quick_reference.md

API synopsis / quick reference

High-level overview

Highway is a collection of 'ops': platform-agnostic pure functions that operate on tuples (multiple values of the same type). These functions are implemented using platform-specific intrinsics, which map to SIMD/vector instructions.

Your code calls these ops and uses them to implement the desired algorithm. Alternatively, hwy/contrib also includes higher-level algorithms such as FindIf or VQSort implemented using these ops.

Static vs. dynamic dispatch

Highway supports two ways of deciding which instruction sets to use: static or dynamic dispatch.

Static means targeting a single instruction set, typically the best one enabled by the given compiler flags. This has no runtime overhead and only compiles your code once, but because compiler flags are typically conservative, you will not benefit from more recent instruction sets. Conversely, if you run the binary on a CPU that does not support this instruction set, it will crash.

Dynamic dispatch means compiling your code multiple times and choosing the best available implementation at runtime. Highway supports three ways of doing this:

• Highway can take care of everything including compilation (by re-#including your code), setting the required compiler #pragmas, and dispatching to the best available implementation. The only changes to your code relative to static dispatch are adding #define HWY_TARGET_INCLUDE, #include "third_party/highway/hwy/foreach_target.h" (which must come before any inclusion of highway.h) and calling HWY_DYNAMIC_DISPATCH instead of HWY_STATIC_DISPATCH.

• Some build systems (e.g. Apple) support the concept of 'fat' binaries which contain code for multiple architectures or instruction sets. Then, the operating system or loader typically takes care of calling the appropriate code. Highway interoperates with this by using the instruction set requested by the current compiler flags during each compilation pass. Your code is the same as with static dispatch.

  Note that this method replicates the entire binary, whereas the Highway-assisted dynamic dispatch method only replicates your SIMD code, which is typically a small fraction of the total size.

• Because Highway is a library (as opposed to a code generator or compiler), the dynamic dispatch method can be inspected, and made to interoperate with existing systems. For compilation, you can replace foreach_target.h if your build system supports compiling for multiple targets. For choosing the best available target, you can replace Highway's CPU detection and decision with your own. HWY_DYNAMIC_DISPATCH calls into a table of function pointers with a zero-based index indicating the desired target. Instead of calling it immediately, you can also save the function pointer returned by HWY_DYNAMIC_POINTER. Note that HWY_DYNAMIC_POINTER returns the same pointer that HWY_DYNAMIC_DISPATCH would. When either of them are first invoked, the function pointer first detects the CPU, then calls your actual function. You can call GetChosenTarget().Update(SupportedTargets()); to ensure future dynamic dispatch avoids the overhead of CPU detection. You can also replace the table lookup with your own choice of index, or even call e.g. N_AVX2::YourFunction directly.

Examples of both static and dynamic dispatch are provided in examples/. Typically, the function that does the dispatch receives a pointer to one or more arrays. Due to differing ABIs, we recommend only passing vector arguments to functions that are inlined, and in particular not the top-level function that does the dispatch.

Note that if your compiler is pre-configured to generate code only for a specific architecture, or your build flags include -m flags that specify a baseline CPU architecture, then this can interfere with dynamic dispatch, which aims to build code for all attainable targets. One example is specializing for a Raspberry Pi CPU that lacks AES, by specifying -march=armv8-a+crc. When we build the HWY_NEON target (which would only be used if the CPU actually does have AES), there is a conflict between the arch=armv8-a+crypto that is set via pragma only for the vector code, and the global -march. This results in a compile error, see #1460, #1570, and #1707. As a workaround, we recommend avoiding -m flags if possible, and otherwise defining HWY_COMPILE_ONLY_STATIC or HWY_SKIP_NON_BEST_BASELINE when building Highway as well as any user code that includes Highway headers. As a result, only the baseline target, or targets at least as good as the baseline, will be compiled. Note that it is fine for user code to still call HWY_DYNAMIC_DISPATCH. When Highway is only built for a single target, HWY_DYNAMIC_DISPATCH results in the same direct call that HWY_STATIC_DISPATCH would produce.

Headers

The public headers are:

• hwy/highway.h: main header, included from source AND/OR header files that use vector types. Note that including in headers may increase compile time, but allows declaring functions implemented out of line.

• hwy/base.h: included from headers that only need compiler/platform-dependent definitions (e.g. PopCount) without the full highway.h.

• hwy/foreach_target.h: re-includes the translation unit (specified by HWY_TARGET_INCLUDE) once per enabled target to generate code from the same source code. highway.h must still be included.

• hwy/aligned_allocator.h: defines functions for allocating memory with alignment suitable for Load/Store.

• hwy/cache_control.h: defines stand-alone functions to control caching (e.g. prefetching), independent of actual SIMD.

• hwy/nanobenchmark.h: library for precisely measuring elapsed time (under varying inputs) for benchmarking small/medium regions of code.

• hwy/print-inl.h: defines Print() for writing vector lanes to stderr.

• hwy/tests/test_util-inl.h: defines macros for invoking tests on all available targets, plus per-target functions useful in tests.

Highway provides helper macros to simplify your vector code and ensure support for dynamic dispatch. To use these, add the following to the start and end of any vector code:

#include "hwy/highway.h"
HWY_BEFORE_NAMESPACE();  // at file scope
namespace project {  // optional
namespace HWY_NAMESPACE {

// implementation

// NOLINTNEXTLINE(google-readability-namespace-comments)
}  // namespace HWY_NAMESPACE
}  // namespace project - optional
HWY_AFTER_NAMESPACE();

If you choose not to use the BEFORE/AFTER lines, you must prefix any function that calls Highway ops such as Load with HWY_ATTR. Either of these will set the compiler #pragma required to generate vector code.

The HWY_NAMESPACE lines ensure each instantiation of your code (one per target) resides in a unique namespace, thus preventing ODR violations. You can omit this if your code will only ever use static dispatch.

Notation in this doc

By vector 'lanes', we mean the 'elements' of that vector. Analogous to the lanes of a highway or swimming pool, most operations act on each lane independently, but it is possible for lanes to interact and change order via 'swizzling' ops.

• T denotes the type of a vector lane (integer or floating-point);
• N is a size_t value that governs (but is not necessarily identical to) the number of lanes;
• D is shorthand for a zero-sized tag type Simd<T, N, kPow2>, used to select the desired overloaded function (see next section). Use aliases such as ScalableTag instead of referring to this type directly;
• d is an lvalue of type D, passed as a function argument e.g. to Zero;
• V is the type of a vector, which may be a class or built-in type.
• v[i] is analogous to C++ array notation, with zero-based index i from the starting address of the vector v.

Vector and tag types

Highway vectors consist of one or more 'lanes' of the same built-in type T: uint##_t, int##_t for ## = 8, 16, 32, 64, or float##_t for ## = 16, 32, 64 and bfloat16_t. T may be retrieved via TFromD<D>. IsIntegerLaneType<T> evaluates to true for these int or uint types.

Beware that char may differ from these types, and is not supported directly. If your code loads from/stores to char*, use T=uint8_t for Highway's d tags (see below) or T=int8_t (which may enable faster less-than/greater-than comparisons), and cast your char* pointers to your T*.

In Highway, float16_t (an IEEE binary16 half-float) and bfloat16_t (the upper 16 bits of an IEEE binary32 float) only support load, store, and conversion to/from float32_t. The behavior of infinity and NaN in float16_t is implementation-defined due to Armv7. To ensure binary compatibility, these types are always wrapper structs and cannot be initialized with values directly. You can initialize them via BitCastScalar or ConvertScalarTo.

On RVV/SVE, vectors are sizeless and cannot be wrapped inside a class. The Highway API allows using built-in types as vectors because operations are expressed as overloaded functions. Instead of constructors, overloaded initialization functions such as Set take a zero-sized tag argument called d of type D and return an actual vector of unspecified type.

The actual lane count (used to increment loop counters etc.) can be obtained via Lanes(d). This value might not be known at compile time, thus storage for vectors should be dynamically allocated, e.g. via AllocateAligned(Lanes(d)).

Note that Lanes(d) could potentially change at runtime. This is currently unlikely, and will not be initiated by Highway without user action, but could still happen in other circumstances:

• upon user request in future via special CPU instructions (switching to 'streaming SVE' mode for Arm SME), or
• via system software (prctl(PR_SVE_SET_VL on Linux for Arm SVE). When the vector length is changed using this mechanism, all but the lower 128 bits of vector registers are invalidated.

Thus we discourage caching the result; it is typically used inside a function or basic block. If the application anticipates that one of the above circumstances could happen, it should ensure by some out-of-band mechanism that such changes will not happen during the critical section (the vector code which uses the result of the previously obtained Lanes(d)).

MaxLanes(d) returns a (potentially loose) upper bound on Lanes(d), and is implemented as a constexpr function.

The actual lane count is guaranteed to be a power of two, even on SVE. This simplifies alignment: remainders can be computed as count & (Lanes(d) - 1) instead of an expensive modulo. It also ensures loop trip counts that are a large power of two (at least MaxLanes) are evenly divisible by the lane count, thus avoiding the need for a second loop to handle remainders.

d lvalues (a tag, NOT actual vector) are obtained using aliases:

• Most common: ScalableTag<T[, kPow2=0]> d; or the macro form HWY_FULL(T[, LMUL=1]) d;. With the default value of the second argument, these both select full vectors which utilize all available lanes.

  Only for targets (e.g. RVV) that support register groups, the kPow2 (-3..3) and LMUL argument (1, 2, 4, 8) specify LMUL, the number of registers in the group. This effectively multiplies the lane count in each operation by LMUL, or left-shifts by kPow2 (negative values are understood as right-shifting by the absolute value). These arguments will eventually be optional hints that may improve performance on 1-2 wide machines (at the cost of reducing the effective number of registers), but RVV target does not yet support fractional LMUL. Thus, mixed-precision code (e.g. demoting float to uint8_t) currently requires LMUL to be at least the ratio of the sizes of the largest and smallest type, and smaller d to be obtained via Half<DLarger>.

  For other targets, kPow2 must lie within [HWY_MIN_POW2, HWY_MAX_POW2]. The *Tag aliases clamp to the upper bound but your code should ensure the lower bound is not exceeded, typically by specializing compile-time recursions for kPow2 = HWY_MIN_POW2 (this avoids compile errors when kPow2 is low enough that it is no longer a valid shift count).

• Less common: CappedTag<T, kCap> d or the macro form HWY_CAPPED(T, kCap) d;. These select vectors or masks where no more than the largest power of two not exceeding kCap lanes have observable effects such as loading/storing to memory, or being counted by CountTrue. The number of lanes may also be less; for the HWY_SCALAR target, vectors always have a single lane. For example, CappedTag<T, 3> will use up to two lanes.

• For applications that require fixed-size vectors: FixedTag<T, kCount> d; will select vectors where exactly kCount lanes have observable effects. These may be implemented using full vectors plus additional runtime cost for masking in Load etc. kCount must be a power of two not exceeding HWY_LANES(T), which is one for HWY_SCALAR. This tag can be used when the HWY_SCALAR target is anyway disabled (superseded by a higher baseline) or unusable (due to use of ops such as TableLookupBytes). As a convenience, we also provide Full128<T>, Full64<T> and Full32<T> aliases which are equivalent to FixedTag<T, 16 / sizeof(T)>, FixedTag<T, 8 / sizeof(T)> and FixedTag<T, 4 / sizeof(T)>.

• The result of UpperHalf/LowerHalf has half the lanes. To obtain a corresponding d, use Half<decltype(d)>; the opposite is Twice<>.

• BlockDFromD<D> returns a d with a lane type of TFromD<D> and HWY_MIN(HWY_MAX_LANES_D(D), 16 / sizeof(TFromD<D>)) lanes.

User-specified lane counts or tuples of vectors could cause spills on targets with fewer or smaller vectors. By contrast, Highway encourages vector-length agnostic code, which is more performance-portable.

For mixed-precision code (e.g. uint8_t lanes promoted to float), tags for the smaller types must be obtained from those of the larger type (e.g. via Rebind<uint8_t, ScalableTag<float>>).

Using unspecified vector types

Vector types are unspecified and depend on the target. Your code could define vector variables using auto, but it is more readable (due to making the type visible) to use an alias such as Vec<D>, or decltype(Zero(d)). Similarly, the mask type can be obtained via Mask<D>. Often your code will first define a d lvalue using ScalableTag<T>. You may wish to define an alias for your vector types such as using VecT = Vec<decltype(d)>. Do not use undocumented types such as Vec128; these may work on most targets, but not all (e.g. SVE).

Vectors are sizeless types on RVV/SVE. Therefore, vectors must not be used in arrays/STL containers (use the lane type T instead), class members, static/thread_local variables, new-expressions (use AllocateAligned instead), and sizeof/pointer arithmetic (increment T* by Lanes(d) instead).

Initializing constants requires a tag type D, or an lvalue d of that type. The D can be passed as a template argument or obtained from a vector type V via DFromV<V>. TFromV<V> is equivalent to TFromD<DFromV<V>>.

Note: Let DV = DFromV<V>. For builtin V (currently necessary on RVV/SVE), DV might not be the same as the D used to create V. In particular, DV must not be passed to Load/Store functions because it may lack the limit on N established by the original D. However, Vec<DV> is the same as V.

Thus a template argument V suffices for generic functions that do not load from/store to memory: template<class V> V Mul4(V v) { return Mul(v, Set(DFromV<V>(), 4)); }.

Example of mixing partial vectors with generic functions:

CappedTag<int16_t, 2> d2;
auto v = Mul4(Set(d2, 2));
Store(v, d2, ptr);  // Use d2, NOT DFromV<decltype(v)>()

Targets

Let Target denote an instruction set, one of SCALAR/EMU128, RVV, SSE2/SSSE3/SSE4/AVX2/AVX3/AVX3_DL/AVX3_ZEN4/AVX3_SPR (x86), PPC8/PPC9/PPC10/Z14/Z15 (POWER), WASM/WASM_EMU256 (WebAssembly), NEON_WITHOUT_AES/NEON/NEON_BF16/SVE/SVE2/SVE_256/SVE2_128 (Arm).

Note that x86 CPUs are segmented into dozens of feature flags and capabilities, which are often used together because they were introduced in the same CPU (example: AVX2 and FMA). To keep the number of targets and thus compile time and code size manageable, we define targets as 'clusters' of related features. To use HWY_AVX2, it is therefore insufficient to pass -mavx2. For definitions of the clusters, see kGroup* in targets.cc. The corresponding Clang/GCC compiler options to enable them (without -m prefix) are defined by HWY_TARGET_STR* in set_macros-inl.h, and also listed as comments in https://gcc.godbolt.org/z/rGnjMevKG.

Targets are only used if enabled (i.e. not broken nor disabled). Baseline targets are those for which the compiler is unconditionally allowed to generate instructions (implying the target CPU must support them).

• HWY_STATIC_TARGET is the best enabled baseline HWY_Target, and matches HWY_TARGET in static dispatch mode. This is useful even in dynamic dispatch mode for deducing and printing the compiler flags.

• HWY_TARGETS indicates which targets to generate for dynamic dispatch, and which headers to include. It is determined by configuration macros and always includes HWY_STATIC_TARGET.

• HWY_SUPPORTED_TARGETS is the set of targets available at runtime. Expands to a literal if only a single target is enabled, or SupportedTargets().

