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<sect1><title>1 Intel Intrinsic porting guide for Power64LE.</title><para>The goal of this project is to provide functional equivalents of the Intel MMX, SSE, and AVX intrinsic functions, that are commonly used in Linux applications, and make them (or equivalents) available for the PowerPC64LE platform. These X86 intrinsics started with the Intel and Microsoft compilers but were then ported to the GCC compiler. The GCC implementation is a set of headers with inline functions. These inline functions provide a implementation mapping from the Intel/Microsoft dialect intrinsic names to the corresponding GCC Intel built-in's or directly via C language vector extension syntax.</para><para/><para>The current proposal is to start with the existing X86 GCC intrinsic headers and port them (copy and change the source)  to POWER using C language vector extensions, VMX and VSX built-ins. Another key assumption is that we will be able to use many of existing Intel DejaGNU test cases on ./gcc/testsuite/ This document is intended as a guide to developers participating in this effort. However this document provides guidance and examples that should be useful to developers who may encounter X86 intrinsics in code that they are porting to another platform.</para><para/></sect1>
<sect1><title>1.1 Look at the source Luke</title><para>So if this is a code porting activity, where is the source? All the source code we need to look at is in the GCC source trees. You can either git ( the gcc source  or down load one of the recent AT source tars (for example:  You will find the intrinsic headers in the ./gcc/config/i386/ sub-directory.</para><para/><para>If you have a Intel Linux workstation or laptop with GCC installed, you already have these headers, if you want to take a look:</para><para/><para/><para/><para/><para/><para/><para/><para/><para>But depending on the vintage of the distro, these may not be the latest versions of the headers. Looking at the header source will tell you a few things.: The include structure (what other headers are implicitly included). The types that are used at the API. And finally, how the API is implemented.</para><para/></sect1>
<sect1><title>1.1.1 The structure of the intrinsic includes</title><para>The GCC x86 intrinsic functions for vector were initially grouped by technology (MMX and SSE), which starts with MMX continues with SSE through SSE4.1 stacked like a set of Russian dolls.</para><para/><para>Basically each higher layer include, needs typedefs and helper macros defined by the lower level intrinsic includes. mm_malloc.h simply provides wrappers for posix_memalign and free. Then it gets a little weird, starting with the crypto extensions:For AVX, AVX2, and AVX512 they must have decided that the Russian Dolls thing was getting out of hand. AVX et all is split across 14 filesbut they do not want the applications include these individually.So immintrin.h  includes everything Intel vector, include all the AVX, AES, SSE and MMX flavors.</para><para/><para>So what is the net? The include structure provides some strong clues about the order that we should approach this effort.  For example if you need to intrinsic from SSE4 (smmintrin.h) we are likely to need to type definitions from SSE (emmintrin.h). So a bottoms up (MMX, SSE, SSE2, …) approach seems like the best plan of attack. Also saving the AVX parts for latter make sense, as most are just wider forms of operations that already exists in SSE.</para><para/><para>We should use the same include structure to implement our PowerISA equivalent API headers. This will make porting easier (drop-in replacement) and should get the application running quickly on POWER. Then we are in a position to profile and analyze the resulting application. This will show any hot spots where the simple one-to-one transformation results in bottlenecks and additional tuning is needed. For these cases we should improve our tools (SDK MA/SCA) to identify opportunities for, and perhaps propose, alternative sequences that are better tuned to PowerISA and our micro-architecture.</para><para/></sect1>
<sect1><title>1.1.2 The types used for intrinsics</title><para>The type system for Intel intrinsics is a little strange. For example from xmmintrin.h:</para><para/><para>So there is one set of types that are used in the function prototypes of the API, and the internal types that are used in the implementation. Notice the special attribute __may_alias__. From the GCC documentation:So there are a couple of issues here: 1)  the API seem to force the compiler to assume aliasing of any parameter passed by reference. Normally the compiler assumes that parameters of different size do not overlap in storage, which allows more optimization. 2) the data type used at the interface may not be the correct type for the implied operation. So parameters of type __m128i (which is defined as vector long long) is also used for parameters and return values of vector [char | short | int ]. </para><para/><para>This may not matter when using x86 built-in's but does matter when the implementation uses C vector extensions or in our case use PowerPC generic vector built-ins (#<link linkend="">PowerISA Vector Intrinsics|outline</link>). For the later cases the type must be correct for the compiler to generate the correct type (char, short, int, long) (<link linkend="">#1.1.3.How the API is implemented.|outline</link>) for the generic builtin operation. There is also concern that excessive use of __may_alias__ will limit compiler optimization. We are not sure how important this attribute is to the correct operation of the API.  So at a later stage we should experiment with removing it from our implementation for PowerPC</para><para/><para>The good news is that PowerISA has good support for 128-bit vectors and (with the addition of VSX) all the required vector data (char, short, int, long, float, double) types. However Intel supports a wider variety of the vector sizes  than PowerISA does. This started with the 64-bit MMX vector support that preceded SSE and extends to 256-bit and 512-bit vectors of AVX, AVX2, and AVX512 that followed SSE.</para><para/><para>Within the GCC Intel intrinsic implementation these are all implemented as vector attribute extensions of the appropriate  size (   __vector_size__ ({8 | 16 | 32, and 64}). For the PowerPC target  GCC currently only supports the native __vector_size__ ( 16 ). These we can support directly in VMX/VSX registers and associated instructions. The GCC will compile with other   __vector_size__ values, but the resulting types are treated as simple arrays of the element type. This does not allow the compiler to use the vector registers and vector instructions for these (nonnative) vectors.   So what is a programmer to do?</para></sect1>
<sect1><title> Dealing with MMX</title><para>MMX is actually the hard case. The __m64 type supports SIMD vector int types (char, short, int, long).  The  Intel API defines  __m64 as:</para><para/><para>Which is problematic for the PowerPC target (not really supported in GCC) and we would prefer to use a native PowerISA type that can be passed in a single register.  The PowerISA Rotate Under Mask instructions can easily extract and insert integer fields of a General Purpose Register (GPR). This implies that MMX integer types can be handled as a internal union of arrays for the supported element types. So an 64-bit unsigned long long is the best type for parameter passing and return values. Especially for the 64-bit (_si64) operations as these normally generate a single PowerISA instruction.</para><para/><para>The SSE extensions include some convert operations for _m128 to / from _m64 and this includes some int to / from float conversions. However in these cases the float operands always reside in SSE (XMM) registers (which match the PowerISA vector registers) and the MMX registers only contain integer values. POWER8 (PowerISA-2.07) has direct move instructions between GPRs and VSRs. So these transfers are normally a single instruction and any conversions can be handed in the vector unit.</para><para/><para>When transferring a __m64 value to a vector register we should also execute a xxsplatd instruction to insure there is valid data in all four element lanes before doing floating point operations. This avoids generating extraneous floating point exceptions that might be generated by uninitialized parts of the vector. The top two lanes will have the floating point results that are in position for direct transfer to a GPR or stored via Store Float Double (stfd). These operation are internal to the intrinsic implementation and there is no requirement to keep temporary vectors in correct Little Endian form.</para><para/><para>Also for the smaller element sizes and higher element counts (MMX _pi8 and _p16 types) the number of  Rotate Under Mask instructions required to disassemble the 64-bit __m64 into elements, perform the element calculations, and reassemble the elements in a single __m64 value can get larger. In this case we can generate shorter instruction sequences by transfering (via direct move instruction) the GPR __m64 value to the a vector register, performance the SIMD operation there, then transfer the __m64 result back to a GPR.</para><para/></sect1>
