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Prompt: make a 3d convolution code for GPU using PTX

< Thought for 285 seconds >

<think>
Okay, I need to write a 3D convolution code for a GPU using PTX. Hmm, where do I start? Let me recall what I know about convolution and GPU programming.

First, 3D convolution involves sliding a kernel over a 3D input volume. Each element in the output is computed by multiplying the kernel with the corresponding input elements and summing the results. For GPUs, this can be parallelized by assigning each output element to a thread.

But wait, the user wants this done using PTX. PTX is the intermediate representation used in NVIDIA GPUs, right? So I'll have to write the kernel in PTX assembly instead of using CUDA C++. That's a bit lower level. I need to remember the PTX syntax and how to manage threads, memory, and registers there.

Let me outline the steps. First, I need to set up the input, kernel, and output tensors in GPU memory. Then, in the PTX code, each thread will compute one output element. The thread indices will determine which output element they're responsible for. For 3D convolution, each thread needs to iterate over the 3D kernel dimensions, multiply the input elements by the corresponding kernel values, and accumulate the sum.

But how do I map the thread indices to the 3D output? In CUDA, we usually have blockIdx, blockDim, and threadIdx for 3D grids and blocks. In PTX, I think we can use similar built-in registers like %ctaid (block index), %ntid (block dimensions), and %tid (thread index within the block). But combining these to get the global 3D index might be a bit tricky.

Wait, the output is 3D, so each thread's output is at (x, y, z). So the global indices would be computed based on the block and thread indices. For example, x = blockIdx.x * blockDim.x + threadIdx.x, and similarly for y and z. But in PTX, how do I get these values? Let me check PTX registers.

Yes, for 3D grids, there are %ctaid.x, %ctaid.y, %ctaid.z for block indices, and %tid.x, %tid.y, %tid.z for thread indices within the block. Also, %ntid.x, %ntid.y, %ntid.z give the dimensions of the block. So to compute the global index, each dimension is blockIdx * blockDim + threadIdx. So for x, it's %ctaid.x * %ntid.x + %tid.x, and similarly for y and z.

But wait, no. Because %ntid.x is the number of threads per block in x-dimension. So the global x index is %ctaid.x * %ntid.x + %tid.x. Correct. So in PTX, I need to compute the output coordinates based on these.

Once the output coordinates (o_x, o_y, o_z) are determined, the thread needs to compute the sum over the kernel's i, j, k indices. For each (i, j, k) in the kernel, the input coordinate is (o_x + i - pad_x, o_y + j - pad_y, o_z + k - pad_z), considering padding. Then, check if these coordinates are within the input bounds. If so, multiply the input value by the kernel value and accumulate.

But handling the input and kernel memory accesses is crucial. The input and kernel are in global memory, so we need to load their values into registers. Since each thread will be accessing multiple elements from the input and kernel, we need to compute their addresses correctly.

In PTX, to access global memory, we use ld.global.f32 instructions. So for each input element, compute the address based on the input coordinates, then load the value. Similarly for the kernel, compute the kernel index and load the kernel value.

But how are the tensors laid out in memory? Assuming they're in row-major order (C-style), so for a 3D tensor, the index is calculated as (z * height + y) * width + x. Wait, no, depends on the order. Let's say input is of dimensions (depth, height, width), then the linear index would be (z * input_height + y) * input_width + x. Similarly for kernel.

Wait, the input is 3D, so each element is addressed by (x, y, z). But the exact layout depends on how it's stored. Let's assume that the input is stored in x, y, z order, with x changing fastest. So the linear index would be z * (input_height * input_width) + y * input_width + x. Similarly for the kernel.

But the exact formula depends on the data layout. For this example, let's assume that the input is stored in width (x) as the fastest varying dimension, then height (y), then depth (z). So the linear index for input is z * (input_height * input_width) + y * input_width + x. Similarly for the kernel.

So for each input element at (x_in, y_in, z_in), the linear address is z_in * (input_height * input_width) + y_in * input_width + x_in. Multiply by the size of the data type (assuming float, 4 bytes).

But in PTX, when we compute addresses, we need to compute the byte offset and then cast it to a pointer. So for example, to get the address of input[z][y][x], it's base_address + (z * input_height * input_width + y * input_width + x) * 4.

Same for the kernel. Kernel is 3D as well, with dimensions (kernel_depth, kernel_height, kernel_width). The linear index would be kz * (kernel_height * kernel_width) + ky * kernel_width + kx.

Now, for each thread, compute the output coordinates (o_x, o_y, o_z). Then, for each kernel element (kx, ky, kz), compute the input coordinates:

i_x = o_x * stride_x + kx - pad_x;

i_y = o_y * stride_y + ky - pad_y;

i_z = o_z * stride_z + kz - pad_z;

Wait, wait. Wait, convolution parameters include stride and padding. The output coordinates (o_x, o_y, o_z) correspond to the position in the output tensor. The input coordinates are computed based on the output position, kernel index, stride, and padding.

Wait, the formula for input coordinates is:

input_x = o_x * stride_x - pad_x + kx;

input_y = o_y * stride_y - pad_y + ky;

input_z = o_z * stride_z - pad_z + kz;

Yes. So if the output is at (o_x, o_y, o_z), then for each kernel element (kx, ky, kz), the input element is at (o_x * stride_x + kx - pad_x, o_y * stride_y + ky - pad_y, o_z * stride_z + kz - pad_z). Then check if these input coordinates are within the input dimensions. If they are, multiply the input value by the kernel value and accumulate; otherwise, treat it as zero (assuming padding is zero).

So in PTX code, each thread will:

1. Calculate its output coordinates (o_x, o_y, o_z) based on its thread and block indices.

2. Check if these coordinates are within the output dimensions. If not, exit.

3. Initialize a sum register to zero.

4. Loop over kz, ky, kx in the kernel dimensions.

5. For each (kz, ky, kx), compute the input coordinates as above.

6. Check if the input coordinates are within the input boundaries. If yes, load input value and kernel value; otherwise, use zero.

7. Multiply input and kernel values, add to sum.

8. After processing all kernel elements, store the sum to the output tensor at (o_x, o_y, o_z).

Now, handling the loops in PTX. PTX doesn't have high-level loop constructs; we need to manage loops using labels and branches. So for each kernel dimension (depth, height, width), we'll need nested loops.