• HWY_TARGET: which HWY_Target is currently being compiled. This is initially identical to HWY_STATIC_TARGET and remains so in static dispatch mode. For dynamic dispatch, this changes before each re-inclusion and finally reverts to HWY_STATIC_TARGET. Can be used in #if expressions to provide an alternative to functions which are not supported by HWY_SCALAR.

  In particular, for x86 we sometimes wish to specialize functions for AVX-512 because it provides many new instructions. This can be accomplished via #if HWY_TARGET <= HWY_AVX3, which means AVX-512 or better (e.g. HWY_AVX3_DL). This is because numerically lower targets are better, and no other platform has targets numerically less than those of x86.

• HWY_WANT_SSSE3, HWY_WANT_SSE4: add SSSE3 and SSE4 to the baseline even if they are not marked as available by the compiler. On MSVC, the only ways to enable SSSE3 and SSE4 are defining these, or enabling AVX.

• HWY_WANT_AVX3_DL: opt-in for dynamic dispatch to HWY_AVX3_DL. This is unnecessary if the baseline already includes AVX3_DL.

You can detect and influence the set of supported targets:

• TargetName(t) returns a string literal identifying the single target t, where t is typically HWY_TARGET.

• SupportedTargets() returns an int64_t bitfield of enabled targets that are supported on this CPU. The return value may change after calling DisableTargets, but will never be zero.

• HWY_SUPPORTED_TARGETS is equivalent to SupportedTargets() but more efficient if only a single target is enabled.

• DisableTargets(b) causes subsequent SupportedTargets() to not return target(s) whose bits are set in b. This is useful for disabling specific targets if they are unhelpful or undesirable, e.g. due to memory bandwidth limitations. The effect is not cumulative; each call overrides the effect of all previous calls. Calling with b == 0 restores the original behavior. Use SetSupportedTargetsForTest instead of this function for iteratively enabling specific targets for testing.

• SetSupportedTargetsForTest(b) causes subsequent SupportedTargets to return b, minus those disabled via DisableTargets. b is typically derived from a subset of SupportedTargets(), e.g. each individual bit in order to test each supported target. Calling with b == 0 restores the normal SupportedTargets behavior.

Operations

In the following, the argument or return type V denotes a vector with N lanes, and M a mask. Operations limited to certain vector types begin with a constraint of the form V: {prefixes}[{bits}]. The prefixes u,i,f denote unsigned, signed, and floating-point types, and bits indicates the number of bits per lane: 8, 16, 32, or 64. Any combination of the specified prefixes and bits are allowed. Abbreviations of the form u32 = {u}{32} may also be used.

Note that Highway functions reside in hwy::HWY_NAMESPACE, whereas user-defined functions reside in project::[nested]::HWY_NAMESPACE. Highway functions generally take either a D or vector/mask argument. For targets where vectors and masks are defined in namespace hwy, the functions will be found via Argument-Dependent Lookup. However, this does not work for function templates, and RVV and SVE both use built-in vectors. Thus portable code must use one of the three following options, in descending order of preference:

• namespace hn = hwy::HWY_NAMESPACE; alias used to prefix ops, e.g. hn::LoadDup128(..);
• using hwy::HWY_NAMESPACE::LoadDup128; declarations for each op used;
• using hwy::HWY_NAMESPACE; directive. This is generally discouraged, especially for SIMD code residing in a header.

Note that overloaded operators were not supported on RVV and SVE until recently. Unfortunately, clang's SVE comparison operators return integer vectors instead of the svbool_t type which exists for this purpose. To ensure your code works on all targets, we recommend instead using the corresponding equivalents mentioned in our description of each overloaded operator, especially for comparisons, for example Lt instead of operator<.

Initialization

• V Zero(D): returns N-lane vector with all bits set to 0.

• V Set(D, T): returns N-lane vector with all lanes equal to the given value of type T.

• V Undefined(D): returns uninitialized N-lane vector, e.g. for use as an output parameter.

• V Iota(D, T2): returns N-lane vector where the lane with index i has the given value of type T2 (the op converts it to T) + i. The least significant lane has index 0. This is useful in tests for detecting lane-crossing bugs.

• V SignBit(D): returns N-lane vector with all lanes set to a value whose representation has only the most-significant bit set.

• V Dup128VecFromValues(D d, T t0, .., T tK): Creates a vector from K+1 values, broadcasted to each 128-bit block if Lanes(d) >= 16/sizeof(T) is true, where K is 16/sizeof(T) - 1.

  Dup128VecFromValues returns the following values in each 128-bit block of the result, with t0 in the least-significant (lowest-indexed) lane of each 128-bit block and tK in the most-significant (highest-indexed) lane of each 128-bit block: {t0, t1, ..., tK}

Getting/setting lanes

• T GetLane(V): returns lane 0 within V. This is useful for extracting SumOfLanes results.

The following may be slow on some platforms (e.g. x86) and should not be used in time-critical code:

• T ExtractLane(V, size_t i): returns lane i within V. i must be in [0, Lanes(DFromV<V>())). Potentially slow, it may be better to store an entire vector to an array and then operate on its elements.

• V InsertLane(V, size_t i, T t): returns a copy of V whose lane i is set to t. i must be in [0, Lanes(DFromV<V>())). Potentially slow, it may be better set all elements of an aligned array and then Load it.

Getting/setting blocks

• Vec<BlockDFromD<DFromV>> ExtractBlock<int kBlock>(V) : returns block kBlock of V, where kBlock is an index to a block that is HWY_MIN(DFromV<V>().MaxBytes(), 16) bytes.

  kBlock must be in [0, DFromV<V>().MaxBlocks()).

• V InsertBlock<int kBlock>(V v, Vec<BlockDFromD<DFromV>> blk_to_insert): Inserts blk_to_insert, with blk_to_insert[i] inserted into lane kBlock * (16 / sizeof(TFromV<V>)) + i of the result vector, if kBlock * 16 < Lanes(DFromV<V>()) * sizeof(TFromV<V>) is true.

  Otherwise, returns v if kBlock * 16 is greater than or equal to Lanes(DFromV<V>()) * sizeof(TFromV<V>).

  kBlock must be in [0, DFromV<V>().MaxBlocks()).

• size_t Blocks(D d): Returns the number of 16-byte blocks if Lanes(d) * sizeof(TFromD<D>) is greater than or equal to 16.

  Otherwise, returns 1 if Lanes(d) * sizeof(TFromD<D>) is less than 16.

Printing

• V Print(D, const char* caption, V [, size_t lane][, size_t max_lanes]): prints caption followed by up to max_lanes comma-separated lanes from the vector argument, starting at index lane. Defined in hwy/print-inl.h, also available if hwy/tests/test_util-inl.h has been included.

Tuples

As a partial workaround to the "no vectors as class members" compiler limitation mentioned in "Using unspecified vector types", we provide special types able to carry 2, 3 or 4 vectors, denoted Tuple{2-4} below. Their type is unspecified, potentially built-in, so use the aliases Vec{2-4}<D>. These can (only) be passed as arguments or returned from functions, and created/accessed using the functions in this section.

• Tuple2 Create2(D, V v0, V v1): returns tuple such that Get2<1>(tuple) returns v1.
• Tuple3 Create3(D, V v0, V v1, V v2): returns tuple such that Get3<2>(tuple) returns v2.
• Tuple4 Create4(D, V v0, V v1, V v2, V v3): returns tuple such that Get4<3>(tuple) returns v3.

The following take a size_t template argument indicating the zero-based index, from left to right, of the arguments passed to Create{2-4}.

• V Get2<size_t>(Tuple2): returns the i-th vector passed to Create2.

• V Get3<size_t>(Tuple3): returns the i-th vector passed to Create3.

• V Get4<size_t>(Tuple4): returns the i-th vector passed to Create4.

• Tuple2 Set2<size_t>(Tuple2 tuple, Vec v): sets the i-th vector

• Tuple3 Set3<size_t>(Tuple3 tuple, Vec v): sets the i-th vector

• Tuple4 Set4<size_t>(Tuple4 tuple, Vec v): sets the i-th vector

Arithmetic

• V operator+(V a, V b): returns a[i] + b[i] (mod 2^bits). Currently unavailable on SVE/RVV; use the equivalent Add instead.

• V operator-(V a, V b): returns a[i] - b[i] (mod 2^bits). Currently unavailable on SVE/RVV; use the equivalent Sub instead.

• V AddSub(V a, V b): returns a[i] - b[i] in the even lanes and a[i] + b[i] in the odd lanes.

  AddSub(a, b) is equivalent to OddEven(Add(a, b), Sub(a, b)) or Add(a, OddEven(b, Neg(b))), but AddSub(a, b) is more efficient than OddEven(Add(a, b), Sub(a, b)) or Add(a, OddEven(b, Neg(b))) on some targets.

• V: {i,f}
V Neg(V a): returns -a[i].

• V: i
V SaturatedNeg(V a): returns a[i] == LimitsMin<T>() ? LimitsMax<T>() : -a[i].

  SaturatedNeg(a) is usually more efficient than IfThenElse(Eq(a, Set(d, LimitsMin<T>())), Set(d, LimitsMax<T>()), Neg(a)).

• V: {i,f}
V Abs(V a) returns the absolute value of a[i]; for integers, LimitsMin() maps to LimitsMax() + 1.

• V: i
V SaturatedAbs(V a) returns a[i] == LimitsMin<T>() ? LimitsMax<T>() : (a[i] < 0 ? (-a[i]) : a[i]).

  SaturatedAbs(a) is usually more efficient than IfThenElse(Eq(a, Set(d, LimitsMin<T>())), Set(d, LimitsMax<T>()), Abs(a)).

• V AbsDiff(V a, V b): returns |a[i] - b[i]| in each lane.

• V: {i,u}{8,16,32},f{16,32}, VW: Vec<RepartitionToWide<DFromV<V>>>
VW SumsOf2(V v) returns the sums of 2 consecutive lanes, promoting each sum into a lane of TFromV<VW>.

• V: {i,u}{8,16}, VW: Vec<RepartitionToWideX2<DFromV<V>>>
VW SumsOf4(V v) returns the sums of 4 consecutive lanes, promoting each sum into a lane of TFromV<VW>.

• V: {i,u}8, VW: Vec<RepartitionToWideX3<DFromV<V>>>
VW SumsOf8(V v) returns the sums of 8 consecutive lanes, promoting each sum into a lane of TFromV<VW>. This is slower on RVV/WASM.

• V: {i,u}8, VW: Vec<RepartitionToWideX3<DFromV<V>>>
VW SumsOf8AbsDiff(V a, V b) returns the same result as SumsOf8(AbsDiff(a, b)), but is more efficient on x86.

• V: {i,u}8, VW: Vec<RepartitionToWide<DFromV<V>>>
VW SumsOfAdjQuadAbsDiff<int kAOffset, int kBOffset>(V a, V b) returns the sums of the absolute differences of 32-bit blocks of 8-bit integers, widened to MakeWide<TFromV<V>>.

  kAOffset must be between 0 and HWY_MIN(1, (HWY_MAX_LANES_D(DFromV<V>) - 1)/4).

  kBOffset must be between 0 and HWY_MIN(3, (HWY_MAX_LANES_D(DFromV<V>) - 1)/4).

  SumsOfAdjQuadAbsDiff computes |a[a_idx] - b[b_idx]| + |a[a_idx+1] - b[b_idx+1]| + |a[a_idx+2] - b[b_idx+2]| + |a[a_idx+3] - b[b_idx+3]| for each lane i of the result, where a_idx is equal to kAOffset*4+((i/8)*16)+(i&7) and where b_idx is equal to kBOffset*4+((i/8)*16).

  If Lanes(DFromV<V>()) < (8 << kAOffset) is true, then SumsOfAdjQuadAbsDiff returns implementation-defined values in any lanes past the first (lowest-indexed) lane of the result vector.

  SumsOfAdjQuadAbsDiff is only available if HWY_TARGET != HWY_SCALAR.

• V: {i,u}8, VW: Vec<RepartitionToWide<DFromV<V>>>
VW SumsOfShuffledQuadAbsDiff<int kIdx3, int kIdx2, int kIdx1, int kIdx0>(V a, V b) first shuffles a as if by the Per4LaneBlockShuffle<kIdx3, kIdx2, kIdx1, kIdx0>(BitCast( RepartitionToWideX2<DFromV<V>>(), a)) operation, and then computes the sum of absolute differences of 32-bit blocks of 8-bit integers taken from the shuffled a vector and the b vector.

  kIdx0, kIdx1, kIdx2, and kIdx3 must be between 0 and 3.

  SumsOfShuffledQuadAbsDiff computes |a_shuf[a_idx] - b[b_idx]| + |a_shuf[a_idx+1] - b[b_idx+1]| + |a_shuf[a_idx+2] - b[b_idx+2]| + |a_shuf[a_idx+3] - b[b_idx+3]| for each lane i of the result, where a_shuf is equal to BitCast(DFromV<V>(), Per4LaneBlockShuffle<kIdx3, kIdx2, kIdx1, kIdx0>(BitCast(RepartitionToWideX2<DFromV<V>>(), a)), a_idx is equal to (i/4)*8+(i&3), and b_idx is equal to (i/2)*4.

  If Lanes(DFromV<V>()) < 16 is true, SumsOfShuffledQuadAbsDiff returns implementation-defined results in any lanes where (i/4)*8+(i&3)+3 >= Lanes(d).

  The results of SumsOfAdjQuadAbsDiff are implementation-defined if kIdx0 >= Lanes(DFromV<V>()) / 4.

  The results of any lanes past the first (lowest-indexed) lane of SumsOfAdjQuadAbsDiff are implementation-defined if kIdx1 >= Lanes(DFromV<V>()) / 4.

  SumsOfShuffledQuadAbsDiff is only available if HWY_TARGET != HWY_SCALAR.

• V: {u,i}{8,16}
V SaturatedAdd(V a, V b) returns a[i] + b[i] saturated to the minimum/maximum representable value.

• V: {u,i}{8,16}
V SaturatedSub(V a, V b) returns a[i] - b[i] saturated to the minimum/maximum representable value.

• V: {u,i}
V AverageRound(V a, V b) returns (a[i] + b[i] + 1) >> 1.

• V Clamp(V a, V lo, V hi): returns a[i] clamped to [lo[i], hi[i]].

• V operator/(V a, V b): returns a[i] / b[i] in each lane. Currently unavailable on SVE/RVV; use the equivalent Div instead.

  For integer vectors, Div(a, b) returns an implementation-defined value in any lanes where b[i] == 0.

  For signed integer vectors, Div(a, b) returns an implementation-defined value in any lanes where a[i] == LimitsMin<T>() && b[i] == -1.

• V: {u,i}
V operator%(V a, V b): returns a[i] % b[i] in each lane. Currently unavailable on SVE/RVV; use the equivalent Mod instead.

  Mod(a, b) returns an implementation-defined value in any lanes where b[i] == 0.

  For signed integer vectors, Mod(a, b) returns an implementation-defined value in any lanes where a[i] == LimitsMin<T>() && b[i] == -1.

• V: {f}
V Sqrt(V a): returns sqrt(a[i]).

• V: {f}
V ApproximateReciprocalSqrt(V a): returns an approximation of 1.0 / sqrt(a[i]). sqrt(a) ~= ApproximateReciprocalSqrt(a) * a. x86 and PPC provide 12-bit approximations but the error on Arm is closer to 1%.

