,
412 + 1.4217746753670583065490040209048757624336e-35L,
413 + 1.2232486914221205004109743560319090913328e-35L,
414 + 8.9696055070830036447361957217943988339065e-35L,
415 + -3.1480394435081884410686066739846269858951e-35L,
416 + -5.0927146040715345013240642517608928352977e-35L,
417 + -5.7431997715924136568133859432702789493569e-35L,
418 + -4.3920451405083770279099766080476485439987e-35L,
419 + 9.1106753984907715563018666776308759323326e-35L,
420 + -3.7032569014272841009512400773061537538358e-35L,
421 + 8.8167419429746714276909825405131416764489e-35L,
422 + -3.8389341696028352503752312861740895209678e-36L,
423 + -3.3462959341960891546340895508017603408404e-35L,
424 + -3.9212626776786074383916188498955828634947e-35L,
425 + -7.8340397396377867255864494568594088378648e-35L,
426 + 7.4681018632456986520600640340627309824469e-35L,
427 + 8.9110918618956918451135594876165314884113e-35L,
428 + 3.9418160632271890530431797145664308529115e-35L,
429 + -4.1048114088580104820193435638327617443913e-35L,
430 + -2.3165419451582153326383944756220900454330e-35L,
431 + -1.8428312581525319409399330203703211113843e-35L,
432 + 7.1477316546709482345411712017906842769961e-35L,
433 + 2.9914501578435874662153637707016094237004e-35L,
379 434 #elif defined(__x86)
380 -1.108243739551347953496477557317e-11L, 3.644022694535396219063202730280e-11L,
381 -7.667835628314065801595065768845e-12L, 5.026377078169301918590803009109e-11L,
382 -1.161327548990211907411719105561e-11L, 4.785569941615255008968280209991e-11L,
383 -5.595107356360146549819920947848e-11L, 1.673930035747684999707469623769e-11L,
384 -2.611250523102718193166964451527e-11L, 1.384250305661681615897729354721e-11L,
385 -2.278105796029649304219088055497e-11L, 3.586371256902077123693302823191e-13L,
386 -3.342842716722085763523965049902e-11L, 3.670968534386232233574504707347e-11L,
387 -6.196832945990602657404893210974e-13L, 4.169679549603939604438777470618e-11L,
388 -2.274351222528987867221331091414e-11L, 8.872382531858169709022188891298e-11L,
389 -4.344925246387385146717580155420e-11L, 8.707377833692929105196832265348e-11L,
390 -2.881671577173773513055821329154e-11L, 9.763393361566846205717315422347e-12L,
391 -6.476296480975626822569454546857e-11L, 3.569597877124574002505169001136e-11L,
392 -1.772007853877284712958549977698e-11L, 1.347141028196192304932683248872e-11L,
393 -3.676555884905046507598141175404e-11L, 4.881564068032948912761478588710e-11L,
394 -4.416715404487185607337693704681e-11L, 2.314128999621257979016734983553e-11L,
395 -5.380138283056477968352133002913e-11L, 4.393022562414389595406841771063e-11L,
396 -6.299816718559209976839402028537e-12L, 7.304511413053165996581483735843e-11L,
397 -1.978381648117426221467592544212e-10L, 2.024381732686578226139414070989e-10L,
398 -2.255178211796380992141612703464e-10L, 1.204566302442290648452508620986e-10L,
399 -1.034473912921080457667329099995e-10L, 2.225691010059030834353745950874e-10L,
400 -4.817137162794350606107263804151e-11L, 6.565755971506095086327587326326e-11L,
401 -1.644791039522307629611529931429e-10L, 2.820930388953087163050126809014e-11L,
402 -1.766182540818701085571546539514e-10L, 2.124059054092171070266466628320e-10L,
403 -1.567258302596026515190288816001e-10L, 1.742241535800378094231540188685e-10L,
404 -3.038550253253096300737572104929e-11L, 5.925991958164150280814584656688e-11L,
405 -3.355266774764151155289750652594e-11L, 2.637254809561744853531409402995e-11L,
406 -3.227621096606048365493782702458e-11L, 1.094459672377587282585894259882e-10L,
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408 -1.428492049425553288966601449688e-11L, 3.032079976125434624889374125094e-10L,
