Hello,
as I wrote before I'm trying to use the Sullivan multi precision
package with GNU APL.
That workspace was written with Dyalog APL in mind, so there're some
Dyalog feature we saw before ([]SIGNAL, []FMT).
Those are now ok.
But I have this problem:
{delta}6:{->}(0^.=x{<-}(-{rho}f),1 {neg}1[s]{times}x,f)/0 @ Put it all
together, quit if zero
it gives me RANK ERROR
RANK ERROR
Fexec[30] →(0∧.=x←(-⍴f),1 ¯1[s]×x,f)/0
^ ^
when i try to calculate '234233' ADD '23434983498'. I suppose the
problem could be the AXIS [s], but I'm not sure how to read exactly
the error message.
Attached there's the workspace (not yet completed) translated from ASCII
thanks,
Fausto
<?xml version='1.0' encoding='UTF-8' standalone='yes'?>
<!DOCTYPE Workspace
[
<!ELEMENT Workspace (Value*,Ravel*,SymbolTable,Symbol*,StateIndicator)>
<!ATTLIST Workspace wsid CDATA #REQUIRED>
<!ATTLIST Workspace year CDATA #REQUIRED>
<!ATTLIST Workspace month CDATA #REQUIRED>
<!ATTLIST Workspace day CDATA #REQUIRED>
<!ATTLIST Workspace hour CDATA #REQUIRED>
<!ATTLIST Workspace minute CDATA #REQUIRED>
<!ATTLIST Workspace second CDATA #REQUIRED>
<!ATTLIST Workspace timezone CDATA #REQUIRED>
<!ELEMENT Value (#PCDATA)>
<!ATTLIST Value flg CDATA #REQUIRED>
<!ATTLIST Value vid CDATA #REQUIRED>
<!ATTLIST Value parent CDATA #IMPLIED>
<!ATTLIST Value rk CDATA #REQUIRED>
<!ATTLIST Value sh-0 CDATA #IMPLIED>
<!ATTLIST Value sh-1 CDATA #IMPLIED>
<!ATTLIST Value sh-2 CDATA #IMPLIED>
<!ATTLIST Value sh-3 CDATA #IMPLIED>
<!ATTLIST Value sh-4 CDATA #IMPLIED>
<!ATTLIST Value sh-5 CDATA #IMPLIED>
<!ATTLIST Value sh-6 CDATA #IMPLIED>
<!ATTLIST Value sh-7 CDATA #IMPLIED>
<!ELEMENT Ravel (#PCDATA)>
<!ATTLIST Ravel vid CDATA #REQUIRED>
<!ATTLIST Ravel cells CDATA #REQUIRED>
<!ELEMENT SymbolTable (Symbol*)>
<!ATTLIST SymbolTable size CDATA #REQUIRED>
<!ELEMENT Symbol (unused-name|Variable|Function|Label|Shared-Variable)*>
<!ATTLIST Symbol name CDATA #REQUIRED>
<!ATTLIST Symbol stack-size CDATA #REQUIRED>
<!ELEMENT unused-name EMPTY>
<!ELEMENT Variable (#PCDATA)>
<!ATTLIST Variable vid CDATA #REQUIRED>
<!ELEMENT Function (UCS)>
<!ELEMENT Label (#PCDATA)>
<!ATTLIST Label value CDATA #REQUIRED>
<!ELEMENT Shared-Variable (#PCDATA)>
<!ATTLIST Shared-Variable key CDATA #REQUIRED>
<!ELEMENT UCS (#PCDATA)>
<!ATTLIST UCS uni CDATA #REQUIRED>
<!ELEMENT StateIndicator (SI-entry*)>
<!ATTLIST StateIndicator levels CDATA #REQUIRED>
<!ELEMENT SI-entry ((Execute|Statements|UserFunction),Parser+)>
<!ATTLIST SI-entry level CDATA #REQUIRED>
<!ATTLIST SI-entry pc CDATA #REQUIRED>
<!ATTLIST SI-entry line CDATA #REQUIRED>
<!ELEMENT Statements (UCS)>
<!ELEMENT Execute (UCS)>
<!ELEMENT UserFunction (#PCDATA)>
<!ATTLIST UserFunction ufun-name CDATA #REQUIRED>
<!ATTLIST UserFunction symbol-level CDATA #REQUIRED>
<!ATTLIST UserFunction creation-time CDATA #IMPLIED>
<!ATTLIST UserFunction exec-properties CDATA #IMPLIED>
<!ELEMENT Parser (Token*)>
<!ATTLIST Parser assign-pending CDATA #REQUIRED>
<!ATTLIST Parser lookahead-high CDATA #REQUIRED>
<!ELEMENT Token (#PCDATA)>
<!ATTLIST Token pc CDATA #REQUIRED>
<!ATTLIST Token tag CDATA #REQUIRED>
<!ATTLIST Token char CDATA #IMPLIED>
<!ATTLIST Token int CDATA #IMPLIED>
<!ATTLIST Token float CDATA #IMPLIED>
<!ATTLIST Token real CDATA #IMPLIED>
<!ATTLIST Token imag CDATA #IMPLIED>
<!ATTLIST Token sym CDATA #IMPLIED>
<!ATTLIST Token line CDATA #IMPLIED>
<!ATTLIST Token vid CDATA #IMPLIED>
<!ATTLIST Token index CDATA #IMPLIED>
<!ATTLIST Token fun-id CDATA #IMPLIED>
<!ATTLIST Token ufun-name CDATA #IMPLIED>
<!ATTLIST Token symbol-level CDATA #IMPLIED>
<!ATTLIST Token comment CDATA #IMPLIED>
]>
<!-- hour/minute/second is )SAVE time in UTC (aka. GMT).
timezone is offset to UTC in seconds.
