Let's show an example of generating code for curve25519 field inversion. Search for the best addition chain and save the result:
addchain search '2^255 - 19 - 2' > inv.accNow we can use the addchain generate command to generate code to
execute the addition chain. By default, the generate command will show us a
concise listing of the instructions required to compute the addition chain.
addchain gen inv.accOutput:
tmp t0 t1 t2 t3 t4
double t0 x
add t0 x t0
shift t1 t0 2
add t1 t0 t1
shift t2 t1 4
add t1 t1 t2
shift t1 t1 2
add t1 t0 t1
shift t2 t1 10
add t2 t1 t2
shift t2 t2 10
add t2 t1 t2
shift t3 t2 30
add t2 t2 t3
shift t3 t2 60
add t2 t2 t3
shift t3 t2 120
add t2 t2 t3
shift t2 t2 10
add t1 t1 t2
shift t1 t1 2
add t4 x t1
shift t4 t4 3
add z t0 t4
This listing is intended to be a simple text format that could directly be turned into code. The directives mean:
tmp v ...: declare temporary variablesv ...add z x y: execute additionz = x+ydouble z x: execute doublingz = 2*xshift z x n: execute repeated doublingz = 2n*x
Under the hood, addchain has processed the addition chain into the ir.Program intermediate representation and used an allocation
pass to assign the minimum number of temporary variables. The listing format is
intended be a convient and easy-to-parse text format to use as input to other
tools.
In addition, addchain also offers templated output. In fact, the
listing is actually produced by the listing builtin template. See
below for details of the templating language
and builtin template examples. The following template
can be used to directly produce Go code to execute the inversion chain:
// Code generated by {{ .Meta.Name }}. DO NOT EDIT.
package fp25519
// Inv computes z = 1/x (mod p) and returns it.
func (z *Elt) Inv(x *Elt) *Elt {
// Inversion computation is derived from the addition chain:
//
{{- range lines (format .Script) }}
// {{ . }}
{{- end }}
//
// Operations: {{ .Ops.Doubles }} squares {{ .Ops.Adds }} multiplies
//
// Generated by {{ .Meta.Module }} {{ .Meta.ReleaseTag }}.
// Allocate Temporaries.
var (
{{- range .Program.Temporaries }}
{{ . }} = new(Elt)
{{- end -}}
)
{{ range $i := .Program.Instructions }}
// {{ printf "Step %d: %s = x^%#x" $i.Output.Index $i.Output (index $.Chain $i.Output.Index) }}
{{- with add $i.Op }}
{{ $i.Output }}.Mul({{ .X }}, {{ .Y }})
{{ end -}}
{{- with double $i.Op }}
{{ $i.Output }}.Sqr({{ .X }})
{{ end -}}
{{- with shift $i.Op -}}
{{- $first := 0 -}}
{{- if ne $i.Output.Identifier .X.Identifier }}
{{ $i.Output }}.Sqr({{ .X }})
{{- $first = 1 -}}
{{- end }}
for s := {{ $first }}; s < {{ .S }}; s++ {
{{ $i.Output }}.Sqr({{ $i.Output }})
}
{{ end -}}
{{- end }}
return z
}
Generate code by passing the template to addchain:
addchain gen -tmpl inv.tmpl inv.acc | gofmt > inv.goThe end product:
// Code generated by addchain. DO NOT EDIT.
package fp25519
// Inv computes z = 1/x (mod p) and returns it.
func (z *Elt) Inv(x *Elt) *Elt {
// Inversion computation is derived from the addition chain:
//
// _10 = 2*1
// _11 = 1 + _10
// _1100 = _11 << 2
// _1111 = _11 + _1100
// _11110000 = _1111 << 4
// _11111111 = _1111 + _11110000
// x10 = _11111111 << 2 + _11
// x20 = x10 << 10 + x10
// x30 = x20 << 10 + x10
// x60 = x30 << 30 + x30
// x120 = x60 << 60 + x60
// x240 = x120 << 120 + x120
// x250 = x240 << 10 + x10
// return (x250 << 2 + 1) << 3 + _11
//
// Operations: 254 squares 12 multiplies
//
// Generated by github.com/mmcloughlin/addchain v0.4.0.
// Allocate Temporaries.
