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MLRISC
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<a href="INTRO.html"><font size="-1">MLRISC</font></a><br>
<a href="contributors.html"><font size="-1">Contributors</font></a><br>
<a href="requirements.html"><font size="-1">Requirements</font></a><br>
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Overview
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<a href="problem.html"><font size="-1">Problem Statement</font></a><br>
<a href="contributions.html"><font size="-1">Contributions</font></a><br>
<a href="mlrisc-compiler.html"><font size="-1">MLRISC Based Compiler</font></a><br>
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System
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<a href="mlrisc-arch.html"><font size="-1">Architecture of MLRISC</font></a><br>
<a href="mltree.html"><font size="-1"><font color="#486591"><b>The MLTREE Language</b></font></font></a><br>
<a href="mltree-ext.html"><font size="-1">MLTree Extensions</font></a><br>
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<a href="mlrisc-ir.html"><font size="-1">The MLRISC IR</font></a><br>
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Back Ends
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<a href="alpha.html"><font size="-1">The Alpha Back End</font></a><br>
<a href="hppa.html"><font size="-1">The PA RISC Back End</font></a><br>
<a href="sparc.html"><font size="-1">The Sparc Back End</font></a><br>
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<a href="mips.html"><font size="-1">The MIPS Back End</font></a><br>
<a href="C6.html"><font size="-1">The TI C6x Back End</font></a><br>
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Basic Types
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<center><h1><font color="#486591"><b>The MLTREE Language</b></font></h1></center>
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The MLTREE Language
</font>
</td></tr></table><tr><td>
<a href="#link0000"><font size="-1" color="#486591">The Definitions</font></a><br>
-<a href="#link0001"><font size="-1" color="#486591">Basic Types</font></a><br>
-<a href="#link0002"><font size="-1" color="#486591">The Basis</font></a><br>
<a href="#link0003"><font size="-1" color="#486591">Integer Expressions</font></a><br>
-<a href="#link0004"><font size="-1" color="#486591">Sign and Zero Extension</font></a><br>
-<a href="#link0005"><font size="-1" color="#486591">Conditional Move</font></a><br>
-<a href="#link0006"><font size="-1" color="#486591">Integer Loads</font></a><br>
-<a href="#link0007"><font size="-1" color="#486591">Miscellaneous Integer Operators</font></a><br>
<a href="#link0008"><font size="-1" color="#486591">Floating Point Expressions</font></a><br>
<a href="#link0009"><font size="-1" color="#486591">Condition Expressions</font></a><br>
<a href="#link0010"><font size="-1" color="#486591">Statements</font></a><br>
-<a href="#link0011"><font size="-1" color="#486591">Assignments</font></a><br>
-<a href="#link0012"><font size="-1" color="#486591">Parallel Copies</font></a><br>
-<a href="#link0013"><font size="-1" color="#486591">Jumps and Conditional Branches</font></a><br>
-<a href="#link0014"><font size="-1" color="#486591">Calls and Returns</font></a><br>
-<a href="#link0015"><font size="-1" color="#486591">Stores</font></a><br>
-<a href="#link0016"><font size="-1" color="#486591">Miscelleneous Statements</font></a><br>
<a href="#link0017"><font size="-1" color="#486591">Annotations</font></a><br>
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<font color="#ff0000">MLTree</font> is the
register transfer language used in the MLRISC system.
It serves two important purposes:
<img alt="MLTree" src=pictures/png/mlrisc-ir.png align=right>
<ol>
<li> As an intermediate representation for a compiler front-end
to talk to the MLRISC system,
<li> As specifications for instruction semantics
</ol>
The latter is needed for optimizations which require precise knowledge of such;
for example, algebraic simplification and constant folding.
<p>
MLTree is a low-level <font color="#ff0000">typed</font> language:
all operations are typed by its width or precision.
Operations on floating point, integer, and condition code
are also segregated, to prevent accidental misuse.
MLTree is also <em>tree-oriented</em> so that it is possible to write efficient
MLTree transformation routines that uses SML pattern matching.
<p>
Here are a few examples of MLTree statements.
<font color="#000000"><small><pre>
MV(32,t,
ADDT(32,
MULT(32,REG(32,b),REG(32,b)),
MULT(32,
MULT(32,LI(4),REG(32,a)),REG(32,c))))
</pre></small></font>
computes <tt>t := b*b + 4*a*c</tt>, all in 32-bit precision and overflow
trap enabled; while
<font color="#000000"><small><pre>
MV(32,t,
ADD(32,
CVTI2I(32,SIGN_EXTEND,8,
LOAD(8,
ADD(32,REG(32,a),REG(32,i))))))
</pre></small></font>
loads the byte in address <tt>a+i</tt> and sign extend it to a 32-bit
value.