• V: {f}
V ApproximateReciprocal(V a): returns an approximation of 1.0 / a[i].

Min/Max

Note: Min/Max corner cases are target-specific and may change. If either argument is qNaN, x86 SIMD returns the second argument, Armv7 Neon returns NaN, Wasm is supposed to return NaN but does not always, but other targets actually uphold IEEE 754-2019 minimumNumber: returning the other argument if exactly one is qNaN, and NaN if both are.

• V Min(V a, V b): returns min(a[i], b[i]).

• V Max(V a, V b): returns max(a[i], b[i]).

All other ops in this section are only available if HWY_TARGET != HWY_SCALAR:

• V: u64
V Min128(D, V a, V b): returns the minimum of unsigned 128-bit values, each stored as an adjacent pair of 64-bit lanes (e.g. indices 1 and 0, where 0 is the least-significant 64-bits).

• V: u64
V Max128(D, V a, V b): returns the maximum of unsigned 128-bit values, each stored as an adjacent pair of 64-bit lanes (e.g. indices 1 and 0, where 0 is the least-significant 64-bits).

• V: u64
V Min128Upper(D, V a, V b): for each 128-bit key-value pair, returns a if it is considered less than b by Lt128Upper, else b.

• V: u64
V Max128Upper(D, V a, V b): for each 128-bit key-value pair, returns a if it is considered > b by Lt128Upper, else b.

Multiply

• V operator*(V a, V b): returns r[i] = a[i] * b[i], truncating it to the lower half for integer inputs. Currently unavailable on SVE/RVV; use the equivalent Mul instead.

• V: f, VI: Vec<RebindToSigned<DFromV<V>>>
V MulByPow2(V a, VI b): Multiplies a[i] by 2^b[i].

  MulByPow2(a, b) is equivalent to std::ldexp(a[i], HWY_MIN(HWY_MAX(b[i], LimitsMin<int>()), LimitsMax<int>())).

• V: f V MulByFloorPow2(V a, V b): Multiplies a[i] by 2^floor(b[i]).

  It is implementation-defined if MulByFloorPow2(a, b) returns zero or NaN in any lanes where a[i] is NaN and b[i] is equal to negative infinity.

  It is implementation-defined if MulByFloorPow2(a, b) returns positive infinity or NaN in any lanes where a[i] is NaN and b[i] is equal to positive infinity.

  If a[i] is a non-NaN value and b[i] is equal to negative infinity, MulByFloorPow2(a, b) is equivalent to a[i] * 0.0.

  If b[i] is NaN or if a[i] is non-NaN and b[i] is positive infinity, MulByFloorPow2(a, b) is equivalent to a[i] * b[i].

  If b[i] is a finite value, MulByFloorPow2(a, b) is equivalent to MulByPow2(a, FloorInt(b)).

• V: {u,i}
V MulHigh(V a, V b): returns the upper half of a[i] * b[i] in each lane.

• V: i16
V MulFixedPoint15(V a, V b): returns the result of multiplying two Q1.15 fixed-point numbers. This corresponds to doubling the multiplication result and storing the upper half. Results are implementation-defined iff both inputs are -32768.

• V: {u,i}
V2 MulEven(V a, V b): returns double-wide result of a[i] * b[i] for every even i, in lanes i (lower) and i + 1 (upper). V2 is a vector with double-width lanes, or the same as V for 64-bit inputs (which are only supported if HWY_TARGET != HWY_SCALAR).

• V: {u,i}
V MulOdd(V a, V b): returns double-wide result of a[i] * b[i] for every odd i, in lanes i - 1 (lower) and i (upper). Only supported if HWY_TARGET != HWY_SCALAR.

• V: {bf,u,i}16, D: RepartitionToWide<DFromV<V>>
Vec<D> WidenMulPairwiseAdd(D d, V a, V b): widens a and b to TFromD<D> and computes a[2*i+1]*b[2*i+1] + a[2*i+0]*b[2*i+0].

• VI: i8, VU: Vec<RebindToUnsigned<DFromV<VI>>>, DI: RepartitionToWide<DFromV<VI>>
Vec<DI> SatWidenMulPairwiseAdd(DI di, VU a_u, VI b_i) : widens a_u and b_i to TFromD<DI> and computes a_u[2*i+1]*b_i[2*i+1] + a_u[2*i+0]*b_i[2*i+0], saturated to the range of TFromD<D>.

• DW: i32, D: Rebind<MakeNarrow<TFromD<DW>>, DW>, VW: Vec<DW>, V: Vec<D>
Vec<D> SatWidenMulPairwiseAccumulate(DW, V a, V b, VW sum) : widens a[i] and b[i] to TFromD<DI> and computes a[2*i]*b[2*i] + a[2*i+1]*b[2*i+1] + sum[i], saturated to the range of TFromD<DW>.

• DW: i32, D: Rebind<MakeNarrow<TFromD<DW>>, DW>, VW: Vec<DW>, V: Vec<D>
VW SatWidenMulAccumFixedPoint(DW, V a, V b, VW sum)**: First, widens a and b to TFromD<DW>, then adds a[i] * b[i] * 2 to sum[i], saturated to the range of TFromD<DW>.

  If a[i] == LimitsMin<TFromD<D>>() && b[i] == LimitsMin<TFromD<D>>(), it is implementation-defined whether a[i] * b[i] * 2 is first saturated to TFromD<DW> prior to the addition of a[i] * b[i] * 2 to sum[i].

• V: {bf,u,i}16, DW: RepartitionToWide<DFromV<V>>, VW: Vec<DW>
VW ReorderWidenMulAccumulate(DW d, V a, V b, VW sum0, VW& sum1): widens a and b to TFromD<DW>, then adds a[i] * b[i] to either sum1[j] or lane j of the return value, where j = P(i) and P is a permutation. The only guarantee is that SumOfLanes(d, Add(return_value, sum1)) is the sum of all a[i] * b[i]. This is useful for computing dot products and the L2 norm. The initial value of sum1 before any call to ReorderWidenMulAccumulate must be zero (because it is unused on some platforms). It is safe to set the initial value of sum0 to any vector v; this has the effect of increasing the total sum by GetLane(SumOfLanes(d, v)) and may be slightly more efficient than later adding v to sum0.

• VW: {f,u,i}32
VW RearrangeToOddPlusEven(VW sum0, VW sum1): returns in each 32-bit lane with index i a[2*i+1]*b[2*i+1] + a[2*i+0]*b[2*i+0]. sum0 must be the return value of a prior ReorderWidenMulAccumulate, and sum1 must be its last (output) argument. In other words, this strengthens the invariant of ReorderWidenMulAccumulate such that each 32-bit lane is the sum of the widened products whose 16-bit inputs came from the top and bottom halves of the 32-bit lane. This is typically called after a series of calls to ReorderWidenMulAccumulate, as opposed to after each one. Exception: if HWY_TARGET == HWY_SCALAR, returns a[0]*b[0]. Note that the initial value of sum1 must be zero, see ReorderWidenMulAccumulate.

• VN: {u,i}{8,16}, D: RepartitionToWideX2<DFromV<VN>>
Vec<D> SumOfMulQuadAccumulate(D d, VN a, VN b, Vec<D> sum): widens a and b to TFromD<D> and computes sum[i] + a[4*i+3]*b[4*i+3] + a[4*i+2]*b[4*i+2] + a[4*i+1]*b[4*i+1] + a[4*i+0]*b[4*i+0]

• VN_I: i8, VN_U: Vec<RebindToUnsigned<DFromV<VN_I>>>, DI: Repartition<int32_t, DFromV<VN_I>>
Vec<DI> SumOfMulQuadAccumulate(DI di, VN_U a_u, VN_I b_i, Vec<DI> sum): widens a and b to TFromD<DI> and computes sum[i] + a[4*i+3]*b[4*i+3] + a[4*i+2]*b[4*i+2] + a[4*i+1]*b[4*i+1] + a[4*i+0]*b[4*i+0]

• V: {u,i}{8,16,32},{f}16,
  VW: Vec<RepartitionToWide<DFromV<V>>:
  VW WidenMulAccumulate(D, V a, V b, VW low, VW& high): widens a and b, multiplies them together, then adds them to the concatenated vectors high:low. Returns the lower half of the result, and sets high to the upper half.

Fused multiply-add

When implemented using special instructions, these functions are more precise and faster than separate multiplication followed by addition. The *Sub variants are somewhat slower on Arm, and unavailable for integer inputs; if the c argument is a constant, it would be better to negate it and use MulAdd.

• V MulAdd(V a, V b, V c): returns a[i] * b[i] + c[i].

• V NegMulAdd(V a, V b, V c): returns -a[i] * b[i] + c[i].

• V MulSub(V a, V b, V c): returns a[i] * b[i] - c[i].

• V NegMulSub(V a, V b, V c): returns -a[i] * b[i] - c[i].

• V MulAddSub(V a, V b, V c): returns a[i] * b[i] - c[i] in the even lanes and a[i] * b[i] + c[i] in the odd lanes.

  MulAddSub(a, b, c) is equivalent to OddEven(MulAdd(a, b, c), MulSub(a, b, c)) or MulAddSub(a, b, OddEven(c, Neg(c)), but MulSub(a, b, c) is more efficient on some targets (including AVX2/AVX3).

• V: bf16, D: RepartitionToWide<DFromV<V>>, VW: Vec<D>
VW MulEvenAdd(D d, V a, V b, VW c): equivalent to and potentially more efficient than MulAdd(PromoteEvenTo(d, a), PromoteEvenTo(d, b), c).

• V: bf16, D: RepartitionToWide<DFromV<V>>, VW: Vec<D>
VW MulOddAdd(D d, V a, V b, VW c): equivalent to and potentially more efficient than MulAdd(PromoteOddTo(d, a), PromoteOddTo(d, b), c).

Masked arithmetic

All ops in this section return no for mask=false lanes, and suppress any exceptions for those lanes if that is supported by the ISA. When exceptions are not a concern, these are equivalent to, and potentially more efficient than, IfThenElse(m, Add(a, b), no); etc.

• V MaskedMinOr(V no, M m, V a, V b): returns Min(a, b)[i] or no[i] if m[i] is false.
• V MaskedMaxOr(V no, M m, V a, V b): returns Max(a, b)[i] or no[i] if m[i] is false.
• V MaskedAddOr(V no, M m, V a, V b): returns a[i] + b[i] or no[i] if m[i] is false.
• V MaskedSubOr(V no, M m, V a, V b): returns a[i] - b[i] or no[i] if m[i] is false.
• V MaskedMulOr(V no, M m, V a, V b): returns a[i] * b[i] or no[i] if m[i] is false.
• V MaskedDivOr(V no, M m, V a, V b): returns a[i] / b[i] or no[i] if m[i] is false.
• V: {u,i}
V MaskedModOr(V no, M m, V a, V b): returns a[i] % b[i] or no[i] if m[i] is false.
• V: {u,i}{8,16}
V MaskedSatAddOr(V no, M m, V a, V b): returns a[i] + b[i] saturated to the minimum/maximum representable value, or no[i] if m[i] is false.
• V: {u,i}{8,16}
V MaskedSatSubOr(V no, M m, V a, V b): returns a[i] + b[i] saturated to the minimum/maximum representable value, or no[i] if m[i] is false.

Shifts

Note: Counts not in [0, sizeof(T)*8) yield implementation-defined results. Left-shifting signed T and right-shifting positive signed T is the same as shifting MakeUnsigned<T> and casting to T. Right-shifting negative signed T is the same as an unsigned shift, except that 1-bits are shifted in.

Compile-time constant shifts: the amount must be in [0, sizeof(T)*8). Generally the most efficient variant, but 8-bit shifts are potentially slower than other lane sizes, and RotateRight is often emulated with shifts:

• V: {u,i}
V ShiftLeft<int>(V a) returns a[i] << int.

• V: {u,i}
V ShiftRight<int>(V a) returns a[i] >> int.

• V: {u,i}
V RoundingShiftRight<int>(V a) returns ((int == 0) ? a[i] : (((a[i] >> (int - 1)) + 1) >> 1).

• V: {u,i}
V RotateLeft<int>(V a) returns (a[i] << int) | (static_cast<TU>(a[i]) >> (sizeof(T)*8 - int)).

• V: {u,i}
V RotateRight<int>(V a) returns (static_cast<TU>(a[i]) >> int) | (a[i] << (sizeof(T)*8 - int)).

Shift all lanes by the same (not necessarily compile-time constant) amount:

• V: {u,i}
V ShiftLeftSame(V a, int bits) returns a[i] << bits.

• V: {u,i}
V ShiftRightSame(V a, int bits) returns a[i] >> bits.

• V: {u,i}
V RoundingShiftRightSame<int kShiftAmt>(V a, int bits) returns ((bits == 0) ? a[i] : (((a[i] >> (bits - 1)) + 1) >> 1).

• V: {u,i}
V RotateLeftSame(V a, int bits) returns (a[i] << shl_bits) | (static_cast<TU>(a[i]) >> (sizeof(T)*8 - shl_bits)), where shl_bits is equal to bits & (sizeof(T)*8 - 1).

• V: {u,i}
V RotateRightSame(V a, int bits) returns (static_cast<TU>(a[i]) >> shr_bits) | (a[i] >> (sizeof(T)*8 - shr_bits)), where shr_bits is equal to bits & (sizeof(T)*8 - 1).

Per-lane variable shifts (slow if SSSE3/SSE4, or 16-bit, or Shr i64 on AVX2):

• V: {u,i}
V operator<<(V a, V b) returns a[i] << b[i]. Currently unavailable on SVE/RVV; use the equivalent Shl instead.

• V: {u,i}
V operator>>(V a, V b) returns a[i] >> b[i]. Currently unavailable on SVE/RVV; use the equivalent Shr instead.

• V: {u,i}
V RoundingShr(V a, V b) returns ((b[i] == 0) ? a[i] : (((a[i] >> (b[i] - 1)) + 1) >> 1).

• V: {u,i}
V Rol(V a, V b) returns (a[i] << (b[i] & shift_amt_mask)) | (static_cast<TU>(a[i]) >> ((sizeof(T)*8 - b[i]) & shift_amt_mask)), where shift_amt_mask is equal to sizeof(T)*8 - 1.

• V: {u,i}
V Ror(V a, V b) returns (static_cast<TU>(a[i]) >> (b[i] & shift_amt_mask)) | (a[i] << ((sizeof(T)*8 - b[i]) & shift_amt_mask)), where shift_amt_mask is equal to sizeof(T)*8 - 1.

Floating-point rounding

• V: {f}
V Round(V v): returns v[i] rounded towards the nearest integer, with ties to even.

• V: {f}
V Trunc(V v): returns v[i] rounded towards zero (truncate).

• V: {f}
V Ceil(V v): returns v[i] rounded towards positive infinity (ceiling).

• V: {f}
V Floor(V v): returns v[i] rounded towards negative infinity.

Floating-point classification

• V: {f}
M IsNaN(V v): returns mask indicating whether v[i] is "not a number" (unordered).

• V: {f}
M IsEitherNaN(V a, V b): equivalent to Or(IsNaN(a), IsNaN(b)), but IsEitherNaN(a, b) is more efficient than Or(IsNaN(a), IsNaN(b)) on x86.

