00001 /*
00002  * jidctint.c
00003  *
00004  * Copyright (C) 1991-1998, Thomas G. Lane.
00005  * This file is part of the Independent JPEG Group's software.
00006  * For conditions of distribution and use, see the accompanying README file.
00007  *
00008  * This file contains a slow-but-accurate integer implementation of the
00009  * inverse DCT (Discrete Cosine Transform).  In the IJG code, this routine
00010  * must also perform dequantization of the input coefficients.
00011  *
00012  * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT
00013  * on each row (or vice versa, but it's more convenient to emit a row at
00014  * a time).  Direct algorithms are also available, but they are much more
00015  * complex and seem not to be any faster when reduced to code.
00016  *
00017  * This implementation is based on an algorithm described in
00018  *   C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT
00019  *   Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,
00020  *   Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.
00021  * The primary algorithm described there uses 11 multiplies and 29 adds.
00022  * We use their alternate method with 12 multiplies and 32 adds.
00023  * The advantage of this method is that no data path contains more than one
00024  * multiplication; this allows a very simple and accurate implementation in
00025  * scaled fixed-point arithmetic, with a minimal number of shifts.
00026  */
00027 
00028 #define JPEG_INTERNALS
00029 #include "jinclude.h"
00030 #include "jpeglib.h"
00031 #include "jdct.h"               /* Private declarations for DCT subsystem */
00032 
00033 #ifdef DCT_ISLOW_SUPPORTED
00034 
00035 
00036 /*
00037  * This module is specialized to the case DCTSIZE = 8.
00038  */
00039 
00040 #if DCTSIZE != 8
00041   Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
00042 #endif
00043 
00044 
00045 /*
00046  * The poop on this scaling stuff is as follows:
00047  *
00048  * Each 1-D IDCT step produces outputs which are a factor of sqrt(N)
00049  * larger than the true IDCT outputs.  The final outputs are therefore
00050  * a factor of N larger than desired; since N=8 this can be cured by
00051  * a simple right shift at the end of the algorithm.  The advantage of
00052  * this arrangement is that we save two multiplications per 1-D IDCT,
00053  * because the y0 and y4 inputs need not be divided by sqrt(N).
00054  *
00055  * We have to do addition and subtraction of the integer inputs, which
00056  * is no problem, and multiplication by fractional constants, which is
00057  * a problem to do in integer arithmetic.  We multiply all the constants
00058  * by CONST_SCALE and convert them to integer constants (thus retaining
00059  * CONST_BITS bits of precision in the constants).  After doing a
00060  * multiplication we have to divide the product by CONST_SCALE, with proper
00061  * rounding, to produce the correct output.  This division can be done
00062  * cheaply as a right shift of CONST_BITS bits.  We postpone shifting
00063  * as long as possible so that partial sums can be added together with
00064  * full fractional precision.
00065  *
00066  * The outputs of the first pass are scaled up by PASS1_BITS bits so that
00067  * they are represented to better-than-integral precision.  These outputs
00068  * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
00069  * with the recommended scaling.  (To scale up 12-bit sample data further, an
00070  * intermediate INT32 array would be needed.)
00071  *
00072  * To avoid overflow of the 32-bit intermediate results in pass 2, we must
00073  * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26.  Error analysis
00074  * shows that the values given below are the most effective.
00075  */
00076 
00077 #if BITS_IN_JSAMPLE == 8
00078 #define CONST_BITS  13
00079 #define PASS1_BITS  2
00080 #else
00081 #define CONST_BITS  13
00082 #define PASS1_BITS  1           /* lose a little precision to avoid overflow */
00083 #endif
00084 
00085 /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
00086  * causing a lot of useless floating-point operations at run time.
00087  * To get around this we use the following pre-calculated constants.
00088  * If you change CONST_BITS you may want to add appropriate values.
00089  * (With a reasonable C compiler, you can just rely on the FIX() macro...)
