@node cl-simd
@section cl-simd
@cindex SSE2 Intrinsics
@cindex Intrinsics, SSE2

The @code{cl-simd} module provides access to SSE2 instructions
(which are nowadays supported by any CPU compatible with x86-64)
in the form of @emph{intrinsic functions}, similar to the way
adopted by modern C compilers. It also provides some lisp-specific
functionality, like setf-able intrinsics for accessing lisp arrays.

When this module is loaded, it defines an @code{:sse2} feature,
which can be subsequently used for conditional compilation of
code that depends on it. Intrinsic functions are available from
the @code{sse} package.

This API, with minor technical differences, is supported by both
ECL and SBCL (x86-64 only).

@menu
* SSE pack types::
* SSE array type::
* Differences from C intrinsics::
* Comparisons and NaN handling::
* Simple extensions::
* Lisp array accessors::
* Example::
@end menu

@node SSE pack types
@subsection SSE pack types

The package defines and/or exports the following types to
represent 128-bit SSE register contents:

@anchor{Type sse:sse-pack}
@deftp {Type} @somepkg{sse-pack,sse} @&optional item-type
The generic SSE pack type.
@end deftp

@anchor{Type sse:int-sse-pack}
@deftp {Type} @somepkg{int-sse-pack,sse}
Same as @code{(sse-pack integer)}.
@end deftp

@anchor{Type sse:float-sse-pack}
@deftp {Type} @somepkg{float-sse-pack,sse}
Same as @code{(sse-pack single-float)}.
@end deftp

@anchor{Type sse:double-sse-pack}
@deftp {Type} @somepkg{double-sse-pack,sse}
Same as @code{(sse-pack double-float)}.
@end deftp

Declaring variable types using the subtype appropriate
for your data is likely to lead to more efficient code
(especially on ECL). However, the compiler implicitly
casts between any subtypes of sse-pack when needed.

Printed representation of SSE packs can be controlled
by binding @code{*sse-pack-print-mode*}:

@anchor{Variable sse:*sse-pack-print-mode*}
@defvr {Variable} @somepkg{@earmuffs{sse-pack-print-mode},sse}
When set to one of @code{:int}, @code{:float} or
@code{:double}, specifies the way SSE packs are
printed. A @code{NIL} value (default) instructs
the implementation to make its best effort to
guess from the data and context.
@end defvr

@node SSE array type
@subsection SSE array type

@anchor{Type sse:sse-array}
@deftp {Type} @somepkg{sse-array,sse} element-type @&optional dimensions
Expands to a lisp array type that is efficiently
supported by AREF-like accessors.
It should be assumed to be a subtype of @code{SIMPLE-ARRAY}.
The type expander signals warnings or errors if it detects
that the element-type argument value is inappropriate or unsafe.
@end deftp

@anchor{Function sse:make-sse-array}
@deffn {Function} @somepkg{make-sse-array,sse} dimensions @&key element-type initial-element displaced-to displaced-index-offset
Creates an object of type @code{sse-array}, or signals an error.
In non-displaced case ensures alignment of the beginning of data to
the 16-byte boundary.
Unlike @code{make-array}, the element type defaults to (unsigned-byte 8).
@end deffn

On ECL this function supports full-featured displacement.
On SBCL it has to simulate it by sharing the underlying
data vector, and does not support nonzero index offset.

@node Differences from C intrinsics
@subsection Differences from C intrinsics

Intel Compiler, GCC and
@url{http://msdn.microsoft.com/en-us/library/y0dh78ez%28VS.80%29.aspx,MSVC}
all support the same set
of SSE intrinsics, originally designed by Intel. This
package generally follows the naming scheme of the C
version, with the following exceptions:

@itemize
@item
Underscores are replaced with dashes, and the @code{_mm_}
prefix is removed in favor of packages.

@item
The 'e' from @code{epi} is dropped because MMX is obsolete
and won't be supported.

@item
@code{_si128} functions are renamed to @code{-pi} for uniformity
and brevity. The author has personally found this discrepancy
in the original C intrinsics naming highly jarring.

@item
Comparisons are named using graphic characters, e.g. @code{<=-ps}
for @code{cmpleps}, or @code{/>-ps} for @code{cmpngtps}. In some
places the set of comparison functions is extended to cover the
full possible range.

