[oct-cvs] Oct commit: oct qd-const.lisp qd-extra.lisp
rtoy
rtoy at common-lisp.net
Thu Oct 11 17:47:09 UTC 2007
Update of /project/oct/cvsroot/oct
In directory clnet:/tmp/cvs-serv32694
Modified Files:
qd-const.lisp qd-extra.lisp
Log Message:
qd-const.lisp:
o Add code for clisp to create the constants we need. (Clisp has
arbitrary length long-float numbers.)
o Update the constants accordingly.
o Move the atan table stuff for CORDIC to qd-extra.lisp, since we
don't need them in oct itself.
qd-extra.lisp:
o atan table stuff for CORDIC moved here.
--- /project/oct/cvsroot/oct/qd-const.lisp 2007/08/27 17:49:19 1.16
+++ /project/oct/cvsroot/oct/qd-const.lisp 2007/10/11 17:47:08 1.17
@@ -31,50 +31,78 @@
(defconstant +qd-one+
(make-qd-d 1d0))
-(defconstant +qd-2pi+
- (%make-qd-d (scale-float (float 7074237752028440 1.0d0) -50)
- (scale-float (float 4967757600021511 1.0d0) -104)
- (scale-float (float -8753721960665020 1.0d0) -160)
- (scale-float (float 5857755168774013 1.0d0) -214)))
-
-;; 3.1415926535897932384626433832795028841971693993751058209749445923078L0
+;; 3.1415926535897932384626433832795028841971693993751058209749445923078L0
+;; #q3.1415926535897932384626433832795028841971693993751058209749445923q0
(defconstant +qd-pi+
- (%make-qd-d (scale-float (float 7074237752028440 1.0d0) -51)
- (scale-float (float 4967757600021511 1.0d0) -105)
- (scale-float (float -8753721960665020 1.0d0) -161)
- (scale-float (float 5857755168774013 1.0d0) -215)))
+ (multiple-value-call #'%make-qd-d
+ (renorm-5 (scale-float (float 7074237752028440 1.0d0) -51)
+ (scale-float (float 4967757600021511 1.0d0) -105)
+ (scale-float (float -8753721960665020 1.0d0) -161)
+ (scale-float (float 5857755168774013 1.0d0) -215)
+ (scale-float (float 5380502254059520 1.0d0) -269))))
+
+;; 6.2831853071795864769252867665590057683943387987502116419498891846156328125724L0
+;; #q6.2831853071795864769252867665590057683943387987502116419498891846q0
+(defconstant +qd-2pi+
+ (multiple-value-call #'%make-qd-d
+ (renorm-5 (scale-float (float 7074237752028440 1.0d0) -50)
+ (scale-float (float 4967757600021511 1.0d0) -104)
+ (scale-float (float -8753721960665020 1.0d0) -160)
+ (scale-float (float 5857755168774013 1.0d0) -214)
+ (scale-float (float 5380502254059520 1.0d0) -268))))
+;; 1.5707963267948966192313216916397514420985846996875529104874722961539082031431L0
+;; #q1.57079632679489661923132169163975144209858469968755291048747229615q0
(defconstant +qd-pi/2+
- (%make-qd-d (scale-float (float 7074237752028440 1.0d0) -52)
- (scale-float (float 4967757600021511 1.0d0) -106)
- (scale-float (float -8753721960665020 1.0d0) -162)
- (scale-float (float 5857755168774013 1.0d0) -216)))
+ (multiple-value-call #'%make-qd-d
+ (renorm-5 (scale-float (float 7074237752028440 1.0d0) -52)
+ (scale-float (float 4967757600021511 1.0d0) -106)
+ (scale-float (float -8753721960665020 1.0d0) -162)
+ (scale-float (float 5857755168774013 1.0d0) -216)
+ (scale-float (float 5380502254059520 1.0d0) -270))))
+;; 0.78539816339744830961566084581987572104929234984377645524373614807695410157155L0
+;; #q0.785398163397448309615660845819875721049292349843776455243736148076q0
(defconstant +qd-pi/4+
- (%make-qd-d (scale-float (float 7074237752028440 1.0d0) -53)
- (scale-float (float 4967757600021511 1.0d0) -107)
- (scale-float (float -8753721960665020 1.0d0) -163)
- (scale-float (float 5857755168774013 1.0d0) -217)))