00090  */
00091 
00092 #if CONST_BITS == 13
00093 #define FIX_0_298631336  ((INT32)  2446)        /* FIX(0.298631336) */
00094 #define FIX_0_390180644  ((INT32)  3196)        /* FIX(0.390180644) */
00095 #define FIX_0_541196100  ((INT32)  4433)        /* FIX(0.541196100) */
00096 #define FIX_0_765366865  ((INT32)  6270)        /* FIX(0.765366865) */
00097 #define FIX_0_899976223  ((INT32)  7373)        /* FIX(0.899976223) */
00098 #define FIX_1_175875602  ((INT32)  9633)        /* FIX(1.175875602) */
00099 #define FIX_1_501321110  ((INT32)  12299)       /* FIX(1.501321110) */
00100 #define FIX_1_847759065  ((INT32)  15137)       /* FIX(1.847759065) */
00101 #define FIX_1_961570560  ((INT32)  16069)       /* FIX(1.961570560) */
00102 #define FIX_2_053119869  ((INT32)  16819)       /* FIX(2.053119869) */
00103 #define FIX_2_562915447  ((INT32)  20995)       /* FIX(2.562915447) */
00104 #define FIX_3_072711026  ((INT32)  25172)       /* FIX(3.072711026) */
00105 #else
00106 #define FIX_0_298631336  FIX(0.298631336)
00107 #define FIX_0_390180644  FIX(0.390180644)
00108 #define FIX_0_541196100  FIX(0.541196100)
00109 #define FIX_0_765366865  FIX(0.765366865)
00110 #define FIX_0_899976223  FIX(0.899976223)
00111 #define FIX_1_175875602  FIX(1.175875602)
00112 #define FIX_1_501321110  FIX(1.501321110)
00113 #define FIX_1_847759065  FIX(1.847759065)
00114 #define FIX_1_961570560  FIX(1.961570560)
00115 #define FIX_2_053119869  FIX(2.053119869)
00116 #define FIX_2_562915447  FIX(2.562915447)
00117 #define FIX_3_072711026  FIX(3.072711026)
00118 #endif
00119 
00120 
00121 /* Multiply an INT32 variable by an INT32 constant to yield an INT32 result.
00122  * For 8-bit samples with the recommended scaling, all the variable
00123  * and constant values involved are no more than 16 bits wide, so a
00124  * 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
00125  * For 12-bit samples, a full 32-bit multiplication will be needed.
00126  */
00127 
00128 #if BITS_IN_JSAMPLE == 8
00129 #define MULTIPLY(var,const)  MULTIPLY16C16(var,const)
00130 #else
00131 #define MULTIPLY(var,const)  ((var) * (const))
00132 #endif
00133 
00134 
00135 /* Dequantize a coefficient by multiplying it by the multiplier-table
00136  * entry; produce an int result.  In this module, both inputs and result
00137  * are 16 bits or less, so either int or short multiply will work.
00138  */
00139 
00140 #define DEQUANTIZE(coef,quantval)  (((ISLOW_MULT_TYPE) (coef)) * (quantval))
00141 
00142 
00143 /*
00144  * Perform dequantization and inverse DCT on one block of coefficients.
00145  */
00146 
00147 GLOBAL(void)
00148 jpeg_idct_islow (j_decompress_ptr cinfo, jpeg_component_info * compptr,
00149                  JCOEFPTR coef_block,
00150                  JSAMPARRAY output_buf, JDIMENSION output_col)
00151 {
00152   INT32 tmp0, tmp1, tmp2, tmp3;
00153   INT32 tmp10, tmp11, tmp12, tmp13;
00154   INT32 z1, z2, z3, z4, z5;
00155   JCOEFPTR inptr;
00156   ISLOW_MULT_TYPE * quantptr;
00157   int * wsptr;
00158   JSAMPROW outptr;
00159   JSAMPLE *range_limit = IDCT_range_limit(cinfo);
00160   int ctr;
00161   int workspace[DCTSIZE2];      /* buffers data between passes */
00162   SHIFT_TEMPS
00163 
00164   /* Pass 1: process columns from input, store into work array. */
00165   /* Note results are scaled up by sqrt(8) compared to a true IDCT; */
00166   /* furthermore, we scale the results by 2**PASS1_BITS. */
00167 
00168   inptr = coef_block;
00169   quantptr = (ISLOW_MULT_TYPE *) compptr->dct_table;
00170   wsptr = workspace;
00171   for (ctr = DCTSIZE; ctr > 0; ctr--) {
00172     /* Due to quantization, we will usually find that many of the input
00173      * coefficients are zero, especially the AC terms.  We can exploit this
00174      * by short-circuiting the IDCT calculation for any column in which all
00175      * the AC terms are zero.  In that case each output is equal to the
00176      * DC coefficient (with scale factor as needed).
00177      * With typical images and quantization tables, half or more of the
00178      * column DCT calculations can be simplified this way.
