Can a constant expression ever be valid in a VHDL case statement? - vhdl

I recall that in Verilog it can be valid to use a constant in the expression of a case statement, but is it also valid in VHDL?
// Verilog example
case(1'b1)
A[2]: Y<=2'b11;
A[1]: Y<=2'b10;
A[0]: Y<=2'b01;
default:Y<=2'b00;
endcase

The following code is not exactly parallel to your example, but it may be useful:
This compiles:
process
constant S : std_logic := '1';
begin
case S is
when '0' =>
when '1' =>
when others =>
end case;
end process;
So does this:
process
begin
case std_logic'('1') is
when '0' =>
when '1' =>
when others =>
end case;
end process;
This does not:
process
begin
case '1' is
when '0' =>
when '1' =>
when others =>
end case;
end process;
'1' is ambiguous (std_logic / character).
Now, what you're actually doing is a bit different, and I'm not sure what your intent is. You seem to want to determine the highest bit that is set. In VHDL, your construct would only be valid syntactically if A is also constant (case choices need to be locally static), in which case there are much easier ways to accomplish this (e.g. a for loop). There's the problem of mutual exclusion, though - in general, case choices are bound to overlap, and I would think that should be illegal (though ModelSim didn't complain when I tried it - synthesis tools may be another story). I would say it's definitely not a great idea either way.

No you can't express the case statement as a VHDL case statement
Unlike Verilog, IEEE Std 1364-2005 9.5 Case statement para 4:
The case expression and the case item expression can be computed at
run time; neither expression is required to be a constant expression.
In IEEE Std 1076-1993 8.8 Case statement, para 8 (also representative of -2008):
The simple expression and discrete ranges given as choices in a case
statement must be locally static. A choice defined by a discrete range
stands for all values in the corresponding range. The choice others is
only allowed for the last alternative and as its only choice; it
stands for all values(possibly none) not given in the choices of
previous alternatives. An element simple name (see 7.3.2 ) is not
allowed as a choice of a case statement alternative.
From the glossary:
locally static expression: An expression that can be evaluated during the analysis of the design unit in which it appears.
analysis: The syntactic and semantic analysis of source code in a VHDL design file and the insertion of intermediate form representations of design units into a design library.
(A fancy way of telling us compile time as opposed to elaboration (linking and loading). VHDL's definitions also embrace interpretive implementation.)
The definition of a locally static expression requires A to be declared as a constant and in the VHDL LRM -1993 version a slice name or index name isn't locally static (See IEEE Std 1076-1993, 7.4.1 Locally static primaries para 1, 7.4.2 Globally static primaries, r. - globally static means at elaboration time). This is changed in the IEEE Std 1076-2008 for static index expressions or static index ranges (See IEEE Std 1076-2008, 9.4.2, n. and o.). It's likely synthesis vendors tools lag, even if you can simulate it, you likely can't synthesis it today.
There's also the issue of multiple choices with the same value. See IEEE Std 1076-1993 8.8 Case statement, para 3 (also representative of -2008 for this issue):
The expression must be of a discrete type, or of a one-dimensional
array type whose element base type is a character type. This type must
be determinable independently of the context in which the expression
occurs, but using the fact that the expression must be of a discrete
type or a one-dimensional character array type. Each choice in a case
statement alternative must be of the same type as the expression; the
list of choices specifies for which values of the expression the
alternative is chosen.
Where the expressions std_logic'('1') or S have a base type of std_ulogic. And this eliminates choices that are not of the base type of std_logic (std_ulogic - 'U', 'X', '0', '1', 'Z', 'W', 'L', 'H', '-', See IEEE Std 1076-2008 16.7 Standard multivalue logic package and Annex A footnote 15 which provides a link to the source for package std_logic_1164).
Notice fru1tbat showed choices '0', '1' and others, evaluation of the expressions A(2), A(1) or A(0) returns a std_ulogic subtype and would give you multiple choices representing the same value ('1'). See IEEE Std 1076-1993, 8.8 para 7:
For other forms of expression, each value of the (base) type of the
expression must be represented once and only once in the set of
choices, and no other value is allowed.
So the case statement isn't directly expressible in VHDL, we're only interested in cases where A(2), A(1) and A(0) are '1' and only one choice is allowed. Instead we can use a conditional signal assignment statement:
library ieee;
use ieee.std_logic_1164.all;
entity constexp is
end entity;
architecture foo of constexp is
signal A: std_logic_vector (2 downto 0) := "001";
signal Y: std_logic_vector (1 downto 0);
begin
COND: -- Conditional Signal Assignment statement
Y <= "11" when A(2) = '1' else
"10" when A(1) = '1' else
"01" when A(0) = '1' else
"00";
end architecture;
(And this design specification analyzes, elaborates and simulates.)
A conditional signal assignment is a concurrent statement in the 1076-1993 standard (See 9.5.1 Conditional signal assignments) while a conditional signal assignment can be used as a sequential statement as well in the 1076-2008 standard (See 11.6 Concurrent signal assignment statements and 10.5.3 Conditional signal assignment). Today it's likely synthesis vendors would be -1993 compliant.
And by definition any of the constructs here can be devolved into if statements which are sequential statements.