409 -3.784543889504767060855636487744e-10L, 3.540092982887960328254439790467e-10L,
410 -4.020318667701700464612998296302e-10L, 4.544042324059585739827798668654e-10L,
411 -3.645299460952866120296998202703e-10L, 2.776662293911361485235212513020e-12L,
412 -1.708865101734375304910370400700e-10L, 3.909810965716415233488278047493e-10L,
413 -7.606461848875826105025137974947e-11L, 3.263814502297453347587046149712e-10L,
414 -1.499334758629144388918183376012e-10L, 3.771581242675818925565576303133e-10L,
415 -1.746932950084818923507049088298e-11L, 2.837781909176306820465786987027e-10L,
416 -3.859312847318946163435901230778e-10L, 4.601335192895268187473357720101e-10L,
417 -2.811262558622337888849804940684e-10L, 4.060360843532416964489955306249e-10L,
418 -8.058369357752989796958168458531e-11L, 3.725546414244147566166855921414e-10L,
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422 -7.687158710333735613246114865100e-11L, 1.334418885622867537060685125566e-10L,
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424 -4.161925466840049254333079881002e-10L, 4.265713490956410156084891599630e-10L,
425 -2.437693664320585461575989523716e-10L, 4.466519138542116247357297503086e-10L,
426 -3.113875178143440979746983590908e-10L, 4.910822904159495654488736486097e-11L,
427 -2.818831329324169810481585538618e-12L, 7.767009768334052125229252512543e-12L,
428 -3.698307026936191862258804165254e-10L,
435 + 1.108243739551347953496477557317e-11L,
436 + 3.644022694535396219063202730280e-11L,
437 + 7.667835628314065801595065768845e-12L,
438 + 5.026377078169301918590803009109e-11L,
439 + 1.161327548990211907411719105561e-11L,
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446 + 3.586371256902077123693302823191e-13L,
447 + 3.342842716722085763523965049902e-11L,
448 + 3.670968534386232233574504707347e-11L,
449 + 6.196832945990602657404893210974e-13L,
450 + 4.169679549603939604438777470618e-11L,
451 + 2.274351222528987867221331091414e-11L,
452 + 8.872382531858169709022188891298e-11L,
453 + 4.344925246387385146717580155420e-11L,
454 + 8.707377833692929105196832265348e-11L,
455 + 2.881671577173773513055821329154e-11L,
456 + 9.763393361566846205717315422347e-12L,
457 + 6.476296480975626822569454546857e-11L,
458 + 3.569597877124574002505169001136e-11L,
459 + 1.772007853877284712958549977698e-11L,
460 + 1.347141028196192304932683248872e-11L,
461 + 3.676555884905046507598141175404e-11L,
462 + 4.881564068032948912761478588710e-11L,
463 + 4.416715404487185607337693704681e-11L,
464 + 2.314128999621257979016734983553e-11L,
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466 + 4.393022562414389595406841771063e-11L,
467 + 6.299816718559209976839402028537e-12L,
468 + 7.304511413053165996581483735843e-11L,
469 + 1.978381648117426221467592544212e-10L,
470 + 2.024381732686578226139414070989e-10L,
471 + 2.255178211796380992141612703464e-10L,
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473 + 1.034473912921080457667329099995e-10L,
474 + 2.225691010059030834353745950874e-10L,
475 + 4.817137162794350606107263804151e-11L,
476 + 6.565755971506095086327587326326e-11L,
477 + 1.644791039522307629611529931429e-10L,
478 + 2.820930388953087163050126809014e-11L,
479 + 1.766182540818701085571546539514e-10L,
480 + 2.124059054092171070266466628320e-10L,
481 + 1.567258302596026515190288816001e-10L,
482 + 1.742241535800378094231540188685e-10L,
483 + 3.038550253253096300737572104929e-11L,
484 + 5.925991958164150280814584656688e-11L,
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488 + 1.094459672377587282585894259882e-10L,
489 + 6.064676448464127209709358607166e-11L,
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491 + 1.428492049425553288966601449688e-11L,
