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Sutran.cin - Revision history
2024-03-29T08:47:57Z
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2019-07-30T09:48:24Z
<p>Text replacement - "\$([^\$]+)\$" to "\\(\1\\)"</p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 09:48, 30 July 2019</td>
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<td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>// sutran.cin is the complex(double) [[C++]] implementation of function [[SuTra]], which is superfunction of the [[Trappmann function]] <del class="diffchange diffchange-inline">$</del>\mathrm{tra}(z)=z+\exp(z)<del class="diffchange diffchange-inline">$</del>.</div></td>
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<td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>// sutran.cin is the complex(double) [[C++]] implementation of function [[SuTra]], which is superfunction of the [[Trappmann function]] <ins class="diffchange diffchange-inline">\(</ins>\mathrm{tra}(z)=z+\exp(z)<ins class="diffchange diffchange-inline">\)</ins>.</div></td>
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<td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>// This implementation is simpler, faster and more precise that [[sutra.cin]], that evaluates the same function [[SuTra]] through function [[SuZex]]</div></td>
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<td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>// This implementation is simpler, faster and more precise that [[sutra.cin]], that evaluates the same function [[SuTra]] through function [[SuZex]]</div></td>
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<td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>// sutran(z) returns value <del class="diffchange diffchange-inline">$</del>\mathrm{SuTra}(z)<del class="diffchange diffchange-inline">$</del> with at least 14 decimal digits, except vicinity of the positive part of the real axis, where the function shows very fast growth (similar to that of [[tetration]]) and very fast and strong oscillations.</div></td>
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<td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>// sutran(z) returns value <ins class="diffchange diffchange-inline">\(</ins>\mathrm{SuTra}(z)<ins class="diffchange diffchange-inline">\)</ins> with at least 14 decimal digits, except vicinity of the positive part of the real axis, where the function shows very fast growth (similar to that of [[tetration]]) and very fast and strong oscillations.</div></td>
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https://mizugadro.mydns.jp/t/index.php?title=Sutran.cin&diff=14880&oldid=prev
Maintenance script at 22:06, 30 November 2018
2018-11-30T22:06:20Z
<p></p>
<p><b>New page</b></p><div>// sutran.cin is the complex(double) [[C++]] implementation of function [[SuTra]], which is superfunction of the [[Trappmann function]] $\mathrm{tra}(z)=z+\exp(z)$.<br />
// This implementation is simpler, faster and more precise that [[sutra.cin]], that evaluates the same function [[SuTra]] through function [[SuZex]]<br />
// sutran(z) returns value $\mathrm{SuTra}(z)$ with at least 14 decimal digits, except vicinity of the positive part of the real axis, where the function shows very fast growth (similar to that of [[tetration]]) and very fast and strong oscillations.<br />
<br />
<poem><nomathjax><nowiki><br />
/*<br />
#define DB double<br />
#define DO(x,y) for(x=0;x<y;x++)<br />
using namespace std;<br />
#include<complex><br />
typedef complex<double> z_type;<br />
#define Re(x) x.real()<br />
#define Im(x) x.imag()<br />
#define I z_type(0.,1.)<br />
#include "conto.cin"<br />
// #include "SuZex.cin"<br />
*/<br />
<br />
z_type tra(z_type z) {return z+exp(z);}<br />
<br />
//z_type sutra(z_type z){ if( Re(z)<2. ) return log(suzex(z));<br />
// return tra(sutra(z-1.));}<br />
//old<br />
<br />
// Warning! A is global array (to print tables)<br />
DB A[12][12]={{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, <br />
{0, -0.5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, <br />
{.16666666666666666,-.25, 0.125, 0, 0, 0, 0, 0, 0, 0, 0, 0},<br />
{.14583333333333334,-.2916666666666667, .1875, -0.041666666666666664, 0, 0, 0, 0, 0, 0, 0, 0},<br />
{.14976851851851852,-.3645833333333333, .3125, -0.11458333333333333, 0.015625, 0, 0, 0, 0, 0, 0, 0},<br />
{.16516203703703702,-.48182870370370373,.5208333333333334, -0.265625, 0.06510416666666667, -0.00625, 0, 0, 0, 0, 0, 0},<br />
{.19026441247795414,-.6538194444444444, .8627025462962963,-.5668402777777778,.19856770833333334,-.03567708333333333,.0026041666666666665,0,0,0,0,0},<br />
{.22588548555996474,-.8977029596560847,1.4120804398148148,-1.1461226851851851,.5244140625,-.13697916666666668,.019140625,-.0011160714285714285,0,0,0,0},<br />
{.2753440585982335, -1.239450679287919,2.2770203993055556,-2.2204885223765434,1.265064380787037,-.43557942708333336,.08947482638888889,<br />
-.010128348214285715, 0.00048828125, 0, 0, 0},<br />
{.34496713297587556,-1.7211015740368936,3.6174115582286155,-4.146271460262346,2.8530207127700615,-1.2298412181712963,.3351236979166667,<br />
-.05619264632936508, 0.005308314732142857, -0.00021701388888888888, 0, 0},<br />
{.4437001055047508, -2.4129028854098866,5.6811843206973185,-7.499253067474096,6.09106574918017,-3.1826392505787036,1.0899427625868054,<br />
-0.2435329861111111, 0.03426252092633929, -0.002762664310515873, 0.00009765625, 0},<br />
{.5803465848040893, -3.4249519702286975,8.872849373873375,-13.218267068232578,12.419599208932706,-7.682385374469521,3.1971707567756558,<br />
-0.9002970377604167, 0.1693393767826141, -0.020416066003224206, 0.0014301602802579364, -0.00004438920454545455}};<br />
<br />
z_type sutra0(z_type z){ z+=-1.1259817765745026;<br />
z_type L=log(-z); z_type s,w, t=1./z; <br />
int M=11; // WARNING!! at TORI, M=11<br />
z_type c[12]; int m,n;<br />
for(m=1;m<=M;m++){ w=A[m][m]; for(n=m-1; n>=0; n--) {w*=L; w+=A[m][n]; }<br />
c[m]=w;}<br />
s=c[M]*t; for(m=M-1;m>0;m--){ s+=c[m]; s*=t;} return -L+s; <br />
}<br />
<br />
z_type sutran(z_type z) { DB x=Re(z); if(x<-10.) return sutra0(z); DB y=Im(z); <br />
if( fabs(y)<6.){int n,m; n=int(x+12.); z_type c=sutra0(z-(0.+n)); DO(m,n) c=tra(c); return c;}<br />
DB x0=x-5.; if(x0*x0+y*y >289.) return sutra0(z);<br />
return tra(sutran(z-1.));<br />
} <br />
<br />
//</nowiki></nomathjax></poem><br />
/*<br />
[[Category:Book]]<br />
[[Category:C++]]<br />
[[Category:SuTra]]<br />
[[Category:Trappmann function]]<br />
[[Category:Superfunction]]<br />
[[Category:Entire function]]<br />
[[Category:Logatirhm]]<br />
*/</div>
Maintenance script