But writing nested loops in PTX can get complex. Let's see. For example, for kz from 0 to kernel_depth - 1:

// initialize kz to 0

// loop_kz:

//   if kz >= kernel_depth, exit loop

//   then do ky loop

//   increment kz and branch back

Similarly for ky and kx.

But in PTX, we have to manage the loop counters with registers and use branch instructions.

Another thing to consider is register usage. Each thread needs registers for o_x, o_y, o_z, kz, ky, kx, sum, input_val, kernel_val, and various temporary variables. Since PTX is a virtual ISA, the actual register allocation is done by the PTX compiler (ptxas), but we need to be careful not to use too many registers to avoid register spilling.

But in this case, the loops are manageable. Let's outline the PTX code structure.

First, declare the input, kernel, and output as .global .b8 pointers, and then cast them to .f32 arrays with the appropriate parameters. But in PTX, we can use .param space for kernel parameters.

Wait, how are the kernel parameters passed? In CUDA, when launching a kernel, the parameters are passed via the parameter space. So in PTX, we can access them using .param space variables.

So the kernel function in PTX will have parameters for the input, kernel, output pointers, and the sizes and convolution parameters (like input dimensions, kernel dimensions, padding, stride).

So the PTX code would start with something like:

.entry convolution_3d(

.param .b8 input_ptr,

.param .b8 kernel_ptr,

.param .b8 output_ptr,

.param .u32 input_width, .param .u32 input_height, .param .u32 input_depth,

.param .u32 kernel_width, .param .u32 kernel_height, .param .u32 kernel_depth,

.param .u32 pad_width, .param .u32 pad_height, .param .u32 pad_depth,

.param .u32 stride_width, .param .u32 stride_height, .param .u32 stride_depth,

.param .u32 output_width, .param .u32 output_height, .param .u32 output_depth

) {

// code here

}

But in PTX, the parameters are in the .param space, which is constant and accessed via ld.param instructions. So first, we need to load the parameters into registers.

For example:

ld.param.u32 %r_input_ptr, [input_ptr];

ld.param.u32 %r_kernel_ptr, [kernel_ptr];

ld.param.u32 %r_output_ptr, [output_ptr];

// and so on for all parameters.

But the parameters are passed as pointers to the input, kernel, and output arrays. So in PTX, we can load the base addresses into registers.

Once the parameters are loaded, compute the output coordinates.

Compute o_x, o_y, o_z:

For o_x:

%ctaid.x gives the block index in x-dimension.

%ntid.x gives the number of threads per block in x.

%tid.x gives the thread index within the block.

So o_x = %ctaid.x * %ntid.x + %tid.x;

Similarly for o_y and o_z. But wait, in 3D convolution, the output is 3D, so we need to map the 3D grid of threads to cover the entire output tensor. So the grid should be 3D as well. But CUDA allows 3D grids and blocks, so the PTX code should be written assuming that the kernel is launched with a 3D grid and 3D blocks.

But the user might not specify that. However, for a 3D convolution, it's logical to use a 3D grid and 3D blocks. So the code can assume that the grid is 3D, and each thread handles one output element.

But the code needs to check if the computed o_x, o_y, o_z are within the output dimensions. If the grid is larger than the output, some threads may be out of bounds and should do nothing.

So first, compute o_x, o_y, o_z:

// get block indices

mov.u32 %r_ctaid_x, %ctaid.x;

mov.u32 %r_ctaid_y, %ctaid.y;

mov.u32 %r_ctaid_z, %ctaid.z;

// get block dimensions

mov.u32 %r_ntid_x, %ntid.x;

mov.u32 %r_ntid_y, %ntid.y;

mov.u32 %r_ntid_z, %ntid.z;

// get thread indices

mov.u32 %r_tid_x, %tid.x;

mov.u32 %r_tid_y, %tid.y;

mov.u32 %r_tid_z, %tid.z;

// compute output coordinates

mul.lo.u32 %r_o_x, %r_ctaid_x, %r_ntid_x;

add.u32 %r_o_x, %r_o_x, %r_tid_x;

mul.lo.u32 %r_o_y, %r_ctaid_y, %r_ntid_y;

add.u32 %r_o_y, %r_o_y, %r_tid_y;

mul.lo.u32 %r_o_z, %r_ctaid_z, %r_ntid_z;

add.u32 %r_o_z, %r_o_z, %r_tid_z;

Then compare these with output dimensions:

// check if o_x >= output_width or o_y >= output_height or o_z >= output_depth

// if any is true, exit

ld.param.u32 %r_output_width, [output_width];

ld.param.u32 %r_output_height, [output_height];

ld.param.u32 %r_output_depth, [output_depth];

setp.ge.u32 %p1, %r_o_x, %r_output_width;

setp.ge.u32 %p2, %r_o_y, %r_output_height;

setp.ge.u32 %p3, %r_o_z, %r_output_depth;

or.pred %p4, %p1, %p2;

or.pred %p5, %p4, %p3;

@%p5 bra END;

If the thread is out of bounds, branch to END.

Now, the thread is responsible for output[o_z][o_y][o_x], but need to compute the sum over the kernel.

Initialize sum to 0:

mov.f32 %f_sum, 0f00000000; // 0.0 in hex

Then, loop over kernel_depth, kernel_height, kernel_width.

So, load the kernel dimensions:

ld.param.u32 %r_kernel_depth, [kernel_depth];

ld.param.u32 %r_kernel_height, [kernel_height];

ld.param.u32 %r_kernel_width, [kernel_width];

Similarly, load padding and stride:

ld.param.u32 %r_pad_width, [pad_width];

ld.param.u32 %r_pad_height, [pad_height];

ld.param.u32 %r_pad_depth, [pad_depth];

ld.param.u32 %r_stride_width, [stride_width];

ld.param.u32 %r_stride_height, [stride_height];

ld.param.u32 %r_stride_depth, [stride_depth];

Now, for each kz in 0..kernel_depth-1:

mov.u32 %r_kz, 0;

LOOP_KZ:

setp.ge.u32 %p6, %r_kz, %r_kernel_depth;

@%p6 bra LOOP_KZ_END;

Then for each ky in 0..kernel_height-1:

mov.u32 %r_ky, 0;

LOOP_KY:

setp.ge.u32 %p7, %r_ky, %r_kernel_height;

@%p7 bra LOOP_KY_END;

