diff --git a/books/bookvol5.pamphlet b/books/bookvol5.pamphlet index 404e339..f51c18d 100644 --- a/books/bookvol5.pamphlet +++ b/books/bookvol5.pamphlet @@ -29041,7 +29041,7 @@ This is used in the DoubleFloat integerDecode function <>= (defun integer-decode-float-denominator (x) (multiple-value-bind (mantissa exponent sign) (integer-decode-float x) - (expt 2 (abs exponent)))) + (declare (ignore mantissa sign)) (expt 2 (abs exponent)))) @ @@ -29050,7 +29050,7 @@ This is used in the DoubleFloat integerDecode function <>= (defun integer-decode-float-sign (x) (multiple-value-bind (mantissa exponent sign) (integer-decode-float x) - sign)) + (declare (ignore mantissa exponent)) sign)) @ @@ -29059,7 +29059,7 @@ This is used in the DoubleFloat integerDecode function <>= (defun integer-decode-float-exponent (x) (multiple-value-bind (mantissa exponent sign) (integer-decode-float x) - exponent)) + (declare (ignore mantissa sign)) exponent)) @ diff --git a/changelog b/changelog index d395f15..c567d7b 100644 --- a/changelog +++ b/changelog @@ -1,7 +1,11 @@ +20100101 tpd src/axiom-website/patches.html 20100101.05.tpd.patch +20100101 tpd books/bookvol5 ignore unused values +20100101 tpd src/input/en.input fix typo +20100101 tpd src/input/e1.input rewrite using machineFraction 20100101 tpd src/axiom-website/patches.html 20100101.04.tpd.patch 20100101 tpd src/axiom-website/patches.html fix 2009->2010 dates 20100101 tpd src/axiom-website/patches.html 20100101.03.tpd.patch -20101010 tpd src/input/en.input rewrite using machineFraction +20100101 tpd src/input/en.input rewrite using machineFraction 20100101 tpd src/axiom-website/patches.html 20100101.02.tpd.patch 20100101 tpd books/bookvol10.4 fix API regression 20100101 tpd src/axiom-website/patches.html 20100101.01.tpd.patch diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 3a14bea..cf84324 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2352,7 +2352,9 @@ books/bookvol10.3 add dfloat machineFraction, integerDecode
books/bookvol10.4 fix API regression
20100101.03.tpd.patch src/input/en.input rewrite using machineFraction
-20100101.03.tpd.patch +20100101.04.tpd.patch src/axiom-website/patches.html fix 2009->2010 dates
+20100101.05.tpd.patch +src/input/e1.input rewrite using machineFraction
diff --git a/src/input/e1.input.pamphlet b/src/input/e1.input.pamphlet index d573de7..1c088ff 100644 --- a/src/input/e1.input.pamphlet +++ b/src/input/e1.input.pamphlet @@ -20,12 +20,17 @@ This is a regression test for E1(x) \end{chunk} Here we enter the value of Gamma \begin{chunk}{*} + --S 1 of 7 -G:DFLOAT:=0.577215664901532860606512::DFLOAT +machineFraction (G:DFLOAT:=0.577215664901532860606512) +--R --R ---R (1) 0.57721566490153287 ---R Type: DoubleFloat +--R 649887063340739 +--R (1) ---------------- +--R 1125899906842624 +--R Type: Fraction Integer --E 1 + \end{chunk} Since the E1 function varies over a couple hundred orders @@ -35,10 +40,13 @@ listed in Abramowitz and Stegun, ``Handbook of Mathematical Functions'', Dover Publications, Inc. New York 1965. pp238 \begin{chunk}{*} + --S 2 of 7 f(x)==x^-1 * (E1(x)::DFLOAT + log(x) + G) +--R --R Type: Void --E 2 + \end{chunk} This table computes the Exponential Integral $E1(x)$ for $x$ @@ -48,7 +56,10 @@ Abramowitz and Stegun, ``Handbook of Mathematical Functions'', Dover Publications, Inc. New York 1965. pp238 \begin{chunk}{*} + --S 3 of 7 +t3:List List Fraction Integer:=[[machineFraction (x::DFLOAT) for x in line]_ + for line in _ [[0.01,0.9975055452, f(0.01), f(0.01)-0.9975055452],_ [0.02,0.9950221392, f(0.02), f(0.02)-0.9950221392],_ [0.03,0.9925497201, f(0.03), f(0.03)-0.9925497201],_ @@ -98,180 +109,329 @@ Dover Publications, Inc. New York 1965. pp238 [0.47,0.8937670423, f(0.47), f(0.47)-0.8937670423],_ [0.48,0.8917309048, f(0.48), f(0.48)-0.8917309048],_ [0.49,0.8897032920, f(0.49), f(0.49)-0.8897032920],_ -[0.50,0.8876841584, f(0.50), f(0.50)-0.8876841584]]::LIST(LIST(DFLOAT)) +[0.50,0.8876841584, f(0.50), f(0.50)-0.8876841584]]] --R --R Compiling function f with type Float -> DoubleFloat --R --R (3) ---R [[1.0E-2,0.99750554520000001,0.99750554515544154,- 4.455846802642327E-11], ---R [2.0E-2,0.99502213920000004,0.99502213915481641,- 4.5183634611589696E-11], ---R ---R [2.9999999999999999E-2, 0.99254972009999998, 0.99254972009439713, ---R - 5.602851516073315E-12] ---R , ---R ---R [4.0000000000000001E-2, 0.99008822649999995, 0.99008822646530492, ---R - 3.4695024631048454E-11] ---R , ---R ---R [5.0000000000000003E-2, 0.98763759709999999, 0.98763759715033261, ---R 5.0332626955196247E-11] ---R , ---R ---R [5.9999999999999998E-2, 0.98519777139999998, 0.98519777142131459, ---R 2.1314616738266068E-11] ---R , ---R ---R [7.0000000000000007E-2, 0.98276868890000002, 0.98276868893648617, ---R 3.648614743667622E-11] ---R , ---R ---R [8.0000000000000002E-2, 0.98035028980000005, 0.98035028973773719, ---R - 6.2262861533213254E-11] ---R , ---R ---R [8.9999999999999997E-2, 0.9779425142, 0.97794251424804735, ---R 4.8047343881307825E-11] ---R , ---R ---R [0.10000000000000001, 0.9755453033, 0.97554530326877553, ---R - 3.1224467456070215E-11] ---R , ---R [0.11,0.97315859800000004,0.97315859797713988,- 2.2860158210846748E-11], ---R [0.12,0.97078233989999996,0.97078233992354002,2.3540058791127194E-11], ---R [0.13,0.96841647099999995,0.96841647102903816,2.9038216275978357E-11], ---R ---R [0.14000000000000001, 0.9660609336, 0.96606093358279166, ---R - 1.7208345859387464E-11] ---R , ---R ---R [0.14999999999999999, 0.96371567020000004, 0.96371567023951998, ---R 3.9519942873766922E-11] ---R , ---R [0.16,0.96138062400000002,0.96138062401698243,1.6982415473876245E-11], ---R ---R [0.17000000000000001, 0.95905573830000002, 0.95905573829349, ---R - 6.5100147494945304E-12] ---R , ---R ---R [0.17999999999999999, 0.95674095690000005, 0.9567409568054186, ---R - 9.4581453780051561E-11] ---R , ---R [0.19,0.95443622370000003,0.95443622364474956,- 5.525047086507584E-11], ---R ---R [0.20000000000000001, 0.95214148330000004, 0.9521414832566294, ---R - 4.3370640412376815E-11] ---R , ---R ---R [0.20999999999999999, 0.94985668040000004, 0.94985668043693772, ---R 3.6937675140791271E-11] ---R , ---R [0.22,0.94758176029999996,0.94758176032988584,2.9885871555279664E-11], ---R ---R [0.23000000000000001, 0.94531666839999995, 0.9453166684256229, ---R 2.562294820762645E-11] ---R , ---R ---R [0.23999999999999999, 0.94306135059999996, 0.94306135055786067, ---R - 4.2139292055765054E-11] ---R , ---R [0.25,0.94081575279999996,0.94081575290152264,1.015226791523105E-10], ---R ---R [0.26000000000000001, 0.93857982210000002, 0.93857982197039913, ---R - 1.2960088557889549E-10] ---R , ---R ---R [0.27000000000000002, 0.9363535046, 0.93635350461483224, ---R 1.4832246542084704E-11] ---R , ---R ---R [0.28000000000000003, 0.93413674810000003, 0.93413674801940527, ---R - 8.0594753093521376E-11] ---R , ---R ---R [0.28999999999999998, 0.93192949970000005, 0.93192949970065808, ---R 6.5802918669533028E-13] ---R , ---R ---R [0.29999999999999999, 0.9297317075, 0.92973170750481327, ---R 4.8132609009599037E-12] ---R , ---R [0.31,0.92754331960000003,0.92754331960551961,5.5195847892264283E-12], ---R ---R [0.32000000000000001, 