simd

package module

v1.2.0-rc.1 Latest Latest Go to latest Published: Jun 2, 2026 License: MIT Imports: 0 Imported by: 0

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github.com/tphakala/simd

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README ¶

simd

A high-performance SIMD (Single Instruction, Multiple Data) library for Go providing vectorized operations on float64, float32, float16, int32, int16, complex128, and complex64 slices.

Features

Pure Go assembly - Native Go assembler, simple cross-compilation
Runtime CPU detection - Automatically selects optimal implementation (AVX-512, AVX+FMA, AVX without FMA, SSE4.1, NEON, NEON+FP16, or pure Go)
Zero allocations - All operations work on pre-allocated slices
80+ operations - Arithmetic, reduction, statistical, vector, signal processing, activation functions, and complex number operations
Multi-architecture - AMD64 (AVX-512/AVX+FMA/SSE4.1) and ARM64 (NEON/NEON+FP16) with pure Go fallback
Half-precision support - Native FP16 SIMD on ARM64 with FP16 extension (Apple Silicon, Cortex-A55+)
Thread-safe - All functions are safe for concurrent use

Installation

go get github.com/tphakala/simd

Requires Go 1.25+

Quick Start

package main

import (
    "fmt"
    "github.com/tphakala/simd/cpu"
    "github.com/tphakala/simd/f64"
)

func main() {
    fmt.Println("SIMD:", cpu.Info())

    // Vector operations
    a := []float64{1, 2, 3, 4, 5, 6, 7, 8}
    b := []float64{8, 7, 6, 5, 4, 3, 2, 1}

    // Dot product
    dot := f64.DotProduct(a, b)
    fmt.Println("Dot product:", dot) // 120

    // Element-wise operations
    dst := make([]float64, len(a))
    f64.Add(dst, a, b)
    fmt.Println("Sum:", dst) // [9, 9, 9, 9, 9, 9, 9, 9]

    // Statistical operations
    mean := f64.Mean(a)
    stddev := f64.StdDev(a)
    fmt.Printf("Mean: %.2f, StdDev: %.2f\n", mean, stddev)

    // Vector operations
    f64.Normalize(dst, a)
    fmt.Println("Normalized:", dst)

    // Distance calculation
    dist := f64.EuclideanDistance(a, b)
    fmt.Println("Distance:", dist)
}

Packages

`cpu` - CPU Feature Detection

import "github.com/tphakala/simd/cpu"

fmt.Println(cpu.Info())        // "AMD64 AVX-512", "AMD64 AVX+FMA", "AMD64 AVX", "AMD64 SSE2", "AMD64 (scalar)", "ARM64 NEON+FP16", or "ARM64 NEON"
fmt.Println(cpu.HasAVX())      // true/false
fmt.Println(cpu.HasAVX2())     // true/false
fmt.Println(cpu.HasFMA())      // true/false
fmt.Println(cpu.HasAVX512VL()) // true/false (AVX-512 F+VL)
fmt.Println(cpu.HasNEON())     // true/false
fmt.Println(cpu.HasFP16())     // true/false (ARM64 half-precision SIMD)

`f64` - float64 Operations

Category	Function	Description	SIMD Width
Arithmetic	`Add(dst, a, b)`	Element-wise addition	8x (AVX-512) / 4x (AVX) / 2x (NEON)
	`Sub(dst, a, b)`	Element-wise subtraction	8x / 4x / 2x
	`Mul(dst, a, b)`	Element-wise multiplication	8x / 4x / 2x
	`Div(dst, a, b)`	Element-wise division	8x / 4x / 2x
	`Scale(dst, a, s)`	Multiply by scalar	8x / 4x / 2x
	`AddScalar(dst, a, s)`	Add scalar	8x / 4x / 2x
	`SubFromScalar(dst, a, s)`	Scalar minus vector	8x / 4x / 2x (composed SIMD)
	`FMA(dst, a, b, c)`	Fused multiply-add: a*b+c	8x / 4x / 2x
	`AddScaled(dst, alpha, s)`	dst += alpha*s (axpy)	8x / 4x / 2x
Unary	`Abs(dst, a)`	Absolute value	8x / 4x / 2x
	`Neg(dst, a)`	Negation	8x / 4x / 2x
	`Sqrt(dst, a)`	Square root	8x / 4x / 2x
	`Reciprocal(dst, a)`	Reciprocal (1/x)	8x / 4x / 2x
	`Round(dst, src)`	Round half away from zero	4x (AVX) / 2x (NEON) / Go fallback
Reduction	`DotProduct(a, b)`	Dot product	8x / 4x / 2x
	`WeightedSum(w, src)`	Weighted sum Σ(wᵢ·srcᵢ)	8x / 4x / 2x
	`SumOfSquares(src)`	Sum of squares Σ(srcᵢ²)	8x / 4x / 2x
	`Sum(a)`	Sum of elements	8x / 4x / 2x
	`Min(a)`	Minimum value	8x / 4x / 2x
	`Max(a)`	Maximum value	8x / 4x / 2x
	`MinIdx(a)`	Index of minimum value	Pure Go
	`MaxIdx(a)`	Index of maximum value	Pure Go
Statistical	`Mean(a)`	Arithmetic mean	8x / 4x / 2x
	`Variance(a)`	Population variance	8x / 4x / 2x
	`StdDev(a)`	Standard deviation	8x / 4x / 2x
Vector	`EuclideanDistance(a, b)`	L2 distance	8x / 4x / 2x
	`Normalize(dst, a)`	Unit vector normalization	8x / 4x / 2x
	`CumulativeSum(dst, a)`	Running sum	Sequential
Range	`Clamp(dst, a, min, max)`	Clamp to range	8x / 4x / 2x
Activation	`Sigmoid(dst, src)`	Sigmoid: 1/(1+e^-x)	4x (AVX2) / 2x (NEON)
	`ReLU(dst, src)`	Rectified Linear Unit	4x (AVX) / 2x (NEON)
	`Tanh(dst, src)`	Hyperbolic tangent	4x (AVX2) / 2x (NEON)
	`Exp(dst, src)`	Exponential e^x	4x (AVX2) / 2x (NEON)
	`ClampScale(dst, src, min, max, s)`	Fused clamp and scale	4x (AVX) / 2x (NEON)
Batch	`DotProductBatch(r, rows, v)`	Multiple dot products	8x / 4x / 2x
Signal	`ConvolveValid(dst, sig, k)`	FIR filter / convolution	8x / 4x / 2x
	`ConvolveValidMulti(dsts, sig, ks)`	Multi-kernel convolution	8x / 4x / 2x
	`ConvolveDecimate(dst,sig,k,f,p)`	Strided FIR downsample (decimate)	8x / 4x / 2x
	`AccumulateAdd(dst, src, off)`	Overlap-add: dst[off:] += src	8x / 4x / 2x
Audio	`Interleave2(dst, a, b)`	Pack stereo: [L,R,L,R,...]	4x / 2x
	`Deinterleave2(a, b, src)`	Unpack stereo to channels	4x / 2x
	`InterleaveN(dst, srcs)`	Pack N planar streams (any N; N-stream Interleave2)	N=2,4,8 AVX, N=3,6 AVX2 / N=2,3,4 NEON; else Go
	`DeinterleaveN(dsts, src)`	Unpack N interleaved streams (any N)	N=2,4,8 AVX, N=3,6 AVX2 / N=2,3,4 NEON; else Go
	`CubicInterpDot(hist,a,b,c,d,x)`	Fused cubic interp dot product	4x / 2x
	`Int32ToFloat32Scale(dst,src,s)`	PCM int32 to normalized float	8x / 4x
	`Int16ToFloat32Scale(dst,src,s)`	PCM int16 to normalized float	8x (AVX2) / 4x (NEON)
	`Float32ToInt16Scale(dst,src,s)`	Normalized float to PCM int16	8x (AVX2) / 4x (NEON)