var (
t0 = new(Elt)
t1 = new(Elt)
t2 = new(Elt)
t3 = new(Elt)
t4 = new(Elt)
)
// Step 1: t0 = x^0x2
t0.Sqr(x)
// Step 2: t0 = x^0x3
t0.Mul(x, t0)
// Step 4: t1 = x^0xc
t1.Sqr(t0)
for s := 1; s < 2; s++ {
t1.Sqr(t1)
}
// Step 5: t1 = x^0xf
t1.Mul(t0, t1)
// Step 9: t2 = x^0xf0
t2.Sqr(t1)
for s := 1; s < 4; s++ {
t2.Sqr(t2)
}
// Step 10: t1 = x^0xff
t1.Mul(t1, t2)
// Step 12: t1 = x^0x3fc
for s := 0; s < 2; s++ {
t1.Sqr(t1)
}
// Step 13: t1 = x^0x3ff
t1.Mul(t0, t1)
// Step 23: t2 = x^0xffc00
t2.Sqr(t1)
for s := 1; s < 10; s++ {
t2.Sqr(t2)
}
// Step 24: t2 = x^0xfffff
t2.Mul(t1, t2)
// Step 34: t2 = x^0x3ffffc00
for s := 0; s < 10; s++ {
t2.Sqr(t2)
}
// Step 35: t2 = x^0x3fffffff
t2.Mul(t1, t2)
// Step 65: t3 = x^0xfffffffc0000000
t3.Sqr(t2)
for s := 1; s < 30; s++ {
t3.Sqr(t3)
}
// Step 66: t2 = x^0xfffffffffffffff
t2.Mul(t2, t3)
// Step 126: t3 = x^0xfffffffffffffff000000000000000
t3.Sqr(t2)
for s := 1; s < 60; s++ {
t3.Sqr(t3)
}
// Step 127: t2 = x^0xffffffffffffffffffffffffffffff
t2.Mul(t2, t3)
// Step 247: t3 = x^0xffffffffffffffffffffffffffffff000000000000000000000000000000
t3.Sqr(t2)
for s := 1; s < 120; s++ {
t3.Sqr(t3)
}
// Step 248: t2 = x^0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
t2.Mul(t2, t3)
// Step 258: t2 = x^0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc00
for s := 0; s < 10; s++ {
t2.Sqr(t2)
}
// Step 259: t1 = x^0x3ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
t1.Mul(t1, t2)
// Step 261: t1 = x^0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc
for s := 0; s < 2; s++ {
t1.Sqr(t1)
}
// Step 262: t4 = x^0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd
t4.Mul(x, t1)
// Step 265: t4 = x^0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe8
for s := 0; s < 3; s++ {
t4.Sqr(t4)
}
// Step 266: z = x^0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeb
z.Mul(t0, t4)
return z
}This code is part of a full working example that passes tests.
Templates use Go text/template syntax. The data structure passed
to the template is:
type Data struct {
// Chain is the addition chain as a list of integers.
Chain addchain.Chain
// Ops is the complete sequence of addition operations required to compute
// the addition chain.
Ops addchain.Program
// Script is the condensed representation of the addition chain computation
// in the "addition chain calculator" language.
Script *ast.Chain
// Program is the intermediate representation of the addition chain
// computation. This representation is likely the most convenient for code
// generation. It contains a sequence of add, double and shift (repeated
// doubling) instructions required to compute the chain. Temporary variable
// allocation has been performed and the list of required temporaries
// populated.
Program *ir.Program
// Metadata about the addchain project and the specific release parameters.
// Please use this to include a reference or citation back to the addchain
// project in your generated output.
Meta *meta.Properties
}In addition to the builtin functions, templates may use:
| Name | Signature | Description |
|---|---|---|
add |
func(ir.Op) ir.Op |
If the input operation is an ir.Add then return it, otherwise return nil |
double |
func(ir.Op) ir.Op |
If the input operation is an ir.Double then return it, otherwise return nil |
shift |
func(ir.Op) ir.Op |
If the input operation is an ir.Shift then return it, otherwise return nil |
inc |
func(int) int |
Increment an integer |
format |
func(interface {}) (string, error) |
Formats an addition chain script (*ast.Chain) as a string |
split |
func(string, string) []string |
Calls strings.Split |
join |
func([]string, string) string |
Calls strings.Join |
lines |
func(string) []string |
Split input string into lines |
Example output for each builtin template is generated from the chain:
_10 = 2*1
_11 = 1 + _10
_1100 = _11 << 2
_1111 = _11 + _1100
_11110000 = _1111 << 4
_11111111 = _1111 + _11110000
x10 = _11111111 << 2 + _11
x20 = x10 << 10 + x10
x30 = x20 << 10 + x10
x60 = x30 << 30 + x30
x120 = x60 << 60 + x60
x240 = x120 << 120 + x120
x250 = x240 << 10 + x10
