1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
|
The design of the primitive operations follows the following principles:
(1) if operand types are known (i.e. FIRRTL front-end), primops whose return type is statically known (no future type introspection needed) are available
(2) if operand types are not known (i.e. hand-writing FIRRTL pass), generic primops can be used, and a future pass will perform type introspection to replace the generic with the specific primop
(3) the FIRRTL's lowered form will never contain any generic primops
(4) resultant widths are always large enough to represent any possible output
(5) specific primops do not grow widths (e.g. add-wrap, sub-wrap) and should be used if that behavior is desired
(6) except for mux, mux-u, and mux-s, all primops can accept operands of differing width to enable optimizations in the backend
(7) autopadding on connect is not allowed, and one should use the pad!/-u/-s expression to autopad
TODO:
rederive div,mod,quo,rem widths.
Write explanations in terms of formulas.
Reread all explanations.
Finish adding primops.
add
adduu(a,b) -> u, max(a.w,b.w) + 1
addus(a,b) -> s, max(a.w,b.w) + 1
addsu(a,b) -> s, max(a.w,b.w) + 1
addss(a,b) -> s, max(a.w,b.w) + 1
sub
subuu(a,b) -> s, max(a.w,b.w) + 1 ; 0@<UInt,3> - 7@<UInt,3> = -7@<SInt,4>
subus(a,b) -> s, max(a.w,b.w) + 1 ; 7@<UInt,3> - -8@<SInt,4> = 15@<SInt,5>
subsu(a,b) -> s, max(a.w,b.w) + 1 ; -8@<SInt,4> - 7@<UInt,3> = -15@<SInt,5>
subss(a,b) -> s, max(a.w,b.w) + 1 ; -8@<UInt,4> - 7@<SInt,4> = -15@<SInt,5>
mul
muluu(a,b) -> u,a.w+b.w
mulus(a,b) -> s,a.w+b.w
mulsu(a,b) -> s,a.w+b.w
mulss(a,b) -> s,a.w+b.w
div
divuu(a,b) -> u,a.w ; if divide by 1
divus(a,b) -> s,a.w+1 ; if divide by -1
divsu(a,b) -> s,a.w ; if divide by 1
divss(a,b) -> s,a.w+1 ; if divide by -1
mod
moduu(a,d) -> u,d.w
modus(a,d) -> u,d.w-1
modsu(a,d) -> u,d.w
modss(a,d) -> u,d.w-1
rem
remuu(a,b) -> u,min(a.w,b.w) ; 15 % 16 = 15. All remainders must be less than b or a.
remus(a,b) -> u,b.w ; -1 % 32 = 31. Remainder can be larger than abs(a), but not larger than b.
remsu(a,b) -> s,b.w ; 1 % -32 = -31. abs(rem) can be larger than abs(a), but not larger than abs(b).
remss(a,b) -> s,b.w ; strictly superset of us and su.
add-mod
add-moduu(a,b) -> u, a.w
add-modus(a,b) -> u, a.w
add-modsu(a,b) -> s, a.w
add-modss(a,b) -> s, a.w
sub-mod
sub-moduu(a,b) -> u, a.w
sub-modus(a,b) -> u, a.w
sub-modsu(a,b) -> s, a.w
sub-modss(a,b) -> s, a.w
Proof:
add-moduu -> u
take inverse:
sub-moduu -> u
add-modus -> u
add-modsu -> s with width of first operand
add-mod and sub-mod always return the type and width of the first operand.
|
