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+/*
+ * jidctfst.c
+ *
+ * Copyright (C) 1994-1996, 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 fast, not so accurate integer implementation of the
+ * inverse DCT (Discrete Cosine Transform). In the IJG code, this routine
+ * must also perform dequantization of the input coefficients.
+ *
+ * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT
+ * on each row (or vice versa, but it's more convenient to emit a row at
+ * a time). 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 Arai, Agui, and Nakajima's algorithm for
+ * scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in
+ * Japanese, but the algorithm is described in the Pennebaker & Mitchell
+ * JPEG textbook (see REFERENCES section in file README). The following code
+ * is based directly on figure 4-8 in P&M.
+ * While an 8-point DCT cannot be done in less than 11 multiplies, it is
+ * possible to arrange the computation so that many of the multiplies are
+ * simple scalings of the final outputs. These multiplies can then be
+ * folded into the multiplications or divisions by the JPEG quantization
+ * table entries. The AA&N method leaves only 5 multiplies and 29 adds
+ * to be done in the DCT itself.
+ * The primary disadvantage of this method is that with fixed-point math,
+ * accuracy is lost due to imprecise representation of the scaled
+ * quantization values. The smaller the quantization table entry, the less
+ * precise the scaled value, so this implementation does worse with high-
+ * quality-setting files than with low-quality ones.
+ */
+
+/*
+ * This module is specialized to the case DCTSIZE = 8.
+ */
+
+/* Scaling decisions are generally the same as in the LL&M algorithm;
+ * see jidctint.c for more details. However, we choose to descale
+ * (right shift) multiplication products as soon as they are formed,
+ * rather than carrying additional fractional bits into subsequent additions.
+ * This compromises accuracy slightly, but it lets us save a few shifts.
+ * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples)
+ * everywhere except in the multiplications proper; this saves a good deal
+ * of work on 16-bit-int machines.
+ *
+ * The dequantized coefficients are not integers because the AA&N scaling
+ * factors have been incorporated. We represent them scaled up by PASS1_BITS,
+ * so that the first and second IDCT rounds have the same input scaling.
+ * For 8-bit JSAMPLEs, we choose IFAST_SCALE_BITS = PASS1_BITS so as to
+ * avoid a descaling shift; this compromises accuracy rather drastically
+ * for small quantization table entries, but it saves a lot of shifts.
+ * For 12-bit JSAMPLEs, there's no hope of using 16x16 multiplies anyway,
+ * so we use a much larger scaling factor to preserve accuracy.
+ *
+ * A final compromise is to represent the multiplicative constants to only
+ * 8 fractional bits, rather than 13. This saves some shifting work on some
+ * machines, and may also reduce the cost of multiplication (since there
+ * are fewer one-bits in the constants).
+ */
+
+#define BITS_IN_JSAMPLE 8
+
+#if BITS_IN_JSAMPLE == 8
+#define CONST_BITS 8
+#define PASS1_BITS 2
+#else
+#define CONST_BITS 8
+#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 == 8
+#define FIX_1_082392200 (277) /* FIX(1.082392200) */
+#define FIX_1_414213562 (362) /* FIX(1.414213562) */
+#define FIX_1_847759065 (473) /* FIX(1.847759065) */
+#define FIX_2_613125930 (669) /* FIX(2.613125930) */
+#else
+#define FIX_1_082392200 FIX(1.082392200)
+#define FIX_1_414213562 FIX(1.414213562)
+#define FIX_1_847759065 FIX(1.847759065)
+#define FIX_2_613125930 FIX(2.613125930)
+#endif
+
+
+/* We can gain a little more speed, with a further compromise in accuracy,
+ * by omitting the addition in a descaling shift. This yields an incorrectly
+ * rounded result half the time...
+ */
+
+
+/* Multiply a DCTELEM variable by an INT32 constant, and immediately
+ * descale to yield a DCTELEM result.
+ */
+
+#define MULTIPLY(var,const) (DESCALE((var) * (const), CONST_BITS))
+
+
+/* Dequantize a coefficient by multiplying it by the multiplier-table
+ * entry; produce a DCTELEM result. For 8-bit data a 16x16->16
+ * multiplication will do. For 12-bit data, the multiplier table is
+ * declared INT32, so a 32-bit multiply will be used.
