libgo/go/image/jpeg/idct.go

   1 // Copyright 2009 The Go Authors. All rights reserved.
   2 // Use of this source code is governed by a BSD-style
   3 // license that can be found in the LICENSE file.
   4
   5 package jpeg
   6
   7 // This is a Go translation of idct.c from
   8 //
   9 // http://standards.iso.org/ittf/PubliclyAvailableStandards/ISO_IEC_13818-4_2004_Conformance_Testing/Video/verifier/mpeg2decode_960109.tar.gz
  10 //
  11 // which carries the following notice:
  12
  13 /* Copyright (C) 1996, MPEG Software Simulation Group. All Rights Reserved. */
  14
  15 /*
  16  * Disclaimer of Warranty
  17  *
  18  * These software programs are available to the user without any license fee or
  19  * royalty on an "as is" basis.  The MPEG Software Simulation Group disclaims
  20  * any and all warranties, whether express, implied, or statuary, including any
  21  * implied warranties or merchantability or of fitness for a particular
  22  * purpose.  In no event shall the copyright-holder be liable for any
  23  * incidental, punitive, or consequential damages of any kind whatsoever
  24  * arising from the use of these programs.
  25  *
  26  * This disclaimer of warranty extends to the user of these programs and user's
  27  * customers, employees, agents, transferees, successors, and assigns.
  28  *
  29  * The MPEG Software Simulation Group does not represent or warrant that the
  30  * programs furnished hereunder are free of infringement of any third-party
  31  * patents.
  32  *
  33  * Commercial implementations of MPEG-1 and MPEG-2 video, including shareware,
  34  * are subject to royalty fees to patent holders.  Many of these patents are
  35  * general enough such that they are unavoidable regardless of implementation
  36  * design.
  37  *
  38  */
  39
  40 const blockSize = 64 // A DCT block is 8x8.
  41
  42 type block [blockSize]int32
  43
  44 const (
  45         w1 = 2841 // 2048*sqrt(2)*cos(1*pi/16)
  46         w2 = 2676 // 2048*sqrt(2)*cos(2*pi/16)
  47         w3 = 2408 // 2048*sqrt(2)*cos(3*pi/16)
  48         w5 = 1609 // 2048*sqrt(2)*cos(5*pi/16)
  49         w6 = 1108 // 2048*sqrt(2)*cos(6*pi/16)
  50         w7 = 565  // 2048*sqrt(2)*cos(7*pi/16)
  51
  52         w1pw7 = w1 + w7
  53         w1mw7 = w1 - w7
  54         w2pw6 = w2 + w6
  55         w2mw6 = w2 - w6
  56         w3pw5 = w3 + w5
  57         w3mw5 = w3 - w5
  58
  59         r2 = 181 // 256/sqrt(2)
  60 )
  61
  62 // idct performs a 2-D Inverse Discrete Cosine Transformation.
  63 //
  64 // The input coefficients should already have been multiplied by the
  65 // appropriate quantization table. We use fixed-point computation, with the
  66 // number of bits for the fractional component varying over the intermediate
  67 // stages.
  68 //
  69 // For more on the actual algorithm, see Z. Wang, "Fast algorithms for the
  70 // discrete W transform and for the discrete Fourier transform", IEEE Trans. on
  71 // ASSP, Vol. ASSP- 32, pp. 803-816, Aug. 1984.
  72 func idct(src *block) {
  73         // Horizontal 1-D IDCT.
  74         for y := 0; y < 8; y++ {
  75                 y8 := y * 8
  76                 s := src[y8 : y8+8 : y8+8] // Small cap improves performance, see https://golang.org/issue/27857
  77                 // If all the AC components are zero, then the IDCT is trivial.
  78                 if s[1] == 0 && s[2] == 0 && s[3] == 0 &&
  79                         s[4] == 0 && s[5] == 0 && s[6] == 0 && s[7] == 0 {
  80                         dc := s[0] << 3
  81                         s[0] = dc
  82                         s[1] = dc
  83                         s[2] = dc
  84                         s[3] = dc
  85                         s[4] = dc
  86                         s[5] = dc
  87                         s[6] = dc
  88                         s[7] = dc
  89                         continue
  90                 }
  91
  92                 // Prescale.
