rustdct 0.7.1

Compute Discrete Cosine Transforms (DCT) of any size in O(nlogn) time, in pure Rust.
Documentation 
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/// This file contains reference implementations of all DCT and DST transforms.
/// The goal of these implementations is not to be fast, but to match the mathematical definitions as closely as possible and to be easy to follow and debug
/// The reference for the mathematical definitions was section 9 of "The Discrete W Transforms" by Wang and Hunt, but with the normalization/orthogonalization factors omitted.
use std::f64;

/// Simplified version of DCT1
pub fn reference_dct1(input: &[f64]) -> Vec<f64> {
    let mut result = Vec::new();

    for output_index in 0..input.len() {
        let mut entry = 0.0;
        for input_index in 0..input.len() {
            let multiplier = if input_index == 0 || input_index == input.len() - 1 {
                0.5
            } else {
                1.0
            };
            let cos_inner = (output_index as f64) * (input_index as f64) * f64::consts::PI
                / ((input.len() - 1) as f64);
            let twiddle = cos_inner.cos();
            entry += input[input_index] * twiddle * multiplier;
        }
        result.push(entry);
    }
    result
}

/// Simplified version of DCT2
pub fn reference_dct2(input: &[f64]) -> Vec<f64> {
    let mut result = Vec::new();

    for output_index in 0..input.len() {
        let mut entry = 0.0;
        for input_index in 0..input.len() {
            let cos_inner = (output_index as f64) * (input_index as f64 + 0.5) * f64::consts::PI
                / (input.len() as f64);
            let twiddle = cos_inner.cos();
            entry += input[input_index] * twiddle;
        }
        result.push(entry);
    }

    result
}

/// Simplified version of DCT3
pub fn reference_dct3(input: &[f64]) -> Vec<f64> {
    let mut result = Vec::new();

    for output_index in 0..input.len() {
        let mut entry = 0.0;
        for input_index in 0..input.len() {
            let multiplier = if input_index == 0 { 0.5 } else { 1.0 };
            let cos_inner = (output_index as f64 + 0.5) * (input_index as f64) * f64::consts::PI
                / (input.len() as f64);
            let twiddle = cos_inner.cos();
            entry += input[input_index] * twiddle * multiplier;
        }
        result.push(entry);
    }

    result
}

/// Simplified version of DCT4
pub fn reference_dct4(input: &[f64]) -> Vec<f64> {
    let mut result = Vec::new();

    for output_index in 0..input.len() {
        let mut entry = 0.0;
        for input_index in 0..input.len() {
            let cos_inner =
                (output_index as f64 + 0.5) * (input_index as f64 + 0.5) * f64::consts::PI
                    / (input.len() as f64);
            let twiddle = cos_inner.cos();
            entry += input[input_index] * twiddle;
        }
        result.push(entry);
    }

    result
}

/// Simplified version of DCT5
pub fn reference_dct5(input: &[f64]) -> Vec<f64> {
    let mut result = Vec::new();

    for output_index in 0..input.len() {
        let mut entry = 0.0;
        for input_index in 0..input.len() {
            let multiplier = if input_index == 0 { 0.5 } else { 1.0 };
            let cos_inner = (output_index as f64) * (input_index as f64) * f64::consts::PI
                / (input.len() as f64 - 0.5);
            let twiddle = cos_inner.cos();
            entry += input[input_index] * twiddle * multiplier;
        }
        result.push(entry);
    }

    result
}

/// Simplified version of DCT6
pub fn reference_dct6(input: &[f64]) -> Vec<f64> {
    let mut result = Vec::new();

    for output_index in 0..input.len() {
        let mut entry = 0.0;
        for input_index in 0..input.len() {
            let multiplier = if input_index == input.len() - 1 {
                0.5
            } else {
                1.0
            };
            let cos_inner = (output_index as f64) * (input_index as f64 + 0.5) * f64::consts::PI
                / (input.len() as f64 - 0.5);
            let twiddle = cos_inner.cos();
            entry += input[input_index] * twiddle * multiplier;
        }
        result.push(entry);
    }

    result
}

/// Simplified version of DCT7
pub fn reference_dct7(input: &[f64]) -> Vec<f64> {
    let mut result = Vec::new();

    for output_index in 0..input.len() {
        let mut entry = 0.0;
        for input_index in 0..input.len() {
            let multiplier = if input_index == 0 { 0.5 } else { 1.0 };
            let cos_inner = (output_index as f64 + 0.5) * (input_index as f64) * f64::consts::PI
                / (input.len() as f64 - 0.5);
            let twiddle = cos_inner.cos();
            entry += input[input_index] * twiddle * multiplier;
        }
        result.push(entry);
    }

    result
}

/// Simplified version of DCT8
pub fn reference_dct8(input: &[f64]) -> Vec<f64> {
    let mut result = Vec::new();