+ (multiple-value-call #'%make-qd-d
+ (renorm-5 (scale-float (float 7074237752028440 1.0d0) -53)
+ (scale-float (float 4967757600021511 1.0d0) -107)
+ (scale-float (float -8753721960665020 1.0d0) -163)
+ (scale-float (float 5857755168774013 1.0d0) -217)
+ (scale-float (float 5380502254059520 1.0d0) -271))))
+;; 2.35619449019234492884698253745962716314787704953132936573120844423086230471467L0
+;; #q2.35619449019234492884698253745962716314787704953132936573120844423q0
(defconstant +qd-3pi/4+
- (%make-qd-d (scale-float (float 5305678314021330 1.0d0) -51)
- (scale-float (float 7451636400032266 1.0d0) -106)
- (scale-float (float 5724553519491610 1.0d0) -160)
- (scale-float (float -6810541066450736 1.0d0) -214)))
+ (multiple-value-call #'%make-qd-d
+ (renorm-5 (scale-float (float 5305678314021330 1.0d0) -51)
+ (scale-float (float 7451636400032266 1.0d0) -106)
+ (scale-float (float 5724553519491610 1.0d0) -160)
+ (scale-float (float -6810541066450737 1.0d0) -214)
+ (scale-float (float -7491566988951552 1.0d0) -273))))
+;; 0.00306796157577128245943617517898388953534879824157725177829584432842560195926387L0
+;; #q0.00306796157577128245943617517898388953534879824157725177829584432842q0
(defconstant +qd-pi/1024+
- (%make-qd-d (scale-float (float 7074237752028440 1.0d0) -61)
- (scale-float (float 4967757600021511 1.0d0) -115)
- (scale-float (float -8753721960665020 1.0d0) -171)
- (scale-float (float 5857755168774013 1.0d0) -225)))
+ (multiple-value-call #'%make-qd-d
+ (renorm-5 (scale-float (float 7074237752028440 1.0d0) -61)
+ (scale-float (float 4967757600021511 1.0d0) -115)
+ (scale-float (float -8753721960665020 1.0d0) -171)
+ (scale-float (float 5857755168774013 1.0d0) -225)
+ (scale-float (float 5380502254059520 1.0d0) -279))))
+;; 2.71828182845904523536028747135266249775724709369995957496696762772407663035355L0
+;; #q2.71828182845904523536028747135266249775724709369995957496696762773q0
(defconstant +qd-e+
- (%make-qd-d (scale-float (float 6121026514868073 1.0d0) -51)
- (scale-float (float 5864240480059706 1.0d0) -105)
- (scale-float (float -6219324074349538 1.0d0) -161)
- (scale-float (float 7980724272743020 1.0d0) -215)))
+ (multiple-value-call #'%make-qd-d
+ (renorm-5 (scale-float (float 6121026514868073 1.0d0) -51)
+ (scale-float (float 5864240480059706 1.0d0) -105)
+ (scale-float (float -6219324074349538 1.0d0) -161)
+ (scale-float (float 7980724272743021 1.0d0) -215)
+ (scale-float (float -8855251465666560 1.0d0) -269))))
-;; 0.6931471805599453094172321214581765680755001343602552541206800094934L0
+;; 0.693147180559945309417232121458176568075500134360255254120680009493393621969696L0
+;; #q0.693147180559945309417232121458176568075500134360255254120680009495q0
(defconstant +qd-log2+
#+nil
(make-qd-d 6.931471805599452862d-01
@@ -82,2510 +110,3198 @@
5.707708438416212066d-34
-3.582432210601811423d-50)
(%make-qd-d (scale-float (float 6243314768165359 1.0d0) -53)
- (scale-float (float 7525737178955839 1.0d0) -108)
- (scale-float (float 6673460182522164 1.0d0) -163)
- (scale-float (float -7545482916914656 1.0d0) -217)))
+ (scale-float (float 7525737178955839 1.0d0) -108)
+ (scale-float (float 6673460182522164 1.0d0) -163)
+ (scale-float (float -7545482916914641 1.0d0) -217)))
;; The rest of log(2) such that (+ +qd-log2+ +qd-log2-extra+) is
;; log(2) to twice the precision of a quad-double.
