1 /* origin: FreeBSD /usr/src/lib/msun/src/s_atanl.c */
2 /*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
9 * is preserved.
10 * ====================================================
11 */
12 /*
13 * See comments in atan.c.
14 * Converted to long double by David Schultz <das@FreeBSD.ORG>.
15 */
16
17 #include "libm.h"
18
19 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
atanl(long double x)20 long double atanl(long double x)
21 {
22 return atan(x);
23 }
24 #elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
25
26 #if LDBL_MANT_DIG == 64
27 #define EXPMAN(u) ((u.i.se & 0x7fff)<<8 | (u.i.m>>55 & 0xff))
28
29 static const long double atanhi[] = {
30 4.63647609000806116202e-01L,
31 7.85398163397448309628e-01L,
32 9.82793723247329067960e-01L,
33 1.57079632679489661926e+00L,
34 };
35
36 static const long double atanlo[] = {
37 1.18469937025062860669e-20L,
38 -1.25413940316708300586e-20L,
39 2.55232234165405176172e-20L,
40 -2.50827880633416601173e-20L,
41 };
42
43 static const long double aT[] = {
44 3.33333333333333333017e-01L,
45 -1.99999999999999632011e-01L,
46 1.42857142857046531280e-01L,
47 -1.11111111100562372733e-01L,
48 9.09090902935647302252e-02L,
49 -7.69230552476207730353e-02L,
50 6.66661718042406260546e-02L,
51 -5.88158892835030888692e-02L,
52 5.25499891539726639379e-02L,
53 -4.70119845393155721494e-02L,
54 4.03539201366454414072e-02L,
55 -2.91303858419364158725e-02L,
56 1.24822046299269234080e-02L,
57 };
58
T_even(long double x)59 static long double T_even(long double x)
60 {
61 return aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] +
62 x * (aT[8] + x * (aT[10] + x * aT[12])))));
63 }
64
T_odd(long double x)65 static long double T_odd(long double x)
66 {
67 return aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] +
68 x * (aT[9] + x * aT[11]))));
69 }
70 #elif LDBL_MANT_DIG == 113
71 #define EXPMAN(u) ((u.i.se & 0x7fff)<<8 | u.i.top>>8)
72
73 static const long double atanhi[] = {
74 4.63647609000806116214256231461214397e-01L,
75 7.85398163397448309615660845819875699e-01L,
76 9.82793723247329067985710611014666038e-01L,
77 1.57079632679489661923132169163975140e+00L,
78 };
79
80 static const long double atanlo[] = {
81 4.89509642257333492668618435220297706e-36L,
82 2.16795253253094525619926100651083806e-35L,
83 -2.31288434538183565909319952098066272e-35L,
84 4.33590506506189051239852201302167613e-35L,
85 };
86
87 static const long double aT[] = {
88 3.33333333333333333333333333333333125e-01L,
89 -1.99999999999999999999999999999180430e-01L,
90 1.42857142857142857142857142125269827e-01L,
91 -1.11111111111111111111110834490810169e-01L,
92 9.09090909090909090908522355708623681e-02L,
93 -7.69230769230769230696553844935357021e-02L,
94 6.66666666666666660390096773046256096e-02L,
95 -5.88235294117646671706582985209643694e-02L,
96 5.26315789473666478515847092020327506e-02L,
97 -4.76190476189855517021024424991436144e-02L,
98 4.34782608678695085948531993458097026e-02L,
99 -3.99999999632663469330634215991142368e-02L,
100 3.70370363987423702891250829918659723e-02L,
101 -3.44827496515048090726669907612335954e-02L,
102 3.22579620681420149871973710852268528e-02L,
103 -3.03020767654269261041647570626778067e-02L,
104 2.85641979882534783223403715930946138e-02L,
105 -2.69824879726738568189929461383741323e-02L,
106 2.54194698498808542954187110873675769e-02L,
107 -2.35083879708189059926183138130183215e-02L,
108 2.04832358998165364349957325067131428e-02L,
109 -1.54489555488544397858507248612362957e-02L,
110 8.64492360989278761493037861575248038e-03L,
111 -2.58521121597609872727919154569765469e-03L,
112 };
113
T_even(long double x)114 static long double T_even(long double x)
115 {
116 return (aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] + x * (aT[8] +
117 x * (aT[10] + x * (aT[12] + x * (aT[14] + x * (aT[16] +
118 x * (aT[18] + x * (aT[20] + x * aT[22])))))))))));
119 }
120
T_odd(long double x)121 static long double T_odd(long double x)
122 {
123 return (aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] + x * (aT[9] +
124 x * (aT[11] + x * (aT[13] + x * (aT[15] + x * (aT[17] +
125 x * (aT[19] + x * (aT[21] + x * aT[23])))))))))));
126 }
127 #endif
128
atanl(long double x)129 long double atanl(long double x)
130 {
131 union ldshape u = {x};
132 long double w, s1, s2, z;
133 int id;
134 unsigned e = u.i.se & 0x7fff;
135 unsigned sign = u.i.se >> 15;
136 unsigned expman;
137
138 if (e >= 0x3fff + LDBL_MANT_DIG + 1) { /* if |x| is large, atan(x)~=pi/2 */
139 if (isnan(x))
140 return x;
141 return sign ? -atanhi[3] : atanhi[3];
142 }
143 /* Extract the exponent and the first few bits of the mantissa. */
144 expman = EXPMAN(u);
145 if (expman < ((0x3fff - 2) << 8) + 0xc0) { /* |x| < 0.4375 */
146 if (e < 0x3fff - (LDBL_MANT_DIG+1)/2) { /* if |x| is small, atanl(x)~=x */
147 /* raise underflow if subnormal */
148 if (e == 0)
149 FORCE_EVAL((float)x);
150 return x;
151 }
152 id = -1;
153 } else {
154 x = fabsl(x);
155 if (expman < (0x3fff << 8) + 0x30) { /* |x| < 1.1875 */
156 if (expman < ((0x3fff - 1) << 8) + 0x60) { /* 7/16 <= |x| < 11/16 */
157 id = 0;
158 x = (2.0*x-1.0)/(2.0+x);
159 } else { /* 11/16 <= |x| < 19/16 */
160 id = 1;
161 x = (x-1.0)/(x+1.0);
162 }
163 } else {
164 if (expman < ((0x3fff + 1) << 8) + 0x38) { /* |x| < 2.4375 */
165 id = 2;
166 x = (x-1.5)/(1.0+1.5*x);
167 } else { /* 2.4375 <= |x| */
168 id = 3;
169 x = -1.0/x;
170 }
171 }
172 }
173 /* end of argument reduction */
174 z = x*x;
175 w = z*z;
176 /* break sum aT[i]z**(i+1) into odd and even poly */
177 s1 = z*T_even(w);
178 s2 = w*T_odd(w);
179 if (id < 0)
180 return x - x*(s1+s2);
181 z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
182 return sign ? -z : z;
183 }
184 #endif
185