Source file src/image/jpeg/fdct.go

     1	// Copyright 2011 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 file implements a Forward Discrete Cosine Transformation.
     8	
     9	/*
    10	It is based on the code in jfdctint.c from the Independent JPEG Group,
    11	found at http://www.ijg.org/files/jpegsrc.v8c.tar.gz.
    12	
    13	The "LEGAL ISSUES" section of the README in that archive says:
    14	
    15	In plain English:
    16	
    17	1. We don't promise that this software works.  (But if you find any bugs,
    18	   please let us know!)
    19	2. You can use this software for whatever you want.  You don't have to pay us.
    20	3. You may not pretend that you wrote this software.  If you use it in a
    21	   program, you must acknowledge somewhere in your documentation that
    22	   you've used the IJG code.
    23	
    24	In legalese:
    25	
    26	The authors make NO WARRANTY or representation, either express or implied,
    27	with respect to this software, its quality, accuracy, merchantability, or
    28	fitness for a particular purpose.  This software is provided "AS IS", and you,
    29	its user, assume the entire risk as to its quality and accuracy.
    30	
    31	This software is copyright (C) 1991-2011, Thomas G. Lane, Guido Vollbeding.
    32	All Rights Reserved except as specified below.
    33	
    34	Permission is hereby granted to use, copy, modify, and distribute this
    35	software (or portions thereof) for any purpose, without fee, subject to these
    36	conditions:
    37	(1) If any part of the source code for this software is distributed, then this
    38	README file must be included, with this copyright and no-warranty notice
    39	unaltered; and any additions, deletions, or changes to the original files
    40	must be clearly indicated in accompanying documentation.
    41	(2) If only executable code is distributed, then the accompanying
    42	documentation must state that "this software is based in part on the work of
    43	the Independent JPEG Group".
    44	(3) Permission for use of this software is granted only if the user accepts
    45	full responsibility for any undesirable consequences; the authors accept
    46	NO LIABILITY for damages of any kind.
    47	
    48	These conditions apply to any software derived from or based on the IJG code,
    49	not just to the unmodified library.  If you use our work, you ought to
    50	acknowledge us.
    51	
    52	Permission is NOT granted for the use of any IJG author's name or company name
    53	in advertising or publicity relating to this software or products derived from
    54	it.  This software may be referred to only as "the Independent JPEG Group's
    55	software".
    56	
    57	We specifically permit and encourage the use of this software as the basis of
    58	commercial products, provided that all warranty or liability claims are
    59	assumed by the product vendor.
    60	*/
    61	
    62	// Trigonometric constants in 13-bit fixed point format.
    63	const (
    64		fix_0_298631336 = 2446
    65		fix_0_390180644 = 3196
    66		fix_0_541196100 = 4433
    67		fix_0_765366865 = 6270
    68		fix_0_899976223 = 7373
    69		fix_1_175875602 = 9633
    70		fix_1_501321110 = 12299
    71		fix_1_847759065 = 15137
    72		fix_1_961570560 = 16069
    73		fix_2_053119869 = 16819
    74		fix_2_562915447 = 20995
    75		fix_3_072711026 = 25172
    76	)
    77	
    78	const (
    79		constBits     = 13
    80		pass1Bits     = 2
    81		centerJSample = 128
    82	)
    83	
    84	// fdct performs a forward DCT on an 8x8 block of coefficients, including a
    85	// level shift.
    86	func fdct(b *block) {
    87		// Pass 1: process rows.