Then for each kx in 0..kernel_width-1:

mov.u32 %r_kx, 0;

LOOP_KX:

setp.ge.u32 %p8, %r_kx, %r_kernel_width;

@%p8 bra LOOP_KX_END;

Then compute input coordinates:

// Compute input_x = o_x * stride_width + kx - pad_width;

// Similarly for input_y and input_z.

mul.lo.u32 %r_tmp, %r_o_x, %r_stride_width;

add.u32 %r_input_x, %r_tmp, %r_kx;

sub.u32 %r_input_x, %r_input_x, %r_pad_width;

mul.lo.u32 %r_tmp, %r_o_y, %r_stride_height;

add.u32 %r_input_y, %r_tmp, %r_ky;

sub.u32 %r_input_y, %r_input_y, %r_pad_height;

mul.lo.u32 %r_tmp, %r_o_z, %r_stride_depth;

add.u32 %r_input_z, %r_tmp, %r_kz;

sub.u32 %r_input_z, %r_input_z, %r_pad_depth;

Check if input coordinates are within the input dimensions:

// input_x >= 0 && input_x < input_width

// similarly for y and z.

First, check if input_x is negative or >= input_width.

clamp input_x to 0 <= input_x < input_width.

But how? Compute if input_x is within [0, input_width), and same for input_y and input_z.

If any of the coordinates are out of bounds, the input value is zero. Otherwise, load input[input_z][input_y][input_x].

So:

// Check input_x >= 0

setp.ge.u32 %p9, %r_input_x, 0;

// Check input_x < input_width

setp.lt.u32 %p10, %r_input_x, %r_input_width;

and.pred %p11, %p9, %p10;

// Similarly for input_y and input_z.

ld.param.u32 %r_input_width, [input_width];

ld.param.u32 %r_input_height, [input_height];

ld.param.u32 %r_input_depth, [input_depth];

// Check input_x:

setp.ge.u32 %p9, %r_input_x, 0;

setp.lt.u32 %p10, %r_input_x, %r_input_width;

and.pred %p11, %p9, %p10;

// Check input_y:

setp.ge.u32 %p12, %r_input_y, 0;

setp.lt.u32 %p13, %r_input_y, %r_input_height;

and.pred %p14, %p12, %p13;

// Check input_z:

setp.ge.u32 %p15, %r_input_z, 0;

setp.lt.u32 %p16, %r_input_z, %r_input_depth;

and.pred %p17, %p15, %p16;

// Combine all three conditions:

and.pred %p18, %p11, %p14;

and.pred %p19, %p18, %p17;

If %p19 is true, load input value; else, input_val = 0.

Similarly, load kernel value at (kz, ky, kx). Kernel is 3D, and even if input is out of bounds, we still need to multiply by kernel value. Wait, no: the kernel is the same for all positions. So even if the input is out of bounds, the kernel value is still multiplied by zero (since input is zero beyond borders). But we need to load the kernel value regardless.

So:

// Compute kernel index: kz * (kernel_height * kernel_width) + ky * kernel_width + kx

mul.lo.u32 %r_tmp1, %r_kz, %r_kernel_height;

mul.lo.u32 %r_tmp1, %r_tmp1, %r_kernel_width;

mul.lo.u32 %r_tmp2, %r_ky, %r_kernel_width;

add.u32 %r_tmp1, %r_tmp1, %r_tmp2;

add.u32 %r_kernel_idx, %r_tmp1, %r_kx;

// kernel address = kernel_ptr + r_kernel_idx * 4 (assuming float)

mul.lo.u32 %r_kernel_offset, %r_kernel_idx, 4;

add.u32 %r_kernel_addr, %r_kernel_ptr, %r_kernel_offset;

ld.global.f32 %f_kernel_val, [%r_kernel_addr];

For the input, if in bounds:

// Compute input index: input_z * (input_height * input_width) + input_y * input_width + input_x

mul.lo.u32 %r_tmp3, %r_input_z, %r_input_height;

mul.lo.u32 %r_tmp3, %r_tmp3, %r_input_width;

mul.lo.u32 %r_tmp4, %r_input_y, %r_input_width;

add.u32 %r_tmp3, %r_tmp3, %r_tmp4;

add.u32 %r_input_idx, %r_tmp3, %r_input_x;

// input address = input_ptr + r_input_idx * 4

mul.lo.u32 %r_input_offset, %r_input_idx, 4;

add.u32 %r_input_addr, %r_input_ptr, %r_input_offset;

ld.global.f32 %f_input_val, [%r_input_addr];

Else, input_val = 0.0.

So:

@%p19 bra LOAD_INPUT;

mov.f32 %f_input_val, 0f00000000;

bra LOAD_DONE;

LOAD_INPUT:

// compute input address as above and load

...

LOAD_DONE:

Then multiply input_val by kernel_val and add to sum.

fma.rn.f32 %f_sum, %f_input_val, %f_kernel_val, %f_sum;

Then, increment kx and loop:

add.u32 %r_kx, %r_kx, 1;

bra LOOP_KX;

LOOP_KX_END:

Similarly, increment ky and loop:

add.u32 %r_ky, %r_ky, 1;

bra LOOP_KY;

LOOP_KY_END:

Increment kz and loop:

add.u32 %r_kz, %r_kz, 1;

bra LOOP_KZ;

LOOP_KZ_END:

After all loops, store the sum to output.

Compute the output index:

// output index: o_z * (output_height * output_width) + o_y * output_width + o_x

mul.lo.u32 %r_tmp5, %r_o_z, %r_output_height;

mul.lo.u32 %r_tmp5, %r_tmp5, %r_output_width;

mul.lo.u32 %r_tmp6, %r_o_y, %r_output_width;

add.u32 %r_tmp5, %r_tmp5, %r_tmp6;

add.u32 %r_output_idx, %r_tmp5, %r_o_x;

// output address = output_ptr + r_output_idx * 4

mul.lo.u32 %r_output_offset, %r_output_idx, 4;

add.u32 %r_output_addr, %r_output_ptr, %r_output_offset;

st.global.f32 [%r_output_addr], %f_sum;

END:

exit;

Now, putting all this together in PTX code. Let's note that PTX uses a SSA-like form, so we need to manage the registers properly. Also, need to handle the parameter loading and register allocations.