  93                 x0 := (s[0] << 11) + 128
  94                 x1 := s[4] << 11
  95                 x2 := s[6]
  96                 x3 := s[2]
  97                 x4 := s[1]
  98                 x5 := s[7]
  99                 x6 := s[5]
 100                 x7 := s[3]
 101
 102                 // Stage 1.
 103                 x8 := w7 * (x4 + x5)
 104                 x4 = x8 + w1mw7*x4
 105                 x5 = x8 - w1pw7*x5
 106                 x8 = w3 * (x6 + x7)
 107                 x6 = x8 - w3mw5*x6
 108                 x7 = x8 - w3pw5*x7
 109
 110                 // Stage 2.
 111                 x8 = x0 + x1
 112                 x0 -= x1
 113                 x1 = w6 * (x3 + x2)
 114                 x2 = x1 - w2pw6*x2
 115                 x3 = x1 + w2mw6*x3
 116                 x1 = x4 + x6
 117                 x4 -= x6
 118                 x6 = x5 + x7
 119                 x5 -= x7
 120
 121                 // Stage 3.
 122                 x7 = x8 + x3
 123                 x8 -= x3
 124                 x3 = x0 + x2
 125                 x0 -= x2
 126                 x2 = (r2*(x4+x5) + 128) >> 8
 127                 x4 = (r2*(x4-x5) + 128) >> 8
 128
 129                 // Stage 4.
 130                 s[0] = (x7 + x1) >> 8
 131                 s[1] = (x3 + x2) >> 8
 132                 s[2] = (x0 + x4) >> 8
 133                 s[3] = (x8 + x6) >> 8
 134                 s[4] = (x8 - x6) >> 8
 135                 s[5] = (x0 - x4) >> 8
 136                 s[6] = (x3 - x2) >> 8
 137                 s[7] = (x7 - x1) >> 8
 138         }
 139
 140         // Vertical 1-D IDCT.
 141         for x := 0; x < 8; x++ {
 142                 // Similar to the horizontal 1-D IDCT case, if all the AC components are zero, then the IDCT is trivial.
 143                 // However, after performing the horizontal 1-D IDCT, there are typically non-zero AC components, so
 144                 // we do not bother to check for the all-zero case.
 145                 s := src[x : x+57 : x+57] // Small cap improves performance, see https://golang.org/issue/27857
 146
 147                 // Prescale.
 148                 y0 := (s[8*0] << 8) + 8192
 149                 y1 := s[8*4] << 8
 150                 y2 := s[8*6]
 151                 y3 := s[8*2]
 152                 y4 := s[8*1]
 153                 y5 := s[8*7]
 154                 y6 := s[8*5]
 155                 y7 := s[8*3]
 156
 157                 // Stage 1.
 158                 y8 := w7*(y4+y5) + 4
 159                 y4 = (y8 + w1mw7*y4) >> 3
 160                 y5 = (y8 - w1pw7*y5) >> 3
 161                 y8 = w3*(y6+y7) + 4
 162                 y6 = (y8 - w3mw5*y6) >> 3
 163                 y7 = (y8 - w3pw5*y7) >> 3
 164
 165                 // Stage 2.
 166                 y8 = y0 + y1
 167                 y0 -= y1
 168                 y1 = w6*(y3+y2) + 4
 169                 y2 = (y1 - w2pw6*y2) >> 3
 170                 y3 = (y1 + w2mw6*y3) >> 3
 171                 y1 = y4 + y6
 172                 y4 -= y6
 173                 y6 = y5 + y7
 174                 y5 -= y7
 175
 176                 // Stage 3.
 177                 y7 = y8 + y3
 178                 y8 -= y3
 179                 y3 = y0 + y2
 180                 y0 -= y2
 181                 y2 = (r2*(y4+y5) + 128) >> 8
 182                 y4 = (r2*(y4-y5) + 128) >> 8
 183
 184                 // Stage 4.
 185                 s[8*0] = (y7 + y1) >> 14
 186                 s[8*1] = (y3 + y2) >> 14
 187                 s[8*2] = (y0 + y4) >> 14
 188                 s[8*3] = (y8 + y6) >> 14
 189                 s[8*4] = (y8 - y6) >> 14
 190                 s[8*5] = (y0 - y4) >> 14
 191                 s[8*6] = (y3 - y2) >> 14
 192                 s[8*7] = (y7 - y1) >> 14
 193         }
 194 }