// Copyright 2009 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package jpeg
// This is a Go translation of idct.c from
//
// http://standards.iso.org/ittf/PubliclyAvailableStandards/ISO_IEC_13818-4_2004_Conformance_Testing/Video/verifier/mpeg2decode_960109.tar.gz
//
// which carries the following notice:
/* Copyright (C) 1996, MPEG Software Simulation Group. All Rights Reserved. */
/*
* Disclaimer of Warranty
*
* These software programs are available to the user without any license fee or
* royalty on an "as is" basis. The MPEG Software Simulation Group disclaims
* any and all warranties, whether express, implied, or statuary, including any
* implied warranties or merchantability or of fitness for a particular
* purpose. In no event shall the copyright-holder be liable for any
* incidental, punitive, or consequential damages of any kind whatsoever
* arising from the use of these programs.
*
* This disclaimer of warranty extends to the user of these programs and user's
* customers, employees, agents, transferees, successors, and assigns.
*
* The MPEG Software Simulation Group does not represent or warrant that the
* programs furnished hereunder are free of infringement of any third-party
* patents.
*
* Commercial implementations of MPEG-1 and MPEG-2 video, including shareware,
* are subject to royalty fees to patent holders. Many of these patents are
* general enough such that they are unavoidable regardless of implementation
* design.
*
*/
const blockSize = 64 // A DCT block is 8x8.
type block [blockSize]int32
const (
w1 = 2841 // 2048*sqrt(2)*cos(1*pi/16)
w2 = 2676 // 2048*sqrt(2)*cos(2*pi/16)
w3 = 2408 // 2048*sqrt(2)*cos(3*pi/16)
w5 = 1609 // 2048*sqrt(2)*cos(5*pi/16)
w6 = 1108 // 2048*sqrt(2)*cos(6*pi/16)
w7 = 565 // 2048*sqrt(2)*cos(7*pi/16)
w1pw7 = w1 + w7
w1mw7 = w1 - w7
w2pw6 = w2 + w6
w2mw6 = w2 - w6
w3pw5 = w3 + w5
w3mw5 = w3 - w5
r2 = 181 // 256/sqrt(2)
)
// idct performs a 2-D Inverse Discrete Cosine Transformation.
//
// The input coefficients should already have been multiplied by the
// appropriate quantization table. We use fixed-point computation, with the
// number of bits for the fractional component varying over the intermediate
// stages.
//
// For more on the actual algorithm, see Z. Wang, "Fast algorithms for the
// discrete W transform and for the discrete Fourier transform", IEEE Trans. on
// ASSP, Vol. ASSP- 32, pp. 803-816, Aug. 1984.
func idct(src *block) {
// Horizontal 1-D IDCT.
for y := 0; y < 8; y++ {
y8 := y * 8
s := src[y8 : y8+8 : y8+8] // Small cap improves performance, see https://golang.org/issue/27857
// If all the AC components are zero, then the IDCT is trivial.
if s[1] == 0 && s[2] == 0 && s[3] == 0 &&
s[4] == 0 && s[5] == 0 && s[6] == 0 && s[7] == 0 {
dc := s[0] << 3
s[0] = dc
s[1] = dc
s[2] = dc
s[3] = dc
s[4] = dc
s[5] = dc
s[6] = dc
s[7] = dc
continue
}
// Prescale.
x0 := (s[0] << 11) + 128
x1 := s[4] << 11
x2 := s[6]
x3 := s[2]
x4 := s[1]
x5 := s[7]
x6 := s[5]
x7 := s[3]
// Stage 1.
x8 := w7 * (x4 + x5)
x4 = x8 + w1mw7*x4
x5 = x8 - w1pw7*x5
x8 = w3 * (x6 + x7)
x6 = x8 - w3mw5*x6
x7 = x8 - w3pw5*x7
// Stage 2.
x8 = x0 + x1
x0 -= x1
x1 = w6 * (x3 + x2)
x2 = x1 - w2pw6*x2
x3 = x1 + w2mw6*x3
x1 = x4 + x6
x4 -= x6
x6 = x5 + x7
x5 -= x7
// Stage 3.
x7 = x8 + x3
x8 -= x3
x3 = x0 + x2
x0 -= x2
x2 = (r2*(x4+x5) + 128) >> 8
x4 = (r2*(x4-x5) + 128) >> 8
// Stage 4.
s[0] = (x7 + x1) >> 8
s[1] = (x3 + x2) >> 8
s[2] = (x0 + x4) >> 8
s[3] = (x8 + x6) >> 8
s[4] = (x8 - x6) >> 8
s[5] = (x0 - x4) >> 8
s[6] = (x3 - x2) >> 8
s[7] = (x7 - x1) >> 8
}
// Vertical 1-D IDCT.
for x := 0; x < 8; x++ {
// Similar to the horizontal 1-D IDCT case, if all the AC components are zero, then the IDCT is trivial.
// However, after performing the horizontal 1-D IDCT, there are typically non-zero AC components, so
// we do not bother to check for the all-zero case.
s := src[x : x+57 : x+57] // Small cap improves performance, see https://golang.org/issue/27857
// Prescale.
y0 := (s[8*0] << 8) + 8192
y1 := s[8*4] << 8
y2 := s[8*6]
y3 := s[8*2]
y4 := s[8*1]
y5 := s[8*7]
y6 := s[8*5]
y7 := s[8*3]
// Stage 1.
y8 := w7*(y4+y5) + 4
y4 = (y8 + w1mw7*y4) >> 3
y5 = (y8 - w1pw7*y5) >> 3
y8 = w3*(y6+y7) + 4
y6 = (y8 - w3mw5*y6) >> 3
y7 = (y8 - w3pw5*y7) >> 3
// Stage 2.
y8 = y0 + y1
y0 -= y1
y1 = w6*(y3+y2) + 4
y2 = (y1 - w2pw6*y2) >> 3
y3 = (y1 + w2mw6*y3) >> 3
y1 = y4 + y6
y4 -= y6
y6 = y5 + y7
y5 -= y7
// Stage 3.
y7 = y8 + y3
y8 -= y3
y3 = y0 + y2
y0 -= y2
y2 = (r2*(y4+y5) + 128) >> 8
y4 = (r2*(y4-y5) + 128) >> 8
// Stage 4.
s[8*0] = (y7 + y1) >> 14
s[8*1] = (y3 + y2) >> 14
s[8*2] = (y0 + y4) >> 14
s[8*3] = (y8 + y6) >> 14
s[8*4] = (y8 - y6) >> 14
s[8*5] = (y0 - y4) >> 14
s[8*6] = (y3 - y2) >> 14
s[8*7] = (y7 - y1) >> 14
}
}