00001 /*
00002  * jfdctfst.c
00003  *
00004  * Copyright (C) 1994-1996, 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 fast, not so accurate integer implementation of the
00009  * forward DCT (Discrete Cosine Transform).
00010  *
00011  * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT
00012  * on each column.  Direct algorithms are also available, but they are
00013  * much more complex and seem not to be any faster when reduced to code.
00014  *
00015  * This implementation is based on Arai, Agui, and Nakajima's algorithm for
00016  * scaled DCT.  Their original paper (Trans. IEICE E-71(11):1095) is in
00017  * Japanese, but the algorithm is described in the Pennebaker & Mitchell
00018  * JPEG textbook (see REFERENCES section in file README).  The following code
00019  * is based directly on figure 4-8 in P&M.
00020  * While an 8-point DCT cannot be done in less than 11 multiplies, it is
00021  * possible to arrange the computation so that many of the multiplies are
00022  * simple scalings of the final outputs.  These multiplies can then be
00023  * folded into the multiplications or divisions by the JPEG quantization
00024  * table entries.  The AA&N method leaves only 5 multiplies and 29 adds
00025  * to be done in the DCT itself.
00026  * The primary disadvantage of this method is that with fixed-point math,
00027  * accuracy is lost due to imprecise representation of the scaled
00028  * quantization values.  The smaller the quantization table entry, the less
00029  * precise the scaled value, so this implementation does worse with high-
00030  * quality-setting files than with low-quality ones.
00031  */
00032 
00033 #define JPEG_INTERNALS
00034 #include "jinclude.h"
00035 #include "jpeglib.h"
00036 #include "jdct.h"               /* Private declarations for DCT subsystem */
00037 
00038 #ifdef DCT_IFAST_SUPPORTED
00039 
00040 
00041 /*
00042  * This module is specialized to the case DCTSIZE = 8.
00043  */
00044 
00045 #if DCTSIZE != 8
00046   Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
00047 #endif
00048 
00049 
00050 /* Scaling decisions are generally the same as in the LL&M algorithm;
00051  * see jfdctint.c for more details.  However, we choose to descale
00052  * (right shift) multiplication products as soon as they are formed,
00053  * rather than carrying additional fractional bits into subsequent additions.
00054  * This compromises accuracy slightly, but it lets us save a few shifts.
00055  * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples)
00056  * everywhere except in the multiplications proper; this saves a good deal
00057  * of work on 16-bit-int machines.
00058  *
00059  * Again to save a few shifts, the intermediate results between pass 1 and
00060  * pass 2 are not upscaled, but are represented only to integral precision.
00061  *
00062  * A final compromise is to represent the multiplicative constants to only
00063  * 8 fractional bits, rather than 13.  This saves some shifting work on some
00064  * machines, and may also reduce the cost of multiplication (since there
00065  * are fewer one-bits in the constants).
00066  */
00067 
00068 #define CONST_BITS  8
00069 
00070 
00071 /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
00072  * causing a lot of useless floating-point operations at run time.
00073  * To get around this we use the following pre-calculated constants.
00074  * If you change CONST_BITS you may want to add appropriate values.
00075  * (With a reasonable C compiler, you can just rely on the FIX() macro...)
00076  */
00077 
00078 #if CONST_BITS == 8
00079 #define FIX_0_382683433  ((INT32)   98)         /* FIX(0.382683433) */
00080 #define FIX_0_541196100  ((INT32)  139)         /* FIX(0.541196100) */
00081 #define FIX_0_707106781  ((INT32)  181)         /* FIX(0.707106781) */
00082 #define FIX_1_306562965  ((INT32)  334)         /* FIX(1.306562965) */
00083 #else
00084 #define FIX_0_382683433  FIX(0.382683433)
00085 #define FIX_0_541196100  FIX(0.541196100)
00086 #define FIX_0_707106781  FIX(0.707106781)
00087 #define FIX_1_306562965  FIX(1.306562965)
00088 #endif
00089 
00090 
00091 /* We can gain a little more speed, with a further compromise in accuracy,
00092  * by omitting the addition in a descaling shift.  This yields an incorrectly
00093  * rounded result half the time...
00094  */
00095 
00096 #ifndef USE_ACCURATE_ROUNDING
00097 #undef DESCALE
00098 #define DESCALE(x,n)  RIGHT_SHIFT(x, n)
00099 #endif
00100 
00101 
00102 /* Multiply a DCTELEM variable by an INT32 constant, and immediately
00103  * descale to yield a DCTELEM result.
