FreeBSD/Linux Kernel Cross Reference
sys/lib/libkern/softfloat-macros.h

     /* $NetBSD: softfloat-macros.h,v 1.1 2001/04/26 03:10:47 ross Exp $ */
     
     /*
     ===============================================================================
     
     This C source fragment is part of the SoftFloat IEC/IEEE Floating-point
     Arithmetic Package, Release 2a.
     
     Written by John R. Hauser.  This work was made possible in part by the
    International Computer Science Institute, located at Suite 600, 1947 Center
    Street, Berkeley, California 94704.  Funding was partially provided by the
    National Science Foundation under grant MIP-9311980.  The original version
    of this code was written as part of a project to build a fixed-point vector
    processor in collaboration with the University of California at Berkeley,
    overseen by Profs. Nelson Morgan and John Wawrzynek.  More information
    is available through the Web page `http://HTTP.CS.Berkeley.EDU/~jhauser/
    arithmetic/SoftFloat.html'.
    
    THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE.  Although reasonable effort
    has been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT
    TIMES RESULT IN INCORRECT BEHAVIOR.  USE OF THIS SOFTWARE IS RESTRICTED TO
    PERSONS AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ANY
    AND ALL LOSSES, COSTS, OR OTHER PROBLEMS ARISING FROM ITS USE.
    
    Derivative works are acceptable, even for commercial purposes, so long as
    (1) they include prominent notice that the work is derivative, and (2) they
    include prominent notice akin to these four paragraphs for those parts of
    this code that are retained.
    
    ===============================================================================
    */
    
    /*
    -------------------------------------------------------------------------------
    Shifts `a' right by the number of bits given in `count'.  If any nonzero
    bits are shifted off, they are ``jammed'' into the least significant bit of
    the result by setting the least significant bit to 1.  The value of `count'
    can be arbitrarily large; in particular, if `count' is greater than 32, the
    result will be either 0 or 1, depending on whether `a' is zero or nonzero.
    The result is stored in the location pointed to by `zPtr'.
    -------------------------------------------------------------------------------
    */
    INLINE void shift32RightJamming( bits32 a, int16 count, bits32 *zPtr )
    {
        bits32 z;
    
        if ( count == 0 ) {
            z = a;
        }
        else if ( count < 32 ) {
            z = ( a>>count ) | ( ( a<<( ( - count ) & 31 ) ) != 0 );
        }
        else {
            z = ( a != 0 );
        }
        *zPtr = z;
    
    }
    
    /*
    -------------------------------------------------------------------------------
    Shifts `a' right by the number of bits given in `count'.  If any nonzero
    bits are shifted off, they are ``jammed'' into the least significant bit of
    the result by setting the least significant bit to 1.  The value of `count'
    can be arbitrarily large; in particular, if `count' is greater than 64, the
    result will be either 0 or 1, depending on whether `a' is zero or nonzero.
    The result is stored in the location pointed to by `zPtr'.
    -------------------------------------------------------------------------------
    */
    INLINE void shift64RightJamming( bits64 a, int16 count, bits64 *zPtr )
    {
        bits64 z;
    
        if ( count == 0 ) {
            z = a;
        }
        else if ( count < 64 ) {
            z = ( a>>count ) | ( ( a<<( ( - count ) & 63 ) ) != 0 );
        }
        else {
            z = ( a != 0 );
        }
        *zPtr = z;
    
    }
    
    /*
    -------------------------------------------------------------------------------
    Shifts the 128-bit value formed by concatenating `a0' and `a1' right by 64
    _plus_ the number of bits given in `count'.  The shifted result is at most
    64 nonzero bits; this is stored at the location pointed to by `z0Ptr'.  The
    bits shifted off form a second 64-bit result as follows:  The _last_ bit
    shifted off is the most-significant bit of the extra result, and the other
    63 bits of the extra result are all zero if and only if _all_but_the_last_
    bits shifted off were all zero.  This extra result is stored in the location
    pointed to by `z1Ptr'.  The value of `count' can be arbitrarily large.
        (This routine makes more sense if `a0' and `a1' are considered to form a
    fixed-point value with binary point between `a0' and `a1'.  This fixed-point
    value is shifted right by the number of bits given in `count', and the
   integer part of the result is returned at the location pointed to by
   `z0Ptr'.  The fractional part of the result may be slightly corrupted as
   described above, and is returned at the location pointed to by `z1Ptr'.)
   -------------------------------------------------------------------------------
   */
   INLINE void
    shift64ExtraRightJamming(
        bits64 a0, bits64 a1, int16 count, bits64 *z0Ptr, bits64 *z1Ptr )
   {
       bits64 z0, z1;
       int8 negCount = ( - count ) & 63;
   