local time is UTC + offset -->
<Workspace wsid="multiprex" year="2015" month="4" day="13"
hour="12" minute="31" second="35" timezone="7200"
saving_SVN=" 582">
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¹2395²IO⁰¹2190²0 ⁰¹25CA² z⁰¹2190²0 Ffmt⁰¹2283²Fadd/Fexec⁰¹A8²a⁰
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¹2395²IO⁰¹2190²0 ⁰¹25CA² b⁰¹2190²mp.Fexec b⁰¹A
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²x⁰¹2190²x1⁰¹A
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¹2206²2:x⁰¹2190²(x⁰¹220A¹2359²D,'.-⁰¹AF²')/x ⁰¹235D² Ignore in⁰
²valid characters⁰¹A
²x⁰¹2190²(s⁰¹2190²x[0]⁰¹220A²'-⁰¹AF²')⁰¹2193²x ⁰¹235D² Negat⁰
²ive No. if s=1. Drop minus sign⁰¹A
¹2192²(0=⁰¹2374²x)/0 ⁰¹235D² Quick quit if null inpu⁰
²t (= 0)⁰¹A
²i⁰¹2190²(q⁰¹2190²x⁰¹2373²'.')⁰¹2191²x ⁰¹235D² Integer p⁰
²art⁰¹A
¹2192²(0=⁰¹2374²f⁰¹2190²(q+1)⁰¹2193²x)/⁰¹2206²3 ⁰¹235D² Fract⁰
²ional part⁰¹A
¹2395²ES(f⁰¹2228².='.')/11 ⁰¹235D² Only one decimal point allo⁰
²wed⁰¹A
¹2206²3:x⁰¹2190¹236C¹A
¹2192²(0=⁰¹2374²i)/⁰¹2206²4⁰¹A
²x⁰¹2190²x,⁰¹234E²(⁰¹233D²(⁰¹230A²p1⁰¹D7¹2374²i)⁰¹2374²(p+1)⁰
¹2191²p⁰¹2374²1)\i ⁰¹235D² Convert integer part to numerics⁰¹A
¹2206²4:⁰¹2192²(0⁰¹2260¹2374²f)/⁰¹2206²5⁰¹A
²f⁰¹2190¹236C² ⁰¹25CA² ⁰¹2192¹2206²6⁰¹A
¹2206²5:f⁰¹2190²,⁰¹234E²((p1⁰¹D7¹2374²f)⁰¹2374²(p+1)⁰¹2191²p⁰
¹2374²1)\f⁰¹2190²f,(p|-⁰¹2374²f)⁰¹2374²'0'⁰¹A
¹2206²6:⁰¹2192²(0⁰¹2227².=x⁰¹2190²(-⁰¹2374²f),1 ⁰¹AF²1[s]⁰¹D7²x⁰
²,f)/0 ⁰¹235D² Put it all together, quit if zero⁰¹A
²x⁰¹2190²(-f⁰¹2190²(0⁰¹2260¹233D²x)⁰¹2373²1)⁰¹2193²x⁰¹A
²f⁰¹2190²x[0]+f ⁰¹235D² Drop trailing zeroes⁰¹A
²x⁰¹2190²f,((x⁰¹2260²0)⁰¹2373²1)⁰¹2193²x⁰¹2190²1⁰¹2193²x ⁰
¹235D² Drop leading zeroes⁰¹A
¹2192²p10/⁰¹2206²7⁰¹A
²x⁰¹2190²(base,100000000)chbase x ⁰¹235D² Change to current r⁰
²adix⁰¹A
¹2206²7:⁰¹2192²(1+⁰¹D7²e)⁰¹2283¹2206²8,0,⁰¹2206²9⁰¹A
¹2206²8:x⁰¹2190²x Fmul Fexec'0.',((⁰¹AF²1-e)⁰¹2374²'0'),'1' ⁰
¹25CA² ⁰¹2192¹2206²9⁰¹A
¹2206²9:x⁰¹2190²x Fmul Fexec'1',e⁰¹2374²'0'⁰¹A
"/>
</Function>
</Symbol>
<Symbol name="Ffmt" stack-size="1">
<Function creation-time="1428919516878931" exec-properties="0,0,0,0">
<UCS uni="²z⁰¹2190²h1 Ffmt a;b;x;k;n;p;s⁰¹A
¹235D² Format a multiprecision number⁰¹A
¹235D² H1 says How: if not supplied then include spaces every ⁰
²p digits⁰¹A
¹235D² where p is the size of the base, otherwise every h digi⁰
²ts.⁰¹A
¹235D² if h is negative use commas instead of spaces.⁰¹A
¹235D² For normal thousand commas, h is ⁰¹AF²3.⁰¹A
¹2192²(0=1|p⁰¹2190²10⁰¹235F²base)/⁰¹2206²1 ⁰¹235D² Radix mu⁰
²st be a power of 10⁰¹A
²a⁰¹2190²(100000000,base)chbase a ⁰¹25CA² p⁰¹2190²8 ⁰¹235D² so⁰
² make it one⁰¹A
¹2206²1:n⁰¹2190²a[0] ⁰¹25CA² a⁰¹2190²1⁰¹2193²a ⁰¹25CA² p⁰¹2190
¹230A²p ⁰¹235D² Make P integer⁰¹A
²a⁰¹2190²(-s⁰¹2190²(0⁰¹2260¹233D²a)⁰¹2373²1)⁰¹2193²a ⁰¹25CA² n⁰
²+⁰¹2190²s ⁰¹235D² Drop trailing zeroes⁰¹A
¹2192²(n⁰¹2264²0)/⁰¹2206²2⁰¹A
²a⁰¹2190²a,n⁰¹2374²0 ⁰¹25CA² n⁰¹2190²0 ⁰¹235D² Now put them ba⁰
²ck if appropriate⁰¹A
¹2206²2:⁰¹2192²(0⁰¹2260²s⁰¹2190¹D7²1⁰¹2191²a⁰¹2190²((a⁰¹2260²0⁰
²)⁰¹2373²1)⁰¹2193²a)/⁰¹2206²3 ⁰¹235D² Sign⁰¹A
²z⁰¹2190²'0' ⁰¹25CA² ⁰¹2192²0 ⁰¹235D² Exit if 0⁰¹A
¹2206²3:a⁰¹2190²|a ⁰¹235D² Make positive⁰¹A
¹2192²(n⁰¹2265²0)/⁰¹2206²4⁰¹A
²a⁰¹2190²(n⁰¹230A²-⁰¹2374²a)⁰¹2191²a ⁰¹235D² Put leading 0s ba⁰
²ck if appropriate⁰¹A
¹235D² ⁰¹2206²4:z⁰¹2190²' ',('ZI',⁰¹2355²p)⁰¹2395²FMT a⁰¹A
¹235D² This change is needed because GNU APL doesn't support⁰¹A
¹235D² the ⁰¹2395²FMT instruction. The code is proposed by Nic⁰
²k Lobachevsky⁰¹A
¹2206²4: t⁰¹2190²((⁰¹2374²,a),1)⁰¹2374²a⁰¹A
²t⁰¹2190²(p,0)⁰¹2355²t⁰¹A
²(((,t)=' ')/,t)⁰¹2190²'0'⁰¹A
²z⁰¹2190²' ',t⁰¹A
¹235D² End of the change.⁰¹A
¹2192²(n⁰¹2265²0)/⁰¹2206²5⁰¹A
²z[(⁰¹2374²z)+n⁰¹D7²p+1]⁰¹2190²'.' ⁰¹235D² Decimal point⁰¹A
¹2206²5:z⁰¹2190²(' '=z[0])⁰¹2193²z ⁰¹235D² Drop leading blank⁰¹A
²z⁰¹2190²((z⁰¹2260²'0')⁰¹2373²1)⁰¹2193²z ⁰¹235D² Drop leadin⁰
²g zeroes⁰¹A
²z⁰¹2190²(('.'=z[0])/'0'),z ⁰¹235D² .1 ⁰¹2192² 0.1⁰¹A
²z⁰¹2190²((s⁰¹3C²1)/'-'),z ⁰¹235D² Negative sign⁰¹A
¹235D² If we have a decimal point, drop trailing zeroes⁰¹A
¹2192²(~'.'⁰¹220A²z)/⁰¹2206²6⁰¹A
²z⁰¹2190²(-('0'⁰¹2260¹233D²z)⁰¹2373²1)⁰¹2193²z⁰¹A
