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+// Copyright 2011 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 file implements a Forward Discrete Cosine Transformation.
+
+/*
+It is based on the code in jfdctint.c from the Independent JPEG Group,
+found at http://www.ijg.org/files/jpegsrc.v8c.tar.gz.
+
+The "LEGAL ISSUES" section of the README in that archive says:
+
+In plain English:
+
+1. We don't promise that this software works. (But if you find any bugs,
+ please let us know!)
+2. You can use this software for whatever you want. You don't have to pay us.
+3. You may not pretend that you wrote this software. If you use it in a
+ program, you must acknowledge somewhere in your documentation that
+ you've used the IJG code.
+
+In legalese:
+
+The authors make NO WARRANTY or representation, either express or implied,
+with respect to this software, its quality, accuracy, merchantability, or
+fitness for a particular purpose. This software is provided "AS IS", and you,
+its user, assume the entire risk as to its quality and accuracy.
+
+This software is copyright (C) 1991-2011, Thomas G. Lane, Guido Vollbeding.
+All Rights Reserved except as specified below.
+
+Permission is hereby granted to use, copy, modify, and distribute this
+software (or portions thereof) for any purpose, without fee, subject to these
+conditions:
+(1) If any part of the source code for this software is distributed, then this
+README file must be included, with this copyright and no-warranty notice
+unaltered; and any additions, deletions, or changes to the original files
+must be clearly indicated in accompanying documentation.
+(2) If only executable code is distributed, then the accompanying
+documentation must state that "this software is based in part on the work of
+the Independent JPEG Group".
+(3) Permission for use of this software is granted only if the user accepts
+full responsibility for any undesirable consequences; the authors accept
+NO LIABILITY for damages of any kind.
+
+These conditions apply to any software derived from or based on the IJG code,
+not just to the unmodified library. If you use our work, you ought to
+acknowledge us.
+
+Permission is NOT granted for the use of any IJG author's name or company name
+in advertising or publicity relating to this software or products derived from
+it. This software may be referred to only as "the Independent JPEG Group's
+software".
+
+We specifically permit and encourage the use of this software as the basis of
+commercial products, provided that all warranty or liability claims are
+assumed by the product vendor.
+*/
+
+// Trigonometric constants in 13-bit fixed point format.
+const (
+ fix_0_298631336 = 2446
+ fix_0_390180644 = 3196
+ fix_0_541196100 = 4433
+ fix_0_765366865 = 6270
+ fix_0_899976223 = 7373
+ fix_1_175875602 = 9633
+ fix_1_501321110 = 12299
+ fix_1_847759065 = 15137
+ fix_1_961570560 = 16069
+ fix_2_053119869 = 16819
+ fix_2_562915447 = 20995
+ fix_3_072711026 = 25172
+)
+
+const (
+ constBits = 13
+ pass1Bits = 2
+ centerJSample = 128
+)
+
+// fdct performs a forward DCT on an 8x8 block of coefficients, including a
+// level shift.
+func fdct(b *block) {
+ // Pass 1: process rows.
