### Symmetric FIR Filter Example using AIE API

Source: https://context7.com/xilinx/aie_api/llms.txt

Illustrates a symmetric FIR filter implementation leveraging coefficient symmetry with `aie::sliding_mul_sym_ops`. This optimized version requires only half the coefficients and automatically applies symmetry during the multiply-accumulate operation. It requires the same AIE API headers as the standard FIR filter.

```cpp
// Symmetric FIR filter (exploits coefficient symmetry)
void symmetric_fir_example() {
    constexpr unsigned Lanes = 8;
    constexpr unsigned Points = 16;  // Total filter length

    using SymMul = aie::sliding_mul_sym_ops<Lanes, Points, 1, 1, 1, int16, int16, acc48>;

    aie::vector<int16, Points/2> coeffs;  // Only half coefficients needed
    aie::vector<int16, 32> data;

    // Symmetric multiply automatically uses coefficient symmetry
    aie::accum<acc48, Lanes> acc = SymMul::mul_sym(coeffs, 0, data, 0);
}
```

--------------------------------

### Sliding Multiply FIR Filter Example using AIE API

Source: https://context7.com/xilinx/aie_api/llms.txt

Demonstrates a standard FIR filter implementation using `aie::sliding_mul_ops`. It configures the operation with specified lanes, filter points, and data types, then performs a multiply-accumulate operation and converts the result to an output vector. Dependencies include the `<aie_api/aie.hpp>` and `<aie_api/sliding_mul.hpp>` headers.

```cpp
#include <aie_api/aie.hpp>
#include <aie_api/sliding_mul.hpp>

void sliding_mul_fir_example() {
    // FIR filter configuration
    constexpr unsigned Lanes = 8;     // Output samples per operation
    constexpr unsigned Points = 8;    // Filter taps
    constexpr unsigned CoeffStep = 1;
    constexpr unsigned DataStepX = 1;
    constexpr unsigned DataStepY = 1;

    using SlidingMul = aie::sliding_mul_ops<Lanes, Points, CoeffStep, DataStepX, DataStepY,
                                            int16, int16, acc48>;

    // Coefficients (filter taps)
    aie::vector<int16, 8> coeffs;

    // Input data (must be larger than output + filter length - 1)
    aie::vector<int16, 16> data;

    // Perform sliding multiply
    aie::accum<acc48, Lanes> acc = SlidingMul::mul(coeffs, /*coeff_start=*/0,
                                                    data, /*data_start=*/0);

    // Convert to output
    aie::vector<int16, Lanes> output = acc.to_vector<int16>(15);

    // Multiply-accumulate variant
    aie::accum<acc48, Lanes> acc2 = SlidingMul::mac(acc, coeffs, 0, data, 0);
}
```

--------------------------------

### Basic Matrix Multiplication with aie::mmul in C++

Source: https://context7.com/xilinx/aie_api/llms.txt

Demonstrates basic matrix multiplication (C = A * B) and multiply-accumulate (C += A * B) using the aie::mmul class template. It shows how to define matrix dimensions, initialize matrices as vectors, perform the operations, and retrieve results. Requires the `<aie_api/aie.hpp>` header.

```cpp
#include <aie_api/aie.hpp>

void matrix_multiplication_basic() {
    // Define matrix multiplication: 4x4 x 4x4 = 4x4 with int16 elements
    using MMUL = aie::mmul<4, 4, 4, int16, int16>;

    // Matrices stored as vectors (row-major)
    aie::vector<int16, MMUL::size_A> A;  // 4x4 = 16 elements
    aie::vector<int16, MMUL::size_B> B;  // 4x4 = 16 elements

    // Create mmul object and perform multiplication
    MMUL mmul;
    mmul.mul(A, B);  // C = A * B

    // Get result as vector
    aie::vector<int16, MMUL::size_C> C = mmul.to_vector<int16>(0);

    // Multiply-accumulate: C += A * B
    mmul.mac(A, B);

    // Get result as accumulator
    auto acc = mmul.to_accum();
}
```