492 + 3.032079976125434624889374125094e-10L,
493 + 3.784543889504767060855636487744e-10L,
494 + 3.540092982887960328254439790467e-10L,
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500 + 3.909810965716415233488278047493e-10L,
501 + 7.606461848875826105025137974947e-11L,
502 + 3.263814502297453347587046149712e-10L,
503 + 1.499334758629144388918183376012e-10L,
504 + 3.771581242675818925565576303133e-10L,
505 + 1.746932950084818923507049088298e-11L,
506 + 2.837781909176306820465786987027e-10L,
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508 + 4.601335192895268187473357720101e-10L,
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510 + 4.060360843532416964489955306249e-10L,
511 + 8.058369357752989796958168458531e-11L,
512 + 3.725546414244147566166855921414e-10L,
513 + 1.040286509953292907344053122733e-10L,
514 + 3.094968093808145773271362531155e-10L,
515 + 4.454811192340438979284756311844e-10L,
516 + 5.676678748199027602705574110388e-11L,
517 + 2.518376833121948163898128509842e-10L,
518 + 3.907837370041422778250991189943e-10L,
519 + 7.687158710333735613246114865100e-11L,
520 + 1.334418885622867537060685125566e-10L,
521 + 1.353147719826124443836432060856e-10L,
522 + 2.825131007652335581739282335732e-10L,
523 + 4.161925466840049254333079881002e-10L,
524 + 4.265713490956410156084891599630e-10L,
525 + 2.437693664320585461575989523716e-10L,
526 + 4.466519138542116247357297503086e-10L,
527 + 3.113875178143440979746983590908e-10L,
528 + 4.910822904159495654488736486097e-11L,
529 + 2.818831329324169810481585538618e-12L,
530 + 7.767009768334052125229252512543e-12L,
531 + 3.698307026936191862258804165254e-10L,
429 532 #endif
430 533 };
431 534
432 535 /*
433 536 * mx_atanl(x, err)
434 537 * Table look-up algorithm
435 538 * By K.C. Ng, March 9, 1989
436 539 *
437 540 * Algorithm.
438 541 *
439 542 * The algorithm is based on atan(x)=atan(y)+atan((x-y)/(1+x*y)).
440 543 * We use poly1(x) to approximate atan(x) for x in [0,1/8] with
441 544 * error (relative)
442 - * |(atan(x)-poly1(x))/x|<= 2^-140
545 + * |(atan(x)-poly1(x))/x|<= 2^-140
443 546 *
444 547 * and use poly2(x) to approximate atan(x) for x in [0,1/65] with
445 548 * error
446 549 * |atan(x)-poly2(x)|<= 2^-143.7
447 550 *
448 551 * Here poly1 and poly2 are odd polynomial with the following form:
449 552 * x + x^3*(a1+x^2*(a2+...))
450 553 *
451 554 * (0). Purge off Inf and NaN and 0
452 555 * (1). Reduce x to positive by atan(x) = -atan(-x).
453 556 * (2). For x <= 1/8, use
454 557 * (2.1) if x < 2^(-prec/2), atan(x) = x with inexact flag raised
455 558 * (2.2) Otherwise
456 559 * atan(x) = poly1(x)
457 560 * (3). For x >= 8 then (prec = 78)
458 561 * (3.1) if x >= 2^prec, atan(x) = atan(inf) - pio2_lo
459 562 * (3.2) if x >= 2^(prec/3), atan(x) = atan(inf) - 1/x
460 563 * (3.3) if x > 65, atan(x) = atan(inf) - poly2(1/x)
461 564 * (3.4) Otherwise, atan(x) = atan(inf) - poly1(1/x)
462 565 *
463 566 * (4). Now x is in (0.125, 8)
464 567 * Find y that match x to 4.5 bit after binary (easy).
465 568 * If iy is the high word of y, then
466 569 * single : j = (iy - 0x3e000000) >> 19
467 570 * double : j = (iy - 0x3fc00000) >> 16
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468 571 * quad : j = (iy - 0x3ffc0000) >> 12
469 572 *
470 573 * Let s = (x-y)/(1+x*y). Then
471 574 * atan(x) = atan(y) + poly1(s)
472 575 * = _TBL_atan_hi[j] + (_TBL_atan_lo[j] + poly2(s) )
473 576 *
474 577 * Note. |s| <= 1.5384615385e-02 = 1/65. Maxium occurs at x = 1.03125
475 578 *
476 579 */
477 580
581 +/* BEGIN CSTYLED */
478 582 /*
479 583 * p[0] - p[16] for atan(x) =
480 584 * x + x^3*(p1+x^2*(p2+...))