return (x250 << 2 + 1) << 3 + _11
{{- range $n, $value := .Chain -}}
{{- printf "%3d: %#x\n" (inc $n) $value -}}
{{- end -}}
Output of chain template
1: 0x1
2: 0x2
3: 0x3
4: 0x6
5: 0xc
6: 0xf
7: 0x1e
8: 0x3c
9: 0x78
10: 0xf0
11: 0xff
12: 0x1fe
13: 0x3fc
14: 0x3ff
15: 0x7fe
16: 0xffc
17: 0x1ff8
18: 0x3ff0
19: 0x7fe0
20: 0xffc0
21: 0x1ff80
22: 0x3ff00
23: 0x7fe00
24: 0xffc00
25: 0xfffff
26: 0x1ffffe
27: 0x3ffffc
28: 0x7ffff8
29: 0xfffff0
30: 0x1ffffe0
31: 0x3ffffc0
32: 0x7ffff80
33: 0xfffff00
34: 0x1ffffe00
35: 0x3ffffc00
36: 0x3fffffff
37: 0x7ffffffe
38: 0xfffffffc
39: 0x1fffffff8
40: 0x3fffffff0
41: 0x7ffffffe0
42: 0xfffffffc0
43: 0x1fffffff80
44: 0x3fffffff00
45: 0x7ffffffe00
46: 0xfffffffc00
47: 0x1fffffff800
48: 0x3fffffff000
49: 0x7ffffffe000
50: 0xfffffffc000
51: 0x1fffffff8000
52: 0x3fffffff0000
53: 0x7ffffffe0000
54: 0xfffffffc0000
55: 0x1fffffff80000
56: 0x3fffffff00000
57: 0x7ffffffe00000
58: 0xfffffffc00000
59: 0x1fffffff800000
60: 0x3fffffff000000
61: 0x7ffffffe000000
62: 0xfffffffc000000
63: 0x1fffffff8000000
64: 0x3fffffff0000000
65: 0x7ffffffe0000000
66: 0xfffffffc0000000
67: 0xfffffffffffffff
68: 0x1ffffffffffffffe
69: 0x3ffffffffffffffc
70: 0x7ffffffffffffff8
71: 0xfffffffffffffff0
72: 0x1ffffffffffffffe0
73: 0x3ffffffffffffffc0
74: 0x7ffffffffffffff80
75: 0xfffffffffffffff00
76: 0x1ffffffffffffffe00
77: 0x3ffffffffffffffc00
78: 0x7ffffffffffffff800
79: 0xfffffffffffffff000
80: 0x1ffffffffffffffe000
81: 0x3ffffffffffffffc000
82: 0x7ffffffffffffff8000
83: 0xfffffffffffffff0000
84: 0x1ffffffffffffffe0000
85: 0x3ffffffffffffffc0000
86: 0x7ffffffffffffff80000
87: 0xfffffffffffffff00000
88: 0x1ffffffffffffffe00000
89: 0x3ffffffffffffffc00000
90: 0x7ffffffffffffff800000
91: 0xfffffffffffffff000000
92: 0x1ffffffffffffffe000000
93: 0x3ffffffffffffffc000000
94: 0x7ffffffffffffff8000000
95: 0xfffffffffffffff0000000
96: 0x1ffffffffffffffe0000000
97: 0x3ffffffffffffffc0000000
98: 0x7ffffffffffffff80000000
99: 0xfffffffffffffff00000000
100: 0x1ffffffffffffffe00000000
101: 0x3ffffffffffffffc00000000
102: 0x7ffffffffffffff800000000
103: 0xfffffffffffffff000000000
104: 0x1ffffffffffffffe000000000
105: 0x3ffffffffffffffc000000000
106: 0x7ffffffffffffff8000000000
107: 0xfffffffffffffff0000000000
108: 0x1ffffffffffffffe0000000000
109: 0x3ffffffffffffffc0000000000
110: 0x7ffffffffffffff80000000000
111: 0xfffffffffffffff00000000000
112: 0x1ffffffffffffffe00000000000
113: 0x3ffffffffffffffc00000000000
114: 0x7ffffffffffffff800000000000
115: 0xfffffffffffffff000000000000
116: 0x1ffffffffffffffe000000000000
117: 0x3ffffffffffffffc000000000000
118: 0x7ffffffffffffff8000000000000
119: 0xfffffffffffffff0000000000000
120: 0x1ffffffffffffffe0000000000000
121: 0x3ffffffffffffffc0000000000000
122: 0x7ffffffffffffff80000000000000
123: 0xfffffffffffffff00000000000000
124: 0x1ffffffffffffffe00000000000000
125: 0x3ffffffffffffffc00000000000000
126: 0x7ffffffffffffff800000000000000
127: 0xfffffffffffffff000000000000000
128: 0xffffffffffffffffffffffffffffff
129: 0x1fffffffffffffffffffffffffffffe
130: 0x3fffffffffffffffffffffffffffffc
131: 0x7fffffffffffffffffffffffffffff8
132: 0xffffffffffffffffffffffffffffff0
133: 0x1fffffffffffffffffffffffffffffe0
134: 0x3fffffffffffffffffffffffffffffc0
135: 0x7fffffffffffffffffffffffffffff80
136: 0xffffffffffffffffffffffffffffff00
137: 0x1fffffffffffffffffffffffffffffe00
138: 0x3fffffffffffffffffffffffffffffc00
139: 0x7fffffffffffffffffffffffffffff800
140: 0xffffffffffffffffffffffffffffff000
141: 0x1fffffffffffffffffffffffffffffe000
142: 0x3fffffffffffffffffffffffffffffc000
143: 0x7fffffffffffffffffffffffffffff8000
144: 0xffffffffffffffffffffffffffffff0000
145: 0x1fffffffffffffffffffffffffffffe0000
146: 0x3fffffffffffffffffffffffffffffc0000
147: 0x7fffffffffffffffffffffffffffff80000
148: 0xffffffffffffffffffffffffffffff00000
149: 0x1fffffffffffffffffffffffffffffe00000
150: 0x3fffffffffffffffffffffffffffffc00000
151: 0x7fffffffffffffffffffffffffffff800000
152: 0xffffffffffffffffffffffffffffff000000
153: 0x1fffffffffffffffffffffffffffffe000000
154: 0x3fffffffffffffffffffffffffffffc000000