--------------------------------

### Tensor Buffer Stream for Multi-dimensional Memory Access (C++)

Source: https://context7.com/xilinx/aie_api/llms.txt

Demonstrates creating and using tensor buffer streams for multi-dimensional addressing in AIE-ML/XDNA. It covers creating tensor descriptors and reading data in patterns suitable for operations like GEMM.

```cpp
#include <aie_api/aie.hpp>

void tensor_buffer_stream_example() {
    alignas(aie::vector_decl_align) int16 buffer[256];

    // Create tensor descriptor for 3D access
    // Parameters: tensor_dim(size, step)
    auto desc = aie::make_tensor_descriptor<int16, 32>(
        aie::tensor_dim(2u, 4),   // Dim 0: 2 iterations, step 4
        aie::tensor_dim(2u, 2),   // Dim 1: 2 iterations, step 2
        aie::tensor_dim(2u, 1)    // Dim 2: 2 iterations, step 1
    );

    // Create tensor buffer stream
    auto tbs = aie::make_tensor_buffer_stream(buffer, desc);

    // Read vectors following tensor pattern
    for (unsigned i = 0; i < 8; ++i) {
        aie::vector<int16, 32> v;
        tbs >> v;  // Or: auto v = tbs.pop();
    }

    // GEMM-style tensor access for matrix multiplication
    // A: M x K matrix, B: K x N matrix
    constexpr unsigned M = 32, K = 64, N = 32;
    alignas(aie::vector_decl_align) int16 A[M * K];
    alignas(aie::vector_decl_align) int16 B[K * N];

    auto desc_A = aie::make_tensor_descriptor<int16, 32>(
        aie::tensor_dim(K / 4, 4),   // K dimension
        aie::tensor_dim(M / 4, K)    // M dimension
    );

    auto desc_B = aie::make_tensor_descriptor<int16, 32>(
        aie::tensor_dim(N / 4, 4),   // N dimension
        aie::tensor_dim(K / 4, N)    // K dimension
    );

    auto stream_A = aie::make_tensor_buffer_stream(A, desc_A);
    auto stream_B = aie::make_tensor_buffer_stream(B, desc_B);
}

```

--------------------------------

### bfloat16 Matrix Multiplication with aie::mmul in C++

Source: https://context7.com/xilinx/aie_api/llms.txt

Shows how to perform matrix multiplication using the bfloat16 data type with the aie::mmul class template. This is relevant for AI/ML workloads on AIE-ML/XDNA architectures. Requires the `<aie_api/aie.hpp>` header.

```cpp
#include <aie_api/aie.hpp>

void matrix_multiplication_bfloat16() {
    // bfloat16 matrix multiplication (AIE-ML/XDNA)
    using MMUL_BF16 = aie::mmul<4, 8, 4, bfloat16, bfloat16>;

    aie::vector<bfloat16, MMUL_BF16::size_A> A;
    aie::vector<bfloat16, MMUL_BF16::size_B> B;

    MMUL_BF16 mmul;
    mmul.mul(A, B);

    aie::vector<bfloat16, MMUL_BF16::size_C> C = mmul.to_vector<bfloat16>();
}
```

--------------------------------

### Parallel and Linear Approximation Lookup Tables (C++)

Source: https://context7.com/xilinx/aie_api/llms.txt

Illustrates hardware-accelerated lookup table operations using the AIE API, including parallel lookups with interleaved data and linear approximation for non-linear functions. Requires specific data layout for parallel access.

```cpp
#include <aie_api/aie.hpp>

void lookup_table_example() {
    // Parallel lookup requires specially laid out data
    // For 4 parallel accesses: data must be duplicated and interleaved
    constexpr unsigned LUT_SIZE = 256;
    alignas(aie::vector_decl_align) int32 lut_ab[LUT_SIZE * 2];  // Bank A+B interleaved
    alignas(aie::vector_decl_align) int32 lut_cd[LUT_SIZE * 2];  // Bank C+D interleaved

    // Create LUT object
    aie::lut<4, int32> my_lut(LUT_SIZE, lut_ab, lut_cd);

    // Parallel lookup
    aie::parallel_lookup<int8, aie::lut<4, int32>> lookup(my_lut,
                                                           /*step_bits=*/0,
                                                           /*bias=*/128);

    // Perform lookup
    alignas(aie::vector_decl_align) int8 indices[32];
    alignas(aie::vector_decl_align) int32 results[32];

    auto it_in  = aie::begin_vector<32>(indices);
    auto it_out = aie::begin_vector<32>(results);

    *it_out = lookup.fetch(*it_in);

    // Linear approximation for non-linear functions
    // Requires offset and slope tables
    alignas(aie::vector_decl_align) int16 offset_ab[LUT_SIZE * 2];
    alignas(aie::vector_decl_align) int16 offset_cd[LUT_SIZE * 2];
    alignas(aie::vector_decl_align) int16 slope_ab[LUT_SIZE * 2];
    alignas(aie::vector_decl_align) int16 slope_cd[LUT_SIZE * 2];

    aie::lut<4, int16, int16> approx_lut(LUT_SIZE,
                                          offset_ab, offset_cd,
                                          slope_ab, slope_cd);

    aie::linear_approx<int8, aie::lut<4, int16, int16>> lin_approx(
        approx_lut,
        /*step_bits=*/4,
        /*bias=*/128,
        /*shift_offset=*/8
    );

    auto acc_result = lin_approx.compute(*it_in);
    aie::vector<int16, 32> approx_result = acc_result.to_vector<int16>(/*shift=*/8);
}

