1 ;;;; -*- Mode: lisp -*-
3 ;;;; Copyright (c) 2007 Raymond Toy
5 ;;;; Permission is hereby granted, free of charge, to any person
6 ;;;; obtaining a copy of this software and associated documentation
7 ;;;; files (the "Software"), to deal in the Software without
8 ;;;; restriction, including without limitation the rights to use,
9 ;;;; copy, modify, merge, publish, distribute, sublicense, and/or sell
10 ;;;; copies of the Software, and to permit persons to whom the
11 ;;;; Software is furnished to do so, subject to the following
14 ;;;; The above copyright notice and this permission notice shall be
15 ;;;; included in all copies or substantial portions of the Software.
17 ;;;; THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
18 ;;;; EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
19 ;;;; OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
20 ;;;; NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
21 ;;;; HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
22 ;;;; WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
23 ;;;; FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
24 ;;;; OTHER DEALINGS IN THE SOFTWARE.
28 (defconstant +qd-zero
+
35 (%make-qd-d
(scale-float (float 7074237752028440 1.0d0
) -
50)
36 (scale-float (float 4967757600021511 1.0d0
) -
104)
37 (scale-float (float -
8753721960665020 1.0d0
) -
160)
38 (scale-float (float 5857755168774013 1.0d0
) -
214)))
40 ;; 3.1415926535897932384626433832795028841971693993751058209749445923078L0
42 (%make-qd-d
(scale-float (float 7074237752028440 1.0d0
) -
51)
43 (scale-float (float 4967757600021511 1.0d0
) -
105)
44 (scale-float (float -
8753721960665020 1.0d0
) -
161)
45 (scale-float (float 5857755168774013 1.0d0
) -
215)))
47 (defconstant +qd-pi
/2+
48 (%make-qd-d
(scale-float (float 7074237752028440 1.0d0
) -
52)
49 (scale-float (float 4967757600021511 1.0d0
) -
106)
50 (scale-float (float -
8753721960665020 1.0d0
) -
162)
51 (scale-float (float 5857755168774013 1.0d0
) -
216)))
53 (defconstant +qd-pi
/4+
54 (%make-qd-d
(scale-float (float 7074237752028440 1.0d0
) -
53)
55 (scale-float (float 4967757600021511 1.0d0
) -
107)
56 (scale-float (float -
8753721960665020 1.0d0
) -
163)
57 (scale-float (float 5857755168774013 1.0d0
) -
217)))
59 (defconstant +qd-3pi
/4+
60 (%make-qd-d
(scale-float (float 5305678314021330 1.0d0
) -
51)
61 (scale-float (float 7451636400032266 1.0d0
) -
106)
62 (scale-float (float 5724553519491610 1.0d0
) -
160)
63 (scale-float (float -
6810541066450736 1.0d0
) -
214)))
65 (defconstant +qd-pi
/1024+
66 (%make-qd-d
(scale-float (float 7074237752028440 1.0d0
) -
61)
67 (scale-float (float 4967757600021511 1.0d0
) -
115)
68 (scale-float (float -
8753721960665020 1.0d0
) -
171)
69 (scale-float (float 5857755168774013 1.0d0
) -
225)))
72 (%make-qd-d
(scale-float (float 6121026514868073 1.0d0
) -
51)
73 (scale-float (float 5864240480059706 1.0d0
) -
105)
74 (scale-float (float -
6219324074349538 1.0d0
) -
161)
75 (scale-float (float 7980724272743020 1.0d0
) -
215)))
77 ;; 0.6931471805599453094172321214581765680755001343602552541206800094934L0
78 (defconstant +qd-log2
+
80 (make-qd-d 6.931471805599452862d-01
81 2.319046813846299558d-17
82 5.707708438416212066d-34
83 -
3.582432210601811423d-50
)
84 (%make-qd-d
(scale-float (float 6243314768165359 1.0d0
) -
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85 (scale-float (float 7525737178955839 1.0d0
) -
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86 (scale-float (float 6673460182522164 1.0d0
) -
163)
87 (scale-float (float -
7545482916914656 1.0d0
) -
217)))
89 ;; The rest of log(2) such that (+ +qd-log2+ +qd-log2-extra+) is
90 ;; log(2) to twice the precision of a quad-double.
