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=={{header|Julia}}==
<syntaxhighlight lang="julia">struct""" PositType3{T<:Integer}Posit number, a quotient of integers, variable size and exponent length """
struct PositType3{T<:Integer}
numbits::UInt16
es::UInt16
Line 21 ⟶ 22:
end
 
""" FromConvert PositType3 to Rational. See also posithub.org/docs/Posits4.pdf """
function Base.Rational(p::PositType3)
s = signbit(signed(p.bits) ) # s for S signbit, is 1 if negative
pabs = p.bits << 1 # shiftShift off signbit (adds a 0 to F at LSB)
pabs == 0 && return s ? 1 // 0 : 0 // 1 # ifIf p is 0, return 0 or if s = 0,1 error if s = 1
expsign = signbits && (pabs) = (-p.bits) << 1) # exponent signIf fromp 2ndis bitnegative, nowflip into MSB2's locationcomplement
k = expsign == 1 ? leading_onessignbit(signed(pabs)) : leading_zeros(pabs) # regimeExponent Rsign from 2nd bit countnow MSB
scaling = 2^p.esr *= (expsign == 01 ? -1leading_ones(pabs) : 1leading_zeros(pabs) # r regime R size
pabs <<= (k + 1) = expsign ? r - 1 : -r # shiftk offfor unwantedthe Rexponent bitscalculation
pabs >><<= (kr + 21) # shift back withoutShift theoff extraunwanted LSBR bitbits
fsize pabs >>= p.numbits(r -+ k2) - p.es - 2 # check how many F bits are actually explicit # Shift back for E, F
fsize <= 0p.numbits && return 0 //- 1 - r - 1 - p.es # Check how # missingmany F isbits 0explicit
f = (pabse &= (2^fsize -< 1)) //? 2^fsizepabs : pabs >> fsize # Get F value. Can# beGet missingE -> 0value
e = pabsf >>= fsize < 1 ? 1 // 1 : 1 + (pabs & (2^fsize - 1)) // 2^fsize # Get EF value.
pw = (1 - 2s) * (scaling2^p.es * k + e + s)
return pw >= 0 ? ((-1 - 3s)^s +* f) * big"2"^pw // 1 : ((-1 - 3s)^s +* f) // big"2"^(-pw)
end
 
@show Rational(PositType3(16, 3, 0b0000110111011101)) == 477 // 134217728
const tests = [
</syntaxhighlight>{{out}} <pre> Rational(PositType3(16, 3, 0x0ddd)) == 477 // 134217728 = true</pre>
(16, 3, 0b0000110111011101),
(16, 3, 0b1000000000000000),
(16, 3, 0b0000000000000000),
(16, 1, 0b0110110010101000),
(16, 1, 0b1001001101011000),
(16, 2, 0b0000000000000001),
(16, 0, 0b0111111111111111),
(16, 6, 0b0111111111111110),
(8, 1, 0b01000000),
(8, 1, 0b11000000),
(8, 1, 0b00110000),
(8, 1, 0b00100000),
(8, 2, 0b00000001),
(8, 2, 0b01111111),
(8, 7, 0b01111110),
(32, 2, 0b00000000000000000000000000000001),
(32, 2, 0b01111111111111111111111111111111),
(32, 5, 0b01111111111111111111111111111110),
]
 
for t in tests
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^k*2^e*f]
]
setpositenv[{16, 3}];
p2x @ 2^^0000110111011101 // TraditionalForm
</syntaxhighlight>
 