<p>
The statement
<font color="#000000"><small><pre>
IF([],CMP(64,GE,REG(64,a),LI 0),
MV(64, t, REG(64, a)),
MV(64, t, NEG(64, REG(64, a)))
)
</pre></small></font>
in more traditional form means:
<font color="#000000"><small><pre>
if a >= 0 then
t := a
else
t := -a
</pre></small></font>
This example can be also expressed in a few different ways:
<ol>
<li> With the conditional move construct described in
Section <a href="mltree.html#sec:cond-move">Conditional Move</a>:
<font color="#000000"><small><pre>
MV(64, t,
COND(CMP(64, GE, REG(64, a)),
REG(64, a),
NEG(64, REG(64, a))))
</pre></small></font>
<li> With explicit branching using the conditional branch
construct <tt>BCC</tt>:
<font color="#000000"><small><pre>
MV(64, t, REG(64, a));
BCC([], CMP(64, GE, REG(64, a)), L1);
MV(64, t, NEG(64, REG(64, a)));
DEFINE L1;
</pre></small></font>
</ol>
<a name="link0000"></a>
<h2><font color="#486591">The Definitions</font></h2>
MLTree is defined in the signature <a href="../../mltree/mltree.sig" target=code><tt>MLTREE</tt></a>
and the functor <a href="../../mltree/mltree.sml" target=code><tt>MLTreeF</tt></a>
<p>
The functor <tt>MLTreeF</tt> is parameterized in terms of
the label expression type, the client supplied region datatype,
the instruction stream type, and the client defined MLTree extensions.
<font color="#000000"><small><pre>
<font color="#6060a0"><b>functor</b></font> MLTreeF
(<font color="#6060a0"><b>structure</b></font> LabelExp : <a href="labelexp.html">LABELEXP</a>
<font color="#6060a0"><b>structure</b></font> Region : <a href="regions.html">REGION</a>
<font color="#6060a0"><b>structure</b></font> Stream : <a href="streams.html">INSTRUCTION_STREAM</a>
<font color="#6060a0"><b>structure</b></font> Extension : <a href="../../mltree/mltree-extension.sig" target=code>MLTREE_EXTENSION</a>
) : MLTREE
</pre></small></font>
<a name="link0001"></a>
<h3><font color="#486591">Basic Types</font></h3>
The basic types in MLTree are statements (<font color="#ff0000"><tt>stm</tt></font>)
integer expressions (<font color="#ff0000"><tt>rexp</tt></font>),
floating point expression (<font color="#ff0000"><tt>fexp</tt></font>),
and conditional expressions (<font color="#ff0000"><tt>ccexp</tt></font>).
Statements are evaluated for their effects,
while expressions are evaluated for their value. (Some expressions
could also have trapping effects. The semantics of traps are unspecified.)
These types are parameterized by an extension
type, which we can use to extend the set of MLTree
operators. How this is used is described in Section <a href="mltree-ext.html#sec:mltree-extension">MLTree Extensions</a>.
<p>
References to registers are represented internally as integers, and are denoted
as the type <tt>reg</tt>. In addition, we use the types <tt>src</tt> and <tt>dst</tt>
as abbreviations for source and destination registers.
<font color="#000000"><small><pre>
<font color="#6060a0"><b>type</b></font> reg = int
<font color="#6060a0"><b>type</b></font> src = reg
<font color="#6060a0"><b>type</b></font> dst = reg
</pre></small></font>
All operators on MLTree are <em>typed</em>
by the number of bits that
they work on. For example, 32-bit addition between <tt>a</tt> and <tt>b</tt>
is written as <tt>ADD(32,a,b)</tt>, while 64-bit addition between the same
is written as <tt>ADD(64,a,b)</tt>. Floating point operations are
denoted in the same manner. For example, IEEE single-precision floating
point add is written as <tt>FADD(32,a,b)</tt>, while the same in
double-precision is written as <tt>FADD(64,a,b)</tt>
<p>
Note that these types are low level. Higher level distinctions such
as signed and unsigned integer value, are not distinguished by the type.
Instead, operators are usually partitioned into signed and unsigned versions,
and it is legal (and often useful!) to mix signed and unsigned operators in
an expression.
<p>
Currently, we don't provide a direct way to specify non-IEEE floating point
together with
IEEE floating point arithmetic. If this distinction is needed then
it can be encoded using the extension mechanism described
in Section <a href="mltree-ext.html#sec:mltree-extension">MLTree Extensions</a>.
<p>
We use the types <tt>ty</tt> and <tt>fty</tt> to stand for the number of
bits in integer and floating point operations.
<font color="#000000"><small><pre>
<font color="#6060a0"><b>type</b></font> ty = int
<font color="#6060a0"><b>type</b></font> fty = int
</pre></small></font>
<a name="link0002"></a>
<h3><font color="#486591">The Basis</font></h3>
The signature <a href="../../mltree/mltree-basis.sig" target=code>MLTREE_BASIS</a>
defines the basic helper types used in the MLTREE signature.