91 (defconstant +qd-log2-extra
+
93 (make-qd-d (scale-float (float 4141960528156623 1d0
) (- -
53 212))
94 (scale-float (float 3973120087747366 1d0
) (- -
106 212))
95 (scale-float (float 752798645508048 1d0
) (- -
159 212))
96 (scale-float (float 7618435247650241 1d0
) (- -
212 212)))
97 (%make-qd-d
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) -
266)
98 (scale-float (float -
8487672633970079 1.0d0
) -
322)
99 (scale-float (float 6075158146775579 1.0d0
) -
376)
100 (scale-float (float 4764384374407424 1.0d0
) -
432)))
102 (defconstant +qd-log10
+
103 (%make-qd-d
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) -
51)
104 (scale-float (float -
8805633374462953 1.0d0
) -
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105 (scale-float (float -
7296007962371596 1.0d0
) -
159)
106 (scale-float (float -
5296362421624049 1.0d0
) -
213)))
108 (defconstant +qd-eps
+
109 (scale-float 1d0 -
209))
111 (defconstant +qd-sin-table
+
115 (%make-qd-d
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) -
224))
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) -
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) -
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123 (%make-qd-d
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) -
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127 (%make-qd-d
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128 (scale-float (float 7185921569156509 1.0d0
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) -
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131 (%make-qd-d
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135 (%make-qd-d
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136 (scale-float (float 7704904742673764 1.0d0
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139 (%make-qd-d
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140 (scale-float (float -
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141 (scale-float (float -
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142 (scale-float (float 8566398131092182 1.0d0
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143 (%make-qd-d
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) -
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144 (scale-float (float -
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145 (scale-float (float 7289253486557291 1.0d0
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146 (scale-float (float -
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) -
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147 (%make-qd-d
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) -
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148 (scale-float (float -
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) -
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149 (scale-float (float -
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150 (scale-float (float -
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) -
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151 (%make-qd-d
(scale-float (float 8841410057981697 1.0d0
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152 (scale-float (float -
5627969559234246 1.0d0
) -
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153 (scale-float (float -
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) -
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154 (scale-float (float -
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) -
225))
155 (%make-qd-d
(scale-float (float 4862615327261055 1.0d0
) -
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156 (scale-float (float -
5217239170857332 1.0d0
) -
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157 (scale-float (float -
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) -
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158 (scale-float (float 5522987872330073 1.0d0
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159 (%make-qd-d
(scale-float (float 5304479856743885 1.0d0
) -
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160 (scale-float (float 6340842145528512 1.0d0
) -
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161 (scale-float (float -
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162 (scale-float (float -
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) -
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163 (%make-qd-d
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) -
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164 (scale-float (float 4845186982751657 1.0d0
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168 (scale-float (float 7360584602593505 1.0d0
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169 (scale-float (float 7946504576809704 1.0d0
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171 (%make-qd-d
(scale-float (float 6629757244884614 1.0d0
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172 (scale-float (float -
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) -
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175 (%make-qd-d
(scale-float (float 7071397114140692 1.0d0
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176 (scale-float (float -
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) -
113)
177 (scale-float (float -
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178 (scale-float (float -
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179 (%make-qd-d
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180 (scale-float (float -
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182 (scale-float (float -
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183 (%make-qd-d
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184 (scale-float (float -
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187 (%make-qd-d
(scale-float (float 8395900745453257 1.0d0
) -
57)
188 (scale-float (float 4839201044457661 1.0d0
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189 (scale-float (float 5799570435052711 1.0d0
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195 (%make-qd-d
