fdct.go

Documentation: image/jpeg

		 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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