Apéry's constant: Difference between revisions

Line 41:

;* [[oeis:A002117|OEIS:A002117 - Decimal expansion of zeta(3)]]

=={{header|Phix}}==

Ugh. If you ran this on the James Webb, you might just be able to pick out a faint small print outline of the word "elegant".

Still, at least it is not like you do this sort of thing every day... and I got to fix a couple of bugs in my mpfr.js code.

with javascript_semantics

requires("1.0.2") -- (missing mpfr_ui_pow_ui() and bug in mpfr_mul_d(), both in mpfr.js)

include mpfr.e

mpfr_set_default_precision(-100)

mpfr {d,a,w,t} = mpfr_inits(4)

mpz {z,pk} = mpz_inits(2)

for k=1 to 1000 do

mpfr_ui_pow_ui(t,k,3)

mpfr_si_div(t,1,t)

mpfr_add(d,d,t)

end for

for k=1 to 158 do

mpz_fac_ui(z,k)

mpz_mul(z,z,z)

mpfr_set_z(t,z)

mpz_fac_ui(z,2*k)

mpfr_div_z(t,t,z)

mpz_ui_pow_ui(z,k,3)

mpfr_div_z(t,t,z)

if even(k) then

mpfr_sub(a,a,t)

else

mpfr_add(a,a,t)

end if

end for

mpfr_mul_d(a,a,5/2)

for k=0 to 19 do

mpz_ui_pow_ui(z,k,5)

mpz_mul_si(z,z,126392)

mpz_ui_pow_ui(pk,k,4)

mpz_mul_si(pk,pk,412708)

mpz_add(z,z,pk)

mpz_ui_pow_ui(pk,k,3)

mpz_mul_si(pk,pk,531578)

mpz_add(z,z,pk)

mpz_add_si(z,z,k*k*336367)

mpz_add_si(z,z,k*104000)

mpz_add_si(z,z,12463)

mpfr_set_z(t,z)

mpz_fac_ui(z,2*k+1)

mpz_pow_ui(z,z,3)

mpfr_mul_z(t,t,z)

mpz_fac_ui(z,2*k)

mpz_pow_ui(z,z,3)

mpfr_mul_z(t,t,z)

mpz_fac_ui(z,k)

mpz_pow_ui(z,z,3)

mpfr_mul_z(t,t,z)

mpz_fac_ui(z,3*k+2)

mpfr_div_z(t,t,z)

mpz_fac_ui(z,4*k+3)

mpz_pow_ui(z,z,3)

mpfr_div_z(t,t,z)

if odd(k) then

mpfr_sub(w,w,t)

else

mpfr_add(w,w,t)

end if

end for

mpfr_div_si(w,w,24)

constant fmt = """

Actual value to 100 decimal places:

1.2020569031595942853997381615114499907649862923404988817922715553418382057863130901864558736093352581

First 1000 terms of zeta(3) truncated to 100 decimal places. (accurate to 6 decimal places):

%s

First 158 terms of Markov / Apery representation truncated to 100 decimal places:

%s

First 20 terms of Wedeniwski representation truncated to 100 decimal places:

%s

"""

string direct = mpfr_get_fixed(d,100),

mapery = mpfr_get_fixed(a,100),

wdnski = mpfr_get_fixed(w,100)

printf(1,fmt,{direct,mapery,wdnski})

<pre>

Actual value to 100 decimal places:

1.2020569031595942853997381615114499907649862923404988817922715553418382057863130901864558736093352581

First 1000 terms of zeta(3) truncated to 100 decimal places. (accurate to 6 decimal places):

1.2020564036593442854830714115115999903483212709031775135036540966118572571921400836130084123260473111

First 158 terms of Markov / Apery representation truncated to 100 decimal places:

1.2020569031595942853997381615114499907649862923404988817922715553418382057863130901864558736093352581

First 20 terms of Wedeniwski representation truncated to 100 decimal places:

1.2020569031595942853997381615114499907649862923404988817922715553418382057863130901864558736093352581

</pre>

Last digit of the 1000 terms line is 2 under pwa/p2js...

