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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 (
        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, followed by a
// +128 level shift and a clip to [0, 255], writing the results to dst.
// stride is the number of elements between successive rows of dst.
//
// 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(dst []byte, stride int, src *block) {
        // Horizontal 1-D IDCT.
        for y := 0; y < 8; y++ {
                // If all the AC components are zero, then the IDCT is trivial.
                if src[y*8+1] == 0 && src[y*8+2] == 0 && src[y*8+3] == 0 &&
                        src[y*8+4] == 0 && src[y*8+5] == 0 && src[y*8+6] == 0 && src[y*8+7] == 0 {
                        dc := src[y*8+0] << 3
                        src[y*8+0] = dc
                        src[y*8+1] = dc
                        src[y*8+2] = dc
                        src[y*8+3] = dc
                        src[y*8+4] = dc
                        src[y*8+5] = dc
                        src[y*8+6] = dc
                        src[y*8+7] = dc
                        continue
                }

                // Prescale.
                x0 := (src[y*8+0] << 11) + 128
                x1 := src[y*8+4] << 11
                x2 := src[y*8+6]
                x3 := src[y*8+2]
                x4 := src[y*8+1]
                x5 := src[y*8+7]
                x6 := src[y*8+5]
                x7 := src[y*8+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.
                src[8*y+0] = (x7 + x1) >> 8
                src[8*y+1] = (x3 + x2) >> 8
                src[8*y+2] = (x0 + x4) >> 8
                src[8*y+3] = (x8 + x6) >> 8
                src[8*y+4] = (x8 - x6) >> 8
                src[8*y+5] = (x0 - x4) >> 8
                src[8*y+6] = (x3 - x2) >> 8
                src[8*y+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.

                // Prescale.
                y0 := (src[8*0+x] << 8) + 8192
                y1 := src[8*4+x] << 8
                y2 := src[8*6+x]
                y3 := src[8*2+x]
                y4 := src[8*1+x]
                y5 := src[8*7+x]
                y6 := src[8*5+x]
                y7 := src[8*3+x]

                // 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.
                src[8*0+x] = (y7 + y1) >> 14
                src[8*1+x] = (y3 + y2) >> 14
                src[8*2+x] = (y0 + y4) >> 14
                src[8*3+x] = (y8 + y6) >> 14
                src[8*4+x] = (y8 - y6) >> 14
                src[8*5+x] = (y0 - y4) >> 14
                src[8*6+x] = (y3 - y2) >> 14
                src[8*7+x] = (y7 - y1) >> 14
        }

        // Level shift by +128, clip to [0, 255], and write to dst.
        for y := 0; y < 8; y++ {
                for x := 0; x < 8; x++ {
                        c := src[y*8+x]
                        if c < -128 {
                                c = 0
                        } else if c > 127 {
                                c = 255
                        } else {
                                c += 128
                        }
                        dst[y*stride+x] = uint8(c)
                }
        }
}