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/*
* jfdctint.c * * Copyright (C) 1991-1994, Thomas G. Lane. * This file is part of the Independent JPEG Group's software. * For conditions of distribution and use, see the accompanying README file. * * This file contains a slow-but-accurate integer implementation of the * forward DCT (Discrete Cosine Transform). * * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT * on each column. Direct algorithms are also available, but they are * much more complex and seem not to be any faster when reduced to code. * * This implementation is based on an algorithm described in * C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT * Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics, * Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991. * The primary algorithm described there uses 11 multiplies and 29 adds. * We use their alternate method with 12 multiplies and 32 adds. * The advantage of this method is that no data path contains more than one * multiplication; this allows a very simple and accurate implementation in * scaled fixed-point arithmetic, with a minimal number of shifts. */
#define JPEG_INTERNALS
#include "jinclude.h"
#include "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 voidjpeg_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 */
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