       if ( count == 0 ) {
           z1 = a1;
           z0 = a0;
       }
       else if ( count < 64 ) {
           z1 = ( a0<<negCount ) | ( a1 != 0 );
           z0 = a0>>count;
       }
       else {
           if ( count == 64 ) {
               z1 = a0 | ( a1 != 0 );
           }
           else {
               z1 = ( ( a0 | a1 ) != 0 );
           }
           z0 = 0;
       }
       *z1Ptr = z1;
       *z0Ptr = z0;
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Shifts the 128-bit value formed by concatenating `a0' and `a1' right by the
   number of bits given in `count'.  Any bits shifted off are lost.  The value
   of `count' can be arbitrarily large; in particular, if `count' is greater
   than 128, the result will be 0.  The result is broken into two 64-bit pieces
   which are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
   -------------------------------------------------------------------------------
   */
   INLINE void
    shift128Right(
        bits64 a0, bits64 a1, int16 count, bits64 *z0Ptr, bits64 *z1Ptr )
   {
       bits64 z0, z1;
       int8 negCount = ( - count ) & 63;
   
       if ( count == 0 ) {
           z1 = a1;
           z0 = a0;
       }
       else if ( count < 64 ) {
           z1 = ( a0<<negCount ) | ( a1>>count );
           z0 = a0>>count;
       }
       else {
           z1 = ( count < 64 ) ? ( a0>>( count & 63 ) ) : 0;
           z0 = 0;
       }
       *z1Ptr = z1;
       *z0Ptr = z0;
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Shifts the 128-bit value formed by concatenating `a0' and `a1' right by the
   number of bits given in `count'.  If any nonzero bits are shifted off, they
   are ``jammed'' into the least significant bit of the result by setting the
   least significant bit to 1.  The value of `count' can be arbitrarily large;
   in particular, if `count' is greater than 128, the result will be either
   0 or 1, depending on whether the concatenation of `a0' and `a1' is zero or
   nonzero.  The result is broken into two 64-bit pieces which are stored at
   the locations pointed to by `z0Ptr' and `z1Ptr'.
   -------------------------------------------------------------------------------
   */
   INLINE void
    shift128RightJamming(
        bits64 a0, bits64 a1, int16 count, bits64 *z0Ptr, bits64 *z1Ptr )
   {
       bits64 z0, z1;
       int8 negCount = ( - count ) & 63;
   
       if ( count == 0 ) {
           z1 = a1;
           z0 = a0;
       }
       else if ( count < 64 ) {
           z1 = ( a0<<negCount ) | ( a1>>count ) | ( ( a1<<negCount ) != 0 );
           z0 = a0>>count;
       }
       else {
           if ( count == 64 ) {
               z1 = a0 | ( a1 != 0 );
           }
           else if ( count < 128 ) {
               z1 = ( a0>>( count & 63 ) ) | ( ( ( a0<<negCount ) | a1 ) != 0 );
           }
           else {
               z1 = ( ( a0 | a1 ) != 0 );
           }
           z0 = 0;
       }
       *z1Ptr = z1;
       *z0Ptr = z0;
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Shifts the 192-bit value formed by concatenating `a0', `a1', and `a2' right
   by 64 _plus_ the number of bits given in `count'.  The shifted result is
   at most 128 nonzero bits; these are broken into two 64-bit pieces which are
   stored at the locations pointed to by `z0Ptr' and `z1Ptr'.  The bits shifted
   off form a third 64-bit result as follows:  The _last_ bit shifted off is
   the most-significant bit of the extra result, and the other 63 bits of the
   extra result are all zero if and only if _all_but_the_last_ bits shifted off
   were all zero.  This extra result is stored in the location pointed to by
   `z2Ptr'.  The value of `count' can be arbitrarily large.
       (This routine makes more sense if `a0', `a1', and `a2' are considered
   to form a fixed-point value with binary point between `a1' and `a2'.  This
   fixed-point value is shifted right by the number of bits given in `count',
   and the integer part of the result is returned at the locations pointed to
   by `z0Ptr' and `z1Ptr'.  The fractional part of the result may be slightly
   corrupted as described above, and is returned at the location pointed to by
   `z2Ptr'.)
   -------------------------------------------------------------------------------
   */
   INLINE void
    shift128ExtraRightJamming(
        bits64 a0,
        bits64 a1,
        bits64 a2,
        int16 count,
        bits64 *z0Ptr,
        bits64 *z1Ptr,
        bits64 *z2Ptr
    )
   {
       bits64 z0, z1, z2;
       int8 negCount = ( - count ) & 63;
   
