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ESPRESSO(5OCTTOOLS) 1986 ESPRESSO(5OCTTOOLS)
NAME
espresso - input file format for espresso(1OCTTOOLS)
DESCRIPTION
Espresso accepts as input a two-level description of a
Boolean function. This is described as a character matrix
with keywords embedded in the input to specify the size of
the matrix and the logical format of the input function.
Programs exist to translate a set of equations into this
format (e.g., eqntott(1OCTTOOLS), bdsyn(1OCTTOOLS),
eqntopla(1OCTTOOLS)). This manual page refers to Version
2.3 of Espresso.
Comments are allowed within the input by placing a pound
sign (#) as the first character on a line. Comments and
unrecognized keywords are passed directly from the input
file to standard output. Any white-space (blanks, tabs,
etc.), except when used as a delimiter in an embedded com-
mand, is ignored. It is generally assumed that the PLA is
specified such that each row of the PLA fits on a single
line in the input file.
KEYWORDS
The following keywords are recognized by espresso. The list
shows the probable order of the keywords in a PLA descrip-
tion. [d] denotes a decimal number and [s] denotes a text
string. The minimum required set of keywords is .i and .o
for binary-valued functions, or .mv for multiple-valued
functions.
.i [d] Specifies the number of input variables.
.o [d] Specifies the number of output functions.
.mv [num_var] [num_binary_var] [d1] . . . [dn]
Specifies the number of variables (num_var), the
number of binary variables (num_binary_var), and
the size of each of the multiple-valued vari-
ables (d1 through dn).
.ilb [s1] [s2] . . . [sn]
Gives the names of the binary valued variables.
This must come after .i and .o (or after .mv).
There must be as many tokens following the key-
word as there are input variables.
.ob [s1] [s2] . . . [sn]
Gives the names of the output functions. This
must come after .i and .o (or after .mv). There
must be as many tokens following the keyword as
there are output variables.
.label var=[d] [s1] [s2] ...
Specifies the names of the parts of a multiple-
valued variable. This must come after .mv.
There must be as many tokens following the key-
word as there are parts for this variable. Note
that the variables are numbered starting from 0.
.type [s] Sets the logical interpretation of the character
matrix as described below under "Logical
Description of a PLA". This keyword must come
before any product terms. [s] is one of f, r,
fd, fr, dr, or fdr.
.phase [s] [s] is a string of as many 0's or 1's as there
are output functions. It specifies which polar-
ity of each output function should be used for
the minimization (a 1 specifies that the ON-set
of the corresponding output function should be
used, and a 0 specifies that the OFF-set of the
corresponding output function should be minim-
ized).
.pair [d] Specifies the number of pairs of variables which
will be paired together using two-bit decoders.
The rest of the line contains pairs of numbers
which specify the binary variables of the PLA
which will be paired together. The binary vari-
ables are numbered starting with 0. The PLA
will be reshaped so that any unpaired binary
variables occupy the leftmost part of the array,
then the paired multiple-valued columns, and
finally any multiple-valued variables. If the
labels have been specified using .ilb, then the
variable names may be used instead of the column
number.
.symbolic [s0] [s1] . . . [sn] ; [t0] [t1] . . . [tm] ;
Specifies that the binary-valued variables named
[s0] thru [sn] are to be considered as a single
multiple-valued variable. Variable [s0] is con-
sidered the most significant bit, [s1] the next
most significant, and [sn] is the least signifi-
cant bit. This creates a variable with 2**n
parts corresponding to the decodes of the
binary-valued variables. The keywords [t0] thru
[tm] provide the labels for each decode of [s0]
thru [sn]. ([t0] corresponds to a value of
00...00, [t1] is the value 00...01, etc.). The
binary-variables may be identified by column
number, or by variable name when .ilb is used.
The binary-variables are removed from the func-
tion after the multiple-valued variable is
created.
.symbolic-
output [s0] [s1] . . . [sn] ; [t0] [t1] . . . [tm] ;
Specifies that the output functions [s0] ...
[sn] are to be considered as a single symbolic
output. This creates 2**n more output variables
corresponding to the possible values of the out-
puts. The outputs may be identified by number
(starting from 0), or by variable name when .ob
is used. The outputs are removed from the func-
tion after the new set of outputs is created.
.kiss Sets up for a kiss-style minimization.
.p [d] Specifies the number of product terms. The pro-
duct terms (one per line) follow immediately
after this keyword. Actually, this line is
ignored, and the ".e", ".end", or the end of the
file indicate the end of the input description.
.e (.end) Optionally marks the end of the PLA description.
LOGICAL DESCRIPTION OF A PLA
When we speak of the ON-set of a Boolean function, we mean
those minterms which imply the function value is a 1. Like-
wise, the OFF-set are those terms which imply the function
is a 0, and the DC-set (don't care set) are those terms for
which the function is unspecified. A function is completely
described by providing its ON-set, OFF-set and DC-set. Note
that all minterms lie in the union of the ON-set, OFF-set
and DC-set, and that the ON-set, OFF-set and DC-set share no
minterms.
