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Line 12: ~~=={{header\|raku}}==~~ =={{header\|Julia}}== ~~<syntaxhighlight lang=raku>unit role Posit[UInt $N, UInt $es];~~ <syntaxhighlight lang="julia">""" Posit number, a quotient of integers, variable size and exponent length """ struct PositType3{T<:Integer} numbits::UInt16 es::UInt16 bits::T PositType3(nb, ne, i) = new{typeof(i)}(UInt16(nb), UInt16(ne), i) end """ Convert PositType3 to Rational. See also posithub.org/docs/Posits4.pdf """ ~~has UInt $.UInt;~~ function Base.Rational(p::PositType3) ~~method sign { self.UInt > 2*($N - 1) ?? -1 !! +1 }~~ s = signbit(signed(p.bits)) # s for S signbit, is 1 if negative pabs = p.bits << 1 # Shift off signbit (adds a 0 to F at LSB) pabs == 0 && return s ? 1 // 0 : 0 // 1 # If p is 0, return 0 or if s 1 error s && (pabs = (-p.bits) << 1) # If p is negative, flip to 2's complement expsign = signbit(signed(pabs)) # Exponent sign from 2nd bit now MSB r = expsign == 1 ? leading_ones(pabs) : leading_zeros(pabs) # r regime R size k = expsign ? r - 1 : -r # k for the exponent calculation pabs <<= (r + 1) # Shift off unwanted R bits pabs >>= (r + 2) # Shift back for E, F fsize = p.numbits - 1 - r - 1 - p.es # Check how many F bits explicit e = fsize < 1 ? pabs : pabs >> fsize # Get E value f = fsize < 1 ? 1 // 1 : 1 + (pabs & (2^fsize - 1)) // 2^fsize # Get F value pw = 2^p.es k + e return pw >= 0 ? (-1)^s * f * big"2"^pw // 1 : (-1)^s * f // big"2"^(-pw) end @show Rational(PositType3(16, 3, 0b0000110111011101)) == 477 // 134217728 ~~method FatRat {~~ const tests = [ ~~return 0 if self.UInt == 0;~~ (16, 3, 0b0000110111011101), ~~my UInt $mask = 2($N - 1);~~ (16, 3, 0b1000000000000000), ~~return Inf if self.UInt == $mask;~~ (16, 3, 0b0000000000000000), ~~my UInt $n = self.UInt;~~ (16, 1, 0b0110110010101000), ~~my $sign = $n +& $mask ?? -1 !! +1;~~ (16, 1, 0b1001001101011000), ~~my $r = $sign;~~ (16, 2, 0b0000000000000001), ~~$n = ((2$n - 1) +^ $n) + 1 if self.sign < 0;~~ (16, 0, 0b0111111111111111), ~~my int $count = 0;~~ (16, 6, 0b0111111111111110), ~~$mask +>= 1;~~ (8, 1, 0b01000000), ~~my Bool $first-bit = ?($n +& $mask);~~ (8, 1, 0b11000000), ~~repeat { $count++; $mask +>= 1;~~ (8, 1, 0b00110000), ~~} while ?($n +& $mask) == $first-bit && $mask;~~ (8, 1, 0b00100000), ~~my $m = $count;~~ (8, 2, 0b00000001), ~~my $k = $first-bit ?? $m - 1 !! -$m;~~ $r = 2($k8, 2*$es, 0b01111111);, (8, 7, 0b01111110), ~~return $r unless $mask > 1;~~ (32, 2, 0b00000000000000000000000000000001), ~~$mask +>= 1;~~ (32, 2, 0b01111111111111111111111111111111), ~~$count = 0;~~ (32, 5, 0b01111111111111111111111111111110), ~~my UInt $exponent = 0;~~ ] ~~while $mask && $count++ < $es {~~ ~~$exponent +<= 1;~~ ~~$exponent +\|= 1 if $n +& $mask;~~ ~~$mask +>= 1;~~ } ~~$r = 2*$exponent;~~ ~~my $fraction = 1.FatRat;~~ ~~while $mask {~~ ~~(state $power-of-two = 1) +<= 1;~~ ~~$fraction += 1/$power-of-two if $n +& $mask;~~ ~~$mask +>= 1;~~ } ~~$r = $fraction;~~ for t in tests ~~return $r;~~ r = Rational(PositType3(t...)) println(string(t[3], base = 2, pad = t[1]), " => $r = ", float(r)) end </syntaxhighlight>{{out}} <pre> Rational(PositType3(16, 3, 0x0ddd)) == 477 // 134217728 = true 0000110111011101 => 477//134217728 = 3.553926944732666015625e-06 1000000000000000 => 1//0 = Inf 0000000000000000 => 0//1 = 0.0 0110110010101000 => 405//32 = 12.65625 1001001101011000 => -405//32 = -12.65625 0000000000000001 => 1//72057594037927936 = 1.387778780781445675529539585113525390625e-17 0111111111111111 => 16384//1 = 16384.0 0111111111111110 => 28638903918474961204418783933674838490721739172170652529441449702311064005352904159345284265824628375429359509218999720074396860757073376700445026041564579620512874307979212102266801261478978776245040008231745247475930553606737583615358787106474295296//1 = 2.86389039184749612044187839336748384907217391721706525294414497023110640053529e+250 01000000 => 1//1 = 1.0 11000000 => -1//1 = -1.0 00110000 => 1//2 = 0.5 00100000 => 1//4 = 0.25 00000001 => 1//16777216 = 5.9604644775390625e-08 01111111 => 16777216//1 = 1.6777216e+07 01111110 => 4562440617622195218641171605700291324893228507248559930579192517899275167208677386505912811317371399778642309573594407310688704721375437998252661319722214188251994674360264950082874192246603776//1 = 4.562440617622195218641171605700291324893228507248559930579192517899275167208677e+192 00000000000000000000000000000001 => 1//1329227995784915872903807060280344576 = 7.523163845262640050999913838222372338039459563341360137656010920181870460510254e-37 01111111111111111111111111111111 => 1329227995784915872903807060280344576//1 = 1.329227995784915872903807060280344576e+36 01111111111111111111111111111110 => 2269007733883335972287082669296112915239349672942191252221331572442536403137824056312817862695551072066953619064625508194663368599769448406663254670871573830845597595897613333042429214224697474472410882236254024057110212260250671521235807709272244389361641091086035023229622419456//1 = 2.269007733883335972287082669296112915239349672942191252221331572442536403137824e+279 </pre> =={{header\|Mathematica}}== Using code written by John Gustafson himself. Reproduced here with minor, mainly stylistic modifications (mostly to convert graphical symbols to their text equivalent). License is included as legally required by copyright laws. <syntaxhighlight lang="mathematica">(* Copyright © 2017 John L. Gustafson Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sub-license, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: This copyright and permission notice shall be included in all copies or substantial portions of the software. THE SOFTWARE IS PROVIDED "AS IS" WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES, OR OTHER LIABILITY, WHETHER IN AN ACTION OR CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. ) setpositenv[{n_Integer /; n >= 2, e_Integer /; e >= 0}] := ( {nbits, es} = {n, e}; npat = 2^nbits; useed = 2^2^es; {minpos, maxpos} = {useed^(-nbits + 2), useed^(nbits - 2)}; qsize = Power[2, Ceiling[Log[2, (nbits - 2) 2^(es + 2) + 5]]]; qextra = qsize - (nbits - 2) 2^(es + 2); ) positQ[p_Integer] := 0 <= p < npat twoscomp[sign_, p_] := Mod[If[sign > 0, p, npat - p], npat] signbit[p_ /; positQ[p]] := IntegerDigits[p, 2, nbits][[1]] regimebits[p_ /; positQ[p]] := Module[ {q = twoscomp[1 - signbit[p], p], bits, bit2, npower, tempbits}, bits = IntegerDigits[q, 2, nbits]; bit2 = bits[[2]]; ( Look for the run length after the sign bit. ) tempbits = Join[Drop[bits, 1], {1 - bit2}]; ( Drop the sign bit, but append a complement bit as a sure-fire way to end the run. ) npower = (Position[tempbits, 1 - bit2, 1, 1])[[1]] - 1; ( Find first opposite bit. ) Take[bits, {2, Min[npower + 1, nbits]}] ] regimevalue[bits_] := If[bits[[1]] == 1, Length[bits] - 1, -Length[bits]] exponentbits[p_ /; positQ[p]] := Module[{q = twoscomp[1 - signbit[p], p], bits, startbit}, startbit = Length[regimebits[q]] + 3; bits = IntegerDigits[q, 2, nbits]; If[startbit > nbits, {}, Take[bits, {startbit, Min[startbit + es - 1, nbits]}]]] fractionbits[p_ /; positQ[p]] := Module[{q = twoscomp[1 - signbit[p], p], bits, startbit}, startbit = Length[regimebits[q]] + 3 + es; bits = IntegerDigits[q, 2, nbits]; If[startbit > nbits, {}, Take[bits, {startbit, nbits}]]] p2x[p_ /; positQ[p]] := Module[{s = (-1)^signbit[p], k = regimevalue[regimebits[p]], e = exponentbits[p], f = fractionbits[p]}, e = Join[e, Table[0, es - Length[e]]]; ( Pad with 0s on the right if they are clipped off. ) e = FromDigits[e, 2]; If[f == {}, f = 1, f = 1 + FromDigits[f, 2] 2^(-Length[f])]; Which[ p == 0, 0, p == npat/2, ComplexInfinity, ( The two exception values, 0 and \[PlusMinus]\[Infinity] ) True, s useed^k2^ef] ] setpositenv[{16, 3}]; p2x @ 2^^0000110111011101 // TraditionalForm </syntaxhighlight> {{out}} <pre>477/134217728</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;">string</span> <span style="color: #000000;">ibits</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">bits</span> <span style="color: #000080;font-style:italic;">-- save for return</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;">exponent</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">fraction</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">fs</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</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: #008080;">if</span> <span style="color: #000000;">r</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">if</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;">ibits</span><span style="color: #0000FF;">,</span><span style="color: #000000;">es</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;">ibits</span><span style="color: #0000FF;">,</span><span style="color: #000000;">es</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: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">nbits</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">else</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: #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: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #004080;">integer</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: #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;">ibits</span><span style="color: #0000FF;">,</span><span style="color: #000000;">es</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: #0000FF;">{</span><span style="color: #000000;">16</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b0111111111111111</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;">0b0111111111111111</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;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b0111111111111110</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;">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: #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;">0b01111111</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;">7</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b01111110</span><span style="color: #0000FF;">},</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: #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;">0b01111111111111111111111111111111</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">32</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b01111111111111111111111111111110</span><span style="color: #0000FF;">}}</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 (es=%d) ==> %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}} <pre> 0000110111011101 (es=3) ==> 