AbstractAlgebra's polynomial interface
This is the initial API of SLPs which hasn't been updated in a while and might not work as-is with the current state of the package.
Currently, SLPs have a polynomial interface (SLPoly).
Examples
julia> using AbstractAlgebra, StraightLinePrograms, BenchmarkTools;
julia> S = SLPolyRing(zz, [:x, :y]); x, y = gens(S)
2-element Vector{SLPoly{Int64,SLPolyRing{Int64,AbstractAlgebra.Integers{Int64}}}}:
x
y
julia> p = 3 + 2x * y^2 # each line of the SLP is shown with current value
#1 = * 2 x ==> (2x)
#2 = ^ y 2 ==> y^2
#3 = * #1 #2 ==> (2xy^2)
#4 = + 3 #3 ==> (3 + (2xy^2))
julia> p.cs # constants used in the program
2-element Vector{Int64}:
3
2
julia> p.lines # each line is a UInt64 encoding an opcode and 2 arguments
Line(0x0500000028000001)
Line(0x8780000020000002)
Line(0x0500000030000004)
Line(0x0300000010000005)
julia> SLP.evaluate(p, [2, 3])
39
julia> p2 = (p*(x*y))^6
#1 = * 2 x ==> (2x)
#2 = ^ y 2 ==> y^2
#3 = * #1 #2 ==> (2xy^2)
#4 = + 3 #3 ==> (3 + (2xy^2))
#5 = * x y ==> (xy)
#6 = * #4 #5 ==> ((3 + (2xy^2))xy)
#7 = ^ #6 6 ==> ((3 + (2xy^2))xy)^6
julia> R, (x1, y1) = polynomial_ring(zz, [:x, :y]); R
Multivariate Polynomial Ring in x, y over Integers
julia> q = convert(R, p2)
64*x^12*y^18+576*x^11*y^16+2160*x^10*y^14+4320*x^9*y^12+4860*x^8*y^10+2916*x^7*y^8+729*x^6*y^6
julia> v = [3, 5]; @btime SLP.evaluate($q, $v)
32.101 μs (634 allocations: 45.45 KiB)
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julia> @btime SLP.evaluate($p2, $v)
270.341 ns (4 allocations: 352 bytes)
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julia> res = Int[]; @btime StraightLinePrograms.evaluate!($res, $p2, $v)
171.013 ns (0 allocations: 0 bytes)
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julia> res # intermediate computations (first 2 elements are constants)
9-element Vector{Int64}:
3
2
6
25
150
153
15
2295
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julia> f2 = StraightLinePrograms.compile!(p2) # compile to machine code
#3 (generic function with 1 method)
julia> @btime SLP.evaluate($p2, $v)
31.153 ns (1 allocation: 16 bytes)
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julia> @btime $f2($v) # use a function barrier for last bit of efficiency
7.980 ns (0 allocations: 0 bytes)
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julia> q
64*x^12*y^18+576*x^11*y^16+2160*x^10*y^14+4320*x^9*y^12+4860*x^8*y^10+2916*x^7*y^8+729*x^6*y^6
julia> p3 = convert(S, q) # convert back q::Mpoly to an SLPoly
#1 = ^ x 6 ==> x^6
#2 = ^ x 7 ==> x^7
#3 = ^ x 8 ==> x^8
#4 = ^ x 9 ==> x^9
#5 = ^ x 10 ==> x^10
#6 = ^ x 11 ==> x^11
#7 = ^ x 12 ==> x^12
#8 = ^ y 6 ==> y^6
#9 = ^ y 8 ==> y^8
#10 = ^ y 10 ==> y^10
#11 = ^ y 12 ==> y^12
#12 = ^ y 14 ==> y^14
#13 = ^ y 16 ==> y^16
#14 = ^ y 18 ==> y^18
#15 = * 64 #7 ==> (64x^12)
#16 = * #15 #14 ==> (64x^12y^18)
#17 = * 576 #6 ==> (576x^11)
#18 = * #17 #13 ==> (576x^11y^16)
#19 = + #16 #18 ==> ((64x^12y^18) + (576x^11y^16))
#20 = * 2160 #5 ==> (2160x^10)
#21 = * #20 #12 ==> (2160x^10y^14)
#22 = + #19 #21 ==> ((64x^12y^18) + (576x^11y^16) + (2160x^10y^14))
#23 = * 4320 #4 ==> (4320x^9)
#24 = * #23 #11 ==> (4320x^9y^12)
#25 = + #22 #24 ==> ((64x^12y^18) + (576x^11y^16) + (2160x^10y^14) + (4320x^9y^12))
#26 = * 4860 #3 ==> (4860x^8)
#27 = * #26 #10 ==> (4860x^8y^10)
#28 = + #25 #27 ==> ((64x^12y^18) + (576x^11y^16) + (2160x^10y^14) + (4320x^9y^12) + (4860x^8y^10))
#29 = * 2916 #2 ==> (2916x^7)
#30 = * #29 #9 ==> (2916x^7y^8)
#31 = + #28 #30 ==> ((64x^12y^18) + (576x^11y^16) + (2160x^10y^14) + (4320x^9y^12) + (4860x^8y^10) + (2916x^7y^8))
#32 = * 729 #1 ==> (729x^6)
#33 = * #32 #8 ==> (729x^6y^6)
#34 = + #31 #33 ==> ((64x^12y^18) + (576x^11y^16) + (2160x^10y^14) + (4320x^9y^12) + (4860x^8y^10) + (2916x^7y^8) + (729x^6y^6))
julia> @btime SLP.evaluate($p3, $v)
699.465 ns (5 allocations: 1008 bytes)
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julia> @time f3 = StraightLinePrograms.compile!(p3);
0.002830 seconds (1.40 k allocations: 90.930 KiB)
julia> @btime $f3($v)
80.229 ns (0 allocations: 0 bytes)
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julia> p4 = convert(S, q, limit_exp=true); # use different encoding
julia> @btime SLP.evaluate($p4, $v)
766.864 ns (5 allocations: 1008 bytes)
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julia> @time f4 = StraightLinePrograms.compile!(p4);
0.002731 seconds (1.74 k allocations: 108.676 KiB)
julia> @btime $f4($v)
11.781 ns (0 allocations: 0 bytes)
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