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* Copyright (C) 1994-1996, Thomas G. Lane.
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* This file is part of the Independent JPEG Group's software.
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* For conditions of distribution and use, see the accompanying README file.
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* This file contains a fast, not so accurate integer implementation of the
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* forward DCT (Discrete Cosine Transform).
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* A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT
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* on each column. Direct algorithms are also available, but they are
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* much more complex and seem not to be any faster when reduced to code.
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* This implementation is based on Arai, Agui, and Nakajima's algorithm for
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* scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in
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* Japanese, but the algorithm is described in the Pennebaker & Mitchell
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* JPEG textbook (see REFERENCES section in file README). The following code
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* is based directly on figure 4-8 in P&M.
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* While an 8-point DCT cannot be done in less than 11 multiplies, it is
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* possible to arrange the computation so that many of the multiplies are
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* simple scalings of the final outputs. These multiplies can then be
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* folded into the multiplications or divisions by the JPEG quantization
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* table entries. The AA&N method leaves only 5 multiplies and 29 adds
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* to be done in the DCT itself.
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* The primary disadvantage of this method is that with fixed-point math,
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* accuracy is lost due to imprecise representation of the scaled
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* quantization values. The smaller the quantization table entry, the less
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* precise the scaled value, so this implementation does worse with high-
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* quality-setting files than with low-quality ones.
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#define JPEG_INTERNALS
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#include "jdct.h" /* Private declarations for DCT subsystem */
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#ifdef DCT_IFAST_SUPPORTED
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* This module is specialized to the case DCTSIZE = 8.
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Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
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/* Scaling decisions are generally the same as in the LL&M algorithm;
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* see jfdctint.c for more details. However, we choose to descale
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* (right shift) multiplication products as soon as they are formed,
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* rather than carrying additional fractional bits into subsequent additions.
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* This compromises accuracy slightly, but it lets us save a few shifts.
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* More importantly, 16-bit arithmetic is then adequate (for 8-bit samples)
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* everywhere except in the multiplications proper; this saves a good deal
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* of work on 16-bit-int machines.
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* Again to save a few shifts, the intermediate results between pass 1 and
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* pass 2 are not upscaled, but are represented only to integral precision.
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* A final compromise is to represent the multiplicative constants to only
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* 8 fractional bits, rather than 13. This saves some shifting work on some
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* machines, and may also reduce the cost of multiplication (since there
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* are fewer one-bits in the constants).
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/* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
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* causing a lot of useless floating-point operations at run time.
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* To get around this we use the following pre-calculated constants.
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* If you change CONST_BITS you may want to add appropriate values.
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* (With a reasonable C compiler, you can just rely on the FIX() macro...)
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#define FIX_0_382683433 ((INT32) 98) /* FIX(0.382683433) */
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#define FIX_0_541196100 ((INT32) 139) /* FIX(0.541196100) */
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#define FIX_0_707106781 ((INT32) 181) /* FIX(0.707106781) */
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#define FIX_1_306562965 ((INT32) 334) /* FIX(1.306562965) */
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#define FIX_0_382683433 FIX(0.382683433)
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#define FIX_0_541196100 FIX(0.541196100)
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#define FIX_0_707106781 FIX(0.707106781)
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#define FIX_1_306562965 FIX(1.306562965)
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/* We can gain a little more speed, with a further compromise in accuracy,
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* by omitting the addition in a descaling shift. This yields an incorrectly
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* rounded result half the time...
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#ifndef USE_ACCURATE_ROUNDING
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#define DESCALE(x,n) RIGHT_SHIFT(x, n)
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/* Multiply a DCTELEM variable by an INT32 constant, and immediately
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* descale to yield a DCTELEM result.
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#define MULTIPLY(var,const) ((DCTELEM) DESCALE((var) * (const), CONST_BITS))
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* Perform the forward DCT on one block of samples.
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jpeg_fdct_ifast (DCTELEM * data)
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DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
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DCTELEM tmp10, tmp11, tmp12, tmp13;
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DCTELEM z1, z2, z3, z4, z5, z11, z13;
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/* Pass 1: process rows. */
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for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
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tmp0 = dataptr[0] + dataptr[7];
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tmp7 = dataptr[0] - dataptr[7];
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tmp1 = dataptr[1] + dataptr[6];
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tmp6 = dataptr[1] - dataptr[6];
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tmp2 = dataptr[2] + dataptr[5];
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tmp5 = dataptr[2] - dataptr[5];
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tmp3 = dataptr[3] + dataptr[4];
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tmp4 = dataptr[3] - dataptr[4];
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tmp10 = tmp0 + tmp3; /* phase 2 */
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dataptr[0] = tmp10 + tmp11; /* phase 3 */
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dataptr[4] = tmp10 - tmp11;
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z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */
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dataptr[2] = tmp13 + z1; /* phase 5 */
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dataptr[6] = tmp13 - z1;
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tmp10 = tmp4 + tmp5; /* phase 2 */
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/* The rotator is modified from fig 4-8 to avoid extra negations. */
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z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */
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z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */
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z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */
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z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */
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z11 = tmp7 + z3; /* phase 5 */
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dataptr[5] = z13 + z2; /* phase 6 */
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dataptr[3] = z13 - z2;
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dataptr[1] = z11 + z4;
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dataptr[7] = z11 - z4;
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dataptr += DCTSIZE; /* advance pointer to next row */
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/* Pass 2: process columns. */
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for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
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tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
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tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
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tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
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tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
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tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
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tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
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tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
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tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
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tmp10 = tmp0 + tmp3; /* phase 2 */
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dataptr[DCTSIZE*0] = tmp10 + tmp11; /* phase 3 */
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dataptr[DCTSIZE*4] = tmp10 - tmp11;
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z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */
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dataptr[DCTSIZE*2] = tmp13 + z1; /* phase 5 */
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dataptr[DCTSIZE*6] = tmp13 - z1;
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tmp10 = tmp4 + tmp5; /* phase 2 */
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/* The rotator is modified from fig 4-8 to avoid extra negations. */
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z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */
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z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */
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z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */
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z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */
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z11 = tmp7 + z3; /* phase 5 */
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dataptr[DCTSIZE*5] = z13 + z2; /* phase 6 */
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dataptr[DCTSIZE*3] = z13 - z2;
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dataptr[DCTSIZE*1] = z11 + z4;
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dataptr[DCTSIZE*7] = z11 - z4;
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dataptr++; /* advance pointer to next column */
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#endif /* DCT_IFAST_SUPPORTED */
added
removed
jfdctfst.c