155: 0x7fffffffffffffffffffffffffffff8000000
156: 0xffffffffffffffffffffffffffffff0000000
157: 0x1fffffffffffffffffffffffffffffe0000000
158: 0x3fffffffffffffffffffffffffffffc0000000
159: 0x7fffffffffffffffffffffffffffff80000000
160: 0xffffffffffffffffffffffffffffff00000000
161: 0x1fffffffffffffffffffffffffffffe00000000
162: 0x3fffffffffffffffffffffffffffffc00000000
163: 0x7fffffffffffffffffffffffffffff800000000
164: 0xffffffffffffffffffffffffffffff000000000
165: 0x1fffffffffffffffffffffffffffffe000000000
166: 0x3fffffffffffffffffffffffffffffc000000000
167: 0x7fffffffffffffffffffffffffffff8000000000
168: 0xffffffffffffffffffffffffffffff0000000000
169: 0x1fffffffffffffffffffffffffffffe0000000000
170: 0x3fffffffffffffffffffffffffffffc0000000000
171: 0x7fffffffffffffffffffffffffffff80000000000
172: 0xffffffffffffffffffffffffffffff00000000000
173: 0x1fffffffffffffffffffffffffffffe00000000000
174: 0x3fffffffffffffffffffffffffffffc00000000000
175: 0x7fffffffffffffffffffffffffffff800000000000
176: 0xffffffffffffffffffffffffffffff000000000000
177: 0x1fffffffffffffffffffffffffffffe000000000000
178: 0x3fffffffffffffffffffffffffffffc000000000000
179: 0x7fffffffffffffffffffffffffffff8000000000000
180: 0xffffffffffffffffffffffffffffff0000000000000
181: 0x1fffffffffffffffffffffffffffffe0000000000000
182: 0x3fffffffffffffffffffffffffffffc0000000000000
183: 0x7fffffffffffffffffffffffffffff80000000000000
184: 0xffffffffffffffffffffffffffffff00000000000000
185: 0x1fffffffffffffffffffffffffffffe00000000000000
186: 0x3fffffffffffffffffffffffffffffc00000000000000
187: 0x7fffffffffffffffffffffffffffff800000000000000
188: 0xffffffffffffffffffffffffffffff000000000000000
189: 0x1fffffffffffffffffffffffffffffe000000000000000
190: 0x3fffffffffffffffffffffffffffffc000000000000000
191: 0x7fffffffffffffffffffffffffffff8000000000000000
192: 0xffffffffffffffffffffffffffffff0000000000000000
193: 0x1fffffffffffffffffffffffffffffe0000000000000000
194: 0x3fffffffffffffffffffffffffffffc0000000000000000
195: 0x7fffffffffffffffffffffffffffff80000000000000000
196: 0xffffffffffffffffffffffffffffff00000000000000000
197: 0x1fffffffffffffffffffffffffffffe00000000000000000
198: 0x3fffffffffffffffffffffffffffffc00000000000000000
199: 0x7fffffffffffffffffffffffffffff800000000000000000
200: 0xffffffffffffffffffffffffffffff000000000000000000
201: 0x1fffffffffffffffffffffffffffffe000000000000000000
202: 0x3fffffffffffffffffffffffffffffc000000000000000000
203: 0x7fffffffffffffffffffffffffffff8000000000000000000
204: 0xffffffffffffffffffffffffffffff0000000000000000000
205: 0x1fffffffffffffffffffffffffffffe0000000000000000000
206: 0x3fffffffffffffffffffffffffffffc0000000000000000000
207: 0x7fffffffffffffffffffffffffffff80000000000000000000
208: 0xffffffffffffffffffffffffffffff00000000000000000000
209: 0x1fffffffffffffffffffffffffffffe00000000000000000000
210: 0x3fffffffffffffffffffffffffffffc00000000000000000000
211: 0x7fffffffffffffffffffffffffffff800000000000000000000
212: 0xffffffffffffffffffffffffffffff000000000000000000000
213: 0x1fffffffffffffffffffffffffffffe000000000000000000000
214: 0x3fffffffffffffffffffffffffffffc000000000000000000000
215: 0x7fffffffffffffffffffffffffffff8000000000000000000000
216: 0xffffffffffffffffffffffffffffff0000000000000000000000
217: 0x1fffffffffffffffffffffffffffffe0000000000000000000000
218: 0x3fffffffffffffffffffffffffffffc0000000000000000000000
219: 0x7fffffffffffffffffffffffffffff80000000000000000000000
220: 0xffffffffffffffffffffffffffffff00000000000000000000000
221: 0x1fffffffffffffffffffffffffffffe00000000000000000000000
222: 0x3fffffffffffffffffffffffffffffc00000000000000000000000
223: 0x7fffffffffffffffffffffffffffff800000000000000000000000
224: 0xffffffffffffffffffffffffffffff000000000000000000000000
225: 0x1fffffffffffffffffffffffffffffe000000000000000000000000
226: 0x3fffffffffffffffffffffffffffffc000000000000000000000000
227: 0x7fffffffffffffffffffffffffffff8000000000000000000000000
228: 0xffffffffffffffffffffffffffffff0000000000000000000000000
229: 0x1fffffffffffffffffffffffffffffe0000000000000000000000000