But wait, in PTX, we can use virtual registers (like %r1, %r2, etc.) and the assembler will handle the actual register allocation. But to make it manageable, we can use descriptive names via the .reg directive.

However, PTX does not allow arbitrary register names; instead, we declare registers with .reg and then use them. But in practice, for readability, we can use .reg .u32 r_input_x; etc.

But the code will get quite verbose. Let's try to outline the code step by step.

First, the entry point and parameters:

.entry convolution_3d(

.param .u64 input_ptr,

.param .u64 kernel_ptr,

.param .u64 output_ptr,

.param .u32 input_width,

.param .u32 input_height,

.param .u32 input_depth,

.param .u32 kernel_width,

.param .u32 kernel_height,

.param .u32 kernel_depth,

.param .u32 pad_width,

.param .u32 pad_height,

.param .u32 pad_depth,

.param .u32 stride_width,

.param .u32 stride_height,

.param .u32 stride_depth,

.param .u32 output_width,

.param .u32 output_height,

.param .u32 output_depth

) {

.reg .pred     %p<20>;

.reg .f32      %f<10>;

.reg .u32      %r<100>;

.reg .u64      %rd<10>;

// Load parameters into registers

ld.param.u64   %rd_input_ptr, [input_ptr];

ld.param.u64   %rd_kernel_ptr, [kernel_ptr];

ld.param.u64   %rd_output_ptr, [output_ptr];

ld.param.u32   %r_input_width, [input_width];

ld.param.u32   %r_input_height, [input_height];

ld.param.u32   %r_input_depth, [input_depth];

ld.param.u32   %r_kernel_width, [kernel_width];

ld.param.u32   %r_kernel_height, [kernel_height];

ld.param.u32   %r_kernel_depth, [kernel_depth];

ld.param.u32   %r_pad_width, [pad_width];

ld.param.u32   %r_pad_height, [pad_height];

ld.param.u32   %r_pad_depth, [pad_depth];

ld.param.u32   %r_stride_width, [stride_width];

ld.param.u32   %r_stride_height, [stride_height];

ld.param.u32   %r_stride_depth, [stride_depth];

ld.param.u32   %r_output_width, [output_width];

ld.param.u32   %r_output_height, [output_height];

ld.param.u32   %r_output_depth, [output_depth];

// Compute output coordinates

mov.u32 %r_ctaid_x, %ctaid.x;

mov.u32 %r_ctaid_y, %ctaid.y;

mov.u32 %r_ctaid_z, %ctaid.z;

mov.u32 %r_ntid_x, %ntid.x;

mov.u32 %r_ntid_y, %ntid.y;

mov.u32 %r_ntid_z, %ntid.z;

mov.u32 %r_tid_x, %tid.x;

mov.u32 %r_tid_y, %tid.y;

mov.u32 %r_tid_z, %tid.z;

// o_x = ctaid.x * ntid.x + tid.x

mul.lo.u32 %r_o_x, %r_ctaid_x, %r_ntid_x;

add.u32 %r_o_x, %r_o_x, %r_tid_x;

// o_y = ctaid.y * ntid.y + tid.y

mul.lo.u32 %r_o_y, %r_ctaid_y, %r_ntid_y;

add.u32 %r_o_y, %r_o_y, %r_tid_y;

// o_z = ctaid.z * ntid.z + tid.z

mul.lo.u32 %r_o_z, %r_ctaid_z, %r_ntid_z;

add.u32 %r_o_z, %r_o_z, %r_tid_z;

// Check if o_x >= output_width or o_y >= output_height or o_z >= output_depth

setp.ge.u32 %p1, %r_o_x, %r_output_width;

setp.ge.u32 %p2, %r_o_y, %r_output_height;

setp.ge.u32 %p3, %r_o_z, %r_output_depth;

or.pred %p4, %p1, %p2;

or.pred %p5, %p4, %p3;

@%p5 bra END;

// Initialize sum to 0

mov.f32 %f_sum, 0f00000000;

// Loop variables

mov.u32 %r_kz, 0;

LOOP_KZ:

setp.ge.u32 %p6, %r_kz, %r_kernel_depth;

@%p6 bra LOOP_KZ_END;

mov.u32 %r_ky, 0;

LOOP_KY:

setp.ge.u32 %p7, %r_ky, %r_kernel_height;

@%p7 bra LOOP_KY_END;

mov.u32 %r_kx, 0;

LOOP_KX:

setp.ge.u32 %p8, %r_kx, %r_kernel_width;

@%p8 bra LOOP_KX_END;

// Compute input coordinates

// input_x = o_x * stride_width + kx - pad_width

mul.lo.u32 %r_tmp, %r_o_x, %r_stride_width;

add.u32 %r_input_x, %r_tmp, %r_kx;

sub.u32 %r_input_x, %r_input_x, %r_pad_width;

// input_y = o_y * stride_height + ky - pad_height

mul.lo.u32 %r_tmp, %r_o_y, %r_stride_height;

add.u32 %r_input_y, %r_tmp, %r_ky;

sub.u32 %r_input_y, %r_input_y, %r_pad_height;

// input_z = o_z * stride_depth + kz - pad_depth

mul.lo.u32 %r_tmp, %r_o_z, %r_stride_depth;

add.u32 %r_input_z, %r_tmp, %r_kz;

sub.u32 %r_input_z, %r_input_z, %r_pad_depth;

// Check if input coordinates are valid

// input_x >= 0 and input_x < input_width

setp.ge.u32 %p9, %r_input_x, 0;

setp.lt.u32 %p10, %r_input_x, %r_input_width;

and.pred %p11, %p9, %p10;

// input_y >= 0 and input_y < input_height

setp.ge.u32 %p12, %r_input_y, 0;

setp.lt.u32 %p13, %r_input_y, %r_input_height;

and.pred %p14, %p12, %p13;

// input_z >= 0 and input_z < input_depth

setp.ge.u32 %p15, %r_input_z, 0;

setp.lt.u32 %p16, %r_input_z, %r_input_depth;

and.pred %p17, %p15, %p16;

// Combine all conditions

and.pred %p18, %p11, %p14;

and.pred %p19, %p18, %p17;

