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Zeckendorf arithmetic: Difference between revisions

Zeckendorf arithmetic (view source)

Revision as of 21:33, 14 May 2021

85,298 bytes added ,  3 years ago
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→‎{{header|Phix}}: added syntax colouring the hard way
m (→‎{{header|Phix}}: added syntax colouring the hard way)
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They are however (and not all that surprisingly) pulled apart into individual bits for addition/subtraction, etc.<br>
Does not handle negative numbers or anything >139583862445 (-ve probably doable but messy, >1.4e12 requires a total rewrite, probably using string representation).
<!--<lang Phix>sequence fib = {1,1}(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
 
function zeckendorf(atom n)
-- Same as [[Zeckendorf_number_representation#Phix]]
atom r = 0
while fib[$]<n do
fib &= fib[$] + fib[$-1]
end while
integer k = length(fib)
while k>2 and n<fib[k] do
k -= 1
end while
for i=k to 2 by -1 do
integer c = n>=fib[i]
r += r+c
n -= c*fib[i]
end for
return r
end function
 
function decimal(object z)
-- Convert Zeckendorf number(s) to decimal
atom dec = 0, bit = 2
if sequence(z) then
for i=1 to length(z) do
z[i] = decimal(z[i])
end for
return z
end if
while z do
if and_bits(z,1) then
dec += fib[bit]
end if
bit += 1
if bit>length(fib) then
fib &= fib[$] + fib[$-1]
end if
z = floor(z/2)
end while
return dec
end function
 
function to_bits(integer x)
-- Simplified copy of int_to_bits(), but in reverse order,
-- and +ve only but (also only) as many bits as needed, and
-- ensures there are *two* trailing 0 (most significant)
sequence bits = {}
if x<0 then ?9/0 end if -- sanity/avoid infinite loop
while 1 do
bits &= remainder(x,2)
if x=0 then exit end if
x = floor(x/2)
end while
bits &= 0 -- (since eg 101+101 -> 10000)
return bits
end function
 
function to_bits2(integer a,b)
-- Apply to_bits() to a and b, and pad to the same length
sequence sa = to_bits(a), sb = to_bits(b)
integer diff = length(sa)-length(sb)
if diff!=0 then
if diff<0 then sa &= repeat(0,-diff)
else sb &= repeat(0,+diff)
end if
end if
return {sa,sb}
end function
 
function to_int(sequence bits)
-- Copy of bits_to_int(), but in reverse order (lsb last)
atom val = 0, p = 1
for i=length(bits) to 1 by -1 do
if bits[i] then
val += p
end if
p += p
end for
return val
end function
<span style="color: #004080;">sequence</span> <span style="color: #000000;">fib</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span>
function zstr(object z)
if sequence(z) then
<span style="color: #008080;">function</span> <span style="color: #000000;">zeckendorf</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
for i=1 to length(z) do
<span style="color: #000080;font-style:italic;">-- Same as [[Zeckendorf_number_representation#Phix]]</span>
z[i] = zstr(z[i])
<span style="color: #004080;">atom</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
end for
<span style="color: #008080;">while</span> <span style="color: #000000;">fib</span><span style="color: #0000FF;">[$]<</span><span style="color: #000000;">n</span> <span style="color: #008080;">do</span>
return z
<span style="color: #000000;">fib</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">fib</span><span style="color: #0000FF;">[$]</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">fib</span><span style="color: #0000FF;">[$-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
end if
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
return sprintf("%b",z)
<span style="color: #004080;">integer</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">fib</span><span style="color: #0000FF;">)</span>
end function
<span style="color: #008080;">while</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">></span><span style="color: #000000;">2</span> <span style="color: #008080;">and</span> <span style="color: #000000;">n</span><span style="color: #0000FF;"><</span><span style="color: #000000;">fib</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">do</span>
 