¹2206²6:⁰¹2192²(0=⁰¹2395²NC'h')/0 ⁰¹235D² If h not supplied th⁰
²en quit⁰¹A
¹2192²(h=p⁰¹D7²1 ⁰¹AF²1)/0,⁰¹2206²8 ⁰¹235D² We already have sp⁰
²aces every P digits⁰¹A
²z⁰¹2190²z~' ' ⁰¹235D² Get rid of all spaces⁰¹A
¹2192²(0=k⁰¹2190²|h)/0 ⁰¹235D² Exit if H=0⁰¹A
²n⁰¹2190²z⁰¹2373²'.' ⁰¹235D² Where is the decimal point?⁰¹A
²s⁰¹2190¹233D²(⁰¹230A²n⁰¹D7²b⁰¹2190²(k+1)⁰¹F7²k)⁰¹2374²c⁰¹2190
²(k⁰¹2374²1),0 ⁰¹235D² For numbers before the decimal point⁰¹A
¹2192²(n=⁰¹2374²z)/⁰¹2206²7 ⁰¹235D² No decimal point⁰¹A
²s⁰¹2190²s,1,(⁰¹230A²((⁰¹2374²z)-n+1)⁰¹D7²b)⁰¹2374²c ⁰¹235D² N⁰
²umbers after the decimal point⁰¹A
¹2206²7:z⁰¹2190²s\z ⁰¹235D² Space out as required⁰¹A
²z⁰¹2190²(' '=z[0])⁰¹2193²z ⁰¹235D² Drop resulting leading bla⁰
²nk⁰¹A
²z⁰¹2190²(-' '=⁰¹AF²1⁰¹2191²z)⁰¹2193²z ⁰¹235D² ... and trailin⁰
²g blank⁰¹A
¹2192²('- '⁰¹2228².⁰¹2260²2⁰¹2191²z)/⁰¹2206²8 ⁰¹235D² blank be⁰
²tween - and number?⁰¹A
²z⁰¹2190²'-',2⁰¹2193²z ⁰¹235D² yes: get rid of the blank⁰¹A
¹2206²8:⁰¹2192²(h⁰¹2265²0)/0⁰¹A
²z[(z=' ')/⁰¹2373¹2374²z]⁰¹2190²',' ⁰¹235D² Commas, if h was n⁰
²egative⁰¹A
"/>
</Function>
</Symbol>
<Symbol name="Fgt" stack-size="1">
<Function creation-time="1428685455035430" exec-properties="0,0,0,0">
<UCS uni="²z⁰¹2190²x Fgt y⁰¹A
¹235D² Multiprecision X > Y⁰¹A
¹235D² Can be used for all the ordering functions, as follows:⁰¹A
¹235D² For X⁰¹3C²Y use Y gt X⁰¹A
¹235D² For X⁰¹2264²Y use ~X gt Y⁰¹A
¹235D² For X⁰¹2265²Y use ~Y gt X⁰¹A
²z⁰¹2190²0⁰¹2228².>1⁰¹2193²y Fsub x⁰¹A
"/>
</Function>
</Symbol>
<Symbol name="Fmul" stack-size="1">
<Function creation-time="1428686687648276" exec-properties="0,0,0,0">
<UCS uni="²z⁰¹2190²a Fmul b;da;db;noconv;s;sa;sb⁰¹A
¹235D² Multiply two numeric multiprecision numbers⁰¹A
²a⁰¹2190²scalar a ⁰¹25CA² b⁰¹2190²scalar b ⁰¹235D² Add leading⁰
² 0 if a scalar⁰¹A
²da⁰¹2190²a[0] ⁰¹25CA² db⁰¹2190²b[0] ⁰¹235D² Decimal pla⁰
²ces⁰¹A
²sa⁰¹2190¹D7²1⁰¹2191²a⁰¹2190²((a⁰¹2260²0)⁰¹2373²1)⁰¹2193²a⁰
¹2190²1⁰¹2193²a ⁰¹235D² Sign of A⁰¹A
²sb⁰¹2190¹D7²1⁰¹2191²b⁰¹2190²((b⁰¹2260²0)⁰¹2373²1)⁰¹2193²b⁰
¹2190²1⁰¹2193²b ⁰¹235D² Sign of B⁰¹A
¹2192²(0⁰¹2260²s⁰¹2190²sa⁰¹D7²sb)/⁰¹2206²1 ⁰¹235D² Sig⁰
²n of the result⁰¹A
²z⁰¹2190²0 0 ⁰¹25CA² ⁰¹2192²0 ⁰¹235D² Quick quit if result is ⁰
²zero⁰¹A
¹2206²1: a⁰¹2190²|a ⁰¹25CA² b⁰¹2190²|b ⁰¹235D² Make number pos⁰
²itive⁰¹A
¹2192²((⁰¹2374²b)⁰¹2265¹2374²a)/⁰¹2206²2⁰¹A
²a b⁰¹2190²b a ⁰¹235D² Prevent avoidable WS FULL⁰¹A
¹2206²2: ⁰¹2192²(noconv⁰¹2190²base=bsqr)/⁰¹2206²3⁰¹A
²a⁰¹2190²,⁰¹2349²(0,bsqr)⁰¹22A4²|a ⁰¹235D² Prevent overflow⁰¹A
²b⁰¹2190²,⁰¹2349²(0,bsqr)⁰¹22A4²|b⁰¹A
¹2206²3: z⁰¹2190²+⁰¹233F²(-1+⁰¹2373²1⁰¹2191¹2374²z)⁰¹233D²z,(2⁰
¹2374²1⁰¹2191¹2374²z⁰¹2190²a⁰¹2218².⁰¹D7²b)⁰¹2374²0 ⁰¹235D² Ra⁰
²w result⁰¹A
¹235D² Refine result by 'carrying'⁰¹A
¹2206²4: ⁰¹2192²((a⁰¹2190²(0,bsqr)⁰¹22A4²z)[0;]⁰¹2227².=0)/⁰
¹2206²5⁰¹A
²z⁰¹2190²(a[0;],0)+0,a[1;]⁰¹A
¹2192¹2206²4⁰¹A
¹2206²5: ⁰¹2192²noconv/⁰¹2206²6⁰¹A
²z⁰¹2190²((2|⁰¹2374²z)⁰¹2374²0),z ⁰¹235D² Make Z an even numbe⁰
²r of elements⁰¹A
²z⁰¹2190²(0,bsqr)⁰¹22A5¹2349²((0.5⁰¹D7¹2374²z),2)⁰¹2374²z ⁰
¹235D² Get Z back to full size⁰¹A
¹2206²6: z⁰¹2190²s⁰¹D7²((z⁰¹2260²0)⁰¹2373²1)⁰¹2193²z ⁰¹235D² D⁰
²rop leading zeroes, get sign right⁰¹A
²da⁰¹2190²da+db ⁰¹235D² Number of decimals⁰¹A
²z⁰¹2190²(-db⁰¹2190²(0⁰¹2260¹233D²z)⁰¹2373²1)⁰¹2193²z ⁰¹235D² ⁰
²Drop trailing zeroes⁰¹A
²z⁰¹2190²(da+db),z ⁰¹235D² Prepend number of decimals⁰¹A
"/>
</Function>
</Symbol>
<Symbol name="Fspow" stack-size="1">
<Function creation-time="1428687686269066" exec-properties="0,0,0,0">
<UCS uni="²z⁰¹2190²m Fspow x;i;n;q;rem⁰¹A
¹235D² This function raises multiprecision ⁰¹3C²m> to the powe⁰
²r of scalar ⁰¹3C²x>⁰¹A
¹235D² for small values of x (otherwise we get WS FULL, and ot⁰
²her rubbish)⁰¹A
¹235D² For the method see Ribenboim [1988] p.38⁰¹A
¹2192²(2⁰¹2260¹2374²,x)/⁰¹2206²1⁰¹A
¹2192²(0⁰¹2260²1⁰¹2191²x)/⁰¹2206²1⁰¹A
²x⁰¹2190²x[1] ⁰¹235D² Allow small M.P. integers⁰¹A
¹2206²1: ⁰¹2395²ES((⁰¹2227²/x⁰¹220A¹2395²AV)⁰¹2228²1⁰¹2260
¹2374²,x)/11 ⁰¹235D² Correct domain for X⁰¹A
¹2395²ES(x⁰¹2264²0)/11 ⁰¹235D² Must be strictly positive⁰¹A
²z⁰¹2190²m ⁰¹235D² Start value for result⁰¹A
¹2192²(1=⁰¹2374²n⁰¹2190²((⁰¹2308²2⁰¹235F²1+x)⁰¹2374²2)⁰¹22A4²x⁰