The purpose of the espresso minimization program is to find
a logically equivalent set of product-terms to represent the
ON-set and optionally minterms which lie in the DC-set,
without containing any minterms of the OFF-set.
A Boolean function can be described in one of the following
ways:
1) By providing the ON-set. In this case, espresso com-
putes the OFF-set as the complement of the ON-set and
the DC-set is empty. This is indicated with the key-
word .type f in the input file.
2) By providing the ON-set and DC-set. In this case,
espresso computes the OFF-set as the complement of the
union of the ON-set and the DC-set. If any minterm
belongs to both the ON-set and DC-set, then it is con-
sidered a don't care and may be removed from the ON-set
during the minimization process. This is indicated
with the keyword .type fd in the input file.
3) By providing the ON-set and OFF-set. In this case,
espresso computes the DC-set as the complement of the
union of the ON-set and the OFF-set. It is an error
for any minterm to belong to both the ON-set and OFF-
set. This error may not be detected during the minimi-
zation, but it can be checked with the subprogram "-
Dcheck" which will check the consistency of a function.
This is indicated with the keyword .type fr in the
input file.
4) By providing the ON-set, OFF-set and DC-set. This is
indicated with the keyword .type fdr in the input file.
If at all possible, espresso should be given the DC-set
(either implicitly or explicitly) in order to improve the
results of the minimization.
A term is represented by a "cube" which can be considered
either a compact representation of an algebraic product term
which implies the function value is a 1, or as a representa-
tion of a row in a PLA which implements the term. A cube
has an input part which corresponds to the input plane of a
PLA, and an output part which corresponds to the output
plane of a PLA (for the multiple-valued case, see below).
SYMBOLS IN THE PLA MATRIX AND THEIR INTERPRETATION
Each position in the input plane corresponds to an input
variable where a 0 implies the corresponding input literal
appears complemented in the product term, a 1 implies the
input literal appears uncomplemented in the product term,
and - implies the input literal does not appear in the pro-
duct term.
With type f, for each output, a 1 means this product term
belongs to the ON-set, and a 0 or - means this product term
has no meaning for the value of this function. This type
corresponds to an actual PLA where only the ON-set is actu-
ally implemented.
With type fd (the default), for each output, a 1 means this
product term belongs to the ON-set, a 0 means this product
term has no meaning for the value of this function, and a -
implies this product term belongs to the DC-set.
With type fr, for each output, a 1 means this product term
belongs to the ON-set, a 0 means this product term belongs
to the OFF-set, and a - means this product term has no mean-
ing for the value of this function.
With type fdr, for each output, a 1 means this product term
belongs to the ON-set, a 0 means this product term belongs
to the OFF-set, a - means this product term belongs to the
DC-set, and a ~ implies this product term has no meaning for
the value of this function.
Note that regardless of the type of PLA, a ~ implies the
product term has no meaning for the value of this function.
2 is allowed as a synonym for -, 4 is allowed for 1, and 3
is allowed for ~.
MULTIPLE-VALUED FUNCTIONS
Espresso will also minimize multiple-valued Boolean func-
tions. There can be an arbitrary number of multiple-valued
variables, and each can be of a different size. If there
are also binary-valued variables, they should be given as
the first variables on the line (for ease of description).
Of course, it is always possible to place them anywhere on
the line as a two-valued multiple-valued variable. The
function size is described by the embedded option .mv rather
than .i and .o.
A multiple-output binary function with ni inputs and no out-
puts would be specified as .mv ni+1 ni no. .mv cannot be
used with either .i or .o - use one or the other to specify
the function size.
The binary variables are given as described above. Each of
the multiple-valued variables are given as a bit-vector of 0
and 1 which have their usual meaning for multiple-valued
functions. The last multiple-valued variable (also called
the output) is interpreted as described above for the output
(to split the function into an ON-set, OFF-set and DC-set).
A vertical bar | may be used to separate the multiple-valued
fields in the input file.
If the size of the multiple-valued field is less than zero,
than a symbolic field is interpreted from the input file.
The absolute value of the size specifies the maximum number
of unique symbolic labels which are expected in this column.
The symbolic labels are white-space delimited strings of
characters.
To perform a kiss-style encoding problem, the keyword .kiss
should be included in the file. The third to last variable
on the input file must be the symbolic "present state", and
the second to last variable must be the "next state". As
always, the last variable is the output. The symbolic "next
state" will be hacked to be actually part of the output.
EXAMPLE #1
A two-bit adder which takes in two 2-bit operands and pro-
duces a 3-bit result can be described completely in minterms
as:
# 2-bit by 2-bit binary adder (with no carry input)
.i 4
.o 3
0000 000
0001 001
0010 010
0011 011
0100 001
0101 010
0110 011
0111 100
1000 010
1001 011
1010 100
1011 101
1100 011
1101 100
1110 101
1111 110
It is also possible to specify some extra options, such as:
# 2-bit by 2-bit binary adder (with no carry input)
.i 4
.o 3
.ilb a1 a0 b1 b0
.ob s2 s1 s0
.pair 2 (a1 b1) (a0 b0)
.phase 011
0000 000
0001 001
0010 010
.