DotProductBatch scores its [][]float64 rows in groups of four, keeping the query vector resident in registers across each group via a fused 4-row kernel on AMD64 (AVX-512 and AVX+FMA) instead of re-loading it per row. Short, ragged, or sub-SIMD-width rows fall back to the per-row dot product, with identical results.

`f32` - float32 Operations

Same API as f64 but for float32 with wider SIMD:

Architecture	SIMD Width
AMD64 (AVX-512)	16x float32
AMD64 (AVX+FMA)	8x float32
AMD64 (SSE2)	4x float32
ARM64 (NEON)	4x float32

InterleaveN/DeinterleaveN add an 8-stream AVX path (8x8 register transpose) and a 3-stream AVX2 path (per-stream VPERMPS gathers merged with VPBLENDD, since 3 streams do not map onto a clean register transpose) on top of the shared N=2/4 (AVX) and N=2/3/4 (NEON) kernels; all other stream counts use the allocation-free generic path. The N=3 case is the 16k -> 48k upsample hot path: the AVX2 gather/blend kernel runs roughly 2.8x (interleave) and 3.2x (deinterleave) over the generic loop on AVX2. The 6-stream AVX2 path (the 8k -> 48k upsample) zips stream pairs into three double-wide pair streams, then reuses the f64 N=3 interleave on those pairs, so it needs no index tables; it runs roughly 2x (interleave and deinterleave) on AVX2. f64 adds N=3 and N=6 (AVX2) plus N=8 (AVX), processing 4 frames per block (a YMM holds 4 doubles): N=3 uses immediate VPERMPD gathers merged with VBLENDPD, N=6 zips pairs at 128-bit-lane granularity with VPERM2F128 (roughly 4x interleave, 1.5x deinterleave), and N=8 runs two stacked 4x4 transposes (streams 0-3 fill each frame's low YMM, streams 4-7 the high YMM).

Row-major batch dot products (for flat vector stores):

Function	Description
`DotProductIndexed(dst, base, query, rowIDs, dims) bool`	Scores selected row-major rows by `uint32` row ID without building `[][]float32`; returns whether an optimized SIMD batch kernel handled at least one batch.
`DotProductStrided(dst, base, query, rowCount, dims, stride) bool`	Scores contiguous or fixed-stride row-major rows; returns whether an optimized SIMD batch kernel handled at least one batch.

Both APIs are allocation-free. The batched SIMD kernel covers AMD64 (AVX-512 / AVX+FMA) and ARM64 (NEON); unsupported CPUs, tiny shapes, tails, and ragged inputs use the per-row fallback.

DotProductBatch scores its [][]float32 rows in groups of four, keeping the query vector resident in registers across each group instead of re-loading it for every row. The fused 4-row kernel runs on AVX-512, AVX+FMA, and ARM64 NEON; short, ragged, or sub-SIMD-width rows fall back to the per-row dot product. Results are identical to the per-row path either way.

Additional split-format complex operations (for FFT pipelines with separate real/imag arrays):

Category	Function	Description	SIMD Width
Complex	`MulComplex(dstRe,dstIm,aRe,aIm,bRe,bIm)`	Split-format complex multiply	8x (AVX) / 4x (NEON)
	`MulConjComplex(dstRe,dstIm,aRe,aIm,bRe,bIm)`	Multiply by conjugate	8x / 4x
	`AbsSqComplex(dst,aRe,aIm)`	Magnitude squared	8x / 4x
	`ButterflyComplex(uRe,uIm,lRe,lIm,twRe,twIm)`	FFT butterfly with twiddle	8x / 4x
	`RealFFTUnpack(outRe,outIm,zRe,zIm,twRe,twIm)`	Real FFT unpack step	8x / 4x
Utility	`Reverse(dst, src)`	Reverse slice order	8x / 4x
	`AddSub(sum, diff, a, b)`	Fused sum and difference	8x / 4x

