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+/*
+ * jidctfst.c
+ *
+ * Copyright (C) 1994-1998, 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.
+ */
+
+#define JPEG_INTERNALS
+#include "jinclude.h"
+#include "jpeglib.h"
+#include "jdct.h" /* Private declarations for DCT subsystem */
+
+#ifdef DCT_IFAST_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
+
+
+/* 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).
+ */
+
+#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 ((INT32) 277) /* FIX(1.082392200) */
+#define FIX_1_414213562 ((INT32) 362) /* FIX(1.414213562) */
+#define FIX_1_847759065 ((INT32) 473) /* FIX(1.847759065) */
+#define FIX_2_613125930 ((INT32) 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...
+ */
+
+#ifndef USE_ACCURATE_ROUNDING
+#undef DESCALE
+#define DESCALE(x,n) RIGHT_SHIFT(x, n)
+#endif
+
+
+/* Multiply a DCTELEM variable by an INT32 constant, and immediately
+ * descale to yield a DCTELEM result.
+ */
+
+#define MULTIPLY(var,const) ((DCTELEM) 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) (((IFAST_MULT_TYPE) (coef)) * (quantval))
+#else
+#define DEQUANTIZE(coef,quantval) \
+ DESCALE((coef)*(quantval), 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.
+ */
+
+#ifdef RIGHT_SHIFT_IS_UNSIGNED
+#define ISHIFT_TEMPS DCTELEM ishift_temp;
+#if BITS_IN_JSAMPLE == 8
+#define DCTELEMBITS 16 /* DCTELEM may be 16 or 32 bits */
+#else
+#define DCTELEMBITS 32 /* DCTELEM must be 32 bits */
+#endif
+#define IRIGHT_SHIFT(x,shft) \
+ ((ishift_temp = (x)) < 0 ? \
+ (ishift_temp >> (shft)) | ((~((DCTELEM) 0)) << (DCTELEMBITS-(shft))) : \
+ (ishift_temp >> (shft)))
+#else
+#define ISHIFT_TEMPS
+#define IRIGHT_SHIFT(x,shft) ((x) >> (shft))
+#endif
+
+#ifdef USE_ACCURATE_ROUNDING
+#define IDESCALE(x,n) ((int) IRIGHT_SHIFT((x) + (1 << ((n)-1)), n))
+#else
+#define IDESCALE(x,n) ((int) IRIGHT_SHIFT(x, n))
+#endif
+
+
+/*
+ * Perform dequantization and inverse DCT on one block of coefficients.
+ */
+
+GLOBAL(void)
+jpeg_idct_ifast (j_decompress_ptr cinfo, jpeg_component_info * compptr,
+ JCOEFPTR coef_block,
+ JSAMPARRAY output_buf, JDIMENSION output_col)
+{
+ DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
+ DCTELEM tmp10, tmp11, tmp12, tmp13;
+ DCTELEM z5, z10, z11, z12, z13;
+ JCOEFPTR inptr;
+ IFAST_MULT_TYPE * quantptr;
+ int * wsptr;
+ JSAMPROW outptr;
+ JSAMPLE *range_limit = IDCT_range_limit(cinfo);
+ int ctr;
+ int workspace[DCTSIZE2]; /* buffers data between passes */
+ SHIFT_TEMPS /* for DESCALE */
+ ISHIFT_TEMPS /* for IDESCALE */
+
+ /* Pass 1: process columns from input, store into work array. */
+
+ inptr = coef_block;
+ quantptr = (IFAST_MULT_TYPE *) compptr->dct_table;
+ wsptr = workspace;
+ for (ctr = DCTSIZE; ctr > 0; ctr--) {
+ /* 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 (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 &&
+ inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 &&
+ inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 &&
+ inptr[DCTSIZE*7] == 0) {
+ /* AC terms all zero */
+ int dcval = (int) DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
+
+ wsptr[DCTSIZE*0] = dcval;
+ wsptr[DCTSIZE*1] = dcval;
+ wsptr[DCTSIZE*2] = dcval;
+ wsptr[DCTSIZE*3] = dcval;
+ wsptr[DCTSIZE*4] = dcval;
+ wsptr[DCTSIZE*5] = dcval;
+ wsptr[DCTSIZE*6] = dcval;
+ wsptr[DCTSIZE*7] = dcval;
+
+ inptr++; /* advance pointers to next column */
+ quantptr++;
+ wsptr++;
+ continue;
+ }
+
+ /* Even part */
+
+ tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
+ tmp1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
+ tmp2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);
+ tmp3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);
+
+ tmp10 = tmp0 + tmp2; /* phase 3 */
+ tmp11 = tmp0 - tmp2;
+
+ tmp13 = tmp1 + tmp3; /* phases 5-3 */