3.553926944e-6 1000000000000000 (es=3) ==> "NaR" 0000000000000000 (es=3) ==> "zero" 0110110010101000 (es=1) ==> 12.65625 1001001101011000 (es=1) ==> -12.65625 0000000000000001 (es=2) ==> 1.38777878e-17 0111111111111111 (es=0) ==> 16384 0111111111111111 (es=2) ==> 7.205759404e+16 0111111111111110 (es=6) ==> 2.863890392e+250 01000000 (es=1) ==> 1 11000000 (es=1) ==> -1 00110000 (es=1) ==> 0.5 00100000 (es=1) ==> 0.25 00000001 (es=2) ==> 5.960464478e-8 01111111 (es=2) ==> 16777216 01111110 (es=7) ==> 4.562440618e+192 00000000000000000000000000000001 (es=2) ==> 7.523163846e-37 01111111111111111111111111111111 (es=2) ==> 1.329227996e+36 01111111111111111111111111111110 (es=5) ==> 2.269007734e+279 </pre> =={{header\|Raku}}== {{trans\|Mathematica}} <syntaxhighlight lang=raku>=begin LICENSE Copyright © 2017 John L. Gustafson Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sub-license, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: This copyright and permission notice shall be included in all copies or substantial portions of the software. THE SOFTWARE IS PROVIDED "AS IS" WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES, OR OTHER LIABILITY, WHETHER IN AN ACTION OR CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. =end LICENSE constant nbits = 16; constant es = 3; constant npat = 2nbits; constant useed = 22es; constant minpos = useed(-nbits + 2); constant maxpos = useed(+nbits - 2); constant qsize = 2((nbits-2)2(es+2)+5).log2.ceiling; constant qextra = qsize - (nbits - 2)2(es+2); constant posit-range = 0..^2nbits; sub twoscomp($sign, $p) { ($sign > 0 ?? $p !! npat - $p) mod npat } sub sign-bit(UInt $p where posit-range) { +$p.polymod(2 xx nbits - 1).tail } sub regime-bits(UInt $p where posit-range) { my $q = twoscomp(1 - sign-bit($p), $p); my @bits = $q.polymod(2 xx nbits - 1).reverse; my $bit2 = @bits[1]; my @temp-bits = flat @bits[1..], 1 - $bit2; my $npower = @temp-bits.first(1 - $bit2, :k) - 1; @bits[1..($npower+1)]; } sub regime-value(@bits) { @bits.head ?? @bits.elems - 1 !! -@bits; } sub exponent-bits(UInt $p where posit-range) { my $q = twoscomp(1 - sign-bit($p), $p); my $startbit = regime-bits($q).elems + 3; my @bits = $q.polymod(2 xx nbits - 1).reverse; @bits[$startbit-1 .. $startbit-1 + es - 1] } sub fraction-bits(UInt $p where posit-range) { my $q = twoscomp(1 - sign-bit($p), $p); my $startbit = regime-bits($q).elems + 3 + es; my @bits = $q.polymod(2 xx nbits - 1).reverse; @bits[$startbit-1 .. ]; } sub p2x(UInt $p where posit-range) { ~~CHECK {~~ my $s = (-1)*sign-bit($p); ~~use Test;~~ my $k = regime-value regime-bits $p; ~~# example from L<http://www.johngustafson.net/pdfs/BeatingFloatingPoint.pdf>~~ my @e = exponent-bits $p; ~~is Posit[16, 3]~~ my @f = fraction-bits $p; ~~.new(UInt => 0b0000110111011101)~~ @e.push: 0 until @e == es; ~~.FatRat, 477.FatRat/134217728;~~ my $e = @e.reduce: 2 * + ; ~~}</syntaxhighlight>~~ my $f = @f == 0 ?? 1 !! 1.FatRat + @f.reduce(2 * + )/2@f; given $p { when 0 { 0 } when npat div 2 { Inf } default { $s useed*$k 2*$e $f } } } dd p2x 0b0000110111011101; </syntaxhighlight> {{out}} <pre>okFatRat.new(477, ~~1 -~~134217728)</pre> =={{header\|Wren}}== {{libheader\|Wren-fmt}} {{libheader\|Wren-~~rat~~big}} <syntaxhighlight lang="~~ecmascript~~wren">import "./fmt" for Conv, Fmt import "./~~rat~~big" for ~~Rat~~BigRat, BigInt var ~~posit16_decode~~positDecode = Fn.new { \|ps, maxExpSize\| var p = ps.map { \|c\| c == "0" ? 0 : 1 }.toList // Deal with exceptional values. if (p[1..