October 2007 - oct-cvs - mailman3.common-lisp.net

[oct-cvs] Oct commit: oct timing2.lisp
by rtoy 11 Oct '07

11 Oct '07

Update of /project/oct/cvsroot/oct In directory clnet:/tmp/cvs-serv8913 Modified Files: timing2.lisp Log Message: Correct the timing info. I accidentally ran the C++ version on a different (slower) machine. The results make some sense now. --- /project/oct/cvsroot/oct/timing2.lisp 2007/10/11 16:29:08 1.1 +++ /project/oct/cvsroot/oct/timing2.lisp 2007/10/11 18:59:05 1.2 @@ -121,27 +121,25 @@ Some test results. These were all run on a Sun Blade 1500 using a 1.5 GHz Ultrasparc III. I used the default configuration when compiling -qd, and used Sun's C++ compiler. For the Lisp timing, I used CMUCL. +qd, and used Sun's C++ compiler with -O. For the Lisp timing, I used +CMUCL. Executive summary: Test Time qd oct ---- ----------- -add 0.036 0.09 -mul 0.117 0.13 -div 0.388 0.29 -sqrt 0.142 0.11 -sin 0.136 0.14 -log 0.231 0.12 +add 0.023 0.09 +mul 0.075 0.13 +div 0.299 0.29 +sqrt 0.105 0.11 +sin 0.115 0.14 +log 0.194 0.12 Times are in sec for the test. The default number of iterations were -used. Some of the results are a bit surprising. I was expecting the -C++ code to be faster, and that's the case for add and mul. But oct -with CMUCL was faster in div, sqrt, and log. Note that oct uses a -different algorithm for log than qd, so that could explain the -difference. Note also that CLOS dispatch is included in these timing -results. CMUCL's CLOS dispatch is ok, but not great. +used. Most of the timings match my expectations, including the log +test. Oct uses a different algorithm (Halley's method) which is +faster (in Lisp) than the algorithm used in qd (Newtwon iteration). ------------------------------------------------------------------------------- @@ -149,45 +147,41 @@ The output from qd_timer -qd -v: -Timing qd_real --------------- - Timing addition... -n = 100000 t = 0.0362288 +n = 100000 t = 0.0231462 b = 1.428571e+04 -100000 operations in 0.0362288 s. - 0.362288 us +100000 operations in 0.0231462 s. + 0.231462 us Timing multiplication ... -n = 100000 t = 0.11686 +n = 100000 t = 0.0749929 b = 2.718268e+00 -100000 operations in 0.11686 s. - 1.168602 us +100000 operations in 0.0749929 s. + 0.749929 us Timing division ... -n = 100000 t = 0.388279 +n = 100000 t = 0.298858 b = 0.367881 -100000 operations in 0.388279 s. - 3.882788 us +100000 operations in 0.298858 s. + 2.988580 us Timing square root ... -n = 10000 t = 0.141866 +n = 10000 t = 0.105049 a = 2.821980 -10000 operations in 0.141866 s. - 14.186575 us +10000 operations in 0.105049 s. + 10.504860 us Timing sin ... -n = 2000 t = 0.136080 +n = 2000 t = 0.114943 a = 3.141593 -2000 operations in 0.136080 s. - 68.039791 us +2000 operations in 0.114943 s. + 57.471350 us Timing log ... -n = 1000 t = 0.230506 +n = 1000 t = 0.193698 a = -50.100000 -1000 operations in 0.230506 s. -230.506166 us - +1000 operations in 0.193698 s. +193.697800 us The output from CMUCL: QD> (time-add)

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[oct-cvs] Oct commit: oct qd-const.lisp qd-extra.lisp
by rtoy 11 Oct '07

11 Oct '07

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) - 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(%make-qd-d (scale-float (float 6486008573510911 1.0d0) -55) - (scale-float (float 5172944262567044 1.0d0) -109) - (scale-float (float -8273960648700810 1.0d0) -163) - (scale-float (float 8265967084369073 1.0d0) -218)) [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. 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[oct-cvs] Oct commit: oct timing2.lisp
by rtoy 11 Oct '07

