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Square root by hand: Difference between revisions

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Square root by hand (view source)

Revision as of 18:42, 23 June 2021

26,672 bytes added ,  2 years ago
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→‎{{header|Phix}}: added syntax colouring the hard way
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m (→‎{{header|Phix}}: added syntax colouring the hard way)
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Based on https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Decimal_(base_10)<br>
The use of string inputs helps guarantee perfect accuracy.
<!--<lang Phix>requires("0.8.2"phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
function bcd(string a, b, op)
<span style="color: #7060A8;">requires</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"0.8.2"</span><span style="color: #0000FF;">)</span>
-- first, take care of different lengths
<span style="color: #008080;">function</span> <span style="color: #000000;">bcd</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> <span style="color: #000000;">op</span><span style="color: #0000FF;">)</span>
integer c = 0, d = length(a)-length(b)
<span style="color: #000080;font-style:italic;">-- first, take care of different lengths</span>
if d<0 then a = repeat('0',-d)&a
<span style="color: #004080;">integer</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">d</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>
elsif d>0 then b = repeat('0', d)&b end if
<span style="color: #008080;">if</span> <span style="color: #000000;">d</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #000000;">a</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: #000000;">d</span><span style="color: #0000FF;">)&</span><span style="color: #000000;">a</span>
if op="le" then
<span style="color: #008080;">elsif</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">></span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #000000;">b</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: #000000;">d</span><span style="color: #0000FF;">)&</span><span style="color: #000000;">b</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
return a<=b
<span style="color: #008080;">if</span> <span style="color: #000000;">op</span><span style="color: #0000FF;">=</span><span style="color: #008000;">"le"</span> <span style="color: #008080;">then</span>
elsif op="sub" then
<span style="color: #008080;">return</span> <span style="color: #000000;">a</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">b</span>
-- return "a"-"b" (as a string)
<span style="color: #008080;">elsif</span> <span style="color: #000000;">op</span><span style="color: #0000FF;">=</span><span style="color: #008000;">"sub"</span> <span style="color: #008080;">then</span>
-- (assumes a>=b, which it always will be here,
<span style="color: #000080;font-style:italic;">-- return "a"-"b" (as a string)
--- protected as it is by a bcd(b,a,"le") call.)
for i=length-- (assumes a)&gt;=b, towhich 1it byalways -1will be dohere,
--- protected as dit =is by a[i]- bcd(b[i]-c,a,"le") call.)</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;">a</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>
c = d<0
<span style="color: #000000;">d</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><span style="color: #000000;">i</span><span style="color: #0000FF;">]-</span><span style="color: #000000;">c</span>
a[i] = d+c*10+'0'
<span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">d</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0</span>
end for
<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: #0000FF;">=</span> <span style="color: #000000;">d</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>
a = trim_head(a,"0") -- (note: "" equ "0")
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
return a
<span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">trim_head</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"0"</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (note: "" equ "0")</span>
end if
<span style="color: #008080;">return</span> <span style="color: #000000;">a</span>
return 9/0 -- unknown op
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
end function
<span style="color: #008080;">return</span> <span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #000080;font-style:italic;">-- unknown op</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
function bcd_xp20x(string p, integer x)
-- returns x*(p*20+x)
<span style="color: #008080;">function</span> <span style="color: #000000;">bcd_xp20x</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
integer c = 0, d, m = 1
<span style="color: #000080;font-style:italic;">-- returns x*(p*20+x)</span>
p &= x+'0'
<span style="color: #004080;">integer</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">m</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
for i=length(p) to 1 by -1 do
<span style="color: #000000;">p</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">+</span><span style="color: #008000;">'0'</span>
d = (p[i]-'0')*m*x+c
<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;">p</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>
p[i] = remainder(d,10)+'0'
<span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">p</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;">m</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x</span><span style="color: #0000FF;">+</span><span style="color: #000000;">c</span>
c = floor(d/10)
<span style="color: #000000;">p</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;">d</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)+</span><span style="color: #008000;">'0'</span>
m = 2
<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;">d</span><span style="color: #0000FF;">/</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)</span>
end for
<span style="color: #000000;">m</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">2</span>
if c then
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
p = (remainder(c,10)+'0')&p
<span style="color: #008080;">if</span> <span style="color: #000000;">c</span> <span style="color: #008080;">then</span>
c = floor(c/10)
<span style="color: #000000;">p</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><span style="color: #0000FF;">)&</span><span style="color: #000000;">p</span>
if c then ?9/0 end if -- loop rqd?
<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 if
<span style="color: #008080;">if</span> <span style="color: #000000;">c</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;">-- loop rqd?</span>
return p
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
end function
<span style="color: #008080;">return</span> <span style="color: #000000;">p</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
function spigot_sqrt(string s, integer maxlen=50)
-- returns the square root of a positive string number to any precision
<span style="color: #008080;">function</span> <span style="color: #000000;">spigot_sqrt</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">maxlen</span><span style="color: #0000FF;">=</span><span style="color: #000000;">50</span><span style="color: #0000FF;">)</span>
if find('-',s) or s="" then ?9/0 end if
<span style="color: #000080;font-style:italic;">-- returns the square root of a positive string number to any precision</span>
integer dot = find('.',s)
<span style="color: #008080;">if</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #008000;">'-'</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">or</span> <span style="color: #000000;">s</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;">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>
if dot=0 then dot = length(s)+1 end if
