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/*
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 * jfdctint.c
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 *
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 * Copyright (C) 1991-1996, Thomas G. Lane.
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 * This file is part of the Independent JPEG Group's software.
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 * For conditions of distribution and use, see the accompanying README file.
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 *
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 * This file contains a slow-but-accurate integer implementation of the
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 * forward DCT (Discrete Cosine Transform).
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 *
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 * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT
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 * on each column.  Direct algorithms are also available, but they are
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 * much more complex and seem not to be any faster when reduced to code.
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 *
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 * This implementation is based on an algorithm described in
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 *   C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT
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 *   Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,
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 *   Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.
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 * The primary algorithm described there uses 11 multiplies and 29 adds.
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 * We use their alternate method with 12 multiplies and 32 adds.
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 * The advantage of this method is that no data path contains more than one
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 * multiplication; this allows a very simple and accurate implementation in
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 * scaled fixed-point arithmetic, with a minimal number of shifts.
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 */
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#include <stdlib.h>
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#include <stdio.h>
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#include "common.h"
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#include "dsputil.h"
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#define SHIFT_TEMPS
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#define DCTSIZE 8
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#define BITS_IN_JSAMPLE 8
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#define GLOBAL(x) x
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#define RIGHT_SHIFT(x, n) ((x) >> (n))
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#define MULTIPLY16C16(var,const) ((var)*(const))
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#if 1 //def USE_ACCURATE_ROUNDING
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#define DESCALE(x,n)  RIGHT_SHIFT((x) + (1 << ((n) - 1)), n)
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#else
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#define DESCALE(x,n)  RIGHT_SHIFT(x, n)
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#endif
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/*
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 * This module is specialized to the case DCTSIZE = 8.
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 */
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#if DCTSIZE != 8
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  Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
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#endif
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/*
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 * The poop on this scaling stuff is as follows:
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 *
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 * Each 1-D DCT step produces outputs which are a factor of sqrt(N)
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 * larger than the true DCT outputs.  The final outputs are therefore
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 * a factor of N larger than desired; since N=8 this can be cured by
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 * a simple right shift at the end of the algorithm.  The advantage of
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 * this arrangement is that we save two multiplications per 1-D DCT,
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 * because the y0 and y4 outputs need not be divided by sqrt(N).
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 * In the IJG code, this factor of 8 is removed by the quantization step
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 * (in jcdctmgr.c), NOT in this module.
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 *
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 * We have to do addition and subtraction of the integer inputs, which
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 * is no problem, and multiplication by fractional constants, which is
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 * a problem to do in integer arithmetic.  We multiply all the constants
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 * by CONST_SCALE and convert them to integer constants (thus retaining
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 * CONST_BITS bits of precision in the constants).  After doing a
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 * multiplication we have to divide the product by CONST_SCALE, with proper
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 * rounding, to produce the correct output.  This division can be done
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 * cheaply as a right shift of CONST_BITS bits.  We postpone shifting
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 * as long as possible so that partial sums can be added together with
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 * full fractional precision.
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 *
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 * The outputs of the first pass are scaled up by PASS1_BITS bits so that
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 * they are represented to better-than-integral precision.  These outputs
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 * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
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 * with the recommended scaling.  (For 12-bit sample data, the intermediate
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 * array is INT32 anyway.)
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 *
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 * To avoid overflow of the 32-bit intermediate results in pass 2, we must
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 * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26.  Error analysis
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 * shows that the values given below are the most effective.
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 */
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#if BITS_IN_JSAMPLE == 8
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#define CONST_BITS  13
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#define PASS1_BITS  4                /* set this to 2 if 16x16 multiplies are faster */
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#else
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#define CONST_BITS  13
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#define PASS1_BITS  1                /* lose a little precision to avoid overflow */
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#endif
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/* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
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 * causing a lot of useless floating-point operations at run time.
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 * To get around this we use the following pre-calculated constants.
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 * If you change CONST_BITS you may want to add appropriate values.
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 * (With a reasonable C compiler, you can just rely on the FIX() macro...)
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 */
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#if CONST_BITS == 13
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#define FIX_0_298631336  ((INT32)  2446)        /* FIX(0.298631336) */
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#define FIX_0_390180644  ((INT32)  3196)        /* FIX(0.390180644) */
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#define FIX_0_541196100  ((INT32)  4433)        /* FIX(0.541196100) */
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#define FIX_0_765366865  ((INT32)  6270)        /* FIX(0.765366865) */
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#define FIX_0_899976223  ((INT32)  7373)        /* FIX(0.899976223) */
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#define FIX_1_175875602  ((INT32)  9633)        /* FIX(1.175875602) */
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#define FIX_1_501321110  ((INT32)  12299)        /* FIX(1.501321110) */
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#define FIX_1_847759065  ((INT32)  15137)        /* FIX(1.847759065) */
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#define FIX_1_961570560  ((INT32)  16069)        /* FIX(1.961570560) */
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#define FIX_2_053119869  ((INT32)  16819)        /* FIX(2.053119869) */
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#define FIX_2_562915447  ((INT32)  20995)        /* FIX(2.562915447) */
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#define FIX_3_072711026  ((INT32)  25172)        /* FIX(3.072711026) */
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#else
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#define FIX_0_298631336  FIX(0.298631336)
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#define FIX_0_390180644  FIX(0.390180644)
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#define FIX_0_541196100  FIX(0.541196100)
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#define FIX_0_765366865  FIX(0.765366865)
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#define FIX_0_899976223  FIX(0.899976223)
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#define FIX_1_175875602  FIX(1.175875602)
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#define FIX_1_501321110  FIX(1.501321110)
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#define FIX_1_847759065  FIX(1.847759065)
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#define FIX_1_961570560  FIX(1.961570560)
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#define FIX_2_053119869  FIX(2.053119869)
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#define FIX_2_562915447  FIX(2.562915447)
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#define FIX_3_072711026  FIX(3.072711026)
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#endif
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/* Multiply an INT32 variable by an INT32 constant to yield an INT32 result.
