RMS Normalization

题面

实现 1D 向量的 RMSNorm 前向：rms = sqrt( (1/N) Σ x_i^2 + eps )，x̂_i = x_i / rms，y_i = gamma * x̂_i + beta。

Implementation Requirements

• Use only native features (external libraries are not permitted)
• The solve function signature must remain unchanged
• 输出写入 output

Examples

见页面两组示例（不同输入长度）。

Constraints

• 1 ≤ N ≤ 100,000；eps=1e-5
• -100.0 ≤ input ≤ 100.0；0.1 ≤ gamma ≤ 10.0；-10.0 ≤ beta ≤ 10.0
• Performance: N = 100,000