0.92536428449999997, 0.92536428450162023, ---R 1.6202594821379535E-12] ---R , ---R ---R [0.33000000000000002, 0.92319455100000003, 0.92319455101492243, ---R 1.4922396651684267E-11] ---R , ---R ---R [0.34000000000000002, 0.92103406840000002, 0.92103406828799361, ---R - 1.1200640415154339E-10] ---R , ---R ---R [0.34999999999999998, 0.91888278580000005, 0.91888278578197524, ---R - 1.8024803871696804E-11] ---R , ---R ---R [0.35999999999999999, 0.91674065329999999, 0.91674065327439791, ---R - 2.5602076014763497E-11] ---R , ---R [0.37,0.91460762090000003,0.91460762085703573,- 4.2964298785364008E-11], ---R [0.38,0.91248363880000005,0.91248363893375239,1.3375234253487633E-10], ---R ---R [0.39000000000000001, 0.91036865820000001, 0.91036865821837942, ---R 1.8379409105762079E-11] ---R , ---R ---R [0.40000000000000002, 0.90826262970000005, 0.90826262973260075, ---R 3.2600699917395559E-11] ---R , ---R ---R [0.40999999999999998, 0.90616550480000002, 0.90616550480385905, ---R 3.8590242112945816E-12] ---R , ---R ---R [0.41999999999999998, 0.90407723500000003, 0.90407723506326909, ---R 6.3269056660431033E-11] ---R , ---R ---R [0.42999999999999999, 0.90199777250000002, 0.90199777244355628, ---R - 5.6443738571942959E-11] ---R , ---R [0.44,0.89992706929999999,0.89992706917700038,- 1.2299961049677677E-10], ---R ---R [0.45000000000000001, 0.89786507780000002, 0.8978650777934013, ---R - 6.5987215691620804E-12] ---R , ---R ---R [0.46000000000000002, 0.8958117511, 0.89581175111805511, ---R 1.8055112960269071E-11] ---R , ---R ---R [0.46999999999999997, 0.89376704230000004, 0.89376704226974857, ---R - 3.0251467997288728E-11] ---R , ---R ---R [0.47999999999999998, 0.89173090479999995, 0.89173090465876237, ---R - 1.412375771892016E-10] ---R , ---R ---R [0.48999999999999999, 0.88970329199999998, 0.88970329198489473, ---R - 1.510525038384003E-11] ---R , ---R [0.5,0.88768415840000003,0.88768415823549685,- 1.6450318884864146E-10]] ---R Type: List List DoubleFloat +--R 2882303761517117 4492365601662723 280772850091425 199923 +--R [[------------------,----------------,---------------,- ----------------], +--R 288230376151711744 4503599627370496 281474976710656 4503599627370496 +--R 2882303761517117 8962362670653027 1120295333780775 406827 +--R [------------------,----------------,----------------,- ----------------], +--R 144115188075855872 9007199254740992 1125899906842624 9007199254740992 +--R 1080863910568919 2235023274794525 2235023274781933 787 +--R [-----------------,----------------,----------------,- ---------------], +--R 36028797018963968 2251799813685248 2251799813685248 140737488355328 +--R 2882303761517117 4458960967929315 1114740241943275 156215 +--R [-----------------,----------------,----------------,- ----------------], +--R 72057594037927936 4503599627370496 1125899906842624 4503599627370496 +--R 7205759403792793 1111981078569163 555990539312915 56667 +--R [------------------,----------------,---------------,----------------], +--R 144115188075855872 1125899906842624 562949953421312 1125899906842624 +--R 1080863910568919 4436936316163283 8873872632518599 192033 +--R [-----------------,----------------,----------------,----------------], +--R 18014398509481984 4503599627370496 9007199254740992 9007199254740992 +--R 5044031582654955 8851993402242861 8851993402571485 20539 +--R [-----------------,----------------,----------------,---------------], +--R 72057594037927936 9007199254740992 9007199254740992 562949953421312 +--R 2882303761517117 8830210399671675 2207552599777725 560775 +--R [-----------------,----------------,----------------,- ----------------], +--R 36028797018963968 9007199254740992 2251799813685248 9007199254740992 +--R 3242591731706757 8808523085081771 8808523085514533 216381 +--R [-----------------,----------------,----------------,----------------], +--R 36028797018963968 9007199254740992 9007199254740992 4503599627370496 +--R 7205759403792793 8786930928849835 2196732732142165 281175 +--R [-----------------,----------------,----------------,- ----------------], +--R 72057594037927936 9007199254740992 2251799813685248 9007199254740992 +--R 990791918021509 2191358349662597 2191358349611127 25735 +--R [----------------,----------------,----------------,- ----------------], +--R 9007199254740992 2251799813685248 2251799813685248 1125899906842624 +--R 1080863910568919 2186007492115749 8744029968675015 212019 +--R [----------------,----------------,----------------,----------------], +--R 9007199254740992 2251799813685248 9007199254740992 9007199254740992 +--R 4683743612465315 8722720115870101 8722720116131645 32693 +--R [-----------------,----------------,----------------,----------------], +--R 36028797018963968 9007199254740992 9007199254740992 1125899906842624 +--R 5044031582654955 4350751660578153 543843957562583 77489 +--R [-----------------,----------------,---------------,- ----------------], +--R 36028797018963968 4503599627370496 562949953421312 4503599627370496 +--R 5404319552844595 8680379066407655 8680379066763613 177979 +--R [-----------------,----------------,----------------,----------------], +--R 36028797018963968 9007199254740992 9007199254740992 4503599627370496 +--R 2882303761517117 8659346840015229 1082418355021025 152971 +--R [-----------------,----------------,----------------,----------------], +--R 18014398509481984 9007199254740992 1125899906842624 9007199254740992 +--R 3062447746611937 8638406131270831 8638406131212199 7329 +--R [-----------------,----------------,----------------,- ----------------], +--R 18014398509481984 9007199254740992 9007199254740992 1125899906842624 +--R 3242591731706757 8617556433969863 1077194554139743 851919 +--R [-----------------,----------------,----------------,- ----------------], +--R 18014398509481984 9007199254740992 1125899906842624 9007199254740992 +--R 6845471433603153 4298398621404223 8596797242310799 497647 +--R [-----------------,----------------,----------------,- ----------------], +--R 36028797018963968 4503599627370496 9007199254740992 9007199254740992 +--R 7205759403792793 4288064029393871 4288064029198545 97663 +--R [-----------------,----------------,----------------,- ----------------], +--R 36028797018963968 4503599627370496 4503599627370496 2251799813685248 +--R 7566047373982433 267360886994051 8555548384142333 332701 +--R [-----------------,---------------,----------------,----------------], +--R 36028797018963968 281474976710656 9007199254740992 9007199254740992 +--R 990791918021509 8535057725180317 2133764431362377 269191 +--R [----------------,----------------,----------------,----------------], +--R 4503599627370496 9007199254740992 2251799813685248 9007199254740992 +--R 517913957147607 8514655591106717 8514655591337513 57699 +--R [----------------,----------------,----------------,----------------], +--R 2251799813685248 9007199254740992 9007199254740992 2251799813685248 +--R 1080863910568919 8494341494299353 8494341493919799 189777 +--R [----------------,----------------,----------------,- ----------------], +--R 4503599627370496 9007199254740992 9007199254740992 4503599627370496 +--R 1 8474114947468745 1059264368547897 914431 +--R [-,----------------,----------------,----------------], +--R 4 9007199254740992 1125899906842624 9007199254740992 +--R 4683743612465315 2113493868533513 8453975472966715 1167337 +--R [-----------------,----------------,----------------,- ----------------], +--R 18014398509481984 2251799813685248 9007199254740992 9007199254740992 +--R 4863887597560135 2108480647201809 2108480647235209 4175 +--R [-----------------,----------------,----------------,---------------], +--R 18014398509481984 2251799813685248 2251799813685248 281474976710656 +--R 5044031582654955 8413955821312493 8413955820586567 362963 +--R [-----------------,----------------,----------------,- ----------------], +--R 18014398509481984 9007199254740992 9007199254740992 4503599627370496 +--R 5224175567749775 8394074695168985 8394074695174917 1483 +--R [-----------------,----------------,----------------,----------------], +--R 18014398509481984 9007199254740992 9007199254740992 2251799813685248 +--R 5404319552844595 8374278742903069 8374278742946419 21675 +--R [-----------------,----------------,----------------,----------------], +--R 18014398509481984 9007199254740992 9007199254740992 4503599627370496 +--R 5584463537939415 8354567497041105 8354567497090819 24857 +--R [-----------------,----------------,----------------,----------------], +--R 18014398509481984 9007199254740992 9007199254740992 4503599627370496 +--R 2882303761517117 8334940493712331 8334940493726925 7297 +--R [----------------,----------------,----------------,----------------], +--R 9007199254740992 9007199254740992 9007199254740992 4503599627370496 +--R 2972375754064527 519712329484259 4157698635941277 67205 +--R [----------------,---------------,----------------,----------------], +--R 9007199254740992 562949953421312 4503599627370496 4503599627370496 +--R 3062447746611937 8295937374483543 64812010730271 1008855 +--R [----------------,----------------,--------------,- ----------------], +--R 9007199254740992 9007199254740992 70368744177664 9007199254740992 +--R 3152519739159347 4138280171726043 4138280171644865 40589 +--R [----------------,----------------,----------------,- ----------------], +--R 9007199254740992 4503599627370496 4503599627370496 2251799813685248 +--R 3242591731706757 4128632864597265 4128632864481965 28825 +--R [----------------,----------------,----------------,- ----------------], +--R 9007199254740992 4503599627370496 4503599627370496 1125899906842624 +--R 3332663724254167 8238053081350911 8238053080963921 193495 +--R [----------------,----------------,----------------,- ----------------], +--R 9007199254740992 9007199254740992 9007199254740992 4503599627370496 +--R 6845471433603153 2054730487840677 8218921952567441 1204733 +--R [-----------------,----------------,----------------,----------------], +--R 18014398509481984 2251799813685248 9007199254740992 9007199254740992 +--R 7025615418697973 2049967974919649 8199871899844143 165547 +--R [-----------------,----------------,----------------,----------------], +--R 18014398509481984 2251799813685248 9007199254740992 9007199254740992 +--R 7205759403792793 8180902481342933 4090451240818289 293645 +--R [-----------------,----------------,----------------,----------------], +--R 18014398509481984 9007199254740992 4503599627370496 9007199254740992 +--R 7385903388887613 4081006629753277 127531457180333 17379 +--R [-----------------,----------------,---------------,----------------], +--R 18014398509481984 4503599627370496 140737488355328 4503599627370496 +--R 7566047373982433 1017900474665037 8143203797890171 569875 +--R [-----------------,----------------,----------------,----------------], +--R 18014398509481984 1125899906842624 9007199254740992 9007199254740992 +--R 7746191359077253 4062236832120017 4062236831865817 31775 +--R [-----------------,----------------,----------------,- ---------------], +--R 18014398509481984 4503599627370496 4503599627370496 562949953421312 +--R 990791918021509 8105822427920205 4052911213406161 1107883 +--R [----------------,----------------,----------------,- ----------------], +--R 2251799813685248 9007199254740992 4503599627370496 9007199254740992 +--R 2026619832316723 4043624829809061 252726551861209 29717 +--R [----------------,----------------,---------------,- ----------------], +--R 4503599627370496 4503599627370496 281474976710656 4503599627370496 +--R 517913957147607 8068754936896143 8068754937058771 40657 +--R [----------------,----------------,----------------,----------------], +--R 1125899906842624 9007199254740992 9007199254740992 2251799813685248 +--R 2116691824864133 2012584459329155 2012584459261035 8515 +--R [----------------,----------------,----------------,- ---------------], +--R 4503599627370496 2251799813685248 2251799813685248 281474976710656 +--R 1080863910568919 4015998970572035 8031997939871911 1272159 +--R [----------------,----------------,----------------,- ----------------], +--R 2251799813685248 4503599627370496 9007199254740992 9007199254740992 +--R 2206763817411543 8013734828643007 8013734828506949 68029 +--R [----------------,----------------,----------------,- ----------------], +--R 4503599627370496 9007199254740992 9007199254740992 4503599627370496 +--R 1 999443511248233 3997774044252075 740857 +--R [-,----------------,----------------,- ----------------]] +--R 2 1125899906842624 4503599627370496 4503599627370496 +--R Type: List List Fraction Integer --E 3 \end{chunk} +The actual table values from above are: +\begin{verbatim} + [1.0E-2, 0.99750554520000001, + 0.99750554515544154, + -4.455846802642327E-11] + [2.0E-2, 0.99502213920000004, + 0.99502213915481641, + -4.5183634611589696E-11] + [2.9999999999999999E-2, 0.99254972009999998, + 0.99254972009439713, + -5.602851516073315E-12] + [4.0000000000000001E-2, 0.99008822649999995, + 0.99008822646530492, + -3.4695024631048454E-11] + [5.0000000000000003E-2, 0.98763759709999999, + 0.98763759715033261, + 5.0332626955196247E-11] + [5.9999999999999998E-2, 0.98519777139999998, + 0.98519777142131459, + 2.1314616738266068E-11] + [7.0000000000000007E-2, 0.98276868890000002, + 0.98276868893648617, + 3.648614743667622E-11] + [8.0000000000000002E-2, 0.98035028980000005, + 0.98035028973773719, + -6.2262861533213254E-11] + [8.9999999999999997E-2, 0.9779425142, + 0.97794251424804735, + 4.8047343881307825E-11] + [0.10000000000000001, 0.9755453033, + 0.97554530326877553, + -3.1224467456070215E-11] + [0.11, 0.97315859800000004, + 0.97315859797713988, + -2.2860158210846748E-11] + [0.12, 0.97078233989999996, + 0.97078233992354002, + 2.3540058791127194E-11] + [0.13, 0.96841647099999995, + 0.96841647102903816, + 2.9038216275978357E-11] + [0.14000000000000001, 0.9660609336, + 0.96606093358279166, + -1.7208345859387464E-11] + [0.14999999999999999, 0.96371567020000004, + 0.96371567023951998, + 3.9519942873766922E-11] + [0.16, 0.96138062400000002, + 0.96138062401698243, + 1.6982415473876245E-11] + [0.17000000000000001, 0.95905573830000002, + 0.95905573829349, + -6.5100147494945304E-12] + [0.17999999999999999, 0.95674095690000005, + 0.9567409568054186, + -9.4581453780051561E-11] + [0.19, 0.95443622370000003, + 