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 * For 8-bit samples with the recommended scaling, all the variable
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 * and constant values involved are no more than 16 bits wide, so a
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 * 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
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 * For 12-bit samples, a full 32-bit multiplication will be needed.
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 */
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#if BITS_IN_JSAMPLE == 8 && CONST_BITS<=13 && PASS1_BITS<=2
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#define MULTIPLY(var,const)  MULTIPLY16C16(var,const)
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#else
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#define MULTIPLY(var,const)  ((var) * (const))
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#endif
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/*
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 * Perform the forward DCT on one block of samples.
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 */
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GLOBAL(void)
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ff_jpeg_fdct_islow (DCTELEM * data)
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{
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  INT32 tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
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  INT32 tmp10, tmp11, tmp12, tmp13;
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  INT32 z1, z2, z3, z4, z5;
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  DCTELEM *dataptr;
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  int ctr;
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  SHIFT_TEMPS
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  /* Pass 1: process rows. */
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  /* Note results are scaled up by sqrt(8) compared to a true DCT; */
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  /* furthermore, we scale the results by 2**PASS1_BITS. */
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  dataptr = data;
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  for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
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    tmp0 = dataptr[0] + dataptr[7];
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    tmp7 = dataptr[0] - dataptr[7];
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    tmp1 = dataptr[1] + dataptr[6];
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    tmp6 = dataptr[1] - dataptr[6];
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    tmp2 = dataptr[2] + dataptr[5];
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    tmp5 = dataptr[2] - dataptr[5];
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    tmp3 = dataptr[3] + dataptr[4];
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    tmp4 = dataptr[3] - dataptr[4];
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    /* Even part per LL&M figure 1 --- note that published figure is faulty;
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     * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
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     */
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    tmp10 = tmp0 + tmp3;
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    tmp13 = tmp0 - tmp3;
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    tmp11 = tmp1 + tmp2;
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    tmp12 = tmp1 - tmp2;
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    dataptr[0] = (DCTELEM) ((tmp10 + tmp11) << PASS1_BITS);
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    dataptr[4] = (DCTELEM) ((tmp10 - tmp11) << PASS1_BITS);
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    z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
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    dataptr[2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
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                                   CONST_BITS-PASS1_BITS);
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    dataptr[6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
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                                   CONST_BITS-PASS1_BITS);
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    /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
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     * cK represents cos(K*pi/16).
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     * i0..i3 in the paper are tmp4..tmp7 here.
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     */
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    z1 = tmp4 + tmp7;
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    z2 = tmp5 + tmp6;
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    z3 = tmp4 + tmp6;
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    z4 = tmp5 + tmp7;
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    z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
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    tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
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    tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
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    tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
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    tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
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    z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
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    z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
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    z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
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    z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
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    z3 += z5;
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    z4 += z5;
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    dataptr[7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS);
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    dataptr[5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS);
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    dataptr[3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS);
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    dataptr[1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS);
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    dataptr += DCTSIZE;                /* advance pointer to next row */
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  }
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  /* Pass 2: process columns.
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   * We remove the PASS1_BITS scaling, but leave the results scaled up
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   * by an overall factor of 8.
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   */
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  dataptr = data;
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  for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
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    tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
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    tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
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    tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
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    tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
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    tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
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    tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
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    tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
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    tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
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    /* Even part per LL&M figure 1 --- note that published figure is faulty;
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     * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
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     */
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    tmp10 = tmp0 + tmp3;
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    tmp13 = tmp0 - tmp3;
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    tmp11 = tmp1 + tmp2;
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    tmp12 = tmp1 - tmp2;
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    dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);
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    dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);
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    z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
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    dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
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                                           CONST_BITS+PASS1_BITS);
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    dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
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                                           CONST_BITS+PASS1_BITS);
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    /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
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     * cK represents cos(K*pi/16).
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     * i0..i3 in the paper are tmp4..tmp7 here.
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     */
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    z1 = tmp4 + tmp7;
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    z2 = tmp5 + tmp6;
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    z3 = tmp4 + tmp6;
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    z4 = tmp5 + tmp7;
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    z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
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    tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
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    tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
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    tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
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    tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
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    z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
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    z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
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    z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
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    z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
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    z3 += z5;
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    z4 += z5;
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    dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3,
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                                           CONST_BITS+PASS1_BITS);
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    dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4,
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                                           CONST_BITS+PASS1_BITS);
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    dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3,
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                                           CONST_BITS+PASS1_BITS);
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    dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4,
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                                           CONST_BITS+PASS1_BITS);
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    dataptr++;                        /* advance pointer to next column */
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  }
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}