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200 (scale-float (float -
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216 (scale-float (float -
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) -
217))
2041 (%make-qd-d
(scale-float (float 6945095779491208 1.0d0
) -
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2042 (scale-float (float -
7230020631985237 1.0d0
) -
107)
2043 (scale-float (float -
8729130008304460 1.0d0
) -
161)
2044 (scale-float (float -
7244986705962520 1.0d0
) -
216))
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) -
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) -
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2047 (scale-float (float 7641557639387694 1.0d0
) -
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2048 (scale-float (float -
8529781507802362 1.0d0
) -
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2049 (%make-qd-d
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) -
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2050 (scale-float (float -
6128826147983157 1.0d0
) -
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2051 (scale-float (float -
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162)
2052 (scale-float (float -
4747232722969418 1.0d0
) -
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2053 (%make-qd-d
(scale-float (float 6892014024666815 1.0d0
) -
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2054 (scale-float (float -
5307050774979789 1.0d0
) -
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2055 (scale-float (float 6534150355198809 1.0d0
) -
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2056 (scale-float (float -
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) -
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2057 (%make-qd-d
(scale-float (float 6874190143201685 1.0d0
) -
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2058 (scale-float (float 6831699276871462 1.0d0
) -
111)
2059 (scale-float (float 6569994269441010 1.0d0
) -
165)
2060 (scale-float (float 6039155211825079 1.0d0
) -
222))
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) -
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2062 (scale-float (float 5730269256517324 1.0d0
) -
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2063 (scale-float (float 7502511311955837 1.0d0
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2064 (scale-float (float -
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) -
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2066 (scale-float (float -
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2068 (scale-float (float -
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) -
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2070 (scale-float (float -
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) -
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2076 (scale-float (float -
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) -
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2080 (scale-float (float -
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2081 (%make-qd-d
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) -
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2082 (scale-float (float 7058239787845383 1.0d0
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2084 (scale-float (float -
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2085 (%make-qd-d
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) -
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2086 (scale-float (float -
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2087 (scale-float (float -
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2088 (scale-float (float 5969459465011328 1.0d0
) -
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2089 (%make-qd-d
(scale-float (float 6729284021401222 1.0d0
) -
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2090 (scale-float (float 7707201987390816 1.0d0
) -
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2091 (scale-float (float 5142737538491299 1.0d0
) -
164)
2092 (scale-float (float 4644279882924390 1.0d0
) -
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2093 (%make-qd-d
(scale-float (float 6710883929767346 1.0d0
) -
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2094 (scale-float (float 4893313667710853 1.0d0
) -
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2095 (scale-float (float 4729360090805088 1.0d0
) -
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2096 (scale-float (float 8707005308054696 1.0d0
) -
216))
2097 (%make-qd-d
(scale-float (float 6692420672738099 1.0d0
) -
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2098 (scale-float (float -
8159898852694060 1.0d0
) -
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) -
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2100 (scale-float (float 6356993048951430 1.0d0
) -
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) -
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2103 (scale-float (float -
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2104 (scale-float (float 6620801067481707 1.0d0
) -
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2105 (%make-qd-d
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) -
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2106 (scale-float (float 5569529363635887 1.0d0
) -
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2107 (scale-float (float -
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2108 (scale-float (float -
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) -
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2109 (%make-qd-d
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) -
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2110 (scale-float (float -
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) -
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2111 (scale-float (float -
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2112 (scale-float (float -