+ */
+
+#if BITS_IN_JSAMPLE == 8
+#define DEQUANTIZE(coef,quantval) (coef)
+#else
+#define DEQUANTIZE(coef,quantval) \
+ DESCALE((coef), IFAST_SCALE_BITS-PASS1_BITS)
+#endif
+
+
+/* Like DESCALE, but applies to a DCTELEM and produces an int.
+ * We assume that int right shift is unsigned if INT32 right shift is.
+ */
+
+#define DESCALE(x,n) ((x)>>(n))
+#define RANGE(n) (n)
+#define BLOCK int
+
+/*
+ * Perform dequantization and inverse DCT on one block of coefficients.
+ */
+#define DCTSIZE 8
+#define DCTSIZE2 64
+
+static void IDCT1(BLOCK *block)
+{
+ int val = RANGE(DESCALE(block[0], PASS1_BITS+3));
+ int i;
+ for(i=0;i<DCTSIZE2;i++) block[i]=val;
+}
+
+void IDCT(BLOCK *block,int k)
+{
+ int tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
+ int z5, z10, z11, z12, z13;
+ BLOCK *ptr;
+ int i;
+
+ /* Pass 1: process columns from input, store into work array. */
+ switch(k){
+ case 1:IDCT1(block); return;
+ }
+
+ ptr = block;
+ for (i = 0; i< DCTSIZE; i++,ptr++) {
+ /* Due to quantization, we will usually find that many of the input
+ * coefficients are zero, especially the AC terms. We can exploit this
+ * by short-circuiting the IDCT calculation for any column in which all
+ * the AC terms are zero. In that case each output is equal to the
+ * DC coefficient (with scale factor as needed).
+ * With typical images and quantization tables, half or more of the
+ * column DCT calculations can be simplified this way.
+ */
+
+ if ((ptr[DCTSIZE*1] | ptr[DCTSIZE*2] | ptr[DCTSIZE*3] |
+ ptr[DCTSIZE*4] | ptr[DCTSIZE*5] | ptr[DCTSIZE*6] |
+ ptr[DCTSIZE*7]) == 0) {
+ /* AC terms all zero */
+ ptr[DCTSIZE*0] =
+ ptr[DCTSIZE*1] =
+ ptr[DCTSIZE*2] =
+ ptr[DCTSIZE*3] =
+ ptr[DCTSIZE*4] =
+ ptr[DCTSIZE*5] =
+ ptr[DCTSIZE*6] =
+ ptr[DCTSIZE*7] =
+ ptr[DCTSIZE*0];
+
+ continue;
+ }
+
+ /* Even part */
+
+ z10 = ptr[DCTSIZE*0] + ptr[DCTSIZE*4]; /* phase 3 */
+ z11 = ptr[DCTSIZE*0] - ptr[DCTSIZE*4];
+ z13 = ptr[DCTSIZE*2] + ptr[DCTSIZE*6]; /* phases 5-3 */
+ z12 = MULTIPLY(ptr[DCTSIZE*2] - ptr[DCTSIZE*6], FIX_1_414213562) - z13; /* 2*c4 */
+
+ tmp0 = z10 + z13; /* phase 2 */
+ tmp3 = z10 - z13;
+ tmp1 = z11 + z12;
+ tmp2 = z11 - z12;
+
+ /* Odd part */
+
+ z13 = ptr[DCTSIZE*3] + ptr[DCTSIZE*5]; /* phase 6 */
+ z10 = ptr[DCTSIZE*3] - ptr[DCTSIZE*5];
+ z11 = ptr[DCTSIZE*1] + ptr[DCTSIZE*7];
+ z12 = ptr[DCTSIZE*1] - ptr[DCTSIZE*7];
+
+ z5 = MULTIPLY(z12 - z10, FIX_1_847759065);
+ tmp7 = z11 + z13; /* phase 5 */
+ tmp6 = MULTIPLY(z10, FIX_2_613125930) + z5 - tmp7; /* phase 2 */
+ tmp5 = MULTIPLY(z11 - z13, FIX_1_414213562) - tmp6;
+ tmp4 = MULTIPLY(z12, FIX_1_082392200) - z5 + tmp5;
+
+ ptr[DCTSIZE*0] = (tmp0 + tmp7);
+ ptr[DCTSIZE*7] = (tmp0 - tmp7);
+ ptr[DCTSIZE*1] = (tmp1 + tmp6);
+ ptr[DCTSIZE*6] = (tmp1 - tmp6);
+ ptr[DCTSIZE*2] = (tmp2 + tmp5);
+ ptr[DCTSIZE*5] = (tmp2 - tmp5);
+ ptr[DCTSIZE*4] = (tmp3 + tmp4);
+ ptr[DCTSIZE*3] = (tmp3 - tmp4);
+
+ }
+
+ /* Pass 2: process rows from work array, store into output array. */
+ /* Note that we must descale the results by a factor of 8 == 2**3, */
+ /* and also undo the PASS1_BITS scaling. */
+
+ ptr = block;
+ for (i = 0; i < DCTSIZE; i++ ,ptr+=DCTSIZE) {
+ /* Rows of zeroes can be exploited in the same way as we did with columns.
