Posit numbers/decoding: Difference between revisions
→{{header|Phix}}
m (→{{header|Julia}}: simplify zero handling) |
|||
Line 41:
@show Rational(PositType3(16, 3, 0b0000110111011101)) == 477 // 134217728
</syntaxhighlight>{{out}} <pre> Rational(PositType3(16, 3, 0x0ddd)) == 477 // 134217728 = true</pre>
=={{header|Phix}}==
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">twos_compliment_2_on</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">bits</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">nbits</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">nbits</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">bits</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;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">bits</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: #008000;">'1'</span><span style="color: #0000FF;">:</span><span style="color: #008000;">'0'</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;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">nbits</span> <span style="color: #008080;">to</span> <span style="color: #000000;">2</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">bits</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: #008080;">then</span>
<span style="color: #000000;">bits</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: #008000;">'1'</span>
<span style="color: #008080;">exit</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">bits</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: #008000;">'0'</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">bits</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">posit_decode</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">nbits</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">es</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">object</span> <span style="color: #000000;">bits</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">--
-- nbits: number of bits (aka n)
-- es: exponent scale
-- bits: (binary) integer or string of nbits 0|1
--</span>
<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #004080;">string</span><span style="color: #0000FF;">(</span><span style="color: #000000;">bits</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<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;">"%%0%db"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nbits</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">bits</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">,</span><span style="color: #000000;">bits</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #7060A8;">assert</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">bits</span><span style="color: #0000FF;">)==</span><span style="color: #000000;">nbits</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">bits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">'1'</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">s</span> <span style="color: #008080;">then</span> <span style="color: #000000;">bits</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">twos_compliment_2_on</span><span style="color: #0000FF;">(</span><span style="color: #000000;">bits</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nbits</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">xor_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">bits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">],</span><span style="color: #000000;">1</span><span style="color: #0000FF;">),</span><span style="color: #000000;">bits</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">b2z</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">bits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">'0'</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b2z</span><span style="color: #0000FF;">?-</span><span style="color: #000000;">r</span><span style="color: #0000FF;">:</span><span style="color: #000000;">r</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">r</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0</span> <span style="color: #008080;">and</span> <span style="color: #000000;">b2z</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">s</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">bits</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"NaR"</span><span style="color: #0000FF;">}</span> <span style="color: #000080;font-style:italic;">-- aka inf</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">bits</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"zero"</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">estart</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">efinish</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">min</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">+</span><span style="color: #000000;">es</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nbits</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">exponent</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">to_integer</span><span style="color: #0000FF;">(</span><span style="color: #000000;">bits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">estart</span><span style="color: #0000FF;">..</span><span style="color: #000000;">efinish</span><span style="color: #0000FF;">],</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">fraction</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">to_integer</span><span style="color: #0000FF;">(</span><span style="color: #000000;">bits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">efinish</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..$],</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">useed</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">es</span><span style="color: #0000FF;">)),</span>
<span style="color: #000000;">fs</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nbits</span><span style="color: #0000FF;">-</span><span style="color: #000000;">efinish</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">iff</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: #0000FF;">:+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)*</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">useed</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">)*</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">exponent</span><span style="color: #0000FF;">)*(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">+</span><span style="color: #000000;">fraction</span><span style="color: #0000FF;">/</span><span style="color: #000000;">fs</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">bits</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;">function</span>
<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: #000000;">16</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b0000110111011101</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">16</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1000000000000000</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">16</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b0000000000000000</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">16</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b0110110010101000</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">16</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1001001101011000</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">16</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b0000000000000001</span><span style="color: #0000FF;">},</span>
<span style="color: #000080;font-style:italic;">-- {16,0,0b0111111111111111}, -- nope</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b01000000</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b11000000</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b00110000</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b00100000</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b00000001</span><span style="color: #0000FF;">},</span>
<span style="color: #000080;font-style:italic;">-- {8,2,0b01111111}, -- nope</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">32</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b00000000000000000000000000000001</span><span style="color: #0000FF;">}}</span>
<span style="color: #000080;font-style:italic;">-- {32,2,0b01111111111111111111111111111111<nowiki>}}</nowiki> -- nope</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">t</span> <span style="color: #008080;">in</span> <span style="color: #000000;">tests</span> <span style="color: #008080;">do</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;">"%s = %v\n"</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">call_func</span><span style="color: #0000FF;">(</span><span style="color: #000000;">posit_decode</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>
<!--</syntaxhighlight>-->
{{out}}
Be warned I could not get the largest positive values to match the Wikipedia page...
<pre>
0000110111011101 = 3.553926944e-6
1000000000000000 = "NaR"
0000000000000000 = "zero"
0110110010101000 = 12.65625
1110110010101000 = -12.65625
0000000000000001 = 1.38777878e-17
01000000 = 1
11000000 = -1
00110000 = 0.5
00100000 = 0.25
00000001 = 5.960464478e-8
00000000000000000000000000000001 = 7.523163846e-37
</pre>
=={{header|raku}}==
| |||