11 Oct '07

Update of /project/oct/cvsroot/oct In directory clnet:/tmp/cvs-serv20797 Added Files: timing2.lisp Log Message: Initial version. --- /project/oct/cvsroot/oct/timing2.lisp 2007/10/11 16:29:08 NONE +++ /project/oct/cvsroot/oct/timing2.lisp 2007/10/11 16:29:08 1.1 ;;;; -*- Mode: lisp -*- ;;;; ;;;; Copyright (c) 2007 Raymond Toy ;;;; ;;;; Permission is hereby granted, free of charge, to any person ;;;; obtaining a copy of this software and associated documentation ;;;; files (the "Software"), to deal in the Software without ;;;; restriction, including without limitation the rights to use, ;;;; copy, modify, merge, publish, distribute, sublicense, and/or sell ;;;; copies of the Software, and to permit persons to whom the ;;;; Software is furnished to do so, subject to the following ;;;; conditions: ;;;; ;;;; The above copyright notice and this permission notice shall be ;;;; included in all copies or substantial portions of the Software. ;;;; ;;;; THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, ;;;; EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES ;;;; OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND ;;;; NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT ;;;; HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, ;;;; WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING ;;;; FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR ;;;; OTHER DEALINGS IN THE SOFTWARE. ;;; Here are some simple timing tests, based on Yozo Hida's qd_timer ;;; test code. I've tried to make these versions time the same ;;; operations as Yozo's. (in-package #:qd) (defun time-add (&optional (n 100000)) (declare (fixnum n) (optimize (speed 3))) (let ((a (/ #q7)) (b #q0)) (declare (type qd-real a b)) (time (dotimes (k n) (declare (fixnum k)) (incf b a))) (format t "n = ~D~%" n) (format t "b = ~W~%" b))) (defun time-mul (&optional (n 100000)) (declare (fixnum n) (optimize (speed 3))) (let ((a (+ 1 (/ (float n #q1)))) (b #q1)) (declare (type qd-real a b)) (time (dotimes (k n) (declare (fixnum k)) (setf b (* a b)))) (format t "n = ~D~%" n) (format t "b = ~W~%" b))) (defun time-mul (&optional (n 100000)) (declare (fixnum n) (optimize (speed 3))) (let ((a (+ 1 (/ (float n #q1)))) (b #q1)) (declare (type qd-real a b)) (time (dotimes (k n) (declare (fixnum k)) (setf b (* a b)))) (format t "n = ~D~%" n) (format t "b = ~W~%" b))) (defun time-div (&optional (n 100000)) (declare (fixnum n) (optimize (speed 3))) (let ((a (+ 1 (/ (float n #q1)))) (b #q1)) (declare (type qd-real a b)) (time (dotimes (k n) (declare (fixnum k)) (setf b (/ b a)))) (format t "n = ~D~%" n) (format t "b = ~W~%" b))) (defun time-sqrt (&optional (n 100000)) (declare (fixnum n) (optimize (speed 3))) (let ((a #q0) (b (+ 2 +pi+))) (declare (type qd-real a b)) (time (dotimes (k n) (declare (fixnum k)) (setf a (sqrt (+ a b))))) (format t "n = ~D~%" n) (format t "a = ~W~%" a))) (defun time-sin (&optional (n 2000)) (declare (fixnum n) (optimize (speed 3))) (let ((a #q0) (b (/ +pi+ n)) (c #q0)) (declare (type qd-real a b c)) (time (dotimes (k n) (declare (fixnum k)) (incf a b) (incf c (sin a)))) (format t "n = ~D~%" n) (format t "a = ~W~%" a))) (defun time-log (&optional (n 1000)) (declare (fixnum n) (optimize (speed 3))) (let ((a #q0) (c (exp #q-50.1)) (d (exp (/ #q100.2 n)))) (declare (type qd-real a c d)) (time (dotimes (k n) (declare (fixnum k)) (incf a (log c)) (setf c (* c d)))) (format t "n = ~D~%" n) (format t "a = ~W~%" a))) #|| Some test results. These were all run on a Sun Blade 1500 using a 1.5 GHz Ultrasparc III. I used the default configuration when compiling qd, and used Sun's C++ compiler. For the Lisp timing, I used CMUCL. Executive summary: Test Time qd oct ---- ----------- add 0.036 0.09 mul 0.117 0.13 div 0.388 0.29 sqrt 0.142 0.11 sin 0.136 0.14 log 0.231 0.12 Times are in sec for the test. The default number of iterations were used. Some of the results are a bit surprising. I was expecting the C++ code to be faster, and that's the case for add and mul. But oct with CMUCL was faster in div, sqrt, and log. Note that oct uses a different algorithm for log than qd, so that could explain the difference. Note also that CLOS dispatch is included in these timing results. CMUCL's CLOS dispatch is ok, but not great. ------------------------------------------------------------------------------- The raw data: The output from qd_timer -qd -v: Timing qd_real -------------- Timing addition... n = 100000 t = 0.0362288 b = 1.428571e+04 100000 operations in 0.0362288 s. 0.362288 us Timing multiplication ... n = 100000 t = 0.11686 b = 2.718268e+00 100000 operations in 0.11686 s. 1.168602 us Timing division ... n = 100000 t = 0.388279 b = 0.367881 100000 operations in 0.388279 s. 3.882788 us Timing square root ... n = 10000 t = 0.141866 a = 2.821980 10000 operations in 0.141866 s. 14.186575 us Timing sin ... n = 2000 t = 0.136080 a = 3.141593 2000 operations in 0.136080 s. 68.039791 us Timing log ... n = 1000 t = 0.230506 a = -50.100000 1000 operations in 0.230506 s. 230.506166 us The output from CMUCL: QD> (time-add) ; Evaluation took: ; 0.09 seconds of real time ; 0.1 seconds of user run time ; 0.0 seconds of system run time ; 147,285,856 CPU cycles ; 0 page faults and ; 7,200,016 bytes consed. ; n = 100000 b = #q14285.7142857142857142857142857142857142857142857142857142857142855q0 NIL QD> (time-mul) ; Evaluation took: ; 0.13 seconds of real time ; 0.1 seconds of user run time ; 0.02 seconds of system run time ; 203,790,588 CPU cycles ; 0 page faults and ; 7,200,824 bytes consed. ; n = 100000 b = #q2.71826823717448966803506482442604644797444693267782286300915989397q0 NIL QD> (time-div) ; Evaluation took: ; 0.29 seconds of real time ; 0.28 seconds of user run time ; 0.01 seconds of system run time ; 460,956,912 CPU cycles ; 0 page faults and ; 7,200,016 bytes consed. ; n = 100000 b = #q0.36788128056098406210328658773118942247132502490133718973918140856q0 NIL QD> (time-sqrt 10000) ; Evaluation took: ; 0.11 seconds of real time ; 0.1 seconds of user run time ; 0.0 seconds of system run time ; 173,209,708 CPU cycles ; 0 page faults and ; 2,402,560 bytes consed. ; n = 10000 a = #q2.82198033014704783016853125515542796898998765943212617578596649019q0 NIL QD> (time-sin) ; Evaluation took: ; 0.14 seconds of real time ; 0.14 seconds of user run time ; 0.0 seconds of system run time ; 213,378,476 CPU cycles ; 0 page faults and ; 3,105,800 bytes consed. ; n = 2000 a = #q3.14159265358979323846264338327950288419716939937510582097494459409q0 NIL QD> (time-log) ; Evaluation took: ; 0.12 seconds of real time ; 0.12 seconds of user run time ; 0.01 seconds of system run time ; 192,187,304 CPU cycles ; 0 page faults and ; 1,621,792 bytes consed. ; n = 1000 a = #q-50.100000000000000000000000000000000000000000000000000000000208796q0 NIL QD> --------------------------------------------- ||#