`f16` - float16 (Half-Precision) Operations

IEEE 754 half-precision floating-point operations, optimized for ML inference, audio DSP, and memory-bandwidth-bound workloads.

import "github.com/tphakala/simd/f16"

// Convert between float32 and float16
h := f16.FromFloat32(3.14)
f := f16.ToFloat32(h)

// Vector operations (same API as f32/f64)
a := make([]f16.Float16, 1024)
b := make([]f16.Float16, 1024)
dst := make([]f16.Float16, 1024)

f16.Add(dst, a, b)           // Element-wise addition
dot := f16.DotProduct(a, b)  // Dot product (returns float32)
f16.ReLU(dst, a)             // Activation functions

Category	Function	Description	SIMD Width
Conversion	`ToFloat32(h)`	FP16 → float32	Scalar
	`FromFloat32(f)`	float32 → FP16	Scalar
	`ToFloat32Slice(dst, src)`	Batch FP16 → float32	8x (NEON+FP16)
	`FromFloat32Slice(dst, src)`	Batch float32 → FP16	8x (NEON+FP16)
Arithmetic	`Add(dst, a, b)`	Element-wise addition	8x (NEON+FP16)
	`Sub(dst, a, b)`	Element-wise subtraction	8x (NEON+FP16)
	`Mul(dst, a, b)`	Element-wise multiplication	8x (NEON+FP16)
	`Div(dst, a, b)`	Element-wise division	8x (NEON+FP16)
	`Scale(dst, a, s)`	Multiply by scalar	8x (NEON+FP16)
	`AddScalar(dst, a, s)`	Add scalar	8x (NEON+FP16)
	`FMA(dst, a, b, c)`	Fused multiply-add: a*b+c	8x (NEON+FP16)
	`AddScaled(dst, alpha, s)`	dst += alpha*s (AXPY)	8x (NEON+FP16)
Unary	`Abs(dst, a)`	Absolute value	8x (NEON+FP16)
	`Neg(dst, a)`	Negation	8x (NEON+FP16)
	`Sqrt(dst, a)`	Square root	8x (NEON+FP16)
	`Reciprocal(dst, a)`	Reciprocal (1/x)	8x (NEON+FP16)
Reduction	`DotProduct(a, b)` → float32	Dot product	8x (NEON+FP16)
	`DotProductF32(a, b)` → float32	Dot product (FP32 widen)	8x (NEON)
	`Sum(a)` → float32	Sum of elements	8x (NEON+FP16)
	`Min(a)`	Minimum value	8x (NEON+FP16)
	`Max(a)`	Maximum value	8x (NEON+FP16)
	`MinIdx(a)`	Index of minimum	Pure Go
	`MaxIdx(a)`	Index of maximum	Pure Go
Statistical	`Mean(a)` → float32	Arithmetic mean	8x (NEON+FP16)
	`Variance(a)` → float32	Population variance	8x (NEON)
	`StdDev(a)` → float32	Standard deviation	8x (NEON)
Vector	`EuclideanDistance(a, b)` → float32	L2 distance	8x (NEON)
	`Normalize(dst, a)`	Unit vector normalization	8x (NEON+FP16)
	`CumulativeSum(dst, a)`	Running sum	Sequential
Range	`Clamp(dst, a, min, max)`	Clamp to range	8x (NEON+FP16)
	`ClampScale(dst, src, min, max, s)`	Fused clamp and scale	8x (NEON)
Activation	`ReLU(dst, src)`	Rectified Linear Unit	8x (NEON+FP16)
	`Sigmoid(dst, src)`	Sigmoid: 1/(1+e^-x)	Pure Go
	`Tanh(dst, src)`	Hyperbolic tangent	Pure Go
	`Exp(dst, src)`	Exponential e^x	Pure Go
Batch	`DotProductBatch(r, rows, v)`	Multiple dot products	8x (NEON+FP16)
Signal	`ConvolveValid(dst, sig, k)`	FIR filter / convolution	Pure Go
	`AccumulateAdd(dst, src, off)`	Overlap-add: dst[off:] += src	8x (NEON+FP16)
Audio	`Interleave2(dst, a, b)`	Pack stereo: [L,R,L,R,...]	8x (NEON)
	`Deinterleave2(a, b, src)`	Unpack stereo to channels	8x (NEON)

Key characteristics:

Storage: IEEE 754 half-precision (1 sign, 5 exponent, 10 mantissa bits)
Precision: ~3.3 decimal digits, range ~6×10⁻⁸ to 65504
Reductions: Accumulate in float32 for numerical stability
Memory efficiency: 2x bandwidth vs float32 (8 elements per 128-bit NEON vector)
DotProduct saturation: On ARM64 with FP16 SIMD, DotProduct computes per-element products in FP16 and saturates to ±Inf when |a[i] * b[i]| > 65504. Use DotProductF32 (FP32 widening before multiply, ~1.5-2x slower) for audio DSP or raw-signal inputs that can produce out-of-range products.
FP32-widened ops: DotProductF32, EuclideanDistance, Variance, StdDev, and ClampScale widen each FP16 lane to FP32 before arithmetic, so they match the pure-Go reference and never saturate. They use only base-NEON instructions (the FCVTL/FCVTN conversions are ARMv8.0-A, not the FEAT_FP16 extension), so they run on any ARM64 NEON core, including non-FP16 parts (Cortex-A72/A53). Interleave2/Deinterleave2 are likewise bit-exact 16-bit lane permutes (ZIP/UZP) that run on any ARM64 NEON core.