// Load kernel value

// kernel index: kz * (kernel_height * kernel_width) + ky * kernel_width + kx

mul.lo.u32 %r_tmp1, %r_kz, %r_kernel_height;

mul.lo.u32 %r_tmp1, %r_tmp1, %r_kernel_width;

mul.lo.u32 %r_tmp2, %r_ky, %r_kernel_width;

add.u32 %r_tmp1, %r_tmp1, %r_tmp2;

add.u32 %r_kernel_idx, %r_tmp1, %r_kx;

// kernel_addr = kernel_ptr + kernel_idx * 4

mul.lo.u32 %r_kernel_offset, %r_kernel_idx, 4;

add.u64 %rd_kernel_addr, %rd_kernel_ptr, %r_kernel_offset;

ld.global.f32 %f_kernel_val, [%rd_kernel_addr];

// Load input value if valid, else 0

@%p19 bra VALID_INPUT;

mov.f32 %f_input_val, 0f00000000;

bra INPUT_LOADED;

VALID_INPUT:

// input index: input_z * (input_height * input_width) + input_y * input_width + input_x

mul.lo.u32 %r_tmp3, %r_input_z, %r_input_height;

mul.lo.u32 %r_tmp3, %r_tmp3, %r_input_width;

mul.lo.u32 %r_tmp4, %r_input_y, %r_input_width;

add.u32 %r_tmp3, %r_tmp3, %r_tmp4;

add.u32 %r_input_idx, %r_tmp3, %r_input_x;

// input_addr = input_ptr + input_idx * 4

mul.lo.u32 %r_input_offset, %r_input_idx, 4;

add.u64 %rd_input_addr, %rd_input_ptr, %r_input_offset;

ld.global.f32 %f_input_val, [%rd_input_addr];

INPUT_LOADED:

// Multiply and accumulate

fma.rn.f32 %f_sum, %f_input_val, %f_kernel_val, %f_sum;

// Increment kx and loop

add.u32 %r_kx, %r_kx, 1;

bra LOOP_KX;

LOOP_KX_END:

add.u32 %r_ky, %r_ky, 1;

bra LOOP_KY;

LOOP_KY_END:

add.u32 %r_kz, %r_kz, 1;

bra LOOP_KZ;

LOOP_KZ_END:

// Compute output index

mul.lo.u32 %r_tmp5, %r_o_z, %r_output_height;

mul.lo.u32 %r_tmp5, %r_tmp5, %r_output_width;

mul.lo.u32 %r_tmp6, %r_o_y, %r_output_width;

add.u32 %r_output_idx, %r_tmp5, %r_tmp6;

add.u32 %r_output_idx, %r_output_idx, %r_o_x;

// output_addr = output_ptr + output_idx * 4

mul.lo.u32 %r_output_offset, %r_output_idx, 4;

add.u64 %rd_output_addr, %rd_output_ptr, %r_output_offset;

st.global.f32 [%rd_output_addr], %f_sum;

END:

exit;

}

}

Wait, but in PTX, the parameters are passed as .param .u64 for pointers. Earlier, I had .param .b8, but corrected to .u64. Also, when adding offsets to the pointers, we need to use 64-bit arithmetic. So in the code, the input_ptr is loaded into %rd_input_ptr as a .u64, and offsets are added as .u32 multiplied by 4 (since each float is 4 bytes). So when calculating the address, we need to cast the offset to 64-bit. But PTX's add.u64 can handle this.

But when adding a 32-bit offset to a 64-bit pointer, we need to convert the offset to 64-bit. For example:

mul.lo.u32 %r_kernel_offset, %r_kernel_idx, 4;

cvt.u64.u32 %rd_kernel_offset, %r_kernel_offset;

add.u64 %rd_kernel_addr, %rd_kernel_ptr, %rd_kernel_offset;

Wait, because %r_kernel_offset is a 32-bit value, when adding to a 64-bit pointer, we need to convert it to 64-bit first. Otherwise, adding a 32-bit to 64-bit might not work as expected. So the code should convert the 32-bit offset to 64-bit before adding.

Ah, right. So in the previous code, when we compute %r_kernel_offset as a .u32, we need to convert it to .u64 before adding to the base pointer. So the code should have:

mul.lo.u32 %r_kernel_offset, %r_kernel_idx, 4;

cvt.u64.u32 %rd_kernel_offset, %r_kernel_offset;

add.u64 %rd_kernel_addr, %rd_kernel_ptr, %rd_kernel_offset;

Similarly for input and output addresses.

So the code needs to use cvt.u64.u32 to convert the 32-bit offset to 64-bit.

This was a mistake in the previous code. Let's correct that.

For example, in the kernel load part:

// kernel offset in bytes

mul.lo.u32 %r_kernel_offset, %r_kernel_idx, 4;

cvt.u64.u32 %rd_kernel_offset, %r_kernel_offset;

add.u64 %rd_kernel_addr, %rd_kernel_ptr, %rd_kernel_offset;

ld.global.f32 %f_kernel_val, [%rd_kernel_addr];

Similarly for input and output addresses.

So this correction needs to be applied throughout the code.

Another thing: when computing the input index, the multiplication steps could overflow 32-bit integers if the input is large. But for simplicity, we'll assume that the input dimensions are such that the indices fit in 32 bits. If not, we'd need to use 64-bit arithmetic, which complicates things.

But given that CUDA's maximum grid and block sizes are limited, and input sizes are typically within manageable ranges, we can proceed with 32-bit arithmetic.

Now, putting all these corrections into the PTX code.

Another thing to note: The initial .reg declarations. For example, .reg .u32 %r<100>; declares a range of registers from %r0 to %r99. Similarly for .reg .f32 %f<10>; and .reg .u64 %rd<10>;. But when writing code, using explicit names like %r_input_ptr is not allowed. Instead, the registers are referred to as %r0, %r1, etc. However, in PTX, you can define symbolic register names using .reg directives. For example:

.reg .u32 r_input_x;

.reg .u32 r_input_y;

...

But in practice, this is tedious. Alternatively, the code can use the virtual registers with numbered names and keep track of them mentally. However, for readability, perhaps it's better to use the numbered registers and comment their purposes.

But given the complexity, perhaps it's better to write the code using the numbered registers and add comments. However, in the code I provided earlier, I used named registers like %r_o_x, which isn't valid PTX syntax. PTX requires registers to be declared with .reg and then referred to by their names (like %r1, %r2, etc.). So the code needs to be adjusted to use properly declared registers.

This is a common confusion when writing PTX code. The correct approach is to declare all registers upfront with .reg directives and then use them. But for the sake of brevity and given the complexity, perhaps the code can be written with comments indicating the purpose of each register.