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[oct-cvs] Oct commit: oct .cvsignore
by rtoy 10 Oct '07

10 Oct '07

Update of /project/oct/cvsroot/oct In directory clnet:/tmp/cvs-serv22969 Modified Files: .cvsignore Log Message: Ignore *.lib and *.fas too. (Files from clisp) --- /project/oct/cvsroot/oct/.cvsignore 2007/09/12 02:03:42 1.3 +++ /project/oct/cvsroot/oct/.cvsignore 2007/10/10 15:25:41 1.4 @@ -3,3 +3,5 @@ *.x86f *.err *.fasl +*.lib +*.fas

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[oct-cvs] Oct commit: oct qd-io.lisp qd-methods.lisp qd-package.lisp
by rtoy 10 Oct '07

10 Oct '07

Update of /project/oct/cvsroot/oct In directory clnet:/tmp/cvs-serv22733 Modified Files: qd-io.lisp qd-methods.lisp qd-package.lisp Log Message: qd-io.lisp: o Add RATIONAL-TO-QD, a simple, fast and accurate method to convert rationals to quad-doubles. (From Richard Fateman.) o Use RATIONAL-TO-QD to create a quad-float qd-methods.lisp: o Use RATIONAL-TO-QD to create a quad-float from a bignum and ratio. qd-package.lisp: o Export RATIONAL-TO-QD --- /project/oct/cvsroot/oct/qd-io.lisp 2007/09/24 21:32:15 1.17 +++ /project/oct/cvsroot/oct/qd-io.lisp 2007/10/10 15:24:07 1.18 @@ -381,78 +381,29 @@ (neg-qd (mul-qd xx yy)) (mul-qd xx yy)))))))) +;; This is a slightly modified version of Richard Fateman's code to +;; convert bignums to qd. This supports converting rationals to qd +;; too. +(defun rational-to-qd (rat) + (declare (rational rat)) + (let* ((p (coerce rat 'double-float)) + (ans (make-qd-d p)) + (remainder rat)) + (declare (double-float p) + (rational remainder) + (type %quad-double ans)) + (dotimes (k 3 ans) + (decf remainder (rational p)) + (setf p (coerce remainder 'double-float)) + (setf ans (add-qd-d ans p))))) + (defun make-float (sign int-part frac-part scale exp) (declare (type (member -1 1) sign) (type unsigned-byte int-part frac-part) (fixnum scale exp)) - (flet ((convert-int (int) - ;; Convert integer INT to a quad-double. - (let ((len (integer-length int))) - (cond ((<= len 53) - ;; The simple case that fits in a double-float - (let ((xx (make-qd-d (float int 1d0)))) - xx)) - (t - ;; The complicated case. We look at the top 5*53 - ;; bits and create doubles from them (properly - ;; scaled) and then combine into a quad-double. - ;; Looking at only 4*53 (212 bits) isn't accurate - ;; enough. In particulare 10^100 isn't converted - ;; as accurately as desired if only 212 bits are - ;; used. - ;; - ;; If the integer doesn't have 5*53 bits, left - ;; shift it until it does, and set the length to - ;; 5*53, so that the scaling is done properly. - (let* - ((new-int (if (< len (* 5 53)) - (progn - (setf len (* 5 53)) - (ash int (- (* 5 53) len))) - int)) - (q0 (ldb (byte 53 (cl:- len 53)) new-int)) - (q1 (ldb (byte 53 (cl:- len (* 2 53))) new-int)) - (q2 (ldb (byte 53 (cl:- len (* 3 53))) new-int)) - (q3 (ldb (byte 53 (cl:- len (* 4 53))) new-int)) - (q4 (ldb (byte 53 (cl:- len (* 5 53))) new-int)) - (xx (multiple-value-call #'%make-qd-d - (renorm-5 (scale-float (float q0 1d0) - (cl:- len 53)) - (scale-float (float q1 1d0) - (cl:- len (* 2 53))) - (scale-float (float q2 1d0) - (cl:- len (* 3 53))) - (scale-float (float q3 1d0) - (cl:- len (* 4 53))) - (scale-float (float q4 1d0) - (cl:- len (* 5 53))))))) - #+(or) - (progn - (format t "xx = ~A~%" xx) - #+(or) - (format t " = ~/qd::qd-format/~%" xx) - (format t "yy = ~A~%" yy) - #+(or) - (format t " = ~/qd::qd-format/~%" yy) - (format t "q0 = ~X (~A)~%" q0 - (scale-float (float q0 1d0) - (cl:- len 53))) - (format t "q1 = ~X (~A)~%" q1 - (scale-float (float q1 1d0) - (cl:- len (* 2 53)))) - #+(or) - (format t "~/qdi::qd-format/~%" (mul-qd xx yy))) - xx)))))) - (let* ((rat (* (cl:+ (cl:* int-part (expt 10 scale)) - frac-part) - (expt 10 (cl:- exp scale)))) - (top (numerator rat)) - (bot (denominator rat))) - (div-qd (let ((top-qd (convert-int top))) - (if (minusp sign) - (neg-qd top-qd) - top-qd)) - (convert-int bot))))) + (rational-to-qd (* sign + (* (+ int-part (/ frac-part (expt 10 scale))) + (expt 10 exp))))) ;; This seems to work, but really needs to be rewritten! --- /project/oct/cvsroot/oct/qd-methods.lisp 2007/09/24 21:30:07 1.61 +++ /project/oct/cvsroot/oct/qd-methods.lisp 2007/10/10 15:24:07 1.62 @@ -250,11 +250,7 @@ (defun bignum-to-qd (bignum) (make-instance 'qd-real - :value (qdi::make-float (if (minusp bignum) -1 1) - (abs bignum) - 0 - 0 - 0))) + :value (rational-to-qd bignum))) (defmethod qfloat ((x real) (num-type cl:float)) (cl:float x num-type)) @@ -276,10 +272,7 @@ (qfloat (denominator x) num-type))) (defmethod qfloat ((x ratio) (num-type qd-real)) - ;; This probably has some issues with roundoff - (let ((top (qd-value (qfloat (numerator x) num-type))) - (bot (qd-value (qfloat (denominator x) num-type)))) - (make-instance 'qd-real :value (div-qd top bot)))) + (make-instance 'qd-real :value (rational-to-qd x))) #+cmu (defmethod qfloat ((x ext:double-double-float) (num-type qd-real)) @@ -1025,4 +1018,3 @@ ;; and make a real qd-real float, instead of the hackish ;; %qd-real. (set-dispatch-macro-character #\# #\Q #'qd-class-reader) - --- /project/oct/cvsroot/oct/qd-package.lisp 2007/09/20 21:04:05 1.41 +++ /project/oct/cvsroot/oct/qd-package.lisp 2007/10/10 15:24:07 1.42 @@ -90,6 +90,7 @@ #:ffloor-qd #:random-qd #:with-qd-parts + #:rational-to-qd ) #+cmu (:export #:add-qd-dd

