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Long multiplication: Difference between revisions

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Long multiplication (view source)

Revision as of 03:01, 6 June 2021

19,361 bytes added ,  2 years ago
m
→‎{{header|Phix}}: added syntax colouring the hard way
m (→‎{{header|Phix}}: added syntax colouring the hard way)
Line 4,170:
If bcd1 is a number split into digits 0..9, bcd9 is a number split into "digits" 000,000,000..999,999,999, which fit in an integer.<br>
They are held lsb-style mainly so that trimming a trailing 0 does not alter their value.
<!--<lang Phix>constant base = 1_000_000_000(phixonline)-->
<span style="color: #008080;">constant</span> <span style="color: #000000;">base</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1_000_000_000</span>
function bcd9_mult(sequence a, sequence b)
<span style="color: #008080;">function</span> <span style="color: #000000;">bcd9_mult</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
 
sequence c = repeat(0,length(a)+length(b))
<span style="color: #004080;">sequence</span> <span style="color: #000000;">c</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;">a</span><span style="color: #0000FF;">)+</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">))</span>
for i=1 to length(a) 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;">a</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
integer j = i+length(b)-1
<span style="color: #004080;">integer</span> <span style="color: #000000;">j</span> <span style="color: #0000FF;">=</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;">b</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">1</span>
c[i..j] = sq_add(c[i..j],sq_mul(a[i],b))
<span style="color: #000000;">c</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sq_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">c</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">j</span><span style="color: #0000FF;">],</span><span style="color: #7060A8;">sq_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span><span style="color: #000000;">b</span><span style="color: #0000FF;">))</span>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
for i=1 to length(c) 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;">c</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
atom ci = c[i]
<span style="color: #004080;">atom</span> <span style="color: #000000;">ci</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
if ci>base then
<span style="color: #008080;">if</span> <span style="color: #000000;">ci</span><span style="color: #0000FF;">></span><span style="color: #000000;">base</span> <span style="color: #008080;">then</span>
c[i+1] += floor(ci/base) -- carry
<span style="color: #000000;">c</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: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ci</span><span style="color: #0000FF;">/</span><span style="color: #000000;">base</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- carry</span>
c[i] = remainder(ci,base)
<span style="color: #000000;">c</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: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ci</span><span style="color: #0000FF;">,</span><span style="color: #000000;">base</span><span style="color: #0000FF;">)</span>
end if
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
if c[$]=0 then
<span style="color: #008080;">if</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">[$]=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
c = c[1..$-1]
<span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..$-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
end if
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
return c
<span style="color: #008080;">return</span> <span style="color: #000000;">c</span>
end function
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
function atom_to_bcd9(atom a)
<span style="color: #008080;">function</span> <span style="color: #000000;">atom_to_bcd9</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
sequence s = {}
<span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
while a>0 do
<span style="color: #008080;">while</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">></span><span style="color: #000000;">0</span> <span style="color: #008080;">do</span>
s = append(s,remainder(a,base))
<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">base</span><span style="color: #0000FF;">))</span>
a = floor(a/base)
<span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">/</span><span style="color: #000000;">base</span><span style="color: #0000FF;">)</span>
end while
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
return s
<span style="color: #008080;">return</span> <span style="color: #000000;">s</span>
end function
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
 
function bcd9_to_str(sequence a)
<span style="color: #008080;">function</span> <span style="color: #000000;">bcd9_to_str</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
string s = sprintf("%d",a[$])
<span style="color: #004080;">string</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%d"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[$])</span>
for i=length(a)-1 to 1 by -1 do
<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;">a</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">1</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>
s &= sprintf("%09d",a[i])
<span style="color: #000000;">s</span> <span style="color: #0000FF;">&=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%09d"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
-- (might want to trim leading 0s here)
<span style="color: #000080;font-style:italic;">-- (might want to trim leading 0s here)</span>
return s
<span style="color: #008080;">return</span> <span style="color: #000000;">s</span>
end function
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
sequence a, b, c
<span style="color: #004080;">sequence</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: #000000;">c</span>
a = atom_to_bcd9(power(2,32))
<span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">atom_to_bcd9</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">32</span><span style="color: #0000FF;">))</span>
printf(1,"a is %s\n",{bcd9_to_str(a)})
<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;">"a is %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">bcd9_to_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">)})</span>
b = bcd9_mult(a,a)
<span style="color: #000000;">b</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">bcd9_mult</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>
printf(1,"a*a is %s\n",{bcd9_to_str(b)})
<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;">"a*a is %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">bcd9_to_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)})</span>
c = bcd9_mult(b,b)
<span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">bcd9_mult</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>
printf(1,"a*a*a*a is %s\n",{bcd9_to_str(c)})</lang>
<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;">"a*a*a*a is %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">bcd9_to_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">c</span><span style="color: #0000FF;">)})</span>
<!--</lang>-->
{{out}}
<pre>
Line 4,230 ⟶ 4,232:
 