00179      */
00180     
00181     if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 &&
00182         inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 &&
00183         inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 &&
00184         inptr[DCTSIZE*7] == 0) {
00185       /* AC terms all zero */
00186       int dcval = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]) << PASS1_BITS;
00187       
00188       wsptr[DCTSIZE*0] = dcval;
00189       wsptr[DCTSIZE*1] = dcval;
00190       wsptr[DCTSIZE*2] = dcval;
00191       wsptr[DCTSIZE*3] = dcval;
00192       wsptr[DCTSIZE*4] = dcval;
00193       wsptr[DCTSIZE*5] = dcval;
00194       wsptr[DCTSIZE*6] = dcval;
00195       wsptr[DCTSIZE*7] = dcval;
00196       
00197       inptr++;                  /* advance pointers to next column */
00198       quantptr++;
00199       wsptr++;
00200       continue;
00201     }
00202     
00203     /* Even part: reverse the even part of the forward DCT. */
00204     /* The rotator is sqrt(2)*c(-6). */
00205     
00206     z2 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
00207     z3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);
00208     
00209     z1 = MULTIPLY(z2 + z3, FIX_0_541196100);
00210     tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065);
00211     tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865);
00212     
00213     z2 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
00214     z3 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);
00215 
00216     tmp0 = (z2 + z3) << CONST_BITS;
00217     tmp1 = (z2 - z3) << CONST_BITS;
00218     
00219     tmp10 = tmp0 + tmp3;
00220     tmp13 = tmp0 - tmp3;
00221     tmp11 = tmp1 + tmp2;
00222     tmp12 = tmp1 - tmp2;
00223     
00224     /* Odd part per figure 8; the matrix is unitary and hence its
00225      * transpose is its inverse.  i0..i3 are y7,y5,y3,y1 respectively.
00226      */
00227     
00228     tmp0 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
00229     tmp1 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
00230     tmp2 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
00231     tmp3 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);
00232     
00233     z1 = tmp0 + tmp3;
00234     z2 = tmp1 + tmp2;
00235     z3 = tmp0 + tmp2;
00236     z4 = tmp1 + tmp3;
00237     z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
00238     
00239     tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
00240     tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
00241     tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
00242     tmp3 = MULTIPLY(tmp3, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
00243     z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
00244     z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
00245     z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
00246     z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
00247     
00248     z3 += z5;
00249     z4 += z5;
00250     
00251     tmp0 += z1 + z3;
00252     tmp1 += z2 + z4;
00253     tmp2 += z2 + z3;
00254     tmp3 += z1 + z4;
00255     
00256     /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */
00257     
00258     wsptr[DCTSIZE*0] = (int) DESCALE(tmp10 + tmp3, CONST_BITS-PASS1_BITS);
00259     wsptr[DCTSIZE*7] = (int) DESCALE(tmp10 - tmp3, CONST_BITS-PASS1_BITS);
00260     wsptr[DCTSIZE*1] = (int) DESCALE(tmp11 + tmp2, CONST_BITS-PASS1_BITS);
00261     wsptr[DCTSIZE*6] = (int) DESCALE(tmp11 - tmp2, CONST_BITS-PASS1_BITS);
00262     wsptr[DCTSIZE*2] = (int) DESCALE(tmp12 + tmp1, CONST_BITS-PASS1_BITS);
00263     wsptr[DCTSIZE*5] = (int) DESCALE(tmp12 - tmp1, CONST_BITS-PASS1_BITS);
00264     wsptr[DCTSIZE*3] = (int) DESCALE(tmp13 + tmp0, CONST_BITS-PASS1_BITS);
00265     wsptr[DCTSIZE*4] = (int) DESCALE(tmp13 - tmp0, CONST_BITS-PASS1_BITS);
00266     
00267     inptr++;                    /* advance pointers to next column */
00268     quantptr++;
00269     wsptr++;
00270   }
00271   
00272   /* Pass 2: process rows from work array, store into output array. */
00273   /* Note that we must descale the results by a factor of 8 == 2**3, */
00274   /* and also undo the PASS1_BITS scaling. */
00275 
00276   wsptr = workspace;
00277   for (ctr = 0; ctr < DCTSIZE; ctr++) {
00278     outptr = output_buf[ctr] + output_col;
00279     /* Rows of zeroes can be exploited in the same way as we did with columns.
00280      * However, the column calculation has created many nonzero AC terms, so
00281      * the simplification applies less often (typically 5% to 10% of the time).
00282      * On machines with very fast multiplication, it's possible that the
00283      * test takes more time than it's worth.  In that case this section
00284      * may be commented out.