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[oct-cvs] Oct commit: oct qd-fun.lisp
by rtoy 10 Oct '07

10 Oct '07

Update of /project/oct/cvsroot/oct In directory clnet:/tmp/cvs-serv22545 Modified Files: qd-fun.lisp Log Message: o Move logb-finite before first use. o Declare arg as double-float, not float. --- /project/oct/cvsroot/oct/qd-fun.lisp 2007/09/12 02:31:14 1.80 +++ /project/oct/cvsroot/oct/qd-fun.lisp 2007/10/10 15:21:47 1.81 @@ -34,6 +34,17 @@ (in-package #:qdi) +(defun logb-finite (x) + "Same as logb but X is not infinity and non-zero and not a NaN, so +that we can always return an integer" + (declare (type cl:double-float x)) + (multiple-value-bind (signif expon sign) + (cl:decode-float x) + (declare (ignore signif sign)) + ;; decode-float is almost right, except that the exponent + ;; is off by one + (1- expon))) + #+cmu (declaim (maybe-inline sqrt-qd)) (defun sqrt-qd (a) @@ -69,17 +80,6 @@ (setf r (add-qd r (mul-qd r (sub-d-qd half (mul-qd h (sqr-qd r))))))) (scale-float-qd (mul-qd r new-a) (ash k -1))))) -(defun logb-finite (x) - "Same as logb but X is not infinity and non-zero and not a NaN, so -that we can always return an integer" - (declare (type cl:float x)) - (multiple-value-bind (signif expon sign) - (cl:decode-float x) - (declare (ignore signif sign)) - ;; decode-float is almost right, except that the exponent - ;; is off by one - (1- expon))) - (defun hypot-aux-qd (x y) (declare (type %quad-double x y)) (let ((k (- (logb-finite (max (cl:abs (qd-0 x))

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