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) -
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2113 (%make-qd-d
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) -
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2114 (scale-float (float -
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) -
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2115 (scale-float (float -
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) -
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2116 (scale-float (float -
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) -
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) -
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2118 (scale-float (float 6139460555376271 1.0d0
) -
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) -
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(scale-float (float 6580324430530404 1.0d0
) -
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) -
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2123 (scale-float (float -
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) -
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2124 (scale-float (float -
6430688881172527 1.0d0
) -
217))
2125 (%make-qd-d
(scale-float (float 6561423914750605 1.0d0
) -
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2126 (scale-float (float 4953302629983138 1.0d0
) -
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2127 (scale-float (float 8830091491978098 1.0d0
) -
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2128 (scale-float (float 6566412636432061 1.0d0
) -
225))
2129 (%make-qd-d
(scale-float (float 6542461640350018 1.0d0
) -
53)
2130 (scale-float (float -
5178910864670558 1.0d0
) -
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2131 (scale-float (float 4504226005724943 1.0d0
) -
162)
2132 (scale-float (float 8731627485611706 1.0d0
) -
217))
2133 (%make-qd-d
(scale-float (float 6523437785808790 1.0d0
) -
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2134 (scale-float (float 4737722843238748 1.0d0
) -
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2135 (scale-float (float 6730894629032702 1.0d0
) -
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2136 (scale-float (float -
8714007801572383 1.0d0
) -
222))
2137 (%make-qd-d
(scale-float (float 6504352530186687 1.0d0
) -
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2138 (scale-float (float -
7746667435587544 1.0d0
) -
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2139 (scale-float (float 6217885893994028 1.0d0
) -
162)
2140 (scale-float (float -
4696784861307301 1.0d0
) -
216))
2141 (%make-qd-d
(scale-float (float 6485206053121402 1.0d0
) -
53)
2142 (scale-float (float -
8336770935428512 1.0d0
) -
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2143 (scale-float (float -
5348661455957571 1.0d0
) -
162)
2144 (scale-float (float 4676263914929793 1.0d0
) -
216))
2145 (%make-qd-d
(scale-float (float 6465998534826869 1.0d0
) -
53)
2146 (scale-float (float 8764102551217140 1.0d0
) -
108)
2147 (scale-float (float -
5344409034097828 1.0d0
) -
164)
2148 (scale-float (float 7727976365078167 1.0d0
) -
219))
2149 (%make-qd-d
(scale-float (float 6446730156091567 1.0d0
) -
53)
2150 (scale-float (float -
8369498756096622 1.0d0
) -
107)
2151 (scale-float (float -
6424186581703649 1.0d0
) -
165)
2152 (scale-float (float 7285509676227856 1.0d0
) -
219))
2153 (%make-qd-d
(scale-float (float 6427401098276813 1.0d0
) -
53)
2154 (scale-float (float -
6870464143590238 1.0d0
) -
107)
2155 (scale-float (float -
4991363196461545 1.0d0
) -
163)
2156 (scale-float (float -
5550457137190991 1.0d0
) -
217))
2157 (%make-qd-d
(scale-float (float 6408011543315061 1.0d0
) -
53)
2158 (scale-float (float 5169145614950999 1.0d0
) -
109)
2159 (scale-float (float 6895537652308040 1.0d0
) -
164)
2160 (scale-float (float 7155016695131698 1.0d0
) -
218))
2161 (%make-qd-d
(scale-float (float 6388561673708188 1.0d0
) -
53)
2162 (scale-float (float -
6100520299916709 1.0d0
) -
107)
2163 (scale-float (float 4963552307172142 1.0d0
) -
165)
2164 (scale-float (float 7537451794849143 1.0d0
) -
219))
2165 (%make-qd-d
(scale-float (float 6369051672525773 1.0d0
) -
53)
2166 (scale-float (float -
7843040109683798 1.0d0
) -
107)
2167 (scale-float (float 6048680740045173 1.0d0
) -
161)
2168 (scale-float (float 5197737643093849 1.0d0
) -
217))))
2169 "A table of cos(k/1024) for k = 1 to 256")
2173 ;; Here is a function for clisp that can be used to create the atan2 table
2176 (defun make-atan-table-data ()
2179 (let* ((x (scale-float 1L0 (- 2 k
)))
2181 (setf scale
(* scale
(cos p
)))
2182 (multiple-value-bind (int exp sign
)
2183 (integer-decode-float p
)
2184 (let* ((len (integer-length int
))
2185 (wanted (ldb (byte 212 (- len
212)) int
))
2186 (bit (ldb (byte 1 (- len
(* 4 53) 1)) int
))
2187 (roundp (not (zerop (ldb (byte (- len
(* 4 53) 2) 0) int
)))))
2188 ;;(format t "~&~v,'0b~%" len int)
2189 ;;(format t "~b~a~%" wanted (make-string (- len 212) :initial-element #\-))
2190 ;;(format t "~v,'-b~%" len (ash bit (- len 212 1)))
2191 ;;(format t "~v,'-b~%" len (ldb (byte (- len (* 4 53) 2) 0) int))
2192 ;; See if we need to round up the answer.
2201 ;;(format t "~b~a~%" wanted (make-string (- len 212) :initial-element #\-))
2203 (let* ((i0 (ldb (byte 53 (* 3 53)) wanted
))
2204 (i1 (ldb (byte 53 (* 2 53)) wanted
))
2205 (i2 (ldb (byte 53 (* 1 53)) wanted
))
2206 (i3 (ldb (byte 53 0) wanted
)))
2208 (scale-float (float ,i0
1d0
) ,(+ exp
(- len
(* 1 53))))
2209 (scale-float (float ,i1
1d0
) ,(+ exp
(- len
(* 2 53))))
2210 (scale-float (float ,i2
1d0
) ,(+ exp
(- len
(* 3 53))))
2211 (scale-float (float ,i3
1d0
) ,(+ exp
(- len
(* 4 53)))))
2212 :case
:downcase
))))))
2218 (defconstant +atan-table
+
2225 ;; Do we need to make these values more accurate? (The
2226 ;; reader has quite a bit of roundoff.)
2227 #.
(qd-from-string "0.46364760900080611621425623146121440202853705428612026381093308872018q0")
2228 #.
(qd-from-string "0.24497866312686415417208248121127581091414409838118406712737591466738q0")
2229 #.