```

--------------------------------

### Blocked Matrix Multiplication with aie::mmul in C++

Source: https://context7.com/xilinx/aie_api/llms.txt

Implements blocked (tiled) General Matrix Multiplication (GEMM) using the aie::mmul class. This approach is suitable for larger matrices by processing them in smaller tiles. It utilizes `aie::load_v` and `aie::store_v` for data loading and storing, assuming pre-tiled data. Requires the `<aie_api/aie.hpp>` header.

```cpp
#include <aie_api/aie.hpp>

void matrix_multiplication_blocked() {
    // Blocked GEMM example: C[M,N] = A[M,K] * B[K,N]
    constexpr unsigned M = 4, K = 4, N = 4;
    using MMUL = aie::mmul<M, K, N, int16, int16>;

    // Tiled matrix pointers (pre-tiled data expected)
    const int16 *pA;  // Size: rowA * colA * MMUL::size_A
    const int16 *pB;  // Size: colA * colB * MMUL::size_B
    int16 *pC;        // Size: rowA * colB * MMUL::size_C

    unsigned rowA = 2, colA = 3, colB = 2;  // Number of tiles

    for (unsigned i = 0; i < rowA; ++i) {
        for (unsigned j = 0; j < colB; ++j) {
            MMUL C_tile;

            for (unsigned k = 0; k < colA; ++k) {
                auto A_tile = aie::load_v<MMUL::size_A>(pA + (i * colA + k) * MMUL::size_A);
                auto B_tile = aie::load_v<MMUL::size_B>(pB + (k * colB + j) * MMUL::size_B);

                if (k == 0)
                    C_tile.mul(A_tile, B_tile);
                else
                    C_tile.mac(A_tile, B_tile);
            }

            aie::store_v(pC + (i * colB + j) * MMUL::size_C, C_tile.to_vector<int16>(0));
        }
    }
}
```

--------------------------------

### Multiplication and Multiply-Accumulate Operations with mul / mac

Source: https://context7.com/xilinx/aie_api/llms.txt

Provides functions for vector multiplication, returning accumulators with extended precision. Supports specifying accumulation precision (e.g., `acc64`) and scalar multiplication. Includes multiply-accumulate (`mac`), multiply-subtract (`msc`), and negative multiply operations. Results can be converted back to vectors with optional right-shifting.

```cpp
#include <aie_api/aie.hpp>

void arithmetic_mul() {
    aie::vector<int16, 16> a, b;

    // Multiply: returns accumulator (uses default accumulation precision)
    auto acc = aie::mul(a, b);  // Returns aie::accum<acc48, 16> for int16 x int16

    // Specify accumulation precision
    auto acc64 = aie::mul<acc64>(a, b);  // Force 64-bit accumulation

    // Vector x Scalar multiplication
    auto acc_scalar = aie::mul(a, int16(10));

    // Multiply-accumulate: acc = acc + (a * b)
    aie::accum<acc48, 16> acc_init;
    auto acc_mac = aie::mac(acc_init, a, b);

    // Multiply-subtract: acc = acc - (a * b)
    auto acc_msc = aie::msc(acc_init, a, b);

    // Negative multiply-accumulate: acc = -acc + (a * b)
    auto acc_negmac = aie::negmul(a, b);  // Equivalent to -mul(a, b)

    // Convert result to vector
    aie::vector<int16, 16> result = acc.to_vector<int16>(15);  // Shift right by 15

    // Element-wise multiplication (returns vector, not accumulator)
    aie::vector<float, 8> f1, f2;
    aie::accum<accfloat, 8> fp_acc = aie::mul(f1, f2);
    aie::vector<float, 8> fp_result = fp_acc.to_vector<float>();
}
```