<font color="#000000"><small><pre>
<font color="#6060a0"><b>signature</b></font> MLTREE_BASIS =
<font color="#6060a0"><b><font color="#6060a0"><b>sig</b></font></b></font>
<font color="#6060a0"><b>datatype</b></font> cond = LT | LTU | LE | LEU | EQ | NE | GE | GEU | GT | GTU
<font color="#6060a0"><b>datatype</b></font> fcond =
? | !<=> | == | ?= | !<> | !?>= | < | ?< | !>= | !?> |
<= | ?<= | !> | !?<= | > | ?> | !<= | !?< | >= | ?>= |
!< | !?= | <> | != | !? | <=> | ?<>
<font color="#6060a0"><b>datatype</b></font> ext = SIGN_EXTEND | ZERO_EXTEND
<font color="#6060a0"><b>datatype</b></font> rounding_mode = TO_NEAREST | TO_NEGINF | TO_POSINF | TO_ZERO
<font color="#6060a0"><b>type</b></font> ty = int
<font color="#6060a0"><b>type</b></font> fty = int
<font color="#6060a0"><b>end</b></font>
</pre></small></font>
The most important of these are the
types <font color="#ff0000"><tt>cond</tt></font> and <font color="#ff0000"><tt>fcond</tt></font>, which represent the set of integer
and floating point comparisions. These types can be combined with
the comparison constructors <tt>CMP</tt> and <tt>FCMP</tt> to form
integer and floating point comparisions.
<table border=1 align=left><tr><td align=center>
Operator </td><td align=center> Comparison </tr><tr><td align=center>
<tt>LT</tt> </td><td align=center> Signed less than </tr><tr><td align=center>
<tt>LTU</tt> </td><td align=center> Unsigned less than </tr><tr><td align=center>
<tt>LE</tt> </td><td align=center> Signed less than or equal </tr><tr><td align=center>
<tt>LEU</tt> </td><td align=center> Unsigned less than or equal </tr><tr><td align=center>
<tt>EQ</tt> </td><td align=center> Equal </tr><tr><td align=center>
<tt>NE</tt> </td><td align=center> Not equal </tr><tr><td align=center>
<tt>GE</tt> </td><td align=center> Signed greater than or equal </tr><tr><td align=center>
<tt>GEU</tt> </td><td align=center> Unsigned greater than or equal </tr><tr><td align=center>
<tt>GT</tt> </td><td align=center> Signed greater than </tr><tr><td align=center>
<tt>GTU</tt> </td><td align=center> Unsigned greater than </tr><tr><td align=center>
</td></tr></table>
Floating point comparisons can be ``decoded'' as follows.
In IEEE floating point, there are four different basic comparisons
tests that we can performed given two numbers <math class="inline"><i>a</i></math> and <math class="inline"><i>y</i></math>:
<dl>
<dt><font color="#000070"><math class="inline"><i>a < b</i></math></font><dd> Is <math class="inline"><i>a</i></math> less than <math class="inline"><i>b</i></math>?
<dt><font color="#000070"><math class="inline"><i>a = b</i></math></font><dd> Is <math class="inline"><i>a</i></math> equal to <math class="inline"><i>b</i></math>?
<dt><font color="#000070"><math class="inline"><i>a > b</i></math></font><dd> Is <math class="inline"><i>a</i></math> greater than to <math class="inline"><i>b</i></math>?
<dt><font color="#000070"><math class="inline"><i>a ? b</i></math></font><dd> Are <math class="inline"><i>a</i></math> and <math class="inline"><i>b</i></math> unordered (incomparable)?
</dl>
Comparisons can be joined together. For example,
given two double-precision floating point expressions <math class="inline"><i>a</i></math> and <math class="inline"><i>b</i></math>,
the expression <tt>FCMP(64,<=>,a,b)</tt>
asks whether <math class="inline"><i>a</i></math> is less than, equal to or greater than <math class="inline"><i>b</i></math>, i.e.~whether
<math class="inline"><i>a</i></math> and <math class="inline"><i>b</i></math> are comparable.
The special symbol <tt>!</tt> negates
the meaning the of comparison. For example, <tt>FCMP(64,!>=,a,b)</tt>
means testing whether <math class="inline"><i>a</i></math> is less than or incomparable with <math class="inline"><i>b</i></math>.
<p>
<a name="link0003"></a>
<h2><font color="#486591">Integer Expressions</font></h2>
A reference to the <math class="inline"><i>i</i></math>th
integer register with an <math class="inline"><i>n</i></math>-bit value is written
as <tt>REG(</tt><math class="inline"><i>n</i></math>,<math class="inline"><i>i</i></math><tt>)</tt>. The operators <tt>LI</tt>, <tt>LI32</tt>,
and <tt>LABEL</tt>, <tt>CONST</tt> are used to represent constant expressions
of various forms. The sizes of these constants are inferred from context.