    for output_index in 0..input.len() {
        let mut entry = 0.0;
        for input_index in 0..input.len() {
            let cos_inner =
                (output_index as f64 + 0.5) * (input_index as f64 + 0.5) * f64::consts::PI
                    / (input.len() as f64 + 0.5);
            let twiddle = cos_inner.cos();
            entry += input[input_index] * twiddle;
        }
        result.push(entry);
    }

    result
}

/// Simplified version of DST1
pub fn reference_dst1(input: &[f64]) -> Vec<f64> {
    let mut result = Vec::new();
    for output_index in 0..input.len() {
        let mut entry = 0.0;
        for input_index in 0..input.len() {
            let sin_inner =
                (output_index as f64 + 1.0) * (input_index as f64 + 1.0) * f64::consts::PI
                    / ((input.len() + 1) as f64);
            let twiddle = sin_inner.sin();
            entry += input[input_index] * twiddle;
        }
        result.push(entry);
    }
    result
}

/// Simplified version of DST2
pub fn reference_dst2(input: &[f64]) -> Vec<f64> {
    let mut result = Vec::new();
    for output_index in 0..input.len() {
        let mut entry = 0.0;
        for input_index in 0..input.len() {
            let sin_inner =
                (output_index as f64 + 1.0) * (input_index as f64 + 0.5) * f64::consts::PI
                    / (input.len() as f64);
            let twiddle = sin_inner.sin();
            entry += input[input_index] * twiddle;
        }
        result.push(entry);
    }
    result
}

/// Simplified version of DST3
pub fn reference_dst3(input: &[f64]) -> Vec<f64> {
    let mut result = Vec::new();
    for output_index in 0..input.len() {
        let mut entry = 0.0;
        for input_index in 0..input.len() {
            let multiplier = if input_index == input.len() - 1 {
                0.5
            } else {
                1.0
            };
            let sin_inner =
                (output_index as f64 + 0.5) * (input_index as f64 + 1.0) * f64::consts::PI
                    / (input.len() as f64);
            let twiddle = sin_inner.sin();
            entry += input[input_index] * twiddle * multiplier;
        }
        result.push(entry);
    }
    result
}

/// Simplified version of DST4
pub fn reference_dst4(input: &[f64]) -> Vec<f64> {
    let mut result = Vec::new();

    for output_index in 0..input.len() {
        let mut entry = 0.0;
        for input_index in 0..input.len() {
            let sin_inner =
                (output_index as f64 + 0.5) * (input_index as f64 + 0.5) * f64::consts::PI
                    / (input.len() as f64);
            let twiddle = sin_inner.sin();
            entry += input[input_index] * twiddle;
        }
        result.push(entry);
    }

    result
}

/// Simplified version of DST5
pub fn reference_dst5(input: &[f64]) -> Vec<f64> {
    let mut result = Vec::new();
    for output_index in 0..input.len() {
        let mut entry = 0.0;
        for input_index in 0..input.len() {
            let sin_inner =
                (output_index as f64 + 1.0) * (input_index as f64 + 1.0) * f64::consts::PI
                    / ((input.len()) as f64 + 0.5);
            let twiddle = sin_inner.sin();
            entry += input[input_index] * twiddle;
        }
        result.push(entry);
    }
    result
}

/// Simplified version of DST6
pub fn reference_dst6(input: &[f64]) -> Vec<f64> {
    let mut result = Vec::new();
    for output_index in 0..input.len() {
        let mut entry = 0.0;
        for input_index in 0..input.len() {
            let sin_inner =
                (output_index as f64 + 1.0) * (input_index as f64 + 0.5) * f64::consts::PI
                    / (input.len() as f64 + 0.5);
            let twiddle = sin_inner.sin();
            entry += input[input_index] * twiddle;
        }
        result.push(entry);
    }
    result
}

/// Simplified version of DST7
pub fn reference_dst7(input: &[f64]) -> Vec<f64> {
    let mut result = Vec::new();
    for output_index in 0..input.len() {
        let mut entry = 0.0;
        for input_index in 0..input.len() {
            let sin_inner =
                (output_index as f64 + 0.5) * (input_index as f64 + 1.0) * f64::consts::PI
                    / (input.len() as f64 + 0.5);
            let twiddle = sin_inner.sin();
            entry += input[input_index] * twiddle;
        }
        result.push(entry);
    }
    result
}

/// Simplified version of DST8
pub fn reference_dst8(input: &[f64]) -> Vec<f64> {
    let mut result = Vec::new();

    for output_index in 0..input.len() {
        let mut entry = 0.0;
        for input_index in 0..input.len() {
            let multiplier = if input_index == input.len() - 1 {
                0.5
            } else {
                1.0
            };
            let sin_inner =
                (output_index as f64 + 0.5) * (input_index as f64 + 0.5) * f64::consts::PI
                    / (input.len() as f64 - 0.5);
            let twiddle = sin_inner.sin();
            entry += input[input_index] * twiddle * multiplier;
        }
        result.push(entry);
    }

    result
}