-1].all { \|i\| i == 0 }) { return (p[0] == 0) ? 0BigRat.zero : Conv.infinity } // Convert bits after sign bit to two's complement if negative. var n = p.count if (p[0] == 1) { for (i in 1..15.n) p[i] = (p[i] == 0) ? 1 : 0 for (i in 15n-1..1) { if (p[i] == 1) { p[i] = 0 Line 94 ⟶ 366: } } var first = p[1] var rs = n - 1 // regime size for (i in 2..15.n) { if (p[i] != first) { rs = i - 1 Line 104 ⟶ 375: } var regime = p[1..rs] var es = 3(rs == n - 1) ? 0 : maxExpSize.min(14n - 2 -rs) // actual exponent size~~, maximum is 3.~~ var exponent = [0] if (es > 0) exponent = p[rs + 2...rs + 2 + es] var fs = 14(es == 0) ? 0 : n - 2 - rs - es // function size var s = (p[0] == 0) ? 1 : -1 // sign var k = regime.all { \|i\| i == 0 } ? -rs : rs - 1 var u = 2BigInt.two.pow(2.pow(esmaxExpSize)) var e = Conv.atoi(exponent.join(""), 2) var f = ~~Rat~~BigRat.~~zero~~one if (fs > 0) { var fraction = psp.join("")[-fs..-1] f = Conv.atoi(fraction~~.join("")~~, 2) f = ~~Rat~~BigRat.one + ~~Rat~~BigRat.new(f, u2.pow(fs)) } return f * ~~Rat~~BigRat.new(u, 1).pow(k) * s * 2.pow(e) } var pstests = ~~"0000110111011101"~~[ [3, "0000110111011101"], ~~System.print(posit16_decode.call(ps))</syntaxhighlight>~~ [3, "1000000000000000"], [3, "0000000000000000"], [1, "0110110010101000"], [1, "1001001101011000"], [2, "0000000000000001"], [0, "0111111111111111"], [6, "0111111111111110"], [1, "01000000"], [1, "11000000"], [1, "00110000"], [1, "00100000"], [2, "00000001"], [2, "01111111"], [7, "01111110"], [2, "00000000000000000000000000000001"], [2, "01111111111111111111111111111111"], [5, "01111111111111111111111111111110"] ] for (test in tests) { var res = positDecode.call(test[1], test[0]) var res2 = (res is BigRat) ? res.toFloat : Num.infinity Fmt.print("$s(es = $d) -> $s or $n", test[1], test[0], res, res2) }</syntaxhighlight> {{out}} <pre> 0000110111011101(es = 3) -> 477/134217728 or 3.5539269447327e-06 1000000000000000(es = 3) -> ∞ or infinity 0000000000000000(es = 3) -> 0/1 or 0 0110110010101000(es = 1) -> 405/32 or 12.65625 1001001101011000(es = 1) -> -405/32 or -12.65625 0000000000000001(es = 2) -> 1/72057594037927936 or 1.3877787807814e-17 0111111111111111(es = 0) -> 16384/1 or 16384 0111111111111110(es = 6) -> 28638903918474961204418783933674838490721739172170652529441449702311064005352904159345284265824628375429359509218999720074396860757073376700445026041564579620512874307979212102266801261478978776245040008231745247475930553606737583615358787106474295296/1 or 2.8638903918475e+250 01000000(es = 1) -> 1/1 or 1 11000000(es = 1) -> -1/1 or -1 00110000(es = 1) -> 1/2 or 0.5 00100000(es = 1) -> 1/4 or 0.25 00000001(es = 2) -> 1/16777216 or 5.9604644775391e-08 01111111(es = 2) -> 16777216/1 or 16777216 01111110(es = 7) -> 4562440617622195218641171605700291324893228507248559930579192517899275167208677386505912811317371399778642309573594407310688704721375437998252661319722214188251994674360264950082874192246603776/1 or 4.5624406176222e+192 00000000000000000000000000000001(es = 2) -> 1/1329227995784915872903807060280344576 or 7.5231638452626e-37 01111111111111111111111111111111(es = 2) -> 1329227995784915872903807060280344576/1 or 1.3292279957849e+36 01111111111111111111111111111110(es = 5) -> 2269007733883335972287082669296112915239349672942191252221331572442536403137824056312817862695551072066953619064625508194663368599769448406663254670871573830845597595897613333042429214224697474472410882236254024057110212260250671521235807709272244389361641091086035023229622419456/1 or 2.2690077338833e+279 </pre>