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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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* This file contains a slow-but-accurate integer implementation of the
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* forward DCT (Discrete Cosine Transform).
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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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* 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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#define JPEG_INTERNALS
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#include "jdct.h" /* Private declarations for DCT subsystem */
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#ifdef DCT_ISLOW_SUPPORTED
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* This module is specialized to the case DCTSIZE = 8.
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Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
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* The poop on this scaling stuff is as follows:
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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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* 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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* 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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* 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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#if BITS_IN_JSAMPLE == 8
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#define PASS1_BITS 1 /* lose a little precision to avoid overflow */
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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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#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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#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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/* 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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#if BITS_IN_JSAMPLE == 8
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#define MULTIPLY(var,const) MULTIPLY16C16(var,const)
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#define MULTIPLY(var,const) ((var) * (const))
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* Perform the forward DCT on one block of samples.
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jpeg_fdct_islow (DCTELEM * data)
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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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/* 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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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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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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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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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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/* 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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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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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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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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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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#endif /* DCT_ISLOW_SUPPORTED */
added
removed
jfdctint.c
