Long multiplication: Difference between revisions
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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> |
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> |
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They are held lsb-style mainly so that trimming a trailing 0 does not alter their value. |
They are held lsb-style mainly so that trimming a trailing 0 does not alter their value. |
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<lang Phix> |
<!--<lang Phix>(phixonline)--> |
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<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> |
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function bcd9_mult(sequence a, sequence b) |
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<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> |
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sequence c = repeat(0,length(a)+length(b)) |
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<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> |
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for i=1 to length(a) do |
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<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> |
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integer j = i+length(b)-1 |
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<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> |
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c[i..j] = sq_add(c[i..j],sq_mul(a[i],b)) |
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<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> |
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end for |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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for i=1 to length(c) do |
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<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> |
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atom ci = c[i] |
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<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> |
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if ci>base then |
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<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> |
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c[i+1] += floor(ci/base) -- carry |
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<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> |
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c[i] = remainder(ci,base) |
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<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> |
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end if |
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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end for |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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if c[$]=0 then |
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<span style="color: #008080;">if</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">[$]=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> |
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c = c[1..$-1] |
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<span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..$-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> |
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end if |
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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return c |
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<span style="color: #008080;">return</span> <span style="color: #000000;">c</span> |
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end function |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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function atom_to_bcd9(atom a) |
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<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> |
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sequence s = {} |
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span> |
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while a>0 do |
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<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> |
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s = append(s,remainder(a,base)) |
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<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> |
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a = floor(a/base) |
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<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> |
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end while |
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<span style="color: #008080;">end</span> <span style="color: #008080;">while</span> |
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return s |
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<span style="color: #008080;">return</span> <span style="color: #000000;">s</span> |
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end function |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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function bcd9_to_str(sequence a) |
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<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> |
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string s = sprintf("%d",a[$]) |
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<span style="color: #004080;">string</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%d"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[$])</span> |
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for i=length(a)-1 to 1 by -1 do |
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<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> |
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s &= sprintf("%09d",a[i]) |
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<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> |
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end for |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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-- (might want to trim leading 0s here) |
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<span style="color: #000080;font-style:italic;">-- (might want to trim leading 0s here)</span> |
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return s |
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<span style="color: #008080;">return</span> <span style="color: #000000;">s</span> |
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end function |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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sequence a, b, c |
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<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> |
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a = atom_to_bcd9(power(2,32)) |
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<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> |
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printf(1,"a is %s\n",{bcd9_to_str(a)}) |
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<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> |
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b = bcd9_mult(a,a) |
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<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> |
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printf(1,"a*a is %s\n",{bcd9_to_str(b)}) |
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<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> |
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c = bcd9_mult(b,b) |
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<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> |
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printf(1,"a*a*a*a is %s\n",{bcd9_to_str(c)})</lang> |
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<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> |
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<!--</lang>--> |
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{{out}} |
{{out}} |
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<pre> |
<pre> |
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=== string === |
=== string === |
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<lang Phix> |
<!--<lang Phix>(phixonline)--> |
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<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span> |
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bool bSign = false |
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<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> |
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if a[1]='-' then {bSign,a} = {not bSign, a[2..$]} end if |
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<span style="color: #004080;">bool</span> <span style="color: #000000;">bSign</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">false</span> |
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if b[1]='-' then {bSign,b} = {not bSign, b[2..$]} end if |
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<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;">..$]}</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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string res = repeat('0',length(a)+length(b)) |
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<span style="color: #008080;">if</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">'-'</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">bSign</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #008080;">not</span> <span style="color: #000000;">bSign</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">..$]}</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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-- |
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<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> |
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-- Note that i,j,k are used as negative indexes, working |
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<span style="color: #000080;font-style:italic;">-- |
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-- from the right hand least significant digit leftwards. |
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-- Note that i,j,k are used as negative indexes, working |
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-- |
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-- from the right hand least significant digit leftwards. |
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for i=1 to length(a) do |
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--</span> |
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integer j=1, k=i, c=0 |
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<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> |
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while j<=length(b) or c do |
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<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> |
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c += res[-k]-'0' |
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<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> |
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if j<=length(b) then |
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<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> |
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c += (a[-i]-'0')*(b[-j]-'0') |
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<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> |
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j += 1 |
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<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> |
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end if |
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<span style="color: #000000;">j</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span> |
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res[-k] = remainder(c,10)+'0' |
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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c = floor(c/10) |
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<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> |
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k += 1 |
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<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> |
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end while |
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<span style="color: #000000;">k</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span> |
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end for |
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<span style="color: #008080;">end</span> <span style="color: #008080;">while</span> |
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res = trim_head(res,"0") |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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if bSign then res = '-'&res end if |
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<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> |
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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> |
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<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}} |
{{out}} |
||
<pre> |
<pre> |
||
Line 4,264: | Line 4,269: | ||
=== builtin === |
=== builtin === |
||
(same output as immediately above) |
(same output as immediately above) |
||
<lang Phix> |
<!--<lang Phix>(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}}== |
=={{header|PHP}}== |