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* Copyright (C) 1994-1998, 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 inverse-DCT routines that produce reduced-size output:
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* either 4x4, 2x2, or 1x1 pixels from an 8x8 DCT block.
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* The implementation is based on the Loeffler, Ligtenberg and Moschytz (LL&M)
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* algorithm used in jidctint.c. We simply replace each 8-to-8 1-D IDCT step
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* with an 8-to-4 step that produces the four averages of two adjacent outputs
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* (or an 8-to-2 step producing two averages of four outputs, for 2x2 output).
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* These steps were derived by computing the corresponding values at the end
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* of the normal LL&M code, then simplifying as much as possible.
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* 1x1 is trivial: just take the DC coefficient divided by 8.
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* See jidctint.c for additional comments.
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#define JPEG_INTERNALS
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#include "jdct.h" /* Private declarations for DCT subsystem */
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#ifdef IDCT_SCALING_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 is the same as in jidctint.c. */
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#if BITS_IN_JSAMPLE == 8
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#define PASS1_BITS 1 /* lose a little precision to avoid overflow */
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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_211164243 ((JPEG_INT32) 1730) /* FIX(0.211164243) */
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#define FIX_0_509795579 ((JPEG_INT32) 4176) /* FIX(0.509795579) */
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#define FIX_0_601344887 ((JPEG_INT32) 4926) /* FIX(0.601344887) */
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#define FIX_0_720959822 ((JPEG_INT32) 5906) /* FIX(0.720959822) */
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#define FIX_0_765366865 ((JPEG_INT32) 6270) /* FIX(0.765366865) */
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#define FIX_0_850430095 ((JPEG_INT32) 6967) /* FIX(0.850430095) */
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#define FIX_0_899976223 ((JPEG_INT32) 7373) /* FIX(0.899976223) */
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#define FIX_1_061594337 ((JPEG_INT32) 8697) /* FIX(1.061594337) */
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#define FIX_1_272758580 ((JPEG_INT32) 10426) /* FIX(1.272758580) */
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#define FIX_1_451774981 ((JPEG_INT32) 11893) /* FIX(1.451774981) */
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#define FIX_1_847759065 ((JPEG_INT32) 15137) /* FIX(1.847759065) */
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#define FIX_2_172734803 ((JPEG_INT32) 17799) /* FIX(2.172734803) */
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#define FIX_2_562915447 ((JPEG_INT32) 20995) /* FIX(2.562915447) */
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#define FIX_3_624509785 ((JPEG_INT32) 29692) /* FIX(3.624509785) */
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#define FIX_0_211164243 FIX(0.211164243)
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#define FIX_0_509795579 FIX(0.509795579)
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#define FIX_0_601344887 FIX(0.601344887)
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#define FIX_0_720959822 FIX(0.720959822)
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#define FIX_0_765366865 FIX(0.765366865)
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#define FIX_0_850430095 FIX(0.850430095)
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#define FIX_0_899976223 FIX(0.899976223)
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#define FIX_1_061594337 FIX(1.061594337)
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#define FIX_1_272758580 FIX(1.272758580)
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#define FIX_1_451774981 FIX(1.451774981)
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#define FIX_1_847759065 FIX(1.847759065)
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#define FIX_2_172734803 FIX(2.172734803)
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#define FIX_2_562915447 FIX(2.562915447)
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#define FIX_3_624509785 FIX(3.624509785)
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/* Multiply an INT32 variable by an INT32 constant to yield an INT32 result.
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* For 8-bit samples with the recommended scaling, all the variable
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* and constant values involved are no more than 16 bits wide, so a
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* 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
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* For 12-bit samples, a full 32-bit multiplication will be needed.
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#if BITS_IN_JSAMPLE == 8
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#define MULTIPLY(var,const) MULTIPLY16C16(var,const)
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#define MULTIPLY(var,const) ((var) * (const))
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/* Dequantize a coefficient by multiplying it by the multiplier-table
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* entry; produce an int result. In this module, both inputs and result
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* are 16 bits or less, so either int or short multiply will work.
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#define DEQUANTIZE(coef,quantval) (((ISLOW_MULT_TYPE) (coef)) * (quantval))
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* Perform dequantization and inverse DCT on one block of coefficients,
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* producing a reduced-size 4x4 output block.