0.95443622364474956, + -5.525047086507584E-11] + [0.20000000000000001, 0.95214148330000004, + 0.9521414832566294, + -4.3370640412376815E-11] + [0.20999999999999999, 0.94985668040000004, + 0.94985668043693772, + 3.6937675140791271E-11] + [0.22, 0.94758176029999996, + 0.94758176032988584, + 2.9885871555279664E-11] + [0.23000000000000001, 0.94531666839999995, + 0.9453166684256229, + 2.562294820762645E-11] + [0.23999999999999999, 0.94306135059999996, + 0.94306135055786067, + -4.2139292055765054E-11] + [0.25, 0.94081575279999996, + 0.94081575290152264, + 1.015226791523105E-10] + [0.26000000000000001, 0.93857982210000002, + 0.93857982197039913, + -1.2960088557889549E-10] + [0.27000000000000002, 0.9363535046, + 0.93635350461483224, + 1.4832246542084704E-11] + [0.28000000000000003, 0.93413674810000003, + 0.93413674801940527, + -8.0594753093521376E-11] + [0.28999999999999998, 0.93192949970000005, + 0.93192949970065808, + 6.5802918669533028E-13] + [0.29999999999999999, 0.9297317075, + 0.92973170750481327, + 4.8132609009599037E-12] + [0.31, 0.92754331960000003, + 0.92754331960551961, + 5.5195847892264283E-12] + [0.32000000000000001, 0.92536428449999997, + 0.92536428450162023, + 1.6202594821379535E-12] + [0.33000000000000002, 0.92319455100000003, + 0.92319455101492243, + 1.4922396651684267E-11] + [0.34000000000000002, 0.92103406840000002, + 0.92103406828799361, + -1.1200640415154339E-10] + [0.34999999999999998, 0.91888278580000005, + 0.91888278578197524, + -1.8024803871696804E-11] + [0.35999999999999999, 0.91674065329999999, + 0.91674065327439791, + -2.5602076014763497E-11] + [0.37, 0.91460762090000003, + 0.91460762085703573, + -4.2964298785364008E-11] + [0.38, 0.91248363880000005, + 0.91248363893375239, + 1.3375234253487633E-10] + [0.39000000000000001, 0.91036865820000001, + 0.91036865821837942, + 1.8379409105762079E-11] + [0.40000000000000002, 0.90826262970000005, + 0.90826262973260075, + 3.2600699917395559E-11] + [0.40999999999999998, 0.90616550480000002, + 0.90616550480385905, + 3.8590242112945816E-12] + [0.41999999999999998, 0.90407723500000003, + 0.90407723506326909, + 6.3269056660431033E-11] + [0.42999999999999999, 0.90199777250000002, + 0.90199777244355628, + -5.6443738571942959E-11] + [0.44, 0.89992706929999999, + 0.89992706917700038, + -1.2299961049677677E-10] + [0.45000000000000001, 0.89786507780000002, + 0.8978650777934013, + -6.5987215691620804E-12] + [0.46000000000000002, 0.8958117511, + 0.89581175111805511, + 1.8055112960269071E-11] + [0.46999999999999997, 0.89376704230000004, + 0.89376704226974857, + -3.0251467997288728E-11] + [0.47999999999999998, 0.89173090479999995, + 0.89173090465876237, + -1.412375771892016E-10] + [0.48999999999999999, 0.88970329199999998, + 0.88970329198489473, + -1.510525038384003E-11] + [0.5, 0.88768415840000003, + 0.88768415823549685, + -1.6450318884864146E-10] +\end{verbatim} + This table computes the Exponential Integral $E1(x)$ for $x$ in 0.50 to 2.00. Column 1 is the point of evaluation, column 2 is the reference value of $E1(x)$ from the book Abramowitz and Stegun, ``Handbook of Mathematical Functions'', Dover Publications, Inc. New York 1965. pp239-241 \begin{chunk}{*} + --S 4 of 7 +t4:List List Fraction Integer:=[[machineFraction (x::DFLOAT) for x in line]_ + for line in _ [[0.50, 0.559773595, E1(0.50), E1(0.50)-0.559773595],_ [0.51, 0.547822352, E1(0.51), E1(0.51)-0.547822352],_ [0.52, 0.536219798, E1(0.52), E1(0.52)-0.536219798],_ @@ -422,431 +582,944 @@ Dover Publications, Inc. New York 1965. pp239-241 [1.97, 0.050976988, E1(1.97), E1(1.97)-0.050976988],_ [1.98, 0.050274392, E1(1.98), E1(1.98)-0.050274392],_ [1.99, 0.049582291, E1(1.99), E1(1.99)-0.049582291],_ -[2.00, 0.048900511, E1(2.00), E1(2.00)-0.048900511]]::LIST(LIST(DFLOAT)) +[2.00, 0.048900511, E1(2.00), E1(2.00)-0.048900511]]] --R --R --R (4) ---R [[0.5,0.55977359500000001,0.55977359477616084,- 2.2383916942203541E-10], ---R ---R [0.51000000000000001, 0.54782235199999996, 0.54782235178082872, ---R - 2.1917123671499894E-10] ---R , ---R ---R [0.52000000000000002, 0.53621979799999997, 0.53621979784563623, ---R - 1.5436374400934483E-10] ---R , ---R ---R [0.53000000000000003, 0.52495150999999995, 0.52495151011486541, ---R 1.148654504845581E-10] ---R , ---R ---R [0.54000000000000004, 0.51400388600000002, 0.51400388570224909, ---R - 2.9775093501882566E-10] ---R , ---R ---R [0.55000000000000004, 0.50336408099999996, 0.50336408139239386, ---R 3.9239389515444145E-10] ---R , ---R ---R [0.56000000000000005, 0.49301995900000001, 0.49301995877649291, ---R - 2.2350710171537003E-10] ---R , ---R ---R [0.56999999999999995, 0.48296003399999998, 0.48296003424511297, ---R 2.451129854641465E-10] ---R , ---R ---R [0.57999999999999996, 0.47317343299999998, 0.47317343333112627, ---R 3.3112629305165342E-10] ---R , ---R ---R [0.58999999999999997, 0.463649849, 0.46364984895652972, ---R - 4.3470282928836923E-11] ---R , ---R ---R [0.59999999999999998, 0.45437950300000002, 0.45437950318940223, ---R 1.8940221613306107E-10] ---R , ---R [0.60999999999999999,0.445353112,0.44535311216282059,1.628205903436708E-10], ---R [0.62,0.43656185400000003,0.43656185384719148,- 1.5280854359644991E-10], ---R [0.63,0.427997338,0.42799733840201848,4.0201847406606817E-10], ---R ---R [0.64000000000000001, 0.419651581, 0.41965158086333326, ---R - 1.366667334856686E-10] ---R , ---R ---R [0.65000000000000002, 0.41151697599999998, 0.41151697594947956, ---R - 5.0520421179811592E-11] ---R , ---R ---R [0.66000000000000003, 0.40358627499999999, 0.40358627479116588, ---R - 2.088341166661678E-10] ---R , ---R ---R [0.67000000000000004, 0.39585256299999999, 0.39585256341213687, ---R 4.1213688017904815E-10] ---R , ---R ---R [0.68000000000000005, 0.38830924300000003, 0.38830924280482559, ---R - 1.9517443217154096E-10] ---R , ---R ---R [0.68999999999999995, 0.38095001000000001, 0.38095001046125104, ---R 4.6125103736471829E-10] ---R , ---R ---R [0.69999999999999996, 0.37376884300000002, 0.37376884323350923, ---R 2.3350921196652052E-10] ---R , ---R ---R [0.70999999999999996, 0.36675998100000001, 0.36675998141067723, ---R 4.1067721445742222E-10] ---R , ---R ---R [0.71999999999999997, 0.35991791400000001, 0.35991791391003464, ---R - 8.9965368488265085E-11] ---R , ---R [0.72999999999999998,0.353237364,0.35323736449036641,4.9036641414090809E-10] ---R , ---R ---R [0.73999999999999999, 0.34671327899999999, 0.34671327890389447, ---R - 9.6105512437105745E-11] ---R , ---R [0.75,0.34034081300000002,0.34034081291123008,- 8.8769935846499948E-11], ---R ---R [0.76000000000000001, 0.33411532100000002, 0.33411532109074837, ---R 9.0748353276381977E-11] ---R , ---R ---R [0.77000000000000002, 0.32803234599999997, 0.3280323463800649, ---R 3.8006492397713032E-10] ---R , ---R ---R [0.78000000000000003, 0.32208761000000002, 0.32208761029292271, ---R 2.9292268610703331E-10] ---R , ---R ---R [0.79000000000000004, 0.31627700399999997, 0.31627700375985612, ---R - 2.4014384925052923E-10] ---R , ---R ---R [0.80000000000000004, 0.31059657899999998, 0.31059657854554301, ---R - 4.5445697205437341E-10] ---R , ---R [0.81000000000000005,0.305042539,0.30504253919985258,1.9985257893040398E-10] ---R , ---R ---R [0.81999999999999995, 0.299611236, 