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Pathological floating point problems: Difference between revisions

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Pathological floating point problems (view source)

Revision as of 15:44, 18 June 2021

35,509 bytes added ,  3 years ago
m
→‎{{header|Phix}}: added syntax colouring the hard way
m (→‎gmp version: mpfr_set_default_precision renamed)
m (→‎{{header|Phix}}: added syntax colouring the hard way)
Line 2,946:
Task2: needs at least 41 decimal places (and 42 passed as the first argument to ba_euler)<br>
Task3: apparently only needs just 15 decimal places, then again ba_scale() defines the minimum, and it may (as in is permitted to) use more.
<!--<lang Phix>include builtins\bigatom.e(phixonline)-->
<span style="color: #008080;">include</span> <span style="color: #000000;">builtins</span><span style="color: #0000FF;">\</span><span style="color: #000000;">bigatom</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
puts(1,"Task 1\n")
<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Task 1\n"</span><span style="color: #0000FF;">)</span>
constant {fns,fmts} = columnize({{3,1},{4,6},{5,6},{6,6},{7,6},{8,7},{20,16},{30,24},{50,40},{100,78}})
<span style="color: #008080;">constant</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">fns</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fmts</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">columnize</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;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">7</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">20</span><span style="color: #0000FF;">,</span><span style="color: #000000;">16</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">30</span><span style="color: #0000FF;">,</span><span style="color: #000000;">24</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">50</span><span style="color: #0000FF;">,</span><span style="color: #000000;">40</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">78</span><span style="color: #0000FF;">}})</span>
{} = ba_scale(196)
<span style="color: #0000FF;">{}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ba_scale</span><span style="color: #0000FF;">(</span><span style="color: #000000;">196</span><span style="color: #0000FF;">)</span>
sequence v = {2,-4}
<span style="color: #004080;">sequence</span> <span style="color: #000000;">v</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">4</span><span style="color: #0000FF;">}</span>
for n=3 to 100 do
<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">3</span> <span style="color: #008080;">to</span> <span style="color: #000000;">100</span> <span style="color: #008080;">do</span>
-- v = append(v,111 - 1130/v[n-1] + 3000/(v[n-1]*v[n-2]))
<span style="color: #000080;font-style:italic;">-- v = append(v,ba_add(ba_sub(111,ba_divide( - 1130,/v[n-1])),ba_divide( + 3000,ba_multiply/(v[n-1],*v[n-2]))))</span>
<span style="color: #000000;">v</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">v</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ba_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ba_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">111</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ba_divide</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1130</span><span style="color: #0000FF;">,</span><span style="color: #000000;">v</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">])),</span><span style="color: #000000;">ba_divide</span><span style="color: #0000FF;">(</span><span style="color: #000000;">3000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ba_multiply</span><span style="color: #0000FF;">(</span><span style="color: #000000;">v</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],</span><span style="color: #000000;">v</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]))))</span>
if n<9 or find(n,{20,30,50,100}) then
<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;"><</span><span style="color: #000000;">9</span> <span style="color: #008080;">or</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">20</span><span style="color: #0000FF;">,</span><span style="color: #000000;">30</span><span style="color: #0000FF;">,</span><span style="color: #000000;">50</span><span style="color: #0000FF;">,</span><span style="color: #000000;">100</span><span style="color: #0000FF;">})</span> <span style="color: #008080;">then</span>
-- printf(1,"n = %-3d %20.16f\n", {n, v[n]})
<span style="color: #000080;font-style:italic;">-- printf(1,"n = %-3d %20.16f\n", {n, v[n]})</span>
string fmt = sprintf("%%.%dB",fmts[find(n,fns)])
