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

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