<span style="color: #000000;">k</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">1</span>
function rep(sequence res, integer ds, sequence was, wth)
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
-- helper for cleanup, validates replacements
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">k</span> <span style="color: #008080;">to</span> <span style="color: #000000;">2</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
integer de = ds+length(was)-1
<span style="color: #004080;">integer</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">>=</span><span style="color: #000000;">fib</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
if res[ds..de]!=was then ?9/0 end if
<span style="color: #000000;">r</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #000000;">c</span>
if length(was)!=length(wth) then ?9/0 end if
<span style="color: #000000;">n</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">*</span><span style="color: #000000;">fib</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
res[ds..de] = wth
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
return res
<span style="color: #008080;">return</span> <span style="color: #000000;">r</span>
end function
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
 
function zcleanup(sequence res)
<span style="color: #008080;">function</span> <span style="color: #000000;">decimal</span><span style="color: #0000FF;">(</span><span style="color: #004080;">object</span> <span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
-- (shared by zadd and zsub)
<span style="color: #000080;font-style:italic;">-- Convert Zeckendorf number(s) to decimal</span>
integer l = length(res)
<span style="color: #008080;">if</span> <span style="color: #004080;">sequence</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
-- first stage, left to right, {020x -> 100x', 030x -> 110x', 021x->110x, 012x->101x}
<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">))</span>
for i=1 to l-3 do
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
switch res[i..i+2]
<span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">decimal</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span>
case {0,2,0}: res[i..i+2] = {1,0,0} res[i+3] += 1
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
case {0,3,0}: res[i..i+2] = {1,1,0} res[i+3] += 1
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
case {0,2,1}: res[i..i+2] = {1,1,0}
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
case {0,1,2}: res[i..i+2] = {1,0,1}
<span style="color: #004080;">atom</span> <span style="color: #000000;">dec</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">bit</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">2</span>
end switch
<span style="color: #008080;">while</span> <span style="color: #000000;">z</span> <span style="color: #008080;">do</span>
end for
<span style="color: #008080;">if</span> <span style="color: #7060A8;">and_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
-- first stage cleanup
<span style="color: #000000;">dec</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">fib</span><span style="color: #0000FF;">[</span><span style="color: #000000;">bit</span><span style="color: #0000FF;">]</span>
if l>1 then
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
if res[l-1]=3 then res = rep(res,l-2,{0,3,0},{1,1,1}) -- 030 -> 111
<span style="color: #000000;">bit</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
elsif res[l-1]=2 then
<span style="color: #008080;">if</span> <span style="color: #000000;">bit</span><span style="color: #0000FF;">></span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">fib</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
if res[l-2]=0 then res = rep(res,l-2,{0,2,0},{1,0,1}) -- 020 -> 101
<span style="color: #000000;">fib</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">fib</span><span style="color: #0000FF;">[$]</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">fib</span><span style="color: #0000FF;">[$-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
else res = rep(res,l-3,{0,1,2,0},{1,0,1,0}) -- 0120 -> 1010
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
end if
<span style="color: #000000;">z</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
end if
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
end if
<span style="color: #008080;">return</span> <span style="color: #000000;">dec</span>
if res[l]=3 then res = rep(res,l-1,{0,3},{1,1}) -- 03 -> 11
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
elsif res[l]=2 then
if res[l-1]=0 then res = rep(res,l-1,{0,2},{1,0}) -- 02 -> 10
<span style="color: #008080;">function</span> <span style="color: #000000;">to_bits</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
else res = rep(res,l-2,{0,1,2},{1,0,1}) -- 012 -> 101
<span style="color: #000080;font-style:italic;">-- Simplified copy of int_to_bits(), but in reverse order,
end if
-- and +ve only but (also only) as many bits as needed, and
end if
-- ensures there are *two* trailing 0 (most significant)</span>
-- second stage, pass 1, right to left, 011 -> 100
<span style="color: #008080;">if</span> <span style="color: #000000;">x</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #000080;font-style:italic;">-- sanity/avoid infinite loop</span>
for i=length(res)-2 to 1 by -1 do
<span style="color: #004080;">sequence</span> <span style="color: #000000;">bits</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
if res[i..i+2]={0,1,1} then res[i..i+2] = {1,0,0} end if
<span style="color: #008080;">while</span> <span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
end for
<span style="color: #000000;">bits</span> <span style="color: #0000FF;">&=</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
-- second stage, pass 2, left to right, 011 -> 100
<span style="color: #008080;">if</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
for i=1 to length(res)-2 do
<span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
if res[i..i+2]={0,1,1} then res[i..i+2] = {1,0,0} end if
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
end for
<span style="color: #000000;">bits</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">0</span> <span style="color: #000080;font-style:italic;">-- (since eg 101+101 -&gt; 10000)</span>
return to_int(res)
<span style="color: #008080;">return</span> <span style="color: #000000;">bits</span>
end function
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
 
