Skip to content

quick_reference.md

Latest commit

 

History

History
1564 lines (1184 loc) · 71.2 KB

quick_reference.md

File metadata and controls

1564 lines (1184 loc) · 71.2 KB

API synopsis / quick reference

[[TOC]]

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. hwy/contrib also includes higher-level algorithms such as FindIf or Sorter implemented using these ops.

Highway can use dynamic dispatch, which chooses the best available implementation at runtime, or static dispatch which has no runtime overhead. Dynamic dispatch works by compiling your code once per target CPU and then selecting (via indirect call) at runtime.

Examples of both are provided in examples/. Dynamic dispatch uses the same source code as static, plus #define HWY_TARGET_INCLUDE, #include "third_party/highway/hwy/foreach_target.h" (which must come before any inclusion of highway.h) and HWY_DYNAMIC_DISPATCH.

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. You can omit the HWY_NAMESPACE lines if not using dynamic dispatch.

Notation in this doc

  • 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.

Vector and tag types

Highway vectors consist of one or more 'lanes' of the same built-in type uint##_t, int##_t for ## = 8, 16, 32, 64, plus float##_t for ## = 16, 32, 64 and bfloat16_t.

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.

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.

T is one of the lane types above, and may be retrieved via TFromD<D>.

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 hardware where vectors can be a multiple of 128 bits (there, the extra lanes remain unused). 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>.

  • 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<>.

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/SSSE3/SSE4/AVX2/AVX3/AVX3_DL/NEON/SVE/SVE2/WASM/RVV. Each of these is represented by a HWY_Target (for example, HWY_SSE4) macro which expands to a unique power-of-two value.

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.

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.

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 builtin vectors. There are three options for portable code, 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 are not yet supported on RVV and SVE. Until that is resolved, code that wishes to run on all targets must use the corresponding equivalents mentioned in the description of each overloaded operator, 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, T): returns N-lane vector where the lane with index i has the given value of type T plus i. The least significant lane has index 0. This is useful in tests for detecting lane-crossing bugs.
  • V SignBit(D, T): returns N-lane vector with all lanes set to a value whose representation has only the most-significant bit set.

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.

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.

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: {i,f}
    V Neg(V a): returns -a[i].

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

  • V: f32
    V AbsDiff(V a, V b): returns |a[i] - b[i]| in each lane.

  • V: u8
    VU64 SumsOf8(V v) returns the sums of 8 consecutive u8 lanes, zero-extending each sum into a u64 lane. This is slower on RVV/WASM.

  • 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}{8,16}
    V AverageRound(V a, V b) returns (a[i] + b[i] + 1) / 2.

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

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

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

  • V: f32
    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: f32
    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
    M 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
    M 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
    M 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
    M 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: {u,i}{16,32,64}
    V operator*(V a, V b): returns the lower half of a[i] * b[i] in each lane. Currently unavailable on SVE/RVV; use the equivalent Mul instead.

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

  • V: i16
    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}{32},u64
    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: u64
    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,i}16, D: RepartitionToWide<DFromV<V>>, VW: Vec<D>
    VW ReorderWidenMulAccumulate(D d, V a, V b, VW sum0, VW& sum1): widens a and b to TFromD<D>, 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,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.

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; it is preferable to replace them with MulAdd using a negated constant.

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

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

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

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

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}{32,64}
    V RotateRight<int>(V a) returns (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.

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

  • V: {u,i}{16,32,64}
    V operator<<(V a, V b) returns a[i] << b[i]. Currently unavailable on SVE/RVV; use the equivalent Shl instead.

  • V: {u,i}{16,32,64}
    V operator>>(V a, V b) returns a[i] >> b[i]. Currently unavailable on SVE/RVV; use the equivalent Shr instead.

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 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]).

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]).

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: i32/64
    V BroadcastSignBit(V a) returns a[i] < 0 ? -1 : 0.

  • V: {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..).

Masks

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

Creation

  • 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.

Conversion

  • 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.

  • 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.

Testing

  • 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.

Ternary operator

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

  • 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.

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.

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.

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

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

  • 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> MaskedLoad(M mask, D, const T* p): returns p[i] or zero if the mask governing element i is false. 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, IfThenElseZero(mask, Load(D(), aligned)).

  • 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).

Scatter/Gather

Note: Offsets/indices are of type VI = Vec<RebindToSigned<D>> and need not be unique. The results are implementation-defined if any are negative.

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 is more expensive than Gather.

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

  • 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]].

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 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).

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>.