<span style="color: #004080;">string</span> <span style="color: #000000;">fmt</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%%.%dB"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fmts</span><span style="color: #0000FF;">[</span><span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fns</span><span style="color: #0000FF;">)])</span>
printf(1,"n = %-3d %s\n", {n, ba_sprintf(fmt,v[n])})
<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;">"n = %-3d %s\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ba_sprintf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">,</span><span style="color: #000000;">v</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</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>
 
puts(1,"\nTask 2\n")
<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\nTask 2\n"</span><span style="color: #0000FF;">)</span>
--atom balance = exp(1)-1
<span style="color: #000080;font-style:italic;">--atom balance = exp(1)-1
--for i=1 to 25 do balance = balance*i-1 end for
--printf(for i=1,"\nTask 2\nBalance afterto 25 years:do $%12.10f",balance = balance)*i-1 end for
--printf(1,"\nTask 2\nBalance after 25 years: $%12.10f", balance)</span>
{} = ba_scale(41)
<span style="color: #0000FF;">{}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ba_scale</span><span style="color: #0000FF;">(</span><span style="color: #000000;">41</span><span style="color: #0000FF;">)</span>
bigatom balance = ba_sub(ba_euler(42,true),1)
<span style="color: #000000;">bigatom</span> <span style="color: #000000;">balance</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ba_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ba_euler</span><span style="color: #0000FF;">(</span><span style="color: #000000;">42</span><span style="color: #0000FF;">,</span><span style="color: #004600;">true</span><span style="color: #0000FF;">),</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
for i=1 to 25 do balance = ba_sub(ba_multiply(balance,i),1) end for
<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;">25</span> <span style="color: #008080;">do</span> <span style="color: #000000;">balance</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ba_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ba_multiply</span><span style="color: #0000FF;">(</span><span style="color: #000000;">balance</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: #008080;">end</span> <span style="color: #008080;">for</span>
ba_printf(1,"Balance after 25 years: $%.16B\n\n", balance)
<span style="color: #000000;">ba_printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Balance after 25 years: $%.16B\n\n"</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">balance</span><span style="color: #0000FF;">)</span>
 
puts(1,"Task 3\n")
<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Task 3\n"</span><span style="color: #0000FF;">)</span>
{} = ba_scale(15) -- fine!
<span style="color: #0000FF;">{}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ba_scale</span><span style="color: #0000FF;">(</span><span style="color: #000000;">15</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- fine!</span>
integer a = 77617,
<span style="color: #004080;">integer</span> <span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">77617</span><span style="color: #0000FF;">,</span>
b = 33096
<span style="color: #000000;">b</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">33096</span>
--atom pa2 = power(a,2),
<span style="color: #000080;font-style:italic;">--atom pa2 = power(a,2),
-- pb2a211 = 11*pa2*power(b,2),
-- pb4121pb2a211 = 12111*pa2*power(b,42),
-- pb6pb4121 = 121*power(b,64),
-- pb855pb6 = 5.5*power(b,86),
-- pb855 = 5.5*power(b,8),
-- f_ab = 333.75 * pb6 + pa2 * (pb2a211 - pb6 - pb4121 - 2) + pb855 + a/(2*b)
-- f_ab = 333.75 * pb6 + pa2 * (pb2a211 - pb6 - pb4121 - 2) + pb855 + a/(2*b)
--printf(1,"f(%d, %d) = %.15f\n\n", {a, b, f_ab})
--printf(1,"f(%d, %d) = %.15f\n\n", {a, b, f_ab})</span>
bigatom pa2 = ba_power(a,2),
<span style="color: #000000;">bigatom</span> <span style="color: #000000;">pa2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ba_power</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>
pb2a211 = ba_multiply(11,ba_multiply(pa2,ba_power(b,2))),
<span style="color: #000000;">pb2a211</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ba_multiply</span><span style="color: #0000FF;">(</span><span style="color: #000000;">11</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ba_multiply</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pa2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ba_power</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>