• V: {f}
M IsInf(V v): returns mask indicating whether v[i] is positive or negative infinity.

• V: {f}
M IsFinite(V v): returns mask indicating whether v[i] is neither NaN nor infinity, i.e. normal, subnormal or zero. Equivalent to Not(Or(IsNaN(v), IsInf(v))).

Logical

• V: {u,i}
V PopulationCount(V a): returns the number of 1-bits in each lane, i.e. PopCount(a[i]).

• V: {u,i}
V LeadingZeroCount(V a): returns the number of leading zeros in each lane. For any lanes where a[i] is zero, sizeof(TFromV<V>) * 8 is returned in the corresponding result lanes.

• V: {u,i}
V TrailingZeroCount(V a): returns the number of trailing zeros in each lane. For any lanes where a[i] is zero, sizeof(TFromV<V>) * 8 is returned in the corresponding result lanes.

• V: {u,i}
V HighestSetBitIndex(V a): returns the index of the highest set bit of each lane. For any lanes of a signed vector type where a[i] is zero, an unspecified negative value is returned in the corresponding result lanes. For any lanes of an unsigned vector type where a[i] is zero, an unspecified value that is greater than HighestValue<MakeSigned<TFromV<V>>>() is returned in the corresponding result lanes.

The following operate on individual bits within each lane. Note that the non-operator functions (And instead of &) must be used for floating-point types, and on SVE/RVV.

• V: {u,i}
V operator&(V a, V b): returns a[i] & b[i]. Currently unavailable on SVE/RVV; use the equivalent And instead.

• V: {u,i}
V operator|(V a, V b): returns a[i] | b[i]. Currently unavailable on SVE/RVV; use the equivalent Or instead.

• V: {u,i}
V operator^(V a, V b): returns a[i] ^ b[i]. Currently unavailable on SVE/RVV; use the equivalent Xor instead.

• V: {u,i}
V Not(V v): returns ~v[i].

• V AndNot(V a, V b): returns ~a[i] & b[i].

The following three-argument functions may be more efficient than assembling them from 2-argument functions:

• V Xor3(V x1, V x2, V x3): returns x1[i] ^ x2[i] ^ x3[i]. This is more efficient than Or3 on some targets. When inputs are disjoint (no bit is set in more than one argument), Xor3 and Or3 are equivalent and you should use the former.
• V Or3(V o1, V o2, V o3): returns o1[i] | o2[i] | o3[i]. This is less efficient than Xor3 on some targets; use that where possible.
• V OrAnd(V o, V a1, V a2): returns o[i] | (a1[i] & a2[i]).
• V BitwiseIfThenElse(V mask, V yes, V no): returns ((mask[i] & yes[i]) | (~mask[i] & no[i])). BitwiseIfThenElse is equivalent to, but potentially more efficient than Or(And(mask, yes), AndNot(mask, no)).

Special functions for signed types:

• V: {f}
V CopySign(V a, V b): returns the number with the magnitude of a and sign of b.

• V: {f}
V CopySignToAbs(V a, V b): as above, but potentially slightly more efficient; requires the first argument to be non-negative.

• V: {i}
V BroadcastSignBit(V a) returns a[i] < 0 ? -1 : 0.

• V: {i,f}
V ZeroIfNegative(V v): returns v[i] < 0 ? 0 : v[i].

• V: {i,f}
V IfNegativeThenElse(V v, V yes, V no): returns v[i] < 0 ? yes[i] : no[i]. This may be more efficient than IfThenElse(Lt..).

• V: {i,f}
V IfNegativeThenElseZero(V v, V yes): returns v[i] < 0 ? yes[i] : 0. IfNegativeThenElseZero(v, yes) is equivalent to but more efficient than IfThenElseZero(IsNegative(v), yes) or IfNegativeThenElse(v, yes, Zero(d)) on some targets.

• V: {i,f}
V IfNegativeThenZeroElse(V v, V no): returns v[i] < 0 ? 0 : no. IfNegativeThenZeroElse(v, no) is equivalent to but more efficient than IfThenZeroElse(IsNegative(v), no) or IfNegativeThenElse(v, Zero(d), no) on some targets.

• V: {i,f}
V IfNegativeThenNegOrUndefIfZero(V mask, V v): returns mask[i] < 0 ? (-v[i]) : ((mask[i] > 0) ? v[i] : impl_defined_val), where impl_defined_val is an implementation-defined value that is equal to either 0 or v[i].

  IfNegativeThenNegOrUndefIfZero(mask, v) is more efficient than IfNegativeThenElse(mask, Neg(v), v) for I8/I16/I32 vectors that are 32 bytes or smaller on SSSE3/SSE4/AVX2/AVX3 targets.

Masks

Let M denote a mask capable of storing a logical true/false for each lane (the encoding depends on the platform).

Create mask

• M FirstN(D, size_t N): returns mask with the first N lanes (those with index < N) true. N >= Lanes(D()) results in an all-true mask. N must not exceed LimitsMax<SignedFromSize<HWY_MIN(sizeof(size_t), sizeof(TFromD<D>))>>(). Useful for implementing "masked" stores by loading prev followed by IfThenElse(FirstN(d, N), what_to_store, prev).

• M MaskFromVec(V v): returns false in lane i if v[i] == 0, or true if v[i] has all bits set. The result is implementation-defined if v[i] is neither zero nor all bits set.

• M LoadMaskBits(D, const uint8_t* p): returns a mask indicating whether the i-th bit in the array is set. Loads bytes and bits in ascending order of address and index. At least 8 bytes of p must be readable, but only (Lanes(D()) + 7) / 8 need be initialized. Any unused bits (happens if Lanes(D()) < 8) are treated as if they were zero.

• M Dup128MaskFromMaskBits(D d, unsigned mask_bits): returns a mask with lane i set to ((mask_bits >> (i & (16 / sizeof(T) - 1))) & 1) != 0.

• M MaskFalse(D): returns an all-false mask. MaskFalse(D()) is equivalent to MaskFromVec(Zero(D())), but MaskFalse(D()) is more efficient than MaskFromVec(Zero(D())) on AVX3, RVV, and SVE.

  MaskFalse(D()) is also equivalent to FirstN(D(), 0) or Dup128MaskFromMaskBits(D(), 0), but MaskFalse(D()) is usually more efficient.

Convert mask

• M1 RebindMask(D, M2 m): returns same mask bits as m, but reinterpreted as a mask for lanes of type TFromD<D>. M1 and M2 must have the same number of lanes.

• V VecFromMask(D, M m): returns 0 in lane i if m[i] == false, otherwise all bits set.

• uint64_t BitsFromMask(D, M m): returns bits b such that (b >> i) & 1 indicates whether m[i] was set, and any remaining bits in the uint64_t are zero. This is only available if HWY_MAX_BYTES <= 64, because 512-bit vectors are the longest for which there are no more than 64 lanes and thus mask bits.

• size_t StoreMaskBits(D, M m, uint8_t* p): stores a bit array indicating whether m[i] is true, in ascending order of i, filling the bits of each byte from least to most significant, then proceeding to the next byte. Returns the number of bytes written: (Lanes(D()) + 7) / 8. At least 8 bytes of p must be writable.

• Mask<DTo> PromoteMaskTo(DTo d_to, DFrom d_from, Mask<DFrom> m): Promotes m to a mask with a lane type of TFromD<DTo>, DFrom is Rebind<TFrom, DTo>.

  PromoteMaskTo(d_to, d_from, m) is equivalent to MaskFromVec(BitCast(d_to, PromoteTo(di_to, BitCast(di_from, VecFromMask(d_from, m))))), where di_from is RebindToSigned<DFrom>() and di_from is RebindToSigned<DFrom>(), but PromoteMaskTo(d_to, d_from, m) is more efficient on some targets.

  PromoteMaskTo requires that sizeof(TFromD<DFrom>) < sizeof(TFromD<DTo>) be true.

• Mask<DTo> DemoteMaskTo(DTo d_to, DFrom d_from, Mask<DFrom> m): Demotes m to a mask with a lane type of TFromD<DTo>, DFrom is Rebind<TFrom, DTo>.

  DemoteMaskTo(d_to, d_from, m) is equivalent to MaskFromVec(BitCast(d_to, DemoteTo(di_to, BitCast(di_from, VecFromMask(d_from, m))))), where di_from is RebindToSigned<DFrom>() and di_from is RebindToSigned<DFrom>(), but DemoteMaskTo(d_to, d_from, m) is more efficient on some targets.

  DemoteMaskTo requires that sizeof(TFromD<DFrom>) > sizeof(TFromD<DTo>) be true.

• M OrderedDemote2MasksTo(DTo, DFrom, M2, M2): returns a mask whose LowerHalf is the first argument and whose UpperHalf is the second argument; M2 is Mask<Half<DFrom>>; DTo is Repartition<TTo, DFrom>.

  OrderedDemote2MasksTo requires that sizeof(TFromD<DTo>) == sizeof(TFromD<DFrom>) * 2 be true.

  OrderedDemote2MasksTo(d_to, d_from, a, b) is equivalent to MaskFromVec(BitCast(d_to, OrderedDemote2To(di_to, va, vb))), where va is BitCast(di_from, MaskFromVec(d_from, a)), vb is BitCast(di_from, MaskFromVec(d_from, b)), di_to is RebindToSigned<DTo>(), and di_from is RebindToSigned<DFrom>(), but OrderedDemote2MasksTo(d_to, d_from, a, b) is more efficient on some targets.

  OrderedDemote2MasksTo is only available if HWY_TARGET != HWY_SCALAR is true.

Combine mask

• M2 LowerHalfOfMask(D d, M m): returns the lower half of mask m, where M is MFromD<Twice<D>> and M2 is MFromD<D>.

  LowerHalfOfMask(d, m) is equivalent to MaskFromVec(LowerHalf(d, VecFromMask(d, m))), but LowerHalfOfMask(d, m) is more efficient on some targets.

• M2 UpperHalfOfMask(D d, M m): returns the upper half of mask m, where M is MFromD<Twice<D>> and M2 is MFromD<D>.

  UpperHalfOfMask(d, m) is equivalent to MaskFromVec(UpperHalf(d, VecFromMask(d, m))), but UpperHalfOfMask(d, m) is more efficient on some targets.

  UpperHalfOfMask is only available if HWY_TARGET != HWY_SCALAR is true.

• M CombineMasks(D, M2, M2): returns a mask whose UpperHalf is the first argument and whose LowerHalf is the second argument; M2 is Mask<Half<D>>.

  CombineMasks(d, hi, lo) is equivalent to MaskFromVec(d, Combine(d, VecFromMask(Half<D>(), hi), VecFromMask(Half<D>(), lo))), but CombineMasks(d, hi, lo) is more efficient on some targets.

  CombineMasks is only available if HWY_TARGET != HWY_SCALAR is true.

Slide mask across blocks

• M SlideMaskUpLanes(D d, M m, size_t N): Slides m up N lanes. SlideMaskUpLanes(d, m, N) is equivalent to MaskFromVec(SlideUpLanes(d, VecFromMask(d, m), N)), but SlideMaskUpLanes(d, m, N) is more efficient on some targets.

  The results of SlideMaskUpLanes is implementation-defined if N >= Lanes(d).

• M SlideMaskDownLanes(D d, M m, size_t N): Slides m down N lanes. SlideMaskDownLanes(d, m, N) is equivalent to MaskFromVec(SlideDownLanes(d, VecFromMask(d, m), N)), but SlideMaskDownLanes(d, m, N) is more efficient on some targets.

  The results of SlideMaskDownLanes is implementation-defined if N >= Lanes(d).

• M SlideMask1Up(D d, M m): Slides m up 1 lane. SlideMask1Up(d, m) is equivalent to MaskFromVec(Slide1Up(d, VecFromMask(d, m))), but SlideMask1Up(d, m) is more efficient on some targets.

• M SlideMask1Down(D d, M m): Slides m down 1 lane. SlideMask1Down(d, m) is equivalent to MaskFromVec(Slide1Down(d, VecFromMask(d, m))), but SlideMask1Down(d, m) is more efficient on some targets.

Test mask

• bool AllTrue(D, M m): returns whether all m[i] are true.

• bool AllFalse(D, M m): returns whether all m[i] are false.

• size_t CountTrue(D, M m): returns how many of m[i] are true [0, N]. This is typically more expensive than AllTrue/False.

• intptr_t FindFirstTrue(D, M m): returns the index of the first (i.e. lowest index) m[i] that is true, or -1 if none are.

• size_t FindKnownFirstTrue(D, M m): returns the index of the first (i.e. lowest index) m[i] that is true. Requires !AllFalse(d, m), otherwise results are undefined. This is typically more efficient than FindFirstTrue.

• intptr_t FindLastTrue(D, M m): returns the index of the last (i.e. highest index) m[i] that is true, or -1 if none are.

• size_t FindKnownLastTrue(D, M m): returns the index of the last (i.e. highest index) m[i] that is true. Requires !AllFalse(d, m), otherwise results are undefined. This is typically more efficient than FindLastTrue.

Ternary operator for masks

For IfThen*, masks must adhere to the invariant established by MaskFromVec: false is zero, true has all bits set:

• V IfThenElse(M mask, V yes, V no): returns mask[i] ? yes[i] : no[i].

• V IfThenElseZero(M mask, V yes): returns mask[i] ? yes[i] : 0.

• V IfThenZeroElse(M mask, V no): returns mask[i] ? 0 : no[i].

• V IfVecThenElse(V mask, V yes, V no): equivalent to and possibly faster than IfVecThenElse(MaskFromVec(mask), yes, no). The result is implementation-defined if mask[i] is neither zero nor all bits set.

Logical mask

• M Not(M m): returns mask of elements indicating whether the input mask element was false.

• M And(M a, M b): returns mask of elements indicating whether both input mask elements were true.

• M AndNot(M not_a, M b): returns mask of elements indicating whether not_a is false and b is true.

• M Or(M a, M b): returns mask of elements indicating whether either input mask element was true.

• M Xor(M a, M b): returns mask of elements indicating whether exactly one input mask element was true.

• M ExclusiveNeither(M a, M b): returns mask of elements indicating a is false and b is false. Undefined if both are true. We choose not to provide NotOr/NotXor because x86 and SVE only define one of these operations. This op is for situations where the inputs are known to be mutually exclusive.

• M SetOnlyFirst(M m): If none of m[i] are true, returns all-false. Otherwise, only lane k is true, where k is equal to FindKnownFirstTrue(m). In other words, sets to false any lanes with index greater than the first true lane, if it exists.

• M SetBeforeFirst(M m): If none of m[i] are true, returns all-true. Otherwise, returns mask with the first k lanes true and all remaining lanes false, where k is equal to FindKnownFirstTrue(m). In other words, if at least one of m[i] is true, sets to true any lanes with index less than the first true lane and all remaining lanes to false.

• M SetAtOrBeforeFirst(M m): equivalent to Or(SetBeforeFirst(m), SetOnlyFirst(m)), but SetAtOrBeforeFirst(m) is usually more efficient than Or(SetBeforeFirst(m), SetOnlyFirst(m)).

• M SetAtOrAfterFirst(M m): equivalent to Not(SetBeforeFirst(m)).

