text: // 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
  		// If all the AC components are zero, then the IDCT is trivial.
  		if src[y8+1] == 0 && src[y8+2] == 0 && src[y8+3] == 0 &&
  			src[y8+4] == 0 && src[y8+5] == 0 && src[y8+6] == 0 && src[y8+7] == 0 {
  			dc := src[y8+0] << 3
  			src[y8+0] = dc
  			src[y8+1] = dc
  			src[y8+2] = dc
  			src[y8+3] = dc
  			src[y8+4] = dc
  			src[y8+5] = dc
  			src[y8+6] = dc
  			src[y8+7] = dc
  			continue
  		}
  
  		// Prescale.
  		x0 := (src[y8+0] << 11) + 128
  		x1 := src[y8+4] << 11
  		x2 := src[y8+6]
  		x3 := src[y8+2]
  		x4 := src[y8+1]
  		x5 := src[y8+7]
  		x6 := src[y8+5]
  		x7 := src[y8+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.
  		src[y8+0] = (x7 + x1) >> 8
  		src[y8+1] = (x3 + x2) >> 8
  		src[y8+2] = (x0 + x4) >> 8
  		src[y8+3] = (x8 + x6) >> 8
  		src[y8+4] = (x8 - x6) >> 8
  		src[y8+5] = (x0 - x4) >> 8
  		src[y8+6] = (x3 - x2) >> 8
  		src[y8+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.
  
  		// Prescale.
  		y0 := (src[8*0+x] << 8) + 8192
  		y1 := src[8*4+x] << 8
  		y2 := src[8*6+x]
  		y3 := src[8*2+x]
  		y4 := src[8*1+x]
  		y5 := src[8*7+x]
  		y6 := src[8*5+x]
  		y7 := src[8*3+x]
  
  		// 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.
  		src[8*0+x] = (y7 + y1) >> 14
  		src[8*1+x] = (y3 + y2) >> 14
  		src[8*2+x] = (y0 + y4) >> 14
  		src[8*3+x] = (y8 + y6) >> 14
  		src[8*4+x] = (y8 - y6) >> 14
  		src[8*5+x] = (y0 - y4) >> 14
  		src[8*6+x] = (y3 - y2) >> 14
  		src[8*7+x] = (y7 - y1) >> 14
  	}
  }
  