<font color="#000000"><small><pre>
REG : ty * reg -> rexp
LI : int -> rexp
LI32 : Word32.word -> rexp
LABEL : LabelExp.labexp -> rexp
CONST : Constant.const -> rexp
</pre></small></font>
The following figure lists all the basic integer operators and their
intuitive meanings. All operators except <tt>NOTB, NEG, NEGT</tt> are binary
and have the type
<font color="#000000"><small><pre>
ty * rexp * rexp -> rexp
</pre></small></font>
The operators <tt>NOTB, NEG, NEGT</tt> have the type
<font color="#000000"><small><pre>
ty * rexp -> rexp
</pre></small></font>
<table border=1 align=center><tr><td align=left>
<tt>ADD</tt> </td><td align=left> Twos complement addition </tr><tr><td align=left>
<tt>NEG</tt> </td><td align=left> negation </tr><tr><td align=left>
<tt>SUB</tt> </td><td align=left> Twos complement subtraction </tr><tr><td align=left>
<tt>MULS</tt> </td><td align=left> Signed multiplication </tr><tr><td align=left>
<tt>DIVS</tt> </td><td align=left> Signed division, round to zero (nontrapping) </tr><tr><td align=left>
<tt>QUOTS</tt> </td><td align=left> Signed division, round to negative infinity (nontrapping) </tr><tr><td align=left>
<tt>REMS</tt> </td><td align=left> Signed remainder (???) </tr><tr><td align=left>
<tt>MULU</tt> </td><td align=left> Unsigned multiplication </tr><tr><td align=left>
<tt>DIVU</tt> </td><td align=left> Unsigned division </tr><tr><td align=left>
<tt>REMU</tt> </td><td align=left> Unsigned remainder </tr><tr><td align=left>
<tt>NEGT</tt> </td><td align=left> signed negation, trap on overflow </tr><tr><td align=left>
<tt>ADDT</tt> </td><td align=left> Signed addition, trap on overflow </tr><tr><td align=left>
<tt>SUBT</tt> </td><td align=left> Signed subtraction, trap on overflow </tr><tr><td align=left>
<tt>MULT</tt> </td><td align=left> Signed multiplication, trap on overflow </tr><tr><td align=left>
<tt>DIVT</tt> </td><td align=left> Signed division, round to zero,
trap on overflow or division by zero </tr><tr><td align=left>
<tt>QUOTT</tt> </td><td align=left> Signed division, round to negative infinity, trap on overflow or division by zero </tr><tr><td align=left>
<tt>REMT</tt> </td><td align=left> Signed remainder, trap on division by zero </tr><tr><td align=left>
<tt>ANDB</tt> </td><td align=left> bitwise and </tr><tr><td align=left>
<tt>ORB</tt> </td><td align=left> bitwise or </tr><tr><td align=left>
<tt>XORB</tt> </td><td align=left> bitwise exclusive or </tr><tr><td align=left>
<tt>NOTB</tt> </td><td align=left> ones complement </tr><tr><td align=left>
<tt>SRA</tt> </td><td align=left> arithmetic right shift </tr><tr><td align=left>
<tt>SRL</tt> </td><td align=left> logical right shift </tr><tr><td align=left>
<tt>SLL</tt> </td><td align=left> logical left shift </tr><tr><td align=left>
</td></tr></table>
<a name="link0004"></a>
<h3><font color="#486591">Sign and Zero Extension</font></h3>
Sign extension and zero extension are written using the operator
<tt>CVTI2I</tt>. <tt>CVTI2I(</tt><math class="inline"><i>m</i></math>,<tt>SIGN_EXTEND</tt>,<math class="inline"><i>n</i></math>,<math class="inline"><i>e</i></math><tt>)</tt>
sign extends the <math class="inline"><i>n</i></math>-bit value <math class="inline"><i>e</i></math> to an <math class="inline"><i>m</i></math>-bit value, i.e. the
<math class="inline"><i>n-1</i></math>th bit is of <math class="inline"><i>e</i></math> is treated as the sign bit. Similarly,
<tt>CVTI2I(</tt><math class="inline"><i>m</i></math>,<tt>ZERO_EXTEND</tt>,<math class="inline"><i>n</i></math>,<math class="inline"><i>e</i></math><tt>)</tt>
zero extends an <math class="inline"><i>n</i></math>-bit value to an <math class="inline"><i>m</i></math>-bit
value. If <math class="inline"><i>m <= n</i></math>, then
<tt>CVTI2I(</tt><math class="inline"><i>m</i></math>,<tt>SIGN_EXTEND</tt>,<math class="inline"><i>n</i></math>,<math class="inline"><i>e</i></math><tt>)</tt> =
<tt>CVTI2I</tt>(<math class="inline"><i>m</i></math>,<tt>ZERO_EXTEND</tt>,<math class="inline"><i>n</i></math>,<math class="inline"><i>e</i></math><tt>)</tt>.
