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Source file src/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			// If all the AC components are zero, then the IDCT is trivial.
    77			if src[y8+1] == 0 && src[y8+2] == 0 && src[y8+3] == 0 &&
    78				src[y8+4] == 0 && src[y8+5] == 0 && src[y8+6] == 0 && src[y8+7] == 0 {
    79				dc := src[y8+0] << 3
    80				src[y8+0] = dc
    81				src[y8+1] = dc
    82				src[y8+2] = dc
    83				src[y8+3] = dc
    84				src[y8+4] = dc
    85				src[y8+5] = dc
    86				src[y8+6] = dc
    87				src[y8+7] = dc
    88				continue
    89			}
    90	
    91			// Prescale.
    92			x0 := (src[y8+0] << 11) + 128
    93			x1 := src[y8+4] << 11
    94			x2 := src[y8+6]
    95			x3 := src[y8+2]
    96			x4 := src[y8+1]
    97			x5 := src[y8+7]
    98			x6 := src[y8+5]
    99			x7 := src[y8+3]
   100	
   101			// Stage 1.
   102			x8 := w7 * (x4 + x5)
   103			x4 = x8 + w1mw7*x4
   104			x5 = x8 - w1pw7*x5
   105			x8 = w3 * (x6 + x7)
   106			x6 = x8 - w3mw5*x6
   107			x7 = x8 - w3pw5*x7
   108	
   109			// Stage 2.
   110			x8 = x0 + x1
   111			x0 -= x1
   112			x1 = w6 * (x3 + x2)
   113			x2 = x1 - w2pw6*x2
   114			x3 = x1 + w2mw6*x3
   115			x1 = x4 + x6
   116			x4 -= x6
   117			x6 = x5 + x7
   118			x5 -= x7
   119	
   120			// Stage 3.
   121			x7 = x8 + x3
   122			x8 -= x3
   123			x3 = x0 + x2
   124			x0 -= x2
   125			x2 = (r2*(x4+x5) + 128) >> 8
   126			x4 = (r2*(x4-x5) + 128) >> 8
   127	
   128			// Stage 4.
   129			src[y8+0] = (x7 + x1) >> 8
   130			src[y8+1] = (x3 + x2) >> 8
   131			src[y8+2] = (x0 + x4) >> 8
   132			src[y8+3] = (x8 + x6) >> 8
   133			src[y8+4] = (x8 - x6) >> 8
   134			src[y8+5] = (x0 - x4) >> 8
   135			src[y8+6] = (x3 - x2) >> 8
   136			src[y8+7] = (x7 - x1) >> 8
   137		}
   138	
   139		// Vertical 1-D IDCT.
   140		for x := 0; x < 8; x++ {
   141			// Similar to the horizontal 1-D IDCT case, if all the AC components are zero, then the IDCT is trivial.
   142			// However, after performing the horizontal 1-D IDCT, there are typically non-zero AC components, so
   143			// we do not bother to check for the all-zero case.
   144	
   145			// Prescale.
   146			y0 := (src[8*0+x] << 8) + 8192
   147			y1 := src[8*4+x] << 8
   148			y2 := src[8*6+x]
   149			y3 := src[8*2+x]
   150			y4 := src[8*1+x]
   151			y5 := src[8*7+x]
   152			y6 := src[8*5+x]
   153			y7 := src[8*3+x]
   154	
   155			// Stage 1.
   156			y8 := w7*(y4+y5) + 4
   157			y4 = (y8 + w1mw7*y4) >> 3
   158			y5 = (y8 - w1pw7*y5) >> 3
   159			y8 = w3*(y6+y7) + 4
   160			y6 = (y8 - w3mw5*y6) >> 3
   161			y7 = (y8 - w3pw5*y7) >> 3
   162	
   163			// Stage 2.
   164			y8 = y0 + y1
   165			y0 -= y1
   166			y1 = w6*(y3+y2) + 4
   167			y2 = (y1 - w2pw6*y2) >> 3
   168			y3 = (y1 + w2mw6*y3) >> 3
   169			y1 = y4 + y6
   170			y4 -= y6
   171			y6 = y5 + y7
   172			y5 -= y7
   173	
   174			// Stage 3.
   175			y7 = y8 + y3
   176			y8 -= y3
   177			y3 = y0 + y2
   178			y0 -= y2
   179			y2 = (r2*(y4+y5) + 128) >> 8
   180			y4 = (r2*(y4-y5) + 128) >> 8
   181	
   182			// Stage 4.
   183			src[8*0+x] = (y7 + y1) >> 14
   184			src[8*1+x] = (y3 + y2) >> 14
   185			src[8*2+x] = (y0 + y4) >> 14
   186			src[8*3+x] = (y8 + y6) >> 14
   187			src[8*4+x] = (y8 - y6) >> 14
   188			src[8*5+x] = (y0 - y4) >> 14
   189			src[8*6+x] = (y3 - y2) >> 14
   190			src[8*7+x] = (y7 - y1) >> 14
   191		}
   192	}
   193	

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