Benchmark (1024 elements, Raspberry Pi 5 / Cortex-A76, zero allocations):

Operation	SIMD	Pure Go	Speedup
EuclideanDistance	481 ns	5995 ns	12.5x
Variance	506 ns	8901 ns	17.6x
Interleave2	178 ns	2163 ns	12.2x
Deinterleave2	178 ns	2167 ns	12.2x
ClampScale	531 ns	12211 ns	23.0x

Hardware requirements:

Native FP16 SIMD: ARM64 with FEAT_FP16 (ARMv8.2-A+)
- Apple Silicon (M1/M2/M3/M4) ✅
- Cortex-A55, A75, A76, A77, A78, X1, X2, X3 ✅
- Raspberry Pi 5 (Cortex-A76) ✅
Pure Go fallback: All other platforms
- Raspberry Pi 3/4 (Cortex-A53/A72 - ARMv8.0) - works but no SIMD acceleration
- AMD64 - works but no SIMD acceleration

`c128` - complex128 Operations

SIMD-accelerated complex number operations for FFT-based signal processing:

Category	Function	Description	SIMD Width
Arithmetic	`Mul(dst, a, b)`	Complex multiplication	4x (AVX-512) / 2x (AVX)
	`MulConj(dst, a, b)`	Multiply by conjugate: a × conj(b)	4x / 2x
	`Scale(dst, a, s)`	Scale by complex scalar	4x / 2x
	`Add(dst, a, b)`	Complex addition	4x / 2x
	`Sub(dst, a, b)`	Complex subtraction	4x / 2x
Unary	`Abs(dst, a)`	Complex magnitude \|a + bi\|	4x (AVX-512) / 2x (AVX)
	`AbsSq(dst, a)`	Magnitude squared \|a + bi\|²	4x / 2x
	`Conj(dst, a)`	Complex conjugate: a - bi	4x / 2x

These operations are designed for FFT-based signal processing pipelines:

import "github.com/tphakala/simd/c128"

// Frequency-domain multiplication (FFT convolution)
signalFFT := make([]complex128, n)
kernelFFT := make([]complex128, n)
result := make([]complex128, n)
magnitude := make([]float64, n)

// Frequency-domain filtering
c128.Mul(result, signalFFT, kernelFFT)          // Complex multiply
c128.MulConj(result, signalFFT, kernelFFT)      // Cross-correlation

// Spectrogram and magnitude analysis
c128.Abs(magnitude, signalFFT)                  // Extract magnitude for display

Use Cases:

Abs/AbsSq: Spectrograms, power spectral density, frequency analysis
Conj: Cross-correlation, frequency-domain filtering
Mul/MulConj: FFT-based convolution, filtering, correlation

Benchmark (1024 elements, Intel Xeon Platinum 8362 AVX-512):

Operation	SIMD	Pure Go	Speedup
Mul	239 ns	1021 ns	4.3x
MulConj	314 ns	1434 ns	4.6x
Scale	180 ns	959 ns	5.3x
Add	255 ns	733 ns	2.9x
Abs	918 ns	3453 ns	3.8x
AbsSq	237 ns	594 ns	2.5x
Conj	163 ns	594 ns	3.7x

`c64` - complex64 Operations

SIMD-accelerated single-precision complex number operations:

Category	Function	Description	SIMD Width
Arithmetic	`Mul(dst, a, b)`	Complex multiplication	8x (AVX-512) / 4x (AVX) / 2x (NEON)
	`MulConj(dst, a, b)`	Multiply by conjugate: a × conj(b)	8x / 4x / 2x
	`Scale(dst, a, s)`	Scale by complex scalar	8x / 4x / 2x
	`Add(dst, a, b)`	Complex addition	8x / 4x / 2x
	`Sub(dst, a, b)`	Complex subtraction	8x / 4x / 2x
Unary	`Abs(dst, a)`	Complex magnitude \|a + bi\|	8x / 4x / 2x
	`AbsSq(dst, a)`	Magnitude squared \|a + bi\|²	8x / 4x / 2x
	`Conj(dst, a)`	Complex conjugate: a - bi	8x / 4x / 2x
Conversion	`FromReal(dst, src)`	Real to complex: src → src+0i	8x / 4x / 2x

Same API as c128 but for complex64 with 2x wider SIMD (8 bytes vs 16 bytes per element):

import "github.com/tphakala/simd/c64"

// Single-precision FFT processing
signalFFT := make([]complex64, n)
kernelFFT := make([]complex64, n)
result := make([]complex64, n)
magnitude := make([]float32, n)

c64.Mul(result, signalFFT, kernelFFT)     // Complex multiply
c64.Abs(magnitude, signalFFT)              // Extract magnitude

`i32` - int32 Operations

SIMD-accelerated integer-domain operations for codec and integer-DSP hot loops (for example a pure-Go FLAC encoder/decoder), where the per-sample work is integer arithmetic and channel (de)interleaving rather than floating-point math:

Category	Function	Description	SIMD Width
Interleave	`Interleave2(dst, a, b)`	Pack two channels into interleaved stereo	8x (AVX) / 4x (NEON)
	`Deinterleave2(a, b, src)`	Split interleaved stereo into two channels	8x (AVX) / 4x (NEON)
Decorrelation	`Add(dst, a, b)`	Element-wise add (RIGHT_SIDE decode)	8x (AVX2) / 4x (NEON)
	`Sub(dst, a, b)`	Element-wise subtract (side channel / LEFT_SIDE decode)	8x (AVX2) / 4x (NEON)
	`MidSideEncode(mid, side, left, right)`	Mid/side forward decorrelation	8x (AVX2) / 4x (NEON)
	`MidSideDecode(left, right, mid, side)`	Mid/side inverse (parity-bit reconstruction)	8x (AVX2) / 4x (NEON)
Fixed predictor	`Diff1`..`Diff4(dst, src)`	Order 1-4 fixed-predictor encode residual (forward diff)	8x (AVX2) / 4x (NEON)
	`Restore1`..`Restore4(dst, src)`	Order 1-4 fixed-predictor decode (inverse; prefix sum)	8x (AVX2) / 4x (NEON)
LPC	`LPCResidualEncode(res, samples, coeffs, shift)`	Quantized-LPC encode residual FIR (parallel across outputs)	8x (AVX2) / 4x (NEON)
	`LPCRestore(out, residual, coeffs, shift)`	Quantized-LPC decode (serial recurrence; vectorized taps)	8x (AVX2) / 4x (NEON)
Rice	`RiceSums(sums, res)`	Per-parameter zigzag unary-bit sums `Σ (zigzag(res)>>k)`	8x (AVX2) / 4x (NEON)
	`RiceBestParam(res, maxParam)`	Cost-minimizing Rice parameter + its bit count	8x (AVX2) / 4x (NEON)

