The Independent JPEG Group's JPEG software v1
diff --git a/jfwddct.c b/jfwddct.c
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+/*
+ * jfwddct.c
+ *
+ * Copyright (C) 1991, 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 Appendix A.2 of the book
+ * "Discrete Cosine Transform---Algorithms, Advantages, Applications"
+ * by K.R. Rao and P. Yip (Academic Press, Inc, London, 1990).
+ * It uses scaled fixed-point arithmetic instead of floating point.
+ */
+
+#include "jinclude.h"
+
+
+/* The poop on this scaling stuff is as follows:
+ *
+ * Most of the numbers (after multiplication by the constants) are
+ * (logically) shifted left by LG2_DCT_SCALE. This is undone by UNFIXH
+ * before assignment to the output array. Note that we want an additional
+ * division by 2 on the output (required by the equations).
+ *
+ * If right shifts are unsigned, then there is a potential problem.
+ * However, shifting right by 16 and then assigning to a short
+ * (assuming short = 16 bits) will keep the sign right!!
+ *
+ * For other shifts,
+ *
+ * ((x + (1 << 30)) >> shft) - (1 << (30 - shft))
+ *
+ * gives a nice right shift with sign (assuming no overflow). However, all the
+ * scaling is such that this isn't a problem. (Is this true?)
+ */
+
+
+#define ONE 1L /* remove L if long > 32 bits */
+
+#ifdef RIGHT_SHIFT_IS_UNSIGNED
+#define LG2_DCT_SCALE 15
+#define RIGHT_SHIFT(_x,_shft) ((((_x) + (ONE << 30)) >> (_shft)) - (ONE << (30 - (_shft))))
+#else
+#define LG2_DCT_SCALE 16
+#define RIGHT_SHIFT(_x,_shft) ((_x) >> (_shft))
+#endif
+
+#define DCT_SCALE (ONE << LG2_DCT_SCALE)
+
+#define LG2_OVERSCALE 2
+#define OVERSCALE (ONE << LG2_OVERSCALE)
+
+#define FIX(x) ((INT32) ((x) * DCT_SCALE + 0.5))
+#define FIXO(x) ((INT32) ((x) * DCT_SCALE / OVERSCALE + 0.5))
+#define UNFIX(x) RIGHT_SHIFT((x) + (ONE << (LG2_DCT_SCALE-1)), LG2_DCT_SCALE)
+#define UNFIXH(x) RIGHT_SHIFT((x) + (ONE << LG2_DCT_SCALE), LG2_DCT_SCALE+1)
+#define UNFIXO(x) RIGHT_SHIFT((x) + (ONE << (LG2_DCT_SCALE-1-LG2_OVERSCALE)), LG2_DCT_SCALE-LG2_OVERSCALE)
+#define OVERSH(x) ((x) << LG2_OVERSCALE)
+
+#define SIN_1_4 FIX(0.7071067811856476)
+#define COS_1_4 SIN_1_4
+
+#define SIN_1_8 FIX(0.3826834323650898)
+#define COS_1_8 FIX(0.9238795325112870)
+#define SIN_3_8 COS_1_8
+#define COS_3_8 SIN_1_8
+
+#define SIN_1_16 FIX(0.1950903220161282)
+#define COS_1_16 FIX(0.9807852804032300)
+#define SIN_7_16 COS_1_16
+#define COS_7_16 SIN_1_16
+
+#define SIN_3_16 FIX(0.5555702330196022)
+#define COS_3_16 FIX(0.8314696123025450)
+#define SIN_5_16 COS_3_16