481 585 */
482 586 static const long double pe[] = {
483 587 1.0L,
484 588 0.0L,
485 589 #if defined(__sparc)
486 590 -0.33333333333333332870740406406184774823L,
487 591 -4.62592926927148558508441072595508240609e-18L,
488 592 0.19999999999999999722444243843710864894L,
489 593 2.77555756156289124602047010782090464486e-18L,
490 594 -0.14285714285714285615158658515611023176L,
491 595 -9.91270557700756738621231719241800559409e-19L,
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492 596 #elif defined(__x86)
493 597 -0.33333333325572311878204345703125L,
494 598 -7.76102145512898763020833333192787755766644373e-11L,
495 599 0.19999999995343387126922607421875L,
496 600 4.65661287307739257812498949613909375938538636e-11L,
497 601 -0.142857142840512096881866455078125L,
498 602 -1.66307602609906877787419703858463013035681375e-11L,
499 603 #endif
500 604 };
501 605
502 -static const long double p[] = { /* p[0] - p[16] */
606 +static const long double p[] = { /* p[0] - p[16] */
503 607 1.0L,
504 608 -3.33333333333333333333333333333333333319278775586e-0001L,
505 609 1.99999999999999999999999999999999894961390937601e-0001L,
506 610 -1.42857142857142857142857142856866970385846301312e-0001L,
507 611 1.11111111111111111111111110742899094415954427738e-0001L,
508 612 -9.09090909090909090909087972707015549231951421806e-0002L,
509 613 7.69230769230769230767699003016385628597359717046e-0002L,
510 614 -6.66666666666666666113842763495291228025226575259e-0002L,
511 615 5.88235294117646915706902204947653640091126695962e-0002L,
512 616 -5.26315789473657016886225044679594035524579379810e-0002L,
513 617 4.76190476186633969331771169790375592681525481267e-0002L,
514 618 -4.34782608290146274616081389793141896576997370161e-0002L,
515 619 3.99999968161267722260103962788865225205057218988e-0002L,
516 620 -3.70368536844778256320786172745225703228683638328e-0002L,
517 621 3.44752320396524479494062858284036892703898522150e-0002L,
518 622 -3.20491216046653214683721787776813360591233428081e-0002L,
519 623 2.67632651033434456758550618122802167256870856514e-0002L,
520 624 };
521 625
522 626 /* q[0] - q[9] */
523 627 static const long double qe[] = {
524 628 1.0L,
525 629 0.0L,
526 630 #if defined(__sparc)
527 631 -0.33333333333333332870740406406184774823486804962158203125L,
528 632 -4.625929269271485585069345465471207312531868714634217630e-18L,
529 633 0.19999999999999999722444243843710864894092082977294921875L,
530 634 2.7755575615628864268260553912956813621977220359134667560e-18L,
531 635 #elif defined(__x86)
532 636 -0.33333333325572311878204345703125L,
533 637 -7.76102145512898763020833333042135150927893e-11L,
534 638 0.19999999995343387126922607421875L,
535 639 4.656612873077392578124507576697622106863058e-11L,
536 640 #endif
537 641 };
538 642
539 643 static const long double q[] = { /* q[0] - q[9] */
540 644 -3.33333333333333333333333333333333333304213515094e-0001L,
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541 645 1.99999999999999999999999999999995075766976221077e-0001L,