Related

Error (10327) can't determine definition of operator ""=""

For this VHDL design description:
library ieee;
use ieee.std_logic_1164.all;
use ieee.std_logic_arith.all;
entity four_bit_counter is
port (
count_out : out unsigned (3 downto 0);
clk : in std_logic;
enable:in std_logic;
reset: in std_logic) ;
end four_bit_counter;
architecture arc of four_bit_counter is
signal count : unsigned (3 downto 0);
begin
process (clk, reset, enable)
begin
if (reset = '1') then
count <= "0000";
elsif (clk' event and clk = '1') then
if (enable = '1') then
if (count="1010") then
count<="0000";
else
count <= count +1;
end if;
end ;
end if;
end process;
count_out <= count;
end arc;
I have the error
Error (10327): VHDL error at four_bit_counter.vhd(22): can't determine definition of operator ""="" -- found 2 possible definitions
and I don't know how to fix this.
The two possible definitions are both from package std_logic_arith
function "="(L: UNSIGNED; R: UNSIGNED) return BOOLEAN;
function "="(L: SIGNED; R: UNSIGNED) return BOOLEAN;
The ambiguity comes from overload resolution for the equality operator due to the package providing the second definition and how the type of the right operand a string literal is determined.
See IEEE Std 1076-2008 9.3.2 Literals:
String and bit string literals are representations of one-dimensional arrays of characters. The type of a string or bit string literal shall be determinable solely from the context in which the literal appears, excluding the literal itself but using the fact that the type of the literal shall be a one-dimensional array of a character type. The lexical structure of string and bit string literals is defined in Clause 15.
Here the context is the equality operator, where 12.5 The context of overload resolution specifies the error:
Overloading is defined for names, subprograms, and enumeration literals.
For overloaded entities, overload resolution determines the actual meaning that an occurrence of an identifier or a character literal has whenever the visibility rules have determined that more than one meaning is acceptable at the place of this occurrence; overload resolution likewise determines the actual meaning of an occurrence of an operator or basic operation (see 5.1).
At such a place, all visible declarations are considered. The occurrence is only legal if there is exactly one interpretation of each constituent of the innermost complete context. ...
Overloads for operators are provided by function declarations (
4.5.2 Operator overloading). For a binary operator the left operand is association with the first function parameter and the right parameter is associated with the second parameter. The return value is a Boolean (again from context, it's an if statement's condition which is a Boolean expression).
The type of the right operand can't be determined from context.
There are several possible solutions
Use the IEEE's numeric_std package instead where functions implementing operators don't have both signed and unsigned operands. Package numeric_std is incorporated into the standard's -2008 revision leading to package std_logic_arith's eventual deprecation.
Use a qualified expression (9.3.5) to specifically state the type of the operand.
if count = unsigned'("1010") then
(the redundant parentheses around the condition have been removed for clarity)
Rely on an abstract literal (15.5) where the ambiguity doesn't exist. This can either be of the form of a decimal literal (15.5.2) or based literal (15.5.3).
Use a function call to the overloaded operator's declaration with a selected name noting that named association can't be used for operator overloads.
Define an object (here a constant) with that value provided by a value expression. The type is inherent in an object declaration.