<p>
<font color="#000000"><small><pre>
<font color="#6060a0"><b>datatype</b></font> ext = SIGN_EXTEND | ZERO_EXTEND
CVTI2I : ty * ext * ty * rexp -> rexp
</pre></small></font>
<a name="link0005"></a>
<h3><font color="#486591">Conditional Move</font></h3>
<a name="sec:cond-move"></a>
Most new superscalar architectures incorporate conditional move
instructions in their ISAs.
Modern VLIW architectures also directly support full predication.
Since branching (especially with data dependent branches) can
introduce extra latencies in highly pipelined architectures,
condtional moves should be used in place of short branch sequences.
MLTree provide a conditional move instruction <tt>COND</tt>,
to make it possible to directly express conditional moves without using
branches.
<font color="#000000"><small><pre>
COND : ty * ccexp * rexp * rexp -> rexp
</pre></small></font>
Semantically, <tt>COND(</tt><em>ty</em>,<em>cc</em>,<math class="inline"><i>a</i></math>,<math class="inline"><i>b</i></math><tt>)</tt> means to evaluate
<em>cc</em>, and if <em>cc</em> evaluates to true then the value of the entire expression is
<math class="inline"><i>a</i></math>; otherwise the value is <math class="inline"><i>b</i></math>. Note that <math class="inline"><i>a</i></math> and <math class="inline"><i>b</i></math> are allowed to be
<em>eagerly</em>
evaluated. In fact, we are allowed to evaluate to <em>both</em>
branches, one branch, or neither~\footnote{When possible.}.
<p>
Various idioms of the <tt>COND</tt> form are useful for expressing common
constructs in many programming languages. For example, MLTree does not
provide a primitive construct for converting an integer value <tt>x</tt> to a
boolean value (0 or 1). But using <tt>COND</tt>, this is expressible as
<tt>COND(32,CMP(32,NE,x,LI 0),LI 1,LI 0)</tt>. SML/NJ represents
the boolean values true and false as machine integers 3 and 1 respectively.
To convert a boolean condition <math class="inline"><i>e</i></math> into an ML boolean value, we can use
<font color="#000000"><small><pre>
COND(32,e,LI 3,LI 1)
</pre></small></font>
Common C idioms can be easily mapped into the <tt>COND</tt> form. For example,
<ul>
<li> <tt>if (e1) x = y</tt> translates into
<tt>MV(32,x,COND(32,e1,REG(32,y),REG(32,x)))</tt>
<li>
<font color="#000000"><small><pre>
x = e1;
if (e2) x = y
</pre></small></font>
translates into
<tt>MV(32,x,COND(32,e2,REG(32,y),e1))</tt>
<li> <tt>x = e1 == e2</tt> translates into
<tt>MV(32,x,COND(32,CMP(32,EQ,e1,e2),LI 1,LI 0)</tt>
<li> <tt>x = ! e</tt> translates into
<tt>MV(32,x,COND(32,CMP(32,NE,e,LI 0),LI 1,LI 0)</tt>
<li> <tt>x = e ? y : z</tt> translates into
<tt>MV(32,x,COND(32,e,REG(32,y),REG(32,z)))</tt>, and
<li> <tt>x = y < z ? y : z</tt> translates into
<font color="#000000"><pre>
MV(32,x,
COND(32,
CMP(32,LT,REG(32,y),REG(32,z)),
REG(32,y),REG(32,z)))
</pre></font>
</ul>
<p>
In general, the <tt>COND</tt> form should be used in place of MLTree's branching
constructs whenever possible, since the former is usually highly
optimized in various MLRISC backends.
<p>
<a name="link0006"></a>
<h3><font color="#486591">Integer Loads</font></h3>
Integer loads are written using the constructor <tt>LOAD</tt>.
<font color="#000000"><small><pre>
LOAD : ty * rexp * Region.region -> rexp
</pre></small></font>
The client is required to specify a <a href="regions.html">region</a> that
serves as aliasing information for the load.
<p>
<a name="link0007"></a>
<h3><font color="#486591">Miscellaneous Integer Operators</font></h3>
An expression of the <tt>LET</tt>(<math class="inline"><i>s</i></math>,<math class="inline"><i>e</i></math>) evaluates the statement <math class="inline"><i>s</i></math> for
its effect, and then return the value of expression <math class="inline"><i>e</i></math>.
<font color="#000000"><small><pre>
LET : stm * rexp -> rexp
</pre></small></font>
Since the order of evaluation is MLTree operators are
<em>unspecified</em>
the use of this operator should be severely restricted to only
<em>side-effect</em>-free forms.