pb4121 = ba_multiply(121,ba_power(b,4)),
<span style="color: #000000;">pb4121</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ba_multiply</span><span style="color: #0000FF;">(</span><span style="color: #000000;">121</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ba_power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">)),</span>
pb6 = ba_power(b,6),
<span style="color: #000000;">pb6</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ba_power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">),</span>
pa2mid = ba_multiply(pa2,ba_sub(ba_sub(ba_sub(pb2a211,pb6),pb4121),2)),
<span style="color: #000000;">pa2mid</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ba_multiply</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pa2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ba_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ba_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ba_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pb2a211</span><span style="color: #0000FF;">,</span><span style="color: #000000;">pb6</span><span style="color: #0000FF;">),</span><span style="color: #000000;">pb4121</span><span style="color: #0000FF;">),</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)),</span>
pb633375 = ba_multiply(333.75,pb6),
<span style="color: #000000;">pb633375</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ba_multiply</span><span style="color: #0000FF;">(</span><span style="color: #000000;">333.75</span><span style="color: #0000FF;">,</span><span style="color: #000000;">pb6</span><span style="color: #0000FF;">),</span>
pb855 = ba_multiply(5.5,ba_power(b,8)),
<span style="color: #000000;">pb855</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ba_multiply</span><span style="color: #0000FF;">(</span><span style="color: #000000;">5.5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ba_power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">)),</span>
f_ab = ba_add(ba_add(ba_add(pb633375,pa2mid),pb855),ba_divide(a,ba_multiply(2,b)))
<span style="color: #000000;">f_ab</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ba_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ba_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ba_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pb633375</span><span style="color: #0000FF;">,</span><span style="color: #000000;">pa2mid</span><span style="color: #0000FF;">),</span><span style="color: #000000;">pb855</span><span style="color: #0000FF;">),</span><span style="color: #000000;">ba_divide</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ba_multiply</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)))</span>
printf(1,"f(%d, %d) = %s\n", {a, b, ba_sprintf("%.15B",f_ab)})</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;">"f(%d, %d) = %s\n"</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;">b</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ba_sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%.15B"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">f_ab</span><span style="color: #0000FF;">)})</span>
<!--</lang>-->
Aside: obviously you don't ''have'' to use lots of temps like that, but I find that style often makes things much easier to debug.
{{out}}
Line 3,020 ⟶ 3,022:
Task2: needs at least 41 decimal places (and e-1 accurately specified to at least 42 decimal places).<br>
Task3: needs at least 36 decimal places (my suspicions above re bigatom in 15 now seem correct).
<!--<lang Phix>(phixonline)-->
<lang Phix>requires("1.0.0") -- (mpfr_set_default_prec[ision] has been renamed)
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
include builtins\mpfr.e
<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>
puts(1,"Task 1\n")
<span style="color: #008080;">include</span> <span style="color: #000000;">builtins</span><span style="color: #0000FF;">\</span><span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
constant {fns,fmts} = columnize({{3,1},{4,6},{5,6},{6,6},{7,6},{8,7},{20,16},{30,24},{50,40},{100,78}})
<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Task 1\n"</span><span style="color: #0000FF;">)</span>
mpfr_set_default_precision(-196)
