628 lines
21 KiB
C
628 lines
21 KiB
C
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/*============================================================================
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This C source fragment is part of the SoftFloat IEC/IEEE Floating-point
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Arithmetic Package, Release 2b.
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Written by John R. Hauser. This work was made possible in part by the
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International Computer Science Institute, located at Suite 600, 1947 Center
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Street, Berkeley, California 94704. Funding was partially provided by the
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National Science Foundation under grant MIP-9311980. The original version
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of this code was written as part of a project to build a fixed-point vector
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processor in collaboration with the University of California at Berkeley,
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overseen by Profs. Nelson Morgan and John Wawrzynek. More information
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is available through the Web page `http://www.cs.berkeley.edu/~jhauser/
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arithmetic/SoftFloat.html'.
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THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort has
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been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT TIMES
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RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO PERSONS
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AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ALL LOSSES,
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COSTS, OR OTHER PROBLEMS THEY INCUR DUE TO THE SOFTWARE, AND WHO FURTHERMORE
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EFFECTIVELY INDEMNIFY JOHN HAUSER AND THE INTERNATIONAL COMPUTER SCIENCE
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INSTITUTE (possibly via similar legal warning) AGAINST ALL LOSSES, COSTS, OR
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OTHER PROBLEMS INCURRED BY THEIR CUSTOMERS AND CLIENTS DUE TO THE SOFTWARE.
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Derivative works are acceptable, even for commercial purposes, so long as
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(1) the source code for the derivative work includes prominent notice that
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the work is derivative, and (2) the source code includes prominent notice with
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these four paragraphs for those parts of this code that are retained.
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=============================================================================*/
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/*----------------------------------------------------------------------------
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| Shifts `a' right by the number of bits given in `count'. If any nonzero
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| bits are shifted off, they are ``jammed'' into the least significant bit of
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| the result by setting the least significant bit to 1. The value of `count'
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| can be arbitrarily large; in particular, if `count' is greater than 32, the
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| result will be either 0 or 1, depending on whether `a' is zero or nonzero.
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| The result is stored in the location pointed to by `zPtr'.
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*----------------------------------------------------------------------------*/
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INLINE void shift32RightJamming( bits32 a, int16 count, bits32 *zPtr )
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{
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bits32 z;
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if ( count == 0 ) {
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z = a;
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}
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else if ( count < 32 ) {
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z = ( a>>count ) | ( ( a<<( ( - count ) & 31 ) ) != 0 );
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}
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else {
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z = ( a != 0 );
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}
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*zPtr = z;
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}
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/*----------------------------------------------------------------------------
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| Shifts the 64-bit value formed by concatenating `a0' and `a1' right by the
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| number of bits given in `count'. Any bits shifted off are lost. The value
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| of `count' can be arbitrarily large; in particular, if `count' is greater
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| than 64, the result will be 0. The result is broken into two 32-bit pieces
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| which are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
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*----------------------------------------------------------------------------*/
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INLINE void
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shift64Right(
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bits32 a0, bits32 a1, int16 count, bits32 *z0Ptr, bits32 *z1Ptr )
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{
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bits32 z0, z1;
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int8 negCount = ( - count ) & 31;
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if ( count == 0 ) {
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z1 = a1;
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z0 = a0;
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}
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else if ( count < 32 ) {
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z1 = ( a0<<negCount ) | ( a1>>count );
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z0 = a0>>count;
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}
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else {
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z1 = ( count < 64 ) ? ( a0>>( count & 31 ) ) : 0;
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z0 = 0;
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}
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*z1Ptr = z1;
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*z0Ptr = z0;
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}
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/*----------------------------------------------------------------------------
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| Shifts the 64-bit value formed by concatenating `a0' and `a1' right by the
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| number of bits given in `count'. If any nonzero bits are shifted off, they
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| are ``jammed'' into the least significant bit of the result by setting the
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| least significant bit to 1. The value of `count' can be arbitrarily large;
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| in particular, if `count' is greater than 64, the result will be either 0
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| or 1, depending on whether the concatenation of `a0' and `a1' is zero or
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| nonzero. The result is broken into two 32-bit pieces which are stored at
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| the locations pointed to by `z0Ptr' and `z1Ptr'.
