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+// Copyright 2009 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 is a Go translation of idct.c from
+//
+// http://standards.iso.org/ittf/PubliclyAvailableStandards/ISO_IEC_13818-4_2004_Conformance_Testing/Video/verifier/mpeg2decode_960109.tar.gz
+//
+// which carries the following notice:
+
+/* Copyright (C) 1996, MPEG Software Simulation Group. All Rights Reserved. */
+
+/*
+ * Disclaimer of Warranty
+ *
+ * These software programs are available to the user without any license fee or
+ * royalty on an "as is" basis. The MPEG Software Simulation Group disclaims
+ * any and all warranties, whether express, implied, or statuary, including any
+ * implied warranties or merchantability or of fitness for a particular
+ * purpose. In no event shall the copyright-holder be liable for any
+ * incidental, punitive, or consequential damages of any kind whatsoever
+ * arising from the use of these programs.
+ *
+ * This disclaimer of warranty extends to the user of these programs and user's
+ * customers, employees, agents, transferees, successors, and assigns.
+ *
+ * The MPEG Software Simulation Group does not represent or warrant that the
+ * programs furnished hereunder are free of infringement of any third-party
+ * patents.
+ *
+ * Commercial implementations of MPEG-1 and MPEG-2 video, including shareware,
+ * are subject to royalty fees to patent holders. Many of these patents are
+ * general enough such that they are unavoidable regardless of implementation
+ * design.
+ *
+ */
+
+const blockSize = 64 // A DCT block is 8x8.
+
+type block [blockSize]int32
+
+const (
+ w1 = 2841 // 2048*sqrt(2)*cos(1*pi/16)
+ w2 = 2676 // 2048*sqrt(2)*cos(2*pi/16)
+ w3 = 2408 // 2048*sqrt(2)*cos(3*pi/16)
+ w5 = 1609 // 2048*sqrt(2)*cos(5*pi/16)
+ w6 = 1108 // 2048*sqrt(2)*cos(6*pi/16)
+ w7 = 565 // 2048*sqrt(2)*cos(7*pi/16)
+
+ w1pw7 = w1 + w7
+ w1mw7 = w1 - w7
+ w2pw6 = w2 + w6
+ w2mw6 = w2 - w6
+ w3pw5 = w3 + w5
+ w3mw5 = w3 - w5
+
+ r2 = 181 // 256/sqrt(2)
+)
+
+// idct performs a 2-D Inverse Discrete Cosine Transformation.
+//
+// The input coefficients should already have been multiplied by the
+// appropriate quantization table. We use fixed-point computation, with the
+// number of bits for the fractional component varying over the intermediate
+// stages.
+//
+// For more on the actual algorithm, see Z. Wang, "Fast algorithms for the
+// discrete W transform and for the discrete Fourier transform", IEEE Trans. on
+// ASSP, Vol. ASSP- 32, pp. 803-816, Aug. 1984.
+func idct(src *block) {
+ // Horizontal 1-D IDCT.
+ for y := 0; y < 8; y++ {
+ y8 := y * 8
+ s := src[y8 : y8+8 : y8+8] // Small cap improves performance, see https://golang.org/issue/27857
+ // If all the AC components are zero, then the IDCT is trivial.
+ if s[1] == 0 && s[2] == 0 && s[3] == 0 &&
+ s[4] == 0 && s[5] == 0 && s[6] == 0 && s[7] == 0 {
+ dc := s[0] << 3
+ s[0] = dc
+ s[1] = dc
+ s[2] = dc
+ s[3] = dc
+ s[4] = dc
+ s[5] = dc
+ s[6] = dc
+ s[7] = dc
+ continue
+ }
+
+ // Prescale.
+ x0 := (s[0] << 11) + 128
+ x1 := s[4] << 11
+ x2 := s[6]
+ x3 := s[2]
+ x4 := s[1]
+ x5 := s[7]
+ x6 := s[5]
+ x7 := s[3]
+
+ // Stage 1.
+ x8 := w7 * (x4 + x5)
+ x4 = x8 + w1mw7*x4
+ x5 = x8 - w1pw7*x5
+ x8 = w3 * (x6 + x7)
+ x6 = x8 - w3mw5*x6
+ x7 = x8 - w3pw5*x7
+
+ // Stage 2.
+ x8 = x0 + x1
+ x0 -= x1
+ x1 = w6 * (x3 + x2)
+ x2 = x1 - w2pw6*x2
+ x3 = x1 + w2mw6*x3
+ x1 = x4 + x6
+ x4 -= x6
+ x6 = x5 + x7
+ x5 -= x7
+
+ // Stage 3.
+ x7 = x8 + x3
+ x8 -= x3
+ x3 = x0 + x2
+ x0 -= x2
+ x2 = (r2*(x4+x5) + 128) >> 8
+ x4 = (r2*(x4-x5) + 128) >> 8
+
+ // Stage 4.
+ s[0] = (x7 + x1) >> 8
+ s[1] = (x3 + x2) >> 8
+ s[2] = (x0 + x4) >> 8
+ s[3] = (x8 + x6) >> 8
+ s[4] = (x8 - x6) >> 8
+ s[5] = (x0 - x4) >> 8
+ s[6] = (x3 - x2) >> 8
+ s[7] = (x7 - x1) >> 8
+ }
+
+ // Vertical 1-D IDCT.
+ for x := 0; x < 8; x++ {
+ // Similar to the horizontal 1-D IDCT case, if all the AC components are zero, then the IDCT is trivial.
+ // However, after performing the horizontal 1-D IDCT, there are typically non-zero AC components, so
+ // we do not bother to check for the all-zero case.
+ s := src[x : x+57 : x+57] // Small cap improves performance, see https://golang.org/issue/27857
+
+ // Prescale.
+ y0 := (s[8*0] << 8) + 8192
+ y1 := s[8*4] << 8
+ y2 := s[8*6]
+ y3 := s[8*2]
+ y4 := s[8*1]
+ y5 := s[8*7]
+ y6 := s[8*5]
+ y7 := s[8*3]
+
+ // Stage 1.
+ y8 := w7*(y4+y5) + 4
+ y4 = (y8 + w1mw7*y4) >> 3
+ y5 = (y8 - w1pw7*y5) >> 3
+ y8 = w3*(y6+y7) + 4
+ y6 = (y8 - w3mw5*y6) >> 3
+ y7 = (y8 - w3pw5*y7) >> 3
+
+ // Stage 2.
+ y8 = y0 + y1
+ y0 -= y1
+ y1 = w6*(y3+y2) + 4
+ y2 = (y1 - w2pw6*y2) >> 3
+ y3 = (y1 + w2mw6*y3) >> 3
+ y1 = y4 + y6
+ y4 -= y6
+ y6 = y5 + y7
+ y5 -= y7
+
+ // Stage 3.
+ y7 = y8 + y3
+ y8 -= y3
+ y3 = y0 + y2
+ y0 -= y2
+ y2 = (r2*(y4+y5) + 128) >> 8
+ y4 = (r2*(y4-y5) + 128) >> 8
+
+ // Stage 4.
+ s[8*0] = (y7 + y1) >> 14
+ s[8*1] = (y3 + y2) >> 14
+ s[8*2] = (y0 + y4) >> 14
+ s[8*3] = (y8 + y6) >> 14
+ s[8*4] = (y8 - y6) >> 14
+ s[8*5] = (y0 - y4) >> 14
+ s[8*6] = (y3 - y2) >> 14
+ s[8*7] = (y7 - y1) >> 14
+ }
+}