+ tmp12 = MULTIPLY(tmp1 - tmp3, FIX_1_414213562) - tmp13; /* 2*c4 */
+
+ tmp0 = tmp10 + tmp13; /* phase 2 */
+ tmp3 = tmp10 - tmp13;
+ tmp1 = tmp11 + tmp12;
+ tmp2 = tmp11 - tmp12;
+
+ /* Odd part */
+
+ tmp4 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);
+ tmp5 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
+ tmp6 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
+ tmp7 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
+
+ z13 = tmp6 + tmp5; /* phase 6 */
+ z10 = tmp6 - tmp5;
+ z11 = tmp4 + tmp7;
+ z12 = tmp4 - tmp7;
+
+ tmp7 = z11 + z13; /* phase 5 */
+ tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */
+
+ z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */
+ tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */
+ tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */
+
+ tmp6 = tmp12 - tmp7; /* phase 2 */
+ tmp5 = tmp11 - tmp6;
+ tmp4 = tmp10 + tmp5;
+
+ wsptr[DCTSIZE*0] = (int) (tmp0 + tmp7);
+ wsptr[DCTSIZE*7] = (int) (tmp0 - tmp7);
+ wsptr[DCTSIZE*1] = (int) (tmp1 + tmp6);
+ wsptr[DCTSIZE*6] = (int) (tmp1 - tmp6);
+ wsptr[DCTSIZE*2] = (int) (tmp2 + tmp5);
+ wsptr[DCTSIZE*5] = (int) (tmp2 - tmp5);
+ wsptr[DCTSIZE*4] = (int) (tmp3 + tmp4);
+ wsptr[DCTSIZE*3] = (int) (tmp3 - tmp4);
+
+ inptr++; /* advance pointers to next column */
+ quantptr++;
+ wsptr++;
+ }
+
+ /* 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. */
+
+ wsptr = workspace;
+ for (ctr = 0; ctr < DCTSIZE; ctr++) {
+ outptr = output_buf[ctr] + output_col;
+ /* 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 (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 &&
+ wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) {
+ /* AC terms all zero */
+ JSAMPLE dcval = range_limit[IDESCALE(wsptr[0], PASS1_BITS+3)
+ & RANGE_MASK];
+
+ outptr[0] = dcval;
+ outptr[1] = dcval;
+ outptr[2] = dcval;
+ outptr[3] = dcval;
+ outptr[4] = dcval;
+ outptr[5] = dcval;
+ outptr[6] = dcval;
+ outptr[7] = dcval;
+
+ wsptr += DCTSIZE; /* advance pointer to next row */
+ continue;
+ }
+#endif
+
+ /* Even part */
+
+ tmp10 = ((DCTELEM) wsptr[0] + (DCTELEM) wsptr[4]);
+ tmp11 = ((DCTELEM) wsptr[0] - (DCTELEM) wsptr[4]);
+
+ tmp13 = ((DCTELEM) wsptr[2] + (DCTELEM) wsptr[6]);
+ tmp12 = MULTIPLY((DCTELEM) wsptr[2] - (DCTELEM) wsptr[6], FIX_1_414213562)
+ - tmp13;
+
+ tmp0 = tmp10 + tmp13;
+ tmp3 = tmp10 - tmp13;
+ tmp1 = tmp11 + tmp12;
+ tmp2 = tmp11 - tmp12;
+
+ /* Odd part */
+
+ z13 = (DCTELEM) wsptr[5] + (DCTELEM) wsptr[3];
+ z10 = (DCTELEM) wsptr[5] - (DCTELEM) wsptr[3];
+ z11 = (DCTELEM) wsptr[1] + (DCTELEM) wsptr[7];
+ z12 = (DCTELEM) wsptr[1] - (DCTELEM) wsptr[7];
+
+ tmp7 = z11 + z13; /* phase 5 */
+ tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */
+
+ z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */
+ tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */
+ tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */
+
+ tmp6 = tmp12 - tmp7; /* phase 2 */
+ tmp5 = tmp11 - tmp6;
+ tmp4 = tmp10 + tmp5;
+
+ /* Final output stage: scale down by a factor of 8 and range-limit */
+
+ outptr[0] = range_limit[IDESCALE(tmp0 + tmp7, PASS1_BITS+3)
+ & RANGE_MASK];
+ outptr[7] = range_limit[IDESCALE(tmp0 - tmp7, PASS1_BITS+3)
+ & RANGE_MASK];
+ outptr[1] = range_limit[IDESCALE(tmp1 + tmp6, PASS1_BITS+3)
+ & RANGE_MASK];
+ outptr[6] = range_limit[IDESCALE(tmp1 - tmp6, PASS1_BITS+3)
+ & RANGE_MASK];
+ outptr[2] = range_limit[IDESCALE(tmp2 + tmp5, PASS1_BITS+3)
+ & RANGE_MASK];
+ outptr[5] = range_limit[IDESCALE(tmp2 - tmp5, PASS1_BITS+3)
+ & RANGE_MASK];
+ outptr[4] = range_limit[IDESCALE(tmp3 + tmp4, PASS1_BITS+3)
+ & RANGE_MASK];
+ outptr[3] = range_limit[IDESCALE(tmp3 - tmp4, PASS1_BITS+3)
+ & RANGE_MASK];
+
+ wsptr += DCTSIZE; /* advance pointer to next row */
+ }
+}
+
+#endif /* DCT_IFAST_SUPPORTED */
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