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*----------------------------------------------------------------------------*/
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INLINE void
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shift64RightJamming(
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bits32 a0, bits32 a1, int16 count, bits32 *z0Ptr, bits32 *z1Ptr )
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{
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bits32 z0, z1;
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int8 negCount = ( - count ) & 31;
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if ( count == 0 ) {
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z1 = a1;
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z0 = a0;
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}
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else if ( count < 32 ) {
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z1 = ( a0<<negCount ) | ( a1>>count ) | ( ( a1<<negCount ) != 0 );
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z0 = a0>>count;
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}
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else {
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if ( count == 32 ) {
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z1 = a0 | ( a1 != 0 );
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}
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else if ( count < 64 ) {
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z1 = ( a0>>( count & 31 ) ) | ( ( ( a0<<negCount ) | a1 ) != 0 );
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}
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else {
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z1 = ( ( a0 | a1 ) != 0 );
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}
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z0 = 0;
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}
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*z1Ptr = z1;
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*z0Ptr = z0;
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}
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/*----------------------------------------------------------------------------
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| Shifts the 96-bit value formed by concatenating `a0', `a1', and `a2' right
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| by 32 _plus_ the number of bits given in `count'. The shifted result is
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| at most 64 nonzero bits; these are broken into two 32-bit pieces which are
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| stored at the locations pointed to by `z0Ptr' and `z1Ptr'. The bits shifted
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| off form a third 32-bit result as follows: The _last_ bit shifted off is
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| the most-significant bit of the extra result, and the other 31 bits of the
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| extra result are all zero if and only if _all_but_the_last_ bits shifted off
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| were all zero. This extra result is stored in the location pointed to by
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| `z2Ptr'. The value of `count' can be arbitrarily large.
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| (This routine makes more sense if `a0', `a1', and `a2' are considered
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| to form a fixed-point value with binary point between `a1' and `a2'. This
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| fixed-point value is shifted right by the number of bits given in `count',
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| and the integer part of the result is returned at the locations pointed to
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| by `z0Ptr' and `z1Ptr'. The fractional part of the result may be slightly
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| corrupted as described above, and is returned at the location pointed to by
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| `z2Ptr'.)
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*----------------------------------------------------------------------------*/
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INLINE void
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shift64ExtraRightJamming(
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bits32 a0,
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bits32 a1,
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bits32 a2,
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int16 count,
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bits32 *z0Ptr,
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bits32 *z1Ptr,
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bits32 *z2Ptr
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)
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{
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bits32 z0, z1, z2;
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int8 negCount = ( - count ) & 31;
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if ( count == 0 ) {
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z2 = a2;
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z1 = a1;
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z0 = a0;
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}
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else {
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if ( count < 32 ) {
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z2 = a1<<negCount;
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z1 = ( a0<<negCount ) | ( a1>>count );
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z0 = a0>>count;
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}
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else {
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if ( count == 32 ) {
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z2 = a1;
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z1 = a0;
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}
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else {
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a2 |= a1;
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if ( count < 64 ) {
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z2 = a0<<negCount;
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z1 = a0>>( count & 31 );
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}
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else {
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z2 = ( count == 64 ) ? a0 : ( a0 != 0 );
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z1 = 0;
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}
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}
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z0 = 0;
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}
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z2 |= ( a2 != 0 );
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}
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*z2Ptr = z2;
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*z1Ptr = z1;
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*z0Ptr = z0;
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}
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/*----------------------------------------------------------------------------
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| Shifts the 64-bit value formed by concatenating `a0' and `a1' left by the
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| number of bits given in `count'. Any bits shifted off are lost. The value
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| of `count' must be less than 32. The result is broken into two 32-bit
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| pieces which are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
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*----------------------------------------------------------------------------*/
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INLINE void
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shortShift64Left(
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bits32 a0, bits32 a1, int16 count, bits32 *z0Ptr, bits32 *z1Ptr )
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{
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*z1Ptr = a1<<count;
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*z0Ptr =
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( count == 0 ) ? a0 : ( a0<<count ) | ( a1>>( ( - count ) & 31 ) );
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}
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/*----------------------------------------------------------------------------
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| Shifts the 96-bit value formed by concatenating `a0', `a1', and `a2' left
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| by the number of bits given in `count'. Any bits shifted off are lost.