542 646 -1.42857142857142857142857142570379604317921113079e-0001L,
543 647 1.11111111111111111111102923861900979127978214077e-0001L,
544 648 -9.09090909090909089586854075816999506863320031460e-0002L,
545 649 7.69230769230756334929213246003824644696974730368e-0002L,
546 650 -6.66666666589192433974402013508912138168133579856e-0002L,
547 651 5.88235013696778007696800252045588307023299350858e-0002L,
548 652 -5.25754959898164576495303840687699583228444695685e-0002L,
549 653 };
550 654
551 -static const long double
552 -two8700 = 9.140338438955067659002088492701e+2618L, /* 2^8700 */
553 -twom8700 = 1.094051392821643668051436593760e-2619L, /* 2^-8700 */
554 -one = 1.0L,
555 -zero = 0.0L,
556 -pi = 3.1415926535897932384626433832795028841971693993751L,
557 -pio2 = 1.57079632679489661923132169163975144209858469968755L,
558 -pio4 = 0.785398163397448309615660845819875721049292349843776L,
559 -pi3o4 = 2.356194490192344928846982537459627163147877049531329L,
655 +static const long double two8700 = 9.140338438955067659002088492701e+2618L, /* 2^8700 */
656 + twom8700 = 1.094051392821643668051436593760e-2619L, /* 2^-8700 */
657 + one = 1.0L,
658 + zero = 0.0L,
659 + pi = 3.1415926535897932384626433832795028841971693993751L,
660 + pio2 = 1.57079632679489661923132169163975144209858469968755L,
661 + pio4 = 0.785398163397448309615660845819875721049292349843776L,
662 + pi3o4 = 2.356194490192344928846982537459627163147877049531329L,
560 663 #if defined(__sparc)
561 -pi_lo = 8.67181013012378102479704402604335196876232e-35L,
562 -pio2_lo = 4.33590506506189051239852201302167598438116e-35L,
563 -pio4_lo = 2.16795253253094525619926100651083799219058e-35L,
564 -pi3o4_lo = 6.50385759759283576859778301953251397657174e-35L;
664 + pi_lo = 8.67181013012378102479704402604335196876232e-35L,
665 + pio2_lo = 4.33590506506189051239852201302167598438116e-35L,
666 + pio4_lo = 2.16795253253094525619926100651083799219058e-35L,
667 + pi3o4_lo = 6.50385759759283576859778301953251397657174e-35L;
565 668 #elif defined(__x86)
566 -pi_lo = -5.01655761266833202355732708e-20L,
567 -pio2_lo = -2.50827880633416601177866354e-20L,
568 -pio4_lo = -1.25413940316708300588933177e-20L,
569 -pi3o4_lo = -9.18342907192877118770525931e-20L;
669 + pi_lo = -5.01655761266833202355732708e-20L,
670 + pio2_lo = -2.50827880633416601177866354e-20L,
671 + pio4_lo = -1.25413940316708300588933177e-20L,
672 + pi3o4_lo = -9.18342907192877118770525931e-20L;
570 673 #endif
674 +/* END CSTYLED */
571 675
572 676 static long double
573 -mx_atanl(long double x, long double *err) {
677 +mx_atanl(long double x, long double *err)
678 +{
574 679 long double y, z, r, s, t, w, s_h, s_l, x_h, x_l, zz[3], ee[2], z_h,
575 - z_l, r_h, r_l, u, v;
680 + z_l, r_h, r_l, u, v;
576 681 int ix, iy, hx, i, j;
577 682 float fx;
578 683
579 684 hx = HI_XWORD(x);
580 685 ix = hx & (~0x80000000);
581 686
582 687 /* for |x| < 1/8 */
583 688 if (ix < 0x3ffc0000) {
584 - if (ix < 0x3ff30000) { /* when |x| < 2**-12 */