VHDL Case choice is not locally static

This code works with some tools
Aldec Riviera Pro
but not others
GHDL ( ERROR choice must be locally static expression)
LIBRARY IEEE;
USE IEEE.std_logic_1164.ALL;
USE IEEE.numeric_std.ALL;
ENTITY INSTRUCTION_PROCESSOR IS
PORT (
clk : IN std_logic;
instruction : IN INTEGER
);
END ENTITY INSTRUCTION_PROCESSOR;
ARCHITECTURE behavioural OF INSTRUCTION_PROCESSOR IS
TYPE INSTRUCTION_t IS RECORD
instr : INTEGER;
cycles : INTEGER;
END RECORD;
CONSTANT CMD_A : INSTRUCTION_t := (instr => 0, cycles => 5);
CONSTANT CMD_B : INSTRUCTION_t := (instr => 1, cycles => 3);
BEGIN
PROCESSOR : PROCESS (clk)
VARIABLE loop_cycles : INTEGER := 0;
BEGIN
IF clk'event AND clk = '1' THEN
CASE instruction IS
WHEN CMD_A.instr =>
loop_cycles := CMD_A.cycles;
WHEN CMD_B.instr =>
loop_cycles := CMD_B.cycles;
WHEN OTHERS =>
NULL;
END CASE;
END IF;
END PROCESS;
END ARCHITECTURE;
https://www.edaplayground.com/x/jYD
since CMD_A and CMD_B are declared as constant records i would expect this to work...
any words of wisdom or is it just a bad idea?
I'm not sure the ghdl-0.35 version on EDA playground is up to handling --std=08 (-2008) for this issue without trying it. A recent ghdl-0.37-dev version shows it works:
ghdl -a --std=08 instruction_processor.vhdl
ghdl -e --std=08 tb
instruction_processor.vhdl:68:8:error: for default port binding of component instance "uut":
instruction_processor.vhdl:68:8:error: type of signal interface "instruction" declared at line 56:9
instruction_processor.vhdl:68:8:error: not compatible with type of port "instruction" declared at line 9:9
instruction_processor.vhdl:68:8:error: signal interface "cycles" has no association in entity "instruction_processor"
ghdl:error: compilation error
even if the testbench and/or entity header needs a bit of work. Both INSTRUCTION_PROCESSOR and TB are located in the same design file used above.
The IEEE Std 1076-2008 revision changed some definitions in 9.4.2 Locally static primaries
9.4.2 Locally static primaries
An expression is said to be locally static if and only if every operator in the expression denotes an implicitly defined operator or an operator defined in one of the packages STD_LOGIC_1164, NUMERIC_BIT, NUMERIC_STD, NUMERIC_BIT_UNSIGNED, or NUMERIC_STD_UNSIGNED in library IEEE, and if every primary in the expression is a locally static primary, where a locally static primary is defined to be one of the following:
...
m) A record aggregate in which all expressions in element associations are locally static expressions.
...
Prior to -2008 a an aggregate could not be locally static. An aggregate is an expression which is 'a formula that defines the computation of a value', previously always globally static for a constant declaration value expression.
Allowing certain expressions to be locally static comes from the VHDL-200x effort producing the -2008 revision (Fast Track Proposal FT-22). The idea is expressions with locally static primaries that produce values from basic or predefined operations including those found in IEEE library packages listed above are implemented as pure functions and are not dependent on elaboration. To avoid confusion a procedure call is a statement.
Analyzing your code with Aldec Riviera Pro used a -2008 compliant flag according to the EDA playground session from your comment:
Should an earlier revision of the standard be required due to tool chain constraints either the case statement can be replaced by an if statement or a concurrent conditional assignment statement which implies and if statement equivalent. A selected signal assignment statement on the other hand implies a case statement and conforms to the same semantics.
Try to put constraint into the integer.
instruction : IN INTEGER RANGE 0 TO ...;