<p>
<a name="link0008"></a>
<h2><font color="#486591">Floating Point Expressions</font></h2>
Floating registers are referenced using the term <tt>FREG</tt>. The
<math class="inline"><i>i</i></math>th floating point register with type <math class="inline"><i>n</i></math> is written
as <tt>FREG(</tt><math class="inline"><i>n</i></math>,<math class="inline"><i>i</i></math><tt>)</tt>.
<font color="#000000"><small><pre>
FREG : fty * src -> fexp
</pre></small></font>
Built-in floating point operations include addition (<tt>FADD</tt>),
subtraction (<tt>FSUB</tt>), multiplication (<tt>FMUL</tt>), division
(<tt>FDIV</tt>), absolute value (<tt>FABS</tt>), negation (<tt>FNEG</tt>)
and square root (<tt>FSQRT</tt>).
<font color="#000000"><small><pre>
FADD : fty * fexp * fexp -> fexp
FSUB : fty * fexp * fexp -> fexp
FMUL : fty * fexp * fexp -> fexp
FDIV : fty * fexp * fexp -> fexp
FABS : fty * fexp -> fexp
FNEG : fty * fexp -> fexp
FSQRT : fty * fexp -> fexp
</pre></small></font>
A special operator is provided for manipulating signs.
To combine the sign of <math class="inline"><i>a</i></math> with the magnitude of <math class="inline"><i>b</i></math>, we can
write <tt>FCOPYSIGN(</tt><math class="inline"><i>a</i></math>,<math class="inline"><i>b</i></math><tt>)</tt>\footnote{What should
happen if <math class="inline"><i>a</i></math> or <math class="inline"><i>b</i></math> is nan?}.
<font color="#000000"><small><pre>
FCOPYSIGN : fty * fexp * fexp -> fexp
</pre></small></font>
To convert an <math class="inline"><i>n</i></math>-bit signed integer <math class="inline"><i>e</i></math> into an <math class="inline"><i>m</i></math>-bit floating point value,
we can write <tt>CVTI2F(</tt><math class="inline"><i>m</i></math>,<math class="inline"><i>n</i></math>,<math class="inline"><i>e</i></math><tt>)</tt>\footnote{What happen to unsigned integers?}.
<font color="#000000"><small><pre>
CVTI2F : fty * ty * rexp -> fexp
</pre></small></font>
Similarly, to convert an <math class="inline"><i>n</i></math>-bit floating point value <math class="inline"><i>e</i></math> to an <math class="inline"><i>m</i></math>-bit
floating point value, we can write <tt>CVTF2F(</tt><math class="inline"><i>m</i></math>,<math class="inline"><i>n</i></math>,<math class="inline"><i>e</i></math><tt>)</tt>\footnote{
What is the rounding semantics?}.
<font color="#000000"><small><pre>
CVTF2F : fty * fty * -> fexp
</pre></small></font>
<font color="#000000"><small><pre>
<font color="#6060a0"><b>datatype</b></font> rounding_mode = TO_NEAREST | TO_NEGINF | TO_POSINF | TO_ZERO
CVTF2I : ty * rounding_mode * fty * fexp -> rexp
</pre></small></font>
<font color="#000000"><small><pre>
FLOAD : fty * rexp * Region.region -> fexp
</pre></small></font>
<a name="link0009"></a>
<h2><font color="#486591">Condition Expressions</font></h2>
Unlike languages like C, MLTree makes the distinction between condition
expressions and integer expressions. This distinction is necessary for
two purposes:
<ul>
<li> It clarifies the proper meaning intended in a program, and
<li> It makes to possible for a MLRISC backend to map condition
expressions efficiently onto various machine architectures with different
condition code models. For example, architectures like the Intel x86,
Sparc V8, and PowerPC contains dedicated condition code registers, which
are read from and written to by branching and comparison instructions.
On the other hand, architectures such as the Texas Instrument C6, PA RISC,
Sparc V9, and Alpha does not include dedicated condition code registers.
Conditional code registers in these architectures
can be simulated by integer registers.
</ul>
<p>
A conditional code register bit can be referenced using the constructors
<tt>CC</tt> and <tt>FCC</tt>. Note that the <em>condition</em> must be specified
together with the condition code register.
<font color="#000000"><small><pre>
CC : Basis.cond * src -> ccexp
FCC : Basis.fcond * src -> ccexp
</pre></small></font>
For example, to test the <tt>Z</tt> bit of the <tt>%psr</tt> register on the
Sparc architecture, we can used <tt>CC(EQ,SparcCells.psr)</tt>.
<p>
The comparison operators <tt>CMP</tt> and <tt>FCMP</tt> performs integer and
floating point tests. Both of these are <em>typed</em> by the precision
in which the test must be performed under.