function zadd(integer a, b)
<span style="color: #008080;">function</span> <span style="color: #000000;">to_bits2</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
sequence {sa,sb} = to_bits2(a,b)
<span style="color: #000080;font-style:italic;">-- Apply to_bits() to a and b, and pad to the same length</span>
return zcleanup(reverse(sq_add(sa,sb)))
<span style="color: #004080;">sequence</span> <span style="color: #000000;">sa</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">to_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">),</span>
end function
<span style="color: #000000;">sb</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">to_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
 
<span style="color: #004080;">integer</span> <span style="color: #000000;">diff</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sa</span><span style="color: #0000FF;">)-</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sb</span><span style="color: #0000FF;">)</span>
function zinc(integer a)
<span style="color: #008080;">if</span> <span style="color: #000000;">diff</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
return zadd(a,0b1)
<span style="color: #008080;">if</span> <span style="color: #000000;">diff</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #000000;">sa</span> <span style="color: #0000FF;">&=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">diff</span><span style="color: #0000FF;">)</span>
end function
<span style="color: #008080;">else</span> <span style="color: #000000;">sb</span> <span style="color: #0000FF;">&=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,+</span><span style="color: #000000;">diff</span><span style="color: #0000FF;">)</span>
 
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
function zsub(integer a, b)
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
sequence {sa,sb} = to_bits2(a,b)
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">sa</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sb</span><span style="color: #0000FF;">}</span>
sequence res = reverse(sq_sub(sa,sb))
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
-- (/not/ combined with the first pass of the add routine!)
for i=1 to length(res)-2 do
<span style="color: #008080;">function</span> <span style="color: #000000;">to_int</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">bits</span><span style="color: #0000FF;">)</span>
switch res[i..i+2] do
<span style="color: #000080;font-style:italic;">-- Copy of bits_to_int(), but in reverse order (lsb last)</span>
case {1, 0, 0}: res[i..i+2] = {0,1,1}
<span style="color: #004080;">atom</span> <span style="color: #000000;">val</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
case {1,-1, 0}: res[i..i+2] = {0,0,1}
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">bits</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
case {1,-1, 1}: res[i..i+2] = {0,0,2}
<span style="color: #008080;">if</span> <span style="color: #000000;">bits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
case {1, 0,-1}: res[i..i+2] = {0,1,0}
<span style="color: #000000;">val</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">p</span>
case {2, 0, 0}: res[i..i+2] = {1,1,1}
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
case {2,-1, 0}: res[i..i+2] = {1,0,1}
<span style="color: #000000;">p</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">p</span>
case {2,-1, 1}: res[i..i+2] = {1,0,2}
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
case {2, 0,-1}: res[i..i+2] = {1,1,0}
<span style="color: #008080;">return</span> <span style="color: #000000;">val</span>
end switch
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
end for
-- copied from PicoLisp: {1,-1} -> {0,1} and {2,-1} -> {1,1}
<span style="color: #008080;">function</span> <span style="color: #000000;">zstr</span><span style="color: #0000FF;">(</span><span style="color: #004080;">object</span> <span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
for i=1 to length(res)-1 do
<span style="color: #008080;">if</span> <span style="color: #004080;">sequence</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
switch res[i..i+1] do
<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">))</span>
case {1,-1}: res[i..i+1] = {0,1}
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
case {2,-1}: res[i..i+1] = {1,1}
<span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">zstr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span>
end switch
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
end for
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
if find(-1,res) then ?9/0 end if -- sanity check
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
return zcleanup(res)
<span style="color: #008080;">return</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%b"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
end function
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
 
function zdec(integer a)
<span style="color: #008080;">function</span> <span style="color: #000000;">rep</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">ds</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">was</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">wth</span><span style="color: #0000FF;">)</span>
return zsub(a,0b1)
<span style="color: #000080;font-style:italic;">-- helper for cleanup, validates replacements </span>
end function
<span style="color: #004080;">integer</span> <span style="color: #000000;">de</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ds</span><span style="color: #0000FF;">+</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">was</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">1</span>
 