²)/0⁰¹A
²i⁰¹2190²1⁰¹A
¹2206²2: z⁰¹2190²z Fmul z⁰¹A
¹2192²(-n[i])/⁰¹2206²3⁰¹A
²z⁰¹2190²z Fmul m⁰¹A
¹2206²3: ⁰¹2192²((⁰¹2374²n)>i⁰¹2190²i+1)/⁰¹2206²2⁰¹A
"/>
</Function>
</Symbol>
<Symbol name="Fsqrt" stack-size="1">
<Function creation-time="1428903932159833" exec-properties="0,0,0,0">
<UCS uni="²z⁰¹2190²Fsqrt a;b;d;r⁰¹A
¹235D² Multiprecision floating point square root⁰¹A
²a⁰¹2190²scalar a ⁰¹235D² add leading zero is scalar⁰¹A
¹2395²ES(0⁰¹2227².>a)/11 ⁰¹235D² Domain error if argument is n⁰
²egative⁰¹A
¹2192²(0⁰¹2228².⁰¹2260²1⁰¹2193²a)/⁰¹2206²1 ⁰¹235D² Is source n⁰
²umber zero ?⁰¹A
²z⁰¹2190²0 0 ⁰¹25CA² ⁰¹2192²0 ⁰¹235D² Quick quit if result ⁰
²is zero⁰¹A
¹2206²1: ⁰¹2192²(~2|d⁰¹2190²a[0])/⁰¹2206²2 ⁰¹235D² Save radix ⁰
²places⁰¹A
²d⁰¹2190²d-1 ⁰¹25CA² a⁰¹2190²a,0 ⁰¹235D² No. of radix places m⁰
²ust be even⁰¹A
¹2206²2: z r⁰¹2190²Isqrt 0,1⁰¹2193²a ⁰¹235D² Integer square ro⁰
²ot⁰¹A
¹2192²(~r Fgt z)/⁰¹2206²4⁰¹A
²z⁰¹2190²z Fadd 0 1 ⁰¹235D² Round up if necessary⁰¹A
¹2206²4: z[0]+⁰¹2190¹230A²0.5⁰¹D7²d ⁰¹235D² Position radix poi⁰
²nt⁰¹A
"/>
</Function>
</Symbol>
<Symbol name="Fsub" stack-size="1">
<Function creation-time="1428904103578095" exec-properties="0,0,0,0">
<UCS uni="²z⁰¹2190²a Fsub b⁰¹A
¹235D² Multiprecision subtraction⁰¹A
²z⁰¹2190²a Fadd(1⁰¹2191²b),-1⁰¹2193²b⁰¹2190²scalar b⁰¹A
"/>
</Function>
</Symbol>
<Symbol name="GNAL" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="Gcd" stack-size="1">
<Function creation-time="1428904528053443" exec-properties="0,0,0,0">
<UCS uni="²z⁰¹2190²a Gcd b⁰¹A
¹235D² Euclid's algorithm for the gcd of 2 numbers⁰¹A
¹2192²(1⁰¹2227².=(⁰¹2374²a),⁰¹2374²b)/⁰¹2206²2 ⁰¹235D² Quick m⁰
²ethod is both scalars⁰¹A
¹234E²(b Fgt a)/'a b⁰¹2190²b a'⁰¹A
¹2206²1: ⁰¹2192²(0 1 Fequal z⁰¹2190²a Imod b)/0⁰¹A
¹234E²(0 0 Fequal z)/'z⁰¹2190²b ⁰¹25CA² ⁰¹2192²0'⁰¹A
¹234E²(0 Fgt z)/'z⁰¹2190²z Fadd b'⁰¹A
²a⁰¹2190²b ⁰¹25CA² b⁰¹2190²z ⁰¹25CA² ⁰¹2192¹2206²1⁰¹A
¹235D¹A
¹2206²2: ⁰¹234E²(b>a)/'a b⁰¹2190²b a'⁰¹A
¹2206²3: ⁰¹2192²(1=z⁰¹2190²b|a)/0⁰¹A
¹234E²(0=z)/'z⁰¹2190²b ⁰¹25CA² ⁰¹2192²0'⁰¹A
¹234E²(0>z)/'z⁰¹2190²z+b'⁰¹A
²a⁰¹2190²b ⁰¹25CA² b⁰¹2190²z ⁰¹25CA² ⁰¹2192¹2206²3⁰¹A
"/>
</Function>
</Symbol>
<Symbol name="HALF" stack-size="1">
<Variable vid="344"/>
</Symbol>
<Symbol name="ISQRT" stack-size="1">
<Function creation-time="1428918006205096" exec-properties="0,0,0,0">
<UCS uni="²z⁰¹2190²ISQRT x;⁰¹2395²IO⁰¹A
¹2395²IO⁰¹2190²0 ⁰¹25CA² z⁰¹2190²0 Ffmt⁰¹A8²Isqrt Fexec x⁰¹A
"/>
</Function>
</Symbol>
<Symbol name="Idiv" stack-size="1">
<Function creation-time="1428905390803829" exec-properties="0,0,0,0">
<UCS uni="²c⁰¹2190²a Idiv b;af;bf;j;q;qf;q1;r;r1;s;t⁰¹A
¹235D² Multiprecision integer divide with remainder⁰¹A
¹235D² Produces quotient ⁰¹26² remainder in c⁰¹A
²a⁰¹2190²scalar a ⁰¹25CA² b⁰¹2190²scalar b ⁰¹235D² Add leading⁰
² 0 if a scalar⁰¹A
¹2395²ES(0⁰¹2228².>a[0],b[0])/11 ⁰¹235D² Domain error if not⁰
² integer⁰¹A
¹2395²ES(0⁰¹2227².=1⁰¹2193²b)/11 ⁰¹235D² Domain error ⁰
²if divisor is zero⁰¹A
¹2192²(0⁰¹2228².⁰¹2260²1⁰¹2193²a)/⁰¹2206²1⁰¹A
²c⁰¹2190²(0 0)(0 0) ⁰¹25CA² ⁰¹2192²0 ⁰¹235D² Quick quit if res⁰
²ult is zero⁰¹A
¹2206²1: s⁰¹2190²1 ⁰¹AF²1[(a⁰¹2228².⁰¹3C²0)⁰¹2260²b⁰¹2228².⁰
¹3C²0] ⁰¹235D² Sign of result⁰¹A
²a⁰¹2190²fullint|a ⁰¹25CA² b⁰¹2190²fullint|b⁰¹A
¹2192²(2⁰¹2260¹2374²b)/⁰¹2206²3 ⁰¹235D² Code for speed if B is⁰
² scalar⁰¹A
¹2192²c⁰¹2190²(2⁰¹D7²(b⁰¹2190²1⁰¹2193²b)=1⁰¹2191²r⁰¹2190²0,1⁰
¹2191²a)⁰¹2374²0⁰¹A
¹2206²2: c⁰¹2190²c,q⁰¹2190¹230A²(t⁰¹2190²base⁰¹22A5²r,1⁰¹2191²a⁰
²)⁰¹F7²b⁰¹A
²r⁰¹2190²0,t-q⁰¹D7²b ⁰¹25CA² ⁰¹2192²(0⁰¹3C¹2374²a⁰¹2190²1⁰
¹2193²a)/⁰¹2206²2⁰¹A
²c⁰¹2190²c Fadd 0 ⁰¹25CA² ⁰¹2192¹2206²99 ⁰¹235D² ... and tidie⁰
²d up⁰¹A
¹235D² B is not scalar.⁰¹A
¹2206²3: r⁰¹2190²a ⁰¹25CA² c⁰¹2190²0 0 ⁰¹235D² Start by creati⁰
²ng remainder⁰¹A
²bf⁰¹2190²b[1]+b[2]⁰¹F7²base ⁰¹235D² Floating point divisor⁰¹A
¹2206²4: ⁰¹2192²(b Fgt r)/⁰¹2206²99 ⁰¹235D² If b>r then we are⁰
² done⁰¹A
¹2206²5: af⁰¹2190²r[1]⁰¹A
¹2192²(2⁰¹2265¹2374²r)/⁰¹2206²6⁰¹A
²af⁰¹2190²af+r[2]⁰¹F7²base⁰¹A
¹2206²6: q⁰¹2190¹230A²qf⁰¹2190²af⁰¹F7²bf ⁰¹25CA² j⁰¹2190²0 ⁰
¹235D² Q is the provisional quotient⁰¹A
¹2192²(1⁰¹2260²qf)/⁰¹2206²7⁰¹A