<sect1><title> Dealing with AVX and AVX512</title><para>AVX is a bit easier for PowerISA and the ELF V2 ABI. First we have lots (64) of vector registers and a super scalar vector pipe-line (can execute two or more independent 128-bit vector operations concurrently). Second the ELF V2 ABI was designed to pass and return larger aggregates in vector registers:</para><para/><orderedlist><listitem><para>Up to 12 qualified vector arguments can be passed in v2–v13.</para></listitem><listitem><para>A qualified vector argument corresponds to:</para></listitem></orderedlist><para>So the ABI allows for passing up to three structures each representing 512-bit vectors and returning such (512-bit) structure all in VMX registers. This can be extended further by spilling parameters (beyond 12 X 128-bit vectors) to the parameter save area, but we should not need that, as most intrinsics only use 2 or 3 operands.. Vector registers not needed for parameter passing, along with an additional 8 volatile vector registers, are available for scratch and local variables. All can be used by the application without requiring register spill to the save area. So most intrinsic operations on 256- or 512-bit vectors can be held within existing PowerISA vector registers. </para><para/><para>For larger functions that might use multiple AVX 256 or 512-bit intrinsics and, as a result, push beyond the 20 volatile vector registers, the compiler will just allocate non-volatile vector registers by allocating a stack frame and spilling non-volatile vector registers to the save area (as needed in the function prologue). This frees up to 64 vectors (32 x 256-bit or 16 x 512-bit structs) for code optimization. </para><para/><para>Based on the specifics of our ISA and ABI we will not not use __vector_size__ (32) or (64) in the PowerPC implementation of __m256 and __m512 types. Instead we will typedef structs of 2 or 4 vector (__m128) fields. This allows efficient handling of these larger data types without require new GCC language extensions. </para><para/><para>In the end we should use the same type names and definitions as the GCC X86 intrinsic headers where possible. Where that is not possible we can define new typedefs that provide the best mapping to the underlying PowerISA hardware.</para></sect1>
<sect1><title>1.1.3 How is this API implemented.</title><para>One pleasant surprise is that many (at least for the older Intel) Intrinsics are implemented directly in C vector extension code and/or a simple mapping to GCC target specific builtins. </para></sect1>
<sect1><title> Some simple examples</title><para>For example; a vector double splat looks like this:</para><para>Another example:</para><para>Note in the example above the cast to __v2df for the operation. Both __m128d and __v2df are vector double, but __v2df does no have the __may_alias__ attribute. And one more example:</para><para>Note this requires a cast for the compiler to generate the correct code for the intended operation. The parameters and result are the generic __m128i, which is a vector long long with the __may_alias__ attribute. But operation is a vector multiply low unsigned short (__v8hu). So not only do we use the cast to drop the __may_alias__ attribute but we also need to cast to the correct (vector unsigned short) type for the specified operation.</para><para/><para>I have successfully copied these (and similar) source snippets over to the PPC64LE implementation unchanged. This of course assumes the associated types are defined and with compatible attributes.</para></sect1>
<sect1><title> Those extra attributes</title><para>You may have noticed there are some special attributes:</para><para>So far I have been using these attributes unchanged.</para><para/><para>But most intrinsics map the Intel intrinsic to one or more target specific GCC builtins. For example:</para><para/><para>The first intrinsic (_mm_load_pd ) is implement as a C vector pointer reference, but from the comment assumes the compiler will use a movapd instruction that requires 16-byte alignment (will raise a general-protection exception if not aligned). This  implies that there is a performance advantage for at least some Intel processors to keep the vector aligned. The second intrinsic uses the explicit GCC builtin __builtin_ia32_loadupd to generate the movupd instruction which handles unaligned references.</para><para/><para>The opposite assumption applies to POWER and PPC64LE, where GCC generates the VSX  lxvd2x / xxswapd instruction sequence by default, which allows unaligned references. The PowerISA equivalent for aligned vector access is the VMX lvx instruction and the vec_ld builtin, which forces quadword aligned access (by ignoring the low order 4 bits of the effective address). The lvx instruction does not raise alignment exceptions, but perhaps should as part of our implementation of the Intel intrinsic. This requires that we use PowerISA VMX/VSX built-ins to insure we get the expected results.</para><para/><para>The current prototype defines the following:</para><para>The aligned  load intrinsic adds an assert which checks alignment (to match the Intel semantic) and uses  the GCC builtin vec_ld (generates an lvx).  The assert generates extra code but this can be eliminated by defining NDEBUG at compile time. The unaligned load intrinsic uses the GCC builtin vec_vsx_ld  (for PPC64LE generates lxvd2x / xxswapd for power8  and will simplify to lxv or lxvx for power9).  And similarly for __mm_store_pd / __mm_storeu_pd, using vec_st and vec_vsx_st. These concepts extent to the load/store intrinsics for vector float and vector int.</para></sect1>
<sect1><title> How did I find this out?</title><para>The next question is where did I get the details above. The GCC documentation for __builtin_ia32_loadupd provides minimal information (the builtin name, parameters and return types). Not very informative. </para><para/><para>Looking up the Intel intrinsic description is more informative. You can Google the intrinsic name or use the <ulink url="">Intel Intrinsic guide </ulink> for this. The Intrinsic Guide is interactive and includes  Intel (Chip) technology and text based search capabilities. Clicking on the intrinsic name opens to a synopsis including; the underlying instruction name, text description, operation pseudo code, and in some cases performance information (latency and throughput).</para><para/><para>The key is to get a description of the intrinsic (operand fields and types, and which fields are updated for the result) and the underlying Intel instruction. If the Intrinsic guide is not clear you can look up the instruction details in the “<ulink url="">Intel® 64 and IA-32 Architectures Software Developer’s Manual</ulink>”.</para><para/><para>Information about the PowerISA vector facilities is found in the <ulink url="">PowerISA Version 2.07B</ulink> (for POWER8 and <ulink url="">3.0 for POWER9</ulink>) manual, Book I, Chapter 6. Vector Facility and Chapter 7. Vector-Scalar Floating-Point Operations. Another good reference is the <ulink url="">OpenPOWER ELF V2 application binary interface</ulink> (ABI) document, Chapter 6. Vector Programming Interfaces and Appendix A. Predefined Functions for Vector Programming.</para><para/><para>Another useful document is the original <ulink url="">Altivec Technology Programers Interface Manual</ulink> with a  user friendly structure and many helpful diagrams. But alas the PIM does does not cover the resent PowerISA (power7,  power8, and power9) enhancements.</para></sect1>
<sect1><title> Examples implemented using other intrinsics</title><para>Some intrinsic implementations are defined in terms of other intrinsics. For example.</para><para/><para/><para/><para/><para/><para/><para/><para/><para/><para/><para/><para/><para/><para/><para/><para>This notion of using part (one fourth or half) of the SSE XMM register and leaving the rest unchanged (or forced to zero) is specific to SSE scalar operations and can generate some complicated (sub-optimal) PowerISA code.  In this case _mm_load_sd passes the dereferenced double value  to _mm_set_sd which uses C vector initializer notation to combine (merge) that double scalar value with a scalar 0.0 constant into a vector double.</para><para/><para>While code like this should work as-is for PPC64LE, you should look at the generated code and assess if it is reasonable.  In this case the code is not awful (a load double splat, vector xor to generate 0.0s, then a xxmrghd to combine __F and 0.0).  Other examples may generate sub-optimal code and justify a rewrite to PowerISA scalar or vector code (<ulink url="">GCC PowerPC AltiVec Built-in Functions</ulink> or inline assembler). </para><para/><para>Net: try using the existing C code if you can, but check on what the compiler generates.  If the generated code is horrendous, it may be worth the effort to write a PowerISA specific equivalent. For codes making extensive use of MMX or SSE scalar intrinsics you will be better off rewriting to use standard C scalar types and letting the the GCC compiler handle the details (see <link linkend="">#2.1.Prefered methods|outline</link>)</para></sect1>
