/* * jfdctint.c * * Copyright (C) 1991-1996, 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(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 */