jdct.h

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/*
 * jdct.h
 *
 * Copyright (C) 1994-1996, Thomas G. Lane.
 * Modified 2002-2025 by Guido Vollbeding.
 * This file is part of the Independent JPEG Group's software.
 * For conditions of distribution and use, see the accompanying README file.
 *
 * This include file contains common declarations for the forward and
 * inverse DCT modules.  These declarations are private to the DCT managers
 * (jcdctmgr.c, jddctmgr.c) and the individual DCT algorithms.
 * The individual DCT algorithms are kept in separate files to ease 
 * machine-dependent tuning (e.g., assembly coding).
 */
 
 
/*
 * A forward DCT routine is given a pointer to an input sample array and
 * a pointer to a work area of type DCTELEM[]; the DCT is to be performed
 * in-place in that buffer.  Type DCTELEM is int or INT32, depending on
 * bit depth parameters.  (NOTE: Floating-point DCT implementations use
 * an array of type FAST_FLOAT, instead.)
 * The input data is to be fetched from the sample array starting at a
 * specified column.  (Any row offset needed will be applied to the array
 * pointer before it is passed to the FDCT code.)
 * Note that the number of samples fetched by the FDCT routine is
 * DCT_h_scaled_size * DCT_v_scaled_size.
 * The DCT outputs are returned scaled up by a factor of 8; they therefore
 * have a range of +-8K for 8-bit data, +-128K for 12-bit data.  This
 * convention improves accuracy in integer implementations and saves some
 * work in floating-point ones.
 * Quantization of the output coefficients is done by jcdctmgr.c.
 */
 
/* Condition for FDCT:
 *   BITS_IN_JSAMPLE <= 10 && JPEG_DATA_PRECISION <= 10
 * Condition for int IDCT where DCTELEM is used (2x2, 1x1, 2x1, 1x2):
 *   JPEG_DATA_PRECISION + RANGE_BITS <= 12
 *     [BITS_IN_JSAMPLE - 1 + RANGE_BITS +
 *       3 - (BITS_IN_JSAMPLE - JPEG_DATA_PRECISION) <= 14]
 *     {3 - (BITS_IN_JSAMPLE - JPEG_DATA_PRECISION) = PASS2_BITS - PASS1_BITS}
 * Condition for fast IDCT where DCTELEM is used:
 *   JPEG_DATA_PRECISION <= 10 && BITS_IN_JSAMPLE <= 13 && RANGE_BITS <= 2
 *     [BITS_IN_JSAMPLE - 1 + RANGE_BITS + PASS2BITS <= 14]
 * Combined for all:
 */
 
#if BITS_IN_JSAMPLE <= 10 && JPEG_DATA_PRECISION <= 10 && RANGE_BITS <= 2
typedef int DCTELEM;        /* 16 or 32 bits is fine */
#else
typedef INT32 DCTELEM;      /* must have 32 bits */
#endif
 
typedef JMETHOD(void, forward_DCT_method_ptr, (DCTELEM * data,
                           JSAMPARRAY sample_data,
                           JDIMENSION start_col));
typedef JMETHOD(void, float_DCT_method_ptr, (FAST_FLOAT * data,
                         JSAMPARRAY sample_data,
                         JDIMENSION start_col));
 
 
/*
 * An inverse DCT routine is given a pointer to the input JBLOCK and a pointer
 * to an output sample array.  The routine must dequantize the input data as
 * well as perform the IDCT; for dequantization, it uses the multiplier table
 * pointed to by compptr->dct_table.  The output data is to be placed into the
 * sample array starting at a specified column.  (Any row offset needed will
 * be applied to the array pointer before it is passed to the IDCT code.)
 * Note that the number of samples emitted by the IDCT routine is
 * DCT_h_scaled_size * DCT_v_scaled_size.
 */
 
/* typedef inverse_DCT_method_ptr is declared in jpegint.h */
 
/*
 * Each IDCT routine has its own ideas about the best dct_table element type.
 */
 
typedef MULTIPLIER ISLOW_MULT_TYPE; /* short or int, whichever is faster */
#if JPEG_DATA_PRECISION <= 10 && BITS_IN_JSAMPLE <= 13
typedef MULTIPLIER IFAST_MULT_TYPE; /* 16 bits is OK, use short if faster */
#define IFAST_SCALE_BITS  (10 - JPEG_DATA_PRECISION)
                /* fractional bits in scale factors */
#else
typedef INT32 IFAST_MULT_TYPE;  /* need 32 bits for scaled quantizers */
#define IFAST_SCALE_BITS  13    /* fractional bits in scale factors */
#endif
typedef FAST_FLOAT FLOAT_MULT_TYPE; /* preferred floating type */
 