<sect1><title>2 How do we work this?</title><para>The working assumption is to start with the existing GCC headers from ./gcc/config/i386/, then convert them to PowerISA and add them to ./gcc/config/rs6000/. I assume we will replicate the existing header structure and retain the existing header file and intrinsic names. This also allows us to reuse existing DejaGNU test cases from ./gcc/testsuite/, modify them as needed for the POWER target, and them to the ./gcc/testsuite/</para><para/><para>We can be flexible on the sequence that headers/intrinsics and test cases are ported.  This should be based on customer need and resolving internal dependencies.  This implies an oldest-to-newest / bottoms-up (MMX, SSE, SSE2, …) strategy. The assumption is, existing community and user application codes, are more likely to have optimized code for previous generation ubiquitous (SSE, SSE2, ...) processors than the latest (and rare) SkyLake AVX512.</para><para/><para>I would start with an existing header from the current GCC  ./gcc/config/i386/ and copy the header comment (including FSF copyright) down to any vector typedefs used in the API or implementation. Skip the Intel intrinsic implementation code for now, but add the ending #end if matching the headers conditional guard against multiple inclusion. You can add  #include &lt;alternative&gt; as needed. For examples:</para><para/><para>Then you can start adding small groups of related intrinsic implementations to the header to be compiled and  examine the generated code. Once you have what looks like reasonable code you can grep through  ./gcc/testsuite/ for examples using the intrinsic names you just added. You should be able to find functional tests for most X86 intrinsics. </para><para/><para>The <ulink url="">GCC testsuite</ulink> uses the DejaGNU  test framework as documented in the <ulink url="">GNU Compiler Collection (GCC) Internals</ulink> manual. GCC adds its own DejaGNU directives and extensions, that are embedded in the testsuite source as comments.  Some are platform specific and will need to be adjusted for tests that are ported to our platform. For example</para><para>should become something like</para><para/><para>Repeat this process until you have equivalent implementations for all the intrinsics in that header and associated test cases that execute without error. </para></sect1>
<sect1><title>2.1 Prefered methods</title><para>As we will see there are multiple ways to implement the logic of these intrinsics. Some implementation methods are preferred because they allow the compiler to select instructions and provided the most flexibility for optimization across the whole sequence. Other methods may be required to deliver a specific semantic or to deliver better optimization than the current compiler is capable of. Some methods are more portable across multiple compilers (GCC, LLVM, ...). All of this should be taken into consideration for each intrinsic implementation. In general we should use the following list as a guide to these decisions:</para><orderedlist><listitem><para/></listitem><listitem><para>Use C vector arithmetic, logical, dereference, etc., operators in preference to intrinsics.</para></listitem><listitem><para>Use the bi-endian interfaces from Appendix A of the ABI in preference to other intrinsics when available, as these are designed for portability among compilers.</para></listitem><listitem><para>Use other, less well documented intrinsics (such as __builtin_vsx_*) when no better facility is available, in preference to assembly.</para></listitem><listitem><para>If necessary, use inline assembly, but know what you're doing.</para></listitem></orderedlist><para/></sect1>
<sect1><title>2.2 Prepare yourself</title><para>To port Intel intrinsics to POWER you will need to prepare yourself with knowledge of PowerISA vector facilities and how to access the associated documentation.</para><para/><orderedlist><listitem><para><ulink url="">GCC vector extention</ulink> syntax and usage. This is one of a set of GCC “<ulink url="">Extentions to the C </ulink><ulink url="">language Family</ulink>” that the intrinsic header implementation depends on.  As many of the GCC intrinsics for x86 are implemented via C vector extensions, reading and understanding of this code is an important part of the porting process. </para></listitem><listitem><para>Intel (x86) intrinsic and type naming conventions and how to find more information. The intrinsic name encodes  some information about the vector size and type of the data, but the pattern is not always  obvious. Using the online <ulink url="">Intel Intrinsic Guide</ulink> to look up the intrinsic by name is a good first step.</para></listitem><listitem><para>PowerISA Vector facilities. The Vector facilities of POWER8 are extensive and cover the usual types and usual operations. However it has a different history and organization from Intel.  Both (Intel and PowerISA) have their quirks and in some cases the mapping may not be obvious. So familiarizing yourself with the PowerISA Vector (VMX) and Vector Scalar Extensions (VSX) is important.</para></listitem></orderedlist><para/></sect1>
<sect1><title>2.2.1 GCC Vector Extensions</title><para>The GCC vector extensions are common syntax but implemented in a target specific way. Using the C vector extensions require the __gnu_inline__ attribute to avoid syntax errors in case the user specified  C standard compliance (-std=c90, -std=c11, etc) that would normally disallow such extensions. </para><para/><para>The GCC implementation for PowerPC64 Little Endian is (mostly) functionally compatible with x86_64 vector extension usage. We can use the same type definitions (at least for  vector_size (16)), operations, syntax &lt;{...}&gt; for vector initializers and constants, and array syntax &lt;[]&gt; for vector element access. So simple arithmetic / logical operations on whole vectors should work as is. </para><para/><para>The caveat is that the interface data type of the Intel Intrinsic may not match the data types of the operation, so it may be necessary to cast the operands to the specific type for the operation. This also applies to vector initializers and accessing vector elements. You need to use the appropriate type to get the expected results. Of course this applies to X86_64 as well. For example:</para><para>Note the cast from the interface type (__m128} to the implementation type (__v4sf, defined in the intrinsic header) for the vector float add (+) operation. This is enough for the compiler to select the appropriate vector add instruction for the float type. Then the result (which is __v4sf) needs to be cast back to the expected interface type (__m128). </para><para/><para>Note also the use of array syntax (__A)[0]) to extract the lowest (left most<footnote><para>Here we are using logical left and logical right which will not match the PowerISA register view in Little endian. Logical left is the left most element for initializers {left, … , right}, storage order and array  order where the left most element is [0].</para></footnote>) element of a vector. The cast (__v4sf) insures that the compiler knows we are extracting the left most 32-bit float. The compiler insures the code generated matches the Intel behavior for PowerPC64 Little Endian. </para><para/><para>The code generation is complicated by the fact that PowerISA vector registers are Big Endian (element 0 is the left most word of the vector) and X86 scalar stores are from the left most (work/dword) for the vector register. Application code with extensive use of scalar (vs packed) intrinsic loads / stores should be flagged for rewrite to native PPC code using exisiing scalar types (float, double, int, long, etc.). </para><para/><para>Another example is the set reverse order:</para><para>Note the use of initializer syntax used to collect a set of scalars into a vector. Code with constant initializer values will generate a vector constant of the appropriate endian. However code with variables in the initializer can get complicated as it often requires transfers between register sets and perhaps format conversions. We can assume that the compiler will generate the correct code, but if this class of intrinsics shows up a hot spot, a rewrite to native PPC vector built-ins may be appropriate. For example initializer of a variable replicated to all the vector fields might not be recognized as a “load and splat” and making this explicit may help the compiler generate better code.</para></sect1>