²q⁰¹2190²r Fgt(⁰¹2374²r)⁰¹2191²b ⁰¹235D² Get more accurate res⁰
²ult if =1⁰¹A
¹2206²7: ⁰¹2192²(0⁰¹2260²q)/⁰¹2206²8⁰¹A
²q⁰¹2190¹230A²qf⁰¹2190²qf⁰¹D7²base ⁰¹25CA² j⁰¹2190²1 ⁰¹235D² i⁰
²f Q=0 shift 1 place right⁰¹A
¹2206²8: r1⁰¹2190²r Fsub b Fmul q1⁰¹2190²(2+(⁰¹2374²r)-j+⁰
¹2374²b)⁰¹2191²q1⁰¹2190²0,⁰¹230A²q⁰¹A
¹2192²(~0 Fgt r1)/⁰¹2206²9⁰¹A
²q⁰¹2190²q-1 ⁰¹25CA² ⁰¹2192¹2206²8⁰¹A
¹2206²9: c⁰¹2190²c Fadd q1 ⁰¹25CA² r⁰¹2190²0,(1⁰¹2193²r1),r1[0⁰
²]⁰¹2374²0⁰¹A
¹235D² It may be that our truncation of the provisional quotie⁰
²nt has⁰¹A
¹235D² resulted in ⁰¹3C²r>=⁰¹3C²b>, so⁰¹A
¹2192²(~b Fequal r)/⁰¹2206²10⁰¹A
²r⁰¹2190²0 0 ⁰¹25CA² c⁰¹2190²c Fadd 1⁰¹A
¹2206²10: ⁰¹2192¹2206²4⁰¹A
¹2206²99: c⁰¹2190²(c⁰¹D7²1,(⁰¹AF²1+⁰¹2374²c)⁰¹2374²s)(r⁰¹D7²1,⁰
²(⁰¹AF²1+⁰¹2374²r)⁰¹2374²s)⁰¹A
"/>
</Function>
</Symbol>
<Symbol name="Imod" stack-size="1">
<Function creation-time="1428905848053167" exec-properties="0,0,0,0">
<UCS uni="²a⁰¹2190²x Imod b;b1;j;q;qf;s⁰¹A
¹235D² Multiprecision integer modulus function⁰¹A
²x⁰¹2190²scalar x ⁰¹25CA² b⁰¹2190²scalar b ⁰¹235D² Allow scala⁰
²r B⁰¹A
¹2395²ES(0⁰¹2228².>b[0],x[0])/11 ⁰¹235D² Must be integers⁰¹A
²s⁰¹2190²0 ⁰¹25CA² a⁰¹2190²x⁰¹A
¹2192²(2⁰¹3C¹2374²,b⁰¹2190²fullint b)/⁰¹2206²1⁰¹A
¹2192²(b[1]⁰¹2264²bsqr)/⁰¹2206²7⁰¹A
¹2206²1:b1⁰¹2190²b[1]+(3⁰¹2191²b)[2]⁰¹F7²base⁰¹A
¹2206²2:⁰¹2192²(~0 0 Fgt a)/⁰¹2206²3⁰¹A
²a⁰¹2190²|a ⁰¹25CA² s⁰¹2190²~s ⁰¹235D² Do everything positivel⁰
²y⁰¹A
¹2206²3:⁰¹2395²ES(a Fgt|x)/11 ⁰¹235D² Program error if this fi⁰
²res⁰¹A
¹2192²(~(a Fgt 0 ⁰¹AF²1)⁰¹2227²b Fgt a)/⁰¹2206²5⁰¹A
¹2192²(~s⁰¹2227²~a Fequal 0 0)/⁰¹2206²4⁰¹A
²a⁰¹2190²b Fsub a⁰¹A
¹2206²4:⁰¹2192²0⁰¹A
¹2206²5: q⁰¹2190¹230A²qf⁰¹2190²(a[1]+(3⁰¹2191²a)[2]⁰¹F7²base)⁰
¹F7²b1⁰¹A
²j⁰¹2190²0⁰¹A
¹2192²(0⁰¹2260²q)/⁰¹2206²6⁰¹A
²q⁰¹2190¹230A²qf⁰¹2190²qf⁰¹D7²base ⁰¹25CA² j⁰¹2190²1 ⁰¹235D² I⁰
²f Q=0 then shift 1 place right⁰¹A
¹2206²6: a⁰¹2190²a Fsub q Fmul(a[0]+(⁰¹2374²a-j)⁰¹2191²b⁰¹A
¹2192¹2206²2⁰¹A
¹235D¹A
¹2206²7:b⁰¹2190²b[1] ⁰¹25CA² x⁰¹2190²fullint x⁰¹A
²a⁰¹2190²x[1] ⁰¹25CA² x⁰¹2190²2⁰¹2193²x⁰¹A
¹2206²8: a⁰¹2190²b|a⁰¹A
¹2192²(0=⁰¹2374²x)/⁰¹2206²9⁰¹A
²a⁰¹2190²base⁰¹22A5²a,1⁰¹2191²x⁰¹A
²x⁰¹2190²1⁰¹2193²x⁰¹A
¹2192¹2206²8⁰¹A
¹2206²9: ⁰¹2192²(~s⁰¹2227²0⁰¹2260²a)/⁰¹2206²10⁰¹A
²a⁰¹2190²b-a⁰¹A
¹2206²10:a⁰¹2190²0,a⁰¹A
"/>
</Function>
</Symbol>
<Symbol name="Impow" stack-size="1">
<Function creation-time="1428918272059017" exec-properties="0,0,0,0">
<UCS uni="²z⁰¹2190²m Impow x;i;mod;n;q;r⁰¹A
¹235D² This function raises multiprecision M to the power of⁰¹A
¹235D² multiprecision X[0] and returns the residue modulo X[1]⁰¹A
¹235D² For the method see Ribenboim [1998] p.38⁰¹A
²x mod⁰¹2190²x ⁰¹235D² separate the parameters⁰¹A
²z⁰¹2190²1 ⁰¹235D² Result if power is 0⁰¹A
¹2192²(0=⁰¹2374²n⁰¹2190²binary x)/0 ⁰¹235D² Get binary version⁰
² of power⁰¹A
²z⁰¹2190²m ⁰¹235D² Start with number⁰¹A
¹2192²(1=⁰¹2374²n)/0 ⁰¹235D² Exit if power is 1⁰¹A
²i⁰¹2190²1⁰¹A
¹2206²1: z⁰¹2190²z Fmul z ⁰¹235D² Square Z⁰¹A
¹2192²(~n[i])/⁰¹2206²2 ⁰¹235D² If the next bit is set ...⁰¹A
²z⁰¹2190²z Fmul m ⁰¹235D² ... multiply by M⁰¹A
¹2206²2: z⁰¹2190²z Imod mod ⁰¹235D² Residue modulo mod⁰¹A
¹2192²((⁰¹2374²n)>i⁰¹2190²i+1)/⁰¹2206²1 ⁰¹235D² Any more bits⁰¹A
"/>
</Function>
</Symbol>
<Symbol name="Isqrt" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="MINUSONE" stack-size="1">
<Variable vid="183"/>
</Symbol>
<Symbol name="MUL" stack-size="1">
<Function creation-time="1428916783189726" exec-properties="0,0,0,0">
<UCS uni="²z⁰¹2190²a MUL b;⁰¹2395²IO⁰¹A
¹235D² Multiprecision multiply⁰¹A
¹2395²IO⁰¹2190²0 ⁰¹25CA² z⁰¹2190²0 Ffmt⁰¹2283²Fmul/Fexec⁰¹A8²a⁰
² b⁰¹A
"/>
</Function>
</Symbol>
<Symbol name="ONE" stack-size="1">
<Variable vid="184"/>
</Symbol>
<Symbol name="SUB" stack-size="1">
<Function creation-time="1428916914323898" exec-properties="0,0,0,0">
<UCS uni="²z⁰¹2190²a SUB b;⁰¹2395²IO⁰¹A
¹235D² Multiprecision subtract⁰¹A
¹2395²IO⁰¹2190²0⁰¹A
¹2192²(0⁰¹2260¹2395²NC'a')/⁰¹2206²1⁰¹A
²a⁰¹2190²0 0 ⁰¹235D² Allow monadic call, which just negates b⁰¹A
¹2206²1: z⁰¹2190²0 Ffmt⁰¹2283²Fsub/Fexec⁰¹A8²a b⁰¹A
"/>
</Function>
</Symbol>
<Symbol name="a" stack-size="3">
<unused-name/>
