jfdctint.cpp

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/* +------------------------------------------------------------------------+
   |                     Mobile Robot Programming Toolkit (MRPT)            |
   |                          http://www.mrpt.org/                          |
   |                                                                        |
   | Copyright (c) 2005-2017, Individual contributors, see AUTHORS file     |
   | See: http://www.mrpt.org/Authors - All rights reserved.                |
   | Released under BSD License. See details in http://www.mrpt.org/License |
   +------------------------------------------------------------------------+ */

#define JPEG_INTERNALS
#include "jinclude.h"
#include "mrpt_jpeglib.h"
#include "jdct.h" /* Private declarations for DCT subsystem */

#ifdef DCT_ISLOW_SUPPORTED

/*
 * This module is specialized to the case DCTSIZE = 8.
 */

#if DCTSIZE != 8
Sorry, this code only copes with 8x8 DCTs./* deliberate syntax err */
#endif

/*
 * The poop on this scaling stuff is as follows:
 *
 * Each 1-D DCT step produces outputs which are a factor of sqrt(N)
 * larger than the true DCT outputs.  The final outputs are therefore
 * a factor of N larger than desired; since N=8 this can be cured by
 * a simple right shift at the end of the algorithm.  The advantage of
 * this arrangement is that we save two multiplications per 1-D DCT,
 * because the y0 and y4 outputs need not be divided by sqrt(N).
 * In the IJG code, this factor of 8 is removed by the quantization step
 * (in jcdctmgr.c), NOT in this module.
 *
 * We have to do addition and subtraction of the integer inputs, which
 * is no problem, and multiplication by fractional constants, which is
 * a problem to do in integer arithmetic.  We multiply all the constants
 * by CONST_SCALE and convert them to integer constants (thus retaining
 * CONST_BITS bits of precision in the constants).  After doing a
 * multiplication we have to divide the product by CONST_SCALE, with proper
 * rounding, to produce the correct output.  This division can be done
 * cheaply as a right shift of CONST_BITS bits.  We postpone shifting
 * as long as possible so that partial sums can be added together with
 * full fractional precision.
 *
 * The outputs of the first pass are scaled up by PASS1_BITS bits so that
 * they are represented to better-than-integral precision.  These outputs
 * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
 * with the recommended scaling.  (For 12-bit sample data, the intermediate
 * array is INT32 anyway.)
 *
 * To avoid overflow of the 32-bit intermediate results in pass 2, we must
 * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26.  Error analysis
 * shows that the values given below are the most effective.
 */

#if BITS_IN_JSAMPLE == 8
#define CONST_BITS 13
#define PASS1_BITS 2
#else
#define CONST_BITS 13
#define PASS1_BITS 1 /* lose a little precision to avoid overflow */
#endif

/* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
 * causing a lot of useless floating-point operations at run time.
 * To get around this we use the following pre-calculated constants.
 * If you change CONST_BITS you may want to add appropriate values.
 * (With a reasonable C compiler, you can just rely on the FIX() macro...)
 */

#if CONST_BITS == 13
#define FIX_0_298631336 ((INT32)2446) /* FIX(0.298631336) */
#define FIX_0_390180644 ((INT32)3196) /* FIX(0.390180644) */
#define FIX_0_541196100 ((INT32)4433) /* FIX(0.541196100) */
#define FIX_0_765366865 ((INT32)6270) /* FIX(0.765366865) */
#define FIX_0_899976223 ((INT32)7373) /* FIX(0.899976223) */
#define FIX_1_175875602 ((INT32)9633) /* FIX(1.175875602) */
#define FIX_1_501321110 ((INT32)12299) /* FIX(1.501321110) */
#define FIX_1_847759065 ((INT32)15137) /* FIX(1.847759065) */
#define FIX_1_961570560 ((INT32)16069) /* FIX(1.961570560) */
#define FIX_2_053119869 ((INT32)16819) /* FIX(2.053119869) */
#define FIX_2_562915447 ((INT32)20995) /* FIX(2.562915447) */
#define FIX_3_072711026 ((INT32)25172) /* FIX(3.072711026) */
#else
#define FIX_0_298631336 FIX(0.298631336)
#define FIX_0_390180644 FIX(0.390180644)
#define FIX_0_541196100 FIX(0.541196100)
#define FIX_0_765366865 FIX(0.765366865)
#define FIX_0_899976223 FIX(0.899976223)
#define FIX_1_175875602 FIX(1.175875602)
#define FIX_1_501321110 FIX(1.501321110)
#define FIX_1_847759065 FIX(1.847759065)
#define FIX_1_961570560 FIX(1.961570560)
#define FIX_2_053119869 FIX(2.053119869)
#define FIX_2_562915447 FIX(2.562915447)
#define FIX_3_072711026 FIX(3.072711026)
#endif