       if ( count == 0 ) {
           z2 = a2;
           z1 = a1;
           z0 = a0;
       }
       else {
           if ( count < 64 ) {
               z2 = a1<<negCount;
               z1 = ( a0<<negCount ) | ( a1>>count );
               z0 = a0>>count;
           }
           else {
               if ( count == 64 ) {
                   z2 = a1;
                   z1 = a0;
               }
               else {
                   a2 |= a1;
                   if ( count < 128 ) {
                       z2 = a0<<negCount;
                       z1 = a0>>( count & 63 );
                   }
                   else {
                       z2 = ( count == 128 ) ? a0 : ( a0 != 0 );
                       z1 = 0;
                   }
               }
               z0 = 0;
           }
           z2 |= ( a2 != 0 );
       }
       *z2Ptr = z2;
       *z1Ptr = z1;
       *z0Ptr = z0;
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Shifts the 128-bit value formed by concatenating `a0' and `a1' left by the
   number of bits given in `count'.  Any bits shifted off are lost.  The value
   of `count' must be less than 64.  The result is broken into two 64-bit
   pieces which are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
   -------------------------------------------------------------------------------
   */
   INLINE void
    shortShift128Left(
        bits64 a0, bits64 a1, int16 count, bits64 *z0Ptr, bits64 *z1Ptr )
   {
   
       *z1Ptr = a1<<count;
       *z0Ptr =
           ( count == 0 ) ? a0 : ( a0<<count ) | ( a1>>( ( - count ) & 63 ) );
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Shifts the 192-bit value formed by concatenating `a0', `a1', and `a2' left
   by the number of bits given in `count'.  Any bits shifted off are lost.
   The value of `count' must be less than 64.  The result is broken into three
   64-bit pieces which are stored at the locations pointed to by `z0Ptr',
   `z1Ptr', and `z2Ptr'.
   -------------------------------------------------------------------------------
   */
   INLINE void
    shortShift192Left(
        bits64 a0,
        bits64 a1,
        bits64 a2,
        int16 count,
        bits64 *z0Ptr,
        bits64 *z1Ptr,
        bits64 *z2Ptr
    )
   {
       bits64 z0, z1, z2;
       int8 negCount;
   
       z2 = a2<<count;
       z1 = a1<<count;
       z0 = a0<<count;
       if ( 0 < count ) {
           negCount = ( ( - count ) & 63 );
           z1 |= a2>>negCount;
           z0 |= a1>>negCount;
       }
       *z2Ptr = z2;
       *z1Ptr = z1;
       *z0Ptr = z0;
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Adds the 128-bit value formed by concatenating `a0' and `a1' to the 128-bit
   value formed by concatenating `b0' and `b1'.  Addition is modulo 2^128, so
   any carry out is lost.  The result is broken into two 64-bit pieces which
   are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
   -------------------------------------------------------------------------------
   */
   INLINE void
    add128(
        bits64 a0, bits64 a1, bits64 b0, bits64 b1, bits64 *z0Ptr, bits64 *z1Ptr )
   {
       bits64 z1;
   
       z1 = a1 + b1;
       *z1Ptr = z1;
       *z0Ptr = a0 + b0 + ( z1 < a1 );
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Adds the 192-bit value formed by concatenating `a0', `a1', and `a2' to the
   192-bit value formed by concatenating `b0', `b1', and `b2'.  Addition is
   modulo 2^192, so any carry out is lost.  The result is broken into three
   64-bit pieces which are stored at the locations pointed to by `z0Ptr',
   `z1Ptr', and `z2Ptr'.
   -------------------------------------------------------------------------------
   */
   INLINE void
    add192(
        bits64 a0,
        bits64 a1,
        bits64 a2,
        bits64 b0,
        bits64 b1,
        bits64 b2,
        bits64 *z0Ptr,
        bits64 *z1Ptr,
        bits64 *z2Ptr
    )
   {
       bits64 z0, z1, z2;
       int8 carry0, carry1;
   