<sect1><title>2.2.2 Intel Intrinsic functions</title><para>So what is an intrinsic function? From Wikipedia:</para><para/><para>In <ulink url="">compiler theory</ulink>, an intrinsic function is a function available for use in a given <ulink url="">programming language</ulink> whose implementation is handled specially by the compiler. Typically, it substitutes a sequence of automatically generated instructions for the original function call, similar to an <ulink url="">inline function</ulink>. Unlike an inline function though, the compiler has an intimate knowledge of the intrinsic function and can therefore better integrate it and optimize it for the situation. This is also called builtin function in many languages.</para><para/><para>The “Intel Intrinsics” API provides access to the many instruction set extensions (Intel Technologies) that Intel has added (and continues to add) over the years. The intrinsics provided access to new instruction capabilities before the compilers could exploit them directly. Initially these intrinsic functions where defined for the Intel and Microsoft compiler and where eventually implemented and contributed to GCC.</para><para/><para>The Intel Intrinsics have a specific type and naming structure. In this naming structure, functions starts with a common prefix (MMX and SSE use _mm_ prefix, while AVX added the _mm256 _mm512 prefixes), then a short functional name (set, load, store, add, mul, blend, shuffle, …) and a suffix (_pd, _sd, _pi32...) with type and packing information. See <link linkend="">Appendix B</link> for the list of common intrisic suffixes.</para><para/><para>Oddly many of the MMX/SSE operations are not vectors at all. There are a lot of scalar operations on a single float, double, or long long type. In effect these are scalars that can take advantage of the larger (xmm) register space. Also in the Intel 32-bit architecture they provided IEEE754 float and double types, and 64-bit integers that did not exist or where hard to implement in the base i386/387 instruction set. These scalar operation use a suffix starting with '_s' (_sd for scalar double float, _ss scalar float, and _si64 for scalar long long).</para><para/><para>True vector operations use the packed or extended packed suffixes, starting with '_p' or '_ep' (_pd for vector double, _ps for vector float, and _epi32 for vector int). The use of '_ep'  seems to be reserved to disambiguate intrinsics that existed in the (64-bit vector) MMX extension from the extended (128-bit vector) SSE equivalent. For example _mm_add_pi32 is a MMX operation on a pair of 32-bit integers, while _mm_add_epi32 is an SSE2 operation on vector of 4 32-bit integers. </para><para/><para>The GCC  builtins for the <ulink url=""></ulink>, (includes x86 and x86_64) are not the same as the Intel Intrinsics. While they have similar intent and cover most of the same functions, they use a different naming (prefixed with __builtin_ia32_, then function name with type suffix) and uses GCC vector type modes for operand types. For example:</para><para>Note: A key difference between GCC builtins for i386 and Powerpc is that the x86 builtins have different names of each operation and type while the powerpc altivec builtins tend to have a single generatic builtin for  each operation, across a set of compatible operand types. </para><para/><para>In GCC the Intel Intrinsic header (*intrin.h) files are implemented as a set of inline functions using the Intel Intrinsic API names and types. These functions are implemented as either GCC C vector extension code or via one or more GCC builtins for the i386 target. So lets take a look at some examples from GCC's SSE2 intrinsic header emmintrin.h:</para><para/><para/><para>Note that the  _mm_add_pd is implemented direct as C vector extension code., while _mm_add_sd is implemented via the GCC builtin __builtin_ia32_addsd. From the discussion above we know the _pd suffix indicates a packed vector double while the _sd suffix indicates a scalar double in a XMM register. </para><para/></sect1>
<sect1><title> Packed vs scalar intrinsics</title><para/><para>So what is actually going on here? The vector code is clear enough if you know that '+' operator is applied to each vector element. The the intent of the builtin is a little less clear, as the GCC documentation for __builtin_ia32_addsd is not very helpful (nonexistent). So perhaps the <ulink url=";expand=97">Intel Intrinsic Guide</ulink> will be more enlightening. To paraphrase:</para><para/><para>From the <ulink url=";expand=97">_mm_add_dp description</ulink> ; for each double float element ([0] and [1] or bits [63:0] and [128:64]) for operands a and b are added and resulting vector is returned. </para><para/><para>From the <ulink url=";expand=97,130">_mm_add_sd</ulink><ulink url=";expand=97,130"> </ulink><ulink url=";expand=97,130">description</ulink> ; Add element 0 of first operand (a[0]) to element 0 of the second operand (b[0]) and return the packed vector double {(a[0] + b[0]), a[1]}. Or said differently the sum of the logical left most half of the the operands are returned in the logical left most half (element [0]) of the  result, along with the logical right half (element [1]) of the first operand (unchanged) in the logical right half of the result.</para><para/><para>So the packed double is easy enough but the scalar double details are more complicated. One source of complication is that while both Instruction Set Architectures (SSE vs VSX) support scalar floating point operations in vector registers the semantics are different. </para><para/><orderedlist><listitem><para>The vector bit and field numbering is different (reversed). </para></listitem><listitem><para>The handling of the non-scalar part of the register for scalar operations are different.</para></listitem></orderedlist><para/><para>To minimize confusion and use consistent nomenclature, I will try to use the terms logical left and logical right elements based on the order they apprear in a C vector initializers and element index order. So in the vector (__v2df){1.0, 20.}, The value 1.0 is the in the logical left element [0] and the value 2.0 is logical right element [1].</para><para/><para>So lets look at how to implement these intrinsics for the PowerISA. For example in this case we can use the GCC vector extension, like so:</para><para/><para/><para>The packed double implementation operates on the vector as a whole. The scalar double implementation operates on and updates only [0] element of the vector and leaves the __A[1] element unchanged.  Form this source the GCC compiler generates the following code for PPC64LE target.:</para><para/><para>The packed vector double generated the corresponding VSX vector double add (xvadddp). But the scalar implementation is bit more complicated.  </para><para/><para>First the PPC64LE vector format, element [0] is not in the correct position for  the scalar operations. So the compiler generates vector splat double (xxspltd) instructions to copy elements __A[0] and __B[0] into position for the VSX scalar add double (xsadddp) that follows. However the VSX scalar operation leaves the other half of the VSR undefined (which does not match the expected Intel semantics). So the compiler must generates a vector merge high double (xxmrghd) instruction to combine the original __A[1] element (from vs34) with the scalar add result from vs35 element [1]. This merge swings the scalar result from vs35[1] element into the vs34[0] position, while preserving the original vs34[1] (from __A[1]) element (copied to itself).<footnote><para>Fun fact: The vector registers in PowerISA are decidedly Big Endian. But we decided to make the PPC64LE ABI behave like a Little Endian system to make application porting easier. This require the compiler to manipulate the PowerISA vector instrinsic behind the the scenes to get the correct Little Endian results. For example the element selector [0|1] for vec_splat and the generation of vec_mergeh vs vec_mergel are reversed for the Little Endian.</para></footnote></para><para/><para>This technique applies to packed and scalar intrinsics for the the usual arithmetic operators (add, subtract, multiply, divide). Using GCC vector extensions in these intrinsic implementations provides the compiler more opportunity to optimize the whole function. </para><para/><para>Now we can look at a slightly more interesting (complicated) case. Square root (sqrt) is not a arithmetic operator in C and is usually handled with a library call or a compiler builtin. We really want to avoid a library calls and want to avoid any unexpected side effects. As you see below the implementation of <ulink url=";expand=4926">_mm_sqrt_pd</ulink> and <ulink url=";expand=4926,4956">_mm_sqrt_sd</ulink> intrinsics are based on GCC x86 built ins. </para><para/><para>For the packed vector sqrt, the PowerISA VSX has an equivalent vector double square root instruction and GCC provides the vec_sqrt builtin. But the scalar implementation involves an additional parameter and an extra move.  This seems intended to mimick the propagation of the __A[1] input to the logical right half of the XMM result that we saw with _mm_add_sd above.</para><para/><para>The instinct is to extract the low scalar (__B[0]) from operand __B and pass this to  the GCC __builtin_sqrt () before recombining that scalar result with __A[1] for the vector result. Unfortunately C language standards force the compiler to call the libm sqrt function unless -ffast-math is specified. The -ffast-math option is not commonly used and we want to avoid the external library dependency for what should be only a few inline instructions. So this is not a good option.</para><para/><para>Thinking outside the box; we do have an inline intrinsic for a (packed) vector double sqrt, that we just implemented. However we need to insure the other half of __B (__B[1]) does not cause an harmful side effects (like raising exceptions for NAN or  negative values). The simplest solution is to splat __B[0] to both halves of a temporary value before taking the vec_sqrt. Then this result can be combined with __A[1] to return the final result. For example:</para><para>In this  example we use <ulink url=";expand=4926,4956,4926,4956,4652">_mm_set1_pd</ulink> to splat the scalar __B[0], before passing that vector to our _mm_sqrt_pd implementation, then pass the sqrt result (c[0])  with __A[1[ to  <ulink url=";expand=4679">_mm_setr_p</ulink><ulink url=";expand=4679">d</ulink> to combine the final result. You could also use the {c[0], __A[1]} initializer instead of _mm_setr_pd.