=== string ===
<!--<lang Phix>function mul(string a, bphixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
bool bSign = false
<span style="color: #008080;">function</span> <span style="color: #000000;">mul</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
if a[1]='-' then {bSign,a} = {not bSign, a[2..$]} end if
<span style="color: #004080;">bool</span> <span style="color: #000000;">bSign</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">false</span>
if b[1]='-' then {bSign,b} = {not bSign, b[2..$]} end if
<span style="color: #008080;">if</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">'-'</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">bSign</span><span style="color: #0000FF;">,</span><span style="color: #000000;">a</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #008080;">not</span> <span style="color: #000000;">bSign</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">..$]}</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
string res = repeat('0',length(a)+length(b))
<span style="color: #008080;">if</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">'-'</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">bSign</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #008080;">not</span> <span style="color: #000000;">bSign</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">..$]}</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
--
<span style="color: #004080;">string</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: #008000;">'0'</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">)+</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">))</span>
-- Note that i,j,k are used as negative indexes, working
<span style="color: #000080;font-style:italic;">--
-- from the right hand least significant digit leftwards.
-- Note that i,j,k are used as negative indexes, working
--
-- from the right hand least significant digit leftwards.
for i=1 to length(a) do
--</span>
integer j=1, k=i, c=0
<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;">a</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
while j<=length(b) or c do
<span style="color: #004080;">integer</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span>
c += res[-k]-'0'
<span style="color: #008080;">while</span> <span style="color: #000000;">j</span><span style="color: #0000FF;"><=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">or</span> <span style="color: #000000;">c</span> <span style="color: #008080;">do</span>
if j<=length(b) then
<span style="color: #000000;">c</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[-</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]-</span><span style="color: #008000;">'0'</span>
c += (a[-i]-'0')*(b[-j]-'0')
<span style="color: #008080;">if</span> <span style="color: #000000;">j</span><span style="color: #0000FF;"><=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
j += 1
<span style="color: #000000;">c</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;">i</span><span style="color: #0000FF;">]-</span><span style="color: #008000;">'0'</span><span style="color: #0000FF;">)*(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">[-</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]-</span><span style="color: #008000;">'0'</span><span style="color: #0000FF;">)</span>
end if
<span style="color: #000000;">j</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
res[-k] = remainder(c,10)+'0'
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
c = floor(c/10)
<span style="color: #000000;">res</span><span style="color: #0000FF;">[-</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)+</span><span style="color: #008000;">'0'</span>
k += 1
<span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">c</span><span style="color: #0000FF;">/</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)</span>
end while
<span style="color: #000000;">k</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
res = trim_head(res,"0")
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
if bSign then res = '-'&res end if
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">trim_head</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"0"</span><span style="color: #0000FF;">)</span>
return res
<span style="color: #008080;">if</span> <span style="color: #000000;">bSign</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">'-'</span><span style="color: #0000FF;">&</span><span style="color: #000000;">res</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
end function
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
?mul("18446744073709551616","18446744073709551616")</lang>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #0000FF;">?</span><span style="color: #000000;">mul</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"18446744073709551616"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"18446744073709551616"</span><span style="color: #0000FF;">)</span>
<!--</lang>-->
{{out}}
<pre>
Line 4,264 ⟶ 4,269:
=== builtin ===
(same output as immediately above)
<!--<lang Phix>include mpfr.e(phixonline)-->
<span style="color: #008080;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
mpz a = mpz_init("18446744073709551616") -- or:
<span style="color: #004080;">mpz</span> <span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"18446744073709551616"</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- or:
--mpz a = mpz_init(); mpz_ui_pow_ui(a,2,64)
--mpz a = mpz_init(); mpz_ui_pow_ui(a,2,64)</span>
mpz_mul(a,a,a)
<span style="color: #7060A8;">mpz_mul</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: #000000;">a</span><span style="color: #0000FF;">)</span>
?mpz_get_str(a)</lang>
<span style="color: #0000FF;">?</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
<!--</lang>-->
 
=={{header|PHP}}==
Petelomax
7,794

edits

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