import "github.com/tphakala/simd/i32"

left := make([]int32, n)
right := make([]int32, n)
stereo := make([]int32, n*2)

i32.Interleave2(stereo, left, right)   // [l0, r0, l1, r1, ...]
i32.Deinterleave2(left, right, stereo) // inverse: split back to channels

res := make([]int32, n)
i32.Diff2(res, left)     // order-2 fixed-predictor encode residual
i32.Restore2(left, res)  // exact inverse: reconstruct the samples

coeffs := []int32{...}             // quantized LPC coefficients (order = len)
i32.LPCResidualEncode(res, left, coeffs, shift) // encode FIR residual
i32.LPCRestore(left, res, coeffs, shift)        // exact inverse: reconstruct

param, bits := i32.RiceBestParam(res, 14) // best Rice parameter and its bit cost

Interleaving is pure 32-bit-lane movement, so those kernels reuse the proven f32 shuffle/permute encodings (AVX VUNPCKLPS/VPERM2F128, NEON ZIP/UZP on .4S); the bit pattern of each lane is irrelevant, so negative values and the type extremes round-trip exactly. The decorrelation and fixed-predictor kernels do integer-ALU work on 256-bit (AVX2) / 128-bit (NEON) lanes. RestoreK is the exact inverse of DiffK: since the order-K fixed predictor is the K-th forward difference, restoration is K cumulative-sum passes built on one SIMD prefix-sum kernel (11x at order 1 down to ~5x at order 4 on AVX2; 6x to 3x on NEON, all zero-allocation). The LPC kernels accumulate the prediction sum in int64 (matching libFLAC), so they stay bit-exact for the full coefficient precision and order: LPCResidualEncode is a FIR that vectorizes across output samples (widening VPMULDQ / SMLAL, ~7-9x on AVX2, ~4-5x on NEON), while LPCRestore is a serial recurrence whose per-output tap dot product is vectorized, keeping the just-written newest samples on store-forwardable scalar loads (~1.4-3.9x on AVX2, ~1.8-3.6x on NEON, order 8 to 32). The Rice cost search folds each residual to its unsigned zigzag symbol (r<<1)^(r>>31), widens it to int64, and accumulates Σ (zigzag(res)>>k) for every Rice parameter k in 0..14 at once (the symbols are halved progressively, exact for the logical shift); RiceBestParam adds the n*(k+1) code overhead and picks the cheapest k. This is the exact bit cost, not the sum>>k approximation, and runs ~13x on AVX2 and ~4x on NEON, zero-allocation.

`i16` - int16 Operations

The 16-bit integer counterpart to i32, for raw-PCM hot loops (such as a pure-Go FLAC codec) where the source samples are 16-bit and the cheapest place to vectorize is the channel (de)interleaving that happens before samples are widened to int32. FLAC decorrelation widens samples (the side and mid channels can exceed the source bit depth by one bit), so the arithmetic primitives live in i32; this package carries only the operations that provably help at 16-bit width:

Category	Function	Description	SIMD Width
Interleave	`Interleave2(dst, a, b)`	Pack two channels into interleaved stereo	16x (AVX2) / 8x (SSE2) / 8x (NEON)
	`Deinterleave2(a, b, src)`	Split interleaved stereo into two channels	16x (AVX2) / 8x (SSE2) / 8x (NEON)

import "github.com/tphakala/simd/i16"

left := make([]int16, n)
right := make([]int16, n)
stereo := make([]int16, n*2)

i16.Interleave2(stereo, left, right)   // [l0, r0, l1, r1, ...]
i16.Deinterleave2(left, right, stereo) // inverse: split back to channels

Like the i32 interleave kernels, these are pure 16-bit-lane movement (AVX2/SSE2 word unpacks plus a lane permute, NEON ZIP/UZP on .8H), so the bit pattern of each lane is irrelevant and every value round-trips exactly: negative values and the int16 extremes are preserved. Both kernels are zero-allocation.

Performance

AMD64 (Intel Core i7-1260P, AVX+FMA)

float64 Operations - SIMD vs Pure Go (1024 elements)

Category	Operation	SIMD (ns)	Go (ns)	Speedup
Arithmetic	Add	84	446	5.3x
	Sub	84	335	4.0x
	Mul	86	436	5.1x
	Div	441	941	2.1x
	Scale	68	272	4.0x
	AddScalar	68	286	4.2x
	FMA	110	557	5.0x
Unary	Abs	66	365	5.6x
	Neg	66	306	4.6x
	Sqrt	658	1323	2.0x
	Reciprocal	447	920	2.1x
Reduction	DotProduct	162	859	5.3x
	Sum	82	184	2.3x
	Min	157	340	2.2x
	Max	154	352	2.3x
Statistical	Mean	82	184	2.3x
	Variance*	820	902	1.1x
	StdDev*	825	905	1.1x
Vector	EuclideanDistance	216	1071	5.0x
	Normalize	220	1080	4.9x
	CumulativeSum	428	425	1.0x
Range	Clamp	81	640	7.9x

*Variance/StdDev benchmarked at 4096 elements (SIMD benefits at larger sizes)

float32 Operations - SIMD vs Pure Go (1024 elements)