(defconstant +qd-log2-extra+
- #+nil
- (make-qd-d (scale-float (float 4141960528156623 1d0) (- -53 212))
- (scale-float (float 3973120087747366 1d0) (- -106 212))
- (scale-float (float 752798645508048 1d0) (- -159 212))
- (scale-float (float 7618435247650241 1d0) (- -212 212)))
- (%make-qd-d (scale-float (float 8283921056313247 1.0d0) -266)
- (scale-float (float -8487672633970079 1.0d0) -322)
- (scale-float (float 6075158146775579 1.0d0) -376)
- (scale-float (float 4764384374407424 1.0d0) -432)))
+ (%make-qd-d (scale-float (float -5130503840205860 1.0d0) -271)
+ (scale-float (float 8312425932334613 1.0d0) -326)
+ (scale-float (float 7130537800999345 1.0d0) -380)
+ (scale-float (float 8345111905183492 1.0d0) -437)))
+;; Log(10)
+;; 2.30258509299404568401799145468436420760110148862877297603332790096757260967737L0
+;; #q2.30258509299404568401799145468436420760110148862877297603332790095q0
(defconstant +qd-log10+
- (%make-qd-d (scale-float (float 5184960683398422 1.0d0) -51)
- (scale-float (float -8805633374462953 1.0d0) -105)
- (scale-float (float -7296007962371596 1.0d0) -159)
- (scale-float (float -5296362421624049 1.0d0) -213)))
+ (multiple-value-call #'%make-qd-d
+ (renorm-5 (scale-float (float 5184960683398422 1.0d0) -51)
+ (scale-float (float -8805633374462953 1.0d0) -105)
+ (scale-float (float -7296007962371596 1.0d0) -159)
+ (scale-float (float -5296362421624049 1.0d0) -213)
+ (scale-float (float 4574234754834432 1.0d0) -267))))
(defconstant +qd-eps+
(scale-float 1d0 -209))
(defconstant +qd-sin-table+
- (make-array 256
- :initial-contents
+ (make-array 256 :initial-contents
(list
- (%make-qd-d (scale-float (float 7074226654454970 1.0d0) -61)
- (scale-float (float 5271335698347442 1.0d0) -115)
- (scale-float (float 7913822574154586 1.0d0) -170)
- (scale-float (float -4804352564403217 1.0d0) -224))
- (%make-qd-d (scale-float (float 7074193361797233 1.0d0) -60)
- (scale-float (float 7522205695703707 1.0d0) -116)
- (scale-float (float 7787047147324868 1.0d0) -175)
- (scale-float (float -6728650631839117 1.0d0) -232))
- (%make-qd-d (scale-float (float 5305603405682435 1.0d0) -59)
- (scale-float (float -5041342953893321 1.0d0) -115)
- (scale-float (float 8335474310793984 1.0d0) -170)
- (scale-float (float 6743025479788607 1.0d0) -225))
- (%make-qd-d (scale-float (float 7074060192106372 1.0d0) -59)
- (scale-float (float 7185921569156509 1.0d0) -113)
- (scale-float (float -6016799991653399 1.0d0) -170)
- (scale-float (float -5577663458559350 1.0d0) -224))
- (%make-qd-d (scale-float (float 8842450394781643 1.0d0) -59)
- (scale-float (float -8771095658131507 1.0d0) -113)
- (scale-float (float 8705573170983202 1.0d0) -167)
- (scale-float (float -4692271881407162 1.0d0) -221))
- (%make-qd-d (scale-float (float 5305378684473085 1.0d0) -58)
- (scale-float (float 7704904742673764 1.0d0) -113)
- (scale-float (float 7308626221243388 1.0d0) -167)
- (scale-float (float 4905810005485122 1.0d0) -223))
- (%make-qd-d (scale-float (float 6189482235310630 1.0d0) -58)
- (scale-float (float -4715432182777116 1.0d0) -113)
- (scale-float (float -8243063834437948 1.0d0) -168)
- (scale-float (float 8566398131092182 1.0d0) -222))
- (%make-qd-d (scale-float (float 7073527528384126 1.0d0) -58)