230: 0x3fffffffffffffffffffffffffffffc0000000000000000000000000
231: 0x7fffffffffffffffffffffffffffff80000000000000000000000000
232: 0xffffffffffffffffffffffffffffff00000000000000000000000000
233: 0x1fffffffffffffffffffffffffffffe00000000000000000000000000
234: 0x3fffffffffffffffffffffffffffffc00000000000000000000000000
235: 0x7fffffffffffffffffffffffffffff800000000000000000000000000
236: 0xffffffffffffffffffffffffffffff000000000000000000000000000
237: 0x1fffffffffffffffffffffffffffffe000000000000000000000000000
238: 0x3fffffffffffffffffffffffffffffc000000000000000000000000000
239: 0x7fffffffffffffffffffffffffffff8000000000000000000000000000
240: 0xffffffffffffffffffffffffffffff0000000000000000000000000000
241: 0x1fffffffffffffffffffffffffffffe0000000000000000000000000000
242: 0x3fffffffffffffffffffffffffffffc0000000000000000000000000000
243: 0x7fffffffffffffffffffffffffffff80000000000000000000000000000
244: 0xffffffffffffffffffffffffffffff00000000000000000000000000000
245: 0x1fffffffffffffffffffffffffffffe00000000000000000000000000000
246: 0x3fffffffffffffffffffffffffffffc00000000000000000000000000000
247: 0x7fffffffffffffffffffffffffffff800000000000000000000000000000
248: 0xffffffffffffffffffffffffffffff000000000000000000000000000000
249: 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
250: 0x1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe
251: 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc
252: 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffff8
253: 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff0
254: 0x1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe0
255: 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc0
256: 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffff80
257: 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff00
258: 0x1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe00
259: 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc00
260: 0x3ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
261: 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe
262: 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc
263: 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd
264: 0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa
265: 0x3ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff4
266: 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe8
267: 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeb
{{ printf "tmp\t%s" (join .Program.Temporaries "\t") }}
{{ range $i := .Program.Instructions -}}
{{- with add $i.Op -}}
{{ printf "add\t%s\t%s\t%s" $i.Output .X .Y }}
{{ end -}}
{{- with double $i.Op -}}
{{ printf "double\t%s\t%s" $i.Output .X }}
{{ end -}}
{{- with shift $i.Op -}}
{{ printf "shift\t%s\t%s\t%d" $i.Output .X .S }}
{{ end -}}
{{- end -}}
Output of listing template
tmp t0 t1 t2 t3 t4
double t0 x
add t0 x t0
shift t1 t0 2
add t1 t0 t1
shift t2 t1 4
add t1 t1 t2
shift t1 t1 2
add t1 t0 t1
shift t2 t1 10
add t2 t1 t2
shift t2 t2 10
add t2 t1 t2
shift t3 t2 30
add t2 t2 t3
shift t3 t2 60
add t2 t2 t3
shift t3 t2 120
add t2 t2 t3
shift t2 t2 10
add t1 t1 t2
shift t1 t1 2
add t4 x t1
shift t4 t4 3
add z t0 t4
{{- range $n, $op := .Ops -}}
{{- printf "[%3d] %4d+%-4d %#x\n" $n $op.I $op.J (index $.Chain (inc $n)) -}}
{{- end -}}
Output of ops template
[ 0] 0+0 0x2
[ 1] 0+1 0x3
[ 2] 2+2 0x6
[ 3] 3+3 0xc
[ 4] 2+4 0xf
[ 5] 5+5 0x1e
[ 6] 6+6 0x3c
[ 7] 7+7 0x78
[ 8] 8+8 0xf0
[ 9] 5+9 0xff
[ 10] 10+10 0x1fe
[ 11] 11+11 0x3fc
[ 12] 2+12 0x3ff
[ 13] 13+13 0x7fe
[ 14] 14+14 0xffc
[ 15] 15+15 0x1ff8
[ 16] 16+16 0x3ff0
[ 17] 17+17 0x7fe0
[ 18] 18+18 0xffc0
[ 19] 19+19 0x1ff80
[ 20] 20+20 0x3ff00
[ 21] 21+21 0x7fe00
[ 22] 22+22 0xffc00
[ 23] 13+23 0xfffff
[ 24] 24+24 0x1ffffe
[ 25] 25+25 0x3ffffc
[ 26] 26+26 0x7ffff8
[ 27] 27+27 0xfffff0
[ 28] 28+28 0x1ffffe0
[ 29] 29+29 0x3ffffc0
[ 30] 30+30 0x7ffff80
[ 31] 31+31 0xfffff00
[ 32] 32+32 0x1ffffe00
[ 33] 33+33 0x3ffffc00
[ 34] 13+34 0x3fffffff
[ 35] 35+35 0x7ffffffe
[ 36] 36+36 0xfffffffc
[ 37] 37+37 0x1fffffff8
[ 38] 38+38 0x3fffffff0
[ 39] 39+39 0x7ffffffe0
[ 40] 40+40 0xfffffffc0
[ 41] 41+41 0x1fffffff80
