Add FP16 Batched Matrix Multiplication Challenge (Medium #57)

[Copilot]

This PR adds a new medium difficulty challenge for FP16 batched matrix multiplication.

Challenge Overview

The challenge implements batched matrix multiplication using 16-bit floating point numbers (FP16/half). Given a batch of matrices A of shape [B, M, K] and B of shape [B, K, N], participants compute the output batch C of shape [B, M, N] where C_b = A_b × B_b for each batch index b.

Key Features

• Data Type: Uses FP16 (half precision) for input/output matrices
• Precision Handling: Requires FP32 accumulation during multiplication for better numerical stability
• Constraints: Supports up to 128 batches and matrix dimensions up to 1024
• Test Coverage: Includes 6 functional tests covering various batch sizes and matrix shapes
• Performance Test: BATCH=32, M=N=K=256

Implementation Details

The challenge combines concepts from:

• Challenge added simple inference challenge #30: FP32 batched matrix multiplication (batch operations)
• Challenge fix 37 matrix power cuda start template #22: FP16 GEMM (half precision handling)

Starter templates are provided for:

• CUDA (with cuda_fp16.h and half type)
• Mojo (Float16)
• PyTorch
• Triton
• CuTe

All starter files follow the medium difficulty pattern with empty solve functions, allowing participants to implement their own optimized solutions.

Original prompt

Create a new challenge for FP16 batched matmul as a medium

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[kunal-mansukhani]

@copilot 56 is duplicated. use something else

[Copilot]

@copilot 56 is duplicated. use something else

Renamed to challenge 57 to avoid duplication with hard/56_linear_attention (commit 4381820)