- (scale-float (float -7632135562854704 1.0d0) -116)
- (scale-float (float 7289253486557291 1.0d0) -170)
- (scale-float (float -7590289326531904 1.0d0) -224))
- (%make-qd-d (scale-float (float 7957506242722589 1.0d0) -58)
- (scale-float (float -8272553670927212 1.0d0) -112)
- (scale-float (float -6591995918745221 1.0d0) -166)
- (scale-float (float -4636857096009409 1.0d0) -220))
- (%make-qd-d (scale-float (float 8841410057981697 1.0d0) -58)
- (scale-float (float -5627969559234246 1.0d0) -118)
- (scale-float (float -5998146560009404 1.0d0) -171)
- (scale-float (float -8771421402740511 1.0d0) -225))
- (%make-qd-d (scale-float (float 4862615327261055 1.0d0) -57)
- (scale-float (float -5217239170857332 1.0d0) -111)
- (scale-float (float -6336246586437174 1.0d0) -165)
- (scale-float (float 5522987872330073 1.0d0) -219))
- (%make-qd-d (scale-float (float 5304479856743885 1.0d0) -57)
- (scale-float (float 6340842145528512 1.0d0) -113)
- (scale-float (float -7566831660699656 1.0d0) -167)
- (scale-float (float -7114412056121165 1.0d0) -221))
- (%make-qd-d (scale-float (float 5746294458442105 1.0d0) -57)
- (scale-float (float 4845186982751657 1.0d0) -113)
- (scale-float (float 6382779118838290 1.0d0) -167)
- (scale-float (float 8090523197847278 1.0d0) -221))
- (%make-qd-d (scale-float (float 6188054973828419 1.0d0) -57)
- (scale-float (float 7360584602593505 1.0d0) -111)
- (scale-float (float 7946504576809704 1.0d0) -165)
- (scale-float (float 5731224328660037 1.0d0) -219))
- (%make-qd-d (scale-float (float 6629757244884614 1.0d0) -57)
- (scale-float (float -5806448969106076 1.0d0) -112)
- (scale-float (float 7037190739826080 1.0d0) -166)
- (scale-float (float 5552037724818900 1.0d0) -223))
- (%make-qd-d (scale-float (float 7071397114140692 1.0d0) -57)
- (scale-float (float -7057477599664784 1.0d0) -113)
- (scale-float (float -8290828586102809 1.0d0) -167)
- (scale-float (float -6697971486035361 1.0d0) -222))
- (%make-qd-d (scale-float (float 7512970424714007 1.0d0) -57)
- (scale-float (float -6294023145184360 1.0d0) -111)
- (scale-float (float -6395720725273163 1.0d0) -165)
- (scale-float (float -7071774105018818 1.0d0) -219))
- (%make-qd-d (scale-float (float 7954473020348387 1.0d0) -57)
- (scale-float (float -6926679705961747 1.0d0) -112)
- (scale-float (float -6427721451859560 1.0d0) -167)
- (scale-float (float 8028310015339695 1.0d0) -222))
- (%make-qd-d (scale-float (float 8395900745453257 1.0d0) -57)
- (scale-float (float 4839201044457661 1.0d0) -114)
- (scale-float (float 5799570435052711 1.0d0) -171)
- (scale-float (float -5529353034270453 1.0d0) -226))
- (%make-qd-d (scale-float (float 8837249445142752 1.0d0) -57)
- (scale-float (float -5314952832401406 1.0d0) -113)
- (scale-float (float -7992910057771694 1.0d0) -167)
- (scale-float (float 8886165424019995 1.0d0) -221))
- (%make-qd-d (scale-float (float 4639257482637412 1.0d0) -56)
- (scale-float (float -5494228531443205 1.0d0) -110)
- (scale-float (float 6222043711193090 1.0d0) -167)
- (scale-float (float 4966112393074763 1.0d0) -221))
- (%make-qd-d (scale-float (float 4859846576245171 1.0d0) -56)
- (scale-float (float -8985502920124077 1.0d0) -110)
- (scale-float (float 7440463379940699 1.0d0) -165)