<Variable vid="43"/>
<Variable vid="25"/>
</Symbol>
<Symbol name="a1" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="addprec" stack-size="1">
<Function creation-time="1428684955003252" exec-properties="0,0,0,0">
<UCS uni="²z⁰¹2190²d addprec z1⁰¹A
¹235D² Add extra digits of precision to z (removing precision ⁰
²not allowed)⁰¹A
²z⁰¹2190²z1⁰¹A
¹2192²(d⁰¹2264²0)/0⁰¹A
²z⁰¹2190²(z[0]-d),(1⁰¹2193²z),d⁰¹2374²0⁰¹A
"/>
</Function>
</Symbol>
<Symbol name="af" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="b" stack-size="3">
<unused-name/>
<Variable vid="44"/>
<Variable vid="26"/>
</Symbol>
<Symbol name="b1" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="base" stack-size="1">
<Variable vid="255"/>
</Symbol>
<Symbol name="bf" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="binary" stack-size="1">
<Function creation-time="1428684955003491" exec-properties="0,0,0,0">
<UCS uni="²z⁰¹2190²binary x⁰¹A
¹235D² Convert a Multiprecision number to bits.⁰¹A
¹235D² The result of chbase must be an integer, not float, so ⁰
²be careful⁰¹A
²z⁰¹2190²(1073741824,base)chbase x⁰¹A
²z⁰¹2190²(z⁰¹2373²1)⁰¹2193²z⁰¹2190²,⁰¹2349²(30⁰¹2374²2)⁰¹22A4²z⁰
¹2190²1⁰¹2193²z,z[0]⁰¹2374²0⁰¹A
"/>
</Function>
</Symbol>
<Symbol name="bsqr" stack-size="1">
<Variable vid="247"/>
</Symbol>
<Symbol name="c" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="chbase" stack-size="1">
<Function creation-time="1428687831053096" exec-properties="0,0,0,0">
<UCS uni="²z⁰¹2190²b chbase z1;base;bsqr⁰¹A
¹235D² Change to radix b[0] from b[1]⁰¹A
²'Invalid radix specification'⁰¹2395²ES(2⁰¹2260¹2374²b)/8⁰¹A
¹2192²(=/b)/0⁰¹A
¹235D² If the new base is less than 32768 then we make base an⁰
²d bsqr the same⁰¹A
¹2192²(b[0]⁰¹2265²32768)/⁰¹2206²1⁰¹A
²bsqr⁰¹2190²base⁰¹2190¹230A²b[0]⁰¹A
¹2192¹2206²2⁰¹A
¹2206²1:'Radix not a square'⁰¹2395²ES(0⁰¹2260²1|bsqr⁰¹2190²(ba⁰
²se⁰¹2190²b[0])⁰¹22C6²0.5)/8⁰¹A
²bsqr⁰¹2190¹230A²bsqr ⁰¹235D² Make sure that ⁰¹3C²bsqr> is an ⁰
²integer⁰¹A
¹2206²2:z⁰¹2190²b[1]frombase z⁰¹A
"/>
</Function>
</Symbol>
<Symbol name="d" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="da" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="db" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="dec" stack-size="1">
<Function creation-time="1428684955004282" exec-properties="0,0,0,0">
<UCS uni="²z⁰¹2190²b dec x⁰¹A
¹235D² Similar to primitive Decode (⁰¹22A5²) except⁰¹A
¹235D² left argument represents a single number⁰¹A
¹235D² right argument is a vector of numbers⁰¹A
²z⁰¹2190²0 0⁰¹A
¹2206²1:z⁰¹2190²(⁰¹2283²x)Fadd b Fmul z⁰¹A
¹2192²(0⁰¹2260¹2374²x⁰¹2190²1⁰¹2193²x)/⁰¹2206²1⁰¹A
"/>
</Function>
</Symbol>
<Symbol name="e" stack-size="3">
<unused-name/>
<Variable vid="36"/>
<Variable vid="18"/>
</Symbol>
<Symbol name="enc" stack-size="1">
<Function creation-time="1428684955004583" exec-properties="0,0,0,0">
<UCS uni="²z⁰¹2190²b enc x⁰¹A
¹235D² Similar to primitive Encode (⁰¹22A4²) except⁰¹A
¹235D² only works on 1 multiprecision number at a time,⁰¹A
¹235D² left argument is a single number⁰¹A
¹235D² left argument is assumed to repeat as often as required⁰
².⁰¹A
²z⁰¹2190¹236C¹A
¹2206²1:⁰¹2192²(b Fgt x)/⁰¹2206²2⁰¹A
²x⁰¹2190²x Idiv b⁰¹A
²z⁰¹2190²x[1],z⁰¹A
²x⁰¹2190¹2283²x⁰¹A
¹2192¹2206²1⁰¹A
¹2206²2:z⁰¹2190²(⁰¹2282²x),z⁰¹A
"/>
</Function>
</Symbol>
<Symbol name="f" stack-size="3">
<unused-name/>
<Variable vid="31"/>
<Variable vid="13"/>
</Symbol>
<Symbol name="floor" stack-size="1">
<Function creation-time="1428684955004811" exec-properties="0,0,0,0">
<UCS uni="²z⁰¹2190²floor z1⁰¹A
²z⁰¹2190²z1⁰¹A
¹2192²(z[0]⁰¹2265²0)/0⁰¹A
²z⁰¹2190²0,1⁰¹2193²z[0]⁰¹2193²z⁰¹A
"/>
</Function>
</Symbol>
<Symbol name="frombase" stack-size="1">
<Function creation-time="1428684955005351" exec-properties="0,0,0,0">
<UCS uni="²z⁰¹2190²b frombase y;a;f;q⁰¹A
¹235D² Converts numbers in radix ⁰¹3C²b> to base ⁰¹3C²base>⁰¹A
¹235D² b is a normal integer representing the new radix⁰¹A
¹2192²(b⁰¹2260²base)/⁰¹2206²1⁰¹A
²z⁰¹2190²y ⁰¹25CA² ⁰¹2192²0 ⁰¹235D² Result is unchanged if the⁰
² base is unchanged⁰¹A
¹2206²1:z⁰¹2190²0 0 ⁰¹235D² Got to start somewhere⁰¹A
