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<font face="Courier New">Stéphane,<br>
<br>
This would be great if it worked for any x. When x is close to
1e16 there are few valid numbers per cycle. For instance</font><span
style="color:rgb(0,0,0);"><br>
<br>
</span><span style="color:rgb(0,0,0);">x</span><span
style="color:rgb(74,85,219);">(</span><span
style="color:rgb(188,143,143);">1</span><span
style="color:rgb(74,85,219);">)</span> <span
style="color:rgb(92,92,92);">=</span> <span
style="color:rgb(188,143,143);">1e16</span>
<br>
<span style="color:rgb(160,32,240);">for</span> <span
style="color:rgb(0,0,0);">k</span><span
style="color:rgb(92,92,92);">=</span><span
style="color:rgb(188,143,143);">1</span><span
style="color:rgb(255,170,0);">:</span><span
style="color:rgb(188,143,143);">5</span> <span
style="color:rgb(0,0,0);"><br>
x</span><span style="color:rgb(74,85,219);">(</span><span
style="color:rgb(0,0,0);">k</span><span
style="color:rgb(92,92,92);">+</span><span
style="color:rgb(188,143,143);">1</span><span
style="color:rgb(74,85,219);">)</span> <span
style="color:rgb(92,92,92);">=</span> <span
style="color:rgb(50,185,185);">nearfloat</span><span
style="color:rgb(74,85,219);">(</span><span
style="color:rgb(188,143,143);">"</span><span
style="color:rgb(188,143,143);">succ</span><span
style="color:rgb(188,143,143);">"</span><span
style="color:rgb(0,0,0);">,</span><span style="color:rgb(0,0,0);">x</span><span
style="color:rgb(74,85,219);">(</span><span
style="color:rgb(0,0,0);">k</span><span
style="color:rgb(74,85,219);">)</span><span
style="color:rgb(74,85,219);">)</span><span
style="color:rgb(0,0,0);">;</span>
<br>
<span style="color:rgb(160,32,240);">end</span>
<span style="color:rgb(74,85,219);"><br>
x</span><span style="color:rgb(74,85,219);"></span><br>
<font face="Courier New"><br>
yields (with format(25))<br>
<br>
10000000000000000. <br>
10000000000000002.<br>
10000000000000004.<br>
10000000000000006.<br>
10000000000000008.<br>
10000000000000010.<br>
<br>
Those few numbers have each a definite exact value and sin(x) has
also a definite exact value which seemingly is already well
approximated, unlike what I had previously supposed. For instance<br>
<br>
[x sin(x)]<br>
<br>
yields<br>
</font><br>
<font face="Courier New"><font face="Courier New">
10000000000000000. 0.779688006606978<u>7</u>8957 <br>
10000000000000002. -0.893837828765730<u>5</u>909519<br>
10000000000000004. -0.035752436952928<u>5</u>263036<br>
10000000000000006. 0.923594355839355<u>2</u>299535<br>
10000000000000008. -0.732949301917758<u>3</u>112977<br>
10000000000000010. -0.313565289154332<u>2</u>384749<br>
</font><br>
I have underlined the last correct digit compared with Alpha, so
it is the expected result with 16 digits.</font><font
face="Courier New"><br>
<br>
Regards,<br>
<br>
Federico Miyara<br>
</font><br>
<br>
<div class="moz-cite-prefix">On 06/01/2021 05:49, Stéphane Mottelet
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:f9f8ddfa-58dd-5496-af47-2fc3a13b1431@utc.fr">x =
(10^[1:16])*%pi<br>
sx = sin(x-floor(x/2/%pi)*%pi*2)<br>
plot("ln",x,sin(x),'-o',x,sx,'-o')<br>
legend("$\Large\sin x$","$\Large\sin
\left(x-2\pi\left\lfloor\frac{x}{2\pi}\right\rfloor\right)$",3)</blockquote>
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