689 + if (ix < 0x3ff30000) { /* when |x| < 2**-12 */
585 690 if (ix < 0x3fc60000) { /* if |x| < 2**-prec/2 */
586 - *err = (long double) ((int) x);
691 + *err = (long double)((int)x);
587 692 return (x);
588 693 }
694 +
589 695 z = x * x;
590 696 t = q[8];
591 - for (i = 7; i >= 0; i--) t = q[i] + z * t;
697 +
698 + for (i = 7; i >= 0; i--)
699 + t = q[i] + z * t;
700 +
592 701 t *= x * z;
593 702 r = x + t;
594 703 *err = t - (r - x);
595 704 return (r);
596 705 }
706 +
597 707 z = x * x;
598 708
599 709 /* use long double precision at p4 and on */
600 710 t = p[16];
601 - for (i = 15; i >= 4; i--) t = p[i] + z * t;
711 +
712 + for (i = 15; i >= 4; i--)
713 + t = p[i] + z * t;
714 +
602 715 ee[0] = z * t;
603 716
604 - x_h = x; HALF(x_h);
605 - z_h = z; HALF(z_h);
717 + x_h = x;
718 + HALF(x_h);
719 + z_h = z;
720 + HALF(z_h);
606 721 x_l = x - x_h;
607 722 z_l = (x_h * x_h - z_h);
608 723 zz[0] = z;
609 724 zz[1] = z_h;
610 725 zz[2] = z_l + x_l * (x + x_h);
611 726
612 727 /* compute (1+z*(p1+z*(p2+z*(p3+e)))) */
613 728
614 729 mx_polyl(zz, pe, ee, 3);
615 730
616 731 /* finally x*(1+z*(p1+...)) */
617 732 r = x_h * ee[0];
618 733 t = x * ee[1] + x_l * ee[0];
619 734 s = t + r;
620 735 *err = t - (s - r);
621 736 return (s);
622 737 }
738 +
623 739 /* for |x| >= 8.0 */
624 - if (ix >= 0x40020000) { /* x >= 8 */
740 + if (ix >= 0x40020000) { /* x >= 8 */
625 741 x = fabsl(x);
626 - if (ix >= 0x402e0000) { /* x >= 2**47 */
627 - if (ix >= 0x408b0000) { /* x >= 2**140 */
742 +
743 + if (ix >= 0x402e0000) { /* x >= 2**47 */
744 + if (ix >= 0x408b0000) /* x >= 2**140 */
628 745 y = -pio2_lo;
629 - } else
746 + else
630 747 y = one / x - pio2_lo;
748 +
631 749 if (hx >= 0) {
632 750 t = pio2 - y;
633 751 *err = -(y - (pio2 - t));
634 752 } else {
635 753 t = y - pio2;
636 754 *err = y - (pio2 + t);
637 755 }
756 +
638 757 return (t);
639 758 } else {
640 759 /* compute r = 1/x */
641 760 r = one / x;
642 761 z = r * r;
643 - x_h = x; HALF(x_h);
644 - r_h = r; HALF(r_h);
645 - z_h = z; HALF(z_h);
762 + x_h = x;
763 + HALF(x_h);
764 + r_h = r;
765 + HALF(r_h);
766 + z_h = z;
767 + HALF(z_h);
646 768 r_l = r * ((x_h - x) * r_h - (x_h * r_h - one));
647 769 z_l = (r_h * r_h - z_h);
648 770 zz[0] = z;
649 771 zz[1] = z_h;
650 772 zz[2] = z_l + r_l * (r + r_h);
773 +
651 774 if (ix < 0x40050400) { /* 8 < x < 65 */
652 775 /* use double precision at p4 and on */
653 776 t = p[16];
654 - for (i = 15; i >= 4; i--) t = p[i] + z * t;
777 +
778 + for (i = 15; i >= 4; i--)
779 + t = p[i] + z * t;
780 +
655 781 ee[0] = z * t;
656 782 /* compute (1+z*(p1+z*(p2+z*(p3+e)))) */
657 783 mx_polyl(zz, pe, ee, 3);
658 - } else { /* x < 65 < 2**47 */
784 + } else { /* x < 65 < 2**47 */
659 785 /* use long double at q3 and on */
660 786 t = q[8];
661 - for (i = 7; i >= 2; i--) t = q[i] + z * t;
787 +
788 + for (i = 7; i >= 2; i--)
789 + t = q[i] + z * t;
790 +
662 791 ee[0] = z * t;
663 792 /* compute (1+z*(q1+z*(q2+e))) */
664 793 mx_polyl(zz, qe, ee, 2);
665 794 }
795 +