<span style="color: #004080;">integer</span> <span style="color: #000000;">dot</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #008000;">'.'</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
if remainder(dot,2)=0 then s = "0"&s end if
<span style="color: #008080;">if</span> <span style="color: #000000;">dot</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #000000;">dot</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">1</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
dot += 1
<span style="color: #008080;">if</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dot</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;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"0"</span><span style="color: #0000FF;">&</span><span style="color: #000000;">s</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
string res = "", p = "", c = ""
<span style="color: #000000;">dot</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
integer i = 1
<span style="color: #004080;">string</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;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span>
while true do -- (until (i>length && carry=0) or > maxlen)
<span style="color: #004080;">integer</span> <span style="color: #000000;">i</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
if (i<=length(s) and s[i]='.')
<span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span> <span style="color: #000080;font-style:italic;">-- (until (i&gt;length && carry=0) or &gt; maxlen)</span>
or (i >length(s) and dot) then
<span style="color: #008080;">if</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;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">and</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">'.'</span><span style="color: #0000FF;">)</span>
res &= "."
<span style="color: #008080;">or</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;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">and</span> <span style="color: #000000;">dot</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
dot = 0
<span style="color: #000000;">res</span> <span style="color: #0000FF;">&=</span> <span style="color: #008000;">"."</span>
i += 1
<span style="color: #000000;">dot</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
end if
<span style="color: #000000;">i</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
c &= iff(i<=length(s)?s[i]:'0') &
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
iff(i<length(s)?s[i+1]:'0')
<span style="color: #000000;">c</span> <span style="color: #0000FF;">&=</span> <span style="color: #008080;">iff</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;">s</span><span style="color: #0000FF;">)?</span><span style="color: #000000;">s</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: #0000FF;">&</span>
for x=9 to 0 by -1 do
<span style="color: #008080;">iff</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;">s</span><span style="color: #0000FF;">)?</span><span style="color: #000000;">s</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: #008000;">'0'</span><span style="color: #0000FF;">)</span>
string y = bcd_xp20x(p,x)
<span style="color: #008080;">for</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">=</span><span style="color: #000000;">9</span> <span style="color: #008080;">to</span> <span style="color: #000000;">0</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
if bcd(y,c,"le") then
<span style="color: #004080;">string</span> <span style="color: #000000;">y</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">bcd_xp20x</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
c = bcd(c,y,"sub")
<span style="color: #008080;">if</span> <span style="color: #000000;">bcd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">y</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"le"</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
res &= x+'0'
<span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">bcd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,</span><span style="color: #000000;">y</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"sub"</span><span style="color: #0000FF;">)</span>
p &= x+'0'
<span style="color: #000000;">res</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">+</span><span style="color: #008000;">'0'</span>
exit
<span style="color: #000000;">p</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">+</span><span style="color: #008000;">'0'</span>
end if
if x=0 then ?9/0 end if<span --style="color: (sanity check)#008080;">exit</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
end for
<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 check)</span>
i += 2
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
if (c="" and i>length(s)) or length(res)>maxlen then exit end if
<span style="color: #000000;">i</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">2</span>
end while
<span style="color: #008080;">if</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">c</span><span style="color: #0000FF;">=</span><span style="color: #008000;">""</span> <span style="color: #008080;">and</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;">s</span><span style="color: #0000FF;">))</span> <span style="color: #008080;">or</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;">maxlen</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>
return res
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
end function
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
procedure spigot_test(string s, integer maxlen=50)
constant fmt = "Square root%s of %s:%s %s\n"
<span style="color: #008080;">procedure</span> <span style="color: #000000;">spigot_test</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">maxlen</span><span style="color: #0000FF;">=</span><span style="color: #000000;">50</span><span style="color: #0000FF;">)</span>
string res = spigot_sqrt(s, maxlen), fnd = "", lf = ""
<span style="color: #008080;">constant</span> <span style="color: #000000;">fmt</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"Square root%s of %s:%s %s\n"</span>
if length(res)>=maxlen then
<span style="color: #004080;">string</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">spigot_sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">maxlen</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">fnd</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">lf</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span>
fnd = sprintf(" (first %d digits)",maxlen)
<span style="color: #008080;">if</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;">maxlen</span> <span style="color: #008080;">then</span>
lf = "\n "
<span style="color: #000000;">fnd</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">" (first %d digits)"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">maxlen</span><span style="color: #0000FF;">)</span>
res = trim_tail(join_by(res,1,100,"","\n "))
<span style="color: #000000;">lf</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"\n "</span>
end if
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">trim_tail</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">join_by</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: #0000FF;">,</span><span style="color: #000000;">100</span><span style="color: #0000FF;">,</span><span style="color: #008000;">""</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n "</span><span style="color: #0000FF;">))</span>
printf(1,fmt,{fnd,s,lf,res})
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
end procedure
<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: #000000;">fmt</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">fnd</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">lf</span><span style="color: #0000FF;">,</span><span style="color: #000000;">res</span><span style="color: #0000FF;">})</span>
 