- (scale-float (float -6641325637598524 1.0d0) -219))
- (%make-qd-d (scale-float (float 5080389927126093 1.0d0) -56)
- (scale-float (float -8898661047761268 1.0d0) -110)
- (scale-float (float -4667727006484474 1.0d0) -164)
- (scale-float (float 8478536563323652 1.0d0) -218))
- (%make-qd-d (scale-float (float 5300885459442166 1.0d0) -56)
- (scale-float (float -7213383224879916 1.0d0) -111)
- (scale-float (float -8534269322822802 1.0d0) -166)
- (scale-float (float -6601733372219099 1.0d0) -221))
- (%make-qd-d (scale-float (float 5521331097805465 1.0d0) -56)
- (scale-float (float 4829604598179156 1.0d0) -114)
- (scale-float (float -7893599535446481 1.0d0) -172)
- (scale-float (float -5384211130874634 1.0d0) -226))
- (%make-qd-d (scale-float (float 5741724767297686 1.0d0) -56)
- (scale-float (float -5824155811343436 1.0d0) -110)
- (scale-float (float 6673985610265747 1.0d0) -164)
- (scale-float (float 4800782739249759 1.0d0) -220))
- (%make-qd-d (scale-float (float 5962064393489674 1.0d0) -56)
- (scale-float (float 7651360099479755 1.0d0) -112)
- (scale-float (float 6974817744235260 1.0d0) -167)
- (scale-float (float 7824970858345265 1.0d0) -224))
- (%make-qd-d (scale-float (float 6182347902460953 1.0d0) -56)
- (scale-float (float -8796242544913562 1.0d0) -111)
- (scale-float (float -7546272905440146 1.0d0) -165)
- (scale-float (float 6512061516709508 1.0d0) -219))
- (%make-qd-d (scale-float (float 6402573220819241 1.0d0) -56)
- (scale-float (float -4868008820827392 1.0d0) -110)
- (scale-float (float 8779206749884591 1.0d0) -164)
- (scale-float (float -8648470131210884 1.0d0) -218))
- (%make-qd-d (scale-float (float 6622738275719969 1.0d0) -56)
- (scale-float (float 6182934508221337 1.0d0) -110)
- (scale-float (float 7353282250945404 1.0d0) -165)
- (scale-float (float -8166192353391047 1.0d0) -220))
- (%make-qd-d (scale-float (float 6842840994885793 1.0d0) -56)
- (scale-float (float -8552477024466766 1.0d0) -110)
- (scale-float (float -4997427595980002 1.0d0) -164)
- (scale-float (float 5821398332046138 1.0d0) -218))
- (%make-qd-d (scale-float (float 7062879306626092 1.0d0) -56)
- (scale-float (float -8487236864497288 1.0d0) -112)
- (scale-float (float -4942162982072151 1.0d0) -168)
- (scale-float (float -4811145377091453 1.0d0) -223))
- (%make-qd-d (scale-float (float 7282851139856476 1.0d0) -56)
- (scale-float (float 8609951212389606 1.0d0) -111)
- (scale-float (float -5614142183842944 1.0d0) -165)
- (scale-float (float 6068416796043208 1.0d0) -219))
- (%make-qd-d (scale-float (float 7502754424118275 1.0d0) -56)
- (scale-float (float 8536169017599928 1.0d0) -110)
- (scale-float (float 7981550951145323 1.0d0) -165)
- (scale-float (float -8340622458345952 1.0d0) -220))
- (%make-qd-d (scale-float (float 7722587089598028 1.0d0) -56)
- (scale-float (float 8362719068102409 1.0d0) -110)
- (scale-float (float -7853008551658302 1.0d0) -166)
- (scale-float (float -6852498985157079 1.0d0) -220))
- (%make-qd-d (scale-float (float 7942347067146965 1.0d0) -56)
- (scale-float (float -5897359216343841 1.0d0) -113)
- (scale-float (float 7767443765766550 1.0d0) -169)
- (scale-float (float 8203371449514667 1.0d0) -225))