<span style="color: #008080;">constant</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">fns</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fdp</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">columnize</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;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">7</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">20</span><span style="color: #0000FF;">,</span><span style="color: #000000;">16</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">30</span><span style="color: #0000FF;">,</span><span style="color: #000000;">24</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">50</span><span style="color: #0000FF;">,</span><span style="color: #000000;">40</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">78</span><span style="color: #0000FF;">}})</span>
sequence v = {mpfr_init(2),mpfr_init(-4)}
<span style="color: #7060A8;">mpfr_set_default_precision</span><span style="color: #0000FF;">(-</span><span style="color: #000000;">196</span><span style="color: #0000FF;">)</span>
mpfr t1 = mpfr_init()
<span style="color: #004080;">sequence</span> <span style="color: #000000;">v</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">),</span><span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">(-</span><span style="color: #000000;">4</span><span style="color: #0000FF;">)}</span>
for n=3 to 100 do
<span style="color: #004080;">mpfr</span> <span style="color: #000000;">t1</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">()</span>
-- v = append(v,111 - 1130/v[n-1] + 3000/(v[n-1]*v[n-2]))
<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">3</span> <span style="color: #008080;">to</span> <span style="color: #000000;">100</span> <span style="color: #008080;">do</span>
mpfr_set_si(t1,1130)
<span style="color: #000080;font-style:italic;">-- v = append(v,111 - 1130/v[n-1] + 3000/(v[n-1]*v[n-2]))</span>
mpfr_div(t1,t1,v[n-1])
<span style="color: #7060A8;">mpfr_set_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1130</span><span style="color: #0000FF;">)</span>
mpfr_si_sub(t1,111,t1)
<span style="color: #7060A8;">mpfr_div</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">v</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">])</span>
mpfr t2 = mpfr_init()
<span style="color: #7060A8;">mpfr_si_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">111</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t1</span><span style="color: #0000FF;">)</span>
mpfr_mul(t2,v[n-1],v[n-2])
<span style="color: #004080;">mpfr</span> <span style="color: #000000;">t2</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">()</span>
mpfr_si_div(t2,3000,t2)
<span style="color: #7060A8;">mpfr_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">v</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],</span><span style="color: #000000;">v</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">])</span>
mpfr_add(t2,t1,t2)
<span style="color: #7060A8;">mpfr_si_div</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t2</span><span style="color: #0000FF;">)</span>
v = append(v,t2)
<span style="color: #7060A8;">mpfr_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t2</span><span style="color: #0000FF;">)</span>
if n<9 or find(n,{20,30,50,100}) then
<span style="color: #000000;">v</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">v</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t2</span><span style="color: #0000FF;">)</span>
-- printf(1,"n = %-3d %20.16f\n", {n, v[n]})
<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;"><</span><span style="color: #000000;">9</span> <span style="color: #008080;">or</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">20</span><span style="color: #0000FF;">,</span><span style="color: #000000;">30</span><span style="color: #0000FF;">,</span><span style="color: #000000;">50</span><span style="color: #0000FF;">,</span><span style="color: #000000;">100</span><span style="color: #0000FF;">})</span> <span style="color: #008080;">then</span>
string fmt = sprintf("%%.%dRf",fmts[find(n,fns)])
<span style="color: #000080;font-style:italic;">-- printf(1,"n = %-3d %s20.16f\n", {n, mpfr_sprintf(fmt,v[n])})</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;">"n = %-3d %s\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #7060A8;">mpfr_get_fixed</span><span style="color: #0000FF;">(</span><span style="color: #000000;">v</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">],</span><span style="color: #000000;">fdp</span><span style="color: #0000FF;">[</span><span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fns</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>
 
puts(1,"\nTask 2\n")
<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\nTask 2\n"</span><span style="color: #0000FF;">)</span>
--atom balance = exp(1)-1
<span style="color: #000080;font-style:italic;">--atom balance = exp(1)-1
--for i=1 to 25 do balance = balance*i-1 end for