+ for y := 0; y < 8; y++ {
+ y8 := y * 8
+ s := b[y8 : y8+8 : y8+8] // Small cap improves performance, see https://golang.org/issue/27857
+ x0 := s[0]
+ x1 := s[1]
+ x2 := s[2]
+ x3 := s[3]
+ x4 := s[4]
+ x5 := s[5]
+ x6 := s[6]
+ x7 := s[7]
+
+ tmp0 := x0 + x7
+ tmp1 := x1 + x6
+ tmp2 := x2 + x5
+ tmp3 := x3 + x4
+
+ tmp10 := tmp0 + tmp3
+ tmp12 := tmp0 - tmp3
+ tmp11 := tmp1 + tmp2
+ tmp13 := tmp1 - tmp2
+
+ tmp0 = x0 - x7
+ tmp1 = x1 - x6
+ tmp2 = x2 - x5
+ tmp3 = x3 - x4
+
+ s[0] = (tmp10 + tmp11 - 8*centerJSample) << pass1Bits
+ s[4] = (tmp10 - tmp11) << pass1Bits
+ z1 := (tmp12 + tmp13) * fix_0_541196100
+ z1 += 1 << (constBits - pass1Bits - 1)
+ s[2] = (z1 + tmp12*fix_0_765366865) >> (constBits - pass1Bits)
+ s[6] = (z1 - tmp13*fix_1_847759065) >> (constBits - pass1Bits)
+
+ tmp10 = tmp0 + tmp3
+ tmp11 = tmp1 + tmp2
+ tmp12 = tmp0 + tmp2
+ tmp13 = tmp1 + tmp3
+ z1 = (tmp12 + tmp13) * fix_1_175875602
+ z1 += 1 << (constBits - pass1Bits - 1)
+ tmp0 *= fix_1_501321110
+ tmp1 *= fix_3_072711026
+ tmp2 *= fix_2_053119869
+ tmp3 *= fix_0_298631336
+ tmp10 *= -fix_0_899976223
+ tmp11 *= -fix_2_562915447
+ tmp12 *= -fix_0_390180644
+ tmp13 *= -fix_1_961570560
+
+ tmp12 += z1
+ tmp13 += z1
+ s[1] = (tmp0 + tmp10 + tmp12) >> (constBits - pass1Bits)
+ s[3] = (tmp1 + tmp11 + tmp13) >> (constBits - pass1Bits)
+ s[5] = (tmp2 + tmp11 + tmp12) >> (constBits - pass1Bits)
+ s[7] = (tmp3 + tmp10 + tmp13) >> (constBits - pass1Bits)
+ }
+ // Pass 2: process columns.
+ // We remove pass1Bits scaling, but leave results scaled up by an overall factor of 8.
+ for x := 0; x < 8; x++ {
+ tmp0 := b[0*8+x] + b[7*8+x]
+ tmp1 := b[1*8+x] + b[6*8+x]
+ tmp2 := b[2*8+x] + b[5*8+x]
+ tmp3 := b[3*8+x] + b[4*8+x]
+
+ tmp10 := tmp0 + tmp3 + 1<<(pass1Bits-1)
+ tmp12 := tmp0 - tmp3
+ tmp11 := tmp1 + tmp2
+ tmp13 := tmp1 - tmp2
+
+ tmp0 = b[0*8+x] - b[7*8+x]
+ tmp1 = b[1*8+x] - b[6*8+x]
+ tmp2 = b[2*8+x] - b[5*8+x]
+ tmp3 = b[3*8+x] - b[4*8+x]
+
+ b[0*8+x] = (tmp10 + tmp11) >> pass1Bits
+ b[4*8+x] = (tmp10 - tmp11) >> pass1Bits
+
+ z1 := (tmp12 + tmp13) * fix_0_541196100
+ z1 += 1 << (constBits + pass1Bits - 1)
+ b[2*8+x] = (z1 + tmp12*fix_0_765366865) >> (constBits + pass1Bits)
+ b[6*8+x] = (z1 - tmp13*fix_1_847759065) >> (constBits + pass1Bits)
+
+ tmp10 = tmp0 + tmp3
+ tmp11 = tmp1 + tmp2
+ tmp12 = tmp0 + tmp2
+ tmp13 = tmp1 + tmp3
+ z1 = (tmp12 + tmp13) * fix_1_175875602
+ z1 += 1 << (constBits + pass1Bits - 1)
+ tmp0 *= fix_1_501321110
+ tmp1 *= fix_3_072711026
+ tmp2 *= fix_2_053119869
+ tmp3 *= fix_0_298631336
+ tmp10 *= -fix_0_899976223
+ tmp11 *= -fix_2_562915447
+ tmp12 *= -fix_0_390180644
+ tmp13 *= -fix_1_961570560
+
+ tmp12 += z1
+ tmp13 += z1
+ b[1*8+x] = (tmp0 + tmp10 + tmp12) >> (constBits + pass1Bits)
+ b[3*8+x] = (tmp1 + tmp11 + tmp13) >> (constBits + pass1Bits)
+ b[5*8+x] = (tmp2 + tmp11 + tmp12) >> (constBits + pass1Bits)
+ b[7*8+x] = (tmp3 + tmp10 + tmp13) >> (constBits + pass1Bits)
+ }
+}