<span style="color: #008080;">if</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">ds</span><span style="color: #0000FF;">..</span><span style="color: #000000;">de</span><span style="color: #0000FF;">]!=</span><span style="color: #000000;">was</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
function zmul(integer a, b)
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">was</span><span style="color: #0000FF;">)!=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">wth</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
integer res = 0
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)</span>
sequence mult = {a,zadd(a,a)} -- (as per task desc)
<span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">ds</span><span style="color: #0000FF;">..</span><span style="color: #000000;">de</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">wth</span>
integer bits = 2
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
while bits<b do
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
mult = append(mult,zadd(mult[$],mult[$-1]))
bits *= 2
<span style="color: #008080;">function</span> <span style="color: #000000;">zcleanup</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">)</span>
end while
<span style="color: #000080;font-style:italic;">-- (shared by zadd and zsub)</span>
integer bit = 1
<span style="color: #004080;">integer</span> <span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)</span>
while b do
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)</span>
if and_bits(b,1) then
<span style="color: #000080;font-style:italic;">-- first stage, left to right, {020x -&gt; 100x', 030x -&gt; 110x', 021x-&gt;110x, 012x-&gt;101x}</span>
res = zadd(res,mult[bit])
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">l</span><span style="color: #0000FF;">-</span><span style="color: #000000;">3</span> <span style="color: #008080;">do</span>
end if
<span style="color: #004080;">sequence</span> <span style="color: #000000;">s3</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span>
b = floor(b/2)
<span style="color: #008080;">if</span> <span style="color: #000000;">s3</span><span style="color: #0000FF;">={</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">}</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">3</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
bit += 1
<span style="color: #008080;">elsif</span> <span style="color: #000000;">s3</span><span style="color: #0000FF;">={</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">}</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">3</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
end while
<span style="color: #008080;">elsif</span> <span style="color: #000000;">s3</span><span style="color: #0000FF;">={</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">}</span>
return res
<span style="color: #008080;">elsif</span> <span style="color: #000000;">s3</span><span style="color: #0000FF;">={</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span>
end function
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
 
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
function zdiv(integer a, b)
<span style="color: #000080;font-style:italic;">-- first stage cleanup</span>
integer res = 0
<span style="color: #008080;">if</span> <span style="color: #000000;">l</span><span style="color: #0000FF;">></span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
sequence mult = {b,zadd(b,b)}
<span style="color: #008080;">if</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">l</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]=</span><span style="color: #000000;">3</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rep</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l</span><span style="color: #0000FF;">-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">})</span> <span style="color: #000080;font-style:italic;">-- 030 -&gt; 111</span>
integer bits = 2
<span style="color: #008080;">elsif</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">l</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]=</span><span style="color: #000000;">2</span> <span style="color: #008080;">then</span>
while mult[$]<a do
<span style="color: #008080;">if</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">l</span><span style="color: #0000FF;">-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rep</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l</span><span style="color: #0000FF;">-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">})</span> <span style="color: #000080;font-style:italic;">-- 020 -&gt; 101</span>
mult = append(mult,zadd(mult[$],mult[$-1]))
<span style="color: #008080;">else</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rep</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l</span><span style="color: #0000FF;">-</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">})</span> <span style="color: #000080;font-style:italic;">-- 0120 -&gt; 1010</span>
bits *= 2
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
end while
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
for i=length(mult) to 1 by -1 do
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
integer mi = mult[i]
<span style="color: #008080;">if</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">l</span><span style="color: #0000FF;">]=</span><span style="color: #000000;">3</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rep</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">})</span> <span style="color: #000080;font-style:italic;">-- 03 -&gt; 11</span>
if mi<=a then
<span style="color: #008080;">elsif</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">l</span><span style="color: #0000FF;">]=</span><span style="color: #000000;">2</span> <span style="color: #008080;">then</span>
res = zadd(res,bits)
<span style="color: #008080;">if</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">l</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rep</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">})</span> <span style="color: #000080;font-style:italic;">-- 02 -&gt; 10</span>
a = zsub(a,mi)
<span style="color: #008080;">else</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rep</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l</span><span style="color: #0000FF;">-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">})</span> <span style="color: #000080;font-style:italic;">-- 012 -&gt; 101</span>
if a=0 then exit end if
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
end if
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
bits = floor(bits/2)
<span style="color: #000080;font-style:italic;">-- second stage, pass 1, right to left, 011 -&gt; 100</span>
end for
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
return {res,a} -- (a is the remainder)
<span style="color: #008080;">if</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]={</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
end function
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
 