Compress

• V Compress(V v, M m): returns r such that r[n] is v[i], with i the n-th lane index (starting from 0) where m[i] is true. Compacts lanes whose mask is true into the lower lanes. For targets and lane type T where CompressIsPartition<T>::value is true, the upper lanes are those whose mask is false (thus Compress corresponds to partitioning according to the mask). Otherwise, the upper lanes are implementation-defined. Potentially slow with 8 and 16-bit lanes. Use this form when the input is already a mask, e.g. returned by a comparison.

• V CompressNot(V v, M m): equivalent to Compress(v, Not(m)) but possibly faster if CompressIsPartition<T>::value is true.

• V: u64
V CompressBlocksNot(V v, M m): equivalent to CompressNot(v, m) when m is structured as adjacent pairs (both true or false), e.g. as returned by Lt128. This is a no-op for 128 bit vectors. Unavailable if HWY_TARGET == HWY_SCALAR.

• size_t CompressStore(V v, M m, D d, T* p): writes lanes whose mask m is true into p, starting from lane 0. Returns CountTrue(d, m), the number of valid lanes. May be implemented as Compress followed by StoreU; lanes after the valid ones may still be overwritten! Potentially slow with 8 and 16-bit lanes.

• size_t CompressBlendedStore(V v, M m, D d, T* p): writes only lanes whose mask m is true into p, starting from lane 0. Returns CountTrue(d, m), the number of lanes written. Does not modify subsequent lanes, but there is no guarantee of atomicity because this may be implemented as Compress, LoadU, IfThenElse(FirstN), StoreU.

• V CompressBits(V v, const uint8_t* HWY_RESTRICT bits): Equivalent to, but often faster than Compress(v, LoadMaskBits(d, bits)). bits is as specified for LoadMaskBits. If called multiple times, the bits pointer passed to this function must also be marked HWY_RESTRICT to avoid repeated work. Note that if the vector has less than 8 elements, incrementing bits will not work as intended for packed bit arrays. As with Compress, CompressIsPartition indicates the mask=false lanes are moved to the upper lanes. Potentially slow with 8 and 16-bit lanes.

• size_t CompressBitsStore(V v, const uint8_t* HWY_RESTRICT bits, D d, T* p): combination of CompressStore and CompressBits, see remarks there.

Expand

• V Expand(V v, M m): returns r such that r[i] is zero where m[i] is false, and otherwise v[s], where s is the number of m[0, i) which are true. Scatters inputs in ascending index order to the lanes whose mask is true and zeros all other lanes. Potentially slow with 8 and 16-bit lanes.

• V LoadExpand(M m, D d, const T* p): returns r such that r[i] is zero where m[i] is false, and otherwise p[s], where s is the number of m[0, i) which are true. May be implemented as LoadU followed by Expand. Potentially slow with 8 and 16-bit lanes.

Comparisons

These return a mask (see above) indicating whether the condition is true.

• M operator==(V a, V b): returns a[i] == b[i]. Currently unavailable on SVE/RVV; use the equivalent Eq instead.

• M operator!=(V a, V b): returns a[i] != b[i]. Currently unavailable on SVE/RVV; use the equivalent Ne instead.

• M operator<(V a, V b): returns a[i] < b[i]. Currently unavailable on SVE/RVV; use the equivalent Lt instead.

• M operator>(V a, V b): returns a[i] > b[i]. Currently unavailable on SVE/RVV; use the equivalent Gt instead.

• M operator<=(V a, V b): returns a[i] <= b[i]. Currently unavailable on SVE/RVV; use the equivalent Le instead.

• M operator>=(V a, V b): returns a[i] >= b[i]. Currently unavailable on SVE/RVV; use the equivalent Ge instead.

• V: {i,f}
M IsNegative(V v): returns v[i] < 0.

  IsNegative(v) is equivalent to MaskFromVec(BroadcastSignBit(v)) or Lt(v, Zero(d)), but IsNegative(v) is more efficient on some targets.

• V: {u,i}
M TestBit(V v, V bit): returns (v[i] & bit[i]) == bit[i]. bit[i] must have exactly one bit set.

• V: u64
M Lt128(D, V a, V b): for each adjacent pair of 64-bit lanes (e.g. indices 1,0), returns whether a[1]:a[0] concatenated to an unsigned 128-bit integer (least significant bits in a[0]) is less than b[1]:b[0]. For each pair, the mask lanes are either both true or both false. Unavailable if HWY_TARGET == HWY_SCALAR.

• V: u64
M Lt128Upper(D, V a, V b): for each adjacent pair of 64-bit lanes (e.g. indices 1,0), returns whether a[1] is less than b[1]. For each pair, the mask lanes are either both true or both false. This is useful for comparing 64-bit keys alongside 64-bit values. Only available if HWY_TARGET != HWY_SCALAR.

• V: u64
M Eq128(D, V a, V b): for each adjacent pair of 64-bit lanes (e.g. indices 1,0), returns whether a[1]:a[0] concatenated to an unsigned 128-bit integer (least significant bits in a[0]) equals b[1]:b[0]. For each pair, the mask lanes are either both true or both false. Unavailable if HWY_TARGET == HWY_SCALAR.

• V: u64
M Ne128(D, V a, V b): for each adjacent pair of 64-bit lanes (e.g. indices 1,0), returns whether a[1]:a[0] concatenated to an unsigned 128-bit integer (least significant bits in a[0]) differs from b[1]:b[0]. For each pair, the mask lanes are either both true or both false. Unavailable if HWY_TARGET == HWY_SCALAR.

• V: u64
M Eq128Upper(D, V a, V b): for each adjacent pair of 64-bit lanes (e.g. indices 1,0), returns whether a[1] equals b[1]. For each pair, the mask lanes are either both true or both false. This is useful for comparing 64-bit keys alongside 64-bit values. Only available if HWY_TARGET != HWY_SCALAR.

• V: u64
M Ne128Upper(D, V a, V b): for each adjacent pair of 64-bit lanes (e.g. indices 1,0), returns whether a[1] differs from b[1]. For each pair, the mask lanes are either both true or both false. This is useful for comparing 64-bit keys alongside 64-bit values. Only available if HWY_TARGET != HWY_SCALAR.

Memory

Memory operands are little-endian, otherwise their order would depend on the lane configuration. Pointers are the addresses of N consecutive T values, either aligned (address is a multiple of the vector size) or possibly unaligned (denoted p).

Even unaligned addresses must still be a multiple of sizeof(T), otherwise StoreU may crash on some platforms (e.g. RVV and Armv7). Note that C++ ensures automatic (stack) and dynamically allocated (via new or malloc) variables of type T are aligned to sizeof(T), hence such addresses are suitable for StoreU. However, casting pointers to char* and adding arbitrary offsets (not a multiple of sizeof(T)) can violate this requirement.

Note: computations with low arithmetic intensity (FLOP/s per memory traffic bytes), e.g. dot product, can be 1.5 times as fast when the memory operands are aligned to the vector size. An unaligned access may require two load ports.

Load

• Vec<D> Load(D, const T* aligned): returns aligned[i]. May fault if the pointer is not aligned to the vector size (using aligned_allocator.h is safe). Using this whenever possible improves codegen on SSSE3/SSE4: unlike LoadU, Load can be fused into a memory operand, which reduces register pressure.

Requires only element-aligned vectors (e.g. from malloc/std::vector, or aligned memory at indices which are not a multiple of the vector length):

• Vec<D> LoadU(D, const T* p): returns p[i].

• Vec<D> LoadDup128(D, const T* p): returns one 128-bit block loaded from p and broadcasted into all 128-bit block[s]. This may be faster than broadcasting single values, and is more convenient than preparing constants for the actual vector length. Only available if HWY_TARGET != HWY_SCALAR.

• Vec<D> MaskedLoadOr(V no, M mask, D, const T* p): returns mask[i] ? p[i] : no[i]. May fault even where mask is false #if HWY_MEM_OPS_MIGHT_FAULT. If p is aligned, faults cannot happen unless the entire vector is inaccessible. Assuming no faults, this is equivalent to, and potentially more efficient than, IfThenElse(mask, LoadU(D(), p), no).

• Vec<D> MaskedLoad(M mask, D d, const T* p): equivalent to MaskedLoadOr(Zero(d), mask, d, p), but potentially slightly more efficient.

• Vec<D> LoadN(D d, const T* p, size_t max_lanes_to_load) : Loads HWY_MIN(Lanes(d), max_lanes_to_load) lanes from p to the first (lowest-index) lanes of the result vector and zeroes out the remaining lanes.

  LoadN does not fault if all of the elements in [p, p + max_lanes_to_load) are accessible, even if HWY_MEM_OPS_MIGHT_FAULT is 1 or max_lanes_to_load < Lanes(d) is true.

• Vec<D> LoadNOr(V no, D d, const T* p, size_t max_lanes_to_load) : Loads HWY_MIN(Lanes(d), max_lanes_to_load) lanes from p to the first (lowest-index) lanes of the result vector and fills the remaining lanes with no. Like LoadN, this does not fault.

Store

• void Store(Vec<D> v, D, T* aligned): copies v[i] into aligned[i], which must be aligned to the vector size. Writes exactly N * sizeof(T) bytes.

• void StoreU(Vec<D> v, D, T* p): as Store, but the alignment requirement is relaxed to element-aligned (multiple of sizeof(T)).

• void BlendedStore(Vec<D> v, M m, D d, T* p): as StoreU, but only updates p where m is true. May fault even where mask is false #if HWY_MEM_OPS_MIGHT_FAULT. If p is aligned, faults cannot happen unless the entire vector is inaccessible. Equivalent to, and potentially more efficient than, StoreU(IfThenElse(m, v, LoadU(d, p)), d, p). "Blended" indicates this may not be atomic; other threads must not concurrently update [p, p + Lanes(d)) without synchronization.

• void SafeFillN(size_t num, T value, D d, T* HWY_RESTRICT to): Sets to[0, num) to value. If num exceeds Lanes(d), the behavior is target-dependent (either filling all, or no more than one vector). Potentially more efficient than a scalar loop, but will not fault, unlike BlendedStore. No alignment requirement. Potentially non-atomic, like BlendedStore.

• void SafeCopyN(size_t num, D d, const T* HWY_RESTRICT from, T* HWY_RESTRICT to): Copies from[0, num) to to. If num exceeds Lanes(d), the behavior is target-dependent (either copying all, or no more than one vector). Potentially more efficient than a scalar loop, but will not fault, unlike BlendedStore. No alignment requirement. Potentially non-atomic, like BlendedStore.

• void StoreN(Vec<D> v, D d, T* HWY_RESTRICT p, size_t max_lanes_to_store): Stores the first (lowest-index) HWY_MIN(Lanes(d), max_lanes_to_store) lanes of v to p.

  StoreN does not modify any memory past p + HWY_MIN(Lanes(d), max_lanes_to_store) - 1.

Interleaved

• void LoadInterleaved2(D, const T* p, Vec<D>& v0, Vec<D>& v1): equivalent to LoadU into v0, v1 followed by shuffling, such that v0[0] == p[0], v1[0] == p[1].

• void LoadInterleaved3(D, const T* p, Vec<D>& v0, Vec<D>& v1, Vec<D>& v2): as above, but for three vectors (e.g. RGB samples).

• void LoadInterleaved4(D, const T* p, Vec<D>& v0, Vec<D>& v1, Vec<D>& v2, Vec<D>& v3): as above, but for four vectors (e.g. RGBA).

• void StoreInterleaved2(Vec<D> v0, Vec<D> v1, D, T* p): equivalent to shuffling v0, v1 followed by two StoreU(), such that p[0] == v0[0], p[1] == v1[0].

• void StoreInterleaved3(Vec<D> v0, Vec<D> v1, Vec<D> v2, D, T* p): as above, but for three vectors (e.g. RGB samples).

• void StoreInterleaved4(Vec<D> v0, Vec<D> v1, Vec<D> v2, Vec<D> v3, D, T* p): as above, but for four vectors (e.g. RGBA samples).

Scatter/Gather

Note: Offsets/indices are of type VI = Vec<RebindToSigned<D>> and need not be unique. The results are implementation-defined for negative offsets, because behavior differs between x86 and RVV (signed vs. unsigned).

Note: Where possible, applications should Load/Store/TableLookup* entire vectors, which is much faster than Scatter/Gather. Otherwise, code of the form dst[tbl[i]] = F(src[i]) should when possible be transformed to dst[i] = F(src[tbl[i]]) because Scatter may be more expensive than Gather.

Note: We provide *Offset functions for the convenience of users that have actual byte offsets. However, the preferred interface is *Index, which takes indices. To reduce the number of ops, we do not intend to add Masked* ops for offsets. If you have offsets, you can convert them to indices via ShiftRight.

• D: {u,i,f}{32,64}
void ScatterOffset(Vec<D> v, D, T* base, VI offsets): stores v[i] to the base address plus byte offsets[i].

• D: {u,i,f}{32,64}
void ScatterIndex(Vec<D> v, D, T* base, VI indices): stores v[i] to base[indices[i]].

• D: {u,i,f}{32,64}
void ScatterIndexN(Vec<D> v, D, T* base, VI indices, size_t max_lanes_to_store): Stores HWY_MIN(Lanes(d), max_lanes_to_store) lanes v[i] to base[indices[i]]

• D: {u,i,f}{32,64}
void MaskedScatterIndex(Vec<D> v, M m, D, T* base, VI indices): stores v[i] to base[indices[i]] if mask[i] is true. Does not fault for lanes whose mask is false.

• D: {u,i,f}{32,64}
Vec<D> GatherOffset(D, const T* base, VI offsets): returns elements of base selected by byte offsets[i].

• D: {u,i,f}{32,64}
Vec<D> GatherIndex(D, const T* base, VI indices): returns vector of base[indices[i]].

• D: {u,i,f}{32,64}
Vec<D> GatherIndexN(D, const T* base, VI indices, size_t max_lanes_to_load): Loads HWY_MIN(Lanes(d), max_lanes_to_load) lanes of base[indices[i]] to the first (lowest-index) lanes of the result vector and zeroes out the remaining lanes.

• D: {u,i,f}{32,64}
Vec<D> MaskedGatherIndexOr(V no, M mask, D d, const T* base, VI indices): returns vector of base[indices[i]] where mask[i] is true, otherwise no[i]. Does not fault for lanes whose mask is false. This is equivalent to, and potentially more efficient than, IfThenElseZero(mask, GatherIndex(d, base, indices)).

• D: {u,i,f}{32,64}
Vec<D> MaskedGatherIndex(M mask, D d, const T* base, VI indices): equivalent to MaskedGatherIndexOr(Zero(d), mask, d, base, indices). Use this when the desired default value is zero; it may be more efficient on some targets, and on others require generating a zero constant.

Cache control

All functions except Stream are defined in cache_control.h.

• void Stream(Vec<D> a, D d, const T* aligned): copies a[i] into aligned[i] with non-temporal hint if available (useful for write-only data; avoids cache pollution). May be implemented using a CPU-internal buffer. To avoid partial flushes and unpredictable interactions with atomics (for example, see Intel SDM Vol 4, Sec. 8.1.2.2), call this consecutively for an entire cache line (typically 64 bytes, aligned to its size). Each call may write a multiple of HWY_STREAM_MULTIPLE bytes, which can exceed Lanes(d) * sizeof(T). The new contents of aligned may not be visible until FlushStream is called.