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| The value of `count' must be less than 32. The result is broken into three
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| 32-bit pieces which are stored at the locations pointed to by `z0Ptr',
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| `z1Ptr', and `z2Ptr'.
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*----------------------------------------------------------------------------*/
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INLINE void
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shortShift96Left(
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bits32 a0,
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bits32 a1,
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bits32 a2,
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int16 count,
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bits32 *z0Ptr,
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bits32 *z1Ptr,
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bits32 *z2Ptr
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)
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{
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bits32 z0, z1, z2;
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int8 negCount;
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z2 = a2<<count;
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z1 = a1<<count;
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z0 = a0<<count;
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if ( 0 < count ) {
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negCount = ( ( - count ) & 31 );
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z1 |= a2>>negCount;
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z0 |= a1>>negCount;
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}
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*z2Ptr = z2;
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*z1Ptr = z1;
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*z0Ptr = z0;
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}
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/*----------------------------------------------------------------------------
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| Adds the 64-bit value formed by concatenating `a0' and `a1' to the 64-bit
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| value formed by concatenating `b0' and `b1'. Addition is modulo 2^64, so
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| any carry out is lost. The result is broken into two 32-bit pieces which
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| are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
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*----------------------------------------------------------------------------*/
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INLINE void
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add64(
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bits32 a0, bits32 a1, bits32 b0, bits32 b1, bits32 *z0Ptr, bits32 *z1Ptr )
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{
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bits32 z1;
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z1 = a1 + b1;
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*z1Ptr = z1;
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*z0Ptr = a0 + b0 + ( z1 < a1 );
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}
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/*----------------------------------------------------------------------------
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| Adds the 96-bit value formed by concatenating `a0', `a1', and `a2' to the
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| 96-bit value formed by concatenating `b0', `b1', and `b2'. Addition is
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| modulo 2^96, so any carry out is lost. The result is broken into three
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| 32-bit pieces which are stored at the locations pointed to by `z0Ptr',
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| `z1Ptr', and `z2Ptr'.
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*----------------------------------------------------------------------------*/
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INLINE void
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add96(
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bits32 a0,
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bits32 a1,
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bits32 a2,
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bits32 b0,
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bits32 b1,
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bits32 b2,
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bits32 *z0Ptr,
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bits32 *z1Ptr,
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bits32 *z2Ptr
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)
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{
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bits32 z0, z1, z2;
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int8 carry0, carry1;
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z2 = a2 + b2;
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carry1 = ( z2 < a2 );
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z1 = a1 + b1;
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carry0 = ( z1 < a1 );
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z0 = a0 + b0;
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z1 += carry1;
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z0 += ( z1 < carry1 );
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z0 += carry0;
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*z2Ptr = z2;
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*z1Ptr = z1;
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*z0Ptr = z0;
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}
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/*----------------------------------------------------------------------------
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| Subtracts the 64-bit value formed by concatenating `b0' and `b1' from the
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| 64-bit value formed by concatenating `a0' and `a1'. Subtraction is modulo
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| 2^64, so any borrow out (carry out) is lost. The result is broken into two
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| 32-bit pieces which are stored at the locations pointed to by `z0Ptr' and
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| `z1Ptr'.
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*----------------------------------------------------------------------------*/
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INLINE void
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sub64(
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bits32 a0, bits32 a1, bits32 b0, bits32 b1, bits32 *z0Ptr, bits32 *z1Ptr )
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{
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*z1Ptr = a1 - b1;
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*z0Ptr = a0 - b0 - ( a1 < b1 );
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}
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/*----------------------------------------------------------------------------
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| Subtracts the 96-bit value formed by concatenating `b0', `b1', and `b2' from
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| the 96-bit value formed by concatenating `a0', `a1', and `a2'. Subtraction
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| is modulo 2^96, so any borrow out (carry out) is lost. The result is broken
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| into three 32-bit pieces which are stored at the locations pointed to by
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| `z0Ptr', `z1Ptr', and `z2Ptr'.