VHDL initialize signal with maximum value of type

I have this definition:
subtype sample_t is signed(SAMPLE_WIDTH-1 downto 0);
Now in the code I want to set a signal to the maximum value of sample_t divided by 2:
signal max_sample : sample_t;
max_sample <= to_signed(max_sample'<some attribute>/2,max_sample'LENGTH);
I've looked at attributes sample_t'HIGH and sample_t'RIGHT but these seem to return the highest subscript of the array.
From this list: https://www.csee.umbc.edu/portal/help/VHDL/attribute.html
T'HIGH is the highest value of type T.
A'HIGH is the highest subscript of array A or constrained array type.
How to use the first definition on sample_t?
One of the commenters suggestions:
max_sample <= (max_sample'LEFT => '0', others => '1');
works. But this:
max_sample <= (max_sample'LEFT => '0', others => '1')/2;
fails with "OTHERS is illegal aggregate choice for unconstrained target".
why this error?
In VHDL, signed is an array type, not an integer. The core language only knows that it is a collection of std_logic objects. It's interpretation as a number is only by convention introduced by the numeric_std library functions defining the operators and type casts for signed. As such, integer specific attributes aren't going to work on an array type.
The reason why your last attempt at division fails is that the aggregate expression forming the dividend doesn't yet have a fully determined range due to the others. The aggregate is still just an intermediate temporary and can't pick up its length from max_sample. That prevents the division operator from compiling.
It will compile if you use a fully constrained range:
max_sample <= (max_sample'high => '0', max_sample'high-1 downto max_sample'low => '1') / 2;
Or if you use a qualified expression:
max_sample <= sample_t'(max_sample'high => '0', others => '1') / 2;
An alternate solution is just to subtype integer instead of using signed. Then you can use it in a more integery way:
constant SAMPLE_T_MAX : integer := 2**(SAMPLE_WIDTH-1)-1;
subtype sample_t is integer range -SAMPLE_T_MAX-1 to SAMPLE_T_MAX;
max_sample <= sample_t'high; -- Assuming that the "divide by 2" was just to avoid the sign bit
This will not work if sample_t_max exceeds the largest integer size your tooling supports which is still typically 32-bits including the sign. Also, for practical reasons, it is best not to use integer types for signals that will be exposed on the top level port after synthesis.
Otherwise you have to work within the limitations of using array types for numerics. Your options are to resort to bit twiddling as above or just directly compute the max value similarly to the integer subtype:
constant SAMPLE_T_MAX : integer := 2**(sample_t'length-1)-1;
max_sample <= to_signed(SAMPLE_T_MAX, max_sample'length);
The accepted answer from Kevin Thibedeau could not be readily reconciled with the actual question (why this error?). The answer can be explained in terms of the VHDL standard.
First a Minimum, Complete, and Verifiable example can be constructed for the question:
library ieee;
use ieee.std_logic_1164.all;
use ieee.numeric_std.all;
entity foo is
end entity;
architecture fum of foo is
constant SAMPLE_WIDTH: natural := 42; -- pick a number
subtype sample_t is signed(SAMPLE_WIDTH-1 downto 0);
signal max_sample : sample_t;
begin
-- max_sample <= (max_sample'LEFT => '0', others => '1'); -- analyzes
max_sample <= (max_sample'LEFT => '0', others => '1')/2; -- Doesn't analyze
end architecture;
Because we're dealing with semantic rules during analysis (compile) the example doesn't have to do anything besides replicate the error. Error messages aren't standardized in VHDL and will vary by implementation.
The semantics for using an others choice in an aggregate:
IEEE Std 1076-2008 9.3 Aggregates, 9.3.3 Array aggregates, para 7 (in part):