¹2192²(base⁰¹2265²b)/⁰¹2206²2⁰¹A
²b⁰¹2190²(0,base)⁰¹22A4²b⁰¹A
¹2206²2:b⁰¹2190²0,b ⁰¹235D² Old base in terms of new base⁰¹A
²f⁰¹2190²0⁰¹2308²-y[0] ⁰¹25CA² y[0]⁰¹2190²0⁰¹2308²y[0]⁰¹A
²y⁰¹2190²1⁰¹2193²fullint y⁰¹A
¹2206²4:⁰¹2192²(base⁰¹2265²q⁰¹2190²y[0])/⁰¹2206²5⁰¹A
²q⁰¹2190²,(0,base)⁰¹22A4²q⁰¹A
¹2206²5:z⁰¹2190²(0,q)Fadd b Fmul z ⁰¹235D² Next digit⁰¹A
¹2192²(0⁰¹2260¹2374²y⁰¹2190²1⁰¹2193²y)/⁰¹2206²4⁰¹A
¹2192²(f=0)/0⁰¹A
²z⁰¹2190²z Fdiv b Fspow f⁰¹A
"/>
</Function>
</Symbol>
<Symbol name="fullint" stack-size="1">
<Function creation-time="1428684955005856" exec-properties="0,0,0,0">
<UCS uni="²z⁰¹2190²fullint z1⁰¹A
¹235D² Make a full integer out of z⁰¹A
²z⁰¹2190²z1⁰¹A
¹2192²(0>1⁰¹2191²z)/0⁰¹A
²z⁰¹2190²0,(1⁰¹2193²z),(1⁰¹2191²z)⁰¹2374²0⁰¹A
"/>
</Function>
</Symbol>
<Symbol name="h" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="h1" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="i" stack-size="3">
<unused-name/>
<Variable vid="33"/>
<Variable vid="15"/>
</Symbol>
<Symbol name="j" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="k" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="m" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="mod" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="mp" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="n" stack-size="3">
<unused-name/>
<Variable vid="37"/>
<Variable vid="19"/>
</Symbol>
<Symbol name="noconv" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="p" stack-size="3">
<unused-name/>
<Variable vid="39"/>
<Variable vid="21"/>
</Symbol>
<Symbol name="p1" stack-size="3">
<unused-name/>
<Variable vid="38"/>
<Variable vid="20"/>
</Symbol>
<Symbol name="p10" stack-size="3">
<unused-name/>
<Variable vid="40"/>
<Variable vid="22"/>
</Symbol>
<Symbol name="q" stack-size="3">
<unused-name/>
<Variable vid="34"/>
<Variable vid="16"/>
</Symbol>
<Symbol name="q1" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="qf" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="r" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="r1" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="rem" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="s" stack-size="3">
<unused-name/>
<Variable vid="35"/>
<Variable vid="17"/>
</Symbol>
<Symbol name="sa" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="sb" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="scalar" stack-size="1">
<Function creation-time="1428684955006049" exec-properties="0,0,0,0">
<UCS uni="²a⁰¹2190²scalar a1⁰¹A
¹235D² Add a leading zero if a number is a scalar⁰¹A
²a⁰¹2190²a1⁰¹A
²a⁰¹2190²((1=⁰¹2374²a⁰¹2190²,a)/0),a⁰¹A
"/>
</Function>
</Symbol>
<Symbol name="t" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="x" stack-size="3">
<unused-name/>
<Variable vid="32"/>
<Variable vid="14"/>
</Symbol>
<Symbol name="x1" stack-size="3">
<unused-name/>
<Variable vid="41"/>
<Variable vid="23"/>
</Symbol>
<Symbol name="y" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="z" stack-size="3">
<unused-name/>
<unused-name/>
<unused-name/>
</Symbol>
<Symbol name="z1" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="λ" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="χ" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="∆1" stack-size="3">
<unused-name/>
<Label value="8"/>
<Label value="8"/>
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<Symbol name="∆10" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="∆2" stack-size="3">
<unused-name/>
<Label value="18"/>
<Label value="18"/>
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<Symbol name="∆3" stack-size="3">
<unused-name/>
<Label value="24"/>
<Label value="24"/>
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<Symbol name="∆4" stack-size="3">
<unused-name/>
<Label value="27"/>
<Label value="27"/>
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<Symbol name="∆5" stack-size="3">
<unused-name/>
<Label value="29"/>
<Label value="29"/>
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<Symbol name="∆6" stack-size="3">
<unused-name/>
<Label value="30"/>
<Label value="30"/>