</para><para/><para>Now we can look at vector and scalar compares that add there own complication: For example:</para><para>The Intel Intrinsic Guide for <ulink url=";expand=779,788,779">_mm_cmpeq_pd</ulink> describes comparing double elements [0|1] and returning either 0s for not equal and 1s (0xFFFFFFFFFFFFFFFF or long long -1) for equal. The comparison result is intended as a select mask (predicates) for selecting or ignoring specific elements in later operations. The scalar version <ulink url=";expand=779,788">_mm_cmpeq_sd</ulink> is similar except for the quirk of only comparing element [0] and combining the result with __A[1] to return the final vector result.</para><para/><para>The packed vector implementation for PowerISA is simple as VSX provides the equivalent instruction and GCC provides the vec_cmpeq builtin supporting the vector double type. The technique of using scalar comparison operators on the __A[0] and __B[0] does not work as the C comparison operators return 0 or 1 results while we need the vector select mask (effectively 0 or -1). Also we need to watch for sequences that mix scalar floats and integers, generating if/then/else logic or requiring expensive transfers across register banks.</para><para/><para>In this case we are better off using explicit vector built-ins for _mm_add_sd as and example. We can use vec_splat from element [0] to temporaries where we can safely use vec_cmpeq to generate the expect selector mask. Note that the vec_cmpeq returns a bool long type so we need the cast the result back to __v2df. Then use the (__m128d){c[0], __A[1]} initializer to combine the comparison result with the original __A[1] input and cast to the require interface type.  So we have this example:</para><para/><para>Now lets look at a similar example that adds some surprising complexity. This is the compare not equal case so we should be able to find the equivalent vec_cmpne builtin:</para><para/></sect1>
<sect1><title> To vec_not or not</title><para>Well not exactly. Looking at the OpenPOWER ABI document we see a reference to vec_cmpne for all numeric types. But when we look in the current GCC 6 documentation we find that vec_cmpne is not on the list. So it is planned in the ABI, but not implemented yet. </para><para/><para>Looking at the PowerISA 2.07B we find a VSX Vector Compare Equal to Double-Precision but no Not Equal. In fact we see only vector double compare instructions for greater than and greater than or equal in addition to the equal compare. Not only can't we find a not equal, there is no less than or less than or equal compares either. </para><para/><para>So what is going on here? Partially this is the Reduced Instruction Set Computer (RISC) design philosophy. In this case the compiler can generate all the required compares using the existing vector instructions and simple transforms based on Boolean algebra. So vec_cmpne(A,B) is simply vec_not (vec_cmpeq(A,B)). And vec_cmplt(A,B) is simply vec_cmpgt(B,A) based on the identity A &lt; B iff B &gt; A. Similarly vec_cmple(A,B) is implemented as vec_cmpge(B,A).</para><para/><para>What a minute, there is no vec_not() either. Can not find it in the PowerISA, the OpenPOWER ABI, or the GCC PowerPC Altivec Built-in documentation. There is no vec_move() either! How can this possible work?</para><para/><para>This is RISC philosophy again. We can always use a logical instruction (like bit wise and or or) to effect a move given that we also have nondestructive 3 register instruction forms. In the PowerISA most instruction have two input registers and a separate result register. So if the result register number is  different from either input register then the inputs are not clobbered (nondestructive). Of course nothing prevents you from specifying the same register for both inputs or even all three registers (result and both inputs).  And some times it is useful.</para><para/><para>The statement B = vec_or (A,A) is is effectively a vector move/copy from A to B. And A = vec_or (A,A) is obviously a nop (no operation). In the the PowerISA defines the preferred nop and register move for vector registers in this way.</para><para/><para>It is also useful to have hardware implement the logical operators nor (not or) and nand (not and).  The PowerISA provides these instruction for fixed point and vector logical operation. So vec_not(A) can be implemented as vec_nor(A,A). So looking at the  implementation of _mm_cmpne we propose the following:</para><para/><para>The Intel Intrinsics also include the not forms of the relational compares:</para><para>The PowerISA and OpenPOWER ABI, or GCC PowerPC Altivec Built-in documentation do not provide any direct equivalents to the  not greater than class of compares. Again you don't really need them if you know Boolean algebra. We can use identities like {not (A &lt; B) iff A &gt;= B} and {not (A &lt;= B) iff A &gt; B}. So the PPC64LE implementation follows:</para><para>These patterns repeat for the scalar version of the not compares. And in general the larger pattern described in this chapter applies to the other float and integer types with similar interfaces.</para><para/></sect1>
<sect1><title> Crossing lanes</title><para>We have seen that, most of the time, vector SIMD units prefer to keep computations in the same “lane” (element number) as the input elements. The only exception in the examples so far are the occasional splat (copy one element to all the other elements of the vector) operations. Splat is an example of the general category of “permute” operations (Intel would call this a “shuffle” or “blend”). Permutes selects and rearrange the elements of (usually) a concatenated pair of vectors and delivers those selected elements, in a specific order, to a result vector. The selection and order of elements in the result is controlled by a third vector, either as 3rd input vector or and immediate field of the instruction.</para><para/><para>For example the Intel intrisics for <ulink url=";expand=2757,4767,409,2757">Horizontal Add / Subtract</ulink> added with SSE3. These instrinsics add (subtract) adjacent element pairs, across pair of input vectors, placing the sum of the adjacent elements in the result vecotr.. For example <ulink url=";expand=2757,4767,409,2757,2757">_mm_hadd_ps</ulink>  which implments the operation on float:</para><para>Horizontal Add (hadd) provides an incremental vector “sum across” operation commonly needed in matrix and vector transform math. Horizontal Add is incremental as you need three hadd instructions to sum across 4 vectors of 4 elements ( 7 for 8 x 8, 15 for 16 x 16, …).</para><para/><para>The PowerISA does not have a sum-across operation for float or double. We can user the vector float add instruction after we rearrange the inputs so that element pairs line up for the horizontal add. For example we would need to permute the input vectors {1, 2, 3, 4} and {101, 102, 103, 104} into vectors {2, 4, 102, 104} and {1, 3, 101, 103} before the  vec_add. This requires two vector permutes to align the elements into the correct lanes for the vector add (to implement Horizontal Add).  </para><para/><para>The PowerISA provides generalized byte-level vector permute (vperm) based a vector register pair source as input and a control vector. The control vector provides 16 indexes (0-31) to select bytes from the concatenated input vector register pair (VRA, VRB). A more specific set of permutes (pack, unpack, merge, splat) operations (across element sizes) are encoded as separate  instruction opcodes or instruction immediate fields.</para><para/><para>Unfortunately only the general vec_perm can provide the realignment we need the _mm_hadd_ps operation or any of the int, short variants of hadd. For example:</para><para/><para>This requires two permute control vectors; one to select the even word elements across __X and __Y, and another to select the odd word elements across __X and __Y. The result of these permutes (vec_perm) are inputs to the vec_add and completes the hadd operation. </para><para/><para>Fortunately the permute required for the double (64-bit) case (IE _mm_hadd_pd) reduces to the equivalent of vec_mergeh / vec_mergel  doubleword (which are variants of  VSX Permute Doubleword Immediate). So the implementation of _mm_hadd_pd can be simplified to this:</para><para>This eliminates the load of the control vectors required by the previous example.</para><para/></sect1>
<sect1><title>2.2.3 PowerISA Vector facilities.</title><para>The PowerISA vector facilities (VMX and VSX) are extensive, but does not always provide a direct or obvious functional equivalent to the Intel Intrinsics. But being not obvious is not the same as imposible. It just requires some basic programing skills.</para><para/><para>It is a good idea to have an overall understanding of the vector capabilities the PowerISA. You do not need to memorize every instructions but is helps to know where to look. Both the PowerISA and OpenPOWER ABI have a specific structure and organization that can help you find what you looking for. </para><para/><para>It also helps to understand the relationship between the PowerISAs low level instructions and the higher abstraction of the vector intrinsics as defined by the OpenPOWER ABIs Vector Programming Interfaces and the the defacto  standard of GCC's PowerPC AltiVec Built-in Functions.</para></sect1>
<sect1><title> The PowerISA</title><para>The PowerISA is for historical reasons is organized at the top level by the distinction between older Vector Facility (Altivec / VMX) and the newer Vector-Scalar Floating-Point Operations (VSX). </para></sect1>