[ 42] 42+42 0x3fffffff00
[ 43] 43+43 0x7ffffffe00
[ 44] 44+44 0xfffffffc00
[ 45] 45+45 0x1fffffff800
[ 46] 46+46 0x3fffffff000
[ 47] 47+47 0x7ffffffe000
[ 48] 48+48 0xfffffffc000
[ 49] 49+49 0x1fffffff8000
[ 50] 50+50 0x3fffffff0000
[ 51] 51+51 0x7ffffffe0000
[ 52] 52+52 0xfffffffc0000
[ 53] 53+53 0x1fffffff80000
[ 54] 54+54 0x3fffffff00000
[ 55] 55+55 0x7ffffffe00000
[ 56] 56+56 0xfffffffc00000
[ 57] 57+57 0x1fffffff800000
[ 58] 58+58 0x3fffffff000000
[ 59] 59+59 0x7ffffffe000000
[ 60] 60+60 0xfffffffc000000
[ 61] 61+61 0x1fffffff8000000
[ 62] 62+62 0x3fffffff0000000
[ 63] 63+63 0x7ffffffe0000000
[ 64] 64+64 0xfffffffc0000000
[ 65] 35+65 0xfffffffffffffff
[ 66] 66+66 0x1ffffffffffffffe
[ 67] 67+67 0x3ffffffffffffffc
[ 68] 68+68 0x7ffffffffffffff8
[ 69] 69+69 0xfffffffffffffff0
[ 70] 70+70 0x1ffffffffffffffe0
[ 71] 71+71 0x3ffffffffffffffc0
[ 72] 72+72 0x7ffffffffffffff80
[ 73] 73+73 0xfffffffffffffff00
[ 74] 74+74 0x1ffffffffffffffe00
[ 75] 75+75 0x3ffffffffffffffc00
[ 76] 76+76 0x7ffffffffffffff800
[ 77] 77+77 0xfffffffffffffff000
[ 78] 78+78 0x1ffffffffffffffe000
[ 79] 79+79 0x3ffffffffffffffc000
[ 80] 80+80 0x7ffffffffffffff8000
[ 81] 81+81 0xfffffffffffffff0000
[ 82] 82+82 0x1ffffffffffffffe0000
[ 83] 83+83 0x3ffffffffffffffc0000
[ 84] 84+84 0x7ffffffffffffff80000
[ 85] 85+85 0xfffffffffffffff00000
[ 86] 86+86 0x1ffffffffffffffe00000
[ 87] 87+87 0x3ffffffffffffffc00000
[ 88] 88+88 0x7ffffffffffffff800000
[ 89] 89+89 0xfffffffffffffff000000
[ 90] 90+90 0x1ffffffffffffffe000000
[ 91] 91+91 0x3ffffffffffffffc000000
[ 92] 92+92 0x7ffffffffffffff8000000
[ 93] 93+93 0xfffffffffffffff0000000
[ 94] 94+94 0x1ffffffffffffffe0000000
[ 95] 95+95 0x3ffffffffffffffc0000000
[ 96] 96+96 0x7ffffffffffffff80000000
[ 97] 97+97 0xfffffffffffffff00000000
[ 98] 98+98 0x1ffffffffffffffe00000000
[ 99] 99+99 0x3ffffffffffffffc00000000
[100] 100+100 0x7ffffffffffffff800000000
[101] 101+101 0xfffffffffffffff000000000
[102] 102+102 0x1ffffffffffffffe000000000
[103] 103+103 0x3ffffffffffffffc000000000
[104] 104+104 0x7ffffffffffffff8000000000
[105] 105+105 0xfffffffffffffff0000000000
[106] 106+106 0x1ffffffffffffffe0000000000
[107] 107+107 0x3ffffffffffffffc0000000000
[108] 108+108 0x7ffffffffffffff80000000000
[109] 109+109 0xfffffffffffffff00000000000
[110] 110+110 0x1ffffffffffffffe00000000000
[111] 111+111 0x3ffffffffffffffc00000000000
[112] 112+112 0x7ffffffffffffff800000000000
[113] 113+113 0xfffffffffffffff000000000000
[114] 114+114 0x1ffffffffffffffe000000000000
[115] 115+115 0x3ffffffffffffffc000000000000
[116] 116+116 0x7ffffffffffffff8000000000000
[117] 117+117 0xfffffffffffffff0000000000000
[118] 118+118 0x1ffffffffffffffe0000000000000
[119] 119+119 0x3ffffffffffffffc0000000000000
[120] 120+120 0x7ffffffffffffff80000000000000
[121] 121+121 0xfffffffffffffff00000000000000
[122] 122+122 0x1ffffffffffffffe00000000000000
[123] 123+123 0x3ffffffffffffffc00000000000000
[124] 124+124 0x7ffffffffffffff800000000000000
[125] 125+125 0xfffffffffffffff000000000000000
[126] 66+126 0xffffffffffffffffffffffffffffff
[127] 127+127 0x1fffffffffffffffffffffffffffffe
[128] 128+128 0x3fffffffffffffffffffffffffffffc
[129] 129+129 0x7fffffffffffffffffffffffffffff8
[130] 130+130 0xffffffffffffffffffffffffffffff0
[131] 131+131 0x1fffffffffffffffffffffffffffffe0
[132] 132+132 0x3fffffffffffffffffffffffffffffc0
[133] 133+133 0x7fffffffffffffffffffffffffffff80
[134] 134+134 0xffffffffffffffffffffffffffffff00
[135] 135+135 0x1fffffffffffffffffffffffffffffe00
[136] 136+136 0x3fffffffffffffffffffffffffffffc00
[137] 137+137 0x7fffffffffffffffffffffffffffff800
[138] 138+138 0xffffffffffffffffffffffffffffff000
[139] 139+139 0x1fffffffffffffffffffffffffffffe000
[140] 140+140 0x3fffffffffffffffffffffffffffffc000
[141] 141+141 0x7fffffffffffffffffffffffffffff8000
[142] 142+142 0xffffffffffffffffffffffffffffff0000
[143] 143+143 0x1fffffffffffffffffffffffffffffe0000
[144] 144+144 0x3fffffffffffffffffffffffffffffc0000
[145] 145+145 0x7fffffffffffffffffffffffffffff80000
[146] 146+146 0xffffffffffffffffffffffffffffff00000
[147] 147+147 0x1fffffffffffffffffffffffffffffe00000