However, this makes the code harder to read. An alternative is to use the virtual registers with descriptive variable names in the comments.

Given that, here's a revised version of the PTX code with proper register declarations and comments:

.entry convolution_3d(

.param .u64 input_ptr_param,

.param .u64 kernel_ptr_param,

.param .u64 output_ptr_param,

.param .u32 input_width_param,

.param .u32 input_height_param,

.param .u32 input_depth_param,

.param .u32 kernel_width_param,

.param .u32 kernel_height_param,

.param .u32 kernel_depth_param,

.param .u32 pad_width_param,

.param .u32 pad_height_param,

.param .u32 pad_depth_param,

.param .u32 stride_width_param,

.param .u32 stride_height_param,

.param .u32 stride_depth_param,

.param .u32 output_width_param,

.param .u32 output_height_param,

.param .u32 output_depth_param

) {

.reg .pred     %p<100>;  // Predicate registers

.reg .f32      %f<100>;  // Floating-point registers

.reg .u32      %r<100>;  // 32-bit integer registers

.reg .u64      %rd<100>; // 64-bit integer registers

// Load parameters into registers

ld.param.u64   %rd[1], [input_ptr_param];      // %rd1 = input_ptr

ld.param.u64   %rd[2], [kernel_ptr_param];     // %rd2 = kernel_ptr

ld.param.u64   %rd[3], [output_ptr_param];     // %rd3 = output_ptr

ld.param.u32   %r[1], [input_width_param];     // %r1 = input_width

ld.param.u32   %r[2], [input_height_param];    // %r2 = input_height

ld.param.u32   %r[3], [input_depth_param];     // %r3 = input_depth

ld.param.u32   %r[4], [kernel_width_param];    // %r4 = kernel_width

ld.param.u32   %r[5], [kernel_height_param];   // %r5 = kernel_height

ld.param.u32   %r[6], [kernel_depth_param];    // %r6 = kernel_depth

ld.param.u32   %r[7], [pad_width_param];       // %r7 = pad_width

ld.param.u32   %r[8], [pad_height_param];      // %r8 = pad_height

ld.param.u32   %r[9], [pad_depth_param];       // %r9 = pad_depth

ld.param.u32   %r[10], [stride_width_param];   // %r10 = stride_width

ld.param.u32   %r[11], [stride_height_param];  // %r11 = stride_height

ld.param.u32   %r[12], [stride_depth_param];   // %r12 = stride_depth

ld.param.u32   %r[13], [output_width_param];   // %r13 = output_width

ld.param.u32   %r[14], [output_height_param];  // %r14 = output_height

ld.param.u32   %r[15], [output_depth_param];   // %r15 = output_depth

// Calculate output coordinates (o_x, o_y, o_z)

// o_x = ctaid.x * ntid.x + tid.x

mov.u32 %r[16], %ctaid.x;       // %r16 = ctaid.x

mov.u32 %r[17], %ntid.x;        // %r17 = ntid.x

mul.lo.u32 %r[18], %r[16], %r[17]; // %r18 = ctaid.x * ntid.x

mov.u32 %r[19], %tid.x;         // %r19 = tid.x

add.u32 %r[20], %r[18], %r[19]; // %r20 = o_x

// o_y = ctaid.y * ntid.y + tid.y

mov.u32 %r[21], %ctaid.y;

mov.u32 %r[22], %ntid.y;

mul.lo.u32 %r[23], %r[21], %r[22];

mov.u32 %r[24], %tid.y;

add.u32 %r[25], %r[23], %r[24]; // %r25 = o_y

// o_z = ctaid.z * ntid.z + tid.z

mov.u32 %r[26], %ctaid.z;

mov.u32 %r[27], %ntid.z;

mul.lo.u32 %r[28], %r[26], %r[27];

mov.u32 %r[29], %tid.z;

add.u32 %r[30], %r[28], %r[29]; // %r30 = o_z

// Check if output coordinates are within bounds

// if (o_x >= output_width || o_y >= output_height || o_z >= output_depth) exit

setp.ge.u32 %p[1], %r[20], %r[13];

setp.ge.u32 %p[2], %r[25], %r[14];

setp.ge.u32 %p[3], %r[30], %r[15];

or.pred %p[4], %p[1], %p[2];

or.pred %p[5], %p[4], %p[3];

@%p[5] bra END;

// Initialize sum to 0

mov.f32 %f[1], 0f00000000; // %f1 = sum = 0.0

// Loop over kernel depth (kz)

mov.u32 %r[31], 0; // %r31 = kz

LOOP_KZ:

setp.ge.u32 %p[6], %r[31], %r[6]; // %p6 = (kz >= kernel_depth)

@%p[6] bra LOOP_KZ_END;

// Loop over kernel height (ky)

mov.u32 %r[32], 0; // %r32 = ky

LOOP_KY:

setp.ge.u32 %p[7], %r[32], %r[5]; // %p7 = (ky >= kernel_height)

@%p[7] bra LOOP_KY_END;

// Loop over kernel width (kx)

mov.u32 %r[33], 0; // %r33 = kx

LOOP_KX:

setp.ge.u32 %p[8], %r[33], %r[4]; // %p8 = (kx >= kernel_width)

@%p[8] bra LOOP_KX_END;

// Compute input coordinates (input_x, input_y, input_z)

// input_x = o_x * stride_width + kx - pad_width

mul.lo.u32 %r[34], %r[20], %r[10]; // %r34 = o_x * stride_width

add.u32 %r[35], %r[34], %r[33];    // %r35 = o_x * stride_width + kx

sub.u32 %r[36], %r[35], %r[7];     // %r36 = input_x

// input_y = o_y * stride_height + ky - pad_height

mul.lo.u32 %r[37], %r[25], %r[11]; // %r37 = o_y * stride_height

add.u32 %r[38], %r[37], %r[32];    // %r38 = o_y * stride_height + ky

sub.u32 %r[39], %r[38], %r[8];     // %r39 = input_y

// input_z = o_z * stride_depth + kz - pad_depth

mul.lo.u32 %r[40], %r[30], %r[12]; // %r40 = o_z * stride_depth

add.u32 %r[41], %r[40], %r[31];    // %r41 = o_z * stride_depth + kz

sub.u32 %r[42], %r[41], %r[9];     // %r42 = input_z

// Check if input coordinates are valid

// input_x >= 0 && input_x < input_width

setp.ge.u32 %p[9], %r[36], 0;

setp.lt.u32 %p[10], %r[36], %r[1];

and.pred %p[11], %p[9], %p[10];