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jpeg_idct_4x4 (j_decompress_ptr cinfo, jpeg_component_info * compptr,
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JSAMPARRAY output_buf, JDIMENSION output_col)
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JPEG_INT32 tmp0, tmp2, tmp10, tmp12;
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JPEG_INT32 z1, z2, z3, z4;
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ISLOW_MULT_TYPE * quantptr;
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JSAMPLE *range_limit = IDCT_range_limit(cinfo);
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int workspace[DCTSIZE*4]; /* buffers data between passes */
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/* Pass 1: process columns from input, store into work array. */
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quantptr = (ISLOW_MULT_TYPE *) compptr->dct_table;
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for (ctr = DCTSIZE; ctr > 0; inptr++, quantptr++, wsptr++, ctr--) {
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/* Don't bother to process column 4, because second pass won't use it */
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if (ctr == DCTSIZE-4)
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if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 &&
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inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*5] == 0 &&
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inptr[DCTSIZE*6] == 0 && inptr[DCTSIZE*7] == 0) {
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/* AC terms all zero; we need not examine term 4 for 4x4 output */
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int dcval = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]) << PASS1_BITS;
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wsptr[DCTSIZE*0] = dcval;
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wsptr[DCTSIZE*1] = dcval;
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wsptr[DCTSIZE*2] = dcval;
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wsptr[DCTSIZE*3] = dcval;
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tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
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tmp0 <<= (CONST_BITS+1);
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z2 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
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z3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);
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tmp2 = MULTIPLY(z2, FIX_1_847759065) + MULTIPLY(z3, - FIX_0_765366865);
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z1 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
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z2 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
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z3 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
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z4 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);
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tmp0 = MULTIPLY(z1, - FIX_0_211164243) /* sqrt(2) * (c3-c1) */
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+ MULTIPLY(z2, FIX_1_451774981) /* sqrt(2) * (c3+c7) */
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+ MULTIPLY(z3, - FIX_2_172734803) /* sqrt(2) * (-c1-c5) */
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+ MULTIPLY(z4, FIX_1_061594337); /* sqrt(2) * (c5+c7) */
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tmp2 = MULTIPLY(z1, - FIX_0_509795579) /* sqrt(2) * (c7-c5) */
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+ MULTIPLY(z2, - FIX_0_601344887) /* sqrt(2) * (c5-c1) */
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+ MULTIPLY(z3, FIX_0_899976223) /* sqrt(2) * (c3-c7) */
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+ MULTIPLY(z4, FIX_2_562915447); /* sqrt(2) * (c1+c3) */
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/* Final output stage */
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wsptr[DCTSIZE*0] = (int) DESCALE(tmp10 + tmp2, CONST_BITS-PASS1_BITS+1);
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wsptr[DCTSIZE*3] = (int) DESCALE(tmp10 - tmp2, CONST_BITS-PASS1_BITS+1);
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wsptr[DCTSIZE*1] = (int) DESCALE(tmp12 + tmp0, CONST_BITS-PASS1_BITS+1);
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wsptr[DCTSIZE*2] = (int) DESCALE(tmp12 - tmp0, CONST_BITS-PASS1_BITS+1);
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/* Pass 2: process 4 rows from work array, store into output array. */
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for (ctr = 0; ctr < 4; ctr++) {
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outptr = output_buf[ctr] + output_col;
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/* It's not clear whether a zero row test is worthwhile here ... */
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#ifndef NO_ZERO_ROW_TEST
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if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 &&
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wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) {
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/* AC terms all zero */
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JSAMPLE dcval = range_limit[(int) DESCALE((JPEG_INT32) wsptr[0], PASS1_BITS+3)
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wsptr += DCTSIZE; /* advance pointer to next row */
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tmp0 = ((JPEG_INT32) wsptr[0]) << (CONST_BITS+1);
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tmp2 = MULTIPLY((JPEG_INT32) wsptr[2], FIX_1_847759065)
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+ MULTIPLY((JPEG_INT32) wsptr[6], - FIX_0_765366865);
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z1 = (JPEG_INT32) wsptr[7];
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z2 = (JPEG_INT32) wsptr[5];
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z3 = (JPEG_INT32) wsptr[3];
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z4 = (JPEG_INT32) wsptr[1];
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tmp0 = MULTIPLY(z1, - FIX_0_211164243) /* sqrt(2) * (c3-c1) */
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+ MULTIPLY(z2, FIX_1_451774981) /* sqrt(2) * (c3+c7) */
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+ MULTIPLY(z3, - FIX_2_172734803) /* sqrt(2) * (-c1-c5) */
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+ MULTIPLY(z4, FIX_1_061594337); /* sqrt(2) * (c5+c7) */
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tmp2 = MULTIPLY(z1, - FIX_0_509795579) /* sqrt(2) * (c7-c5) */
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+ MULTIPLY(z2, - FIX_0_601344887) /* sqrt(2) * (c5-c1) */
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+ MULTIPLY(z3, FIX_0_899976223) /* sqrt(2) * (c3-c7) */
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+ MULTIPLY(z4, FIX_2_562915447); /* sqrt(2) * (c1+c3) */
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/* Final output stage */
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outptr[0] = range_limit[(int) DESCALE(tmp10 + tmp2,
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CONST_BITS+PASS1_BITS+3+1)
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outptr[3] = range_limit[(int) DESCALE(tmp10 - tmp2,
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CONST_BITS+PASS1_BITS+3+1)
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outptr[1] = range_limit[(int) DESCALE(tmp12 + tmp0,
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CONST_BITS+PASS1_BITS+3+1)
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outptr[2] = range_limit[(int) DESCALE(tmp12 - tmp0,
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CONST_BITS+PASS1_BITS+3+1)
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wsptr += DCTSIZE; /* advance pointer to next row */
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* Perform dequantization and inverse DCT on one block of coefficients,
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* producing a reduced-size 2x2 output block.
