209 lines
7.1 KiB
C
209 lines
7.1 KiB
C
/*
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* jfwddct.c
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*
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* Copyright (C) 1991, 1992, 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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*
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* This file contains the basic DCT (Discrete Cosine Transform)
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* transformation subroutine.
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*
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* This implementation is based on Appendix A.2 of the book
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* "Discrete Cosine Transform---Algorithms, Advantages, Applications"
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* by K.R. Rao and P. Yip (Academic Press, Inc, London, 1990).
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* It uses scaled fixed-point arithmetic instead of floating point.
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*/
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#include "jinclude.h"
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/*
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* This routine is specialized to the case DCTSIZE = 8.
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*/
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#if DCTSIZE != 8
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Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
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#endif
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/* The poop on this scaling stuff is as follows:
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*
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* We have to do addition and subtraction of the integer inputs, which
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* is no problem, and multiplication by fractional constants, which is
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* a problem to do in integer arithmetic. We multiply all the constants
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* by DCT_SCALE and convert them to integer constants (thus retaining
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* LG2_DCT_SCALE bits of precision in the constants). After doing a
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* multiplication we have to divide the product by DCT_SCALE, with proper
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* rounding, to produce the correct output. The division can be implemented
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* cheaply as a right shift of LG2_DCT_SCALE bits. The DCT equations also
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* specify an additional division by 2 on the final outputs; this can be
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* folded into the right-shift by shifting one more bit (see UNFIXH).
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*
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* If you are planning to recode this in assembler, you might want to set
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* LG2_DCT_SCALE to 15. This loses a bit of precision, but then all the
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* multiplications are between 16-bit quantities (given 8-bit JSAMPLEs!)
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* so you could use a signed 16x16=>32 bit multiply instruction instead of
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* full 32x32 multiply. Unfortunately there's no way to describe such a
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* multiply portably in C, so we've gone for the extra bit of accuracy here.
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*/
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#ifdef EIGHT_BIT_SAMPLES
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#define LG2_DCT_SCALE 16
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#else
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#define LG2_DCT_SCALE 15 /* lose a little precision to avoid overflow */
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#endif
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#define ONE ((INT32) 1)
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#define DCT_SCALE (ONE << LG2_DCT_SCALE)
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/* In some places we shift the inputs left by a couple more bits, */
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/* so that they can be added to fractional results without too much */
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/* loss of precision. */
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#define LG2_OVERSCALE 2
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#define OVERSCALE (ONE << LG2_OVERSCALE)
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#define OVERSHIFT(x) ((x) <<= LG2_OVERSCALE)
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/* Scale a fractional constant by DCT_SCALE */
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#define FIX(x) ((INT32) ((x) * DCT_SCALE + 0.5))
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/* Scale a fractional constant by DCT_SCALE/OVERSCALE */
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/* Such a constant can be multiplied with an overscaled input */
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/* to produce something that's scaled by DCT_SCALE */
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#define FIXO(x) ((INT32) ((x) * DCT_SCALE / OVERSCALE + 0.5))
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/* Descale and correctly round a value that's scaled by DCT_SCALE */
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#define UNFIX(x) RIGHT_SHIFT((x) + (ONE << (LG2_DCT_SCALE-1)), LG2_DCT_SCALE)
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/* Same with an additional division by 2, ie, correctly rounded UNFIX(x/2) */
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#define UNFIXH(x) RIGHT_SHIFT((x) + (ONE << LG2_DCT_SCALE), LG2_DCT_SCALE+1)
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/* Take a value scaled by DCT_SCALE and round to integer scaled by OVERSCALE */
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#define UNFIXO(x) RIGHT_SHIFT((x) + (ONE << (LG2_DCT_SCALE-1-LG2_OVERSCALE)),\
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LG2_DCT_SCALE-LG2_OVERSCALE)
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/* Here are the constants we need */
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/* SIN_i_j is sine of i*pi/j, scaled by DCT_SCALE */
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/* COS_i_j is cosine of i*pi/j, scaled by DCT_SCALE */
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#define SIN_1_4 FIX(0.707106781)
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#define COS_1_4 SIN_1_4
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#define SIN_1_8 FIX(0.382683432)
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#define COS_1_8 FIX(0.923879533)
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#define SIN_3_8 COS_1_8
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#define COS_3_8 SIN_1_8
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#define SIN_1_16 FIX(0.195090322)
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#define COS_1_16 FIX(0.980785280)
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#define SIN_7_16 COS_1_16
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#define COS_7_16 SIN_1_16
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#define SIN_3_16 FIX(0.555570233)
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#define COS_3_16 FIX(0.831469612)
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#define SIN_5_16 COS_3_16
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#define COS_5_16 SIN_3_16
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/* OSIN_i_j is sine of i*pi/j, scaled by DCT_SCALE/OVERSCALE */
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/* OCOS_i_j is cosine of i*pi/j, scaled by DCT_SCALE/OVERSCALE */
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#define OSIN_1_4 FIXO(0.707106781)
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#define OCOS_1_4 OSIN_1_4
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#define OSIN_1_8 FIXO(0.382683432)
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#define OCOS_1_8 FIXO(0.923879533)
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#define OSIN_3_8 OCOS_1_8
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#define OCOS_3_8 OSIN_1_8
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#define OSIN_1_16 FIXO(0.195090322)
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#define OCOS_1_16 FIXO(0.980785280)
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#define OSIN_7_16 OCOS_1_16
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#define OCOS_7_16 OSIN_1_16
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#define OSIN_3_16 FIXO(0.555570233)
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#define OCOS_3_16 FIXO(0.831469612)
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#define OSIN_5_16 OCOS_3_16
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#define OCOS_5_16 OSIN_3_16
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/*
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* Perform the forward DCT on one block of samples.