Category	Operation	SIMD (ns)	Go (ns)	Speedup
Arithmetic	Add	47	441	9.4x
	Sub	49	339	6.9x
	Mul	49	436	8.9x
	Div	138	655	4.8x
	Scale	40	299	7.4x
	AddScalar	39	272	7.0x
	FMA	64	444	6.9x
Unary	Abs	37	656	17.6x
	Neg	40	273	6.9x
Reduction	DotProduct	71	424	5.9x
	Sum	41	123	3.0x
	Min	65	340	5.2x
	Max	66	352	5.3x
Range	Clamp	47	701	14.8x

Activation Functions - SIMD vs Pure Go

float32 (1024 elements):

Function	SIMD (ns)	Go (ns)	Speedup	SIMD Throughput
Sigmoid	138	5906	43x	59.3 GB/s
ReLU	39	662	17x	211 GB/s
Tanh	138	28116	204x	59.5 GB/s
Exp	312	5555	18x	26.3 GB/s

float64 (1024 elements):

Function	SIMD (ns)	Go (ns)	Speedup	SIMD Throughput
Sigmoid	745	5640	7.6x	22.0 GB/s
ReLU	68	646	9.5x	240 GB/s
Tanh	836	6529	7.8x	19.6 GB/s
Exp	606	4698	7.8x	27.0 GB/s

Key Characteristics:

Tanh: 200x+ speedup for f32 - fast approximation with saturation vs math.Tanh
ReLU: Highest throughput (211-240 GB/s) - simple max(0, x) operation
Sigmoid: 43x speedup for f32 - fast approximation with exponential
Exp: 18x speedup for f32 (12x on ARM64 NEON) via range reduction plus a degree-5 polynomial; max relative error ~7e-6 (f32), ~3e-6 (f64)

Batch & Signal Processing (varied sizes)

Operation	Config	SIMD	Go	Speedup
DotProductBatch (f64)	256 vec × 100 rows	3.2 µs	20.5 µs	6.4x
DotProductBatch (f32)	256 vec × 100 rows	1.5 µs	9.8 µs	6.7x
ConvolveValid (f64)	4096 sig × 64 ker	26.6 µs	169 µs	6.3x
ConvolveValid (f32)	4096 sig × 64 ker	17.9 µs	80 µs	4.5x
ConvolveValidMulti (f64)	1000 sig × 64 ker × 2	13.4 µs	-	-
CubicInterpDot (f64)	241 taps	47 ns	88 ns	1.9x
CubicInterpDot (f32)	241 taps	21 ns	66 ns	3.1x
Int32ToFloat32Scale	1024 elements	50 ns	405 ns	8.1x
Int32ToFloat32Scale	4096 elements	157 ns	1586 ns	10.1x
Int16ToFloat32Scale	1024 elements	58 ns	483 ns	8.3x
Int16ToFloat32Scale	4096 elements	200 ns	1914 ns	9.6x
Float32ToInt16Scale	1024 elements	92 ns	1360 ns	14.8x
Float32ToInt16Scale	4096 elements	365 ns	5420 ns	14.8x
Interleave2 (f64)	1000 pairs	216 ns	-	-
Deinterleave2 (f64)	1000 pairs	216 ns	-	-
Interleave2 (f32)	1000 pairs	109 ns	-	-
Deinterleave2 (f32)	1000 pairs	216 ns	-	-

ConvolveDecimate (fused strided convolution)

ConvolveDecimate fuses an FIR downsample loop into one call. The relevant baseline is what a consumer writes today: a Go loop calling DotProductUnsafe at each strided window (the inner dot is already SIMD). Both compute identical results; the fused kernel removes the per-output call, dispatch and slice-header overhead and keeps the kernel pointer resident, so the win is largest for short kernels. Signal length 4096, allocation-free. Measured (AVX2 on x86-64, NEON on a Raspberry Pi 5):

Config	f32 x86	f64 x86	f32 NEON	f64 NEON
20 taps, 2x decimate	2.0x	2.3x	1.7x	1.9x
32 taps, 2x decimate	2.3x	1.7x	1.9x	1.7x
64 taps, 2x decimate	2.0x	1.8x	1.7x	1.3x
241 taps, 2x decimate	1.5x	1.3x	1.2x	1.1x
241 taps, 4x decimate	1.4x	1.2x	1.2x	1.1x

Performance Summary

Package	Average Speedup	Best	Operations
f32	6.5x	21.8x (Abs)	35 functions
f64	3.2x	7.9x (Clamp)	32 functions
c128	2.7x	3.4x (Abs)	8 functions
c64	~2x	~3x (Mul)	9 functions

ARM64 (Raspberry Pi 5, NEON)

float64 Operations

Operation	Size	Time	Throughput
DotProduct	277	151 ns	29 GB/s
DotProduct	1000	513 ns	31 GB/s
Add	1000	775 ns	31 GB/s
Mul	1000	727 ns	33 GB/s
FMA	1000	890 ns	36 GB/s
Sum	1000	635 ns	13 GB/s
Mean	1000	677 ns	12 GB/s

float32 Operations

Operation	Size	Time	Throughput
DotProduct	100	37 ns	21 GB/s
DotProduct	1000	263 ns	30 GB/s
DotProduct	10000	2.78 µs	29 GB/s
Add	1000	389 ns	31 GB/s
Mul	1000	390 ns	31 GB/s
FMA	1000	479 ns	33 GB/s

Comparison vs Pure Go

Operation	Size	SIMD	Pure Go	Speedup
DotProduct (f32)	100	37 ns	137 ns	3.7x
DotProduct (f32)	1000	262 ns	1350 ns	5.2x
DotProduct (f64)	100	62 ns	138 ns	2.2x
DotProduct (f64)	1000	513 ns	1353 ns	2.6x
Add (f32)	1000	389 ns	2015 ns	5.2x
Sum (f32)	1000	343 ns	1327 ns	3.9x

int32 (i32) - SIMD vs Pure Go (1000 elements)