- (%make-qd-d (scale-float (float 8162032288300481 1.0d0) -56)
- (scale-float (float 7035687121204020 1.0d0) -111)
- (scale-float (float 5733124558862890 1.0d0) -168)
- (scale-float (float 6681272325774503 1.0d0) -223))
- (%make-qd-d (scale-float (float 8381640685297609 1.0d0) -56)
- (scale-float (float 5345425417737710 1.0d0) -112)
- (scale-float (float -8790124191829010 1.0d0) -166)
- (scale-float (float 7297964455931531 1.0d0) -225))
- (%make-qd-d (scale-float (float 8601170191100479 1.0d0) -56)
- (scale-float (float -5127404751534987 1.0d0) -110)
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- (scale-float (float 6354475203379338 1.0d0) -221))
- (%make-qd-d (scale-float (float 8820618739413774 1.0d0) -56)
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- (%make-qd-d (scale-float (float 4519992132352091 1.0d0) -55)
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- (%make-qd-d (scale-float (float 4629632351109917 1.0d0) -55)
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- (%make-qd-d (scale-float (float 4739228994004870 1.0d0) -55)
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- (%make-qd-d (scale-float (float 6377249128729266 1.0d0) -55)
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- (%make-qd-d (scale-float (float 6486008573510911 1.0d0) -55)
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[5397 lines skipped]
--- /project/oct/cvsroot/oct/qd-extra.lisp 2007/08/25 17:08:48 1.2
+++ /project/oct/cvsroot/oct/qd-extra.lisp 2007/10/11 17:47:08 1.3
@@ -477,6 +477,416 @@
(cl:* s y))))
||#
+#||
+;; Here is a function for clisp that can be used to create the atan2 table
+;; that we need.
+
+(defun make-atan-table-data ()
+ (let ((scale 1l0))
+ (dotimes (k 67)
+ (let* ((x (scale-float 1L0 (- 2 k)))
+ (p (atan x)))
+ (setf scale (* scale (cos p)))
+ (multiple-value-bind (int exp sign)
+ (integer-decode-float p)
+ (let* ((len (integer-length int))
+ (wanted (ldb (byte 212 (- len 212)) int))
+ (bit (ldb (byte 1 (- len (* 4 53) 1)) int))
+ (roundp (not (zerop (ldb (byte (- len (* 4 53) 2) 0) int)))))
+ ;;(format t "~&~v,'0b~%" len int)
+ ;;(format t "~b~a~%" wanted (make-string (- len 212) :initial-element #\-))
+ ;;(format t "~v,'-b~%" len (ash bit (- len 212 1)))
+ ;;(format t "~v,'-b~%" len (ldb (byte (- len (* 4 53) 2) 0) int))
+ ;; See if we need to round up the answer.
+ (when (= bit 1)
+ ;; Round to even
+ (cond (roundp
+ (incf wanted))
+ (t
+ ;; Round to even
+ (when (oddp wanted)
+ (incf wanted)))))
+ ;;(format t "~b~a~%" wanted (make-string (- len 212) :initial-element #\-))
+
+ (let* ((i0 (ldb (byte 53 (* 3 53)) wanted))
+ (i1 (ldb (byte 53 (* 2 53)) wanted))
+ (i2 (ldb (byte 53 (* 1 53)) wanted))
+ (i3 (ldb (byte 53 0) wanted)))
+ (write `(make-qd-d
+ (scale-float (float ,i0 1d0) ,(+ exp (- len (* 1 53))))
+ (scale-float (float ,i1 1d0) ,(+ exp (- len (* 2 53))))
+ (scale-float (float ,i2 1d0) ,(+ exp (- len (* 3 53))))
+ (scale-float (float ,i3 1d0) ,(+ exp (- len (* 4 53)))))
+ :case :downcase))))))
+ scale))
+||#
+
+
+#+nil
+(defconstant +atan-table+
+ (make-array 66
+ :initial-contents
+ (list
+ +qd-pi/4+
+ +qd-pi/4+
+ +qd-pi/4+
+ ;; Do we need to make these values more accurate? (The
+ ;; reader has quite a bit of roundoff.)