{{out}}
 
<pre>477/134217728</pre>
 
=={{header|Phix}}==
Line 70 ⟶ 193:
<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;">kexponent</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8000000;">iff0</span><span style="color: #0000FF;">(,</span> <span style="color: #000000;">b2zfraction</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;">)0</span>
<span style="color: #008080004080;">ifatom</span> <span style="color: #000000;">rfs</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0useed</span> <span style="color: #0080800000FF;">and=</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b2z2</span><span style="color: #0000FF;">,</span><span style="color: #0080807060A8;">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;">then))</span>
<span style="color: #008080;">if</span> <span style="color: #008080000000;">ifr</span><span style="color: #0000FF;"><</span><span style="color: #000000;">s0</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">returnif</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">bitsb2z</span><span style="color: #0000FF;">,</span><span style="color: #008000008080;">"NaR"</span><span style="color: #0000FF;">}</span> <span style="color: #000080;font-style:italic;">-- aka infthen</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: #008080000000;">returnr</span> <span style="color: #0000FF;">{=</span> <span style="color: #000000;">bitsnbits</span><span style="color: #0000FF;">,-</span><span style="color: #008000;">"zero"</span><span style="color: #0000FF000000;">}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;">estartk</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;">31</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;">bitsibits</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>
Line 96 ⟶ 225:
<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: #000080;font-style:italic;">-- {16,0,0b0111111111111111}, -- nope</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>
Line 103 ⟶ 233:
<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: #000080;font-style:italic;">-- {8,2,0b01111111}, -- nope</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: #000080;font-style:italic;">-- {32,2,0b01111111111111111111111111111111<nowiki>}}</nowiki> -- nope</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) ==&gt; %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... and instead I've put in some bigger values, which are either wrong or prove that table on the wp page is wrong. (As I vaguely understand it, there is only an upper bound for a given es, but a bigger es will always give you a bigger number, at least until something breaks internally.)
<pre>
0000110111011101 (es=3) ==> 3.553926944e-6
1000000000000000 (es=3) ==> "NaR"
0000000000000000 (es=3) ==> "zero"
0110110010101000 (es=1) ==> 12.65625
11101100101010001001001101011000 (es=1) ==> -12.65625
0000000000000001 (es=2) ==> 1.38777878e-17
0111111111111111 (es=0) ==> 16384
0111111111111110 = 2.863890392e+250
0111111111111111 (es=2) ==> 7.205759404e+16
01000000 = 1
0111111111111110 (es=6) ==> 2.863890392e+250
11000000 = -1
01000000 (es=1) ==> 1
00110000 = 0.5
11000000 (es=1) ==> -1
00100000 = 0.25
00110000 (es=1) ==> 0.5
00000001 = 5.960464478e-8
00100000 (es=1) ==> 0.25
01111110 = 4.562440618e+192
00000001 (es=2) ==> 5.960464478e-8
00000000000000000000000000000001 = 7.523163846e-37
01111111 (es=2) ==> 16777216
01111111111111111111111111111110 = 2.269007734e+279
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|rakuRaku}}==
{{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:
<syntaxhighlight lang=raku>unit role Posit[UInt $N, UInt $es];
 
This copyright and permission notice shall be included in all copies or substantial portions of the software.
has UInt $.UInt;
method sign { self.UInt > 2**($N - 1) ?? -1 !! +1 }
 
THE SOFTWARE IS PROVIDED "AS IS" WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT
method FatRat {
LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN
return 0 if self.UInt == 0;
NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES, OR OTHER LIABILITY,
my UInt $mask = 2**($N - 1);
WHETHER IN AN ACTION OR CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
return Inf if self.UInt == $mask;
SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
my UInt $n = self.UInt;
=end LICENSE
my $sign = $n +& $mask ?? -1 !! +1;
my $r = $sign;
$n = ((2**$n - 1) +^ $n) + 1 if self.sign < 0;
my int $count = 0;
$mask +>= 1;
my Bool $first-bit = ?($n +& $mask);
repeat { $count++; $mask +>= 1;
} while ?($n +& $mask) == $first-bit && $mask;
my $m = $count;
my $k = $first-bit ?? $m - 1 !! -$m;
$r *= 2**($k*2**$es);
return $r unless $mask > 1;
$mask +>= 1;
$count = 0;
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;
 
constant nbits = 16;
return $r;
constant es = 3;
constant npat = 2**nbits;
constant useed = 2**2**es;
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..^2**nbits;
 
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-big}}
<syntaxhighlight lang="ecmascriptwren">import "./fmt" for Conv, Fmt
import "./big" for BigRat, BigInt
 
var posit16_decodepositDecode = 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 215 ⟶ 367:
}
var first = p[1]
var rs = 15n - 1 // regime size
for (i in 2..15.n) {
if (p[i] != first) {
rs = i - 1
Line 223 ⟶ 375:
}
var regime = p[1..rs]
var es = (rs == 15n - 1) ? 0 : maxExpSize.min(14n - 2 -rs) // actual exponent size
var exponent = [0]
if (es > 0) exponent = p[rs + 2...rs + 2 + es]
var fs = (es == 0) ? 0 : 14n - 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(maxExpSize))
var e = Conv.atoi(exponent.join(""), 2)
var f = BigRat.one
if (fs > 0) {
var fraction = psp.join("")[-fs..-1]
f = Conv.atoi(fraction.join(""), 2)
f = BigRat.one + BigRat.new(f, 2.pow(fs))
}
Line 240 ⟶ 392:
}
 
var pstests = "0000110111011101"[
[3, "0000110111011101"],
System.print(posit16_decode.call(ps, 3))</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>
PureFox
9,476

edits

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