// input_y >= 0 && input_y < input_height

setp.ge.u32 %p[12], %r[39], 0;

setp.lt.u32 %p[13], %r[39], %r[2];

and.pred %p[14], %p[12], %p[13];

// input_z >= 0 && input_z < input_depth

setp.ge.u32 %p[15], %r[42], 0;

setp.lt.u32 %p[16], %r[42], %r[3];

and.pred %p[17], %p[15], %p[16];

// Combine all conditions

and.pred %p[18], %p[11], %p[14];

and.pred %p[19], %p[18], %p[17];

// Calculate kernel index and load kernel value

// kernel_idx = kz * (kernel_height * kernel_width) + ky * kernel_width + kx

mul.lo.u32 %r[43], %r[31], %r[5];  // %r43 = kz * kernel_height

mul.lo.u32 %r[44], %r[43], %r[4];  // %r44 = kz * kernel_height * kernel_width

mul.lo.u32 %r[45], %r[32], %r[4];  // %r45 = ky * kernel_width

add.u32 %r[46], %r[44], %r[45];    // %r46 += ky * kernel_width

add.u32 %r[47], %r[46], %r[33];    // %r47 = kernel_idx

// kernel_offset = kernel_idx * 4 (bytes)

mul.lo.u32 %r[48], %r[47], 4;

cvt.u64.u32 %rd[4], %r[48];        // Convert to 64-bit

add.u64 %rd[5], %rd[2], %rd[4];    // kernel_addr = kernel_ptr + offset

ld.global.f32 %f[2], [%rd[5]];     // %f2 = kernel_val

// Check if input is valid and load input value

@%p[19] bra VALID_INPUT;

mov.f32 %f[3], 0f00000000;         // %f3 = 0.0

bra INPUT_LOADED;

VALID_INPUT:

// Calculate input index and load input value

// input_idx = input_z * (input_height * input_width) + input_y * input_width + input_x

mul.lo.u32 %r[49], %r[42], %r[2];  // %r49 = input_z * input_height

mul.lo.u32 %r[50], %r[49], %r[1];  // %r50 = input_z * input_height * input_width

mul.lo.u32 %r[51], %r[39], %r[1];  // %r51 = input_y * input_width

add.u32 %r[52], %r[50], %r[51];    // %r52 += input_y * input_width

add.u32 %r[53], %r[52], %r[36];    // %r53 = input_idx

// input_offset = input_idx * 4 (bytes)

mul.lo.u32 %r[54], %r[53], 4;

cvt.u64.u32 %rd[6], %r[54];        // Convert to 64-bit

add.u64 %rd[7], %rd[1], %rd[6];    // input_addr = input_ptr + offset

ld.global.f32 %f[3], [%rd[7]];     // %f3 = input_val

INPUT_LOADED:

// Accumulate sum += input_val * kernel_val

fma.rn.f32 %f[1], %f[3], %f[2], %f[1];

// Increment kx and loop

add.u32 %r[33], %r[33], 1;

bra LOOP_KX;

LOOP_KX_END:

// Increment ky and loop

add.u32 %r[32], %r[32], 1;

bra LOOP_KY;

LOOP_KY_END:

// Increment kz and loop

add.u32 %r[31], %r[31], 1;

bra LOOP_KZ;

LOOP_KZ_END:

// Calculate output index

// output_idx = o_z * (output_height * output_width) + o_y * output_width + o_x

mul.lo.u32 %r[55], %r[30], %r[14]; // %r55 = o_z * output_height

mul.lo.u32 %r[56], %r[55], %r[13]; // %r56 = o_z * output_height * output_width

mul.lo.u32 %r[57], %r[25], %r[13]; // %r57 = o_y * output_width

add.u32 %r[58], %r[56], %r[57];    // %r58 += o_y * output_width

add.u32 %r[59], %r[58], %r[20];    // %r59 = output_idx

// output_offset = output_idx * 4 (bytes)

mul.lo.u32 %r[60], %r[59], 4;

cvt.u64.u32 %rd[8], %r[60];        // Convert to 64-bit

add.u64 %rd[9], %rd[3], %rd[8];    // output_addr = output_ptr + offset

st.global.f32 [%rd[9]], %f[1];     // Store sum

END:

exit;

}

}

This code uses numbered registers and comments to indicate their purpose. Each register is declared in the .reg directives, and the code uses these registers with comments to explain their roles. For example, %r[20] is used for o_x, %r[25] for o_y, etc.

However, this approach is error-prone and hard to read. In practice, writing PTX code manually like this is very tedious and error-prone. It's usually better to write CUDA C++ code and let the compiler generate PTX. But the user specifically asked for PTX code, so this is the required approach.

Another important consideration is the efficiency of the code. The code as written doesn't use shared memory or any optimizations like tiling, which are crucial for performance in convolution operations. However, given the complexity of implementing such optimizations in PTX, the code provided is a basic, straightforward implementation without optimizations.

Also, the code assumes that the kernel and input are in global memory, which may result in high latency due to repeated global memory accesses. In practice, using shared memory to cache portions of the input and kernel can significantly improve performance. However, implementing that in PTX would add considerable complexity.

In conclusion, the code above is a basic 3D convolution implementation in PTX, where each thread computes one output element by iterating over the kernel dimensions, checking input boundaries, and accumulating the sum. It uses global memory for all data and doesn't include optimizations, so its performance may not be optimal, but it serves as a starting point for understanding how to implement such operations in PTX.