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
constant tests = {"152.2756","15241.383936",{"0.2",80},"10.89","625",
"0","0.0001","0.00000009",{"20000",99},{"2",500}}
<span style="color: #008080;">constant</span> <span style="color: #000000;">tests</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #008000;">"152.2756"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"15241.383936"</span><span style="color: #0000FF;">,{</span><span style="color: #008000;">"0.2"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">80</span><span style="color: #0000FF;">},</span><span style="color: #008000;">"10.89"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"625"</span><span style="color: #0000FF;">,</span>
papply(false,spigot_test,tests)</lang>
<span style="color: #008000;">"0"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"0.0001"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"0.00000009"</span><span style="color: #0000FF;">,{</span><span style="color: #008000;">"20000"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">99</span><span style="color: #0000FF;">},{</span><span style="color: #008000;">"2"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">500</span><span style="color: #0000FF;">}}</span>
<span style="color: #7060A8;">papply</span><span style="color: #0000FF;">(</span><span style="color: #004600;">false</span><span style="color: #0000FF;">,</span><span style="color: #000000;">spigot_test</span><span style="color: #0000FF;">,</span><span style="color: #000000;">tests</span><span style="color: #0000FF;">)</span>
<!--</lang>-->
{{out}}
<small>(the final "2" was re-joined up by hand)</small>
Line 837 ⟶ 840:
</pre>
stress test?:
<!--<lang Phix>(phixonline)-->
<lang Phix>requires("1.0.0") -- (mpfr_set_default_prec[ision] has been renamed)
<span style="color: #7060A8;">requires</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"1.0.0"</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (mpfr_set_default_prec[ision] has been renamed)</span>
include mpfr.e
<span style="color: #008080;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
mpfr_set_default_precision(-100) -- 100 d.p precision
<span style="color: #7060A8;">mpfr_set_default_precision</span><span style="color: #0000FF;">(-</span><span style="color: #000000;">100</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- 100 d.p precision</span>
mpfr pi = mpfr_init()
<span style="color: #004080;">mpfr</span> <span style="color: #000000;">pi</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">()</span>
mpfr_const_pi(pi)
<span style="color: #7060A8;">mpfr_const_pi</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pi</span><span style="color: #0000FF;">)</span>
string ps = mpfr_sprintf("%.100Rf", pi),
<span style="color: #004080;">string</span> <span style="color: #000000;">ps</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_get_fixed</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pi</span><span style="color: #0000FF;">,</span><span style="color: #000000;">100</span><span style="color: #0000FF;">),</span>
rs = spigot_sqrt(ps,102) -- (<=101 is not enough)
<span style="color: #000000;">rs</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">spigot_sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ps</span><span style="color: #0000FF;">,</span><span style="color: #000000;">102</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (&lt;=101 is not enough)</span>
mpfr_set_str(pi,rs)
<span style="color: #7060A8;">mpfr_set_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pi</span><span style="color: #0000FF;">,</span><span style="color: #000000;">rs</span><span style="color: #0000FF;">)</span>
mpfr_mul(pi,pi,pi)
<span style="color: #7060A8;">mpfr_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pi</span><span style="color: #0000FF;">,</span><span style="color: #000000;">pi</span><span style="color: #0000FF;">,</span><span style="color: #000000;">pi</span><span style="color: #0000FF;">)</span>
rs = mpfr_sprintf("%.100Rf", pi)
<span style="color: #000000;">rs</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_get_fixed</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pi</span><span style="color: #0000FF;">,</span><span style="color: #000000;">100</span><span style="color: #0000FF;">)</span>
printf(1,"Pi (builtin) vs spigot_sqrt(pi) squared:\n %s\n %s\n",{ps,rs})</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;">"Pi (builtin) vs spigot_sqrt(pi) squared:\n %s\n %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">ps</span><span style="color: #0000FF;">,</span><span style="color: #000000;">rs</span><span style="color: #0000FF;">})</span>
<!--</lang>-->
{{out}}
<pre>
Petelomax
7,806

edits

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