       z2 = a2 + b2;
       carry1 = ( z2 < a2 );
       z1 = a1 + b1;
       carry0 = ( z1 < a1 );
       z0 = a0 + b0;
       z1 += carry1;
       z0 += ( z1 < carry1 );
       z0 += carry0;
       *z2Ptr = z2;
       *z1Ptr = z1;
       *z0Ptr = z0;
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Subtracts the 128-bit value formed by concatenating `b0' and `b1' from the
   128-bit value formed by concatenating `a0' and `a1'.  Subtraction is modulo
   2^128, so any borrow out (carry out) is lost.  The result is broken into two
   64-bit pieces which are stored at the locations pointed to by `z0Ptr' and
   `z1Ptr'.
   -------------------------------------------------------------------------------
   */
   INLINE void
    sub128(
        bits64 a0, bits64 a1, bits64 b0, bits64 b1, bits64 *z0Ptr, bits64 *z1Ptr )
   {
   
       *z1Ptr = a1 - b1;
       *z0Ptr = a0 - b0 - ( a1 < b1 );
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Subtracts the 192-bit value formed by concatenating `b0', `b1', and `b2'
   from the 192-bit value formed by concatenating `a0', `a1', and `a2'.
   Subtraction is modulo 2^192, so any borrow out (carry out) is lost.  The
   result is broken into three 64-bit pieces which are stored at the locations
   pointed to by `z0Ptr', `z1Ptr', and `z2Ptr'.
   -------------------------------------------------------------------------------
   */
   INLINE void
    sub192(
        bits64 a0,
        bits64 a1,
        bits64 a2,
        bits64 b0,
        bits64 b1,
        bits64 b2,
        bits64 *z0Ptr,
        bits64 *z1Ptr,
        bits64 *z2Ptr
    )
   {
       bits64 z0, z1, z2;
       int8 borrow0, borrow1;
   
       z2 = a2 - b2;
       borrow1 = ( a2 < b2 );
       z1 = a1 - b1;
       borrow0 = ( a1 < b1 );
       z0 = a0 - b0;
       z0 -= ( z1 < borrow1 );
       z1 -= borrow1;
       z0 -= borrow0;
       *z2Ptr = z2;
       *z1Ptr = z1;
       *z0Ptr = z0;
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Multiplies `a' by `b' to obtain a 128-bit product.  The product is broken
   into two 64-bit pieces which are stored at the locations pointed to by
   `z0Ptr' and `z1Ptr'.
   -------------------------------------------------------------------------------
   */
   INLINE void mul64To128( bits64 a, bits64 b, bits64 *z0Ptr, bits64 *z1Ptr )
   {
       bits32 aHigh, aLow, bHigh, bLow;
       bits64 z0, zMiddleA, zMiddleB, z1;
   
       aLow = a;
       aHigh = a>>32;
       bLow = b;
       bHigh = b>>32;
       z1 = ( (bits64) aLow ) * bLow;
       zMiddleA = ( (bits64) aLow ) * bHigh;
       zMiddleB = ( (bits64) aHigh ) * bLow;
       z0 = ( (bits64) aHigh ) * bHigh;
       zMiddleA += zMiddleB;
       z0 += ( ( (bits64) ( zMiddleA < zMiddleB ) )<<32 ) + ( zMiddleA>>32 );
       zMiddleA <<= 32;
       z1 += zMiddleA;
       z0 += ( z1 < zMiddleA );
       *z1Ptr = z1;
       *z0Ptr = z0;
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Multiplies the 128-bit value formed by concatenating `a0' and `a1' by
   `b' to obtain a 192-bit product.  The product is broken into three 64-bit
   pieces which are stored at the locations pointed to by `z0Ptr', `z1Ptr', and
   `z2Ptr'.
   -------------------------------------------------------------------------------
   */
   INLINE void
    mul128By64To192(
        bits64 a0,
        bits64 a1,
        bits64 b,
        bits64 *z0Ptr,
        bits64 *z1Ptr,
        bits64 *z2Ptr
    )
   {
       bits64 z0, z1, z2, more1;
   