 
/*
 * Each IDCT routine is responsible for range-limiting its results and
 * converting them to unsigned form (0..MAXJSAMPLE).  The raw outputs could
 * be quite far out of range if the input data is corrupt, so a bulletproof
 * range-limiting step is required.  We use a mask-and-table-lookup method
 * to do the combined operations quickly, assuming that RANGE_CENTER
 * (defined in jpegint.h) is a power of 2.  See the comments with
 * prepare_range_limit_table (in jdmaster.c) for more info.
 */
 
#define RANGE_MASK  (RANGE_CENTER * 2 - 1)
#define RANGE_SUBSET  (RANGE_CENTER - CENTERJSAMPLE)
 
#define IDCT_range_limit(cinfo)  ((cinfo)->sample_range_limit - RANGE_SUBSET)
 
 
/* Short forms of external names for systems with brain-damaged linkers. */
 
#ifdef NEED_SHORT_EXTERNAL_NAMES
#define jpeg_fdct_islow     jFDislow
#define jpeg_fdct_ifast     jFDifast
#define jpeg_fdct_float     jFDfloat
#define jpeg_fdct_7x7       jFD7x7
#define jpeg_fdct_6x6       jFD6x6
#define jpeg_fdct_5x5       jFD5x5
#define jpeg_fdct_4x4       jFD4x4
#define jpeg_fdct_3x3       jFD3x3
#define jpeg_fdct_2x2       jFD2x2
#define jpeg_fdct_1x1       jFD1x1
#define jpeg_fdct_9x9       jFD9x9
#define jpeg_fdct_10x10     jFD10x10
#define jpeg_fdct_11x11     jFD11x11
#define jpeg_fdct_12x12     jFD12x12
#define jpeg_fdct_13x13     jFD13x13
#define jpeg_fdct_14x14     jFD14x14
#define jpeg_fdct_15x15     jFD15x15
#define jpeg_fdct_16x16     jFD16x16
#define jpeg_fdct_16x8      jFD16x8
#define jpeg_fdct_14x7      jFD14x7
#define jpeg_fdct_12x6      jFD12x6
#define jpeg_fdct_10x5      jFD10x5
#define jpeg_fdct_8x4       jFD8x4
#define jpeg_fdct_6x3       jFD6x3
#define jpeg_fdct_4x2       jFD4x2
#define jpeg_fdct_2x1       jFD2x1
#define jpeg_fdct_8x16      jFD8x16
#define jpeg_fdct_7x14      jFD7x14
#define jpeg_fdct_6x12      jFD6x12
#define jpeg_fdct_5x10      jFD5x10
#define jpeg_fdct_4x8       jFD4x8
#define jpeg_fdct_3x6       jFD3x6
#define jpeg_fdct_2x4       jFD2x4
#define jpeg_fdct_1x2       jFD1x2
#define jpeg_idct_islow     jRDislow
#define jpeg_idct_ifast     jRDifast
#define jpeg_idct_float     jRDfloat
#define jpeg_idct_7x7       jRD7x7
#define jpeg_idct_6x6       jRD6x6
#define jpeg_idct_5x5       jRD5x5
#define jpeg_idct_4x4       jRD4x4
#define jpeg_idct_3x3       jRD3x3
#define jpeg_idct_2x2       jRD2x2
#define jpeg_idct_1x1       jRD1x1
#define jpeg_idct_9x9       jRD9x9
#define jpeg_idct_10x10     jRD10x10
#define jpeg_idct_11x11     jRD11x11
#define jpeg_idct_12x12     jRD12x12
#define jpeg_idct_13x13     jRD13x13
#define jpeg_idct_14x14     jRD14x14
#define jpeg_idct_15x15     jRD15x15
#define jpeg_idct_16x16     jRD16x16
#define jpeg_idct_16x8      jRD16x8
#define jpeg_idct_14x7      jRD14x7
#define jpeg_idct_12x6      jRD12x6
#define jpeg_idct_10x5      jRD10x5
#define jpeg_idct_8x4       jRD8x4
#define jpeg_idct_6x3       jRD6x3
#define jpeg_idct_4x2       jRD4x2
#define jpeg_idct_2x1       jRD2x1
#define jpeg_idct_8x16      jRD8x16
#define jpeg_idct_7x14      jRD7x14
#define jpeg_idct_6x12      jRD6x12
#define jpeg_idct_5x10      jRD5x10
#define jpeg_idct_4x8       jRD4x8
#define jpeg_idct_3x6       jRD3x6
#define jpeg_idct_2x4       jRD2x4
#define jpeg_idct_1x2       jRD1x2
#endif /* NEED_SHORT_EXTERNAL_NAMES */
 