--printf(for i=1,"\nTask 2\nBalance afterto 25 years:do $%12.10f",balance = balance)*i-1 end for
--printf(1,"\nTask 2\nBalance after 25 years: $%12.10f", balance)</span>
mpfr_set_default_precision(-41)
<span style="color: #7060A8;">mpfr_set_default_precision</span><span style="color: #0000FF;">(-</span><span style="color: #000000;">41</span><span style="color: #0000FF;">)</span>
mpfr balance = mpfr_init("1.71828182845904523536028747135266249775724709369995"&
<span style="color: #004080;">mpfr</span> <span style="color: #000000;">balance</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"1.71828182845904523536028747135266249775724709369995"</span><span style="color: #0000FF;">&</span>
"95749669676277240766303535475945713821785251664274")
<span style="color: #008000;">"95749669676277240766303535475945713821785251664274"</span><span style="color: #0000FF;">)</span>
for i=1 to 25 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: #000000;">25</span> <span style="color: #008080;">do</span>
mpfr_mul_si(balance,balance,i)
<span style="color: #7060A8;">mpfr_mul_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">balance</span><span style="color: #0000FF;">,</span><span style="color: #000000;">balance</span><span style="color: #0000FF;">,</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</span>
mpfr_sub_si(balance,balance,1)
<span style="color: #7060A8;">mpfr_sub_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">balance</span><span style="color: #0000FF;">,</span><span style="color: #000000;">balance</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
mpfr_printf(1,"Balance after 25 years: $%.16Rf\n\n", balance)
<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;">"Balance after 25 years: $%s\n\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #7060A8;">mpfr_get_fixed</span><span style="color: #0000FF;">(</span><span style="color: #000000;">balance</span><span style="color: #0000FF;">,</span><span style="color: #000000;">16</span><span style="color: #0000FF;">)})</span>
 
 
puts(1,"Task 3\n")
<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Task 3\n"</span><span style="color: #0000FF;">)</span>
mpfr_set_default_precision(-36)
<span style="color: #7060A8;">mpfr_set_default_precision</span><span style="color: #0000FF;">(-</span><span style="color: #000000;">36</span><span style="color: #0000FF;">)</span>
integer a = 77617,
<span style="color: #004080;">integer</span> <span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">77617</span><span style="color: #0000FF;">,</span>
b = 33096
<span style="color: #000000;">b</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">33096</span>
--atom pa2 = power(a,2),
<span style="color: #000080;font-style:italic;">--atom pa2 = power(a,2),
-- pb2a211 = 11*pa2*power(b,2),
-- pb4121pb2a211 = 12111*pa2*power(b,42),
-- pb6pb4121 = 121*power(b,64),
-- pb855pb6 = 5.5*power(b,86),
-- pb855 = 5.5*power(b,8),
-- f_ab = 333.75 * pb6 + pa2 * (pb2a211 - pb6 - pb4121 - 2) + pb855 + a/(2*b)
-- f_ab = 333.75 * pb6 + pa2 * (pb2a211 - pb6 - pb4121 - 2) + pb855 + a/(2*b)
--printf(1,"f(%d, %d) = %.15f\n\n", {a, b, f_ab})
--printf(1,"f(%d, %d) = %.15f\n\n", {a, b, f_ab})
-- (translation of FreeBASIC)
-- (translation of FreeBASIC)</span>
mpfr {t2,t3,t4,t5,t6,t7} = mpfr_inits(6)
<span style="color: #004080;">mpfr</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">t2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t7</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_inits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">6</span><span style="color: #0000FF;">)</span>
mpfr_set_d(t1, a) -- a
<span style="color: #7060A8;">mpfr_set_d</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t1</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</span>
mpfr_set_d(t2, b) -- b
<span style="color: #7060A8;">mpfr_set_d</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- b </span>
mpfr_set_d(t3, 333.75) -- 333.75
<span style="color: #7060A8;">mpfr_set_d</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">333.75</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- 333.75</span>
mpfr_pow_si(t4, t2, 6) -- b ^ 6
<span style="color: #7060A8;">mpfr_pow_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- b ^ 6</span>
mpfr_mul(t3, t3, t4) -- 333.75 * b^6
<span style="color: #7060A8;">mpfr_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t4</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- 333.75 * b^6</span>
mpfr_pow_si(t5, t1, 2) -- a^2
<span style="color: #7060A8;">mpfr_pow_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- a^2</span>
mpfr_pow_si(t6, t2, 2) -- b^2