--------------------------------

### Aligned Memory Access with load_v / store_v

Source: https://context7.com/xilinx/aie_api/llms.txt

Functions for loading and storing vectors from/to memory with strict alignment requirements. The buffer must be declared with `alignas(aie::vector_decl_align)` and pointers used with `load_v` and `store_v` must be aligned to the vector size. Supports explicit sizing and auto-sizing based on architecture.

```cpp
#include <aie_api/aie.hpp>

void memory_aligned_access() {
    // Aligned buffer declaration (required for vector load/store)
    alignas(aie::vector_decl_align) int16 buffer[64];

    // Aligned load - pointer must be aligned to vector size
    aie::vector<int16, 16> v1 = aie::load_v<16>(buffer);      // Load 16 elements
    aie::vector<int16, 32> v2 = aie::load_v<32>(buffer);      // Load 32 elements

    // Auto-sized load (uses optimal size for architecture)
    auto v_auto = aie::load_v(buffer);

    // Aligned store
    aie::store_v(buffer, v1);
    aie::store_v(buffer + 16, v2);

    // Example: copy aligned data
    alignas(aie::vector_decl_align) int32 src[128];
    alignas(aie::vector_decl_align) int32 dst[128];

    for (unsigned i = 0; i < 128; i += 8) {
        aie::vector<int32, 8> v = aie::load_v<8>(src + i);
        aie::store_v(dst + i, v);
    }
}
```

--------------------------------

### Vector Operations with aie::vector

Source: https://context7.com/xilinx/aie_api/llms.txt

Demonstrates the usage of the `aie::vector` class for SIMD operations. This class represents a collection of elements mapped to vector registers and supports various operations like initialization, element access, subvector extraction/insertion, concatenation, broadcasting, zero initialization, casting, packing, and unpacking. It is fundamental for performing parallel computations on AI Engine architectures.

```cpp
#include <aie_api/aie.hpp>

void vector_operations() {
    // Declare a 32-element int16 vector (512 bits)
    aie::vector<int16, 32> v1;

    // Initialize from values
    aie::vector<int16, 8> v2(1, 2, 3, 4, 5, 6, 7, 8);

    // Element access
    v1.set(42, 0);           // Set element at index 0
    int16 val = v1.get(0);   // Get element at index 0
    v1[1] = 100;             // Operator[] access

    // Extract subvector (elements 0-7)
    aie::vector<int16, 8> sub = v1.extract<8>(0);

    // Insert subvector at position 1 (elements 8-15)
    v1.insert(1, v2);

    // Concatenate two vectors
    aie::vector<int16, 16> concat_v = aie::concat(v2, v2);

    // Broadcast scalar to all elements
    aie::vector<int32, 8> broadcast_v = aie::broadcast<int32, 8>(42);

    // Zero-initialized vector
    aie::vector<float, 16> zeros_v = aie::zeros<float, 16>();

    // Cast vector to different element type (same total bits)
    aie::vector<int32, 16> v_int32 = v1.cast_to<int32>();

    // Pack to smaller type / unpack to larger type
    aie::vector<int8, 32> packed = v1.pack<int8>();
    aie::vector<int32, 32> unpacked = v1.unpack<int32>();
}
```

--------------------------------

### Absolute Value and Negation with abs / neg

Source: https://context7.com/xilinx/aie_api/llms.txt

Provides functions to compute the absolute value and negation of vector elements. `aie::abs` computes the absolute value, while `aie::neg` computes the negation. Also includes `aie::abs_square` for calculating the square of the absolute value of complex numbers.

```cpp
#include <aie_api/aie.hpp>

void arithmetic_abs_neg() {
    aie::vector<int16, 16> v;

    // Absolute value
    aie::vector<int16, 16> v_abs = aie::abs(v);

    // Negation
    aie::vector<int16, 16> v_neg = aie::neg(v);

    // Square of absolute value (for complex)
    aie::vector<cint16, 8> cv;
    aie::accum<acc48, 8> cv_abs_sq = aie::abs_square(cv);
}
```