[148] 148+148 0x3fffffffffffffffffffffffffffffc00000
[149] 149+149 0x7fffffffffffffffffffffffffffff800000
[150] 150+150 0xffffffffffffffffffffffffffffff000000
[151] 151+151 0x1fffffffffffffffffffffffffffffe000000
[152] 152+152 0x3fffffffffffffffffffffffffffffc000000
[153] 153+153 0x7fffffffffffffffffffffffffffff8000000
[154] 154+154 0xffffffffffffffffffffffffffffff0000000
[155] 155+155 0x1fffffffffffffffffffffffffffffe0000000
[156] 156+156 0x3fffffffffffffffffffffffffffffc0000000
[157] 157+157 0x7fffffffffffffffffffffffffffff80000000
[158] 158+158 0xffffffffffffffffffffffffffffff00000000
[159] 159+159 0x1fffffffffffffffffffffffffffffe00000000
[160] 160+160 0x3fffffffffffffffffffffffffffffc00000000
[161] 161+161 0x7fffffffffffffffffffffffffffff800000000
[162] 162+162 0xffffffffffffffffffffffffffffff000000000
[163] 163+163 0x1fffffffffffffffffffffffffffffe000000000
[164] 164+164 0x3fffffffffffffffffffffffffffffc000000000
[165] 165+165 0x7fffffffffffffffffffffffffffff8000000000
[166] 166+166 0xffffffffffffffffffffffffffffff0000000000
[167] 167+167 0x1fffffffffffffffffffffffffffffe0000000000
[168] 168+168 0x3fffffffffffffffffffffffffffffc0000000000
[169] 169+169 0x7fffffffffffffffffffffffffffff80000000000
[170] 170+170 0xffffffffffffffffffffffffffffff00000000000
[171] 171+171 0x1fffffffffffffffffffffffffffffe00000000000
[172] 172+172 0x3fffffffffffffffffffffffffffffc00000000000
[173] 173+173 0x7fffffffffffffffffffffffffffff800000000000
[174] 174+174 0xffffffffffffffffffffffffffffff000000000000
[175] 175+175 0x1fffffffffffffffffffffffffffffe000000000000
[176] 176+176 0x3fffffffffffffffffffffffffffffc000000000000
[177] 177+177 0x7fffffffffffffffffffffffffffff8000000000000
[178] 178+178 0xffffffffffffffffffffffffffffff0000000000000
[179] 179+179 0x1fffffffffffffffffffffffffffffe0000000000000
[180] 180+180 0x3fffffffffffffffffffffffffffffc0000000000000
[181] 181+181 0x7fffffffffffffffffffffffffffff80000000000000
[182] 182+182 0xffffffffffffffffffffffffffffff00000000000000
[183] 183+183 0x1fffffffffffffffffffffffffffffe00000000000000
[184] 184+184 0x3fffffffffffffffffffffffffffffc00000000000000
[185] 185+185 0x7fffffffffffffffffffffffffffff800000000000000
[186] 186+186 0xffffffffffffffffffffffffffffff000000000000000
[187] 187+187 0x1fffffffffffffffffffffffffffffe000000000000000
[188] 188+188 0x3fffffffffffffffffffffffffffffc000000000000000
[189] 189+189 0x7fffffffffffffffffffffffffffff8000000000000000
[190] 190+190 0xffffffffffffffffffffffffffffff0000000000000000
[191] 191+191 0x1fffffffffffffffffffffffffffffe0000000000000000
[192] 192+192 0x3fffffffffffffffffffffffffffffc0000000000000000
[193] 193+193 0x7fffffffffffffffffffffffffffff80000000000000000
[194] 194+194 0xffffffffffffffffffffffffffffff00000000000000000
[195] 195+195 0x1fffffffffffffffffffffffffffffe00000000000000000
[196] 196+196 0x3fffffffffffffffffffffffffffffc00000000000000000
[197] 197+197 0x7fffffffffffffffffffffffffffff800000000000000000
[198] 198+198 0xffffffffffffffffffffffffffffff000000000000000000
[199] 199+199 0x1fffffffffffffffffffffffffffffe000000000000000000
[200] 200+200 0x3fffffffffffffffffffffffffffffc000000000000000000
[201] 201+201 0x7fffffffffffffffffffffffffffff8000000000000000000
[202] 202+202 0xffffffffffffffffffffffffffffff0000000000000000000
[203] 203+203 0x1fffffffffffffffffffffffffffffe0000000000000000000
[204] 204+204 0x3fffffffffffffffffffffffffffffc0000000000000000000
[205] 205+205 0x7fffffffffffffffffffffffffffff80000000000000000000
[206] 206+206 0xffffffffffffffffffffffffffffff00000000000000000000
[207] 207+207 0x1fffffffffffffffffffffffffffffe00000000000000000000
[208] 208+208 0x3fffffffffffffffffffffffffffffc00000000000000000000
[209] 209+209 0x7fffffffffffffffffffffffffffff800000000000000000000
[210] 210+210 0xffffffffffffffffffffffffffffff000000000000000000000
[211] 211+211 0x1fffffffffffffffffffffffffffffe000000000000000000000
[212] 212+212 0x3fffffffffffffffffffffffffffffc000000000000000000000
[213] 213+213 0x7fffffffffffffffffffffffffffff8000000000000000000000
[214] 214+214 0xffffffffffffffffffffffffffffff0000000000000000000000