<span style="color: #7060A8;">mpfr_pow_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- b^2</span>
mpfr_mul_si(t7, t5, 11) -- 11 * a^2
<span style="color: #7060A8;">mpfr_mul_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">11</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- 11 * a^2</span>
mpfr_mul(t7, t7, t6) -- 11 * a^2 * b^2
<span style="color: #7060A8;">mpfr_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t6</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- 11 * a^2 * b^2</span>
mpfr_sub(t7, t7, t4) -- 11 * a^2 * b^2 - b^6
<span style="color: #7060A8;">mpfr_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t4</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- 11 * a^2 * b^2 - b^6</span>
mpfr_pow_si(t4, t2, 4) -- b^4
<span style="color: #7060A8;">mpfr_pow_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- b^4</span>
mpfr_mul_si(t4, t4, 121) -- 121 * b^4
<span style="color: #7060A8;">mpfr_mul_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">121</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- 121 * b^4</span>
mpfr_sub(t7, t7, t4) -- 11 * a^2 * b^2 - b^6 - 121 * b^4
<span style="color: #7060A8;">mpfr_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t4</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- 11 * a^2 * b^2 - b^6 - 121 * b^4</span>
mpfr_sub_si(t7, t7, 2) -- 11 * a^2 * b^2 - b^6 - 121 * b^4 - 2
<span style="color: #7060A8;">mpfr_sub_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- 11 * a^2 * b^2 - b^6 - 121 * b^4 - 2</span>
mpfr_mul(t7, t7, t5) -- (11 * a^2 * b^2 - b^6 - 121 * b^4 - 2) * a^2
<span style="color: #7060A8;">mpfr_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t5</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (11 * a^2 * b^2 - b^6 - 121 * b^4 - 2) * a^2</span>
mpfr_add(t3, t3, t7) -- 333.75 * b^6 + (11 * a^2 * b^2 - b^6 - 121 * b^4 - 2) * a^2
<span style="color: #7060A8;">mpfr_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t7</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- 333.75 * b^6 + (11 * a^2 * b^2 - b^6 - 121 * b^4 - 2) * a^2</span>
mpfr_set_d(t4, 5.5) -- 5.5
<span style="color: #7060A8;">mpfr_set_d</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5.5</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- 5.5</span>
mpfr_pow_si(t5, t2, 8) -- b^8
<span style="color: #7060A8;">mpfr_pow_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">8</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- b^8 </span>
mpfr_mul(t4, t4, t5) -- 5.5 * b^8
<span style="color: #7060A8;">mpfr_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t5</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- 5.5 * b^8</span>
mpfr_add(t3, t3, t4) -- 333.75 * b^6 + (11 * a^2 * b^2 - b^6 - 121 * b^4 - 2) * a^2 + 5.5 * b^8
<span style="color: #7060A8;">mpfr_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t4</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- 333.75 * b^6 + (11 * a^2 * b^2 - b^6 - 121 * b^4 - 2) * a^2 + 5.5 * b^8</span>
mpfr_mul_si(t4, t2, 2) -- 2 * b
<span style="color: #7060A8;">mpfr_mul_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- 2 * b</span>
mpfr_div(t5, t1, t4) -- a / (2 * b)
<span style="color: #7060A8;">mpfr_div</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t4</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- a / (2 * b)</span>
mpfr_add(t3, t3, t5) -- 333.75 * b^6 + (11 * a^2 * b^2 - b^6 - 121 * b^4 - 2) * a^2 + 5.5 * b^8 + a / (2 * b)
<span style="color: #7060A8;">mpfr_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t5</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- 333.75 * b^6 + (11 * a^2 * b^2 - b^6 - 121 * b^4 - 2) * a^2 + 5.5 * b^8 + a / (2 * b)</span>
printf(1,"f(%d, %d) = %s\n", {a, b, mpfr_sprintf("%.15Rf",t3)})
<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;">"f(%d, %d) = %s\n"</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;">b</span><span style="color: #0000FF;">,</span> <span style="color: #7060A8;">mpfr_get_fixed</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">15</span><span style="color: #0000FF;">)})</span>
{t1,t2,t3,t4,t5,t6,t7} = mpfr_free({t1,t2,t3,t4,t5,t6,t7})</lang>
<span style="color: #0000FF;">{</span><span style="color: #000000;">t1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t7</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_free</span><span style="color: #0000FF;">({</span><span style="color: #000000;">t1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t7</span><span style="color: #0000FF;">})</span>
<!--</lang>-->
Identical output
 
Petelomax
7,822

edits

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