Operation	AMD64 (AVX/AVX2)	ARM64 (NEON, Pi 5)
Interleave2	121 ns vs 487 ns (4.0x)	322 ns vs 1679 ns (5.2x)
Deinterleave2	228 ns vs 482 ns (2.1x)	322 ns vs 1682 ns (5.2x)
Restore1	181 ns vs 2019 ns (11.2x)	605 ns vs 3763 ns (6.2x)
Restore2	320 ns vs 2296 ns (7.2x)	1101 ns vs 4592 ns (4.2x)
Restore3	462 ns vs 2493 ns (5.4x)	1608 ns vs 5421 ns (3.4x)
Restore4	575 ns vs 2778 ns (4.8x)	2093 ns vs 6245 ns (3.0x)
LPCResidualEncode (order 8)	743 ns vs 5333 ns (7.2x)	2495 ns vs 10707 ns (4.3x)
LPCResidualEncode (order 32)	2397 ns vs 22046 ns (9.2x)	8148 ns vs 40811 ns (5.0x)
LPCRestore (order 8)	3583 ns vs 4944 ns (1.4x)	6128 ns vs 10889 ns (1.8x)
LPCRestore (order 32)	4443 ns vs 17529 ns (3.9x)	11303 ns vs 41026 ns (3.6x)
RiceSums (k=0..14)	810 ns vs 10490 ns (13.0x)	4090 ns vs 17163 ns (4.2x)
RiceBestParam (k=0..14)	810 ns vs 10490 ns (13.0x)	4081 ns vs 17163 ns (4.2x)

int16 (i16) - SIMD vs Pure Go (1000 elements)

Operation	AMD64 (AVX2/SSE2)	ARM64 (NEON, Pi 5)
Interleave2	60 ns vs 585 ns (9.8x)	165 ns vs 2106 ns (12.8x)
Deinterleave2	59 ns vs 640 ns (10.9x)	165 ns vs 2120 ns (12.9x)

Both i16 kernels are zero-allocation and bit-exact against the pure-Go reference (verified with negative values and the int16 extremes); they move whole 16-bit lanes, so the bit pattern of each sample is irrelevant to correctness.

All int32 kernels are zero-allocation and bit-exact against the pure-Go reference (verified across the sign and high bits with negative values and the type extremes). The Restore baseline is the pure-Go decode recurrence; RestoreK reconstructs samples as K SIMD prefix-sum passes (the inverse of the order-K forward difference). The LPC kernels accumulate in int64 and are checked against an arbitrary-precision math.big oracle and the encode->decode round-trip; LPCRestore is the serial decode recurrence (vectorized per-output tap dot product), dispatched to SIMD only at order >= 8 where it beats the scalar path. The Rice kernels compute the exact per-parameter unary-bit sums Σ (zigzag(res)>>k) for all 15 FLAC parameters in one pass (15 int64 accumulators; AVX2 sweeps the data twice for its 16-register file, NEON fits one pass in its 32 registers), checked against an independent oracle and brute-force parameter scan.

Performance Notes

AMD64: Explicit SIMD provides 5x speedups for most operations compared to pure Go, with consistent high throughput across all vector sizes.
ARM64: NEON SIMD provides substantial speedups over pure Go across all operations:
- float32: 3.7x - 5.2x faster (4 elements per 128-bit vector)
- float64: 2.2x - 2.6x faster (2 elements per 128-bit vector)
CumulativeSum is inherently sequential (each element depends on the previous) and uses pure Go on all platforms.

Known Limitations

Small Slice Fallback for Min/Max (AMD64)

On AMD64, the Min and Max functions fall back to pure Go for small slices:

float64: slices with fewer than 4 elements
float32: slices with fewer than 8 elements

This is because AVX assembly loads multiple elements at once (4 float64s or 8 float32s), which would cause out-of-bounds memory access on smaller slices.

The Go fallback for small slices is intentional and likely optimal - SIMD setup overhead (register loading, masking, horizontal reduction) would exceed the cost of a simple 2-3 element comparison loop.

Architecture Support

Architecture	Instruction Set	f64/f32/c128/c64	f16
AMD64	AVX-512	Full SIMD support	Pure Go fallback
AMD64	AVX + FMA	Full SIMD support	Pure Go fallback
AMD64	SSE4.1	Full SIMD support	Pure Go fallback
ARM64	NEON + FP16	Full SIMD support	Full SIMD support
ARM64	NEON only	Full SIMD support	Pure Go fallback
Other	-	Pure Go fallback	Pure Go fallback

ARM64 FP16 support by device:

Device / SoC	Core(s)	Architecture	FP16 SIMD
Apple Silicon (M1-M4)	Firestorm+	ARMv8.4-A	✅ Yes
Raspberry Pi 5	Cortex-A76	ARMv8.2-A	✅ Yes
Raspberry Pi 4	Cortex-A72	ARMv8.0-A	❌ No
Raspberry Pi 3	Cortex-A53	ARMv8.0-A	❌ No
AWS Graviton 2/3	Neoverse N1/V1	ARMv8.2-A+	✅ Yes
Ampere Altra	Neoverse N1	ARMv8.2-A	✅ Yes

Design Principles

Pure Go assembly - Native Go assembler for maximum portability and easy cross-compilation
Runtime dispatch - CPU features detected once at init time, zero runtime overhead
Zero allocations - No heap allocations in hot paths
Safe defaults - Gracefully falls back to pure Go on unsupported CPUs
Boundary safe - Handles any slice length, not just SIMD-aligned sizes

Testing

The library includes comprehensive tests with pure Go reference implementations for validation:

# Run all tests
go test ./...

# Run tests with verbose output
task test

# Run benchmarks
task bench

# Compare SIMD vs pure Go performance
task bench:compare

# Show CPU SIMD capabilities
task cpu

See Taskfile.yml for all available tasks.