    88		for y := 0; y < 8; y++ {
    89			y8 := y * 8
    90			s := b[y8 : y8+8 : y8+8] // Small cap improves performance, see https://golang.org/issue/27857
    91			x0 := s[0]
    92			x1 := s[1]
    93			x2 := s[2]
    94			x3 := s[3]
    95			x4 := s[4]
    96			x5 := s[5]
    97			x6 := s[6]
    98			x7 := s[7]
    99	
   100			tmp0 := x0 + x7
   101			tmp1 := x1 + x6
   102			tmp2 := x2 + x5
   103			tmp3 := x3 + x4
   104	
   105			tmp10 := tmp0 + tmp3
   106			tmp12 := tmp0 - tmp3
   107			tmp11 := tmp1 + tmp2
   108			tmp13 := tmp1 - tmp2
   109	
   110			tmp0 = x0 - x7
   111			tmp1 = x1 - x6
   112			tmp2 = x2 - x5
   113			tmp3 = x3 - x4
   114	
   115			s[0] = (tmp10 + tmp11 - 8*centerJSample) << pass1Bits
   116			s[4] = (tmp10 - tmp11) << pass1Bits
   117			z1 := (tmp12 + tmp13) * fix_0_541196100
   118			z1 += 1 << (constBits - pass1Bits - 1)
   119			s[2] = (z1 + tmp12*fix_0_765366865) >> (constBits - pass1Bits)
   120			s[6] = (z1 - tmp13*fix_1_847759065) >> (constBits - pass1Bits)
   121	
   122			tmp10 = tmp0 + tmp3
   123			tmp11 = tmp1 + tmp2
   124			tmp12 = tmp0 + tmp2
   125			tmp13 = tmp1 + tmp3
   126			z1 = (tmp12 + tmp13) * fix_1_175875602
   127			z1 += 1 << (constBits - pass1Bits - 1)
   128			tmp0 *= fix_1_501321110
   129			tmp1 *= fix_3_072711026
   130			tmp2 *= fix_2_053119869
   131			tmp3 *= fix_0_298631336
   132			tmp10 *= -fix_0_899976223
   133			tmp11 *= -fix_2_562915447
   134			tmp12 *= -fix_0_390180644
   135			tmp13 *= -fix_1_961570560
   136	
   137			tmp12 += z1
   138			tmp13 += z1
   139			s[1] = (tmp0 + tmp10 + tmp12) >> (constBits - pass1Bits)
   140			s[3] = (tmp1 + tmp11 + tmp13) >> (constBits - pass1Bits)
   141			s[5] = (tmp2 + tmp11 + tmp12) >> (constBits - pass1Bits)
   142			s[7] = (tmp3 + tmp10 + tmp13) >> (constBits - pass1Bits)
   143		}
   144		// Pass 2: process columns.
   145		// We remove pass1Bits scaling, but leave results scaled up by an overall factor of 8.
   146		for x := 0; x < 8; x++ {
   147			tmp0 := b[0*8+x] + b[7*8+x]
   148			tmp1 := b[1*8+x] + b[6*8+x]
   149			tmp2 := b[2*8+x] + b[5*8+x]
   150			tmp3 := b[3*8+x] + b[4*8+x]
   151	
   152			tmp10 := tmp0 + tmp3 + 1<<(pass1Bits-1)
   153			tmp12 := tmp0 - tmp3
   154			tmp11 := tmp1 + tmp2
   155			tmp13 := tmp1 - tmp2
   156	
   157			tmp0 = b[0*8+x] - b[7*8+x]
   158			tmp1 = b[1*8+x] - b[6*8+x]
   159			tmp2 = b[2*8+x] - b[5*8+x]
   160			tmp3 = b[3*8+x] - b[4*8+x]
   161	
   162			b[0*8+x] = (tmp10 + tmp11) >> pass1Bits
   163			b[4*8+x] = (tmp10 - tmp11) >> pass1Bits
   164	
   165			z1 := (tmp12 + tmp13) * fix_0_541196100
   166			z1 += 1 << (constBits + pass1Bits - 1)
   167			b[2*8+x] = (z1 + tmp12*fix_0_765366865) >> (constBits + pass1Bits)
   168			b[6*8+x] = (z1 - tmp13*fix_1_847759065) >> (constBits + pass1Bits)
   169	
   170			tmp10 = tmp0 + tmp3
   171			tmp11 = tmp1 + tmp2
   172			tmp12 = tmp0 + tmp2
   173			tmp13 = tmp1 + tmp3
   174			z1 = (tmp12 + tmp13) * fix_1_175875602
   175			z1 += 1 << (constBits + pass1Bits - 1)
   176			tmp0 *= fix_1_501321110
   177			tmp1 *= fix_3_072711026
   178			tmp2 *= fix_2_053119869
   179			tmp3 *= fix_0_298631336
   180			tmp10 *= -fix_0_899976223
   181			tmp11 *= -fix_2_562915447
   182			tmp12 *= -fix_0_390180644
   183			tmp13 *= -fix_1_961570560
   184	
   185			tmp12 += z1
   186			tmp13 += z1
   187			b[1*8+x] = (tmp0 + tmp10 + tmp12) >> (constBits + pass1Bits)
   188			b[3*8+x] = (tmp1 + tmp11 + tmp13) >> (constBits + pass1Bits)
   189			b[5*8+x] = (tmp2 + tmp11 + tmp12) >> (constBits + pass1Bits)
   190			b[7*8+x] = (tmp3 + tmp10 + tmp13) >> (constBits + pass1Bits)
   191		}
   192	}
   193	

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