00285      */
00286     
00287 #ifndef NO_ZERO_ROW_TEST
00288     if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 &&
00289         wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) {
00290       /* AC terms all zero */
00291       JSAMPLE dcval = range_limit[(int) DESCALE((INT32) wsptr[0], PASS1_BITS+3)
00292                                   & RANGE_MASK];
00293       
00294       outptr[0] = dcval;
00295       outptr[1] = dcval;
00296       outptr[2] = dcval;
00297       outptr[3] = dcval;
00298       outptr[4] = dcval;
00299       outptr[5] = dcval;
00300       outptr[6] = dcval;
00301       outptr[7] = dcval;
00302 
00303       wsptr += DCTSIZE;         /* advance pointer to next row */
00304       continue;
00305     }
00306 #endif
00307     
00308     /* Even part: reverse the even part of the forward DCT. */
00309     /* The rotator is sqrt(2)*c(-6). */
00310     
00311     z2 = (INT32) wsptr[2];
00312     z3 = (INT32) wsptr[6];
00313     
00314     z1 = MULTIPLY(z2 + z3, FIX_0_541196100);
00315     tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065);
00316     tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865);
00317     
00318     tmp0 = ((INT32) wsptr[0] + (INT32) wsptr[4]) << CONST_BITS;
00319     tmp1 = ((INT32) wsptr[0] - (INT32) wsptr[4]) << CONST_BITS;
00320     
00321     tmp10 = tmp0 + tmp3;
00322     tmp13 = tmp0 - tmp3;
00323     tmp11 = tmp1 + tmp2;
00324     tmp12 = tmp1 - tmp2;
00325     
00326     /* Odd part per figure 8; the matrix is unitary and hence its
00327      * transpose is its inverse.  i0..i3 are y7,y5,y3,y1 respectively.
00328      */
00329     
00330     tmp0 = (INT32) wsptr[7];
00331     tmp1 = (INT32) wsptr[5];
00332     tmp2 = (INT32) wsptr[3];
00333     tmp3 = (INT32) wsptr[1];
00334     
00335     z1 = tmp0 + tmp3;
00336     z2 = tmp1 + tmp2;
00337     z3 = tmp0 + tmp2;
00338     z4 = tmp1 + tmp3;
00339     z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
00340     
00341     tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
00342     tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
00343     tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
00344     tmp3 = MULTIPLY(tmp3, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
00345     z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
00346     z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
00347     z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
00348     z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
00349     
00350     z3 += z5;
00351     z4 += z5;
00352     
00353     tmp0 += z1 + z3;
00354     tmp1 += z2 + z4;
00355     tmp2 += z2 + z3;
00356     tmp3 += z1 + z4;
00357     
00358     /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */
00359     
00360     outptr[0] = range_limit[(int) DESCALE(tmp10 + tmp3,
00361                                           CONST_BITS+PASS1_BITS+3)
00362                             & RANGE_MASK];
00363     outptr[7] = range_limit[(int) DESCALE(tmp10 - tmp3,
00364                                           CONST_BITS+PASS1_BITS+3)
00365                             & RANGE_MASK];
00366     outptr[1] = range_limit[(int) DESCALE(tmp11 + tmp2,
00367                                           CONST_BITS+PASS1_BITS+3)
00368                             & RANGE_MASK];
00369     outptr[6] = range_limit[(int) DESCALE(tmp11 - tmp2,
00370                                           CONST_BITS+PASS1_BITS+3)
00371                             & RANGE_MASK];
00372     outptr[2] = range_limit[(int) DESCALE(tmp12 + tmp1,
00373                                           CONST_BITS+PASS1_BITS+3)
00374                             & RANGE_MASK];
00375     outptr[5] = range_limit[(int) DESCALE(tmp12 - tmp1,
00376                                           CONST_BITS+PASS1_BITS+3)
00377                             & RANGE_MASK];
00378     outptr[3] = range_limit[(int) DESCALE(tmp13 + tmp0,
00379                                           CONST_BITS+PASS1_BITS+3)
00380                             & RANGE_MASK];
00381     outptr[4] = range_limit[(int) DESCALE(tmp13 - tmp0,
00382                                           CONST_BITS+PASS1_BITS+3)
00383                             & RANGE_MASK];
00384     
00385     wsptr += DCTSIZE;           /* advance pointer to next row */
00386   }
00387 }
00388 
00389 #endif /* DCT_ISLOW_SUPPORTED */