@item
Scalar comparison predicates are named like @code{..-ss?} for
@code{comiss}, and @code{..-ssu?} for @code{ucomiss} wrappers.

@item
Conversion functions are renamed to @code{convert-*-to-*} and
@code{truncate-*-to-*}.

@item
A few functions are completely renamed: @code{cpu-mxcsr} (setf-able),
@code{cpu-pause}, @code{cpu-load-fence}, @code{cpu-store-fence},
@code{cpu-memory-fence}, @code{cpu-clflush}, @code{cpu-prefetch-*}.
@end itemize

In addition, foreign pointer access intrinsics have an additional
optional integer offset parameter to allow more efficient coding
of pointer deference, and the most common ones have been renamed
and made SETF-able:

@itemize
@item
@code{mem-ref-ss}, @code{mem-ref-ps}, @code{mem-ref-aps}

@item
@code{mem-ref-sd}, @code{mem-ref-pd}, @code{mem-ref-apd}

@item
@code{mem-ref-pi}, @code{mem-ref-api}, @code{mem-ref-si64}
@end itemize

(The @code{-ap*} version requires alignment.)

@node Comparisons and NaN handling
@subsection Comparisons and NaN handling

Floating-point arithmetic intrinsics have trivial IEEE semantics
when given QNaN and SNaN arguments. Comparisons have more complex
behavior, detailed in the following table:

@multitable { @code{/>=-ss, />=-ps} } { @code{/>=-sd, />=-pd} } { Not greater or equal } { Result for NaN } { QNaN traps }
@item Single-float @tab Double-float @tab Condition @tab Result for NaN @tab QNaN traps
@item @code{=-ss}, @code{=-ps} @tab @code{=-sd}, @code{=-pd} @tab Equal @tab False @tab No
@item @code{<-ss}, @code{<-ps} @tab @code{<-sd}, @code{<-pd} @tab Less @tab False @tab Yes
@item @code{<=-ss}, @code{<=-ps} @tab @code{<=-sd}, @code{<=-pd} @tab Less or equal @tab False @tab Yes
@item @code{>-ss}, @code{>-ps} @tab @code{>-sd}, @code{>-pd} @tab Greater @tab False @tab Yes
@item @code{>=-ss}, @code{>=-ps} @tab @code{>=-sd}, @code{>=-pd} @tab Greater or equal @tab False @tab Yes
@item @code{/=-ss}, @code{/=-ps} @tab @code{/=-sd}, @code{/=-pd} @tab Not equal @tab True @tab No
@item @code{/<-ss}, @code{/<-ps} @tab @code{/<-sd}, @code{/<-pd} @tab Not less @tab True @tab Yes
@item @code{/<=-ss}, @code{/<=-ps} @tab @code{/<=-sd}, @code{/<=-pd} @tab Not less or equal @tab True @tab Yes
@item @code{/>-ss}, @code{/>-ps} @tab @code{/>-sd}, @code{/>-pd} @tab Not greater @tab True @tab Yes
@item @code{/>=-ss}, @code{/>=-ps} @tab @code{/>=-sd}, @code{/>=-pd} @tab Not greater or equal @tab True @tab Yes
@item @code{cmpord-ss}, @code{cmpord-ps} @tab @code{cmpord-sd}, @code{cmpord-pd}
@tab Ordered, i.e. no NaN args @tab False @tab No
@item @code{cmpunord-ss}, @code{cmpunord-ps} @tab @code{cmpunord-sd}, @code{cmpunord-pd}
@tab Unordered, i.e. with NaN args @tab True @tab No
@end multitable

Likewise for scalar comparison predicates, i.e. functions that return the
result of the comparison as a Lisp boolean instead of a bitmask sse-pack:

@multitable { Single-float } { Double-float } { Not greater or equal } { Result for NaN } { QNaN traps }
@item Single-float @tab Double-float @tab Condition @tab Result for NaN @tab QNaN traps
@item @code{=-ss?} @tab @code{=-sd?} @tab Equal @tab True @tab Yes
@item @code{=-ssu?} @tab @code{=-sdu?} @tab Equal @tab True @tab No
@item @code{<-ss?} @tab @code{<-sd?} @tab Less @tab True @tab Yes
@item @code{<-ssu?} @tab @code{<-sdu?} @tab Less @tab True @tab No
@item @code{<=-ss?} @tab @code{<=-sd?} @tab Less or equal @tab True @tab Yes
@item @code{<=-ssu?} @tab @code{<=-sdu?} @tab Less or equal @tab True @tab No
@item @code{>-ss?} @tab @code{>-sd?} @tab Greater @tab False @tab Yes
@item @code{>-ssu?} @tab @code{>-sdu?} @tab Greater @tab False @tab No
@item @code{>=-ss?} @tab @code{>=-sd?} @tab Greater or equal @tab False @tab Yes
@item @code{>=-ssu?} @tab @code{>=-sdu?} @tab Greater or equal @tab False @tab No
@item @code{/=-ss?} @tab @code{/=-sd?} @tab Not equal @tab False @tab Yes
@item @code{/=-ssu?} @tab @code{/=-sdu?} @tab Not equal @tab False @tab No
@end multitable

Note that MSDN specifies different return values for the C counterparts of some
of these functions when called with NaN arguments, but that seems to disagree
with the actually generated code.

@node Simple extensions
@subsection Simple extensions

This module extends the set of basic intrinsics with the following
simple compound functions:

@itemize
@item
@code{neg-ss}, @code{neg-ps}, @code{neg-sd}, @code{neg-pd},
@code{neg-pi8}, @code{neg-pi16}, @code{neg-pi32}, @code{neg-pi64}:

implement numeric negation of the corresponding data type.

@item
@code{not-ps}, @code{not-pd}, @code{not-pi}:

implement bitwise logical inversion.

@item
@code{if-ps}, @code{if-pd}, @code{if-pi}:

perform element-wise combining of two values based on a boolean
condition vector produced as a combination of comparison function
results through bitwise logical functions.

The condition value must use all-zero bitmask for false, and
all-one bitmask for true as a value for each logical vector
element. The result is undefined if any other bit pattern is used.

N.B.: these are @emph{functions}, so both branches of the
conditional are always evaluated.
@end itemize

The module also provides symbol macros that expand into expressions
producing certain constants in the most efficient way:

@itemize
@item
0.0-ps 0.0-pd 0-pi for zero

@item
true-ps true-pd true-pi for all 1 bitmask

@item
false-ps false-pd false-pi for all 0 bitmask (same as zero)
@end itemize

@node Lisp array accessors
@subsection Lisp array accessors

In order to provide better integration with ordinary lisp code,
this module implements a set of AREF-like memory accessors:

@itemize
@item
@code{(ROW-MAJOR-)?AREF-PREFETCH-(T0|T1|T2|NTA)} for cache prefetch.

@item
@code{(ROW-MAJOR-)?AREF-CLFLUSH} for cache flush.

@item
@code{(ROW-MAJOR-)?AREF-[AS]?P[SDI]} for whole-pack read & write.

@item
@code{(ROW-MAJOR-)?AREF-S(S|D|I64)} for scalar read & write.
@end itemize

(Where A = aligned; S = aligned streamed write.)

These accessors can be used with any non-bit specialized
array or vector, without restriction on the precise element
type (although it should be declared at compile time to
ensure generation of the fastest code).

Additional index bound checking is done to ensure that enough
bytes of memory are accessible after the specified index.

As an exception, ROW-MAJOR-AREF-PREFETCH-* does not do any
range checks at all, because the prefetch instructions
are officially safe to use with bad addresses. The
AREF-PREFETCH-* and *-CLFLUSH functions do only ordinary
index checks without the usual 16-byte extension.

@node Example
@subsection Example

This code processes several single-float arrays, storing
either the value of a*b, or c/3.5 into result, depending
on the sign of mode:

@example
(loop for i from 0 below 128 by 4
   do (setf (aref-ps result i)
            (if-ps (<-ps (aref-ps mode i) 0.0-ps)
                   (mul-ps (aref-ps a i) (aref-ps b i))
                   (div-ps (aref-ps c i) (set1-ps 3.5)))))
@end example

As already noted above, both branches of the if are always
evaluated.