Contributing

Contributions are welcome! Please see CONTRIBUTING.md for guidelines.

License

This project is licensed under the MIT License - see the LICENSE file for details.

Documentation ¶

Overview ¶

Package simd provides high-performance SIMD-accelerated operations for Go.

This module contains subpackages for CPU feature detection and vectorized numeric operations:

github.com/tphakala/simd/cpu - CPU feature detection
github.com/tphakala/simd/f64 - float64 SIMD operations
github.com/tphakala/simd/f32 - float32 SIMD operations
github.com/tphakala/simd/i32 - int32 SIMD operations (integer DSP)
github.com/tphakala/simd/c128 - complex128 SIMD operations

Architecture Support ¶

The library automatically selects the optimal implementation at runtime:

AMD64: AVX-512 (8x float64, 16x float32), AVX+FMA (4x float64, 8x float32), or SSE2 fallback
ARM64: NEON/ASIMD instructions (2x float64, 4x float32)
Other: Pure Go fallback

Quick Start ¶

import (
    "github.com/tphakala/simd/cpu"
    "github.com/tphakala/simd/f64"
)

func main() {
    fmt.Println("SIMD:", cpu.Info())

    a := []float64{1, 2, 3, 4, 5, 6, 7, 8}
    b := []float64{8, 7, 6, 5, 4, 3, 2, 1}

    // Dot product
    dot := f64.DotProduct(a, b)

    // Element-wise operations
    dst := make([]float64, len(a))
    f64.Add(dst, a, b)
    f64.Mul(dst, a, b)
}

Available Operations ¶

Core arithmetic: Add, Sub, Mul, Div, Scale, AddScalar, AddScaled, FMA

Reductions: Sum, DotProduct, DotProductBatch, DotProductIndexed, DotProductStrided, Min, Max, MinIdx, MaxIdx

Statistics: Mean, Variance, StdDev, EuclideanDistance, Normalize

Element-wise: Abs, Neg, Sqrt, Reciprocal, Clamp

Activation functions: Sigmoid, ReLU, Tanh, Exp, ClampScale

Audio DSP: Interleave2, Deinterleave2, ConvolveValid, ConvolveValidMulti, ConvolveDecimate, AccumulateAdd, CumulativeSum, CubicInterpDot, Int32ToFloat32Scale, Int16ToFloat32Scale, Float32ToInt16Scale

Integer DSP (i32): Interleave2, Deinterleave2, Add, Sub, MidSideEncode, MidSideDecode, Diff1..Diff4, Restore1..Restore4, LPCResidualEncode, LPCRestore, RiceSums, RiceBestParam

Complex (c128): Add, Sub, Mul, MulConj, Conj, Abs, AbsSq, Scale

Design Principles ¶

No CGO: Pure Go assembly for easy cross-compilation
Zero allocations: All operations work on pre-allocated slices
Thread-safe: All functions are safe for concurrent use
Safe defaults: Graceful fallback to pure Go on unsupported CPUs

Source Files ¶

View all Source files

doc.go

Directories ¶

Path	Synopsis
c128 Package c128 provides SIMD-accelerated operations on complex128 slices.	Package c128 provides SIMD-accelerated operations on complex128 slices.
c64 Package c64 provides SIMD-accelerated operations on complex64 slices.	Package c64 provides SIMD-accelerated operations on complex64 slices.
cpu Package cpu provides CPU feature detection for SIMD operations.	Package cpu provides CPU feature detection for SIMD operations.
f16 Package f16 provides SIMD-accelerated operations on float16 (half-precision) slices.	Package f16 provides SIMD-accelerated operations on float16 (half-precision) slices.
f32 Package f32 provides SIMD-accelerated operations on float32 slices.	Package f32 provides SIMD-accelerated operations on float32 slices.
f64 Package f64 provides SIMD-accelerated operations on float64 slices.	Package f64 provides SIMD-accelerated operations on float64 slices.
i16 Package i16 provides SIMD-accelerated operations on int16 slices.	Package i16 provides SIMD-accelerated operations on int16 slices.
i32 Package i32 provides SIMD-accelerated operations on int32 slices.	Package i32 provides SIMD-accelerated operations on int32 slices.
internal
asmencoding Package asmencoding validates hand-encoded ARM64 WORD directives against the instruction described in their comment.	Package asmencoding validates hand-encoded ARM64 WORD directives against the instruction described in their comment.

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README ¶

simd

Features

Installation

Quick Start

Packages

cpu - CPU Feature Detection

f64 - float64 Operations

f32 - float32 Operations

f16 - float16 (Half-Precision) Operations

c128 - complex128 Operations

c64 - complex64 Operations

i32 - int32 Operations

i16 - int16 Operations

Performance

AMD64 (Intel Core i7-1260P, AVX+FMA)

float64 Operations - SIMD vs Pure Go (1024 elements)

float32 Operations - SIMD vs Pure Go (1024 elements)

Activation Functions - SIMD vs Pure Go

Batch & Signal Processing (varied sizes)

ConvolveDecimate (fused strided convolution)

Performance Summary

ARM64 (Raspberry Pi 5, NEON)

float64 Operations

float32 Operations

Comparison vs Pure Go

int32 (i32) - SIMD vs Pure Go (1000 elements)

int16 (i16) - SIMD vs Pure Go (1000 elements)

Performance Notes

Known Limitations

Small Slice Fallback for Min/Max (AMD64)

Architecture Support

Design Principles

Testing

Contributing

License

Documentation ¶

Overview ¶

Architecture Support ¶

Quick Start ¶

Available Operations ¶

Design Principles ¶

Source Files ¶

Directories ¶

`cpu` - CPU Feature Detection

`f64` - float64 Operations

`f32` - float32 Operations

`f16` - float16 (Half-Precision) Operations

`c128` - complex128 Operations

`c64` - complex64 Operations

`i32` - int32 Operations

`i16` - int16 Operations