[215] 215+215 0x1fffffffffffffffffffffffffffffe0000000000000000000000
[216] 216+216 0x3fffffffffffffffffffffffffffffc0000000000000000000000
[217] 217+217 0x7fffffffffffffffffffffffffffff80000000000000000000000
[218] 218+218 0xffffffffffffffffffffffffffffff00000000000000000000000
[219] 219+219 0x1fffffffffffffffffffffffffffffe00000000000000000000000
[220] 220+220 0x3fffffffffffffffffffffffffffffc00000000000000000000000
[221] 221+221 0x7fffffffffffffffffffffffffffff800000000000000000000000
[222] 222+222 0xffffffffffffffffffffffffffffff000000000000000000000000
[223] 223+223 0x1fffffffffffffffffffffffffffffe000000000000000000000000
[224] 224+224 0x3fffffffffffffffffffffffffffffc000000000000000000000000
[225] 225+225 0x7fffffffffffffffffffffffffffff8000000000000000000000000
[226] 226+226 0xffffffffffffffffffffffffffffff0000000000000000000000000
[227] 227+227 0x1fffffffffffffffffffffffffffffe0000000000000000000000000
[228] 228+228 0x3fffffffffffffffffffffffffffffc0000000000000000000000000
[229] 229+229 0x7fffffffffffffffffffffffffffff80000000000000000000000000
[230] 230+230 0xffffffffffffffffffffffffffffff00000000000000000000000000
[231] 231+231 0x1fffffffffffffffffffffffffffffe00000000000000000000000000
[232] 232+232 0x3fffffffffffffffffffffffffffffc00000000000000000000000000
[233] 233+233 0x7fffffffffffffffffffffffffffff800000000000000000000000000
[234] 234+234 0xffffffffffffffffffffffffffffff000000000000000000000000000
[235] 235+235 0x1fffffffffffffffffffffffffffffe000000000000000000000000000
[236] 236+236 0x3fffffffffffffffffffffffffffffc000000000000000000000000000
[237] 237+237 0x7fffffffffffffffffffffffffffff8000000000000000000000000000
[238] 238+238 0xffffffffffffffffffffffffffffff0000000000000000000000000000
[239] 239+239 0x1fffffffffffffffffffffffffffffe0000000000000000000000000000
[240] 240+240 0x3fffffffffffffffffffffffffffffc0000000000000000000000000000
[241] 241+241 0x7fffffffffffffffffffffffffffff80000000000000000000000000000
[242] 242+242 0xffffffffffffffffffffffffffffff00000000000000000000000000000
[243] 243+243 0x1fffffffffffffffffffffffffffffe00000000000000000000000000000
[244] 244+244 0x3fffffffffffffffffffffffffffffc00000000000000000000000000000
[245] 245+245 0x7fffffffffffffffffffffffffffff800000000000000000000000000000
[246] 246+246 0xffffffffffffffffffffffffffffff000000000000000000000000000000
[247] 127+247 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
[248] 248+248 0x1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe
[249] 249+249 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc
[250] 250+250 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffff8
[251] 251+251 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff0
[252] 252+252 0x1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe0
[253] 253+253 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc0
[254] 254+254 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffff80
[255] 255+255 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff00
[256] 256+256 0x1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe00
[257] 257+257 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc00
[258] 13+258 0x3ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
[259] 259+259 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe
[260] 260+260 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc
[261] 0+261 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd
[262] 262+262 0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa
[263] 263+263 0x3ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff4
[264] 264+264 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe8
[265] 2+265 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeb
{{- format .Script -}}
Output of script template
_10 = 2*1
_11 = 1 + _10
_1100 = _11 << 2
_1111 = _11 + _1100
_11110000 = _1111 << 4
_11111111 = _1111 + _11110000
x10 = _11111111 << 2 + _11
x20 = x10 << 10 + x10
x30 = x20 << 10 + x10
x60 = x30 << 30 + x30
x120 = x60 << 60 + x60
x240 = x120 << 120 + x120
x250 = x240 << 10 + x10
return (x250 << 2 + 1) << 3 + _11