michael@0: /* michael@0: * jfdctint.c michael@0: * michael@0: * Copyright (C) 1991-1996, Thomas G. Lane. michael@0: * This file is part of the Independent JPEG Group's software. michael@0: * For conditions of distribution and use, see the accompanying README file. michael@0: * michael@0: * This file contains a slow-but-accurate integer implementation of the michael@0: * forward DCT (Discrete Cosine Transform). michael@0: * michael@0: * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT michael@0: * on each column. Direct algorithms are also available, but they are michael@0: * much more complex and seem not to be any faster when reduced to code. michael@0: * michael@0: * This implementation is based on an algorithm described in michael@0: * C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT michael@0: * Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics, michael@0: * Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991. michael@0: * The primary algorithm described there uses 11 multiplies and 29 adds. michael@0: * We use their alternate method with 12 multiplies and 32 adds. michael@0: * The advantage of this method is that no data path contains more than one michael@0: * multiplication; this allows a very simple and accurate implementation in michael@0: * scaled fixed-point arithmetic, with a minimal number of shifts. michael@0: */ michael@0: michael@0: #define JPEG_INTERNALS michael@0: #include "jinclude.h" michael@0: #include "jpeglib.h" michael@0: #include "jdct.h" /* Private declarations for DCT subsystem */ michael@0: michael@0: #ifdef DCT_ISLOW_SUPPORTED michael@0: michael@0: michael@0: /* michael@0: * This module is specialized to the case DCTSIZE = 8. michael@0: */ michael@0: michael@0: #if DCTSIZE != 8 michael@0: Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */ michael@0: #endif michael@0: michael@0: michael@0: /* michael@0: * The poop on this scaling stuff is as follows: michael@0: * michael@0: * Each 1-D DCT step produces outputs which are a factor of sqrt(N) michael@0: * larger than the true DCT outputs. The final outputs are therefore michael@0: * a factor of N larger than desired; since N=8 this can be cured by michael@0: * a simple right shift at the end of the algorithm. The advantage of michael@0: * this arrangement is that we save two multiplications per 1-D DCT, michael@0: * because the y0 and y4 outputs need not be divided by sqrt(N). michael@0: * In the IJG code, this factor of 8 is removed by the quantization step michael@0: * (in jcdctmgr.c), NOT in this module. michael@0: * michael@0: * We have to do addition and subtraction of the integer inputs, which michael@0: * is no problem, and multiplication by fractional constants, which is michael@0: * a problem to do in integer arithmetic. We multiply all the constants michael@0: * by CONST_SCALE and convert them to integer constants (thus retaining michael@0: * CONST_BITS bits of precision in the constants). After doing a michael@0: * multiplication we have to divide the product by CONST_SCALE, with proper michael@0: * rounding, to produce the correct output. This division can be done michael@0: * cheaply as a right shift of CONST_BITS bits. We postpone shifting michael@0: * as long as possible so that partial sums can be added together with michael@0: * full fractional precision. michael@0: * michael@0: * The outputs of the first pass are scaled up by PASS1_BITS bits so that michael@0: * they are represented to better-than-integral precision. These outputs michael@0: * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word michael@0: * with the recommended scaling. (For 12-bit sample data, the intermediate michael@0: * array is INT32 anyway.) michael@0: * michael@0: * To avoid overflow of the 32-bit intermediate results in pass 2, we must michael@0: * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26. Error analysis michael@0: * shows that the values given below are the most effective. michael@0: */ michael@0: michael@0: #if BITS_IN_JSAMPLE == 8 michael@0: #define CONST_BITS 13 michael@0: #define PASS1_BITS 2 michael@0: #else michael@0: #define CONST_BITS 13 michael@0: #define PASS1_BITS 1 /* lose a little precision to avoid overflow */ michael@0: #endif michael@0: michael@0: /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus michael@0: * causing a lot of useless floating-point operations at run time. michael@0: * To get around this we