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jpeg_idct_2x2 (j_decompress_ptr cinfo, jpeg_component_info * compptr,
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JSAMPARRAY output_buf, JDIMENSION output_col)
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JPEG_INT32 tmp0, tmp10, z1;
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ISLOW_MULT_TYPE * quantptr;
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JSAMPLE *range_limit = IDCT_range_limit(cinfo);
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int workspace[DCTSIZE*2]; /* buffers data between passes */
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/* Pass 1: process columns from input, store into work array. */
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quantptr = (ISLOW_MULT_TYPE *) compptr->dct_table;
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for (ctr = DCTSIZE; ctr > 0; inptr++, quantptr++, wsptr++, ctr--) {
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/* Don't bother to process columns 2,4,6 */
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if (ctr == DCTSIZE-2 || ctr == DCTSIZE-4 || ctr == DCTSIZE-6)
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if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*3] == 0 &&
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inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*7] == 0) {
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/* AC terms all zero; we need not examine terms 2,4,6 for 2x2 output */
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int dcval = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]) << PASS1_BITS;
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wsptr[DCTSIZE*0] = dcval;
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wsptr[DCTSIZE*1] = dcval;
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z1 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
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tmp10 = z1 << (CONST_BITS+2);
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z1 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
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tmp0 = MULTIPLY(z1, - FIX_0_720959822); /* sqrt(2) * (c7-c5+c3-c1) */
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z1 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
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tmp0 += MULTIPLY(z1, FIX_0_850430095); /* sqrt(2) * (-c1+c3+c5+c7) */
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z1 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
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tmp0 += MULTIPLY(z1, - FIX_1_272758580); /* sqrt(2) * (-c1+c3-c5-c7) */
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z1 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);
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tmp0 += MULTIPLY(z1, FIX_3_624509785); /* sqrt(2) * (c1+c3+c5+c7) */
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/* Final output stage */
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wsptr[DCTSIZE*0] = (int) DESCALE(tmp10 + tmp0, CONST_BITS-PASS1_BITS+2);
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wsptr[DCTSIZE*1] = (int) DESCALE(tmp10 - tmp0, CONST_BITS-PASS1_BITS+2);
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/* Pass 2: process 2 rows from work array, store into output array. */
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for (ctr = 0; ctr < 2; ctr++) {
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outptr = output_buf[ctr] + output_col;
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/* It's not clear whether a zero row test is worthwhile here ... */
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#ifndef NO_ZERO_ROW_TEST
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if (wsptr[1] == 0 && wsptr[3] == 0 && wsptr[5] == 0 && wsptr[7] == 0) {
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/* AC terms all zero */
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JSAMPLE dcval = range_limit[(int) DESCALE((JPEG_INT32) wsptr[0], PASS1_BITS+3)
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wsptr += DCTSIZE; /* advance pointer to next row */
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tmp10 = ((JPEG_INT32) wsptr[0]) << (CONST_BITS+2);
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tmp0 = MULTIPLY((JPEG_INT32) wsptr[7], - FIX_0_720959822) /* sqrt(2) * (c7-c5+c3-c1) */
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+ MULTIPLY((JPEG_INT32) wsptr[5], FIX_0_850430095) /* sqrt(2) * (-c1+c3+c5+c7) */
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+ MULTIPLY((JPEG_INT32) wsptr[3], - FIX_1_272758580) /* sqrt(2) * (-c1+c3-c5-c7) */
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+ MULTIPLY((JPEG_INT32) wsptr[1], FIX_3_624509785); /* sqrt(2) * (c1+c3+c5+c7) */
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/* Final output stage */
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outptr[0] = range_limit[(int) DESCALE(tmp10 + tmp0,
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CONST_BITS+PASS1_BITS+3+2)
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outptr[1] = range_limit[(int) DESCALE(tmp10 - tmp0,
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CONST_BITS+PASS1_BITS+3+2)
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wsptr += DCTSIZE; /* advance pointer to next row */
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* Perform dequantization and inverse DCT on one block of coefficients,
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* producing a reduced-size 1x1 output block.
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jpeg_idct_1x1 (j_decompress_ptr cinfo, jpeg_component_info * compptr,
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JSAMPARRAY output_buf, JDIMENSION output_col)
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ISLOW_MULT_TYPE * quantptr;
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JSAMPLE *range_limit = IDCT_range_limit(cinfo);
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/* We hardly need an inverse DCT routine for this: just take the
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* average pixel value, which is one-eighth of the DC coefficient.
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quantptr = (ISLOW_MULT_TYPE *) compptr->dct_table;
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dcval = DEQUANTIZE(coef_block[0], quantptr[0]);
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dcval = (int) DESCALE((JPEG_INT32) dcval, 3);
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output_buf[0][output_col] = range_limit[dcval & RANGE_MASK];
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#endif /* IDCT_SCALING_SUPPORTED */