--------------------------------

### Mask Operations with aie::mask

Source: https://context7.com/xilinx/aie_api/llms.txt

Details the functionality of the `aie::mask` class, which stores the results of comparison operations. It supports standard comparison operators (`lt`, `gt`, `eq`, `neq`, `le`, `ge`), initialization from integer types, bitwise operations (`&`, `|`, `^`, `~`), checking if all or any elements meet a condition, and usage with the `select` operation for conditional element selection.

```cpp
#include <aie_api/aie.hpp>

void mask_operations() {
    aie::vector<int16, 16> a, b;

    // Comparison operations return masks
    aie::mask<16> m_lt = aie::lt(a, b);   // a[i] < b[i]
    aie::mask<16> m_gt = aie::gt(a, b);   // a[i] > b[i]
    aie::mask<16> m_eq = aie::eq(a, b);   // a[i] == b[i]
    aie::mask<16> m_ne = aie::neq(a, b);  // a[i] != b[i]
    aie::mask<16> m_le = aie::le(a, b);   // a[i] <= b[i]
    aie::mask<16> m_ge = aie::ge(a, b);   // a[i] >= b[i]

    // Initialize mask from constant
    auto m1 = aie::mask<64>::from_uint64(0xAAAABBBBCCCCDDDDULL);
    auto m2 = aie::mask<16>::from_uint32(0b1010101010101010);

    // Bitwise operations on masks
    aie::mask<16> m_and = m_lt & m_gt;
    aie::mask<16> m_or  = m_lt | m_gt;
    aie::mask<16> m_xor = m_lt ^ m_gt;
    aie::mask<16> m_not = ~m_lt;

    // Check all/any elements
    bool all_true = aie::equal(a, a);      // Returns true if all elements equal
    bool any_diff = aie::not_equal(a, b);  // Returns true if any element differs

    // Use mask with select operation
    aie::vector<int16, 16> selected = aie::select(a, b, m_lt);  // m[i]==0 ? a[i] : b[i]
}
```

--------------------------------

### Accumulator Operations with aie::accum

Source: https://context7.com/xilinx/aie_api/llms.txt

Illustrates the use of the `aie::accum` class for accumulator operations. This class provides extended precision (32-80 bits) for storing multiplication results and performing reduction operations. It supports initialization from vectors, conversion to vectors with downshifting, sub-accumulator extraction, growing to larger accumulators, and can be used with free functions for conversion.

```cpp
#include <aie_api/aie.hpp>

void accumulator_operations() {
    // Declare 16-element 48-bit accumulator
    aie::accum<acc48, 16> acc1;

    // Initialize from vector with optional upshift
    aie::vector<int16, 16> v;
    aie::accum<acc48, 16> acc2(v, 0);  // shift = 0

    // Alternative initialization
    acc1.from_vector(v, 4);  // upshift by 4 bits

    // Convert accumulator to vector with downshift
    aie::vector<int16, 16> result = acc1.to_vector<int16>(8);  // downshift by 8 bits

    // For floating-point accumulators
    aie::accum<accfloat, 8> fp_acc;
    aie::vector<float, 8> fp_result = fp_acc.to_vector<float>();

    // Extract sub-accumulator
    aie::accum<acc48, 8> sub_acc = acc1.extract<8>(0);

    // Grow to larger accumulator
    aie::accum<acc48, 32> large_acc = acc1.grow<32>();

    // Using from_vector free function
    aie::accum<acc64, 16> acc3 = aie::from_vector<acc64>(v, 0);

    // Using to_vector free function
    aie::vector<int32, 16> vec_out = aie::to_vector<int32>(acc3, 15);
}
```