<span style="color: #000080;font-style:italic;">-- second stage, pass 2, left to right, 011 -&gt; 100</span>
for i=0 to 20 do
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
integer zi = zeckendorf(i)
<span style="color: #008080;">if</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]={</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
atom d = decimal(zi)
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
printf(1,"%2d: %7b (%d)\n",{i,zi,d})
<span style="color: #008080;">return</span> <span style="color: #000000;">to_int</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)</span>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
 
procedure test(atom a, string op, atom b, object res, string expected)
<span style="color: #008080;">function</span> <span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
string zres = iff(atom(res)?zstr(res):join(zstr(res)," rem ")),
<span style="color: #004080;">sequence</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">sa</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sb</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">to_bits2</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
dres = sprintf(iff(atom(res)?"%d":"%d rem %d"),decimal(res)),
<span style="color: #008080;">return</span> <span style="color: #000000;">zcleanup</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">reverse</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sa</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sb</span><span style="color: #0000FF;">)))</span>
aka = sprintf("aka %d %s %d = %s",{decimal(a),op,decimal(b),dres}),
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
ok = iff(zres=expected?"":" *** ERROR ***!!")
printf(1,"%s %s %s = %s, %s %s\n",{zstr(a),op,zstr(b),zres,aka,ok})
<span style="color: #008080;">function</span> <span style="color: #000000;">zinc</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
end procedure
<span style="color: #008080;">return</span> <span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1</span><span style="color: #0000FF;">)</span>
 
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
test(0b0,"+",0b0,zadd(0b0,0b0),"0")
test(0b101,"+",0b101,zadd(0b101,0b101),"10000")
<span style="color: #008080;">function</span> <span style="color: #000000;">zsub</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
test(0b10100,"-",0b1000,zsub(0b10100,0b1000),"1001")
<span style="color: #004080;">sequence</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">sa</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sb</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">to_bits2</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
test(0b100100,"-",0b1000,zsub(0b100100,0b1000),"10100")
<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">reverse</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sa</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sb</span><span style="color: #0000FF;">))</span>
test(0b1001,"*",0b101,zmul(0b1001,0b101),"1000100")
<span style="color: #000080;font-style:italic;">-- (/not/ combined with the first pass of the add routine!)</span>
test(0b1000101,"/",0b101,zdiv(0b1000101,0b101),"1001 rem 1")
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
 
<span style="color: #004080;">sequence</span> <span style="color: #000000;">s3</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span>
test(0b10,"+",0b10,zadd(0b10,0b10),"101")
<span style="color: #008080;">if</span> <span style="color: #000000;">s3</span><span style="color: #0000FF;">={</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span>
test(0b101,"+",0b10,zadd(0b101,0b10),"1001")
<span style="color: #008080;">elsif</span> <span style="color: #000000;">s3</span><span style="color: #0000FF;">={</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span>
test(0b1001,"+",0b1001,zadd(0b1001,0b1001),"10101")
<span style="color: #008080;">elsif</span> <span style="color: #000000;">s3</span><span style="color: #0000FF;">={</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">}</span>
test(0b10101,"+",0b1000,zadd(0b10101,0b1000),"100101")
<span style="color: #008080;">elsif</span> <span style="color: #000000;">s3</span><span style="color: #0000FF;">={</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">}</span>
test(0b100101,"+",0b10101,zadd(0b100101,0b10101),"1010000")
<span style="color: #008080;">elsif</span> <span style="color: #000000;">s3</span><span style="color: #0000FF;">={</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span>
test(0b1000,"-",0b101,zsub(0b1000,0b101),"1")
<span style="color: #008080;">elsif</span> <span style="color: #000000;">s3</span><span style="color: #0000FF;">={</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span>
test(0b10101010,"-",0b1010101,zsub(0b10101010,0b1010101),"1000000")
<span style="color: #008080;">elsif</span> <span style="color: #000000;">s3</span><span style="color: #0000FF;">={</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">}</span>
test(0b1001,"*",0b101,zmul(0b1001,0b101),"1000100")
<span style="color: #008080;">elsif</span> <span style="color: #000000;">s3</span><span style="color: #0000FF;">={</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">}</span>
test(0b101010,"+",0b101,zadd(0b101010,0b101),"1000100")
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
 
