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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
}
|