use the following pre-calculated constants. michael@0: * If you change CONST_BITS you may want to add appropriate values. michael@0: * (With a reasonable C compiler, you can just rely on the FIX() macro...) michael@0: */ michael@0: michael@0: #if CONST_BITS == 13 michael@0: #define FIX_0_298631336 ((INT32) 2446) /* FIX(0.298631336) */ michael@0: #define FIX_0_390180644 ((INT32) 3196) /* FIX(0.390180644) */ michael@0: #define FIX_0_541196100 ((INT32) 4433) /* FIX(0.541196100) */ michael@0: #define FIX_0_765366865 ((INT32) 6270) /* FIX(0.765366865) */ michael@0: #define FIX_0_899976223 ((INT32) 7373) /* FIX(0.899976223) */ michael@0: #define FIX_1_175875602 ((INT32) 9633) /* FIX(1.175875602) */ michael@0: #define FIX_1_501321110 ((INT32) 12299) /* FIX(1.501321110) */ michael@0: #define FIX_1_847759065 ((INT32) 15137) /* FIX(1.847759065) */ michael@0: #define FIX_1_961570560 ((INT32) 16069) /* FIX(1.961570560) */ michael@0: #define FIX_2_053119869 ((INT32) 16819) /* FIX(2.053119869) */ michael@0: #define FIX_2_562915447 ((INT32) 20995) /* FIX(2.562915447) */ michael@0: #define FIX_3_072711026 ((INT32) 25172) /* FIX(3.072711026) */ michael@0: #else michael@0: #define FIX_0_298631336 FIX(0.298631336) michael@0: #define FIX_0_390180644 FIX(0.390180644) michael@0: #define FIX_0_541196100 FIX(0.541196100) michael@0: #define FIX_0_765366865 FIX(0.765366865) michael@0: #define FIX_0_899976223 FIX(0.899976223) michael@0: #define FIX_1_175875602 FIX(1.175875602) michael@0: #define FIX_1_501321110 FIX(1.501321110) michael@0: #define FIX_1_847759065 FIX(1.847759065) michael@0: #define FIX_1_961570560 FIX(1.961570560) michael@0: #define FIX_2_053119869 FIX(2.053119869) michael@0: #define FIX_2_562915447 FIX(2.562915447) michael@0: #define FIX_3_072711026 FIX(3.072711026) michael@0: #endif michael@0: michael@0: michael@0: /* Multiply an INT32 variable by an INT32 constant to yield an INT32 result. michael@0: * For 8-bit samples with the recommended scaling, all the variable michael@0: * and constant values involved are no more than 16 bits wide, so a michael@0: * 16x16->32 bit multiply can be used instead of a full 32x32 multiply. michael@0: * For 12-bit samples, a full 32-bit multiplication will be needed. michael@0: */ michael@0: michael@0: #if BITS_IN_JSAMPLE == 8 michael@0: #define MULTIPLY(var,const) MULTIPLY16C16(var,const) michael@0: #else michael@0: #define MULTIPLY(var,const) ((var) * (const)) michael@0: #endif michael@0: michael@0: michael@0: /* michael@0: * Perform the forward DCT on one block of samples. michael@0: */ michael@0: michael@0: GLOBAL(void) michael@0: jpeg_fdct_islow (DCTELEM * data) michael@0: { michael@0: INT32 tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; michael@0: INT32 tmp10, tmp11, tmp12, tmp13; michael@0: INT32 z1, z2, z3, z4, z5; michael@0: DCTELEM *dataptr; michael@0: int ctr; michael@0: SHIFT_TEMPS michael@0: michael@0: /* Pass 1: process rows. */ michael@0: /* Note results are scaled up by sqrt(8) compared to a true DCT; */ michael@0: /* furthermore, we scale the results by 2**PASS1_BITS. */ michael@0: michael@0: dataptr = data; michael@0: for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { michael@0: tmp0 = dataptr[0] + dataptr[7]; michael@0: tmp7 = dataptr[0] - dataptr[7]; michael@0: tmp1 = dataptr[1] + dataptr[6]; michael@0: tmp6 = dataptr[1] - dataptr[6]; michael@0: tmp2 = dataptr[2] + dataptr[5]; michael@0: tmp5 = dataptr[2] - dataptr[5]; michael@0: tmp3 = dataptr[3] + dataptr[4]; michael@0: tmp4 = dataptr[3] - dataptr[4]; michael@0: michael@0: /* Even part per LL&M figure 1 --- note that published figure is faulty; michael@0: * rotator "sqrt(2)*c1" should be "sqrt(2)*c6". michael@0: */ michael@0: michael@0: tmp10 = tmp0 + tmp3; michael@0: tmp13 = tmp0 - tmp3; michael@0: tmp11 = tmp1 + tmp2; michael@0: tmp12 = tmp1 - tmp2; michael@0: michael@0: dataptr[0] = (DCTELEM) ((tmp10 + tmp11) << PASS1_BITS); michael@0: dataptr[4] = (DCTELEM) ((tmp10 - tmp11) << PASS1_BITS); michael@0: michael@0: z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); michael@0: dataptr[2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865), michael@0: CONST_BITS-PASS1_BITS); michael@0: dataptr[6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065), michael@0: CONST_BITS-PASS1_BITS); michael@0: michael@0: /* Odd part per figure 8 --- note paper omits factor of sqrt(2). michael@0: * cK represents cos(K*pi/16). michael@0: * i0..i3 in the paper are tmp4..tmp7 here. michael@0: */ michael@0: michael@0: z1 = tmp4 + tmp7; michael@0: z2 = tmp5 + tmp6; michael@0: z3 = tmp4 + tmp6; michael@0: z4 = tmp5 + tmp7; michael@0: z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */ michael@0: michael@0: tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */ michael@0: tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */ michael@0: tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */ michael@0: tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */ michael@0: z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */ michael@0: z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */ michael@0: z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */ michael@0: z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */ michael@0: michael@0: z3 += z5; michael@0: z4 += z5; michael@0: michael@0: dataptr[7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS); michael@0: dataptr[5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS); michael@0: dataptr[3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS); michael@0: dataptr[1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS); michael@0: michael@0: dataptr += DCTSIZE; /* advance pointer to next row */ michael@0: } michael@0: michael@0: /* Pass 2: process columns. michael@0: * We remove the PASS1_BITS scaling, but leave the results scaled up michael@0: * by an overall factor of 8. michael@0: */ michael@0: michael@0: dataptr = data; michael@0: for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { michael@0: tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7]; michael@0: tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7]; michael@0: tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6]; michael@0: tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6]; michael@0: tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5]; michael@0: tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5]; michael@0: tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4]; michael@0: tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4]; michael@0: michael@0: /* Even part per LL&M figure 1 --- note that published figure is faulty; michael@0: * rotator "sqrt(2)*c1" should be "sqrt(2)*c6". michael@0: */ michael@0: michael@0: tmp10 = tmp0 + tmp3; michael@0: tmp13 = tmp0 - tmp3; michael@0: tmp11 = tmp1 + tmp2; michael@0: tmp12 = tmp1 - tmp2; michael@0: michael@0: dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS); michael@0: dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS); michael@0: michael@0: z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); michael@0: dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865), michael@0: CONST_BITS+PASS1_BITS); michael@0: dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065), michael@0: CONST_BITS+PASS1_BITS); michael@0: michael@0: /* Odd part per figure 8 --- note paper omits factor of sqrt(2). michael@0: * cK represents cos(K*pi/16). michael@0: * i0..i3 in the paper are tmp4..tmp7 here. michael@0: */ michael@0: michael@0: z1 = tmp4 + tmp7; michael@0: z2 = tmp5 + tmp6; michael@0: z3 = tmp4 + tmp6; michael@0: z4 = tmp5 + tmp7; michael@0: z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */ michael@0: michael@0: tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */ michael@0: tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */ michael@0: tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */ michael@0: tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */ michael@0: z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */ michael@0: z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */ michael@0: z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */ michael@0: z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */ michael@0: michael@0: z3 += z5; michael@0: z4 += z5; michael@0: michael@0: dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, michael@0: CONST_BITS+PASS1_BITS); michael@0: dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, michael@0: CONST_BITS+PASS1_BITS); michael@0: dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, michael@0: CONST_BITS+PASS1_BITS); michael@0: dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, michael@0: CONST_BITS+PASS1_BITS); michael@0: michael@0: dataptr++; /* advance pointer to next column */ michael@0: } michael@0: } michael@0: michael@0: #endif /* DCT_ISLOW_SUPPORTED */