/* Extern declarations for the forward and inverse DCT routines. */
 
EXTERN(void) jpeg_fdct_islow
    JPP((DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col));
EXTERN(void) jpeg_fdct_ifast
    JPP((DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col));
EXTERN(void) jpeg_fdct_float
    JPP((FAST_FLOAT * data, JSAMPARRAY sample_data, JDIMENSION start_col));
EXTERN(void) jpeg_fdct_7x7
    JPP((DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col));
EXTERN(void) jpeg_fdct_6x6
    JPP((DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col));
EXTERN(void) jpeg_fdct_5x5
    JPP((DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col));
EXTERN(void) jpeg_fdct_4x4
    JPP((DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col));
EXTERN(void) jpeg_fdct_3x3
    JPP((DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col));
EXTERN(void) jpeg_fdct_2x2
    JPP((DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col));
EXTERN(void) jpeg_fdct_1x1
    JPP((DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col));
EXTERN(void) jpeg_fdct_9x9
    JPP((DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col));
EXTERN(void) jpeg_fdct_10x10
    JPP((DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col));
EXTERN(void) jpeg_fdct_11x11
    JPP((DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col));
EXTERN(void) jpeg_fdct_12x12
    JPP((DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col));
EXTERN(void) jpeg_fdct_13x13
    JPP((DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col));
EXTERN(void) jpeg_fdct_14x14
    JPP((DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col));
EXTERN(void) jpeg_fdct_15x15
    JPP((DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col));
EXTERN(void) jpeg_fdct_16x16
    JPP((DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col));
EXTERN(void) jpeg_fdct_16x8
    JPP((DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col));
EXTERN(void) jpeg_fdct_14x7
    JPP((DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col));
EXTERN(void) jpeg_fdct_12x6
    JPP((DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col));
EXTERN(void) jpeg_fdct_10x5
    JPP((DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col));
EXTERN(void) jpeg_fdct_8x4
    JPP((DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col));
EXTERN(void) jpeg_fdct_6x3
    JPP((DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col));
EXTERN(void) jpeg_fdct_4x2
    JPP((DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col));
EXTERN(void) jpeg_fdct_2x1
    JPP((DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col));
EXTERN(void) jpeg_fdct_8x16
    JPP((DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col));
EXTERN(void) jpeg_fdct_7x14
    JPP((DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col));
EXTERN(void) jpeg_fdct_6x12
    JPP((DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col));
EXTERN(void) jpeg_fdct_5x10
    JPP((DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col));
EXTERN(void) jpeg_fdct_4x8
    JPP((DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col));
EXTERN(void) jpeg_fdct_3x6
    JPP((DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col));
EXTERN(void) jpeg_fdct_2x4
    JPP((DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col));
EXTERN(void) jpeg_fdct_1x2
    JPP((DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col));
 