+#define COS_5_16 SIN_3_16
+
+#define OSIN_1_4 FIXO(0.707106781185647)
+#define OCOS_1_4 OSIN_1_4
+
+#define OSIN_1_8 FIXO(0.3826834323650898)
+#define OCOS_1_8 FIXO(0.9238795325112870)
+#define OSIN_3_8 OCOS_1_8
+#define OCOS_3_8 OSIN_1_8
+
+#define OSIN_1_16 FIXO(0.1950903220161282)
+#define OCOS_1_16 FIXO(0.9807852804032300)
+#define OSIN_7_16 OCOS_1_16
+#define OCOS_7_16 OSIN_1_16
+
+#define OSIN_3_16 FIXO(0.5555702330196022)
+#define OCOS_3_16 FIXO(0.8314696123025450)
+#define OSIN_5_16 OCOS_3_16
+#define OCOS_5_16 OSIN_3_16
+
+
+INLINE
+LOCAL void
+fast_dct_8 (DCTELEM *in, int stride)
+{
+ /* tmp1x are new values of tmpx -- flashy register colourers
+ * should be able to do this lot very well
+ */
+ INT32 tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
+ INT32 tmp10, tmp11, tmp12, tmp13, tmp14, tmp15, tmp16, tmp17;
+ INT32 tmp25, tmp26;
+ INT32 in0, in1, in2, in3, in4, in5, in6, in7;
+
+ in0 = in[ 0];
+ in1 = in[stride ];
+ in2 = in[stride*2];
+ in3 = in[stride*3];
+ in4 = in[stride*4];
+ in5 = in[stride*5];
+ in6 = in[stride*6];
+ in7 = in[stride*7];
+
+ tmp0 = in7 + in0;
+ tmp1 = in6 + in1;
+ tmp2 = in5 + in2;
+ tmp3 = in4 + in3;
+ tmp4 = in3 - in4;
+ tmp5 = in2 - in5;
+ tmp6 = in1 - in6;
+ tmp7 = in0 - in7;
+
+ tmp10 = tmp3 + tmp0 ;
+ tmp11 = tmp2 + tmp1 ;
+ tmp12 = tmp1 - tmp2 ;
+ tmp13 = tmp0 - tmp3 ;
+
+ /* Now using tmp10, tmp11, tmp12, tmp13 */
+
+ in[ 0] = UNFIXH((tmp10 + tmp11) * SIN_1_4);
+ in[stride*4] = UNFIXH((tmp10 - tmp11) * COS_1_4);
+
+ in[stride*2] = UNFIXH(tmp13*COS_1_8 + tmp12*SIN_1_8);
+ in[stride*6] = UNFIXH(tmp13*SIN_1_8 - tmp12*COS_1_8);
+
+ tmp16 = UNFIXO((tmp6 + tmp5) * SIN_1_4);
+ tmp15 = UNFIXO((tmp6 - tmp5) * COS_1_4);
+
+ /* Now using tmp10, tmp11, tmp13, tmp14, tmp15, tmp16 */
+
+ tmp14 = OVERSH(tmp4) + tmp15;
+ tmp25 = OVERSH(tmp4) - tmp15;
+ tmp26 = OVERSH(tmp7) - tmp16;
+ tmp17 = OVERSH(tmp7) + tmp16;
+
+ /* These are now overscaled by OVERSCALE */
+
+ /* tmp10, tmp11, tmp12, tmp13, tmp14, tmp25, tmp26, tmp17 */
+
+ in[stride ] = UNFIXH(tmp17*OCOS_1_16 + tmp14*OSIN_1_16);
+ in[stride*7] = UNFIXH(tmp17*OCOS_7_16 - tmp14*OSIN_7_16);
+ in[stride*5] = UNFIXH(tmp26*OCOS_5_16 + tmp25*OSIN_5_16);
+ in[stride*3] = UNFIXH(tmp26*OCOS_3_16 - tmp25*OSIN_3_16);
+}
+
+
+/*
+ * Perform the forward DCT on one block of samples.
+ *
+ * Note that this code is specialized to the case DCTSIZE = 8.
+ */
+
+GLOBAL void
+j_fwd_dct (DCTBLOCK data)
+{
+ int i;
+
+ for (i = 0; i < DCTSIZE; i++)
+ fast_dct_8(data+i*DCTSIZE, 1);
+
+ for (i = 0; i < DCTSIZE; i++)
+ fast_dct_8(data+i, DCTSIZE);
+}