0.29961123550328894, ---R - 4.967110611708847E-10] ---R , ---R ---R [0.82999999999999996, 0.29429915499999998, 0.29429915537086676, ---R 3.7086678172926213E-10] ---R , ---R ---R [0.83999999999999997, 0.28910291799999999, 0.28910291818146794, ---R 1.8146795177642616E-10] ---R , ---R ---R [0.84999999999999998, 0.28401926900000002, 0.2840192685024614, ---R - 4.975386214134403E-10] ---R , ---R ---R [0.85999999999999999, 0.27904507000000001, 0.27904507018183955, ---R 1.818395434227682E-10] ---R , ---R [0.87,0.27417730099999998,0.27417730078237224,- 2.1762774915501382E-10], ---R [0.88,0.26941304599999999,0.26941304633432023,3.343202381600463E-10], ---R ---R [0.89000000000000001, 0.26474949599999997, 0.26474949638510148, ---R 3.8510150623949357E-10] ---R , ---R ---R [0.90000000000000002, 0.26018393899999998, 0.26018393932599954, ---R 3.259995606796906E-10] ---R , ---R ---R [0.91000000000000003, 0.25571375800000001, 0.25571375797753926, ---R - 2.2460755477737848E-11] ---R , ---R ---R [0.92000000000000004, 0.25133642499999997, 0.25133642541656154, ---R 4.1656156302138925E-10] ---R , ---R [0.93000000000000005,0.247049501,0.24704950102931605,2.9316049587890802E-11] ---R , ---R ---R [0.93999999999999995, 0.24285062700000001, 0.24285062677606084, ---R - 2.2393917276097852E-10] ---R , ---R ---R [0.94999999999999996, 0.23873752400000001, 0.23873752365373468, ---R - 3.4626532197101767E-10] ---R , ---R ---R [0.95999999999999996, 0.23470798800000001, 0.23470798834425491, ---R 3.4425490236245082E-10] ---R , ---R [0.96999999999999997,0.23075989,0.23075989003689171,3.6891711907571789E-11], ---R [0.97999999999999998,0.226891167,0.22689116741400336,4.1400335937247235E-10] ---R , ---R ---R [0.98999999999999999, 0.223099826, 0.22309982579017718, ---R - 2.0982282578074773E-10] ---R , ---R [1.,0.219383934,0.21938393439552029,3.9552028319178589E-10], ---R [1.01,0.21574162399999999,0.21574162379448991,- 2.0551008117486447E-10], ---R [1.02,0.21217108300000001,0.2121710834322488,4.3224879231473778E-10], ---R [1.03,0.20867055900000001,0.20867055930107367,3.0107366599807506E-10], ---R [1.04,0.20523835200000001,0.20523835171985597,- 2.8014404684917338E-10], ---R [1.05,0.20187281300000001,0.20187281322019657,2.2019655543381589E-10], ---R ---R [1.0600000000000001, 0.19857234700000001, 0.19857234653302808, ---R - 4.6697193334388487E-10] ---R , ---R ---R [1.0700000000000001, 0.19533540299999999, 0.19533540267009863, ---R - 3.2990135623300887E-10] ---R , ---R [1.0800000000000001,0.192160479,0.19216047909501838,9.5018382051392791E-11], ---R ---R [1.0900000000000001, 0.18904611800000001, 0.18904611797891213, ---R - 2.1087881441061995E-11] ---R , ---R ---R [1.1000000000000001, 0.18599090500000001, 0.18599090453604011, ---R - 4.6395989827807682E-10] ---R , ---R ---R [1.1100000000000001, 0.18299346499999999, 0.1829934654350395, ---R 4.3503950442058681E-10] ---R , ---R ---R [1.1200000000000001, 0.18005246699999999, 0.18005246728171573, ---R 2.8171573407398398E-10] ---R , ---R [1.1299999999999999,0.177166615,0.17716661516956422,1.6956422377312208E-10], ---R ---R [1.1399999999999999, 0.17433465100000001, 0.17433465129443812, ---R 2.9443811278007104E-10] ---R , ---R ---R [1.1499999999999999, 0.17155535399999999, 0.1715553536299986, ---R - 3.7000139063714244E-10] ---R , ---R ---R [1.1599999999999999, 0.168827535, 0.16882753466078662, ---R - 3.3921337960762799E-10] ---R , ---R [1.1699999999999999,0.16615004,0.16615004016994619,1.6994619600474437E-10], ---R ---R [1.1799999999999999, 0.16352174799999999, 0.16352174807880468, ---R 7.8804684999767005E-11] ---R , ---R ---R [1.1899999999999999, 0.16094156700000001, 0.1609415673356836, ---R 3.3568359203428599E-10] ---R , ---R [1.2,0.15840843700000001,0.15840843685146253,- 1.4853748786514132E-10], ---R [1.21,0.155921324,0.15592132447956802,4.7956802418092082E-10], ---R [1.22,0.153479226,0.15347922603818942,3.8189423845480519E-11], ---R [1.23,0.15108116399999999,0.15108116437265298,3.7265299179800593E-10], ---R [1.24,0.14872618800000001,0.14872618845599739,4.559973787454652E-10], ---R [1.25,0.14641337300000001,0.14641337252591019,- 4.7408982295493729E-10], ---R [1.26,0.14414181500000001,0.14414181525628297,2.5628296707047582E-10], ---R [1.27,0.14191063900000001,0.14191063896174164,- 3.8258368695309741E-11], ---R [1.28,0.13971898899999999,0.1397189888335964,- 1.6640358535546795E-10], ---R [1.29,0.137566032,0.13756603220574354,2.0574353332136752E-10], ---R [1.3,0.13545095800000001,0.13545095784912908,- 1.5087092686272285E-10], ---R [1.3100000000000001,0.133372975,0.13337297529345732,2.9345731400454156E-10], ---R [1.3200000000000001,0.131331314,0.13133131417489974,1.7489973358486566E-10], ---R ---R [1.3300000000000001, 0.12932522399999999, 0.12932522360862764, ---R - 3.9137235119390823E-10] ---R , ---R ---R [1.3400000000000001, 0.12735397200000001, 0.12735397158504419, ---R - 4.1495581970529827E-10] ---R , ---R [1.3500000000000001,0.125416844,0.12541684438866441,3.8866440621454501E-10], ---R [1.3600000000000001,0.123513146,0.12351314603863212,3.8632111398761992E-11], ---R ---R [1.3700000000000001, 0.12164219800000001, 0.1216421977499248, ---R - 2.5007521053943549E-10] ---R , ---R [1.3799999999999999,0.119803337,0.11980333741433752,4.1433752262509671E-10], ---R [1.3899999999999999,0.117995919,0.11799591910039325,1.0039324926935933E-10], ---R ---R [1.3999999999999999, 0.116219313, 0.11621931257135804, ---R - 4.2864196914127461E-10] ---R , ---R ---R [1.4099999999999999, 0.114472903, 0.11447290282058709, ---R - 1.7941291508005719E-10] ---R , ---R [1.4199999999999999,0.11275609,0.11275608962347,- 3.7653000162229944E-10], ---R [1.4299999999999999,0.111068287,0.11106828710526567,1.0526567117974395E-10], ---R ---R [1.4399999999999999, 0.10940892300000001, 0.10940892332417007, ---R 3.2417006579077423E-10] ---R , ---R [1.45,0.10777744,0.10777743986897642,- 1.3102358087380139E-10], ---R [1.46,0.106173291,0.10617329147072579,4.7072579167917183E-10], ---R [1.47,0.104595946,0.10459594562777519,- 3.7222480653298362E-10], ---R [1.48,0.103044882,0.10304488224373387,2.4373386642295714E-10], ---R [1.49,0.10151959300000001,0.10151959327774779,2.7774778310618586E-10], ---R [1.5,0.100019582,0.10001958240663256,4.0663256095641032E-10], ---R [1.51,9.8544364999999995E-2,9.85443646983854E-2,- 3.0161459441124805E-10], ---R [1.52,9.7093466000000003E-2,9.7093466296618358E-2,2.9661835487804211E-10], ---R [1.53,9.5666424E-2,9.5666424115486592E-2,1.1548659251126026E-10], ---R [1.54,9.4262786000000001E-2,9.4262785544698136E-2,- 4.5530186565390096E-10], ---R [1.55,9.2882108000000005E-2,9.2882108164209165E-2,1.6420916015835729E-10], ---R ---R [1.5600000000000001, 9.1523960000000001E-2, 9.152395946823666E-2, ---R - 5.3176334169346973E-10] ---R , ---R ---R [1.5700000000000001, 9.0187917000000006E-2, 9.0187916598222728E-2, ---R - 4.0177727811396835E-10] ---R , ---R ---R [1.5800000000000001, 8.8873566000000001E-2, 8.8873566084412048E-2, ---R 8.441204679687786E-11] ---R , ---R ---R [1.5900000000000001, 8.7580504000000003E-2, 8.7580503595714843E-2, ---R - 4.0428516090429412E-10] ---R , ---R ---R [1.6000000000000001, 8.6308334E-2, 8.6308333697539708E-2, ---R - 