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
test(0b10100,"+",0b1010,zadd(0b10100,0b1010),"101000")
<span style="color: #000080;font-style:italic;">-- copied from PicoLisp: {1,-1} -&gt; {0,1} and {2,-1} -&gt; {1,1}</span>
test(0b101000,"-",0b1010,zsub(0b101000,0b1010),"10100")
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
 
<span style="color: #004080;">sequence</span> <span style="color: #000000;">s2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
test(0b100010,"*",0b100101,zmul(0b100010,0b100101),"100001000001")
<span style="color: #008080;">if</span> <span style="color: #000000;">s2</span><span style="color: #0000FF;">={</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span>
test(0b100001000001,"/",0b100,zdiv(0b100001000001,0b100),"101010001 rem 0")
<span style="color: #008080;">elsif</span> <span style="color: #000000;">s2</span><span style="color: #0000FF;">={</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span>
test(0b101000101,"*",0b101001,zmul(0b101000101,0b101001),"101010000010101")
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
test(0b101010000010101,"/",0b100,zdiv(0b101010000010101,0b100),"1001010001001 rem 10")
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
 
<span style="color: #008080;">if</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #000080;font-style:italic;">-- sanity check</span>
test(0b10100010010100,"+",0b1001000001,zadd(0b10100010010100,0b1001000001),"100000000010101")
<span style="color: #008080;">return</span> <span style="color: #000000;">zcleanup</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)</span>
test(0b10100010010100,"-",0b1001000001,zsub(0b10100010010100,0b1001000001),"10010001000010")
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
test(0b10000,"*",0b1001000001,zmul(0b10000,0b1001000001),"10100010010100")
test(0b1010001010000001001,"/",0b100000000100000,zdiv(0b1010001010000001001,0b100000000100000),"10001 rem 10100001010101")
<span style="color: #008080;">function</span> <span style="color: #000000;">zdec</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
 