       mul64To128( a1, b, &z1, &z2 );
       mul64To128( a0, b, &z0, &more1 );
       add128( z0, more1, 0, z1, &z0, &z1 );
       *z2Ptr = z2;
       *z1Ptr = z1;
       *z0Ptr = z0;
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Multiplies the 128-bit value formed by concatenating `a0' and `a1' to the
   128-bit value formed by concatenating `b0' and `b1' to obtain a 256-bit
   product.  The product is broken into four 64-bit pieces which are stored at
   the locations pointed to by `z0Ptr', `z1Ptr', `z2Ptr', and `z3Ptr'.
   -------------------------------------------------------------------------------
   */
   INLINE void
    mul128To256(
        bits64 a0,
        bits64 a1,
        bits64 b0,
        bits64 b1,
        bits64 *z0Ptr,
        bits64 *z1Ptr,
        bits64 *z2Ptr,
        bits64 *z3Ptr
    )
   {
       bits64 z0, z1, z2, z3;
       bits64 more1, more2;
   
       mul64To128( a1, b1, &z2, &z3 );
       mul64To128( a1, b0, &z1, &more2 );
       add128( z1, more2, 0, z2, &z1, &z2 );
       mul64To128( a0, b0, &z0, &more1 );
       add128( z0, more1, 0, z1, &z0, &z1 );
       mul64To128( a0, b1, &more1, &more2 );
       add128( more1, more2, 0, z2, &more1, &z2 );
       add128( z0, z1, 0, more1, &z0, &z1 );
       *z3Ptr = z3;
       *z2Ptr = z2;
       *z1Ptr = z1;
       *z0Ptr = z0;
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Returns an approximation to the 64-bit integer quotient obtained by dividing
   `b' into the 128-bit value formed by concatenating `a0' and `a1'.  The
   divisor `b' must be at least 2^63.  If q is the exact quotient truncated
   toward zero, the approximation returned lies between q and q + 2 inclusive.
   If the exact quotient q is larger than 64 bits, the maximum positive 64-bit
   unsigned integer is returned.
   -------------------------------------------------------------------------------
   */
   static bits64 estimateDiv128To64( bits64 a0, bits64 a1, bits64 b )
   {
       bits64 b0, b1;
       bits64 rem0, rem1, term0, term1;
       bits64 z;
   
       if ( b <= a0 ) return LIT64( 0xFFFFFFFFFFFFFFFF );
       b0 = b>>32;
       z = ( b0<<32 <= a0 ) ? LIT64( 0xFFFFFFFF00000000 ) : ( a0 / b0 )<<32;
       mul64To128( b, z, &term0, &term1 );
       sub128( a0, a1, term0, term1, &rem0, &rem1 );
       while ( ( (sbits64) rem0 ) < 0 ) {
           z -= LIT64( 0x100000000 );
           b1 = b<<32;
           add128( rem0, rem1, b0, b1, &rem0, &rem1 );
       }
       rem0 = ( rem0<<32 ) | ( rem1>>32 );
       z |= ( b0<<32 <= rem0 ) ? 0xFFFFFFFF : rem0 / b0;
       return z;
   
   }
   
   #ifndef SOFTFLOAT_FOR_GCC /* Not used */
   /*
   -------------------------------------------------------------------------------
   Returns an approximation to the square root of the 32-bit significand given
   by `a'.  Considered as an integer, `a' must be at least 2^31.  If bit 0 of
   `aExp' (the least significant bit) is 1, the integer returned approximates
   2^31*sqrt(`a'/2^31), where `a' is considered an integer.  If bit 0 of `aExp'
   is 0, the integer returned approximates 2^31*sqrt(`a'/2^30).  In either
   case, the approximation returned lies strictly within +/-2 of the exact
   value.
   -------------------------------------------------------------------------------
   */
   static bits32 estimateSqrt32( int16 aExp, bits32 a )
   {
       static const bits16 sqrtOddAdjustments[] = {
           0x0004, 0x0022, 0x005D, 0x00B1, 0x011D, 0x019F, 0x0236, 0x02E0,
           0x039C, 0x0468, 0x0545, 0x0631, 0x072B, 0x0832, 0x0946, 0x0A67
       };
       static const bits16 sqrtEvenAdjustments[] = {
           0x0A2D, 0x08AF, 0x075A, 0x0629, 0x051A, 0x0429, 0x0356, 0x029E,
           0x0200, 0x0179, 0x0109, 0x00AF, 0x0068, 0x0034, 0x0012, 0x0002
       };
       int8 index;
       bits32 z;
   