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*
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* A 2-D DCT can be done by 1-D DCT on each row
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* followed by 1-D DCT on each column.
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*/
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GLOBAL void
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j_fwd_dct (DCTBLOCK data)
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{
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int pass, rowctr;
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register DCTELEM *inptr, *outptr;
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DCTBLOCK workspace;
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/* Each iteration of the inner loop performs one 8-point 1-D DCT.
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* It reads from a *row* of the input matrix and stores into a *column*
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* of the output matrix. In the first pass, we read from the data[] array
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* and store into the local workspace[]. In the second pass, we read from
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* the workspace[] array and store into data[], thus performing the
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* equivalent of a columnar DCT pass with no variable array indexing.
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*/
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inptr = data; /* initialize pointers for first pass */
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outptr = workspace;
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for (pass = 1; pass >= 0; pass--) {
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for (rowctr = DCTSIZE-1; rowctr >= 0; rowctr--) {
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/* many tmps have nonoverlapping lifetime -- flashy register colourers
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* should be able to do this lot very well
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*/
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INT32 tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
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INT32 tmp10, tmp11, tmp12, tmp13;
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INT32 tmp14, tmp15, tmp16, tmp17;
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INT32 tmp25, tmp26;
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SHIFT_TEMPS
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tmp0 = inptr[7] + inptr[0];
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tmp1 = inptr[6] + inptr[1];
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tmp2 = inptr[5] + inptr[2];
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tmp3 = inptr[4] + inptr[3];
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tmp4 = inptr[3] - inptr[4];
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tmp5 = inptr[2] - inptr[5];
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tmp6 = inptr[1] - inptr[6];
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tmp7 = inptr[0] - inptr[7];
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tmp10 = tmp3 + tmp0;
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tmp11 = tmp2 + tmp1;
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tmp12 = tmp1 - tmp2;
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tmp13 = tmp0 - tmp3;
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outptr[ 0] = (DCTELEM) UNFIXH((tmp10 + tmp11) * SIN_1_4);
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outptr[DCTSIZE*4] = (DCTELEM) UNFIXH((tmp10 - tmp11) * COS_1_4);
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outptr[DCTSIZE*2] = (DCTELEM) UNFIXH(tmp13*COS_1_8 + tmp12*SIN_1_8);
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outptr[DCTSIZE*6] = (DCTELEM) UNFIXH(tmp13*SIN_1_8 - tmp12*COS_1_8);
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tmp16 = UNFIXO((tmp6 + tmp5) * SIN_1_4);
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tmp15 = UNFIXO((tmp6 - tmp5) * COS_1_4);
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OVERSHIFT(tmp4);
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OVERSHIFT(tmp7);
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/* tmp4, tmp7, tmp15, tmp16 are overscaled by OVERSCALE */
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tmp14 = tmp4 + tmp15;
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tmp25 = tmp4 - tmp15;
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tmp26 = tmp7 - tmp16;
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tmp17 = tmp7 + tmp16;
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outptr[DCTSIZE ] = (DCTELEM) UNFIXH(tmp17*OCOS_1_16 + tmp14*OSIN_1_16);
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outptr[DCTSIZE*7] = (DCTELEM) UNFIXH(tmp17*OCOS_7_16 - tmp14*OSIN_7_16);
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outptr[DCTSIZE*5] = (DCTELEM) UNFIXH(tmp26*OCOS_5_16 + tmp25*OSIN_5_16);
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outptr[DCTSIZE*3] = (DCTELEM) UNFIXH(tmp26*OCOS_3_16 - tmp25*OSIN_3_16);
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inptr += DCTSIZE; /* advance inptr to next row */
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outptr++; /* advance outptr to next column */
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}
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/* end of pass; in case it was pass 1, set up for pass 2 */
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inptr = workspace;
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outptr = data;
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}
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}
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