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*----------------------------------------------------------------------------*/
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INLINE void
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sub96(
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bits32 a0,
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bits32 a1,
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bits32 a2,
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bits32 b0,
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bits32 b1,
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bits32 b2,
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bits32 *z0Ptr,
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bits32 *z1Ptr,
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bits32 *z2Ptr
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)
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{
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bits32 z0, z1, z2;
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int8 borrow0, borrow1;
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z2 = a2 - b2;
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borrow1 = ( a2 < b2 );
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z1 = a1 - b1;
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borrow0 = ( a1 < b1 );
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z0 = a0 - b0;
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z0 -= ( z1 < borrow1 );
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z1 -= borrow1;
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z0 -= borrow0;
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*z2Ptr = z2;
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*z1Ptr = z1;
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*z0Ptr = z0;
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}
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/*----------------------------------------------------------------------------
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| Multiplies `a' by `b' to obtain a 64-bit product. The product is broken
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| into two 32-bit pieces which are stored at the locations pointed to by
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| `z0Ptr' and `z1Ptr'.
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*----------------------------------------------------------------------------*/
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INLINE void mul32To64( bits32 a, bits32 b, bits32 *z0Ptr, bits32 *z1Ptr )
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{
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bits16 aHigh, aLow, bHigh, bLow;
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bits32 z0, zMiddleA, zMiddleB, z1;
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aLow = a;
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aHigh = a>>16;
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bLow = b;
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bHigh = b>>16;
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z1 = ( (bits32) aLow ) * bLow;
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zMiddleA = ( (bits32) aLow ) * bHigh;
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zMiddleB = ( (bits32) aHigh ) * bLow;
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z0 = ( (bits32) aHigh ) * bHigh;
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zMiddleA += zMiddleB;
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z0 += ( ( (bits32) ( zMiddleA < zMiddleB ) )<<16 ) + ( zMiddleA>>16 );
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zMiddleA <<= 16;
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z1 += zMiddleA;
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z0 += ( z1 < zMiddleA );
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*z1Ptr = z1;
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*z0Ptr = z0;
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}
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/*----------------------------------------------------------------------------
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| Multiplies the 64-bit value formed by concatenating `a0' and `a1' by `b'
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| to obtain a 96-bit product. The product is broken into three 32-bit pieces
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| which are stored at the locations pointed to by `z0Ptr', `z1Ptr', and
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| `z2Ptr'.
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*----------------------------------------------------------------------------*/
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INLINE void
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mul64By32To96(
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bits32 a0,
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bits32 a1,
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bits32 b,
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bits32 *z0Ptr,
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bits32 *z1Ptr,
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bits32 *z2Ptr
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)
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{
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bits32 z0, z1, z2, more1;
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mul32To64( a1, b, &z1, &z2 );
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mul32To64( a0, b, &z0, &more1 );
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add64( z0, more1, 0, z1, &z0, &z1 );
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*z2Ptr = z2;
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*z1Ptr = z1;
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*z0Ptr = z0;
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}
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/*----------------------------------------------------------------------------
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| Multiplies the 64-bit value formed by concatenating `a0' and `a1' to the
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| 64-bit value formed by concatenating `b0' and `b1' to obtain a 128-bit
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| product. The product is broken into four 32-bit pieces which are stored at
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| the locations pointed to by `z0Ptr', `z1Ptr', `z2Ptr', and `z3Ptr'.