(qd-from-string "0.12435499454676143503135484916387102557317019176980408991511411911572q0")
2230 #.
(qd-from-string "0.062418809995957348473979112985505113606273887797499194607527816898697q0")
2231 #.
(qd-from-string "0.031239833430268276253711744892490977032495663725400040255315586255793q0")
2232 #.
(qd-from-string "0.0156237286204768308028015212565703189111141398009054178814105073966645q0")
2233 #.
(qd-from-string "0.0078123410601011112964633918421992816212228117250147235574539022483893q0")
2234 #.
(qd-from-string "0.003906230131966971827628665311424387140357490115202856215213095149011q0")
2235 #.
(qd-from-string "0.00195312251647881868512148262507671393161074677723351033905753396043094q0")
2236 #.
(qd-from-string "9.7656218955931943040343019971729085163419701581008759004900725226773q-4")
2237 #.
(qd-from-string "4.8828121119489827546923962564484866619236113313500303710940335348752q-4")
2238 #.
(qd-from-string "2.4414062014936176401672294325965998621241779097061761180790046091019q-4")
2239 #.
(qd-from-string "1.22070311893670204239058646117956300930829409015787498451939837846645q-4")
2240 #.
(qd-from-string "6.1035156174208775021662569173829153785143536833346179337671134316588q-5")
2241 #.
(qd-from-string "3.0517578115526096861825953438536019750949675119437837531021156883611q-5")
2242 #.
(qd-from-string "1.5258789061315762107231935812697885137429238144575874846241186407446q-5")
2243 #.
(qd-from-string "7.6293945311019702633884823401050905863507439184680771577638306965336q-6")
2244 #.
(qd-from-string "3.8146972656064962829230756163729937228052573039688663101874392503939q-6")
2245 #.
(qd-from-string "1.9073486328101870353653693059172441687143421654501533666700577234671q-6")
2246 #.
(qd-from-string "9.53674316405960879420670689923112390019634124498790160133611802076q-7")
2247 #.
(qd-from-string "4.7683715820308885992758382144924707587049404378664196740053215887142q-7")
2248 #.
(qd-from-string "2.3841857910155798249094797721893269783096898769063155913766911372218q-7")
2249 #.
(qd-from-string "1.19209289550780685311368497137922112645967587664586735576738225215437q-7")
2250 #.
(qd-from-string "5.9604644775390554413921062141788874250030195782366297314294565710003q-8")
2251 #.
(qd-from-string "2.9802322387695303676740132767709503349043907067445107249258477840843q-8")
2252 #.
(qd-from-string "1.4901161193847655147092516595963247108248930025964720012170057805491q-8")
2253 #.
(qd-from-string "7.4505805969238279871365645744953921132066925545665870075947601416172q-9")
2254 #.
(qd-from-string "3.725290298461914045267070571811923583671948328737040524231998269239q-9")
2255 #.
(qd-from-string "1.8626451492309570290958838214764904345065282835738863513491050124951q-9")
2256 #.
(qd-from-string "9.3132257461547851535573547768456130389292649614929067394376854242196q-10")
2257 #.
(qd-from-string "4.6566128730773925777884193471057016297347863891561617421323492554414q-10")
2258 #.
(qd-from-string "2.32830643653869628902042741838821270371274293204981860525486662280605q-10")
2259 #.
(qd-from-string "1.16415321826934814452599092729852658796396457380014290026584979170883q-10")
2260 #.
(qd-from-string "5.8207660913467407226496761591231582349549156257795272423976206167147q-11")
2261 #.
(qd-from-string "2.9103830456733703613273032698903947793693632003639830495829934525029q-11")
2262 #.
(qd-from-string "1.4551915228366851806639597837362993474211703608936710732067270213307q-11")
2263 #.
(qd-from-string "7.2759576141834259033201841046703741842764629388821429640111752890838q-12")
2264 #.
(qd-from-string "3.6379788070917129516601402005837967730345578669779258118296083646486q-12")
2265 #.
(qd-from-string "1.81898940354585647583007611882297459662931973336029253714520765350336q-12")
2266 #.
(qd-from-string "9.094947017729282379150388117278718245786649666696631862264792881855q-13")
2267 #.
(qd-from-string "4.5474735088646411895751949990348397807233312083369623012466392138249q-13")
2268 #.
(qd-from-string "2.2737367544323205947875976170668549725904164010421166413578155299654q-13")
2269 #.