The index range of an array aggregate that has an others choice shall be determinable from the context. That is, an array aggregate with an others choice shall appear only in one of the following contexts:
...
e) As a value expression in an assignment statement, where the target is a declared object (or member thereof), and either the subtype of the target is a fully constrained array subtype or the target is a slice name
This is why the first example (commented out) analyzes. sample_t is a fully constrained subtype, see 5. Types, 5.1 General the definition of fully constrained, para 6 (in part):
A composite subtype is said to be fully constrained if:
-- It is an array subtype with an index constraint and the element subtype either is not a composite subtype or is a fully constrained composite type, or
...
Where the sample_t element base type is std_ulogic and the subtype has an index constraint.
Back to the second example.
We don't satisfy rule e), the aggregate isn't a value expression for the assignment statement, it's an operand for the division operator defined by the "/" function for overload in IEEE package numeric_std:
-- Id: A.25
function "/" (L : UNRESOLVED_SIGNED; R : INTEGER) return UNRESOLVED_SIGNED;
-- Result subtype: UNRESOLVED_SIGNED(L'LENGTH-1 downto 0)
-- Result: Divides an UNRESOLVED_SIGNED vector, L, by an INTEGER, R.
-- If NO_OF_BITS(R) > L'LENGTH, result is truncated to L'LENGTH.
(For earlier revisions of numeric_std the parameter and result types would be SIGNED instead of UNRESOLVED_SIGNED, -2008 formally defines how resolution functions of composite types drivers are defined.)
Because the rules of 9.3.3 paragraph 7 are inclusive instead of exclusive we
need to find a rule that allows us to use the aggregate, and one is readily identified:
i) As the operand of a qualified expression whose type mark denotes a fully constrained array subtype
We can use a qualified expression:
max_sample <= sample_t'(max_sample'LEFT => '0', others => '1')/2;
And this analyzes (compiles) successfully.
To clarify the value expression being assigned to max_sample is the result of division by 2 which uses an operator overload and who's function does not return a constrained subtype. (UNRESOLVED_SIGNED or SIGNED is not constrained).
The reason why there are inclusive rules is to allow the code for associating values with elements of an aggregate to be determined at analysis time (compile time). You'd find by examining previous revisions of the VHDL standard that the list of inclusive rules has been expanded.
The answer to your question with respect to the second example:
max_sample <= (max_sample'LEFT => '0', others => '1')/2;
is that the elements of the aggregate can't be identified without knowing the subtype from context.
If you were to look at the output of the parser producing an abstract syntax tree used for semantic analysis the right hand side expression in the assignment statement can be expressed hierarchically. (11.6 Concurrent signal assignment statements, the waveform is comprised of one or more waveform elements, see 10.5.2 Simple signal assignments, 10.5.2.1 General, a waveform element can contain a value expression, see 10.5.2.2 Executing a simple assignment statement, 9. Expressions, 9.1 General the BNF.)
Using inclusive rules alleviates the need of traversing the expression hierarchy and calculating the subtype of the aggregate (an operand) during analysis and would require semantic characterization of the "/" function not required by the standard. You can also construct cases where the subtype can't be readily ascertained by characterization at analysis time. The result is the rules found in 9.3.3 Array aggregates paragraph 7.
The qualified expression provides the subtype directly.

