/* $Xorg: jfwddct.c,v 1.3 2000/08/17 19:47:48 cpqbld Exp $ */ /* Module jfwddct.c */ /**************************************************************************** Copyright 1993, 1994, 1998 The Open Group All Rights Reserved. The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE OPEN GROUP BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. Except as contained in this notice, the name of The Open Group shall not be used in advertising or otherwise to promote the sale, use or other dealings in this Software without prior written authorization from The Open Group. NOTICE This software is being provided by AGE Logic, Inc. under the following license. By obtaining, using and/or copying this software, you agree that you have read, understood, and will comply with these terms and conditions: Permission to use, copy, modify, distribute and sell this software and its documentation for any purpose and without fee or royalty and to grant others any or all rights granted herein is hereby granted, provided that you agree to comply with the following copyright notice and statements, including the disclaimer, and that the same appears on all copies and derivative works of the software and documentation you make. "Copyright 1993, 1994 by AGE Logic, Inc." THIS SOFTWARE IS PROVIDED "AS IS". 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Title to this software shall at all times remain with AGE Logic, Inc. ***************************************************************************** Gary Rogers, AGE Logic, Inc., October 1993 Gary Rogers, AGE Logic, Inc., January 1994 ****************************************************************************/ /* * jfwddct.c * * Copyright (C) 1991, 1992, 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 the basic DCT (Discrete Cosine Transform) * transformation subroutine. * * 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 "jinclude.h" /* * This routine is specialized to the case DCTSIZE = 8. */ #if DCTSIZE != 8 Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */ #endif /* * 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. * * 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). * * 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 long 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. (To scale up 12-bit sample data, an * intermediate INT32 array would be needed.) * * To avoid overflow of the 32-bit intermediate results in pass 2, we must * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 25. Error analysis * shows that the values given below are the most effective. */ #ifdef EIGHT_BIT_SAMPLES #define CONST_BITS 13 #define PASS1_BITS 2 #else #define CONST_BITS 13 #define PASS1_BITS 0 /* lose a little precision to avoid overflow */ #endif #define ONE ((INT32) 1) #define CONST_SCALE (ONE << CONST_BITS) /* Convert a positive real constant to an integer scaled by CONST_SCALE. */ #define FIX(x) ((INT32) ((x) * CONST_SCALE + 0.5)) /* 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 ((INT32) 2446) /* FIX(0.298631336) */ #define FIX_0_390180644 ((INT32) 3196) /* FIX(0.390180644) */ #define FIX_0_541196100 ((INT32) 4433) /* FIX(0.541196100) */ #define FIX_0_765366865 ((INT32) 6270) /* FIX(0.765366865) */ #define FIX_0_899976223 ((INT32) 7373) /* FIX(0.899976223) */ #define FIX_1_175875602 ((INT32) 9633) /* FIX(1.175875602) */ #define FIX_1_501321110 ((INT32) 12299) /* FIX(1.501321110) */ #define FIX_1_847759065 ((INT32) 15137) /* FIX(1.847759065) */ #define FIX_1_961570560 ((INT32) 16069) /* FIX(1.961570560) */ #define FIX_2_053119869 ((INT32) 16819) /* FIX(2.053119869) */ #define FIX_2_562915447 ((INT32) 20995) /* FIX(2.562915447) */ #define FIX_3_072711026 ((INT32) 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 /* 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) RIGHT_SHIFT((x) + (ONE << ((n)-1)), n) /* Multiply an INT32 variable by an INT32 constant to yield an INT32 result. * For 8-bit samples with the recommended scaling, all the variable * and constant values involved are no more than 16 bits wide, so a * 16x16->32 bit multiply can be used instead of a full 32x32 multiply; * this provides a useful speedup on many machines. * There is no way to specify a 16x16->32 multiply in portable C, but * some C compilers will do the right thing if you provide the correct * combination of casts. * NB: for 12-bit samples, a full 32-bit multiplication will be needed. */ #ifdef EIGHT_BIT_SAMPLES #ifdef SHORTxSHORT_32 /* may work if 'int' is 32 bits */ #define MULTIPLY(var,const) (((INT16) (var)) * ((INT16) (const))) #endif #ifdef SHORTxLCONST_32 /* known to work with Microsoft C 6.0 */ #define MULTIPLY(var,const) (((INT16) (var)) * ((INT32) (const))) #endif #endif #ifndef MULTIPLY /* default definition */ #define MULTIPLY(var,const) ((var) * (const)) #endif /* * Perform the forward DCT on one block of samples. */ GLOBAL void #ifdef XIE_SUPPORTED #if NeedFunctionPrototypes j_fwd_dct (DCTBLOCK data) #else j_fwd_dct (data) DCTBLOCK data; #endif /* NeedFunctionPrototypes */ #else j_fwd_dct (DCTBLOCK data) #endif /* XIE_SUPPORTED */ { INT32 tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; INT32 tmp10, tmp11, tmp12, tmp13; INT32 z1, z2, z3, z4, z5; register DCTELEM *dataptr; int rowctr; SHIFT_TEMPS /* 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; for (rowctr = DCTSIZE-1; rowctr >= 0; rowctr--) { 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 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] = (DCTELEM) ((tmp10 + tmp11) << PASS1_BITS); dataptr[4] = (DCTELEM) ((tmp10 - tmp11) << PASS1_BITS); z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); dataptr[2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865), CONST_BITS-PASS1_BITS); dataptr[6] = (DCTELEM) DESCALE(z1 + MULTIPLY(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 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */ tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */ tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */ tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */ tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */ z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */ z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */ z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */ z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */ z3 += z5; z4 += z5; dataptr[7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS); dataptr[5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS); dataptr[3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS); dataptr[1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS); dataptr += DCTSIZE; /* advance pointer to next row */ } /* Pass 2: process columns. */ /* Note that we must descale the results by a factor of 8 == 2**3, */ /* and also undo the PASS1_BITS scaling. */ dataptr = data; for (rowctr = DCTSIZE-1; rowctr >= 0; rowctr--) { 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 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[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS+3); dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS+3); z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865), CONST_BITS+PASS1_BITS+3); dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065), CONST_BITS+PASS1_BITS+3); /* 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 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */ tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */ tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */ tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */ tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */ z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */ z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */ z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */ z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */ z3 += z5; z4 += z5; dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS+PASS1_BITS+3); dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS+PASS1_BITS+3); dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS+PASS1_BITS+3); dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITS+PASS1_BITS+3); dataptr++; /* advance pointer to next column */ } }