• void FlushStream(): ensures values written by previous Stream calls are visible on the current core. This is NOT sufficient for synchronizing across cores; when Stream outputs are to be consumed by other core(s), the producer must publish availability (e.g. via mutex or atomic_flag) after FlushStream.

• void FlushCacheline(const void* p): invalidates and flushes the cache line containing "p", if possible.

• void Prefetch(const T* p): optionally begins loading the cache line containing "p" to reduce latency of subsequent actual loads.

• void Pause(): when called inside a spin-loop, may reduce power consumption.

Type conversion

• Vec<D> BitCast(D, V): returns the bits of V reinterpreted as type Vec<D>.

• Vec<D> ResizeBitCast(D, V): resizes V to a vector of Lanes(D()) * sizeof(TFromD<D>) bytes, and then returns the bits of the resized vector reinterpreted as type Vec<D>.

  If Vec<D> is a larger vector than V, then the contents of any bytes past the first Lanes(DFromV<V>()) * sizeof(TFromV<V>) bytes of the result vector is unspecified.

• Vec<DTo> ZeroExtendResizeBitCast(DTo, DFrom, V): resizes V, which is a vector of type Vec<DFrom>, to a vector of Lanes(D()) * sizeof(TFromD<D>) bytes, and then returns the bits of the resized vector reinterpreted as type Vec<DTo>.

  If Lanes(DTo()) * sizeof(TFromD<DTo>) is greater than Lanes(DFrom()) * sizeof(TFromD<DFrom>), then any bytes past the first Lanes(DFrom()) * sizeof(TFromD<DFrom>) bytes of the result vector are zeroed out.

• V,V8: (u32,u8)
  V8 U8FromU32(V): special-case u32 to u8 conversion when all lanes of V are already clamped to [0, 256).

• D: {f}
Vec<D> ConvertTo(D, V): converts a signed/unsigned integer value to same-sized floating point.

• V: {f}
Vec<D> ConvertTo(D, V): rounds floating point towards zero and converts the value to same-sized signed/unsigned integer. Returns the closest representable value if the input exceeds the destination range.

• V: {f}
Vec<D> ConvertInRangeTo(D, V): rounds floating point towards zero and converts the value to same-sized signed/unsigned integer. Returns an implementation-defined value if the input exceeds the destination range.

• V: f; Ret: Vec<RebindToSigned<DFromV<V>>>
Ret NearestInt(V a): returns the integer nearest to a[i]; results are undefined for NaN.

• V: f; Ret: Vec<RebindToSigned<DFromV<V>>>
Ret CeilInt(V a): equivalent to ConvertTo(RebindToSigned<DFromV<V>>(), Ceil(a)), but CeilInt(a) is more efficient on some targets, including SSE2, SSSE3, and AArch64 NEON.

• V: f; Ret: Vec<RebindToSigned<DFromV<V>>>
Ret FloorInt(V a): equivalent to ConvertTo(RebindToSigned<DFromV<V>>(), Floor(a)), but FloorInt(a) is more efficient on some targets, including SSE2, SSSE3, and AArch64 NEON.

• D: i32, V: f64 Vec<D> DemoteToNearestInt(D d, V v): converts v[i] to TFromD<D>, rounding to nearest (with ties to even).

  DemoteToNearestInt(d, v) is equivalent to DemoteTo(d, Round(v)), but DemoteToNearestInt(d, v) is more efficient on some targets, including x86 and RVV.

Single vector demotion

These functions demote a full vector (or parts thereof) into a vector of half the size. Use Rebind<MakeNarrow<T>, D> or Half<RepartitionToNarrow<D>> to obtain the D that describes the return type.

• V,D: (u64,u32), (u64,u16), (u64,u8), (u32,u16), (u32,u8), (u16,u8)
  Vec<D> TruncateTo(D, V v): returns v[i] truncated to the smaller type indicated by T = TFromD<D>, with the same result as if the more-significant input bits that do not fit in T had been zero. Example: ScalableTag<uint32_t> du32; Rebind<uint8_t> du8; TruncateTo(du8, Set(du32, 0xF08F)) is the same as Set(du8, 0x8F).

• V,D: (i16,i8), (i32,i8), (i64,i8), (i32,i16), (i64,i16), (i64,i32), (u16,i8), (u32,i8), (u64,i8), (u32,i16), (u64,i16), (u64,i32), (i16,u8), (i32,u8), (i64,u8), (i32,u16), (i64,u16), (i64,u32), (u16,u8), (u32,u8), (u64,u8), (u32,u16), (u64,u16), (u64,u32), (f64,f32)
  Vec<D> DemoteTo(D, V v): returns v[i] after packing with signed/unsigned saturation to MakeNarrow<T>.

• V,D: f64,{u,i}32
Vec<D> DemoteTo(D, V v): rounds floating point towards zero and converts the value to 32-bit integers. Returns the closest representable value if the input exceeds the destination range.

• V,D: f64,{u,i}32
Vec<D> DemoteInRangeTo(D, V v): rounds floating point towards zero and converts the value to 32-bit integers. Returns an implementation-defined value if the input exceeds the destination range.

• V,D: {u,i}64,f32
Vec<D> DemoteTo(D, V v): converts 64-bit integer to float.

• V,D: (f32,f16), (f64,f16), (f32,bf16)
  Vec<D> DemoteTo(D, V v): narrows float to half (for bf16, it is unspecified whether this truncates or rounds).

Single vector promotion

These functions promote a half vector to a full vector. To obtain halves, use LowerHalf or UpperHalf, or load them using a half-sized D.

• Unsigned V to wider signed/unsigned D; signed to wider signed, f16 to f32, f16 to f64, bf16 to f32, f32 to f64
Vec<D> PromoteTo(D, V part): returns part[i] zero- or sign-extended to the integer type MakeWide<T>, or widened to the floating-point type MakeFloat<MakeWide<T>>.

• {u,i}32 to f64
Vec<D> PromoteTo(D, V part): returns part[i] widened to double.

• f32 to i64 or u64
Vec<D> PromoteTo(D, V part): rounds part[i] towards zero and converts the rounded value to a 64-bit signed or unsigned integer. Returns the representable value if the input exceeds the destination range.

• f32 to i64 or u64
Vec<D> PromoteInRangeTo(D, V part): rounds part[i] towards zero and converts the rounded value to a 64-bit signed or unsigned integer. Returns an implementation-defined value if the input exceeds the destination range.

The following may be more convenient or efficient than also calling LowerHalf / UpperHalf:

• Unsigned V to wider signed/unsigned D; signed to wider signed, f16 to f32, bf16 to f32, f32 to f64
Vec<D> PromoteLowerTo(D, V v): returns v[i] widened to MakeWide<T>, for i in [0, Lanes(D())). Note that V has twice as many lanes as D and the return value.

• {u,i}32 to f64
Vec<D> PromoteLowerTo(D, V v): returns v[i] widened to double, for i in [0, Lanes(D())). Note that V has twice as many lanes as D and the return value.

• f32 to i64 or u64
Vec<D> PromoteLowerTo(D, V v): rounds v[i] towards zero and converts the rounded value to a 64-bit signed or unsigned integer, for i in [0, Lanes(D())). Note that V has twice as many lanes as D and the return value.

• f32 to i64 or u64
Vec<D> PromoteInRangeLowerTo(D, V v): rounds v[i] towards zero and converts the rounded value to a 64-bit signed or unsigned integer, for i in [0, Lanes(D())). Note that V has twice as many lanes as D and the return value. Returns an implementation-defined value if the input exceeds the destination range.

• Unsigned V to wider signed/unsigned D; signed to wider signed, f16 to f32, bf16 to f32, f32 to f64
Vec<D> PromoteUpperTo(D, V v): returns v[i] widened to MakeWide<T>, for i in [Lanes(D()), 2 * Lanes(D())). Note that V has twice as many lanes as D and the return value. Only available if HWY_TARGET != HWY_SCALAR.

• {u,i}32 to f64
Vec<D> PromoteUpperTo(D, V v): returns v[i] widened to double, for i in [Lanes(D()), 2 * Lanes(D())). Note that V has twice as many lanes as D and the return value. Only available if HWY_TARGET != HWY_SCALAR.

• f32 to i64 or u64
Vec<D> PromoteUpperTo(D, V v): rounds v[i] towards zero and converts the rounded value to a 64-bit signed or unsigned integer, for i in [Lanes(D()), 2 * Lanes(D())). Note that V has twice as many lanes as D and the return value. Only available if HWY_TARGET != HWY_SCALAR.

• f32 to i64 or u64
Vec<D> PromoteInRangeUpperTo(D, V v): rounds v[i] towards zero and converts the rounded value to a 64-bit signed or unsigned integer, for i in [Lanes(D()), 2 * Lanes(D())). Note that V has twice as many lanes as D and the return value. Returns an implementation-defined value if the input exceeds the destination range. Only available if HWY_TARGET != HWY_SCALAR.

The following may be more convenient or efficient than also calling ConcatEven or ConcatOdd followed by PromoteLowerTo:

• V:{u,i}{8,16,32},f{16,32},bf16, D:RepartitionToWide<DFromV<V>>
Vec<D> PromoteEvenTo(D, V v): promotes the even lanes of v to TFromD<D>. Note that V has twice as many lanes as D and the return value. PromoteEvenTo(d, v) is equivalent to, but potentially more efficient than PromoteLowerTo(d, ConcatEven(Repartition<TFromV<V>, D>(), v, v)).

• V:{u,i}{8,16,32},f{16,32},bf16, D:RepartitionToWide<DFromV<V>>
Vec<D> PromoteOddTo(D, V v): promotes the odd lanes of v to TFromD<D>. Note that V has twice as many lanes as D and the return value. PromoteOddTo(d, v) is equivalent to, but potentially more efficient than PromoteLowerTo(d, ConcatOdd(Repartition<TFromV<V>, D>(), v, v)). Only available if HWY_TARGET != HWY_SCALAR.

• V:f32, D:{u,i}64
Vec<D> PromoteInRangeEvenTo(D, V v): promotes the even lanes of v to TFromD<D>. Note that V has twice as many lanes as D and the return value. PromoteInRangeEvenTo(d, v) is equivalent to, but potentially more efficient than PromoteInRangeLowerTo(d, ConcatEven( Repartition<TFromV<V>, D>(), v, v)).

• V:f32, D:{u,i}64
Vec<D> PromoteInRangeOddTo(D, V v): promotes the odd lanes of v to TFromD<D>. Note that V has twice as many lanes as D and the return value. PromoteInRangeOddTo(d, v) is equivalent to, but potentially more efficient than PromoteInRangeLowerTo(d, ConcatOdd( Repartition<TFromV<V>, D>(), v, v)).

Two-vector demotion

• V,D: (i16,i8), (i32,i16), (i64,i32), (u16,i8), (u32,i16), (u64,i32), (i16,u8), (i32,u16), (i64,u32), (u16,u8), (u32,u16), (u64,u32), (f32,bf16)
  Vec<D> ReorderDemote2To(D, V a, V b): as above, but converts two inputs, D and the output have twice as many lanes as V, and the output order is some permutation of the inputs. Only available if HWY_TARGET != HWY_SCALAR.

• V,D: (i16,i8), (i32,i16), (i64,i32), (u16,i8), (u32,i16), (u64,i32), (i16,u8), (i32,u16), (i64,u32), (u16,u8), (u32,u16), (u64,u32), (f32,bf16)
  Vec<D> OrderedDemote2To(D d, V a, V b): as above, but converts two inputs, D and the output have twice as many lanes as V, and the output order is the result of demoting the elements of a in the lower half of the result followed by the result of demoting the elements of b in the upper half of the result. OrderedDemote2To(d, a, b) is equivalent to Combine(d, DemoteTo(Half<D>(), b), DemoteTo(Half<D>(), a)), but OrderedDemote2To(d, a, b) is typically more efficient than Combine(d, DemoteTo(Half<D>(), b), DemoteTo(Half<D>(), a)). Only available if HWY_TARGET != HWY_SCALAR.

• V,D: (u16,u8), (u32,u16), (u64,u32),
  Vec<D> OrderedTruncate2To(D d, V a, V b): as above, but converts two inputs, D and the output have twice as many lanes as V, and the output order is the result of truncating the elements of a in the lower half of the result followed by the result of truncating the elements of b in the upper half of the result. OrderedTruncate2To(d, a, b) is equivalent to Combine(d, TruncateTo(Half<D>(), b), TruncateTo(Half<D>(), a)), but OrderedTruncate2To(d, a, b) is typically more efficient than Combine(d, TruncateTo(Half<D>(), b), TruncateTo(Half<D>(), a)). Only available if HWY_TARGET != HWY_SCALAR.

Combine

• V2 LowerHalf([D, ] V): returns the lower half of the vector V. The optional D (provided for consistency with UpperHalf) is Half<DFromV<V>>.

All other ops in this section are only available if HWY_TARGET != HWY_SCALAR:

• V2 UpperHalf(D, V): returns upper half of the vector V, where D is Half<DFromV<V>>.

• V ZeroExtendVector(D, V2): returns vector whose UpperHalf is zero and whose LowerHalf is the argument; D is Twice<DFromV<V2>>.

• V Combine(D, V2, V2): returns vector whose UpperHalf is the first argument and whose LowerHalf is the second argument; D is Twice<DFromV<V2>>.

Note: the following operations cross block boundaries, which is typically more expensive on AVX2/AVX-512 than per-block operations.

• V ConcatLowerLower(D, V hi, V lo): returns the concatenation of the lower halves of hi and lo without splitting into blocks. D is DFromV<V>.

• V ConcatUpperUpper(D, V hi, V lo): returns the concatenation of the upper halves of hi and lo without splitting into blocks. D is DFromV<V>.

• V ConcatLowerUpper(D, V hi, V lo): returns the inner half of the concatenation of hi and lo without splitting into blocks. Useful for swapping the two blocks in 256-bit vectors. D is DFromV<V>.

• V ConcatUpperLower(D, V hi, V lo): returns the outer quarters of the concatenation of hi and lo without splitting into blocks. Unlike the other variants, this does not incur a block-crossing penalty on AVX2/3. D is DFromV<V>.

• V ConcatOdd(D, V hi, V lo): returns the concatenation of the odd lanes of hi and the odd lanes of lo.

• V ConcatEven(D, V hi, V lo): returns the concatenation of the even lanes of hi and the even lanes of lo.

• V InterleaveWholeLower([D, ] V a, V b): returns alternating lanes from the lower halves of a and b (a[0] in the least-significant lane). The optional D (provided for consistency with InterleaveWholeUpper) is DFromV<V>.

• V InterleaveWholeUpper(D, V a, V b): returns alternating lanes from the upper halves of a and b (a[N/2] in the least-significant lane). D is DFromV<V>.

Blockwise

Note: if vectors are larger than 128 bits, the following operations split their operands into independently processed 128-bit blocks.

• V Broadcast<int i>(V): returns individual blocks, each with lanes set to input_block[i], i = [0, 16/sizeof(T)).

All other ops in this section are only available if HWY_TARGET != HWY_SCALAR:

• V: {u,i}
VI TableLookupBytes(V bytes, VI indices): returns bytes[indices[i]]. Uses byte lanes regardless of the actual vector types. Results are implementation-defined if indices[i] < 0 or indices[i] >= HWY_MIN(Lanes(DFromV<V>()), 16). VI are integers, possibly of a different type than those in V. The number of lanes in V and VI may differ, e.g. a full-length table vector loaded via LoadDup128, plus partial vector VI of 4-bit indices.