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List List Fraction Integer --E 4 + \end{chunk} +The actual table values from above are: +\begin{verbatim} + [0.5, 0.55977359500000001, + 0.55977359477616084, + -2.2383916942203541E-10] + [0.51000000000000001, 0.54782235199999996, + 0.54782235178082872, + -2.1917123671499894E-10] + [0.52000000000000002, 0.53621979799999997, + 0.53621979784563623, + -1.5436374400934483E-10] + [0.53000000000000003, 0.52495150999999995, + 0.52495151011486541, + 1.148654504845581E-10] + [0.54000000000000004, 0.51400388600000002, + 0.51400388570224909, + -2.9775093501882566E-10] + [0.55000000000000004, 0.50336408099999996, + 0.50336408139239386, + 3.9239389515444145E-10] + [0.56000000000000005, 0.49301995900000001, + 0.49301995877649291, + -2.2350710171537003E-10] + [0.56999999999999995, 0.48296003399999998, + 0.48296003424511297, + 2.451129854641465E-10] + [0.57999999999999996, 0.47317343299999998, + 0.47317343333112627, + 3.3112629305165342E-10] + [0.58999999999999997, 0.463649849, + 0.46364984895652972, + 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0.14191063896174164, + -3.8258368695309741E-11] + [1.28, 0.13971898899999999, + 0.1397189888335964, + -1.6640358535546795E-10] + [1.29, 0.137566032, + 0.13756603220574354, + 2.0574353332136752E-10] + [1.3, 0.13545095800000001, + 0.13545095784912908, + -1.5087092686272285E-10] + [1.3100000000000001, 0.133372975, + 0.13337297529345732, + 2.9345731400454156E-10] + [1.3200000000000001, 0.131331314, + 0.13133131417489974, + 1.7489973358486566E-10] + [1.3300000000000001, 0.12932522399999999, + 0.12932522360862764, + -3.9137235119390823E-10] + [1.3400000000000001, 0.12735397200000001, + 0.12735397158504419, + -4.1495581970529827E-10] + [1.3500000000000001, 0.125416844, + 0.12541684438866441, + 3.8866440621454501E-10] + [1.3600000000000001, 0.123513146, + 0.12351314603863212, + 3.8632111398761992E-11] + [1.3700000000000001, 0.12164219800000001, + 0.1216421977499248, + -2.5007521053943549E-10] + [1.3799999999999999, 0.119803337, + 0.11980333741433752, + 4.1433752262509671E-10] + [1.3899999999999999, 0.117995919, + 0.11799591910039325, + 1.0039324926935933E-10] + [1.3999999999999999, 0.116219313, + 0.11621931257135804, + -4.2864196914127461E-10] + [1.4099999999999999, 0.114472903, + 0.11447290282058709, + -1.7941291508005719E-10] + [1.4199999999999999, 0.11275609, + 0.11275608962347, + -3.7653000162229944E-10] + [1.4299999999999999, 0.111068287, + 0.11106828710526567, + 1.0526567117974395E-10] + [1.4399999999999999, 0.10940892300000001, + 0.10940892332417007, + 3.2417006579077423E-10] + [1.45, 0.10777744, + 0.10777743986897642, + -1.3102358087380139E-10] + [1.46, 0.106173291, + 0.10617329147072579, + 4.7072579167917183E-10] + [1.47, 0.104595946, + 0.10459594562777519, + -3.7222480653298362E-10] + [1.48, 0.103044882, + 0.10304488224373387, + 2.4373386642295714E-10] + [1.49, 0.10151959300000001, + 0.10151959327774779, + 2.7774778310618586E-10] + [1.5, 0.100019582, + 0.10001958240663256, + 4.0663256095641032E-10] + [1.51, 9.8544364999999995E-2, + 9.85443646983854E-2, + -3.0161459441124805E-10] + [1.52, 9.7093466000000003E-2, + 9.7093466296618358E-2, + 2.9661835487804211E-10] + [1.53, 9.5666424E-2, + 9.5666424115486592E-2, + 1.1548659251126026E-10] + [1.54, 9.4262786000000001E-2, + 9.4262785544698136E-2, + -4.5530186565390096E-10] + [1.55, 9.2882108000000005E-2, + 9.2882108164209165E-2, + 1.6420916015835729E-10] + [1.5600000000000001, 9.1523960000000001E-2, + 9.152395946823666E-2, + -5.3176334169346973E-10] + [1.5700000000000001, 9.0187917000000006E-2, + 9.0187916598222728E-2, + -4.0177727811396835E-10] + [1.5800000000000001, 8.8873566000000001E-2, + 8.8873566084412048E-2, + 8.441204679687786E-11] + [1.5900000000000001, 8.7580504000000003E-2, + 8.7580503595714843E-2, + -4.0428516090429412E-10] + [1.6000000000000001, 8.6308334E-2, + 8.6308333697539708E-2, + -3.0246029292246845E-10] + [1.6100000000000001, 8.5056670000000001E-2, + 8.5056669617302794E-2, + -3.8269720725736533E-10] + [1.6200000000000001, 8.3825132999999996E-2, + 8.3825133017319142E-2, + 1.7319146117245054E-11] + [1.6299999999999999, 8.2613354E-2, + 8.2613353774808662E-2, + -2.25191337799302E-10] + [1.6399999999999999, 8.1420969999999995E-2, + 8.1420969768751517E-2, + -2.3124847869926413E-10] + [1.6499999999999999, 8.0247627000000002E-2, + 8.0247626673343175E-2, + -3.266568265880565E-10] + [1.6599999999999999, 7.9092977999999994E-2, + 7.9092977757806437E-2, + -2.4219355687638E-10] + [1.6699999999999999, 7.7956683999999998E-2, + 7.7956683692333661E-2, + -3.0766633685175293E-10] + [1.6799999999999999, 7.6838411999999995E-2, + 7.6838412359934938E-2, + 3.5993494296171491E-10] + [1.6899999999999999, 7.5737839000000001E-2, + 7.5737838673983093E-2, + -3.2601690791445037E-10] + [1.7, 7.4654644000000006E-2, + 7.4654644401252912E-2, + 4.0125290590165008E-10] + [1.71, 7.3588518000000006E-2, + 7.358851799025623E-2, + -9.7437752311080317E-12] + [1.72, 7.2539153999999995E-2, + 7.2539154404693273E-2, + 4.0469327888814632E-10] + [1.73, 7.1506255000000005E-2, + 7.150625496183538E-2, + -3.8164624238667955E-11] + [1.74, 7.0489526999999996E-2, + 7.0489527175668809E-2, + 1.7566881282959912E-10] + [1.75, 6.9488684999999994E-2, + 6.9488684604638751E-2, + -3.9536124374350834E-10] + [1.76, 6.8503446999999995E-2, + 6.8503446703828352E-2, + -2.9617164276629637E-10] + [1.77, 6.7533539000000004E-2, + 6.7533538681429195E-2, + -3.1857080862174314E-10] + [1.78, 6.6578690999999995E-2, + 6.657869135934702E-2, + 3.5934702435902466E-10] + [1.79, 6.5638640999999998E-2, + 6.5638641037815026E-2, + 3.7815028886001301E-11] + [1.8, 6.4713128999999994E-2, + 6.4713129363868749E-2, + 3.638687545715058E-10] + [1.8100000000000001, 6.3801902999999993E-2, + 6.3801903203559385E-2, + 2.0355939156502245E-10] + [1.8200000000000001, 6.2904715E-2, + 6.2904714517779237E-2, + -4.8222076332038455E-10] + [1.8300000000000001, 6.2021319999999998E-2, + 6.2021320241580469E-2, + 2.4158047090550028E-10] + [1.8400000000000001, 6.1151482E-2, + 6.1151482166870164E-2, + 1.6687016352046058E-10] + [1.8500000000000001, 6.0294966999999998E-2, + 6.0294966828373431E-2, + -1.7162656712477187E-10] + [1.8600000000000001, 5.9451545000000001E-2, + 5.9451545392755656E-2, + 3.9275565438812166E-10] + [1.8700000000000001, 5.8620994000000003E-2, + 5.8620993550804079E-2, + -4.4919592351311266E-10] + [1.8799999999999999, 5.7803091000000001E-2, + 5.7803091412567897E-2, + 4.1256789651278325E-10] + [1.8899999999999999, 5.6997622999999997E-2, + 5.6997623405359299E-2, + 4.0535930168061896E-10] + [1.8999999999999999, 5.6204377999999999E-2, + 5.6204378174534608E-2, + 1.7453460898764206E-10] + [1.9099999999999999, 5.5423148999999998E-2, + 5.5423148486950402E-2, + -5.1304959586273569E-10] + [1.9199999999999999, 5.4653730999999997E-2, + 5.4653731137026984E-2, + 1.3702698697937166E-10] + [1.9299999999999999, 5.3895927000000003E-2, + 5.3895926855324849E-2, + -1.4467515380145457E-10] + [1.9399999999999999, 5.3149540000000002E-2, + 5.3149540219563307E-2, + 2.1956330503725141E-10] + [1.95, 5.2414380000000003E-2, + 5.2414379567998548E-2, + -4.3200145544153301E-10] + [1.96, 5.1690257000000003E-2, + 