write on invalid address to RAM in VHDL, Verilog, sim behaviour

Lets have a BRAM or any other memory under Verilog or VHDL.
For example this:
module raminfr (clk, we, a, di, do);
input clk;
input we;
input [4:0] a;
input [3:0] di;
output [3:0] do;
reg [3:0] ram [31:0];
always #(posedge clk) begin
if (we)
ram[a] <= di;
end
assign do = ram[a];
endmodule
Now lets assume that we have already write valid data to "ram".
Does simulators invavalidate all items in "ram" if address "a" will have invalid value (4'bxxxx) ("we"=1 and clk will have posedge)?
Or it lets values in ram as they were?
For Verilog
The IEEE Std 1800-2009 SystemVerilog standard subsumed both the IEEE Std 1364-2005 Verilog standard and the IEEE Std 1800-2005 SystemVerilog standard. The IEEE Std 1800-2012 SystemVerilog standard supplanted the -2009 version.
See IEEE Std 1800-2012 7.4.6 Indexing and slicing of array:
If an index expression is out of bounds or if any bit in the index expression is x or z, then the index shall be invalid. Reading from an unpacked array of any kind with an invalid index shall return the value specified in Table 7-1. Writing to an array with an invalid index shall perform no operation, with the exceptions of writing to element [$+1] of a queue (described in 7.10.1) and creating a new element of an associative array (described in 7.8.6). Implementations may issue a warning if an invalid index occurs for a read or write operation on an array.
For VHDL
An equivalent VHDL design description might be:
library ieee;
use ieee.std_logic_1164.all;
use ieee.numeric_std.all;
entity raminfr is
port (
clk: in std_logic;
we: in std_logic;
a: in std_logic_vector(4 downto 0);
di: in std_logic_vector(3 downto 0);
do: out std_logic_vector(3 downto 0)
);
end entity;
architecture behave of raminfr is
type ram_type is array (0 to 15) of std_logic_vector (3 downto 0);
signal ram: ram_type;
begin
process (clk)
begin
if rising_edge(clk) then
if we = '1' then
ram(to_integer(unsigned(a))) <= di;
end if;
end if;
end process;
do <= ram(to_integer(unsigned(a)));
end architecture;
Where the numeric_std package to_integer function is used to convert the array value of a to an integer index. (VHDL is a bit more flexible here, array indexes can either be integer types or enumerated types, together referred to as discrete types).
Reading the source for to_integer we see it will convert an input unsigned array value containing an 'X' to all 'X's and the 'LEFT value of that being 'X' will return a natural integer subtype value of 0 and optionally report that:
if (XARG(XARG'left) = 'X') then
assert NO_WARNING
report "NUMERIC_STD.TO_INTEGER: metavalue detected, returning 0"
severity warning;
return 0;
end if;
These warnings can be disabled implementation wide by changing the value of NO_WARNING which is locally static. Using to_integer (or with Synopsys package std_logic_arith and function conv_integer) the index will be 0.
Additionally VHDL implementations have the ability to stop simulation on severity warning reports.
While you could handle the result of an assignment with an index provided as an array value differently in (as in 2, 4, 8, 16 or 32 invalidated memory locations depending on the number of 'X' element values of a here), you've already compromised the integrity of your design model state and some corrective should be taken before counting on the simulation results for either a SystemVerilog or VHDL design model.
The overhead of complex fiddling doesn't seem worthwhile in general. These warnings are of a class of warnings that should be reviewed before synthesis.
These warning can occur before array values are reset when their default initial values are metavalues. You can prevent that in most FPGA designs by initializing a and any predecessors so a contains a binary representing value or simply ignoring reports at time 0 before a reset takes affect.
You can also prevent the write to address 0 by initializing we and any predecessor(s) to '0'.
Simulator will not invalidate anything. Instead the write will be ignored.
For reads in such a situation, it will return 'x' though.