EXTERN(void) jpeg_idct_islow
    JPP((j_decompress_ptr cinfo, jpeg_component_info * compptr,
     JCOEFPTR coef_block, JSAMPARRAY output_buf, JDIMENSION output_col));
EXTERN(void) jpeg_idct_ifast
    JPP((j_decompress_ptr cinfo, jpeg_component_info * compptr,
     JCOEFPTR coef_block, JSAMPARRAY output_buf, JDIMENSION output_col));
EXTERN(void) jpeg_idct_float
    JPP((j_decompress_ptr cinfo, jpeg_component_info * compptr,
     JCOEFPTR coef_block, JSAMPARRAY output_buf, JDIMENSION output_col));
EXTERN(void) jpeg_idct_7x7
    JPP((j_decompress_ptr cinfo, jpeg_component_info * compptr,
     JCOEFPTR coef_block, JSAMPARRAY output_buf, JDIMENSION output_col));
EXTERN(void) jpeg_idct_6x6
    JPP((j_decompress_ptr cinfo, jpeg_component_info * compptr,
     JCOEFPTR coef_block, JSAMPARRAY output_buf, JDIMENSION output_col));
EXTERN(void) jpeg_idct_5x5
    JPP((j_decompress_ptr cinfo, jpeg_component_info * compptr,
     JCOEFPTR coef_block, JSAMPARRAY output_buf, JDIMENSION output_col));
EXTERN(void) jpeg_idct_4x4
    JPP((j_decompress_ptr cinfo, jpeg_component_info * compptr,
     JCOEFPTR coef_block, JSAMPARRAY output_buf, JDIMENSION output_col));
EXTERN(void) jpeg_idct_3x3
    JPP((j_decompress_ptr cinfo, jpeg_component_info * compptr,
     JCOEFPTR coef_block, JSAMPARRAY output_buf, JDIMENSION output_col));
EXTERN(void) jpeg_idct_2x2
    JPP((j_decompress_ptr cinfo, jpeg_component_info * compptr,
     JCOEFPTR coef_block, JSAMPARRAY output_buf, JDIMENSION output_col));
EXTERN(void) jpeg_idct_1x1
    JPP((j_decompress_ptr cinfo, jpeg_component_info * compptr,
     JCOEFPTR coef_block, JSAMPARRAY output_buf, JDIMENSION output_col));
EXTERN(void) jpeg_idct_9x9
    JPP((j_decompress_ptr cinfo, jpeg_component_info * compptr,
     JCOEFPTR coef_block, JSAMPARRAY output_buf, JDIMENSION output_col));
EXTERN(void) jpeg_idct_10x10
    JPP((j_decompress_ptr cinfo, jpeg_component_info * compptr,
     JCOEFPTR coef_block, JSAMPARRAY output_buf, JDIMENSION output_col));
EXTERN(void) jpeg_idct_11x11
    JPP((j_decompress_ptr cinfo, jpeg_component_info * compptr,
     JCOEFPTR coef_block, JSAMPARRAY output_buf, JDIMENSION output_col));
EXTERN(void) jpeg_idct_12x12
    JPP((j_decompress_ptr cinfo, jpeg_component_info * compptr,
     JCOEFPTR coef_block, JSAMPARRAY output_buf, JDIMENSION output_col));
EXTERN(void) jpeg_idct_13x13
    JPP((j_decompress_ptr cinfo, jpeg_component_info * compptr,
     JCOEFPTR coef_block, JSAMPARRAY output_buf, JDIMENSION output_col));
EXTERN(void) jpeg_idct_14x14
    JPP((j_decompress_ptr cinfo, jpeg_component_info * compptr,
     JCOEFPTR coef_block, JSAMPARRAY output_buf, JDIMENSION output_col));
EXTERN(void) jpeg_idct_15x15
    JPP((j_decompress_ptr cinfo, jpeg_component_info * compptr,
     JCOEFPTR coef_block, JSAMPARRAY output_buf, JDIMENSION output_col));
EXTERN(void) jpeg_idct_16x16
    JPP((j_decompress_ptr cinfo, jpeg_component_info * compptr,
     JCOEFPTR coef_block, JSAMPARRAY output_buf, JDIMENSION output_col));
EXTERN(void) jpeg_idct_16x8
    JPP((j_decompress_ptr cinfo, jpeg_component_info * compptr,
     JCOEFPTR coef_block, JSAMPARRAY output_buf, JDIMENSION output_col));
EXTERN(void) jpeg_idct_14x7
    JPP((j_decompress_ptr cinfo, jpeg_component_info * compptr,
     JCOEFPTR coef_block, JSAMPARRAY output_buf, JDIMENSION output_col));
EXTERN(void) jpeg_idct_12x6
    JPP((j_decompress_ptr cinfo, jpeg_component_info * compptr,
     JCOEFPTR coef_block, JSAMPARRAY output_buf, JDIMENSION output_col));
EXTERN(void) jpeg_idct_10x5
    JPP((j_decompress_ptr cinfo, jpeg_component_info * compptr,
     JCOEFPTR coef_block, JSAMPARRAY output_buf, JDIMENSION output_col));
EXTERN(void) jpeg_idct_8x4
    JPP((j_decompress_ptr cinfo, jpeg_component_info * compptr,
     JCOEFPTR coef_block, JSAMPARRAY output_buf, JDIMENSION output_col));
EXTERN(void) jpeg_idct_6x3
    JPP((j_decompress_ptr cinfo, jpeg_component_info * compptr,
     JCOEFPTR coef_block, JSAMPARRAY output_buf, JDIMENSION output_col));
EXTERN(void) jpeg_idct_4x2
    JPP((j_decompress_ptr cinfo, jpeg_component_info * compptr,
     JCOEFPTR coef_block, JSAMPARRAY output_buf, JDIMENSION output_col));
EXTERN(void) jpeg_idct_2x1
    JPP((j_decompress_ptr cinfo, jpeg_component_info * compptr,
     JCOEFPTR coef_block, JSAMPARRAY output_buf, JDIMENSION output_col));
EXTERN(void) jpeg_idct_8x16
    JPP((j_decompress_ptr cinfo, jpeg_component_info * compptr,
     JCOEFPTR coef_block, JSAMPARRAY output_buf, JDIMENSION output_col));
EXTERN(void) jpeg_idct_7x14
    JPP((j_decompress_ptr cinfo, jpeg_component_info * compptr,
     JCOEFPTR coef_block, JSAMPARRAY output_buf, JDIMENSION output_col));
EXTERN(void) jpeg_idct_6x12
    JPP((j_decompress_ptr cinfo, jpeg_component_info * compptr,
     JCOEFPTR coef_block, JSAMPARRAY output_buf, JDIMENSION output_col));
EXTERN(void) jpeg_idct_5x10
    JPP((j_decompress_ptr cinfo, jpeg_component_info * compptr,
     JCOEFPTR coef_block, JSAMPARRAY output_buf, JDIMENSION output_col));
EXTERN(void) jpeg_idct_4x8
    JPP((j_decompress_ptr cinfo, jpeg_component_info * compptr,
     JCOEFPTR coef_block, JSAMPARRAY output_buf, JDIMENSION output_col));
EXTERN(void) jpeg_idct_3x6
    JPP((j_decompress_ptr cinfo, jpeg_component_info * compptr,
     JCOEFPTR coef_block, JSAMPARRAY output_buf, JDIMENSION output_col));
EXTERN(void) jpeg_idct_2x4
    JPP((j_decompress_ptr cinfo, jpeg_component_info * compptr,
     JCOEFPTR coef_block, JSAMPARRAY output_buf, JDIMENSION output_col));
EXTERN(void) jpeg_idct_1x2
    JPP((j_decompress_ptr cinfo, jpeg_component_info * compptr,
     JCOEFPTR coef_block, JSAMPARRAY output_buf, JDIMENSION output_col));
 