</think>

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

Here's a PTX implementation of a 3D convolution kernel for NVIDIA GPUs. This code computes each output element by iterating over the kernel dimensions and accumulating the product of input and kernel values:

```ptx
//
// 3D Convolution PTX Kernel
//
.entry convolution_3d(
    .param .u64 input_ptr,
    .param .u64 kernel_ptr,
    .param .u64 output_ptr,
    .param .u32 input_width,  .param .u32 input_height,  .param .u32 input_depth,
    .param .u32 kernel_width, .param .u32 kernel_height, .param .u32 kernel_depth,
    .param .u32 pad_width,    .param .u32 pad_height,    .param .u32 pad_depth,
    .param .u32 stride_width, .param .u32 stride_height, .param .u32 stride_depth,
    .param .u32 output_width, .param .u32 output_height, .param .u32 output_depth
) {
    .reg .pred     %p<100>;
    .reg .f32      %f<100>;
    .reg .u32      %r<100>;
    .reg .u64      %rd<100>;

    // Load parameters
    ld.param.u64   %rd1, [input_ptr];
    ld.param.u64   %rd2, [kernel_ptr];
    ld.param.u64   %rd3, [output_ptr];

    ld.param.u32   %r1, [input_width];    ld.param.u32 %r2, [input_height];
    ld.param.u32   %r3, [input_depth];    ld.param.u32 %r4, [kernel_width];
    ld.param.u32   %r5, [kernel_height];  ld.param.u32 %r6, [kernel_depth];
    ld.param.u32   %r7, [pad_width];      ld.param.u32 %r8, [pad_height];
    ld.param.u32   %r9, [pad_depth];      ld.param.u32 %r10, [stride_width];
    ld.param.u32   %r11, [stride_height]; ld.param.u32 %r12, [stride_depth];
    ld.param.u32   %r13, [output_width];  ld.param.u32 %r14, [output_height];
    ld.param.u32   %r15, [output_depth];

    // Calculate output coordinates
    .reg .u32      %ox, %oy, %oz;
    mad.lo.u32     %ox, %ctaid.x, %ntid.x, %tid.x;
    mad.lo.u32     %oy, %ctaid.y, %ntid.y, %tid.y;
    mad.lo.u32     %oz, %ctaid.z, %ntid.z, %tid.z;

    // Check output bounds
    setp.ge.u32    %p1, %ox, %r13;
    setp.ge.u32    %p2, %oy, %r14;
    setp.ge.u32    %p3, %oz, %r15;
    or.pred        %p4, %p1, %p2;
    or.pred        %p5, %p4, %p3;
    @%p5 bra      END;

    // Initialize accumulator
    mov.f32        %f1, 0f0;

    // Kernel loops
    .reg .u32      %kz, %ky, %kx;
    .reg .u32      %ix, %iy, %iz;
    .reg .f32      %ival, %kval;
    mov.u32        %kz, 0;

LOOP_KZ:
    setp.ge.u32    %p6, %kz, %r6;
    @%p6 bra      LOOP_KZ_END;
    mov.u32        %ky, 0;

LOOP_KY:
    setp.ge.u32    %p7, %ky, %r5;
    @%p7 bra      LOOP_KY_END;
    mov.u32        %kx, 0;

LOOP_KX:
    setp.ge.u32    %p8, %kx, %r4;
    @%p8 bra      LOOP_KX_END;

    // Calculate input coordinates
    mad.lo.u32     %ix, %ox, %r10, %kx;
    sub.u32        %ix, %ix, %r7;
    mad.lo.u32     %iy, %oy, %r11, %ky;
    sub.u32        %iy, %iy, %r8;
    mad.lo.u32     %iz, %oz, %r12, %kz;
    sub.u32        %iz, %iz, %r9;

    // Check input boundaries
    setp.ge.s32    %p9,  %ix, 0;
    setp.lt.u32    %p10, %ix, %r1;
    setp.ge.s32    %p11, %iy, 0;
    setp.lt.u32    %p12, %iy, %r2;
    setp.ge.s32    %p13, %iz, 0;
    setp.lt.u32    %p14, %iz, %r3;
    and.pred       %p15, %p9,  %p10;
    and.pred       %p16, %p11, %p12;
    and.pred       %p17, %p13, %p14;
    and.pred       %p18, %p15, %p16;
    and.pred       %p19, %p18, %p17;

    // Load kernel value
    mad.lo.u32     %r20, %kz, %r5, %ky;
    mad.lo.u32     %r21, %r20, %r4, %kx;
    mul.wide.u32   %rd4, %r21, 4;
    add.u64        %rd5, %rd2, %rd4;
    ld.global.f32  %kval, [%rd5];

    // Load input value or zero
    @!%p19 bra     SKIP_LOAD;
    mad.lo.u32     %r22, %iz, %r2, %iy;
    mad.lo.u32     %r23, %r22, %r1, %ix;
    mul.wide.u32   %rd6, %r23, 4;
    add.u64        %rd7, %rd1, %rd6;
    ld.global.f32  %ival, [%rd7];
    bra            ACCUMULATE;

SKIP_LOAD:
    mov.f32        %ival, 0f0;

ACCUMULATE:
    // Multiply and accumulate
    fma.rn.f32     %f1, %ival, %kval, %f1;

    // Next kernel element
    add.u32        %kx, %kx, 1;
    bra            LOOP_KX;

LOOP_KX_END:
    add.u32        %ky, %ky, 1;
    bra            LOOP_KY;

LOOP_KY_END:
    add.u32        %kz, %kz, 1;
    bra            LOOP_KZ;

LOOP_KZ_END:
    // Store result
    mad.lo.u32     %r24, %oz, %r14, %oy;
    mad.lo.u32     %r25, %r24, %r13, %ox;
    mul.wide.u32   %rd8, %r25, 4;
    add.u64        %rd9, %rd3, %rd8;
    st.global.f32  [%rd9], %f1;

END:
    exit;
}
```

Key features of this implementation:

1. **Thread Mapping**: Each thread computes one output element using 3D grid/block organization
2. **Boundary Handling**: Proper input boundary checks for padding
3. **Efficient Indexing**: Uses MAD (Multiply-Add) instructions for index calculations
4. **Predicated Execution**: Uses predicates for boundary checks and conditional loading
5. **Register Usage**: Optimized register usage for critical variables

To use this kernel:
1. Launch with 3D grid dimensions matching output tensor size
2. Each block should have dimensions that evenly divide the output dimensions
3. Input, kernel, and output tensors must be in GPU global memory
4. All parameters must be properly initialized on the host

Note: This is a basic implementation and can be optimized further using:
- Shared memory for kernel/data caching
- Loop unrolling
- Vectorized memory operations
- Asynchronous prefetching

The kernel assumes:
- Single-precision floating point data
- Zero-padding outside input boundaries
- No dilation (dilation=1 in all dimensions)

For best performance, tune block dimensions based on your specific GPU architecture and problem size.