+ * However, the column calculation has created many nonzero AC terms, so
+ * the simplification applies less often (typically 5% to 10% of the time).
+ * On machines with very fast multiplication, it's possible that the
+ * test takes more time than it's worth. In that case this section
+ * may be commented out.
+ */
+
+#ifndef NO_ZERO_ROW_TEST
+ if ((ptr[1] | ptr[2] | ptr[3] | ptr[4] | ptr[5] | ptr[6] |
+ ptr[7]) == 0) {
+ /* AC terms all zero */
+ ptr[0] =
+ ptr[1] =
+ ptr[2] =
+ ptr[3] =
+ ptr[4] =
+ ptr[5] =
+ ptr[6] =
+ ptr[7] =
+ RANGE(DESCALE(ptr[0], PASS1_BITS+3));;
+
+ continue;
+ }
+#endif
+
+ /* Even part */
+
+ z10 = ptr[0] + ptr[4];
+ z11 = ptr[0] - ptr[4];
+ z13 = ptr[2] + ptr[6];
+ z12 = MULTIPLY(ptr[2] - ptr[6], FIX_1_414213562) - z13;
+
+ tmp0 = z10 + z13;
+ tmp3 = z10 - z13;
+ tmp1 = z11 + z12;
+ tmp2 = z11 - z12;
+
+ /* Odd part */
+
+ z13 = ptr[3] + ptr[5];
+ z10 = ptr[3] - ptr[5];
+ z11 = ptr[1] + ptr[7];
+ z12 = ptr[1] - ptr[7];
+
+ z5 = MULTIPLY(z12 - z10, FIX_1_847759065);
+ tmp7 = z11 + z13; /* phase 5 */
+ tmp6 = MULTIPLY(z10, FIX_2_613125930) + z5 - tmp7; /* phase 2 */
+ tmp5 = MULTIPLY(z11 - z13, FIX_1_414213562) - tmp6;
+ tmp4 = MULTIPLY(z12, FIX_1_082392200) - z5 + tmp5;
+
+ /* Final output stage: scale down by a factor of 8 and range-limit */
+
+ ptr[0] = RANGE(DESCALE(tmp0 + tmp7, PASS1_BITS+3));;
+ ptr[7] = RANGE(DESCALE(tmp0 - tmp7, PASS1_BITS+3));;
+ ptr[1] = RANGE(DESCALE(tmp1 + tmp6, PASS1_BITS+3));;
+ ptr[6] = RANGE(DESCALE(tmp1 - tmp6, PASS1_BITS+3));;
+ ptr[2] = RANGE(DESCALE(tmp2 + tmp5, PASS1_BITS+3));;
+ ptr[5] = RANGE(DESCALE(tmp2 - tmp5, PASS1_BITS+3));;
+ ptr[4] = RANGE(DESCALE(tmp3 + tmp4, PASS1_BITS+3));;
+ ptr[3] = RANGE(DESCALE(tmp3 - tmp4, PASS1_BITS+3));;
+
+ }
+}
+
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