=={{header|Raku}}==

@@ Line 41: / Line 41: @@
 ;* [[oeis:A002117|OEIS:A002117 - Decimal expansion of zeta(3)]]
+=={{header|Phix}}==
+Ugh. If you ran this on the James Webb, you might just be able to pick out a faint small print outline of the word "elegant".<br>
+Still, at least it is not like you do this sort of thing every day... and I got to fix a couple of bugs in my mpfr.js code.
+<!--<syntaxhighlight lang="phix">(phixonline)-->
+ <span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
+ <span style="color: #7060A8;">requires</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"1.0.2"</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (missing mpfr_ui_pow_ui() and bug in mpfr_mul_d(), both in mpfr.js)</span>
+ <span style="color: #008080;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
+ <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: #004080;">mpfr</span> <span style="color: #0000FF;">{</span><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;">w</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</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;">4</span><span style="color: #0000FF;">)</span>
+ <span style="color: #004080;">mpz</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">pk</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_inits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
+ <span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1000</span> <span style="color: #008080;">do</span>
+     <span style="color: #7060A8;">mpfr_ui_pow_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpfr_si_div</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpfr_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)</span>
+ <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
+ <span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">158</span> <span style="color: #008080;">do</span>
+     <span style="color: #7060A8;">mpz_fac_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpz_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpfr_set_z</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpz_fac_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #000000;">k</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpfr_div_z</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpz_ui_pow_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpfr_div_z</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
+     <span style="color: #008080;">if</span> <span style="color: #7060A8;">even</span><span style="color: #0000FF;">(</span><span style="color: #000000;">k</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
+         <span style="color: #7060A8;">mpfr_sub</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;">t</span><span style="color: #0000FF;">)</span>
+     <span style="color: #008080;">else</span>
+         <span style="color: #7060A8;">mpfr_add</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;">t</span><span style="color: #0000FF;">)</span>
+     <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
+ <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
+ <span style="color: #7060A8;">mpfr_mul_d</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;">5</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
+ <span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">19</span> <span style="color: #008080;">do</span>
+     <span style="color: #7060A8;">mpz_ui_pow_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpz_mul_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">126392</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpz_ui_pow_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pk</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpz_mul_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pk</span><span style="color: #0000FF;">,</span><span style="color: #000000;">pk</span><span style="color: #0000FF;">,</span><span style="color: #000000;">412708</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpz_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">pk</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpz_ui_pow_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pk</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpz_mul_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pk</span><span style="color: #0000FF;">,</span><span style="color: #000000;">pk</span><span style="color: #0000FF;">,</span><span style="color: #000000;">531578</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpz_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">pk</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpz_add_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">*</span><span style="color: #000000;">k</span><span style="color: #0000FF;">*</span><span style="color: #000000;">336367</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpz_add_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">*</span><span style="color: #000000;">104000</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpz_add_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">12463</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpfr_set_z</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpz_fac_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpz_pow_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpfr_mul_z</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpz_fac_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #000000;">k</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpz_pow_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpfr_mul_z</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpz_fac_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpz_pow_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpfr_mul_z</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpz_fac_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">*</span><span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpfr_div_z</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpz_fac_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">*</span><span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">3</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpz_pow_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpfr_div_z</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
+     <span style="color: #008080;">if</span> <span style="color: #7060A8;">odd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">k</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
+         <span style="color: #7060A8;">mpfr_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">w</span><span style="color: #0000FF;">,</span><span style="color: #000000;">w</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)</span>
+     <span style="color: #008080;">else</span>
+         <span style="color: #7060A8;">mpfr_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">w</span><span style="color: #0000FF;">,</span><span style="color: #000000;">w</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)</span>
+     <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
+ <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
+ <span style="color: #7060A8;">mpfr_div_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">w</span><span style="color: #0000FF;">,</span><span style="color: #000000;">w</span><span style="color: #0000FF;">,</span><span style="color: #000000;">24</span><span style="color: #0000FF;">)</span>
+ <span style="color: #008080;">constant</span> <span style="color: #000000;">fmt</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"""
+ Actual value to 100 decimal places:
+.2020569031595942853997381615114499907649862923404988817922715553418382057863130901864558736093352581
+ First 1000 terms of zeta(3) truncated to 100 decimal places. (accurate to 6 decimal places):
+ %s
+ First 158 terms of Markov / Apery representation truncated to 100 decimal places:
+ %s
+ First 20 terms of Wedeniwski representation truncated to 100 decimal places:
+ %s
+ """</span>
+ <span style="color: #004080;">string</span> <span style="color: #000000;">direct</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_get_fixed</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d</span><span style="color: #0000FF;">,</span><span style="color: #000000;">100</span><span style="color: #0000FF;">),</span>
+        <span style="color: #000000;">mapery</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_get_fixed</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">100</span><span style="color: #0000FF;">),</span>
+        <span style="color: #000000;">wdnski</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_get_fixed</span><span style="color: #0000FF;">(</span><span style="color: #000000;">w</span><span style="color: #0000FF;">,</span><span style="color: #000000;">100</span><span style="color: #0000FF;">)</span>
+ <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">direct</span><span style="color: #0000FF;">,</span><span style="color: #000000;">mapery</span><span style="color: #0000FF;">,</span><span style="color: #000000;">wdnski</span><span style="color: #0000FF;">})</span>
+<!--</syntaxhighlight>-->
+{{out}}
+<pre>
+Actual value to 100 decimal places:
+.2020569031595942853997381615114499907649862923404988817922715553418382057863130901864558736093352581
+First 1000 terms of zeta(3) truncated to 100 decimal places. (accurate to 6 decimal places):
+.2020564036593442854830714115115999903483212709031775135036540966118572571921400836130084123260473111
+First 158 terms of Markov / Apery representation truncated to 100 decimal places:
+.2020569031595942853997381615114499907649862923404988817922715553418382057863130901864558736093352581
+First 20 terms of Wedeniwski representation truncated to 100 decimal places:
+.2020569031595942853997381615114499907649862923404988817922715553418382057863130901864558736093352581
+</pre>
+<small>Last digit of the 1000 terms line is 2 under pwa/p2js...</small>
 =={{header|Raku}}==