--------------------------------

### Unaligned Memory Access with load_unaligned_v / store_unaligned_v

Source: https://context7.com/xilinx/aie_api/llms.txt

Functions designed for memory access when pointer alignment is not guaranteed. These functions allow specifying alignment and offset, providing flexibility for unaligned data. `load_floor_v` is also available to align pointers down to the nearest boundary before loading.

```cpp
#include <aie_api/aie.hpp>

void memory_unaligned_access() {
    int16 buffer[100];  // May not be aligned

    // Unaligned load - specify alignment in elements
    aie::vector<int16, 16> v1 = aie::load_unaligned_v<16>(buffer, 1);      // 1-element aligned
    aie::vector<int16, 16> v2 = aie::load_unaligned_v<16>(buffer + 3, 1);  // Offset by 3

    // Unaligned store
    aie::store_unaligned_v<16>(buffer + 5, v1, 1);

    // Floor-aligned load (aligns pointer down to boundary before loading)
    alignas(aie::vector_decl_align) int16 data[32] = {0, 1, 2, 3, /*...*/};
    int16 *ptr = &data[3];  // Not aligned to 16 elements

    // Load from floor-aligned address
    aie::vector<int16, 16> v_floor = aie::load_floor_v<16>(ptr, 16);
    // v_floor contains data[0..15] (floored to 16-element boundary)
}
```

--------------------------------

### Element-wise Addition and Subtraction with add / sub

Source: https://context7.com/xilinx/aie_api/llms.txt

Performs element-wise addition and subtraction operations on vectors. Supports operations between two vectors, a vector and a scalar, or a scalar and a vector. Includes saturating arithmetic options that clamp results to the type's range and accumulator addition.

```cpp
#include <aie_api/aie.hpp>

void arithmetic_add_sub() {
    aie::vector<int16, 16> a, b;

    // Vector + Vector
    aie::vector<int16, 16> sum = aie::add(a, b);
    aie::vector<int16, 16> diff = aie::sub(a, b);

    // Vector + Scalar
    aie::vector<int16, 16> sum_scalar = aie::add(a, int16(10));
    aie::vector<int16, 16> diff_scalar = aie::sub(a, int16(5));

    // Scalar + Vector
    aie::vector<int16, 16> sum2 = aie::add(int16(10), b);

    // Saturating arithmetic (clamps to type range)
    aie::vector<int16, 16> sat_sum = aie::saturating_add(a, b);
    aie::vector<int16, 16> sat_diff = aie::saturating_sub(a, b);

    // Accumulator addition
    aie::accum<acc48, 16> acc_a, acc_b;
    aie::accum<acc48, 16> acc_sum = aie::add(acc_a, acc_b);
}
```

--------------------------------

### Vector Shuffling: shuffle_up, shuffle_down, reverse, filter

Source: https://context7.com/xilinx/aie_api/llms.txt

Reorders elements within a vector using various shuffle modes including shifts, rotations, fills, replication, and reversal. Also includes filtering of even/odd elements. Requires the `<aie_api/aie.hpp>` header.

```cpp
#include <aie_api/aie.hpp>

void reshaping_shuffle() {
    aie::vector<int16, 16> v;

    // Shift elements up (new elements undefined)
    aie::vector<int16, 16> v_up = aie::shuffle_up(v, 4);

    // Shift elements down
    aie::vector<int16, 16> v_down = aie::shuffle_down(v, 4);

    // Rotate elements (wrap around)
    aie::vector<int16, 16> v_rot_up = aie::shuffle_up_rotate(v, 4);
    aie::vector<int16, 16> v_rot_down = aie::shuffle_down_rotate(v, 4);

    // Fill with elements from another vector
    aie::vector<int16, 16> fill_v;
    aie::vector<int16, 16> v_fill = aie::shuffle_up_fill(v, fill_v, 4);

    // Replicate first element while shifting
    aie::vector<int16, 16> v_repl = aie::shuffle_up_replicate(v, 4);

    // Reverse vector order
    aie::vector<int16, 16> v_rev = aie::reverse(v);

    // Filter even/odd elements
    aie::vector<int16, 8> v_even = aie::filter_even(v, 1);
    aie::vector<int16, 8> v_odd = aie::filter_odd(v, 1);
}
```