5.1690256915094213E-2, + -8.4905790731504283E-11] + [1.97, 5.0976988000000001E-2, + 5.0976987869409074E-2, + -1.3059092696110497E-10] + [1.98, 5.0274392000000001E-2, + 5.0274391553638775E-2, + -4.4636122575880677E-10] + [1.99, 4.9582291000000001E-2, + 4.9582290526736128E-2, + -4.732638725357674E-10] + [2., 4.8900511000000001E-2, + 4.8900510708061007E-2, + -2.9193899381274591E-10]] +\end{verbatim} + Now that we move into larger numbers we need a new scaling function. \begin{chunk}{*} + --S 5 of 7 g(x)==x * %e^x * E1(x)::DFLOAT +--R --R Type: Void --E 5 + \end{chunk} And we compute the scaled value of E1(x) in the range 2.0 to 10.0 from Abramowitz and Stegun,``Handbook of Mathematical Functions'', Dover Publications, Inc. New York 1965. pp242-243 \begin{chunk}{*} + --S 6 of 7 +t6:List List Fraction Integer:=[[machineFraction (x::DFLOAT) for x in line]_ + for line in _ [[2.0,0.722657234,g(2.0),g(2.0)-0.722657234],_ [2.1,0.730791502,g(2.1),g(2.1)-0.730791502],_ [2.2,0.738431132,g(2.2),g(2.2)-0.738431132],_ @@ -927,291 +1600,517 @@ Dover Publications, Inc. New York 1965. pp242-243 [9.7,0.913417043,g(9.7),g(9.7)-0.913417043],_ [9.8,0.914168766,g(9.8),g(9.8)-0.914168766],_ [9.9,0.914907418,g(9.9),g(9.9)-0.914907418],_ -[10.0,0.915633339,g(10.0),g(10.0)-0.915633339]] +[10.0,0.915633339,g(10.0),g(10.0)-0.915633339]]] --R --R Compiling function g with type Float -> Expression DoubleFloat --R --R (6) ---R [[2.,0.72265723400000004,0.72265723377644353,- 2.2355650663996585E-10], ---R ---R [2.1000000000000001, 0.73079150199999998, 0.73079150228850298, ---R 2.8850299926830303E-10] ---R , ---R ---R [2.2000000000000002, 0.73843113199999999, 0.73843113069659072, ---R - 1.3034092694041988E-9] ---R , ---R ---R [2.2999999999999998, 0.74562214900000001, 0.74562214881923961, ---R - 1.8076040664283255E-10] ---R , ---R ---R [2.3999999999999999, 0.75240482900000005, 0.75240483025618621, ---R 1.2561861550963727E-9] ---R , ---R [2.5,0.75881459200000001,0.75881459121494477,- 7.850552430355151E-10], ---R ---R [2.6000000000000001, 0.76488272199999996, 0.76488272217978248, ---R 1.7978252220274271E-10] ---R , ---R ---R [2.7000000000000002, 0.77063698700000005, 0.77063698825333671, ---R 1.2533366566813697E-9] ---R , ---R ---R [2.7999999999999998, 0.77610212300000003, 0.77610212535832457, ---R 2.3583245356562088E-9] ---R , ---R ---R [2.8999999999999999, 0.78130025199999997, 0.78130025314743023, ---R 1.1474302619163268E-9] ---R , ---R [3.,0.786251221,0.78625122076592868,- 2.3407131788388824E-10], ---R ---R [3.1000000000000001, 0.79097280000000003, 0.79097289808240101, ---R 9.8082400978860562E-8] ---R , ---R ---R [3.2000000000000002, 0.79548142200000005, 0.7954814223275547, ---R 3.2755465007028306E-10] ---R , ---R ---R [3.2999999999999998, 0.79979140800000004, 0.79979140803702831, ---R 3.7028269339600683E-11] ---R , ---R ---R [3.3999999999999999, 0.80391612700000004, 0.80391612661323797, ---R - 3.8676206681742542E-10] ---R , ---R [3.5,0.80786766099999996,0.80786766059300552,- 4.0699443815128689E-10], ---R ---R [3.6000000000000001, 0.81165703700000003, 0.81165703674711587, ---R - 2.5288415805846398E-10] ---R , ---R ---R [3.7000000000000002, 0.81529434199999995, 0.81529434137285406, ---R - 6.2714589077472738E-10] ---R , ---R ---R [3.7999999999999998, 0.81878882100000006, 0.81878882054050406, ---R - 4.5949599680739084E-10] ---R , ---R ---R [3.8999999999999999, 0.82214896699999995, 0.8221489675670105, ---R 5.6701054962360331E-10] ---R , ---R [4.,0.82538250000000002,0.82538259960411076,9.9604110737061546E-8], ---R ---R [4.0999999999999996, 0.82849692600000002, 0.82849692490970006, ---R - 1.0902999614259556E-9] ---R , ---R ---R [4.2000000000000002, 0.83149860200000003, 0.83149860211639337, ---R 1.1639333941104724E-10] ---R , ---R ---R [4.2999999999999998, 0.83439379400000002, 0.83439379260257418, ---R - 1.397425841709321E-9] ---R , ---R ---R [4.4000000000000004, 0.83718820699999996, 0.83718820689462137, ---R - 1.0537859473913613E-10] ---R , ---R [4.5,0.83988714399999997,0.83988714589085944,1.8908594690003611E-9], ---R ---R [4.5999999999999996, 0.84249553899999996, 0.84249553757701434, ---R - 1.4229856182268463E-9] ---R , ---R ---R [4.7000000000000002, 0.84501797099999998, 0.84501796980531307, ---R - 1.1946869049594966E-9] ---R , ---R ---R [4.7999999999999998, 0.84745872099999997, 0.84745871962692243, ---R - 1.3730775405562667E-9] ---R , ---R ---R [4.9000000000000004, 0.84982177800000003, 0.84982177959827732, ---R 1.5982772882949803E-9] ---R , ---R [5.,0.85211088000000001,0.85211088142366165,1.4236616330265406E-9], ---R ---R [5.0999999999999996, 0.85432951899999998, 0.85432951724709605, ---R - 1.7529039331165563E-9] ---R , ---R ---R [5.2000000000000002, 0.85648095800000001, 0.85648095886487274, ---R 8.6487272898949641E-10] ---R , ---R ---R [5.2999999999999998, 0.85856827499999999, 0.85856827509448064, ---R 9.4480645529415597E-11] ---R , ---R ---R [5.4000000000000004, 0.86059434800000001, 0.86059434750532948, ---R - 4.946705267627749E-10] ---R , ---R [5.5,0.86256188499999997,0.86256188469070161,- 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265797 +--R [----------------,----------------,----------------,----------------], +--R 140737488355328 4503599627370496 4503599627370496 1125899906842624 +--R 19 8213421427716063 128334709895015 5564897 +--R [--,----------------,---------------,----------------], +--R 2 9007199254740992 140737488355328 9007199254740992 +--R 5404319552844595 256888671453011 64222167818743 178039 +--R [----------------,---------------,--------------,- ---------------], +--R 562949953421312 281474976710656 70368744177664 281474976710656 +--R 2730307274093363 1028416163622165 8227329312589529 3612209 +--R [----------------,----------------,----------------,----------------], +--R 281474976710656 1125899906842624 9007199254740992 9007199254740992 +--R 5516909543528857 2058525056955673 2058525057098693 35755 +--R [----------------,----------------,----------------,---------------], +--R 562949953421312 2251799813685248 2251799813685248 562949953421312 +--R 1393301134717747 8240753413566605 4120376705584929 2396747 +--R [----------------,----------------,----------------,- ----------------], +--R 140737488355328 9007199254740992 4503599627370496 9007199254740992 +--R 4123645964328403 1030911491530075 1791897 +--R [10,----------------,----------------,----------------]] +--R 4503599627370496 1125899906842624 4503599627370496 +--R Type: List List Fraction Integer --E 6 +\end{chunk} + +The actual table values from above are: +\begin{verbatim} + [2., 0.72265723400000004, + 0.72265723377644353, + -2.2355650663996585E-10] + [2.1000000000000001, 0.73079150199999998, + 0.73079150228850298, + 2.8850299926830303E-10] + [2.2000000000000002, 0.73843113199999999, + 0.73843113069659072, + -1.3034092694041988E-9] + [2.2999999999999998, 0.74562214900000001, + 0.74562214881923961, + -1.8076040664283255E-10] + [2.3999999999999999, 0.75240482900000005, + 0.75240483025618621, + 1.2561861550963727E-9] + [2.5, 0.75881459200000001, + 0.75881459121494477, + -7.850552430355151E-10] + [2.6000000000000001, 0.76488272199999996, + 0.76488272217978248, + 