+ #.(qd-from-string "0.46364760900080611621425623146121440202853705428612026381093308872018q0")
+ #.(qd-from-string "0.24497866312686415417208248121127581091414409838118406712737591466738q0")
+ #.(qd-from-string "0.12435499454676143503135484916387102557317019176980408991511411911572q0")
+ #.(qd-from-string "0.062418809995957348473979112985505113606273887797499194607527816898697q0")
+ #.(qd-from-string "0.031239833430268276253711744892490977032495663725400040255315586255793q0")
+ #.(qd-from-string "0.0156237286204768308028015212565703189111141398009054178814105073966645q0")
+ #.(qd-from-string "0.0078123410601011112964633918421992816212228117250147235574539022483893q0")
+ #.(qd-from-string "0.003906230131966971827628665311424387140357490115202856215213095149011q0")
+ #.(qd-from-string "0.00195312251647881868512148262507671393161074677723351033905753396043094q0")
+ #.(qd-from-string "9.7656218955931943040343019971729085163419701581008759004900725226773q-4")
+ #.(qd-from-string "4.8828121119489827546923962564484866619236113313500303710940335348752q-4")
+ #.(qd-from-string "2.4414062014936176401672294325965998621241779097061761180790046091019q-4")
+ #.(qd-from-string "1.22070311893670204239058646117956300930829409015787498451939837846645q-4")
+ #.(qd-from-string "6.1035156174208775021662569173829153785143536833346179337671134316588q-5")
+ #.(qd-from-string "3.0517578115526096861825953438536019750949675119437837531021156883611q-5")
+ #.(qd-from-string "1.5258789061315762107231935812697885137429238144575874846241186407446q-5")
+ #.(qd-from-string "7.6293945311019702633884823401050905863507439184680771577638306965336q-6")
+ #.(qd-from-string "3.8146972656064962829230756163729937228052573039688663101874392503939q-6")
+ #.(qd-from-string "1.9073486328101870353653693059172441687143421654501533666700577234671q-6")
+ #.(qd-from-string "9.53674316405960879420670689923112390019634124498790160133611802076q-7")
+ #.(qd-from-string "4.7683715820308885992758382144924707587049404378664196740053215887142q-7")
+ #.(qd-from-string "2.3841857910155798249094797721893269783096898769063155913766911372218q-7")
+ #.(qd-from-string "1.19209289550780685311368497137922112645967587664586735576738225215437q-7")
+ #.(qd-from-string "5.9604644775390554413921062141788874250030195782366297314294565710003q-8")
+ #.(qd-from-string "2.9802322387695303676740132767709503349043907067445107249258477840843q-8")
+ #.(qd-from-string "1.4901161193847655147092516595963247108248930025964720012170057805491q-8")
+ #.(qd-from-string "7.4505805969238279871365645744953921132066925545665870075947601416172q-9")
+ #.(qd-from-string "3.725290298461914045267070571811923583671948328737040524231998269239q-9")
+ #.(qd-from-string "1.8626451492309570290958838214764904345065282835738863513491050124951q-9")
+ #.(qd-from-string "9.3132257461547851535573547768456130389292649614929067394376854242196q-10")
+ #.(qd-from-string "4.6566128730773925777884193471057016297347863891561617421323492554414q-10")
+ #.(qd-from-string "2.32830643653869628902042741838821270371274293204981860525486662280605q-10")
+ #.(qd-from-string "1.16415321826934814452599092729852658796396457380014290026584979170883q-10")
+ #.(qd-from-string "5.8207660913467407226496761591231582349549156257795272423976206167147q-11")
+ #.(qd-from-string "2.9103830456733703613273032698903947793693632003639830495829934525029q-11")
+ #.(qd-from-string "1.4551915228366851806639597837362993474211703608936710732067270213307q-11")
+ #.(qd-from-string "7.2759576141834259033201841046703741842764629388821429640111752890838q-12")
+ #.(qd-from-string "3.6379788070917129516601402005837967730345578669779258118296083646486q-12")
+ #.(qd-from-string "1.81898940354585647583007611882297459662931973336029253714520765350336q-12")
+ #.(qd-from-string "9.094947017729282379150388117278718245786649666696631862264792881855q-13")