<font color="#000000"><small><pre>
CMP : ty * Basis.cond * rexp * rexp -> ccexp
FCMP : fty * Basis.fcond * fexp * fexp -> ccexp
</pre></small></font>
Condition code expressions may be combined with the following
logical connectives, which have the obvious meanings.
<font color="#000000"><small><pre>
TRUE : ccexp
FALSE : ccexp
NOT : ccexp -> ccexp
AND : ccexp * ccexp -> ccexp
OR : ccexp * ccexp -> ccexp
XOR : ccexp * ccexp -> ccexp
</pre></small></font>
<a name="link0010"></a>
<h2><font color="#486591">Statements</font></h2>
Statement forms in MLTree includes assignments, parallel copies,
jumps and condition branches, calls and returns, stores, sequencing,
and annotation.
<p>
<a name="link0011"></a>
<h3><font color="#486591">Assignments</font></h3>
Assignments are segregated among the integer, floating point and
conditional code types. In addition, all assignments are <em>typed</em>
by the precision of destination register.
<p>
<font color="#000000"><small><pre>
MV : ty * dst * rexp -> stm
FMV : fty * dst * fexp -> stm
CCMV : dst * ccexp -> stm
</pre></small></font>
<a name="link0012"></a>
<h3><font color="#486591">Parallel Copies</font></h3>
Special forms are provided for parallel copies for integer and
floating point registers. It is important to emphasize that
the semantics is that all assignments are performed in parallel.
<p>
<font color="#000000"><small><pre>
COPY : ty * dst list * src list -> stm
FCOPY : fty * dst list * src list -> stm
</pre></small></font>
<a name="link0013"></a>
<h3><font color="#486591">Jumps and Conditional Branches</font></h3>
Jumps and conditional branches in MLTree take two additional set of
annotations. The first represents the <font color="#ff0000">control flow</font> and is denoted
by the type <tt>controlflow</tt>. The second represent
<font color="#ff0000">control-dependence</font> and <font color="#ff0000">anti-control-dependence</font>
and is denoted by the type <tt>ctrl</tt>.
<p>
<font color="#000000"><small><pre>
<font color="#6060a0"><b>type</b></font> controlflow = Label.label list
<font color="#6060a0"><b>type</b></font> ctrl = reg list
</pre></small></font>
Control flow annotation is simply a list of labels, which represents
the set of possible targets of the associated jump. Control dependence
annotations attached to a branch or jump instruction represents the
new definition of <font color="#ff0000">pseudo control dependence predicates</font>. These
predicates have no associated dynamic semantics; rather they are used
to constraint the set of potential code motion in an optimizer
(more on this later).
<p>
The primitive jumps and conditional branch forms are represented
by the constructors <tt>JMP</tt>, <tt>BCC</tt>.
<font color="#000000"><small><pre>
JMP : ctrl * rexp * controlflow -> stm
BCC : ctrl * ccexp * Label.label -> stm
</pre></small></font>
In addition to <tt>JMP</tt> and <tt>BCC</tt>,
there is a <em>structured</em> if/then/else statement.
<font color="#000000"><small><pre>
IF : ctrl * ccexp * stm * stm -> stm
</pre></small></font>
Semantically, <tt>IF</tt>(<math class="inline"><i>c,x,y,z</i></math>) is identical to
<font color="#000000"><small><pre>
BCC(<math class="inline"><i>c</i></math>, <math class="inline"><i>x</i></math>, L1)
<math class="inline"><i>z</i></math>
JMP([], L2)
DEFINE L1
<math class="inline"><i>y</i></math>
DEFINE L2
</pre></small></font>
where <tt>L1</tt> and <tt>L2</tt> are new labels, as expected.
<p>
Here's an example of how control dependence predicates are used.
Consider the following MLTree statement:
<font color="#000000"><small><pre>
IF([p], CMP(32, NE, REG(32, a), LI 0),
MV(32, b, PRED(LOAD(32, m, ...)), p),
MV(32, b, LOAD(32, n, ...)))
</pre></small></font>
In the first alternative of the <tt>IF</tt>, the <tt>LOAD</tt>
expression is constrainted by the control dependence
predicate <tt>p</tt> defined in the <tt>IF</tt>,
using the predicate constructor <tt>PRED</tt>. These states that
the load is <em>control dependent</em> on the test of the branch,
and thus it may not be legally hoisted above the branch without
potentially violating the semantics of the program.
For example,
semantics violation may happen if the value of <tt>m</tt> and <tt>a</tt>
is corrolated, and whenever <tt>a</tt> = 0, the address in <tt>m</tt> is
not a legal address.
<p>
Note that on architectures with speculative loads,
the control dependence information can be used to
guide the transformation of control dependent loads into speculative loads.