(qd-from-string "1.1368683772161602973937988232271068715738020501302644662229139921281q-13")
2270 #.
(qd-from-string "5.6843418860808014869689941345026335894672525626628305471702634435609q-14")
2271 #.
(qd-from-string "2.8421709430404007434844970695472041986834065703328538172835210852389q-14")
2272 #.
(qd-from-string "1.42108547152020037174224853506058802483542582129160672712566632799217q-14")
2273 #.
(qd-from-string "7.1054273576010018587112426756616725310442822766145084088962160950957q-15")
2274 #.
(qd-from-string "3.5527136788005009293556213378756778163805352845768135511116874239215q-15")
2275 #.
(qd-from-string "1.7763568394002504646778106689434441020475669105721016938889503158663q-15")
2276 #.
(qd-from-string "8.881784197001252323389053344724227002559458638215127117361184578544q-16")
2277 #.
(qd-from-string "4.440892098500626161694526672362989312819932329776890889670147968684q-16")
2278 #.
(qd-from-string "2.22044604925031308084726333618160413285249154122211136120876849284695q-16")
2279 #.
(qd-from-string "1.11022302462515654042363166809081575098156144265276392015109606150467q-16")
2280 #.
(qd-from-string "5.5511151231257827021181583404540958606019518033159549001888700768492q-17")
2281 #.
(qd-from-string "2.7755575615628913510590791702270500685127439754144943625236087596052q-17")
2282 #.
(qd-from-string "1.3877787807814456755295395851135253015328429969268117953154510949506q-17")
2283 #.
(qd-from-string "6.9388939039072283776476979255676268417598037461585147441443138686883q-18")
2284 #.
(qd-from-string "3.4694469519536141888238489627838134626418504682698143430180392335861q-18")
2285 #.
(qd-from-string "1.7347234759768070944119244813919067365411688085337267928772549041983q-18")
2286 #.
(qd-from-string "8.673617379884035472059622406959533689231148510667158491096568630248q-19")
2287 #.
(qd-from-string "4.336808689942017736029811203479766845431237313833394811387071078781q-19")
2288 #.
(qd-from-string "2.16840434497100886801490560173988342281757653922917435142338388484765q-19")
2289 #.
(qd-from-string "1.08420217248550443400745280086994171142153300490364679392792298560597q-19")
2292 "Table of atan(2^(-k)) for k = 1 to 64. But the first three entries are 1")
2294 (defconstant +atan-table
+
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) -
167)
2552 (scale-float (float 9007153441756501 1.0d0
) -
220)
2553 (scale-float (float 3002399751580331 1.0d0
) -
273))
2554 (%make-qd-d
(scale-float (float 9007199254740991 1.0d0
) -
115)
2555 (scale-float (float 9007199254740991 1.0d0
) -
168)
2556 (scale-float (float 9007187801494869 1.0d0
) -
221)
2557 (scale-float (float 3002399751580331 1.0d0
) -
274))
2558 (%make-qd-d
(scale-float (float 9007199254740991 1.0d0
) -
116)
2559 (scale-float (float 9007199254740991 1.0d0
) -
169)
2560 (scale-float (float 9007196391429461 1.0d0
) -
222)
2561 (scale-float (float 3002399751580331 1.0d0
) -
275))
2562 (%make-qd-d
(scale-float (float 9007199254740991 1.0d0
) -
117)
2563 (scale-float (float 9007199254740991 1.0d0
) -
170)
2564 (scale-float (float 9007198538913109 1.0d0
) -
223)
2565 (scale-float (float 3002399751580331 1.0d0
) -
276))
2567 "Table of atan(2^(-k)) for k = -2 to 64. But the first three entries are 1")
2569 (defconstant +atan-power-table
+
2571 :element-type
'double-float
2573 (loop for k from
0 below
67
2574 collect
(scale-float 1d0
(- 2 k
)))
2576 "Table of (2^(-k)) for k = -2 to 64. But the first three entries are 1")
2578 (defconstant +cordic-scale
+
2579 #.
(qd-from-string "0.065865828601599636584870082133151126045971796871364763285694473524426q0"))
2583 (multiple-value-bind (int exp sign
)
2584 (integer-decode-float d
)
2585 `(scale-float (float ,(* sign int
) 1d0
) ,exp
))))
2586 (multiple-value-bind (q0 q1 q2 q3
)
2588 `(%make-qd-d
,(dump-d q0
)