Address of array provided as std_logic_vector

I'm trying to construct a ROM, which has as declaration a : in std_logic_vector(5 downto 0) for the access address. My problem its that I don't know how to access the ROM array with a std_logic_vector, Should I use a cast to integer or what else can I do?
My code:
library ieee;
use ieee.std_logic_1164.all;
use ieee.numeric_std.all;
--------------------------------------------------------------------------------
entity imem is
GENERIC(CONSTANT N : INTEGER := 32);
port (a : in std_logic_vector(5 downto 0);
result : out std_logic_vector(N-1 downto 0));
end imem;
architecture behavior of imem is
signal addres : integer;
type memory is array (0 to 64) of std_logic_vector(N-1 downto 0) ;
constant myrom : memory := (
2 => x"11111111" , --255
3 => x"11010101" ,
4 => x"01101000" ,
6 => x"10011011" ,
8 => x"01101101" ,
9 => x"00110111" ,
others => x"00000000" ) ;
begin
addres <= signed(a);
result <= memory(addres);
end behavior;
With this code as shown I get the following error:
imem.vhd:25:21: can't match type conversion with type integer
imem.vhd:25:21: (location of type conversion)
imem.vhd:26:21: conversion not allowed between not closely related types
imem.vhd:26:21: can't match type conversion with type array type "std_logic_vector"
imem.vhd:26:21: (location of type conversion)
ghdl: compilation error
Assuming that a is an unsigned address value, then you must first cast it to unsigned, and then to integer. Note that the result should access myrom and not memory type. The code can then be:
addres <= to_integer(unsigned(a));
result <= myrom(addres);
And you can even skip the intermediate addres signal and do:
result <= myrom(to_integer(unsigned(a)));
The memory type is also one longer than required, since the 6-bit a input can only cover 0 .. 63, and not 0 .. 64. A better way to declare the memory type would be through use the the 'length attribute for a, like:
type memory is array (0 to 2 ** a'length - 1) of std_logic_vector(N-1 downto 0);
ghdl semantics are by default strict -1993 which has an impact on Morten's answer's changes
For:
type memory is array (0 to 2 ** a'length - 1) of
std_logic_vector(N-1 downto 0);
we get:
ghdl -a imem.vhdl
imem.vhdl:15:29:warning: universal integer bound must be numeric literal or attribute
Tristan Gingold the author of ghdl authored an Issue Report leading to a Language Change Specification in 2006, which gave explicit permission to then current (-2002) implementations to treat a range with an expression as one bound as convertible to an integer range when the other bound is a universal integer (a literal). The LCS didn't give permission to do the conversion in implementations conforming to earlier versions of the standard. Tristan's ghdl is strictly by the book here and by default is -1993 compliant and generates an error.
There are two ways to deal with the error. Either use the command line option to ghdl during analysis to specify a version of the standard where the range can be converted to type integer or provide the range directly.
From ghdl --help-options we see:
--std=87/93/00/02/08 select vhdl 87/93/00/02/08 standard
Where this command line flag can be passed as in ghdl -a --std=02 imem.vhdl.
Also the range type can be declared directly as in:
type memory is array (natural range 0 to 2 ** a'length - 1) of
std_logic_vector(N-1 downto 0);
Both methods of analyzing type memory work.
And the moral of all this is that VHDL is a tightly typed language.
Notes
-2008 compliance is not fully implemented in current versions of ghdl.)
There's historical support for interpreting the standard to support the conversion anyway. The LCS overcomes ambiguity.
See IEEE Std 1076-1993 3.2.1.1 Index constraints and discrete ranges para 2 and IEEE Std-1076-2008 5.3.2.2 Index constraints and discrete ranges para 2.
Tristan has since changed the --std= options eliminating -2000 compliance as well as the default standard to 93c which introduces a set of standard relaxations to more closely match industry practices of VHDL tool vendors. The user of a more recent version of ghdl can use --std=93 for strict standard compliance. The issue originally hinged on the VASG (VHDL Analysis and Standardization Group) sponsored by DAC not being allowed to issued Interpretations of standards after -1987. It's safe to say there is no single implementation of any VHDL standard that completely adheres to a particular revision.

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