• V: {u,i}
VI TableLookupBytesOr0(V bytes, VI indices): returns bytes[indices[i]], or 0 if indices[i] & 0x80. Uses byte lanes regardless of the actual vector types. Results are implementation-defined for indices[i] < 0 or in [HWY_MIN(Lanes(DFromV<V>()), 16), 0x80). The zeroing behavior has zero cost on x86 and Arm. For vectors of >= 256 bytes (can happen on SVE and RVV), this will set all lanes after the first 128 to 0. VI are integers, possibly of a different type than those in V. The number of lanes in V and VI may differ.

• V: {u,i}64, VI: {u,i}8
V BitShuffle(V vals, VI indices): returns a vector with (vals[i] >> indices[i*8+j]) & 1 in bit j of r[i] for each j between 0 and 7.

  BitShuffle(vals, indices) zeroes out the upper 56 bits of r[i].

  If indices[i*8+j] is less than 0 or greater than 63, bit j of r[i] is implementation-defined.

  VI must be either Vec<Repartition<int8_t, DFromV<V>>> or Vec<Repartition<uint8_t, DFromV<V>>>.

  BitShuffle(v, indices) is equivalent to the following loop (where N is equal to Lanes(DFromV<V>())):

  for(size_t i = 0; i < N; i++) {
    uint64_t shuf_result = 0;
    for(int j = 0; j < 7; j++) {
      shuf_result |= ((v[i] >> indices[i*8+j]) & 1) << j;
    }
    r[i] = shuf_result;
  }
  

Interleave

Ops in this section are only available if HWY_TARGET != HWY_SCALAR:

• V InterleaveLower([D, ] V a, V b): returns blocks with alternating lanes from the lower halves of a and b (a[0] in the least-significant lane). The optional D (provided for consistency with InterleaveUpper) is DFromV<V>.

• V InterleaveUpper(D, V a, V b): returns blocks with alternating lanes from the upper halves of a and b (a[N/2] in the least-significant lane). D is DFromV<V>.

• V InterleaveEven([D, ] V a, V b): returns alternating lanes from the even lanes of a and b (a[0] in the least-significant lane, followed by b[0], followed by a[2], followed by b[2], and so on). The optional D (provided for consistency with InterleaveOdd) is DFromV<V>. Note that no lanes move across block boundaries.

  InterleaveEven(a, b) and InterleaveEven(d, a, b) are both equivalent to OddEven(DupEven(b), a), but InterleaveEven(a, b) is usually more efficient than OddEven(DupEven(b), a).

• V InterleaveOdd(D, V a, V b): returns alternating lanes from the odd lanes of a and b (a[1] in the least-significant lane, followed by b[1], followed by a[3], followed by b[3], and so on). D is DFromV<V>. Note that no lanes move across block boundaries.

  InterleaveOdd(d, a, b) is equivalent to OddEven(b, DupOdd(a)), but InterleaveOdd(d, a, b) is usually more efficient than OddEven(b, DupOdd(a)).

Zip

• Ret: MakeWide<T>; V: {u,i}{8,16,32}
Ret ZipLower([DW, ] V a, V b): returns the same bits as InterleaveLower, but repartitioned into double-width lanes (required in order to use this operation with scalars). The optional DW (provided for consistency with ZipUpper) is RepartitionToWide<DFromV<V>>.

• Ret: MakeWide<T>; V: {u,i}{8,16,32}
Ret ZipUpper(DW, V a, V b): returns the same bits as InterleaveUpper, but repartitioned into double-width lanes (required in order to use this operation with scalars). DW is RepartitionToWide<DFromV<V>>. Only available if HWY_TARGET != HWY_SCALAR.

Shift within blocks

Ops in this section are only available if HWY_TARGET != HWY_SCALAR:

• V: {u,i}
V ShiftLeftBytes<int>([D, ] V): returns the result of shifting independent blocks left by int bytes [1, 15]. The optional D (provided for consistency with ShiftRightBytes) is DFromV<V>.

• V ShiftLeftLanes<int>([D, ] V): returns the result of shifting independent blocks left by int lanes. The optional D (provided for consistency with ShiftRightLanes) is DFromV<V>.

• V: {u,i}
V ShiftRightBytes<int>(D, V): returns the result of shifting independent blocks right by int bytes [1, 15], shifting in zeros even for partial vectors. D is DFromV<V>.

• V ShiftRightLanes<int>(D, V): returns the result of shifting independent blocks right by int lanes, shifting in zeros even for partial vectors. D is DFromV<V>.

• V: {u,i}
V CombineShiftRightBytes<int>(D, V hi, V lo): returns a vector of blocks each the result of shifting two concatenated blocks hi[i] || lo[i] right by int bytes [1, 16). D is DFromV<V>.

• V CombineShiftRightLanes<int>(D, V hi, V lo): returns a vector of blocks each the result of shifting two concatenated blocks hi[i] || lo[i] right by int lanes [1, 16/sizeof(T)). D is DFromV<V>.

Other fixed-pattern permutations within blocks

• V OddEven(V a, V b): returns a vector whose odd lanes are taken from a and the even lanes from b.

• V DupEven(V v): returns r, the result of copying even lanes to the next higher-indexed lane. For each even lane index i, r[i] == v[i] and r[i + 1] == v[i].

• V DupOdd(V v): returns r, the result of copying odd lanes to the previous lower-indexed lane. For each odd lane index i, r[i] == v[i] and r[i - 1] == v[i]. Only available if HWY_TARGET != HWY_SCALAR.

Ops in this section are only available if HWY_TARGET != HWY_SCALAR:

• V: {u,i,f}{32}
V Shuffle1032(V): returns blocks with 64-bit halves swapped.

• V: {u,i,f}{32}
V Shuffle0321(V): returns blocks rotated right (toward the lower end) by 32 bits.

• V: {u,i,f}{32}
V Shuffle2103(V): returns blocks rotated left (toward the upper end) by 32 bits.

The following are equivalent to Reverse2 or Reverse4, which should be used instead because they are more general:

• V: {u,i,f}{32}
V Shuffle2301(V): returns blocks with 32-bit halves swapped inside 64-bit halves.

• V: {u,i,f}{64}
V Shuffle01(V): returns blocks with 64-bit halves swapped.

• V: {u,i,f}{32}
V Shuffle0123(V): returns blocks with lanes in reverse order.

Swizzle

Reverse

• V Reverse(D, V a) returns a vector with lanes in reversed order (out[i] == a[Lanes(D()) - 1 - i]).

• V ReverseBlocks(V v): returns a vector with blocks in reversed order.

The following ReverseN must not be called if Lanes(D()) < N:

• V Reverse2(D, V a) returns a vector with each group of 2 contiguous lanes in reversed order (out[i] == a[i ^ 1]).

• V Reverse4(D, V a) returns a vector with each group of 4 contiguous lanes in reversed order (out[i] == a[i ^ 3]).

• V Reverse8(D, V a) returns a vector with each group of 8 contiguous lanes in reversed order (out[i] == a[i ^ 7]).

• V: {u,i}{16,32,64}
V ReverseLaneBytes(V a) returns a vector where the bytes of each lane are swapped.

• V: {u,i}
V ReverseBits(V a) returns a vector where the bits of each lane are reversed.

User-specified permutation across blocks

• V TableLookupLanes(V a, unspecified) returns a vector of a[indices[i]], where unspecified is the return value of SetTableIndices(D, &indices[0]) or IndicesFromVec. The indices are not limited to blocks, hence this is slower than TableLookupBytes* on AVX2/AVX-512. Results are implementation-defined unless 0 <= indices[i] < Lanes(D()) and indices[i] <= LimitsMax<TFromD<RebindToUnsigned<D>>>(). Note that the latter condition is only a (potential) limitation for 8-bit lanes on the RVV target; otherwise, Lanes(D()) <= LimitsMax<..>(). indices are always integers, even if V is a floating-point type.

• V TwoTablesLookupLanes(D d, V a, V b, unspecified) returns a vector of indices[i] < N ? a[indices[i]] : b[indices[i] - N], where unspecified is the return value of SetTableIndices(d, &indices[0]) or IndicesFromVec and N is equal to Lanes(d). The indices are not limited to blocks. Results are implementation-defined unless 0 <= indices[i] < 2 * Lanes(d) and indices[i] <= LimitsMax<TFromD<RebindToUnsigned<D>>>(). Note that the latter condition is only a (potential) limitation for 8-bit lanes on the RVV target; otherwise, Lanes(D()) <= LimitsMax<..>(). indices are always integers, even if V is a floating-point type.

• V TwoTablesLookupLanes(V a, V b, unspecified) returns TwoTablesLookupLanes(DFromV<V>(), a, b, indices), see above. Note that the results of TwoTablesLookupLanes(d, a, b, indices) may differ from TwoTablesLookupLanes(a, b, indices) on RVV/SVE if Lanes(d) < Lanes(DFromV<V>()).

• unspecified IndicesFromVec(D d, V idx) prepares for TableLookupLanes with integer indices in idx, which must be the same bit width as TFromD<D> and in the range [0, 2 * Lanes(d)), but need not be unique.

• unspecified SetTableIndices(D d, TI* idx) prepares for TableLookupLanes by loading Lanes(d) integer indices from idx, which must be in the range [0, 2 * Lanes(d)) but need not be unique. The index type TI must be an integer of the same size as TFromD<D>.

• V Per4LaneBlockShuffle<size_t kIdx3, size_t kIdx2, size_t kIdx1, size_t kIdx0>(V v) does a per 4-lane block shuffle of v if Lanes(DFromV<V>()) is greater than or equal to 4 or a shuffle of the full vector if Lanes(DFromV<V>()) is less than 4.

  kIdx0, kIdx1, kIdx2, and kIdx3 must all be between 0 and 3.

  Per4LaneBlockShuffle is equivalent to doing a TableLookupLanes with the following indices (but Per4LaneBlockShuffle is more efficient than TableLookupLanes on some platforms): {kIdx0, kIdx1, kIdx2, kIdx3, kIdx0+4, kIdx1+4, kIdx2+4, kIdx3+4, ...}

  If Lanes(DFromV<V>()) is less than 4 and kIdx0 >= Lanes(DFromV<V>()) is true, Per4LaneBlockShuffle returns an unspecified value in the first lane of the result. Otherwise, Per4LaneBlockShuffle returns v[kIdx0] in the first lane of the result.

  If Lanes(DFromV<V>()) is equal to 2 and kIdx1 >= 2 is true, Per4LaneBlockShuffle returns an unspecified value in the second lane of the result. Otherwise, Per4LaneBlockShuffle returns v[kIdx1] in the first lane of the result.

Slide across blocks

• V SlideUpLanes(D d, V v, size_t N): slides up v by N lanes

  If N < Lanes(d) is true, returns a vector with the first (lowest-index) Lanes(d) - N lanes of v shifted up to the upper (highest-index) Lanes(d) - N lanes of the result vector and the first (lowest-index) N lanes of the result vector zeroed out.

  In other words, result[0..N-1] would be zero, result[N] = v[0], result[N+1] = v[1], and so on until result[Lanes(d)-1] = v[Lanes(d)-1-N].

  The result of SlideUpLanes is implementation-defined if N >= Lanes(d).

• V SlideDownLanes(D d, V v, size_t N): slides down v by N lanes

  If N < Lanes(d) is true, returns a vector with the last (highest-index) Lanes(d) - N of v shifted down to the first (lowest-index) Lanes(d) - N lanes of the result vector and the last (highest-index) N lanes of the result vector zeroed out.

  In other words, result[0] = v[N], result[1] = v[N + 1], and so on until result[Lanes(d)-1-N] = v[Lanes(d)-1], and then result[Lanes(d)-N..N-1] would be zero.

  The results of SlideDownLanes is implementation-defined if N >= Lanes(d).

• V Slide1Up(D d, V v): slides up v by 1 lane

  If Lanes(d) == 1 is true, returns Zero(d).

  If Lanes(d) > 1 is true, Slide1Up(d, v) is equivalent to SlideUpLanes(d, v, 1), but Slide1Up(d, v) is more efficient than SlideUpLanes(d, v, 1) on some platforms.

• V Slide1Down(D d, V v): slides down v by 1 lane

  If Lanes(d) == 1 is true, returns Zero(d).

  If Lanes(d) > 1 is true, Slide1Down(d, v) is equivalent to SlideDownLanes(d, v, 1), but Slide1Down(d, v) is more efficient than SlideDownLanes(d, v, 1) on some platforms.

• V SlideUpBlocks<int kBlocks>(D d, V v) slides up v by kBlocks blocks.

  kBlocks must be between 0 and d.MaxBlocks() - 1.

  Equivalent to SlideUpLanes(d, v, kBlocks * (16 / sizeof(TFromD<D>))), but SlideUpBlocks<kBlocks>(d, v) is more efficient than SlideUpLanes(d, v, kBlocks * (16 / sizeof(TFromD<D>))) on some platforms.

  The results of SlideUpBlocks<kBlocks>(d, v) is implementation-defined if kBlocks >= Blocks(d) is true.

• V SlideDownBlocks<int kBlocks>(D d, V v) slides down v by kBlocks blocks.

  kBlocks must be between 0 and d.MaxBlocks() - 1.

  Equivalent to SlideDownLanes(d, v, kBlocks * (16 / sizeof(TFromD<D>))), but SlideDownBlocks<kBlocks>(d, v) is more efficient than SlideDownLanes(d, v, kBlocks * (16 / sizeof(TFromD<D>))) on some platforms.

  The results of SlideDownBlocks<kBlocks>(d, v) is implementation-defined if kBlocks >= Blocks(d) is true.

Other fixed-pattern across blocks

• V BroadcastLane<int kLane>(V v): returns a vector with all of the lanes set to v[kLane].

  kLane must be in [0, MaxLanes(DFromV<V>())).

• V BroadcastBlock<int kBlock>(V v): broadcasts the 16-byte block of vector v at index kBlock to all of the blocks of the result vector if Lanes(DFromV<V>()) * sizeof(TFromV<V>) > 16 is true. Otherwise, if Lanes(DFromV<V>()) * sizeof(TFromV<V>) <= 16 is true, returns v.

  kBlock must be in [0, DFromV<V>().MaxBlocks()).

• V OddEvenBlocks(V a, V b): returns a vector whose odd blocks are taken from a and the even blocks from b. Returns b if the vector has no more than one block (i.e. is 128 bits or scalar).

• V SwapAdjacentBlocks(V v): returns a vector where blocks of index 2*i and 2*i+1 are swapped. Results are undefined for vectors with less than two blocks; callers must first check that via Lanes. Only available if HWY_TARGET != HWY_SCALAR.

Reductions

Note: Horizontal operations (across lanes of the same vector) such as reductions are slower than normal SIMD operations and are typically used outside critical loops.

The following broadcast the result to all lanes. To obtain a scalar, you can call GetLane on the result, or instead use Reduce* below.

• V SumOfLanes(D, V v): returns the sum of all lanes in each lane.
• V MinOfLanes(D, V v): returns the minimum-valued lane in each lane.
• V MaxOfLanes(D, V v): returns the maximum-valued lane in each lane.

The following are equivalent to GetLane(SumOfLanes(d, v)) etc. but potentially more efficient on some targets.