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*----------------------------------------------------------------------------*/
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INLINE void
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mul64To128(
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bits32 a0,
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bits32 a1,
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bits32 b0,
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bits32 b1,
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bits32 *z0Ptr,
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bits32 *z1Ptr,
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bits32 *z2Ptr,
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bits32 *z3Ptr
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)
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{
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bits32 z0, z1, z2, z3;
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bits32 more1, more2;
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mul32To64( a1, b1, &z2, &z3 );
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mul32To64( a1, b0, &z1, &more2 );
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add64( z1, more2, 0, z2, &z1, &z2 );
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mul32To64( a0, b0, &z0, &more1 );
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add64( z0, more1, 0, z1, &z0, &z1 );
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mul32To64( a0, b1, &more1, &more2 );
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add64( more1, more2, 0, z2, &more1, &z2 );
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add64( z0, z1, 0, more1, &z0, &z1 );
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*z3Ptr = z3;
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*z2Ptr = z2;
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*z1Ptr = z1;
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*z0Ptr = z0;
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}
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/*----------------------------------------------------------------------------
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| Returns an approximation to the 32-bit integer quotient obtained by dividing
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| `b' into the 64-bit value formed by concatenating `a0' and `a1'. The
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| divisor `b' must be at least 2^31. If q is the exact quotient truncated
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| toward zero, the approximation returned lies between q and q + 2 inclusive.
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| If the exact quotient q is larger than 32 bits, the maximum positive 32-bit
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| unsigned integer is returned.
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*----------------------------------------------------------------------------*/
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static bits32 estimateDiv64To32( bits32 a0, bits32 a1, bits32 b )
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{
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bits32 b0, b1;
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bits32 rem0, rem1, term0, term1;
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bits32 z;
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if ( b <= a0 ) return 0xFFFFFFFF;
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b0 = b>>16;
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z = ( b0<<16 <= a0 ) ? 0xFFFF0000 : ( a0 / b0 )<<16;
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mul32To64( b, z, &term0, &term1 );
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sub64( a0, a1, term0, term1, &rem0, &rem1 );
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while ( ( (sbits32) rem0 ) < 0 ) {
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z -= 0x10000;
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b1 = b<<16;
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add64( rem0, rem1, b0, b1, &rem0, &rem1 );
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}
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rem0 = ( rem0<<16 ) | ( rem1>>16 );
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z |= ( b0<<16 <= rem0 ) ? 0xFFFF : rem0 / b0;
|
|
return z;
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| 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 ( ( estimateDiv64To32( a, 0, z ) )>>1 ) + ( z>>1 );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| 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 1 if the 64-bit value formed by concatenating `a0' and `a1' is
|
|
| equal to the 64-bit value formed by concatenating `b0' and `b1'. Otherwise,
|
|
| returns 0.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
INLINE flag eq64( bits32 a0, bits32 a1, bits32 b0, bits32 b1 )
|
|
{
|
|
|
|
return ( a0 == b0 ) && ( a1 == b1 );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns 1 if the 64-bit value formed by concatenating `a0' and `a1' is less
|
|
| than or equal to the 64-bit value formed by concatenating `b0' and `b1'.
|
|
| Otherwise, returns 0.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
INLINE flag le64( bits32 a0, bits32 a1, bits32 b0, bits32 b1 )
|
|
{
|
|
|
|
return ( a0 < b0 ) || ( ( a0 == b0 ) && ( a1 <= b1 ) );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns 1 if the 64-bit value formed by concatenating `a0' and `a1' is less
|
|
| than the 64-bit value formed by concatenating `b0' and `b1'. Otherwise,
|
|
| returns 0.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
INLINE flag lt64( bits32 a0, bits32 a1, bits32 b0, bits32 b1 )
|
|
{
|
|
|
|
return ( a0 < b0 ) || ( ( a0 == b0 ) && ( a1 < b1 ) );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns 1 if the 64-bit value formed by concatenating `a0' and `a1' is not
|
|
| equal to the 64-bit value formed by concatenating `b0' and `b1'. Otherwise,
|
|
| returns 0.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
INLINE flag ne64( bits32 a0, bits32 a1, bits32 b0, bits32 b1 )
|
|
{
|
|
|
|
return ( a0 != b0 ) || ( a1 != b1 );
|
|
|
|
}
|
|
|