/* Multiply an INT32 variable by an INT32 constant to yield an INT32 result.
 * For 8-bit samples with the recommended scaling, all the variable
 * and constant values involved are no more than 16 bits wide, so a
 * 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
 * For 12-bit samples, a full 32-bit multiplication will be needed.
 */

#if BITS_IN_JSAMPLE == 8
#define MULTIPLY(var, const) MULTIPLY16C16(var, const)
#else
#define MULTIPLY(var, const) ((var) * (const))
#endif

           /*
                * Perform the forward DCT on one block of samples.
                */

           GLOBAL(void) jpeg_fdct_islow(DCTELEM* data)
{
        INT32 tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
        INT32 tmp10, tmp11, tmp12, tmp13;
        INT32 z1, z2, z3, z4, z5;
        DCTELEM* dataptr;
        int ctr;
        SHIFT_TEMPS

        /* Pass 1: process rows. */
        /* Note results are scaled up by sqrt(8) compared to a true DCT; */
        /* furthermore, we scale the results by 2**PASS1_BITS. */

        dataptr = data;
        for (ctr = DCTSIZE - 1; ctr >= 0; ctr--)
        {
                tmp0 = dataptr[0] + dataptr[7];
                tmp7 = dataptr[0] - dataptr[7];
                tmp1 = dataptr[1] + dataptr[6];
                tmp6 = dataptr[1] - dataptr[6];
                tmp2 = dataptr[2] + dataptr[5];
                tmp5 = dataptr[2] - dataptr[5];
                tmp3 = dataptr[3] + dataptr[4];
                tmp4 = dataptr[3] - dataptr[4];

                /* Even part per LL&M figure 1 --- note that published figure is faulty;
                 * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
                 */

                tmp10 = tmp0 + tmp3;
                tmp13 = tmp0 - tmp3;
                tmp11 = tmp1 + tmp2;
                tmp12 = tmp1 - tmp2;

                dataptr[0] = (DCTELEM)((tmp10 + tmp11) << PASS1_BITS);
                dataptr[4] = (DCTELEM)((tmp10 - tmp11) << PASS1_BITS);

                z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
                dataptr[2] = (DCTELEM)DESCALE(
                        z1 + MULTIPLY(tmp13, FIX_0_765366865), CONST_BITS - PASS1_BITS);
                dataptr[6] = (DCTELEM)DESCALE(
                        z1 + MULTIPLY(tmp12, -FIX_1_847759065), CONST_BITS - PASS1_BITS);

                /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
                 * cK represents cos(K*pi/16).
                 * i0..i3 in the paper are tmp4..tmp7 here.
                 */

                z1 = tmp4 + tmp7;
                z2 = tmp5 + tmp6;
                z3 = tmp4 + tmp6;
                z4 = tmp5 + tmp7;
                z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */

                tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
                tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
                tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
                tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
                z1 = MULTIPLY(z1, -FIX_0_899976223); /* sqrt(2) * (c7-c3) */
                z2 = MULTIPLY(z2, -FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
                z3 = MULTIPLY(z3, -FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
                z4 = MULTIPLY(z4, -FIX_0_390180644); /* sqrt(2) * (c5-c3) */

                z3 += z5;
                z4 += z5;

