Posit numbers/encoding: Difference between revisions

<syntaxhighlight lang="julia">struct""" PositType3{T<:Integer}Posit floating point numbers """

e = fsize < 1 ? pabs : pabs >> fsize # Get E value, then F value next line

f = fsize < 1 ? 1 // 1 : big"1" + (pabs & (2^fsize - 1)) // big"2"^fsize # Get F value

pw = 2^p.es * k + e # pw multiplier, power of 2 exponent

tindex = Int(round(log2(numbits / 8))) + 1 # choice of output type

typT = [UInt8, UInt16, UInt32, UInt64, UInt128][tindex]

x == 0 && return zero(typT) # bits for 0 if 0, Inf if Inf, etc

x in [-Inf, Inf, NaN] && return typemax(typT) - typemax((signed(typemax(typT))))

xabs = abs(x) # work with abs(x)

useed = 2^es # the useed

expopw = Int(floor(log2(xabs))) # x can be written as # xabs = 1.bits.. * 2^expopw

k, e = expnegk ?- k1, *e + useed + expo : expo - k * useed # e must be unsigned

rbitsr = expnegk < 0 ? (2^(r-k : k + 1) - 1) ⊻ 1 : 01 # r is number of R repetitions

fsizerbits = numbitspw ->= 10 -? (2^(r +1)-1) ⊻ 1 -: 01 # bit pattern of R esportion

pabsf = typround(f)(xabs |/ typ(e2^pw) <<- fsize1) |* typ(rbits2^fsize) <<# f (fsizemantissa - 1 as +binary esdigits)

#@showpabs s= expoT(f) expneg k| T(e r<< fsize) | T(BigInt(rbits) << (fsize f+ pabses)) # rbits | e | f

return s ? -pabs : pabs # S and two's complement if negative

posit16posit8(x, es = 2) = PositType3(168, 2, positbits(x, 168, es))

posit32posit16(x, es = 2) = PositType3(3216, 2, positbits(x, 3216, es))

posit64posit32(x, es = 2) = PositType3(6432, 2, positbits(x, 6432, es))

endingπending = floatBigFloat(Rational(p))

err = Float64(abs(πt - endingπending))

println("\nπn$t to $(p.numbits)-bit posit is $p.")

println("This posit with bits reinterpreted as integer is $i.")

println("This posit as float is $endingπending,\n with error $err.")

π0.0 to 8-bit posit is PositType3{UInt8}(0x0008, 0x0002, 0x4d0x00).

This posit with bits reinterpreted as integer is 770.

with error 0.1084073464102067610840734641020688.

π3.141592653589793 to 16-bit posit is PositType3{UInt16}(0x0010, 0x0002, 0x4c91).

This posit with bits reinterpreted as integer is 19601.

with error 8.908910206761538e908910206884002e-6.

π3.141592653589793 to 32-bit posit is PositType3{UInt32}(0x0020, 0x0002, 0x4c90fdaa).

This posit with bits reinterpreted as integer is 1284570538.

with error 1.984187159361081e984187036896401e-9.

π3.141592653589793 to 64-bit posit is PositType3{UInt64}(0x0040, 0x0002, 0x4c90fdaa22168c00).

This posit with bits reinterpreted as integer is 5517188450687028224.

This posit as float is 3.141592653589793115997963468544185161590576171875,

with error 10.2246467991473532e-160.

* Copyright © 2017 John L . Gustafson

positableQ[x_] := (Abs[x] == \[Infinity]∞ \[Or]|| x \[Element]∈ Reals)

y == 0, 0, (* all 0 bits s *)

y == ∞, BitShiftLeft[1, nbits - 1], (* 1 followed by all 0 bits s *)

p = 1; i = 2; (* Shift in 1s from the right and scale down. *)

While[y >= useed \[And]&&

p = 0; i = 1; (* Shift in 0s from the right and scale up. *)

While[y < 1 \[And]&& i <= nbits, {y, i} = {y useed, i + 1}];

While[e > 1/2 \[And]&& i <= nbits, p = 2 p;

While[y > 0 \[And]&& i <= nbits, y = 2 y;

p = 2 p + \[LeftFloor]y\[RightFloor]⌊y⌋;

y -= \[LeftFloor]y\[RightFloor]⌊y⌋; i++];

i = BitAnd[p, 1]; p = \[LeftFloor]p⌊p/2\[RightFloor]2⌋;

y == 1 \[Or]|| y == 0,

=={{header|rakuPhix}}==

<syntaxhighlight lang="ecmascriptwren">/* See original Mathematica example for copyright notice and comments. */