• T ReduceSum(D, V v): returns the sum of all lanes.
• T ReduceMin(D, V v): returns the minimum of all lanes.
• T ReduceMax(D, V v): returns the maximum of all lanes.

Crypto

Ops in this section are only available if HWY_TARGET != HWY_SCALAR:

• V: u8
V AESRound(V state, V round_key): one round of AES encryption: MixColumns(SubBytes(ShiftRows(state))) ^ round_key. This matches x86 AES-NI. The latency is independent of the input values.

• V: u8
V AESLastRound(V state, V round_key): the last round of AES encryption: SubBytes(ShiftRows(state)) ^ round_key. This matches x86 AES-NI. The latency is independent of the input values.

• V: u8
V AESRoundInv(V state, V round_key): one round of AES decryption using the AES Equivalent Inverse Cipher: InvMixColumns(InvShiftRows(InvSubBytes(state))) ^ round_key. This matches x86 AES-NI. The latency is independent of the input values.

• V: u8
V AESLastRoundInv(V state, V round_key): the last round of AES decryption: InvShiftRows(InvSubBytes(state)) ^ round_key. This matches x86 AES-NI. The latency is independent of the input values.

• V: u8
V AESInvMixColumns(V state): the InvMixColumns operation of the AES decryption algorithm. AESInvMixColumns is used in the key expansion step of the AES Equivalent Inverse Cipher algorithm. The latency is independent of the input values.

• V: u8
V AESKeyGenAssist<uint8_t kRcon>(V v): AES key generation assist operation

  The AESKeyGenAssist operation is equivalent to doing the following, which matches the behavior of the x86 AES-NI AESKEYGENASSIST instruction:

  • Applying the AES SubBytes operation to each byte of v.
  • Doing a TableLookupBytes operation on each 128-bit block of the result of the SubBytes(v) operation with the following indices (which is broadcast to each 128-bit block in the case of vectors with 32 or more lanes): {4, 5, 6, 7, 5, 6, 7, 4, 12, 13, 14, 15, 13, 14, 15, 12}
  • Doing a bitwise XOR operation with the following vector (where kRcon is the rounding constant that is the first template argument of the AESKeyGenAssist function and where the below vector is broadcasted to each 128-bit block in the case of vectors with 32 or more lanes): {0, 0, 0, 0, kRcon, 0, 0, 0, 0, 0, 0, 0, kRcon, 0, 0, 0}

• V: u64
V CLMulLower(V a, V b): carryless multiplication of the lower 64 bits of each 128-bit block into a 128-bit product. The latency is independent of the input values (assuming that is true of normal integer multiplication) so this can safely be used in crypto. Applications that wish to multiply upper with lower halves can Shuffle01 one of the operands; on x86 that is expected to be latency-neutral.

• V: u64
V CLMulUpper(V a, V b): as CLMulLower, but multiplies the upper 64 bits of each 128-bit block.

Preprocessor macros

• HWY_ALIGN: Prefix for stack-allocated (i.e. automatic storage duration) arrays to ensure they have suitable alignment for Load()/Store(). This is specific to HWY_TARGET and should only be used inside HWY_NAMESPACE.

  Arrays should also only be used for partial (<= 128-bit) vectors, or LoadDup128, because full vectors may be too large for the stack and should be heap-allocated instead (see aligned_allocator.h).

  Example: HWY_ALIGN float lanes[4];

• HWY_ALIGN_MAX: as HWY_ALIGN, but independent of HWY_TARGET and may be used outside HWY_NAMESPACE.

Advanced macros

Beware that these macros describe the current target being compiled. Imagine a test (e.g. sort_test) with SIMD code that also uses dynamic dispatch. There we must test the macros of the target we will call, e.g. via hwy::HaveFloat64() instead of HWY_HAVE_FLOAT64, which describes the current target.

• HWY_IDE is 0 except when parsed by IDEs; adding it to conditions such as #if HWY_TARGET != HWY_SCALAR || HWY_IDE avoids code appearing greyed out.

The following indicate full support for certain lane types and expand to 1 or 0.

• HWY_HAVE_INTEGER64: support for 64-bit signed/unsigned integer lanes.
• HWY_HAVE_FLOAT16: support for 16-bit floating-point lanes.
• HWY_HAVE_FLOAT64: support for double-precision floating-point lanes.

The above were previously known as HWY_CAP_INTEGER64, HWY_CAP_FLOAT16, and HWY_CAP_FLOAT64, respectively. Those HWY_CAP_* names are DEPRECATED.

Even if HWY_HAVE_FLOAT16 is 0, the following ops generally support float16_t and bfloat16_t:

• Lanes, MaxLanes
• Zero, Set, Undefined
• BitCast
• Load, LoadU, LoadN, LoadNOr, LoadInterleaved[234], MaskedLoad, MaskedLoadOr
• Store, StoreU, StoreN, StoreInterleaved[234], BlendedStore
• PromoteTo, DemoteTo
• PromoteUpperTo, PromoteLowerTo
• PromoteEvenTo, PromoteOddTo
• Combine, InsertLane, ZeroExtendVector
• RebindMask, FirstN
• IfThenElse, IfThenElseZero, IfThenZeroElse

Exception: UpperHalf, PromoteUpperTo, PromoteOddTo and Combine are not supported for the HWY_SCALAR target.

Neg also supports float16_t and *Demote2To also supports bfloat16_t.

• HWY_HAVE_SCALABLE indicates vector sizes are unknown at compile time, and determined by the CPU.

• HWY_HAVE_TUPLE indicates Vec{2-4}, Create{2-4} and Get{2-4} are usable. This is already true #if !HWY_HAVE_SCALABLE, and for SVE targets, and the RVV target when using Clang 16. We anticipate it will also become, and then remain, true starting with GCC 14.

• HWY_MEM_OPS_MIGHT_FAULT is 1 iff MaskedLoad may trigger a (page) fault when attempting to load lanes from unmapped memory, even if the corresponding mask element is false. This is the case on ASAN/MSAN builds, AMD x86 prior to AVX-512, and Arm NEON. If so, users can prevent faults by ensuring memory addresses are aligned to the vector size or at least padded (allocation size increased by at least Lanes(d)).

• HWY_NATIVE_FMA expands to 1 if the MulAdd etc. ops use native fused multiply-add for floating-point inputs. Otherwise, MulAdd(f, m, a) is implemented as Add(Mul(f, m), a). Checking this can be useful for increasing the tolerance of expected results (around 1E-5 or 1E-6).

• HWY_IS_LITTLE_ENDIAN expands to 1 on little-endian targets and to 0 on big-endian targets.

• HWY_IS_BIG_ENDIAN expands to 1 on big-endian targets and to 0 on little-endian targets.

The following were used to signal the maximum number of lanes for certain operations, but this is no longer necessary (nor possible on SVE/RVV), so they are DEPRECATED:

• HWY_CAP_GE256: the current target supports vectors of >= 256 bits.
• HWY_CAP_GE512: the current target supports vectors of >= 512 bits.

Detecting supported targets

SupportedTargets() returns a non-cached (re-initialized on each call) bitfield of the targets supported on the current CPU, detected using CPUID on x86 or equivalent. This may include targets that are not in HWY_TARGETS, and vice versa. If there is no overlap the binary will likely crash. This can only happen if:

• the specified baseline is not supported by the current CPU, which contradicts the definition of baseline, so the configuration is invalid; or
• the baseline does not include the enabled/attainable target(s), which are also not supported by the current CPU, and baseline targets (in particular HWY_SCALAR) were explicitly disabled.

Advanced configuration macros

The following macros govern which targets to generate. Unless specified otherwise, they may be defined per translation unit, e.g. to disable >128 bit vectors in modules that do not benefit from them (if bandwidth-limited or only called occasionally). This is safe because HWY_TARGETS always includes at least one baseline target which HWY_EXPORT can use.

• HWY_DISABLE_CACHE_CONTROL makes the cache-control functions no-ops.
• HWY_DISABLE_BMI2_FMA prevents emitting BMI/BMI2/FMA instructions. This allows using AVX2 in VMs that do not support the other instructions, but only if defined for all translation units.

The following *_TARGETS are zero or more HWY_Target bits and can be defined as an expression, e.g. -DHWY_DISABLED_TARGETS=(HWY_SSE4|HWY_AVX3).

• HWY_BROKEN_TARGETS defaults to a blocklist of known compiler bugs. Defining to 0 disables the blocklist.

• HWY_DISABLED_TARGETS defaults to zero. This allows explicitly disabling targets without interfering with the blocklist.

• HWY_BASELINE_TARGETS defaults to the set whose predefined macros are defined (i.e. those for which the corresponding flag, e.g. -mavx2, was passed to the compiler). If specified, this should be the same for all translation units, otherwise the safety check in SupportedTargets (that all enabled baseline targets are supported) may be inaccurate.

Zero or one of the following macros may be defined to replace the default policy for selecting HWY_TARGETS:

• HWY_COMPILE_ONLY_EMU128 selects only HWY_EMU128, which avoids intrinsics but implements all ops using standard C++.
• HWY_COMPILE_ONLY_SCALAR selects only HWY_SCALAR, which implements single-lane-only ops using standard C++.
• HWY_COMPILE_ONLY_STATIC selects only HWY_STATIC_TARGET, which effectively disables dynamic dispatch.
• HWY_COMPILE_ALL_ATTAINABLE selects all attainable targets (i.e. enabled and permitted by the compiler, independently of autovectorization), which maximizes coverage in tests. Defining HWY_IS_TEST, which CMake does for the Highway tests, has the same effect.
• HWY_SKIP_NON_BEST_BASELINE compiles all targets at least as good as the baseline. This is also the default if nothing is defined. By skipping targets older than the baseline, this reduces binary size and may resolve compile errors caused by conflicts between dynamic dispatch and -m flags.

At most one HWY_COMPILE_ONLY_* may be defined. HWY_COMPILE_ALL_ATTAINABLE may also be defined even if one of HWY_COMPILE_ONLY_* is, but will then be ignored because the flags are tested in the order listed. As an exception, HWY_SKIP_NON_BEST_BASELINE overrides the effect of HWY_COMPILE_ALL_ATTAINABLE and HWY_IS_TEST.

Compiler support

Clang and GCC require opting into SIMD intrinsics, e.g. via -mavx2 flags. However, the flag enables AVX2 instructions in the entire translation unit, which may violate the one-definition rule (that all versions of a function such as std::abs are equivalent, thus the linker may choose any). This can cause crashes if non-SIMD functions are defined outside of a target-specific namespace, and the linker happens to choose the AVX2 version, which means it may be called without verifying AVX2 is indeed supported.

To prevent this problem, we use target-specific attributes introduced via #pragma. Function using SIMD must reside between HWY_BEFORE_NAMESPACE and HWY_AFTER_NAMESPACE. Conversely, non-SIMD functions and in particular, #include of normal or standard library headers must NOT reside between HWY_BEFORE_NAMESPACE and HWY_AFTER_NAMESPACE. Alternatively, individual functions may be prefixed with HWY_ATTR, which is more verbose, but ensures that #include-d functions are not covered by target-specific attributes.

WARNING: avoid non-local static objects (namespace scope 'global variables') between HWY_BEFORE_NAMESPACE and HWY_AFTER_NAMESPACE. We have observed crashes on PPC because the compiler seems to have generated an initializer using PPC10 code to splat a constant to all vector lanes, see #1739. To prevent this, you can replace static constants with a function returning the desired value.

If you know the SVE vector width and are using static dispatch, you can specify -march=armv9-a+sve2-aes -msve-vector-bits=128 and Highway will then use HWY_SVE2_128 as the baseline. Similarly, -march=armv8.2-a+sve -msve-vector-bits=256 enables the HWY_SVE_256 specialization for Neoverse V1. Note that these flags are unnecessary when using dynamic dispatch. Highway will automatically detect and dispatch to the best available target, including HWY_SVE2_128 or HWY_SVE_256.

Immediates (compile-time constants) are specified as template arguments to avoid constant-propagation issues with Clang on Arm.

Type traits

• IsFloat<T>() returns true if the T is a floating-point type.

• IsSigned<T>() returns true if the T is a signed or floating-point type.

• LimitsMin/Max<T>() return the smallest/largest value representable in integer T.

• SizeTag<N> is an empty struct, used to select overloaded functions appropriate for N bytes.

• MakeUnsigned<T> is an alias for an unsigned type of the same size as T.

• MakeSigned<T> is an alias for a signed type of the same size as T.

• MakeFloat<T> is an alias for a floating-point type of the same size as T.

• MakeWide<T> is an alias for a type with twice the size of T and the same category (unsigned/signed/float).

• MakeNarrow<T> is an alias for a type with half the size of T and the same category (unsigned/signed/float).

Memory allocation

AllocateAligned<T>(items) returns a unique pointer to newly allocated memory for items elements of POD type T. The start address is aligned as required by Load/Store. Furthermore, successive allocations are not congruent modulo a platform-specific alignment. This helps prevent false dependencies or cache conflicts. The memory allocation is analogous to using malloc() and free() with a std::unique_ptr since the returned items are not initialized or default constructed and it is released using FreeAlignedBytes() without calling ~T().

MakeUniqueAligned<T>(Args&&... args) creates a single object in newly allocated aligned memory as above but constructed passing the args argument to T's constructor and returning a unique pointer to it. This is analogous to using std::make_unique with new but for aligned memory since the object is constructed and later destructed when the unique pointer is deleted. Typically this type T is a struct containing multiple members with HWY_ALIGN or HWY_ALIGN_MAX, or arrays whose lengths are known to be a multiple of the vector size.

MakeUniqueAlignedArray<T>(size_t items, Args&&... args) creates an array of objects in newly allocated aligned memory as above and constructs every element of the new array using the passed constructor parameters, returning a unique pointer to the array. Note that only the first element is guaranteed to be aligned to the vector size; because there is no padding between elements, the alignment of the remaining elements depends on the size of T.

Speeding up code for older x86 platforms

Thanks to @dzaima for inspiring this section.

It is possible to improve the performance of your code on older x86 CPUs while remaining portable to all platforms. These older CPUs might indeed be the ones for which optimization is most impactful, because modern CPUs are usually faster and thus likelier to meet performance expectations.

For those without AVX3, preferably avoid Scatter*; some algorithms can be reformulated to use Gather* instead. For pre-AVX2, it is also important to avoid Gather*.

It is typically much more efficient to pad arrays and use Load instead of MaskedLoad and Store instead of BlendedStore.

If possible, use signed 8..32 bit types instead of unsigned types for comparisons and Min/Max.

Other ops which are considerably more expensive especially on SSSE3, and preferably avoided if possible: MulEven, i32 Mul, Shl/Shr, Round/Trunc/Ceil/Floor, float16 PromoteTo/DemoteTo, AESRound.

Ops which are moderately more expensive on older CPUs: 64-bit Abs/ShiftRight/ConvertTo, i32->u16 DemoteTo, u32->f32 ConvertTo, Not, IfThenElse, RotateRight, OddEven, BroadcastSignBit.

It is likely difficult to avoid all of these ops (about a fifth of the total). Apps usually also cannot more efficiently achieve the same result as any op without using it - this is an explicit design goal of Highway. However, sometimes it is possible to restructure your code to avoid Not, e.g. by hoisting it outside the SIMD code, or fusing with AndNot or CompressNot.