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+/*
+ * jidctint.c
+ *
+ * Copyright (C) 1991-1998, 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 slow-but-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 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 IDCT step produces outputs which are a factor of sqrt(N)
+ * larger than the true IDCT 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 IDCT,
+ * because the y0 and y4 inputs need not be divided by sqrt(N).
+ *
+ * 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. (To scale up 12-bit sample data further, an
+ * intermediate INT32 array would be needed.)
+ *
+ * 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
+
+
+/* Dequantize a coefficient by multiplying it by the multiplier-table
+ * entry; produce an int result. In this module, both inputs and result
+ * are 16 bits or less, so either int or short multiply will work.
+ */
+
+#define DEQUANTIZE(coef,quantval) (((ISLOW_MULT_TYPE) (coef)) * (quantval))
+
+
+/*
+ * Perform dequantization and inverse DCT on one block of coefficients.
+ */
+
+GLOBAL(void)
+jpeg_idct_islow (j_decompress_ptr cinfo, jpeg_component_info * compptr,
+ JCOEFPTR coef_block,
+ JSAMPARRAY output_buf, JDIMENSION output_col)
+{
+ INT32 tmp0, tmp1, tmp2, tmp3;
+ INT32 tmp10, tmp11, tmp12, tmp13;
+ INT32 z1, z2, z3, z4, z5;
+ JCOEFPTR inptr;
+ ISLOW_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
+
+ /* Pass 1: process columns from input, store into work array. */
+ /* Note results are scaled up by sqrt(8) compared to a true IDCT; */
+ /* furthermore, we scale the results by 2**PASS1_BITS. */
+
+ inptr = coef_block;
+ quantptr = (ISLOW_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 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]) << PASS1_BITS;
+
+ 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: reverse the even part of the forward DCT. */
+ /* The rotator is sqrt(2)*c(-6). */
+
+ z2 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
+ z3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);
+
+ z1 = MULTIPLY(z2 + z3, FIX_0_541196100);
+ tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065);
+ tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865);
+
+ z2 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
+ z3 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);
+
+ tmp0 = (z2 + z3) << CONST_BITS;
+ tmp1 = (z2 - z3) << CONST_BITS;
+
+ tmp10 = tmp0 + tmp3;
+ tmp13 = tmp0 - tmp3;
+ tmp11 = tmp1 + tmp2;
+ tmp12 = tmp1 - tmp2;
+
+ /* Odd part per figure 8; the matrix is unitary and hence its
+ * transpose is its inverse. i0..i3 are y7,y5,y3,y1 respectively.
+ */
+
+ tmp0 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
+ tmp1 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
+ tmp2 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
+ tmp3 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);
+
+ z1 = tmp0 + tmp3;
+ z2 = tmp1 + tmp2;
+ z3 = tmp0 + tmp2;
+ z4 = tmp1 + tmp3;
+ z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
+
+ tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
+ tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
+ tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
+ tmp3 = MULTIPLY(tmp3, 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;
+
+ tmp0 += z1 + z3;
+ tmp1 += z2 + z4;
+ tmp2 += z2 + z3;
+ tmp3 += z1 + z4;
+
+ /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */
+
+ wsptr[DCTSIZE*0] = (int) DESCALE(tmp10 + tmp3, CONST_BITS-PASS1_BITS);
+ wsptr[DCTSIZE*7] = (int) DESCALE(tmp10 - tmp3, CONST_BITS-PASS1_BITS);
+ wsptr[DCTSIZE*1] = (int) DESCALE(tmp11 + tmp2, CONST_BITS-PASS1_BITS);
+ wsptr[DCTSIZE*6] = (int) DESCALE(tmp11 - tmp2, CONST_BITS-PASS1_BITS);
+ wsptr[DCTSIZE*2] = (int) DESCALE(tmp12 + tmp1, CONST_BITS-PASS1_BITS);
+ wsptr[DCTSIZE*5] = (int) DESCALE(tmp12 - tmp1, CONST_BITS-PASS1_BITS);
+ wsptr[DCTSIZE*3] = (int) DESCALE(tmp13 + tmp0, CONST_BITS-PASS1_BITS);
+ wsptr[DCTSIZE*4] = (int) DESCALE(tmp13 - tmp0, CONST_BITS-PASS1_BITS);
+
+ 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[(int) DESCALE((INT32) 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: reverse the even part of the forward DCT. */
+ /* The rotator is sqrt(2)*c(-6). */
+
+ z2 = (INT32) wsptr[2];
+ z3 = (INT32) wsptr[6];
+
+ z1 = MULTIPLY(z2 + z3, FIX_0_541196100);
+ tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065);
+ tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865);
+
+ tmp0 = ((INT32) wsptr[0] + (INT32) wsptr[4]) << CONST_BITS;
+ tmp1 = ((INT32) wsptr[0] - (INT32) wsptr[4]) << CONST_BITS;
+
+ tmp10 = tmp0 + tmp3;
+ tmp13 = tmp0 - tmp3;
+ tmp11 = tmp1 + tmp2;
+ tmp12 = tmp1 - tmp2;
+
+ /* Odd part per figure 8; the matrix is unitary and hence its
+ * transpose is its inverse. i0..i3 are y7,y5,y3,y1 respectively.
+ */
+
+ tmp0 = (INT32) wsptr[7];
+ tmp1 = (INT32) wsptr[5];
+ tmp2 = (INT32) wsptr[3];
+ tmp3 = (INT32) wsptr[1];
+
+ z1 = tmp0 + tmp3;
+ z2 = tmp1 + tmp2;
+ z3 = tmp0 + tmp2;
+ z4 = tmp1 + tmp3;
+ z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
+
+ tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
+ tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
+ tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
+ tmp3 = MULTIPLY(tmp3, 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;
+
+ tmp0 += z1 + z3;
+ tmp1 += z2 + z4;
+ tmp2 += z2 + z3;
+ tmp3 += z1 + z4;
+
+ /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */
+
+ outptr[0] = range_limit[(int) DESCALE(tmp10 + tmp3,
+ CONST_BITS+PASS1_BITS+3)
+ & RANGE_MASK];
+ outptr[7] = range_limit[(int) DESCALE(tmp10 - tmp3,
+ CONST_BITS+PASS1_BITS+3)
+ & RANGE_MASK];
+ outptr[1] = range_limit[(int) DESCALE(tmp11 + tmp2,
+ CONST_BITS+PASS1_BITS+3)
+ & RANGE_MASK];
+ outptr[6] = range_limit[(int) DESCALE(tmp11 - tmp2,
+ CONST_BITS+PASS1_BITS+3)
+ & RANGE_MASK];
+ outptr[2] = range_limit[(int) DESCALE(tmp12 + tmp1,
+ CONST_BITS+PASS1_BITS+3)
+ & RANGE_MASK];
+ outptr[5] = range_limit[(int) DESCALE(tmp12 - tmp1,
+ CONST_BITS+PASS1_BITS+3)
+ & RANGE_MASK];
+ outptr[3] = range_limit[(int) DESCALE(tmp13 + tmp0,
+ CONST_BITS+PASS1_BITS+3)
+ & RANGE_MASK];
+ outptr[4] = range_limit[(int) DESCALE(tmp13 - tmp0,
+ CONST_BITS+PASS1_BITS+3)
+ & RANGE_MASK];
+
+ wsptr += DCTSIZE; /* advance pointer to next row */
+ }
+}
+
+#endif /* DCT_ISLOW_SUPPORTED */
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