00104  */
00105 
00106 #define MULTIPLY(var,const)  ((DCTELEM) DESCALE((var) * (const), CONST_BITS))
00107 
00108 
00109 /*
00110  * Perform the forward DCT on one block of samples.
00111  */
00112 
00113 GLOBAL(void)
00114 jpeg_fdct_ifast (DCTELEM * data)
00115 {
00116   DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
00117   DCTELEM tmp10, tmp11, tmp12, tmp13;
00118   DCTELEM z1, z2, z3, z4, z5, z11, z13;
00119   DCTELEM *dataptr;
00120   int ctr;
00121   SHIFT_TEMPS
00122 
00123   /* Pass 1: process rows. */
00124 
00125   dataptr = data;
00126   for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
00127     tmp0 = dataptr[0] + dataptr[7];
00128     tmp7 = dataptr[0] - dataptr[7];
00129     tmp1 = dataptr[1] + dataptr[6];
00130     tmp6 = dataptr[1] - dataptr[6];
00131     tmp2 = dataptr[2] + dataptr[5];
00132     tmp5 = dataptr[2] - dataptr[5];
00133     tmp3 = dataptr[3] + dataptr[4];
00134     tmp4 = dataptr[3] - dataptr[4];
00135     
00136     /* Even part */
00137     
00138     tmp10 = tmp0 + tmp3;        /* phase 2 */
00139     tmp13 = tmp0 - tmp3;
00140     tmp11 = tmp1 + tmp2;
00141     tmp12 = tmp1 - tmp2;
00142     
00143     dataptr[0] = tmp10 + tmp11; /* phase 3 */
00144     dataptr[4] = tmp10 - tmp11;
00145     
00146     z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */
00147     dataptr[2] = tmp13 + z1;    /* phase 5 */
00148     dataptr[6] = tmp13 - z1;
00149     
00150     /* Odd part */
00151 
00152     tmp10 = tmp4 + tmp5;        /* phase 2 */
00153     tmp11 = tmp5 + tmp6;
00154     tmp12 = tmp6 + tmp7;
00155 
00156     /* The rotator is modified from fig 4-8 to avoid extra negations. */
00157     z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */
00158     z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */
00159     z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */
00160     z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */
00161 
00162     z11 = tmp7 + z3;            /* phase 5 */
00163     z13 = tmp7 - z3;
00164 
00165     dataptr[5] = z13 + z2;      /* phase 6 */
00166     dataptr[3] = z13 - z2;
00167     dataptr[1] = z11 + z4;
00168     dataptr[7] = z11 - z4;
00169 
00170     dataptr += DCTSIZE;         /* advance pointer to next row */
00171   }
00172 
00173   /* Pass 2: process columns. */
00174 
00175   dataptr = data;
00176   for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
00177     tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
00178     tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
00179     tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
00180     tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
00181     tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
00182     tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
00183     tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
00184     tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
00185     
00186     /* Even part */
00187     
00188     tmp10 = tmp0 + tmp3;        /* phase 2 */
00189     tmp13 = tmp0 - tmp3;
00190     tmp11 = tmp1 + tmp2;
00191     tmp12 = tmp1 - tmp2;
00192     
00193     dataptr[DCTSIZE*0] = tmp10 + tmp11; /* phase 3 */
00194     dataptr[DCTSIZE*4] = tmp10 - tmp11;
00195     
00196     z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */
00197     dataptr[DCTSIZE*2] = tmp13 + z1; /* phase 5 */
00198     dataptr[DCTSIZE*6] = tmp13 - z1;
00199     
00200     /* Odd part */
00201 
00202     tmp10 = tmp4 + tmp5;        /* phase 2 */
00203     tmp11 = tmp5 + tmp6;
00204     tmp12 = tmp6 + tmp7;
00205 
00206     /* The rotator is modified from fig 4-8 to avoid extra negations. */
00207     z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */
00208     z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */
00209     z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */
00210     z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */
00211 
00212     z11 = tmp7 + z3;            /* phase 5 */
00213     z13 = tmp7 - z3;
00214 
00215     dataptr[DCTSIZE*5] = z13 + z2; /* phase 6 */
00216     dataptr[DCTSIZE*3] = z13 - z2;
00217     dataptr[DCTSIZE*1] = z11 + z4;
00218     dataptr[DCTSIZE*7] = z11 - z4;
00219 
00220     dataptr++;                  /* advance pointer to next column */
00221   }
00222 }
00223 
00224 #endif /* DCT_IFAST_SUPPORTED */