JPEG.rar_fft_fft jpeg

/* * jfdctint.c * * Copyright (C) 1991-1996, 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 * forward DCT (Discrete Cosine Transform). * * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT * on each column. 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. */ #include "jpeg.h" /* * The poop on this scaling stuff is as follows: * * Each 1-D DCT step produces outputs which are a factor of sqrt(N) * larger than the true DCT 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 DCT, * because the y0 and y4 outputs need not be divided by sqrt(N). * In the IJG code, this factor of 8 is removed by the quantization step * (in jcdctmgr.c), NOT in this module. * * 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 int 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. (For 12-bit sample data, the intermediate * array is INT32 anyway.) * * 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. */ #define CONST_BITS 13 #define PASS1_BITS 2 /* 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 ((int) 2446) /* FIX(0.298631336) */ #define FIX_0_390180644 ((int) 3196) /* FIX(0.390180644) */ #define FIX_0_541196100 ((int) 4433) /* FIX(0.541196100) */ #define FIX_0_765366865 ((int) 6270) /* FIX(0.765366865) */ #define FIX_0_899976223 ((int) 7373) /* FIX(0.899976223) */ #define FIX_1_175875602 ((int) 9633) /* FIX(1.175875602) */ #define FIX_1_501321110 ((int) 12299) /* FIX(1.501321110) */ #define FIX_1_847759065 ((int) 15137) /* FIX(1.847759065) */ #define FIX_1_961570560 ((int) 16069) /* FIX(1.961570560) */ #define FIX_2_053119869 ((int) 16819) /* FIX(2.053119869) */ #define FIX_2_562915447 ((int) 20995) /* FIX(2.562915447) */ #define FIX_3_072711026 ((int) 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 /* Convert a positive real constant to an integer scaled by CONST_SCALE. * Caution: some C compilers fail to reduce "FIX(constant)" at compile time, * thus causing a lot of useless floating-point operations at run time. */ #define FIX(x) ((int) ((x) * (1 << CONST_BITS) + 0.5)) #define RIGHT_SHIFT(x,shft) ((x) >> (shft)) /* Descale and correctly round an INT32 value that's scaled by N bits. * We assume RIGHT_SHIFT rounds towards minus infinity, so adding * the fudge factor is correct for either sign of X. */ #define DESCALE(x,n) ((short)RIGHT_SHIFT((x) + (1 << ((n)-1)), n)) /* * Perform an integer forward DCT on one block of samples. */ void jpeg_fdct_islow(short * block) { int tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; int tmp10, tmp11, tmp12, tmp13; int z1, z2, z3, z4, z5; short *blkptr; short *dataptr; short data[64]; int i; /* Pass 1: process rows. */ /* Note results are scaled up by sqrt(8) compared to a true DCT; */ /* furthermore, we scale the results by 2**PASS1_BITS. */ dataptr = data; blkptr = block; for (i = 0; i < 8; i++) { tmp0 = blkptr[0] + blkptr[7]; tmp7 = blkptr[0] - blkptr[7]; tmp1 = blkptr[1] + blkptr[6]; tmp6 = blkptr[1] - blkptr[6]; tmp2 = blkptr[2] + blkptr[5]; tmp5 = blkptr[2] - blkptr[5]; tmp3 = blkptr[3] + blkptr[4]; tmp4 = blkptr[3] - blkptr[4]; /* Even part per LL&M figure 1 --- note that published figure is faulty; * rotator "sqrt(2)*c1" should be "sqrt(2)*c6". */ tmp10 = tmp0 + tmp3; tmp13 = tmp0 - tmp3; tmp11 = tmp1 + tmp2; tmp12 = tmp1 - tmp2; dataptr[0] = (tmp10 + tmp11) << PASS1_BITS; dataptr[4] = (tmp10 - tmp11) << PASS1_BITS; z1 = (tmp12 + tmp13) * FIX_0_541196100; dataptr[2] = DESCALE(z1 + tmp13 * FIX_0_765366865, CONST_BITS - PASS1_BITS); dataptr[6] = DESCALE(z1 + tmp12 * (-FIX_1_847759065), CONST_BITS - PASS1_BITS); /* Odd part per figure 8 --- note paper omits factor of sqrt(2). * cK represents cos(K*pi/16). * i0..i3 in the paper are tmp4..tmp7 here. */ z1 = tmp4 + tmp7; z2 = tmp5 + tmp6; z3 = tmp4 + tmp6; z4 = tmp5 + tmp7; z5 = (z3 + z4) * FIX_1_175875602; /* sqrt(2) * c3 */ tmp4 *= FIX_0_298631336; /* sqrt(2) * (-c1+c3+c5-c7) */ tmp5 *= FIX_2_053119869; /* sqrt(2) * ( c1+c3-c5+c7) */ tmp6 *= FIX_3_072711026; /* sqrt(2) * ( c1+c3+c5-c7) */ tmp7 *= FIX_1_501321110; /* sqrt(2) * ( c1+c3-c5-c7) */ z1 *= -FIX_0_899976223; /* sqrt(2) * (c7-c3) */ z2 *= -FIX_2_562915447; /* sqrt(2) * (-c1-c3) */ z3 *= -FIX_1_961570560; /* sqrt(2) * (-c3-c5) */ z4 *= -FIX_0_390180644; /* sqrt(2) * (c5-c3) */ z3 += z5; z4 += z5; dataptr[7] = DESCALE(tmp4 + z1 + z3, CONST_BITS - PASS1_BITS); dataptr[5] = DESCALE(tmp5 + z2 + z4, CONST_BITS - PASS1_BITS); dataptr[3] = DESCALE(tmp6 + z2 + z3, CONST_BITS - PASS1_BITS); dataptr[1] = DESCALE(tmp7 + z1 + z4, CONST_BITS - PASS1_BITS); dataptr += 8; /* advance pointer to next row */ blkptr += 8; } /* Pass 2: process columns. * We remove the PASS1_BITS scaling, but leave the results scaled up * by an overall factor of 8. */ dataptr = data; for (i = 0; i < 8; i++) { tmp0 = dataptr[0] + dataptr[