<sect1><title> The Vector Facility (VMX)</title><para>The orginal VMX supported SIMD integer byte, halfword, and word, and single float data types within a separate (from GPR and FPR) bank of 32 x 128-bit vector registers. These operations like to stay within their (SIMD) lanes except where the operation changes the element data size (integer multiply, pack, and unpack). </para><para/><para>This is complimented by bit logical and shift / rotate / permute / merge instuctions that operate on the vector as a whole.  Some operation (permute, pack, merge, shift double, select) will select 128 bits from a pair of vectors (256-bits) and deliver 128-bit vector result. These instructions will cross lanes or multiple registers to grab fields and assmeble them into the single register result.</para><para/><para>The PowerISA 2.07B Chapter 6. Vector Facility is organised starting with an overview (chapters 6.1- 6.6) :</para><para>Then a chapter on storage (load/store) access for vector and vector elements:</para></sect1>
<sect1><title> Vector permute and formatting instructions</title><para>The vector Permute and formatting chapter follows and is an important one to study. These operation operation on the byte, halfword, word (and with 2.07 doubleword) integer types . Plus special Pixel type. The shifts instructions in this chapter operate on the vector as a whole at either the bit or the byte (octet) level, This is an important chapter to study for moving PowerISA vector results into the vector elements that Intel Intrinsics expect:</para><para/><para>The Vector Integer instructions include the add / subtract / Multiply / Multiply Add/Sum / (no divide) operations for the standard integer types. There are instruction forms that  provide signed, unsigned, modulo, and saturate results for most operations. The PowerISA 2.07 extension add / subtract of 128-bit integers with carry and extend to 256, 512-bit and beyond , is included here. There are signed / unsigned compares across the standard integer types (byte, .. doubleword). The usual and bit-wise logical operations. And the SIMD shift / rotate instructions that operate on the vector elements for various types.</para><para/><para/><para>The vector [single] float instructions are grouped into this chapter. This chapter does not include the double float instructions which are described in the VSX chapter. VSX also include additional float instructions that operate on the whole 64 register vector-scalar set.</para><para/><para/><para>The vector XOR based instructions are new with PowerISA 2.07 (POWER8) and provide vector  crypto and check-sum operations:</para><para/><para>The vector gather and bit permute support bit level rearrangement of bits with in the vector. While the vector versions of the count leading zeros and population count are useful to accelerate specific algorithms </para><para/><para>The Decimal Integer add / subtract instructions complement the Decimal Floating-Point instructions. They can also be used to accelerated some binary to/from decimal conversions. The VSCR instruction provides access the the Non-Java mode floating-point control and the saturation status. These instruction are not normally of interest in porting Intel intrinsics.</para><para/><para>With PowerISA 2.07B (Power8) several major extension where added to the Vector Facility:</para><orderedlist><listitem><para>Vector Crypto: Under “Vector Exclusive-OR-based Instructions Vector Exclusive-OR-based Instructions”, AES [inverse] Cipher, SHA 256 / 512 Sigma, Polynomial Multiplication, and Permute and XOR instructions.</para></listitem><listitem><para>64-bit Integer; signed and unsigned add / subtract, signed and unsigned compare, Even / Odd 32 x 32 multiple with 64-bit product, signed / unsigned max / min, rotate and shift left/right.</para></listitem><listitem><para>Direct Move between GRPs and the FPRs / Left half of Vector Registers.</para></listitem><listitem><para>128-bit integer add / subtract with carry / extend, direct support for vector __int128 and multiple precision arithmetic.</para></listitem><listitem><para>Decimal Integer add subtract for 31 digit BCD.</para></listitem><listitem><para>Miscellaneous SIMD extensions: Count leading Zeros, Population count, bit gather / permute, and vector forms of eqv, nand, orc.</para></listitem></orderedlist><para/><para>The rational for why these are included in the Vector Facilities (VMX) (vs Vector-Scalar Floating-Point Operations (VSX)) has more to do with how the instruction where encoded then with the type of operations or the ISA version of introduction. This is primarily a trade-off between the bits required for register selection vs bits for extended op-code space within in a fixed 32-bit instruction. Basically accessing 32 vector registers require 5-bits per register, while accessing all 64 vector-scalar registers require 6-bits per register. When you consider the most vector instructions require  3  and some (select, fused multiply-add) require 4 register operand forms,  the impact on op-code space is significant. The larger register set of VSX was justified by queuing theory of larger HPC matrix codes using double float, while 32 registers are sufficient for most applications.</para><para/><para>So by definition the VMX instructions are restricted to the original 32 vector registers while VSX instructions are encoded to  access all 64 floating-point scalar and vector double registers. This distinction can be troublesome when programming at the assembler level, but the compiler and compiler built-ins can hide most of this detail from the programmer. </para><para/></sect1>
<sect1><title> Vector-Scalar Floating-Point Operations (VSX)</title><para>With PowerISA 2.06 (POWER7) we extended the vector SIMD capabilities of the PowerISA:</para><orderedlist><listitem><para>Extend the available vector and floating-point scalar register sets from 32 registers each to a combined 64 x 64-bit scalar floating-point and 64 x 128-bit vector registers.</para></listitem><listitem><para>Enable scalar double float operations on all 64 scalar registers.</para></listitem><listitem><para>Enable vector double and vector float operations for all 64 vector registers.</para></listitem><listitem><para>Enable super-scalar execution of vector instructions and support 2 independent vector floating point  pipelines for parallel execution of 4 x 64-bit Floating point Fused Multiply Adds (FMAs) and 8 x 32-bit (FMAs) per cycle.</para></listitem></orderedlist><para/><para>With PowerISA 2.07 (POWER8) we added single-precision scalar floating-point instruction to VSX. This completes the floating-point computational set for VSX. This ISA release also clarified how these operate in the Little Endian storage model.</para><para/><para>While the focus was on enhanced floating-point computation (for High Performance Computing),  VSX also extended  the ISA with additional storage access, logical, and permute (merge, splat, shift) instructions. This was necessary to extend these operations cover 64 VSX registers, and improves unaligned storage access for vectors  (not available in VMX).</para><para/><para>The PowerISA 2.07B Chapter 7. Vector-Scalar Floating-Point Operations is organized starting with an introduction and overview (chapters 7.1- 7.5) . The early sections (7.1 and 7.2) describe the layout of the 64 VSX registers and how they relate (overlap and inter-operate) to the existing floating point scalar (FPRs) and (VMX VRs) vector registers.</para><para/><para>The definitions given in “ Compatibility with Category Floating-Point and Category Decimal Floating-Point Operations”, and “ Compatibility with Category Vector Operations” </para><para>Note; the reference to scalar element 0 above is from the big endian register perspective of the ISA. In the PPC64LE ABI implementation, and for the purpose of porting Intel intrinsics, this is logical element 1.  Intel SSE scalar intrinsics operated on logical element [0],  which is in the wrong position for PowerISA FPU and VSX scalar floating-point  operations. Another important note is what happens to the other half of the VSR when you execute a scalar floating-point instruction (The contents of doubleword 1 of a VSR … are undefined.)</para><para/><para>The compiler will hide some of this detail when generating code for little endian vector element [] notation and most vector built-ins. For example vec_splat (A, 0) is transformed for PPC64LE to xxspltd VRT,VRA,1. What the compiler can not hide is the different placement of scalars within vector registers.</para><para/><para>Vector registers (VRs) 0-31 overlay and can be accessed from vector scalar registers (VSRs) 32-63. The ABI also specifies that VR2-13 are used to pass parameter and return values. In some cases the same (similar) operations exist in both VMX and VSX instruction forms, while in the other cases operations only exist for VMX (byte level permute and shift) or VSX (Vector double).  </para><para/><para>So resister selection that; avoids unnecessary vector moves, follows the ABI, while maintaining the correct instruction specific register numbering, can be tricky. The <ulink url="">GCC register constraint</ulink> annotations for Inline assembler using vector instructions  is challenging, even for experts. So only experts should be writing assembler and then only in extraordinary circumstances. You should leave these details to the compiler (using vector extensions and vector built-ins) when ever possible.