  • V,D: (u8,u16), (u16,u32), (u8,u32), (u32,u64), (u8,i16),
    (u8,i32), (u16,i32), (i8,i16), (i8,i32), (i16,i32), (i32,i64) Vec<D> PromoteTo(D, V part): returns part[i] zero- or sign-extended to the integer type MakeWide<T>.

  • V,D: (f16,f32), (bf16,f32), (f32,f64)
    Vec<D> PromoteTo(D, V part): returns part[i] widened to the floating-point type MakeWide<T>.

  • V,D:
    Vec<D> PromoteTo(D, V part): returns part[i] converted to 64-bit floating point.

  • V,D: (bf16,f32) 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.

  • V,D: (bf16,f32) 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.

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

  • 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).

DemoteTo and float-to-int ConvertTo return the closest representable value if the input exceeds the destination range.

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

  • V,D: f64,i32
    Vec<D> DemoteTo(D, V a): rounds floating point towards zero and converts the value to 32-bit integers.

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

  • D: {bf,i}16, V: RepartitionToWide<D>
    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: (i32,f32), (i64,f64)
    Vec<D> ConvertTo(D, V): converts an integer value to same-sized floating point.

  • V,D: (f32,i32), (f64,i64)
    Vec<D> ConvertTo(D, V): rounds floating point towards zero and converts the value to same-sized integer.

  • V: f32; Ret: i32
    Ret NearestInt(V a): returns the integer nearest to a[i]; results are undefined for NaN.

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.

Blockwise

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

  • V: {u,i}{16,32,64}, {f}
    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.

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>.

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

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>.

Shuffle

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

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

  • 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: {u,i,f}{32,64}
    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 ReverseBlocks(V v): returns a vector with blocks in reversed order.

  • V: {u,i,f}{32,64}
    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()). indices are always integers, even if V is a floating-point type.

  • D: {u,i}{32,64}
    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, Lanes(d)), but need not be unique.

  • D: {u,i}{32,64}
    unspecified SetTableIndices(D d, TI* idx) prepares for TableLookupLanes by loading Lanes(d) integer indices from idx, which must be in the range [0, Lanes(d)) but need not be unique. The index type TI must be an integer of the same size as TFromD<D>.

  • V: {u,i,f}{16,32,64}
    V Reverse(D, V a) returns a vector with lanes in reversed order (out[i] == a[Lanes(D()) - 1 - i]).

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

  • V: {u,i,f}{16,32,64}
    V Reverse2(D, V a) returns a vector with each group of 2 contiguous lanes in reversed order (out[i] == a[i ^ 1]).

  • V: {u,i,f}{16,32,64}
    V Reverse4(D, V a) returns a vector with each group of 4 contiguous lanes in reversed order (out[i] == a[i ^ 3]).

  • V: {u,i,f}{16,32,64}
    V Reverse8(D, V a) returns a vector with each group of 8 contiguous lanes in reversed order (out[i] == a[i ^ 7]).

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

  • V: {u,i,f}{32,64}
    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].

  • 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.

Reductions

Note: these 'reduce' all lanes to a single result (e.g. sum), which is broadcasted to all lanes. To obtain a scalar, you can call GetLane.

Being a horizontal operation (across lanes of the same vector), these are slower than normal SIMD operations and are typically used outside critical loops.

There are additional {u,i}{8} implementations on SSE4.1+ and NEON.

  • V: {u,i,f}{32,64},{u,i}{16}
    V SumOfLanes(D, V v): returns the sum of all lanes in each lane.

  • V: {u,i,f}{32,64},{u,i}{16}
    V MinOfLanes(D, V v): returns the minimum-valued lane in each lane.

  • V: {u,i,f}{32,64},{u,i}{16}
    V MaxOfLanes(D, V v): returns the maximum-valued lane in each lane.

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: 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

  • 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 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.

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

  • 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. 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).

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.

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.

If none are defined, but HWY_IS_TEST is defined, the default is HWY_COMPILE_ALL_ATTAINABLE. Otherwise, the default is to select all attainable targets except any non-best baseline (typically HWY_SCALAR), which reduces code size.

Compiler support

Clang and GCC require e.g. -mavx2 flags in order to use SIMD intrinsics. However, this enables AVX2 instructions in the entire translation unit, which may violate the one-definition rule and cause crashes. Instead, we use target-specific attributes introduced via #pragma. Function using SIMD must reside between HWY_BEFORE_NAMESPACE and HWY_AFTER_NAMESPACE. Alternatively, individual functions or lambdas may be prefixed with HWY_ATTR.

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.