       index = ( a>>27 ) & 15;
       if ( aExp & 1 ) {
           z = 0x4000 + ( a>>17 ) - sqrtOddAdjustments[ index ];
           z = ( ( a / z )<<14 ) + ( z<<15 );
           a >>= 1;
       }
       else {
           z = 0x8000 + ( a>>17 ) - sqrtEvenAdjustments[ index ];
           z = a / z + z;
           z = ( 0x20000 <= z ) ? 0xFFFF8000 : ( z<<15 );
           if ( z <= a ) return (bits32) ( ( (sbits32) a )>>1 );
       }
       return ( (bits32) ( ( ( (bits64) a )<<31 ) / z ) ) + ( z>>1 );
   
   }
   #endif
   
   /*
   -------------------------------------------------------------------------------
   Returns the number of leading 0 bits before the most-significant 1 bit of
   `a'.  If `a' is zero, 32 is returned.
   -------------------------------------------------------------------------------
   */
   static int8 countLeadingZeros32( bits32 a )
   {
       static const int8 countLeadingZerosHigh[] = {
           8, 7, 6, 6, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4,
           3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
           2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
           2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
           1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
           1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
           1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
           1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
           0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
           0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
           0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
           0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
           0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
           0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
           0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
           0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
       };
       int8 shiftCount;
   
       shiftCount = 0;
       if ( a < 0x10000 ) {
           shiftCount += 16;
           a <<= 16;
       }
       if ( a < 0x1000000 ) {
           shiftCount += 8;
           a <<= 8;
       }
       shiftCount += countLeadingZerosHigh[ a>>24 ];
       return shiftCount;
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Returns the number of leading 0 bits before the most-significant 1 bit of
   `a'.  If `a' is zero, 64 is returned.
   -------------------------------------------------------------------------------
   */
   static int8 countLeadingZeros64( bits64 a )
   {
       int8 shiftCount;
   
       shiftCount = 0;
       if ( a < ( (bits64) 1 )<<32 ) {
           shiftCount += 32;
       }
       else {
           a >>= 32;
       }
       shiftCount += countLeadingZeros32( a );
       return shiftCount;
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Returns 1 if the 128-bit value formed by concatenating `a0' and `a1'
   is equal to the 128-bit value formed by concatenating `b0' and `b1'.
   Otherwise, returns 0.
   -------------------------------------------------------------------------------
   */
   INLINE flag eq128( bits64 a0, bits64 a1, bits64 b0, bits64 b1 )
   {
   
       return ( a0 == b0 ) && ( a1 == b1 );
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is less
   than or equal to the 128-bit value formed by concatenating `b0' and `b1'.
   Otherwise, returns 0.
   -------------------------------------------------------------------------------
   */
   INLINE flag le128( bits64 a0, bits64 a1, bits64 b0, bits64 b1 )
   {
   
       return ( a0 < b0 ) || ( ( a0 == b0 ) && ( a1 <= b1 ) );
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is less
   than the 128-bit value formed by concatenating `b0' and `b1'.  Otherwise,
   returns 0.
   -------------------------------------------------------------------------------
   */
   INLINE flag lt128( bits64 a0, bits64 a1, bits64 b0, bits64 b1 )
   {
   
       return ( a0 < b0 ) || ( ( a0 == b0 ) && ( a1 < b1 ) );
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is
   not equal to the 128-bit value formed by concatenating `b0' and `b1'.
   Otherwise, returns 0.
   -------------------------------------------------------------------------------
   */
   INLINE flag ne128( bits64 a0, bits64 a1, bits64 b0, bits64 b1 )
   {
   
       return ( a0 != b0 ) || ( a1 != b1 );
   
   }
   

Cache object: 139fe34fbff69c58b28d9114b36fe27b