Integer Absolute Value Operations

Conditional Value Processing

The absi function performs intelligent conditional processing to ensure all numeric values become positive. This operation examines each input value and applies selective transformation based on mathematical sign determination.

Unlike standard absolute value functions, absi maintains computational precision across different numeric types while providing consistent behavior for both scalar and vector operations.

ライブエディター

const fragment = () => {
      const uv = position.xy.div(iResolution).sub(0.5).mul(2)

      // Create symmetric patterns using absolute value
      const pattern = absi(uv.x.mul(8).sin().sub(0.3))
      const color = vec3(pattern)

      return vec4(color, 1)

}

Dynamic Threshold Visualization

Threshold-based visual effects leverage absolute value operations to create dynamic boundaries that respond to mathematical conditions and time-based parameters.

ライブエディター

const fragment = () => {
      const uv = position.xy.div(iResolution).sub(0.5).mul(4)
      const time = iTime.mul(0.8)

      // Create dynamic threshold patterns
      const noise1 = uv.x.mul(3).add(time).sin().mul(uv.y.mul(2).sub(time.mul(0.7)).cos())
      const noise2 = uv.x.mul(1.5).sub(time.mul(0.5)).cos().add(uv.y.mul(4).add(time.mul(1.2)).sin())

      const threshold = time.mul(2).sin().mul(0.4)

      const pattern1 = absi(noise1.sub(threshold))
      const pattern2 = absi(noise2.add(threshold.mul(0.8)))

      const finalPattern = pattern1.mul(pattern2)

      const color = vec3(
              finalPattern.mul(time.sin().mul(0.5).add(0.7)),
              finalPattern.mul(time.mul(1.3).cos().mul(0.5).add(0.6)),
              finalPattern.mul(time.mul(0.7).sin().mul(0.5).add(0.5))
      )

      return vec4(color, 1)

}

Implementation Architecture

Mathematical Foundation

The absi function implements conditional logic through mathematical comparison operations:

$$\text{absi}(x) = \begin{cases} x \cdot (-1) & \text{if } x < 0 \\ x & \text{otherwise} \end{cases}$$

This can be expressed as a branchless operation: $\text{absi}(x) = x \cdot \text{sign}(x) \cdot \text{sign}(x)$

Or using conditional selection: $\text{absi}(x) = \text{select}(x, -x, x < 0)$

The function ensures optimal execution across different processing architectures by avoiding branching penalties.

Computational Structure

Operation Phase	Mathematical Logic	Implementation Detail
Sign Detection	Negative value identification	x.lessThan(0)
Conditional Negation	Selective value inversion	x.mul(-1)
Value Selection	Conditional result choice	select(negative, positive, condition)