666 796 /* pio2 - r*(1+...) */
667 797 v = r_h * ee[0];
668 798 t = pio2_lo - (r * ee[1] + r_l * ee[0]);
799 +
669 800 if (hx >= 0) {
670 801 s = pio2 - v;
671 802 t -= (v - (pio2 - s));
672 803 } else {
673 804 s = v - pio2;
674 805 t = -(t - (v - (s + pio2)));
675 806 }
807 +
676 808 w = s + t;
677 809 *err = t - (w - s);
678 810 return (w);
679 811 }
680 812 }
813 +
681 814 /* now x is between 1/8 and 8 */
682 815 iy = (ix + 0x00000800) & 0x7ffff000;
683 816 j = (iy - 0x3ffc0000) >> 12;
684 - ((int *) &fx)[0] = 0x3e000000 + (j << 19);
685 - y = (long double) fx;
817 + ((int *)&fx)[0] = 0x3e000000 + (j << 19);
818 + y = (long double)fx;
686 819 x = fabsl(x);
687 820
688 821 w = (x - y);
689 822 v = 1.0L / (one + x * y);
690 823 s = w * v;
691 824 z = s * s;
692 825 /* use long double precision at q3 and on */
693 826 t = q[8];
694 - for (i = 7; i >= 2; i--) t = q[i] + z * t;
827 +
828 + for (i = 7; i >= 2; i--)
829 + t = q[i] + z * t;
830 +
695 831 ee[0] = z * t;
696 - s_h = s; HALF(s_h);
697 - z_h = z; HALF(z_h);
698 - x_h = x; HALF(x_h);
699 - t = one + x * y; HALF(t);
832 + s_h = s;
833 + HALF(s_h);
834 + z_h = z;
835 + HALF(z_h);
836 + x_h = x;
837 + HALF(x_h);
838 + t = one + x * y;
839 + HALF(t);
700 840 r = -((x_h - x) * y - (x_h * y - (t - one)));
701 841 s_l = -v * (s_h * r - (w - s_h * t));
702 842 z_l = (s_h * s_h - z_h);
703 843 zz[0] = z;
704 844 zz[1] = z_h;
705 845 zz[2] = z_l + s_l * (s + s_h);
706 846 /* compute (1+z*(q1+z*(q2+e))) by call mx_poly */
707 847 mx_polyl(zz, qe, ee, 2);
708 848 v = s_h * ee[0];
709 849 t = TBL_atan_lol[j] + (s * ee[1] + s_l * ee[0]);
710 850 u = TBL_atan_hil[j];
711 851 s = u + v;
712 852 t += (v - (s - u));
713 853 w = s + t;
714 854 *err = t - (w - s);
855 +
715 856 if (hx < 0) {
716 857 w = -w;
717 858 *err = -*err;
718 859 }
860 +
719 861 return (w);
720 862 }
721 863
722 864 long double
723 -__k_atan2l(long double y, long double x, long double *w) {
865 +__k_atan2l(long double y, long double x, long double *w)
866 +{
724 867 long double t, xh, th, t1, t2, w1, w2;
725 868 int ix, iy, hx, hy;
726 869
727 870 hy = HI_XWORD(y);
728 871 hx = HI_XWORD(x);
729 872 iy = hy & ~0x80000000;
730 873 ix = hx & ~0x80000000;
731 874
732 875 *w = 0.0;
876 +
733 877 if (ix >= 0x7fff0000 || iy >= 0x7fff0000) { /* ignore inexact */
734 - if (isnanl(x) || isnanl(y))
878 + if (isnanl(x) || isnanl(y)) {
735 879 return (x * y);
736 - else if (iy < 0x7fff0000) {
880 + } else if (iy < 0x7fff0000) {
737 881 if (hx >= 0) { /* ATAN2(+-finite, +inf) is +-0 */
738 882 *w *= y;
739 883 return (*w);
740 884 } else { /* ATAN2(+-finite, -inf) is +-pi */
741 885 *w = copysignl(pi_lo, y);
742 886 return (copysignl(pi, y));
743 887 }
744 888 } else if (ix < 0x7fff0000) {
745 - /* ATAN2(+-inf, finite) is +-pi/2 */
746 - *w = (hy >= 0)? pio2_lo : -pio2_lo;
747 - return ((hy >= 0)? pio2 : -pio2);
889 + /* ATAN2(+-inf, finite) is +-pi/2 */
890 + *w = (hy >= 0) ? pio2_lo : -pio2_lo;
891 + return ((hy >= 0) ? pio2 : -pio2);
