+/*
+ * 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 */
projects / opencv / blobdiff