                dataptr[7] = (DCTELEM)DESCALE(tmp4 + z1 + z3, CONST_BITS - PASS1_BITS);
                dataptr[5] = (DCTELEM)DESCALE(tmp5 + z2 + z4, CONST_BITS - PASS1_BITS);
                dataptr[3] = (DCTELEM)DESCALE(tmp6 + z2 + z3, CONST_BITS - PASS1_BITS);
                dataptr[1] = (DCTELEM)DESCALE(tmp7 + z1 + z4, CONST_BITS - PASS1_BITS);

                dataptr += DCTSIZE; /* advance pointer to next row */
        }

        /* Pass 2: process columns.
         * We remove the PASS1_BITS scaling, but leave the results scaled up
         * by an overall factor of 8.
         */

        dataptr = data;
        for (ctr = DCTSIZE - 1; ctr >= 0; ctr--)
        {
                tmp0 = dataptr[DCTSIZE * 0] + dataptr[DCTSIZE * 7];
                tmp7 = dataptr[DCTSIZE * 0] - dataptr[DCTSIZE * 7];
                tmp1 = dataptr[DCTSIZE * 1] + dataptr[DCTSIZE * 6];
                tmp6 = dataptr[DCTSIZE * 1] - dataptr[DCTSIZE * 6];
                tmp2 = dataptr[DCTSIZE * 2] + dataptr[DCTSIZE * 5];
                tmp5 = dataptr[DCTSIZE * 2] - dataptr[DCTSIZE * 5];
                tmp3 = dataptr[DCTSIZE * 3] + dataptr[DCTSIZE * 4];
                tmp4 = dataptr[DCTSIZE * 3] - dataptr[DCTSIZE * 4];

                /* Even part per LL&M figure 1 --- note that published figure is faulty;
                 * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
                 */

                tmp10 = tmp0 + tmp3;
                tmp13 = tmp0 - tmp3;
                tmp11 = tmp1 + tmp2;
                tmp12 = tmp1 - tmp2;

                dataptr[DCTSIZE * 0] = (DCTELEM)DESCALE(tmp10 + tmp11, PASS1_BITS);
                dataptr[DCTSIZE * 4] = (DCTELEM)DESCALE(tmp10 - tmp11, PASS1_BITS);

                z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
                dataptr[DCTSIZE * 2] = (DCTELEM)DESCALE(
                        z1 + MULTIPLY(tmp13, FIX_0_765366865), CONST_BITS + PASS1_BITS);
                dataptr[DCTSIZE * 6] = (DCTELEM)DESCALE(
                        z1 + MULTIPLY(tmp12, -FIX_1_847759065), CONST_BITS + PASS1_BITS);

                /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
                 * cK represents cos(K*pi/16).
                 * i0..i3 in the paper are tmp4..tmp7 here.
                 */

                z1 = tmp4 + tmp7;
                z2 = tmp5 + tmp6;
                z3 = tmp4 + tmp6;
                z4 = tmp5 + tmp7;
                z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */

                tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
                tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
                tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
                tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
                z1 = MULTIPLY(z1, -FIX_0_899976223); /* sqrt(2) * (c7-c3) */
                z2 = MULTIPLY(z2, -FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
                z3 = MULTIPLY(z3, -FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
                z4 = MULTIPLY(z4, -FIX_0_390180644); /* sqrt(2) * (c5-c3) */

                z3 += z5;
                z4 += z5;

                dataptr[DCTSIZE * 7] =
                        (DCTELEM)DESCALE(tmp4 + z1 + z3, CONST_BITS + PASS1_BITS);
                dataptr[DCTSIZE * 5] =
                        (DCTELEM)DESCALE(tmp5 + z2 + z4, CONST_BITS + PASS1_BITS);
                dataptr[DCTSIZE * 3] =
                        (DCTELEM)DESCALE(tmp6 + z2 + z3, CONST_BITS + PASS1_BITS);
                dataptr[DCTSIZE * 1] =
                        (DCTELEM)DESCALE(tmp7 + z1 + z4, CONST_BITS + PASS1_BITS);

                dataptr++; /* advance pointer to next column */
        }
}

#endif /* DCT_ISLOW_SUPPORTED */