--------------------------------

### Vector Reductions: reduce_add, reduce_max, reduce_min

Source: https://context7.com/xilinx/aie_api/llms.txt

Performs reduction operations on vectors to compute a single scalar value. Supports integer and floating-point vectors, as well as accumulators. Requires the `<aie_api/aie.hpp>` header.

```cpp
#include <aie_api/aie.hpp>

void reduction_operations() {
    aie::vector<int16, 32> v;

    // Sum all elements
    int16 sum = aie::reduce_add(v);

    // Find maximum element
    int16 max_val = aie::reduce_max(v);

    // Find minimum element
    int16 min_val = aie::reduce_min(v);

    // For floating point
    aie::vector<float, 16> fv;
    float f_sum = aie::reduce_add(fv);
    float f_max = aie::reduce_max(fv);
    float f_min = aie::reduce_min(fv);

    // Accumulator reduction
    aie::accum<acc48, 16> acc;
    auto reduced_acc = aie::reduce_add(acc);
}
```

--------------------------------

### Interleaving Operations: interleave_zip, interleave_unzip

Source: https://context7.com/xilinx/aie_api/llms.txt

Interleaves or deinterleaves elements between two vectors. The 'step' parameter controls the granularity of the interleaving. Requires the `<aie_api/aie.hpp>` header.

```cpp
#include <aie_api/aie.hpp>

void reshaping_interleave() {
    aie::vector<int16, 16> even = {0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30};
    aie::vector<int16, 16> odd  = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31};

    // Interleave (zip) - combine alternating elements
    auto [lo, hi] = aie::interleave_zip(even, odd, 1);
    // lo = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}
    // hi = {16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31}

    // Deinterleave (unzip) - separate alternating elements
    aie::vector<int16, 16> mixed = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15};
    auto [evens, odds] = aie::interleave_unzip(mixed, mixed, 1);

    // Step parameter controls granularity
    auto [zip_lo2, zip_hi2] = aie::interleave_zip(even, odd, 2);  // Zip pairs
    auto [zip_lo4, zip_hi4] = aie::interleave_zip(even, odd, 4);  // Zip quads
}
```

--------------------------------

### Vector Iterators for Memory Access - C++

Source: https://context7.com/xilinx/aie_api/llms.txt

Provides iterators for sequential and circular access to memory buffers as vectors. Supports various access modes including restricted and unaligned access, enabling efficient data processing with Xilinx AIE vector types.

```cpp
#include <aie_api/aie.hpp>

void iterator_operations() {
    alignas(aie::vector_decl_align) int16 buffer[128];

    // Basic vector iterator
    auto it = aie::begin_vector<16>(buffer);
    auto it_end = aie::end_vector<16>(buffer);

    // Read vectors sequentially
    while (it != it_end) {
        aie::vector<int16, 16> v = *it++;
        // Process v...
    }

    // Random access
    auto it_rand = aie::begin_vector<16>(buffer);
    aie::vector<int16, 16> v0 = it_rand[0];  // First vector
    aie::vector<int16, 16> v2 = it_rand[2];  // Third vector
    it_rand += 3;  // Advance by 3 vectors

    // Circular iterator (wraps around)
    auto it_circ = aie::begin_vector_circular<16, 64>(buffer);  // 64-element circular buffer
    for (int i = 0; i < 10; ++i) {
        aie::vector<int16, 16> v = *it_circ++;  // Wraps after 4 vectors (64/16)
    }

    // Restrict iterator (allows compiler optimization)
    auto it_restrict = aie::begin_restrict_vector<16>(buffer);

    // Unaligned iterator
    auto it_unaligned = aie::begin_unaligned_vector<16>(buffer + 3);

    // Writing with iterators
    auto out_it = aie::begin_vector<16>(buffer);
    aie::vector<int16, 16> data = aie::broadcast<int16, 16>(42);
    *out_it++ = data;
}

```

--------------------------------

### Matrix Transpose: transpose

Source: https://context7.com/xilinx/aie_api/llms.txt

Transposes elements of a vector, treating it as a matrix. The function takes the vector and its dimensions (rows, columns) as arguments. Requires the `<aie_api/aie.hpp>` header.

```cpp
#include <aie_api/aie.hpp>

void reshaping_transpose() {
    // Transpose a 4x4 matrix stored as vector
    aie::vector<int32, 16> matrix;  // 4x4 matrix in row-major order

    // Transpose: Row/Col = 4
    aie::vector<int32, 16> transposed = aie::transpose(matrix, 4, 4);

    // Transpose 2x8 -> 8x2
    aie::vector<int16, 16> m2x8;
    aie::vector<int16, 16> m8x2 = aie::transpose(m2x8, 2, 8);
}
```