1.7978252220274271E-10] + [2.7000000000000002, 0.77063698700000005, + 0.77063698825333671, + 1.2533366566813697E-9] + [2.7999999999999998, 0.77610212300000003, + 0.77610212535832457, + 2.3583245356562088E-9] + [2.8999999999999999, 0.78130025199999997, + 0.78130025314743023, + 1.1474302619163268E-9] + [3., 0.786251221, + 0.78625122076592868, + -2.3407131788388824E-10] + [3.1000000000000001, 0.79097280000000003, + 0.79097289808240101, + 9.8082400978860562E-8] + [3.2000000000000002, 0.79548142200000005, + 0.7954814223275547, + 3.2755465007028306E-10] + [3.2999999999999998, 0.79979140800000004, + 0.79979140803702831, + 3.7028269339600683E-11] + [3.3999999999999999, 0.80391612700000004, + 0.80391612661323797, + -3.8676206681742542E-10] + [3.5, 0.80786766099999996, + 0.80786766059300552, + -4.0699443815128689E-10] + [3.6000000000000001, 0.81165703700000003, + 0.81165703674711587, + -2.5288415805846398E-10] + [3.7000000000000002, 0.81529434199999995, + 0.81529434137285406, + -6.2714589077472738E-10] + [3.7999999999999998, 0.81878882100000006, + 0.81878882054050406, + -4.5949599680739084E-10] + [3.8999999999999999, 0.82214896699999995, + 0.8221489675670105, + 5.6701054962360331E-10] + [4., 0.82538250000000002, + 0.82538259960411076, + 9.9604110737061546E-8] + [4.0999999999999996, 0.82849692600000002, + 0.82849692490970006, + -1.0902999614259556E-9] + [4.2000000000000002, 0.83149860200000003, + 0.83149860211639337, + 1.1639333941104724E-10] + [4.2999999999999998, 0.83439379400000002, + 0.83439379260257418, + -1.397425841709321E-9] + [4.4000000000000004, 0.83718820699999996, + 0.83718820689462137, + -1.0537859473913613E-10] + [4.5, 0.83988714399999997, + 0.83988714589085944, + 1.8908594690003611E-9] + [4.5999999999999996, 0.84249553899999996, + 0.84249553757701434, + -1.4229856182268463E-9] + [4.7000000000000002, 0.84501797099999998, + 0.84501796980531307, + -1.1946869049594966E-9] + [4.7999999999999998, 0.84745872099999997, + 0.84745871962692243, + -1.3730775405562667E-9] + [4.9000000000000004, 0.84982177800000003, + 0.84982177959827732, + 1.5982772882949803E-9] + [5., 0.85211088000000001, + 0.85211088142366165, + 1.4236616330265406E-9] + [5.0999999999999996, 0.85432951899999998, + 0.85432951724709605, + -1.7529039331165563E-9] + [5.2000000000000002, 0.85648095800000001, + 0.85648095886487274, + 8.6487272898949641E-10] + [5.2999999999999998, 0.85856827499999999, + 0.85856827509448064, + 9.4480645529415597E-11] + [5.4000000000000004, 0.86059434800000001, + 0.86059434750532948, + -4.946705267627749E-10] + [5.5, 0.86256188499999997, + 0.86256188469070161, + -3.0929836469795191E-10] + [5.5999999999999996, 0.86447343600000004, + 0.86447343523800879, + -7.6199124787734718E-10] + [5.7000000000000002, 0.866331399, + 0.8663313995352464, + 5.3524640275526281E-10] + [5.7999999999999998, 0.86813804000000006, + 0.86813804053493893, + 5.3493887097744164E-10] + [5.9000000000000004, 0.86989549399999999, + 0.86989549358247464, + -4.1752534762906635E-10] + [6., 0.87160577500000003, + 0.87160577540332174, + 4.0332170936352441E-10] + [6.0999999999999996, 0.87327079299999999, + 0.8732707923327413, + -6.6725869274364413E-10] + [6.2000000000000002, 0.87489234699999996, + 0.8748923478621643, + 8.6216433992092334E-10] + [6.2999999999999998, 0.87647215000000001, + 0.87647214956817143, + -4.3182857289991716E-10] + [6.4000000000000004, 0.878011816, + 0.87801181548273155, + -5.1726845029520518E-10] + [6.5, 0.87951288100000002, + 0.87951287995710281, + -1.0428972130327452E-9] + [6.5999999999999996, 0.88097679699999998, + 0.88097679906610149, + 2.0661015120992943E-9] + [6.7000000000000002, 0.88240495500000005, + 0.8824049555946607, + 5.9466065405189283E-10] + [6.7999999999999998, 0.88379866200000001, + 0.88379866364416337, + 1.6441633610142503E-9] + [6.9000000000000004, 0.88515917600000005, + 0.88515917289225332, + -3.1077467266271697E-9] + [7., 0.88648767500000003, + 0.88648767253642946, + -2.4635705697662047E-9] + [7.0999999999999996, 0.88778529399999995, + 0.8877852949486843, + 9.4868435329686918E-10] + [7.2000000000000002, 0.88905311899999995, + 0.88905311906582485, + 6.5824901085420606E-11] + [7.2999999999999998, 0.89029217299999996, + 0.89029217353766843, + 5.3766846530578505E-10] + [7.4000000000000004, 0.89150344000000004, + 0.89150343965322676, + -3.4677327676035929E-10] + [7.5, 0.89268785399999995, + 0.89268785406308437, + 6.308442657143587E-11] + [7.5999999999999996, 0.89384631199999998, + 0.89384631131444836, + -6.8555161547578791E-10] + [7.7000000000000002, 0.89497966600000001, + 0.89497966621388148, + 2.1388146809186992E-10] + [7.7999999999999998, 0.89608873700000002, + 0.89608873603132189, + -9.686781377027387E-10] + [7.9000000000000004, 0.89717430200000003, + 0.8971743025577732, + 5.5777316099181462E-10] + [8., 0.89823711299999998, + 0.89823711402799578, + 1.0279957995962263E-9] + [8.0999999999999996, 0.89927788799999997, + 0.89927788691844668, + -1.0815532913710513E-9] + [8.1999999999999993, 0.90029730600000002, + 0.90029730762992677, + 1.629926749124877E-9] + [8.3000000000000007, 0.90129603300000005, + 0.90129603406349046, + 1.0634904068496098E-9] + [8.4000000000000004, 0.90227469500000002, + 0.90227469709753316, + 2.0975331471717595E-9] + [8.5, 0.90323390000000003, + 0.90323390197320852, + 1.9732084854950926E-9] + [8.5999999999999996, 0.90417422800000002, + 0.9041742295948515, + 1.5948514731078944E-9] + [8.6999999999999993, 0.90509623500000003, + 0.90509623775141723, + 2.7514172051823493E-9] + [8.8000000000000007, 0.90600045900000004, + 0.90600046226454201, + 3.264541970082746E-9] + [8.9000000000000004, 0.90688741399999995, + 0.90688741806836271, + 4.0683627577919879E-9] + [9., 0.907757602, + 0.90775760022576812, + -1.7742318725311179E-9] + [9.0999999999999996, 0.90861148300000005, + 0.90861148488548271, + 1.8854826588921014E-9] + [9.1999999999999993, 0.90944952999999995, + 0.90944953018395813, + 1.8395818202066039E-10] + [9.3000000000000007, 0.91027217699999996, + 0.91027217709579178, + 9.5791818921497907E-11] + [9.4000000000000004, 0.91107985000000002, + 0.91107985023607185, + 2.3607182875196031E-10] + [9.5, 0.91187295800000001, + 0.91187295861782769, + 6.1782767790674598E-10] + [9.5999999999999996, 0.91265189700000005, + 0.91265189636747834, + -6.3252170168226485E-10] + [9.6999999999999993, 0.91341704300000004, + 0.91341704340103613, + 4.010360932227286E-10] + [9.8000000000000007, 0.91416876599999997, + 0.91416876606351216, + 6.3512195502823943E-11] + [9.9000000000000004, 0.91490741799999997, + 0.9149074177339066, + -2.6609336956084917E-10] + [10., 0.91563333899999999, + 0.91563333939788116, + 3.9788117245365129E-10]] +\end{verbatim} +\begin{chunk}{*} + --S 7 of 7 E1(0.0) +--R --R --R (7) infinity --R Type: OnePointCompletion DoubleFloat --E 7 + )spool + )lisp (bye) \end{chunk} diff --git a/src/input/en.input.pamphlet b/src/input/en.input.pamphlet index ccf48c4..623ec5c 100644 --- a/src/input/en.input.pamphlet +++ b/src/input/en.input.pamphlet @@ -7668,7 +7668,6 @@ The actual table values from above are: )spool )lisp (bye) -\end{chunk} \eject \begin{thebibliography}{99} \bibitem{1} Abramowitz and Stegun,``Handbook of Mathematical Functions'',