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[diderot] Annotation of /trunk/src/compiler/IL/kernel.sml
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Annotation of /trunk/src/compiler/IL/kernel.sml

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1 : jhr 108 (* kernel.sml
2 :     *
3 :     * COPYRIGHT (c) 2010 The Diderot Project (http://diderot.cs.uchicago.edu)
4 :     * All rights reserved.
5 : jhr 117 *
6 :     * QUESTION: should we
7 : jhr 108 *)
8 :    
9 :     structure Kernel : sig
10 :    
11 : jhr 117 type coefficient = Rational.rat
12 : jhr 108
13 :     (* polynomial represented as list of coefficients, where ith element is
14 :     * coefficient for x^i.
15 :     *)
16 :     type polynomial = coefficient list
17 :    
18 :     type kernel = {
19 :     support : int, (* number of samples to left/right *)
20 : jhr 117 segs : polynomial list, (* piece-wise polynomial that defines the kernel. Since *)
21 :     (* a kernel is symmetric, we only store the positive *)
22 :     (* segments, with segs[i] covering the domain [i,i+1) *)
23 : jhr 108 }
24 :    
25 :     val differentiate : polynomial -> polynomial
26 :    
27 : jhr 117 val evaluate : polynomial * int -> Rational.rat
28 : jhr 108
29 :     end = struct
30 :    
31 : jhr 117 structure R = Rational
32 : jhr 108
33 : jhr 117 type coefficient = R.rat
34 : jhr 108
35 : jhr 117 val zero = R.fromInt 0
36 :     val one = R.fromInt 1
37 :    
38 : jhr 108 (* polynomial represented as list of coefficients, where ith element is
39 :     * coefficient for x^i.
40 :     *)
41 :     type polynomial = coefficient list
42 :    
43 :     type kernel = {
44 :     support : int, (* number of samples to left/right *)
45 :     segs : polynomial list, (* piece-wise polynomial that defines the *)
46 :     (* kernel; there are 2*support segments *)
47 :     }
48 :    
49 :     fun differentiate [] = raise Fail "invalid polynomial"
50 : jhr 117 | differentiate [_] = [zero]
51 : jhr 108 | differentiate (_::coeffs) = let
52 :     fun lp (_, []) = []
53 : jhr 117 | lp (i, c::r) = R.mul(F.fromInt i, c) :: lp(i+1, r)
54 : jhr 108 in
55 :     lp (1, coeffs)
56 :     end
57 :    
58 :     (* evaluate a polynomial at an integer coordinate (used to test continuity) *)
59 :     fun evaluate (poly, x) = let
60 :     val x = F.fromInt x
61 :     fun eval (sum, [], xn) = sum
62 : jhr 117 | eval (sum, c::r, xn) = eval(F.add(sum, R.mul(c, xn)), r, R.mul(x, xn))
63 : jhr 108 in
64 : jhr 117 eval (zero, poly, one)
65 : jhr 108 end
66 :    
67 : jhr 117 (* some standard kernels *)
68 :     local
69 :     val op / = R./
70 :     fun r i = R.fromInt i
71 :     in
72 :     val tent : kernel = { (* linear interpolation *)
73 :     support = 1,
74 :     segs = [[r 1, r ~1]]
75 :     }
76 :     val ctmr : kernel = { (* Catmull-Rom interpolation *)
77 :     support = 2,
78 :     segs = [
79 :     [r 1, r 0, ~5/2, 3/2],
80 :     [r 2, r ~4, 5/2, ~1/2]
81 :     ]
82 :     }
83 :     val bspl3 : kernel = { (* cubic bspline reconstruction, doesn't interpolate *)
84 :     support = 2,
85 :     segs = [
86 :     [ 2/3, 0, -1, 1/2 ],
87 :     [ 4/3, -2, 1, ~1/6 ]'
88 :     ]
89 :     }
90 :     val bspl5 : kernel = { (* quintic bspline reconstruction, doesn't interpolate *)
91 :     support = 3,
92 :     segs = [
93 :     [ 11/20, r 0, ~1/2, r 0, 1/4, ~1/12 ],
94 :     [ 17/40, 5/8, ~7/4, 5/4, ~3/8, 1/24 ]
95 :     [ 81/40, ~27/8, 9/4, ~3/4, 1/8, ~1/120 ]
96 :     ]
97 :     }
98 :     end
99 :    
100 : jhr 108 end

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