--------------------------------

### FFT Stage Functions (Radix-2 and Mixed Radix) - C++

Source: https://context7.com/xilinx/aie_api/llms.txt

Implements decimation-in-time FFTs using radix-2 and mixed radix-4 stages. These functions require specific twiddle factor arrays and shift parameters for computation. They are designed for use within the Xilinx AIE environment.

```cpp
#include <aie_api/aie.hpp>
#include <aie_api/fft.hpp>

// 1024-point FFT using radix-2 stages
void fft_1024pt(const cint16 *x, cint16 *y, cint16 *tmp,
                const cint16 *tw1, const cint16 *tw2, const cint16 *tw4,
                const cint16 *tw8, const cint16 *tw16, const cint16 *tw32,
                const cint16 *tw64, const cint16 *tw128, const cint16 *tw256,
                const cint16 *tw512,
                unsigned shift_tw, unsigned shift, bool inv)
{
    constexpr unsigned N = 1024;

    // Each stage: fft_dit_r2_stage<Vectorization>(in, twiddles, N, shift_tw, shift, inv, out)
    aie::fft_dit_r2_stage<512>(x,   tw1,   N, shift_tw, shift, inv, tmp);
    aie::fft_dit_r2_stage<256>(tmp, tw2,   N, shift_tw, shift, inv, y);
    aie::fft_dit_r2_stage<128>(y,   tw4,   N, shift_tw, shift, inv, tmp);
    aie::fft_dit_r2_stage<64> (tmp, tw8,   N, shift_tw, shift, inv, y);
    aie::fft_dit_r2_stage<32> (y,   tw16,  N, shift_tw, shift, inv, tmp);
    aie::fft_dit_r2_stage<16> (tmp, tw32,  N, shift_tw, shift, inv, y);
    aie::fft_dit_r2_stage<8>  (y,   tw64,  N, shift_tw, shift, inv, tmp);
    aie::fft_dit_r2_stage<4>  (tmp, tw128, N, shift_tw, shift, inv, y);
    aie::fft_dit_r2_stage<2>  (y,   tw256, N, shift_tw, shift, inv, tmp);
    aie::fft_dit_r2_stage<1>  (tmp, tw512, N, shift_tw, shift, inv, y);
}

// 512-point FFT using mixed radix-2 and radix-4 stages
void fft_512pt(const cint16 *x, cint16 *y, cint16 *tmp,
               const cint16 *tw1, const cint16 *tw2, const cint16 *tw4, const cint16 *tw2_4,
               const cint16 *tw8, const cint16 *tw16, const cint16 *tw8_16,
               const cint16 *tw32, const cint16 *tw64, const cint16 *tw32_64,
               const cint16 *tw128, const cint16 *tw256, const cint16 *tw128_256,
               unsigned shift_tw, unsigned shift, bool inv)
{
    constexpr unsigned N = 512;

    // Radix-2 first stage
    aie::fft_dit_r2_stage<256>(x, tw1, N, shift_tw, shift, inv, y);

    // Radix-4 stages (three twiddle pointers per stage)
    aie::fft_dit_r4_stage<64>(y,   tw2,   tw4,   tw2_4,     N, shift_tw, shift, inv, tmp);
    aie::fft_dit_r4_stage<16>(tmp, tw8,   tw16,  tw8_16,    N, shift_tw, shift, inv, y);
    aie::fft_dit_r4_stage<4> (y,   tw32,  tw64,  tw32_64,   N, shift_tw, shift, inv, tmp);
    aie::fft_dit_r4_stage<1> (tmp, tw128, tw256, tw128_256, N, shift_tw, shift, inv, y);
}

// Twiddle factor generation (conceptual - run on host)
void generate_twiddles_r2(cint16 *tw, unsigned n_stage, unsigned shift_tw) {
    // tw[i] = exp(-2j * pi * i / n_stage) * (1 << shift_tw)
    for (unsigned i = 0; i < n_stage / 2; ++i) {
        float angle = -2.0f * M_PI * i / n_stage;
        tw[i].real = (int16)(cos(angle) * (1 << shift_tw));
        tw[i].imag = (int16)(sin(angle) * (1 << shift_tw));
    }
}

```

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