Medium Precision Boundary Control

Mathematical Foundation: Precision-Aware Value Clamping

The saturateMediump function implements numerical stability for medium precision floating-point environments by constraining values within the representable range of 16-bit floats commonly used in mobile graphics architectures.

Mathematical Definition:

$$\text{saturateMediump}(x) = \min(x, 65504.0)$$

Precision Analysis:

• $x \in \mathbb{R}$: Input value (unrestricted domain)
• $65504.0$: Maximum representable value in IEEE 754 half-precision format
• Prevents numerical overflow in constrained precision environments
• Maintains computational stability across diverse hardware architectures

Hardware Optimization: The function serves as a mathematical bridge between full-precision calculations and hardware-constrained rendering pipelines, ensuring visual consistency across platforms while optimizing for mobile GPU architectures.

Mobile Hardware Compatibility

Shows how saturateMediump maintains visual consistency across different precision architectures by demonstrating computational patterns that remain stable within medium precision constraints.

ライブエディター

const fragment = () => {
      const p = uv.sub(0.5).mul(4)
      const t = iTime.mul(0.6)

      // Complex calculations that might overflow on mobile
      const complex1 = p.x.mul(3).add(t).sin().abs().pow(8).mul(10000)
      const complex2 = p.y.mul(2).sub(t.mul(1.3)).cos().exp().mul(5000)
      const complex3 = p.length().add(t.mul(2).sin()).pow(6).mul(8000)

      // Apply saturateMediump for mobile stability
      const stable1 = saturateMediump(complex1).div(65504)
      const stable2 = saturateMediump(complex2).div(65504)
      const stable3 = saturateMediump(complex3).div(65504)

      // Create stable interference pattern
      const interference = stable1.mul(stable2).add(stable2.mul(stable3))
      const pattern = saturateMediump(interference.mul(3)).div(3)

      // Visualize precision-safe computation
      const safety = smoothstep(0.8, 1.0, pattern)

      return vec4(vec3(
              pattern.mul(0.8).add(safety.mul(0.2)),
              pattern.mul(0.9),
              pattern.mul(0.7).add(safety.mul(0.4))
      ), 1)

}

結果

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