<p>
Now in constrast, the <tt>LOAD</tt> in the second alternative is not
control dependent on the control dependent predicate <tt>p</tt>, and
thus it is safe and legal to hoist the load above the test, as in
<font color="#000000"><small><pre>
MV(32, b, LOAD(32, n, ...));
IF([p], CMP(32, NE, REG(32, a), LI 0),
MV(32, b, PRED(LOAD(32, m, ...)), p),
SEQ []
)
</pre></small></font>
Of course, such transformation is only performed if the optimizer
phases think that it can benefit performance. Thus the control dependence
information does <em>not</em> directly specify any transformations, but it
is rather used to indicate when aggressive code motions are legal and safe.
<p>
<a name="link0014"></a>
<h3><font color="#486591">Calls and Returns</font></h3>
Calls and returns in MLTree are specified using the constructors
<tt>CALL</tt> and <tt>RET</tt>, which have the following types.
<font color="#000000"><small><pre>
CALL : rexp * controlflow * mlrisc * mlrisc *
ctrl * ctrl * Region.region -> stm
RET : ctrl * controlflow -> stm
</pre></small></font>
The <tt>CALL</tt> form is particularly complex, and require some explanation.
Basically the seven parameters are, in order:
<dl>
<dt><font color="#000070">address</font><dd> of the called routine.
<dt><font color="#000070">control flow</font><dd> annotation for this call. This information
specifies the potential targets of this call instruction. Currently
this information is ignored but will be useful for interprocedural
optimizations in the future.
<dt><font color="#000070">definition and use</font><dd> These lists specify the list of
potential definition and uses during the execution of the call.
Definitions and uses are represented as the type <font color="#ff0000"><tt>mlrisc</tt></font> list.
The contructors for this type is:
<font color="#000000"><small><pre>
CCR : ccexp -> mlrisc
GPR : rexp -> mlrisc
FPR : fexp -> mlrisc
</pre></small></font>
<dt><font color="#000070">definition of control and anti-control dependence</font><dd>
These two lists specifies definitions of control and anti-control dependence.
<dt><font color="#000070">region</font><dd> annotation for the call, which summarizes
the set of potential memory references during execution of the call.
</dl>
<p>
The matching return statement constructor <tt>RET</tt> has two
arguments. These are:
<dl>
<dt><font color="#000070">anti-control dependence</font><dd> This parameter represents
the set of anti-control dependence predicates defined by the return
statement.
<dt><font color="#000070">control flow</font><dd> This parameter specifies the set of matching
procedure entry points of this return. For example, suppose we have
a procedure with entry points <tt>f</tt> and <tt>f'</tt>.
Then the MLTree statements
<font color="#000000"><small><pre>
f: ...
JMP L1
f': ...
L1: ...
RET ([], [f, f'])
</pre></small></font>
can be used to specify that the return is either from
the entries <tt>f</tt> or <tt>f'</tt>.
</dl>
<p>
<a name="link0015"></a>
<h3><font color="#486591">Stores</font></h3>
Stores to integer and floating points are specified using the
constructors <tt>STORE</tt> and <tt>FSTORE</tt>.
<font color="#000000"><small><pre>
STORE : ty * rexp * rexp * Region.region -> stm
FSTORE : fty * rexp * fexp * Region.region -> stm
</pre></small></font>
The general form is
<font color="#000000"><small><pre>
STORE(<math class="inline"><i>width</i></math>, <math class="inline"><i>address</i></math>, <math class="inline"><i>data</i></math>, <math class="inline"><i>region</i></math>)
</pre></small></font>
Stores for condition codes are not provided.
<a name="link0016"></a>
<h3><font color="#486591">Miscelleneous Statements</font></h3>
Other useful statement forms of MLTree are for sequencing (<tt>SEQ</tt>),
defining a local label (<tt>DEFINE</tt>).
<font color="#000000"><small><pre>
SEQ : stm list -> stm
DEFINE : Label.label -> stm
</pre></small></font>
The constructor <tt>DEFINE L</tt> has the same meaning as
executing the method <tt>defineLabel L</tt> in the
<a href="stream.html">stream interface</a>.
<p>
<a name="link0017"></a>
<h2><font color="#486591">Annotations</font></h2>
<a href="annotations.html">Annotations</a> are used as the generic mechanism for
exchanging information between different phases of the MLRISC system, and
between a compiler front end and the MLRISC back end.
The following constructors can be used to annotate a MLTree term with
an annotation:
<font color="#000000"><small><pre>
MARK : rexp * Annotations.annotation -> rexp
FMARK : fexp * Annotations.annotation -> fexp
CCMARK : ccexp * Annotations.annotation -> ccexp
ANNOTATION : stm * Annotations.annotation -> stm
</pre></small></font>
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<a href="mailto:leunga@cs.nyu.edu">Allen Leung</a>
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