</para><para/><para>The next sections get is into the details of floating point representation, operations, and exceptions. Basically the implementation details for the IEEE754R and C/C++ language standards that most developers only access via higher level APIs. So most programmers will not need this level of detail, but it is there if needed.</para><para/><para>Finally an overview the VSX storage access instructions for big and little endian and for aligned and unaligned data addresses. This included diagrams that illuminate the differences </para><para/><para>Section 7.6 starts with a VSX instruction Set Summary which is the place to start to get an feel for the types and operations supported.  The emphasis on float-point, both scalar and vector (especially vector double), is pronounced. Many of the scalar and single-precision vector instruction look like duplicates of what we have seen in the Chapter 4 Floating-Point and Chapter 6 Vector facilities. The difference here is, new instruction encodings to access the full 64 VSX register space. </para><para/><para>In addition there are small number of logical instructions are include to support predication (selecting / masking vector elements based on compare results). And set of permute, merge, shift, and splat instructions that operation on VSX word (float) and doubleword (double) elements. As mentioned about VMX section 6.8 these instructions are good to study as they are useful for realigning elements from PowerISA vector results to that required for Intel Intrinsics.</para><para/><para/><para>The VSX Instruction Descriptions section contains the detail description for each VSX category instruction.  The table entries from the Instruction Set Summary are formatted in the document at hyperlinks to corresponding instruction description.</para><para/></sect1>
<sect1><title> PowerISA Vector Intrinsics</title><para>The OpenPOWER ELF V2 application binary interface (ABI): Chapter 6. Vector Programming Interfaces and Appendix A. Predefined Functions for Vector Programming document the current and proposed vector built-ins we expect all C/C++ compilers implement. </para><para/><para>Some of these operations are endian sensitive and the compiler needs to make corresponding adjustments as  it generate code for endian sensitive built-ins. There is a good overview for this in the OpenPOWER ABI section 6.4. Vector Built-in Functions.</para><para/><para>Appendix A is organized (sorted) by built-in name, output type, then parameter types. Most built-ins are generic as the named the operation (add, sub, mul, cmpeq, ...) applies to multiple types. </para><para/><para>So the build vec_add built-in applies to all the signed and unsigned integer types (char, short, in, and long) plus float and double floating-point types. The compiler looks at the parameter type to select the vector instruction (or instruction sequence) that implements the (add) operation on that type. The compiler infers the output result type from the operation and input parameters and will complain if the target variable type is not compatible. For example:</para><para/><para>This is one key difference between PowerISA built-ins and Intel Intrinsics (Intel Intrinsics are not generic and include type information in the name). This is why it is so important to understand the vector element types and to add the appropriate type casts to get the correct results.</para><para/><para>The defacto standard implementation is GCC as defined in the include file &lt;altivec.h&gt; and documented in the GCC online documentation in <ulink url="">6.59.20 PowerPC AltiVec Built-in Functions</ulink>. The header file name and section title reflect the origin of the Vector Facility, but recent versions of GCC altivec.h include built-ins for newer PowerISA 2.06 and 2.07 VMX plus VSX extensions. This is a work in progress where your  (older) distro GCC compiler may not include built-ins for the latest PowerISA 3.0 or ABI edition. So before you use a built-in you find in the ABI Appendix A, check the specific <ulink url="">GCC online documentation</ulink> for the GCC version you are using.</para><para/></sect1>
<sect1><title> How vector elements change size and type</title><para>Most vector built ins return the same vector type as the (first) input parameters, but there are exceptions. Examples include; conversions between types, compares , pack, unpack,  merge, and integer multiply operations.  </para><para/><para>Converting floats to from integer will change the type and something change the element size as well (double ↔ int and float ↔ long). For the VMX the conversions are always the same size (float ↔ [unsigned] int). But VSX allows conversion of 64-bit (long or double) to from 32-bit (float or  int)  with the inherent size changes. The PowerISA VSX defines a 4 element vector layout where little endian elements 0, 2 are used for input/output and elements 1,3 are undefined. The OpenPOWER ABI Appendix A define vec_double and vec_float with even/odd and high/low extensions as program aids. These are not included in GCC 7 or earlier but are planned for GCC 8.</para><para/><para>Compare operations produce either vector bool &lt;input element type&gt; (effectively bit masks) or predicates (the condition code for all and any are represented as an int truth variable). When a predicate compare (ie vec_all_eq, vec_any_gt), is used in a if statement,  the condition code is used directly in the conditional branch and the int truth value is not generated.</para><para/><para>Pack operations pack integer elements into the next smaller (half) integer sized elements. Pack operations include signed and unsigned saturate and unsigned modulo forms. As the packed result will be half the size (in bits), pack instructions require 2 vectors (256-bits) as input and generate a single 128-bit vector results.</para><para/><para>Unpack operations expand integer elements into the next larger size elements. The integers are always treated as signed values and sign-extended. The processor design avoids instructions that return multiple register values. So the PowerISA defines unpack-high and unpack low forms where instruction takes (the high or low) half of vector elements and extends them to fill the vector output. Element order is maintained and an unpack high / low sequence with same input vector has the effect of unpacking to a 256-bit result in two vector registers.</para><para/><para>Merge operations resemble shuffling two (vectors) card decks together, alternating (elements) cards in the result.   As we are merging from 2 vectors (256-bits) into 1 vector (128-bits) and the elements do not change size, we have merge high and merge low instruction forms for each (byte, halfword and word) integer type. The merge high operations alternate elements from the (vector register left) high half of the two input vectors. The merge low operation alternate elements from the (vector register right) low half of the two input vectors. </para><para/><para>For PowerISA 2.07 we added vector merge word even / odd instructions. Instead of high or low elements the shuffle is from the even or odd number elements of the two input vectors. Passing the same vector to both inputs to merge produces splat like results for each doubleword half, which is handy in some convert operations. </para><para/><para>Integer multiply has the potential to generate twice as many bits in the product as input. A multiply of 2 int (32-bit) values produces a long (64-bits). Normal C language * operations ignore this and discard the top 32-bits of the result. However  in some computations it useful to preserve the double product precision for intermediate computation before reducing the final result back to the original precision. </para><para/><para>The PowerISA VMX instruction set took the later approach ie keep all the product bits until the programmer explicitly asks for the truncated result. So the vector integer multiple are split into even/odd forms across signed and unsigned; byte, halfword and word inputs. This requires two instructions (given the same inputs) to generated the full vector  multiply across 2 vector registers and 256-bits. Again as POWER processors are super-scalar this pair of instructions should execute in parallel.</para><para/><para>The set of expanded product values can either be used directly in further (doubled precision) computation or merged/packed into the single single vector at the smaller bit size. This is what the compiler will generate for C vector extension multiply of vector integer types.</para><para/></sect1>