748 892 } else if (hx > 0) { /* ATAN2(+-INF,+INF) = +-pi/4 */
749 - *w = (hy >= 0)? pio4_lo : -pio4_lo;
750 - return ((hy >= 0)? pio4 : -pio4);
893 + *w = (hy >= 0) ? pio4_lo : -pio4_lo;
894 + return ((hy >= 0) ? pio4 : -pio4);
751 895 } else { /* ATAN2(+-INF,-INF) = +-3pi/4 */
752 - *w = (hy >= 0)? pi3o4_lo : -pi3o4_lo;
753 - return ((hy >= 0)? pi3o4 : -pi3o4);
896 + *w = (hy >= 0) ? pi3o4_lo : -pi3o4_lo;
897 + return ((hy >= 0) ? pi3o4 : -pi3o4);
754 898 }
755 899 } else if (x == zero || y == zero) {
756 900 if (y == zero) {
757 - if (hx >= 0) /* ATAN2(+-0, +(0 <= x <= inf)) is +-0 */
901 + if (hx >= 0) { /* ATAN2(+-0, +(0 <= x <= inf)) is +-0 */
758 902 return (y);
759 - else { /* ATAN2(+-0, -(0 <= x <= inf)) is +-pi */
760 - *w = (hy >= 0)? pi_lo : -pi_lo;
761 - return ((hy >= 0)? pi : -pi);
903 + } else { /* ATAN2(+-0, -(0 <= x <= inf)) is +-pi */
904 + *w = (hy >= 0) ? pi_lo : -pi_lo;
905 + return ((hy >= 0) ? pi : -pi);
762 906 }
763 - } else { /* ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2 */
764 - *w = (hy >= 0)? pio2_lo : -pio2_lo;
765 - return ((hy >= 0)? pio2 : -pio2);
907 + } else { /* ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2 */
908 + *w = (hy >= 0) ? pio2_lo : -pio2_lo;
909 + return ((hy >= 0) ? pio2 : -pio2);
766 910 }
767 - } else if (iy - ix > 0x00640000) { /* |x/y| < 2 ** -100 */
768 - *w = (hy >= 0)? pio2_lo : -pio2_lo;
769 - return ((hy >= 0)? pio2 : -pio2);
770 - } else if (ix - iy > 0x00640000) { /* |y/x| < 2 ** -100 */
911 + } else if (iy - ix > 0x00640000) { /* |x/y| < 2 ** -100 */
912 + *w = (hy >= 0) ? pio2_lo : -pio2_lo;
913 + return ((hy >= 0) ? pio2 : -pio2);
914 + } else if (ix - iy > 0x00640000) { /* |y/x| < 2 ** -100 */
771 915 if (hx < 0) {
772 - *w = (hy >= 0)? pi_lo : -pi_lo;
773 - return ((hy >= 0)? pi : -pi);
916 + *w = (hy >= 0) ? pi_lo : -pi_lo;
917 + return ((hy >= 0) ? pi : -pi);
774 918 } else {
775 919 t = y / x;
776 - th = t; HALF(th);
777 - xh = x; HALF(xh);
920 + th = t;
921 + HALF(th);
922 + xh = x;
923 + HALF(xh);
778 924 t1 = (x - xh) * t + xh * (t - th);
779 925 t2 = y - xh * th;
780 926 *w = (t2 - t1) / x;
781 927 return (t);
782 928 }
783 929 } else {
784 930 if (ix >= 0x5fff3000) {
785 931 x *= twom8700;
786 932 y *= twom8700;
787 933 } else if (ix < 0x203d0000) {
788 934 x *= two8700;
789 935 y *= two8700;
790 936 }
937 +
791 938 y = fabsl(y);
792 939 x = fabsl(x);
793 940 t = y / x;
794 - th = t; HALF(th);
795 - xh = x; HALF(xh);
941 + th = t;
942 + HALF(th);
943 + xh = x;
944 + HALF(xh);
796 945 t1 = (x - xh) * t + xh * (t - th);
797 946 t2 = y - xh * th;
798 947 w1 = mx_atanl(t, &w2);
799 948 w2 += (t2 - t1) / (x + y * t);
949 +
800 950 if (hx < 0) {
801 951 t1 = pi - w1;
802 952 t2 = pi - t1;
803 953 w2 = (pi_lo - w2) - (w1 - t2);
804 954 w1 = t1;
805 955 }
806 - *w = (hy >= 0)? w2 : -w2;
807 - return ((hy >= 0)? w1 : -w1);
956 +
957 + *w = (hy >= 0) ? w2 : -w2;
958 + return ((hy >= 0) ? w1 : -w1);
808 959 }
809 960 }
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