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<Symbol name="∆7" stack-size="3">
<unused-name/>
<Label value="36"/>
<Label value="36"/>
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<Symbol name="∆8" stack-size="3">
<unused-name/>
<Label value="37"/>
<Label value="37"/>
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<Symbol name="∆9" stack-size="3">
<unused-name/>
<Label value="38"/>
<Label value="38"/>
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<Symbol name="∆99" stack-size="1">
<unused-name/>
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<Symbol name="⍙D" stack-size="1">
<Variable vid="196"/>
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<Symbol name="⍵" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="⍶" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="⍹" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="⍺" stack-size="1">
<unused-name/>
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</SymbolTable>
<Symbol name="⎕AI" stack-size="1">
<Variable vid="504"/>
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<Symbol name="⎕ARG" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="⎕AV" stack-size="1">
<Variable vid="503"/>
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<Symbol name="⎕CT" stack-size="1">
<Variable vid="195"/>
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<Symbol name="⎕EM" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="⎕ET" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="⎕FC" stack-size="1">
<Variable vid="194"/>
</Symbol>
<Symbol name="⎕IO" stack-size="3">
<Variable vid="193"/>
<Variable vid="42"/>
<Variable vid="24"/>
</Symbol>
<Symbol name="⎕L" stack-size="1">
<Variable vid="496"/>
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<Symbol name="⎕LC" stack-size="1">
<Variable vid="502"/>
</Symbol>
<Symbol name="⎕LX" stack-size="1">
<Variable vid="192"/>
</Symbol>
<Symbol name="⎕PP" stack-size="1">
<Variable vid="191"/>
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<Symbol name="⎕PR" stack-size="1">
<Variable vid="190"/>
</Symbol>
<Symbol name="⎕PS" stack-size="1">
<Variable vid="189"/>
</Symbol>
<Symbol name="⎕PW" stack-size="1">
<Variable vid="188"/>
</Symbol>
<Symbol name="⎕R" stack-size="1">
<Variable vid="495"/>
</Symbol>
<Symbol name="⎕RL" stack-size="1">
<Variable vid="187"/>
</Symbol>
<Symbol name="⎕SVE" stack-size="1">
<Variable vid="501"/>
</Symbol>
<Symbol name="⎕SYL" stack-size="1">
<Variable vid="494"/>
</Symbol>
<Symbol name="⎕TC" stack-size="1">
<Variable vid="500"/>
</Symbol>
<Symbol name="⎕TS" stack-size="1">
<Variable vid="499"/>
</Symbol>
<Symbol name="⎕TZ" stack-size="1">
<Variable vid="493"/>
</Symbol>
<Symbol name="⎕UL" stack-size="1">
<Variable vid="498"/>
</Symbol>
<Symbol name="⎕X" stack-size="1">
<Variable vid="492"/>
</Symbol>
<Symbol name="⎕WA" stack-size="1">
<Variable vid="497"/>
</Symbol>
<Symbol name="λ" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="⍺" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="⍵" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="χ" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="⍶" stack-size="1">
<unused-name/>
</Symbol>
<Symbol name="⍹" stack-size="1">
<unused-name/>
</Symbol>
<StateIndicator levels="8">
<SI-entry level="0" pc="3" line="0">
<Statements>
<UCS uni="²'34565' MUL '23423'⁰"/>
</Statements>
<Parser assign-pending="0" lookahead-high="2">
<Token pc="2" tag="53050013"/>
</Parser>
</SI-entry>
<SI-entry level="1" pc="9" line="2">
<UserFunction ufun-name="MUL" symbol-level="0"/>
<Parser assign-pending="0" lookahead-high="8">
<Token pc="7" tag="53050013"/>
</Parser>
</SI-entry>
<SI-entry level="2" pc="341" line="30">
<UserFunction ufun-name="Fexec" symbol-level="0"/>
<Parser assign-pending="0" lookahead-high="340">
<Token pc="340" tag="4107070F" vid="63"/>
<Token pc="339" tag="708" vid="29"/>
<Token pc="336" tag="54040907" fun-id="5404"/>
<Token pc="335" tag="4105070F" vid="30"/>
<Token pc="332" tag="5205020C" int="4294967337"/>
<Token pc="331" tag="52080909" fun-id="5208"/>
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