.
.
1111 110
.e
The option .pair indicates that the first binary-valued
variable should be paired with the third binary-valued vari-
able, and that the second variable should be paired with the
fourth variable. The function will then be mapped into an
equivalent multiple-valued minimization problem.
The option .phase indicates that the positive-phase should
be used for the second and third outputs, and that the nega-
tive phase should be used for the first output.
EXAMPLE #2
This example shows a description of a multiple-valued func-
tion with 5 binary variables and 3 multiple-valued variables
(8 variables total) where the multiple-valued variables have
sizes of 4 27 and 10 (note that the last multiple-valued
variable is the "output" and also encodes the ON-set, DC-set
and OFF-set information).
.mv 8 5 4 27 10
.ilb in1 in2 in3 in4 in5
.label var=5 part1 part2 part3 part4
.label var=6 a b c d e f g h i j k l m n
o p q r s t u v w x y z a1
.label var=7 out1 out2 out3 out4 out5 out6
out7 out8 out9 out10
0-010|1000|100000000000000000000000000|0010000000
10-10|1000|010000000000000000000000000|1000000000
0-111|1000|001000000000000000000000000|0001000000
0-10-|1000|000100000000000000000000000|0001000000
00000|1000|000010000000000000000000000|1000000000
00010|1000|000001000000000000000000000|0010000000
01001|1000|000000100000000000000000000|0000000010
0101-|1000|000000010000000000000000000|0000000000
0-0-0|1000|000000001000000000000000000|1000000000
10000|1000|000000000100000000000000000|0000000000
11100|1000|000000000010000000000000000|0010000000
10-10|1000|000000000001000000000000000|0000000000
11111|1000|000000000000100000000000000|0010000000
.
.
.
11111|0001|000000000000000000000000001|0000000000
EXAMPLE #3
This example shows a description of a multiple-valued func-
tion setup for kiss-style minimization. There are 5 binary
variables, 2 symbolic variables (the present-state and the
next-state of the FSM) and the output (8 variables total).
.mv 8 5 -10 -10 6
.ilb io1 io0 init swr mack
.ob wait minit mrd sack mwr dli
.type fr
.kiss
--1-- - init0 110000
--1-- init0 init0 110000
--0-- init0 init1 110000
--00- init1 init1 110000
--01- init1 init2 110001
--0-- init2 init4 110100
--01- init4 init4 110100
--00- init4 iowait 000000
0000- iowait iowait 000000
1000- iowait init1 110000
01000 iowait read0 101000
11000 iowait write0 100010
01001 iowait rmack 100000
11001 iowait wmack 100000
--01- iowait init2 110001
--0-0 rmack rmack 100000
--0-1 rmack read0 101000
--0-0 wmack wmack 100000
--0-1 wmack write0 100010
--0-- read0 read1 101001
--0-- read1 iowait 000000
--0-- write0 iowait 000000
EXAMPLE 4
This example shows the use of the .symbolic keyword to setup
a multiple-valued minimization problem.
.i 15
.o 4
.ilb SeqActive<0> CacheOp<6> CacheOp<5> CacheOp<4>
CacheOp<3> CacheOp<2> CacheOp<1> CacheOp<0>
userKernel<0> Protection<1> Protection<0>
cacheState<1> cacheState<0> PageDirty<0>
WriteCycleIn<0>
.ob CacheBusy<0> dataMayBeValid<0> dataIsValid<0>
WriteCycleOut<0>
.symbolic CacheOp<6> CacheOp<5> CacheOp<4> CacheOp<3>
CacheOp<2> CacheOp<1> CacheOp<0> ;
FET NA PHY_FET PR32 PRE_FET PW32 RA32 RD32
RD64 RDCACHE RFO32 RFO64 TS32 WR32 WR64 WRCACHE ;
.symbolic Protection<1> Protection<0> ;
PROT_KRO_UNA PROT_KRW_UNA PROT_KRW_URO PROT_KRW_URW ;
.symbolic cacheState<1> cacheState<0> ;
CS_Invalid CS_OwnPrivate CS_OwnShared CS_UnOwned ;
.p 22
0000001--010110 0001
0000001-1-00110 0001
00001011-01011- 0100
000010111-0011- 0100
0000--001--01-- 0100
0000-10--0-1--- 0100
0000-10-1--1--- 0100
00000-0--0-1--- 0100
00000-0-1--1--- 0100
0000-10--0--1-- 0100
0000-10-1---1-- 0100
00000-0--0--1-- 0100
00000-0-1---1-- 0100
---1----------- 1000
--1------------ 1000
-1------------- 1000
1-------------- 1000
-------0------- 1000
----1---------- 1000
-----0--------- 1000
------0-------- 1000
--------------1 1110
.e
August Last change: 22 10