+ #.(qd-from-string "4.5474735088646411895751949990348397807233312083369623012466392138249q-13")
+ #.(qd-from-string "2.2737367544323205947875976170668549725904164010421166413578155299654q-13")
+ #.(qd-from-string "1.1368683772161602973937988232271068715738020501302644662229139921281q-13")
+ #.(qd-from-string "5.6843418860808014869689941345026335894672525626628305471702634435609q-14")
+ #.(qd-from-string "2.8421709430404007434844970695472041986834065703328538172835210852389q-14")
+ #.(qd-from-string "1.42108547152020037174224853506058802483542582129160672712566632799217q-14")
+ #.(qd-from-string "7.1054273576010018587112426756616725310442822766145084088962160950957q-15")
+ #.(qd-from-string "3.5527136788005009293556213378756778163805352845768135511116874239215q-15")
+ #.(qd-from-string "1.7763568394002504646778106689434441020475669105721016938889503158663q-15")
+ #.(qd-from-string "8.881784197001252323389053344724227002559458638215127117361184578544q-16")
+ #.(qd-from-string "4.440892098500626161694526672362989312819932329776890889670147968684q-16")
+ #.(qd-from-string "2.22044604925031308084726333618160413285249154122211136120876849284695q-16")
+ #.(qd-from-string "1.11022302462515654042363166809081575098156144265276392015109606150467q-16")
+ #.(qd-from-string "5.5511151231257827021181583404540958606019518033159549001888700768492q-17")
+ #.(qd-from-string "2.7755575615628913510590791702270500685127439754144943625236087596052q-17")
+ #.(qd-from-string "1.3877787807814456755295395851135253015328429969268117953154510949506q-17")
+ #.(qd-from-string "6.9388939039072283776476979255676268417598037461585147441443138686883q-18")
+ #.(qd-from-string "3.4694469519536141888238489627838134626418504682698143430180392335861q-18")
+ #.(qd-from-string "1.7347234759768070944119244813919067365411688085337267928772549041983q-18")
+ #.(qd-from-string "8.673617379884035472059622406959533689231148510667158491096568630248q-19")
+ #.(qd-from-string "4.336808689942017736029811203479766845431237313833394811387071078781q-19")
+ #.(qd-from-string "2.16840434497100886801490560173988342281757653922917435142338388484765q-19")
+ #.(qd-from-string "1.08420217248550443400745280086994171142153300490364679392792298560597q-19")
+
+ ))
+ "Table of atan(2^(-k)) for k = 1 to 64. But the first three entries are 1")
+
+(defconstant +atan-table+
+ (make-array 67
+ :initial-contents
+ (list
+ (%make-qd-d (scale-float (float 5970951936056572 1.0d0) -52)
+ (scale-float (float 5427585433121543 1.0d0) -105)
+ (scale-float (float 5608515294538868 1.0d0) -158)
+ (scale-float (float 445395631680583 1.0d0) -211))
+ (%make-qd-d (scale-float (float 4986154552901188 1.0d0) -52)
+ (scale-float (float 3814906810089799 1.0d0) -105)
+ (scale-float (float 1896417689773139 1.0d0) -158)
+ (scale-float (float 3393132800284032 1.0d0) -211))
+ (%make-qd-d (scale-float (float 7074237752028440 1.0d0) -53)
+ (scale-float (float 2483878800010755 1.0d0) -106)
+ (scale-float (float 3956492004828932 1.0d0) -159)
+ (scale-float (float 2434854662709436 1.0d0) -212))
+ (%make-qd-d (scale-float (float 8352332796509007 1.0d0) -54)
+ (scale-float (float 3683087214424816 1.0d0) -107)
+ (scale-float (float 8240297260223171 1.0d0) -160)
+ (scale-float (float 5174086704442609 1.0d0) -213))
+ (%make-qd-d (scale-float (float 8826286527774941 1.0d0) -55)
+ (scale-float (float 3471944699336670 1.0d0) -108)
+ (scale-float (float 4798212191802497 1.0d0) -161)
+ (scale-float (float 6908472993489831 1.0d0) -214))
+ (%make-qd-d (scale-float (float 8960721713639277 1.0d0) -56)
+ (scale-float (float 6978747913895162 1.0d0) -109)
+ (scale-float (float 1204496828771308 1.0d0) -162)
+ (scale-float (float 6150314016033077 1.0d0) -215))
+ (%make-qd-d (scale-float (float 8995498542038505 1.0d0) -57)
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+ (%make-qd-d (scale-float (float 9007196391431099 1.0d0) -63)
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