 
/*
 * Macros for handling fixed-point arithmetic; these are used by many
 * but not all of the DCT/IDCT modules.
 *
 * All values are expected to be of type INT32.
 * Fractional constants are scaled left by CONST_BITS bits.
 * CONST_BITS is defined within each module using these macros,
 * and may differ from one module to the next.
 */
 
#define ONE ((INT32) 1)
#define CONST_SCALE (ONE << CONST_BITS)
 
/* 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)  ((INT32) ((x) * CONST_SCALE + 0.5))
 
/* Multiply an INT32 variable by an INT32 constant to yield an INT32 result.
 * This macro is used only when the two inputs will actually be no more than
 * 16 bits wide, so that a 16x16->32 bit multiply can be used instead of a
 * full 32x32 multiply.  This provides a useful speedup on many machines.
 * Unfortunately there is no way to specify a 16x16->32 multiply portably
 * in C, but some C compilers will do the right thing if you provide the
 * correct combination of casts.
 */
 
#ifdef SHORTxSHORT_32       /* may work if 'int' is 32 bits */
#define MULTIPLY16C16(var,const)  (((INT16) (var)) * ((INT16) (const)))
#endif
#ifdef SHORTxLCONST_32      /* known to work with Microsoft C 6.0 */
#define MULTIPLY16C16(var,const)  (((INT16) (var)) * ((INT32) (const)))
#endif
 
#ifndef MULTIPLY16C16       /* default definition */
#define MULTIPLY16C16(var,const)  ((var) * (const))
#endif
 
/* Same except both inputs are variables. */
 
#ifdef SHORTxSHORT_32       /* may work if 'int' is 32 bits */
#define MULTIPLY16V16(var1,var2)  (((INT16) (var1)) * ((INT16) (var2)))
#endif
 
#ifndef MULTIPLY16V16       /* default definition */
#define MULTIPLY16V16(var1,var2)  ((var1) * (var2))
#endif
 
/* Like RIGHT_SHIFT, but applies to a DCTELEM.
 * We assume that int right shift is unsigned if INT32 right shift is.
 */
 
#ifdef RIGHT_SHIFT_IS_UNSIGNED
#define ISHIFT_TEMPS    DCTELEM ishift_temp;
#if BITS_IN_JSAMPLE <= 10 && JPEG_DATA_PRECISION <= 10 && RANGE_BITS <= 2
#define DCTELEMBITS  16     /* DCTELEM may be 16 or 32 bits */
#else
#define DCTELEMBITS  32     /* DCTELEM must be 32 bits */
#endif
#define IRIGHT_SHIFT(x,shft)  \
    ((ishift_temp = (x)) < 0 ? \
     (ishift_temp >> (shft)) | ((~((DCTELEM) 0)) << (DCTELEMBITS-(shft))) : \
     (ishift_temp >> (shft)))
#else
#define ISHIFT_TEMPS
#define IRIGHT_SHIFT(x,shft)    ((x) >> (shft))
#endif