<sect1><title>2.2.4 Some more Intrinsic examples</title><para>The intrinsic <ulink url=";expand=1624">_mm_cvtpd_ps</ulink> converts a packed vector double into a packed vector single float. Since only 2 doubles fit into a 128-bit vector only 2 floats are returned and occupy only half (64-bits) of the XMM register. For this intrinsic the 64-bit are packed into the logical left half of the registers and the logical right half of the register is set to zero (as per the Intel cvtpd2ps instruction).</para><para/><para>The PowerISA provides the VSX Vector round and Convert Double-Precision to Single-Precision format (xvcvdpsp) instruction. In the ABI this is vec_floato (vector double) .  This instruction convert each double element then transfers converted element 0 to float element 1, and converted element 1 to float element 3. Float elements 0 and 2 are undefined (the hardware can do what ever). This does not match the expected results for _mm_cvtpd_ps.</para><para/><para>So we need to re-position the results to word elements 0 and 2, which allows a pack operation to deliver the correct format. Here the merge odd splats element 1 to 0 and element 3 to 2. The Pack operation combines the low half of each doubleword from the vector result and vector of zeros to generate the require format.</para><para/><para>This  technique is also used to implement  <ulink url=";expand=1624,1859">_mm_cvttpd_epi32</ulink> which converts a packed vector double in to a packed vector int. The PowerISA instruction xvcvdpsxws uses a similar layout for the result as  xvcvdpsp and requires the same fix up.</para></sect1>
<sect1><title>2.3 Profound differences </title><para>We have already mentioned above a number of architectural differences that effect porting of codes containing Intel intrinsics to POWER. The fact that Intel supports multiple vector extensions with different vector widths (64, 128, 256, and 512-bits) while the PowerISA only supports vectors of 128-bits is one issue. Another is the difference in how the respective ISAs support scalars in vector registers is another.  In the text above we propose workable alternatives for the PowerPC port. There also differences in the handling of floating point exceptions and rounding modes that may impact the application's performance or behavior. </para><para/></sect1>
<sect1><title>2.3.1 Floating Point Exceptions</title><para>Nominally both ISAs support the IEEE754 specifications, but there are some subtle differences. Both architecture define a status and control register to record exceptions and enable / disable floating exceptions for program interrupt or default action. Intel has a MXCSR and PowerISA has a FPSCR which basically do the same thing but with different bit layout. </para><para/><para>Intel provides _mm_setcsr / _mm_getcsr intrinsics to allow direct access to the MXCSR. In the early days before the OS POSIX run-times where updated  to manage the MXCSR, this might have been useful. Today this would be highly discouraged with a strong preference to use the POSIX APIs (feclearexceptflag, fegetexceptflag, fesetexceptflag, ...) instead.</para><para/><para>If we implement _mm_setcsr / _mm_getcs at all, we should simply redirect the implementation to use the POSIX APIs from &lt;fenv.h&gt;. But it might be simpler just to replace these intrinsics with macros that generate #error.</para><para/><para>The Intel MXCSR does have some none (POSIX/IEEE754) standard quirks; Flush-To-Zero and Denormals-Are-Zeros flags. This simplifies the hardware response to what should be a rare condition (underflows where the result can not be represented in the exponent range and precision of the format) by simply returning a signed 0.0 value. The intrinsic header implementation does provide constant masks for _MM_DENORMALS_ZERO_ON (&lt;pmmintrin.h&gt;) and _MM_FLUSH_ZERO_ON (&lt;xmmintrin.h&gt;, so technically it is available to users of the Intel Intrinsics API.</para><para/><para>The VMX Vector facility provides a separate Vector Status and Control register (VSCR) with a Non-Java Mode control bit. This control combines the flush-to-zero semantics for floating Point underflow and denormal values. But this control only applies to VMX vector float instructions and does not apply to VSX scalar floating Point or vector double instructions. The FPSCR does define a Floating-Point non-IEEE mode which is optional in the architecture. This would apply to Scalar and VSX floating-point operations if it was implemented. This was largely intended for embedded processors and is not implemented in the POWER processor line.</para><para/><para>As the flush-to-zero is primarily a performance enhansement and is clearly outside the IEEE754 standard, it may be best to simply ignore this option for the intrinsic port.</para><para/></sect1>
<sect1><title>2.3.2 Floating-point rounding modes</title><para>The Intel (x86 / x86_64) and PowerISA architectures both support the 4 IEEE754 rounding modes. Again while the Intel Intrinsic API allows the application to change rounding modes via updates to the MXCSR it is a bad idea and should be replaced with the POSIX APIs (fegetround and fesetround). </para><para/></sect1>
<sect1><title>2.3.3 Performance</title><para>The performance of a ported intrinsic depends on the specifics of the intrinsic and the context it is used in. Many of the SIMD operations have equivalent instructions in both architectures. For example the vector float and vector double match very closely. However the SSE and VSX scalars have subtle differences of how the scalar is positioned with the vector registers and what happens to the rest (non-scalar part) of the register (previously discussed in <link linkend="">here</link>). This requires additional PowerISA instructions to preserve the non-scalar portion of the vector registers. This may or may not be important to the logic of the program being ported, but we have handle the case where it is. </para><para/><para>This is where the context of now the intrinsic is used starts to matter. If the scalar intrinsics are used within a larger program the compiler may be able to eliminate the redundant register moves as the results are never used. In the other cases common set up (like permute vectors or bit masks) can be common-ed up and hoisted out of the loop. So it is very important to let the compiler do its job with higher optimization levels (-O3, -funroll-loops).</para><para/></sect1>
<sect1><title> Using SSE float and double scalars</title><para>SSE scalar float / double intrinsics  “hand” optimization is no longer necessary. This was important, when SSE was initially introduced, and compiler support was limited or nonexistent.  Also SSE scalar float / double provided additional (16) registers and IEEE754 compliance, not available from the 8087 floating point architecture that preceded it. So application developers where motivated to use SSE instruction versus what the compiler was generating at the time.</para><para/><para>Modern compilers can now to generate and  optimize these (SSE scalar) instructions for Intel from C standard scalar code. Of course PowerISA supported IEEE754 float and double and had 32 dedicated floating point registers from the start (and now 64 with VSX). So replacing a Intel specific scalar intrinsic implementation with the equivalent C language scalar implementation is usually a win; allows the compiler to apply the latest optimization and tuning for the latest generation processor, and is portable to other platforms where the compiler can also apply the latest optimization and tuning for that processors latest generation.</para><para/></sect1>
<sect1><title> Using MMX intrinsics</title><para>MMX was the first and oldest SIMD extension and initially filled a need for wider (64-bit) integer and additional register. This is back when processors were 32-bit and 8 x 32-bit registers was starting to cramp our programming style. Now 64-bit processors, larger register sets, and 128-bit (or larger) vector SIMD extensions are common. There is simply no good reasons write new code using the (now) very limited MMX capabilities. </para><para/><para>We recommend that existing MMX codes be rewritten to use the newer SSE  and VMX/VSX intrinsics or using the more portable GCC  builtin vector support or in the case of si64 operations use C scalar code. The MMX si64 scalars which are just (64-bit) operations on long long int types and any modern C compiler can handle this type. The char short in SIMD operations should all be promoted to 128-bit SIMD operations on GCC builtin vectors. Both will improve cross platform portability and performance.</para><para/></sect1>
<title>Appendix A: Document References</title>
<sect1><title>A.1 OpenPOWER and Power documents</title><para><ulink url="">OpenPOWER</ulink><ulink url="">TM</ulink><ulink url=""> Technical Specification</ulink></para><para><ulink url="">Power ISA</ulink><ulink url="">TM</ulink><ulink url=""> Version 2.07 B</ulink></para><para><ulink url="">Power ISA</ulink><ulink url="">TM</ulink><ulink url=""> Version 3.0</ulink></para><para><ulink url="">Power Architecture 64-bit ELF ABI Specification (AKA OpenPower ABI for Linux Supplement)</ulink></para><para><ulink url="">AltiVec™ Technology </ulink><ulink url="">Programming Environments Manual</ulink></para><para/></sect1>
<sect1><title>A.2 Intel Documents</title><para><ulink url="">Intel® 64 and IA-32 Architectures Software Developer’s Manual</ulink></para><para><ulink url="">Intel</ulink><ulink url="">TM</ulink><ulink url=""> Intrinsics Guide</ulink></para><para/></sect1>
<sect1><title>A.3 GNU Compiler Collection (GCC) documents</title><para><ulink url="">GCC online documentation</ulink></para><para><ulink url="">GCC Manual (GCC 6.3)</ulink></para><para><ulink url="">GCC Internals Manual</ulink></para><para/></sect1>
<title>Appendix B: Intel Intrinsic suffixes</title>
<sect1><title>B.1 MMX</title></sect1>
<sect1><title>B.2 SSE</title></sect1>
<sect1><title>B.3 SSE2</title></sect1>
<sect1><title>B.4 AVX/AVX2 __m256_*</title></sect1>
<sect1><title>B.5 AVX512 __m512_*</title><para/></sect1>