<span style="color: #008080;">return</span> <span style="color: #000000;">zsub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1</span><span style="color: #0000FF;">)</span>
test(0b10100,"+",0b1010,zadd(0b10100,0b1010),"101000")
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
test(0b10100,"-",0b1010,zsub(0b10100,0b1010),"101")
test(0b10100,"*",0b1010,zmul(0b10100,0b1010),"101000001")
<span style="color: #008080;">function</span> <span style="color: #000000;">zmul</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
test(0b10100,"/",0b1010,zdiv(0b10100,0b1010),"1 rem 101")
<span style="color: #004080;">sequence</span> <span style="color: #000000;">mult</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">a</span><span style="color: #0000FF;">)}</span> <span style="color: #000080;font-style:italic;">-- (as per task desc)</span>
integer m = zmul(0b10100,0b1010)
<span style="color: #004080;">integer</span> <span style="color: #000000;">bits</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">2</span>
test(m,"/",0b1010,zdiv(m,0b1010),"10100 rem 0")</lang>
<span style="color: #008080;">while</span> <span style="color: #000000;">bits</span><span style="color: #0000FF;"><</span><span style="color: #000000;">b</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">mult</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mult</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mult</span><span style="color: #0000FF;">[$],</span><span style="color: #000000;">mult</span><span style="color: #0000FF;">[$-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]))</span>
<span style="color: #000000;">bits</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">2</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">bit</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">while</span> <span style="color: #000000;">b</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">and_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">mult</span><span style="color: #0000FF;">[</span><span style="color: #000000;">bit</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">b</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">bit</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">zdiv</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">mult</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">b</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)}</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">bits</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">2</span>
<span style="color: #008080;">while</span> <span style="color: #000000;">mult</span><span style="color: #0000FF;">[$]<</span><span style="color: #000000;">a</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">mult</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mult</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mult</span><span style="color: #0000FF;">[$],</span><span style="color: #000000;">mult</span><span style="color: #0000FF;">[$-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]))</span>
<span style="color: #000000;">bits</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">2</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mult</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">mi</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">mult</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">mi</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">a</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">bits</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">zsub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">mi</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">bits</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">bits</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">a</span><span style="color: #0000FF;">}</span> <span style="color: #000080;font-style:italic;">-- (a is the remainder)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">20</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">zi</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">zeckendorf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">decimal</span><span style="color: #0000FF;">(</span><span style="color: #000000;">zi</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%2d: %7b (%d)\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zi</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">string</span> <span style="color: #000000;">op</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">object</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">string</span> <span style="color: #000000;">expected</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">zres</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)?</span><span style="color: #000000;">zstr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">):</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">zstr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">),</span><span style="color: #008000;">" rem "</span><span style="color: #0000FF;">)),</span>
<span style="color: #000000;">dres</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)?</span><span style="color: #008000;">"%d"</span><span style="color: #0000FF;">:</span><span style="color: #008000;">"%d rem %d"</span><span style="color: #0000FF;">),</span><span style="color: #000000;">decimal</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)),</span>
<span style="color: #000000;">aka</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"aka %d %s %d = %s"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">decimal</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">),</span><span style="color: #000000;">op</span><span style="color: #0000FF;">,</span><span style="color: #000000;">decimal</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">),</span><span style="color: #000000;">dres</span><span style="color: #0000FF;">}),</span>
<span style="color: #000000;">ok</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">zres</span><span style="color: #0000FF;">=</span><span style="color: #000000;">expected</span><span style="color: #0000FF;">?</span><span style="color: #008000;">""</span><span style="color: #0000FF;">:</span><span style="color: #008000;">" *** ERROR ***!!"</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%s %s %s = %s, %s %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">zstr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">),</span><span style="color: #000000;">op</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zstr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">),</span><span style="color: #000000;">zres</span><span style="color: #0000FF;">,</span><span style="color: #000000;">aka</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ok</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b0</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"+"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b0</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"0"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b101</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"+"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b101</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b101</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b101</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"10000"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10100</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"-"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zsub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1000</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"1001"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b100100</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"-"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zsub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b100100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1000</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"10100"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b1001</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"*"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b101</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zmul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b1001</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b101</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"1000100"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b1000101</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"/"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b101</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zdiv</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b1000101</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b101</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"1001 rem 1"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"+"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b10</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"101"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b101</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"+"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b101</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b10</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"1001"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b1001</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"+"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1001</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b1001</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1001</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"10101"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10101</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"+"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10101</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1000</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"100101"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b100101</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"+"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b10101</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b100101</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b10101</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"1010000"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b1000</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"-"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b101</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zsub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b1000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b101</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"1"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10101010</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"-"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1010101</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zsub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10101010</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1010101</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"1000000"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b1001</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"*"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b101</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zmul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b1001</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b101</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"1000100"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b101010</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"+"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b101</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b101010</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b101</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"1000100"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10100</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"+"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1010</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1010</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"101000"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b101000</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"-"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1010</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zsub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b101000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1010</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"10100"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b100010</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"*"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b100101</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zmul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b100010</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b100101</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"100001000001"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b100001000001</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"/"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zdiv</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b100001000001</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b100</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"101010001 rem 0"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b101000101</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"*"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b101001</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zmul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b101000101</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b101001</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"101010000010101"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b101010000010101</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"/"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zdiv</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b101010000010101</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b100</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"1001010001001 rem 10"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10100010010100</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"+"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1001000001</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10100010010100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1001000001</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"100000000010101"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10100010010100</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"-"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1001000001</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zsub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10100010010100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1001000001</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"10010001000010"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10000</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"*"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1001000001</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zmul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1001000001</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"10100010010100"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b1010001010000001001</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"/"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b100000000100000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zdiv</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b1010001010000001001</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b100000000100000</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"10001 rem 10100001010101"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10100</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"+"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1010</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1010</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"101000"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10100</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"-"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1010</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zsub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1010</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"101"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10100</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"*"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1010</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zmul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1010</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"101000001"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10100</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"/"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1010</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zdiv</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1010</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"1 rem 101"</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">m</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">zmul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1010</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">m</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"/"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1010</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zdiv</span><span style="color: #0000FF;">(</span><span style="color: #000000;">m</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1010</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"10100 rem 0"</span><span style="color: #0000FF;">)</span>
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<pre>
Petelomax
7,805

edits

Retrieved from "https://rosettacode.org/wiki/Special:MobileDiff/221100"
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