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/*
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* QEMU float support macros
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*
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* Derived from SoftFloat.
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*/
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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 notice) 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( uint32_t a, int16 count, uint32_t *zPtr )
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{ |
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uint32_t 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 `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 64, 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 shift64RightJamming( uint64_t a, int16 count, uint64_t *zPtr )
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{ |
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uint64_t 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 < 64 ) { |
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z = ( a>>count ) | ( ( a<<( ( - count ) & 63 ) ) != 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 128-bit value formed by concatenating `a0' and `a1' right by 64
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| _plus_ the number of bits given in `count'. The shifted result is at most
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| 64 nonzero bits; this is stored at the location pointed to by `z0Ptr'. The
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| bits shifted off form a second 64-bit result as follows: The _last_ bit
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| shifted off is the most-significant bit of the extra result, and the other
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| 63 bits of the extra result are all zero if and only if _all_but_the_last_
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| bits shifted off were all zero. This extra result is stored in the location
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| pointed to by `z1Ptr'. The value of `count' can be arbitrarily large.
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| (This routine makes more sense if `a0' and `a1' are considered to form
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| a fixed-point value with binary point between `a0' and `a1'. This fixed-
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| point value is shifted right by the number of bits given in `count', and
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| the integer part of the result is returned at the location pointed to by
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| `z0Ptr'. The fractional part of the result may be slightly corrupted as
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| described above, and is returned at the location pointed to by `z1Ptr'.)
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*----------------------------------------------------------------------------*/
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INLINE void
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shift64ExtraRightJamming( |
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uint64_t a0, uint64_t a1, int16 count, uint64_t *z0Ptr, uint64_t *z1Ptr ) |
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{ |
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uint64_t z0, z1; |
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int8 negCount = ( - count ) & 63;
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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 < 64 ) { |
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z1 = ( a0<<negCount ) | ( a1 != 0 );
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z0 = a0>>count; |
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} |
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else {
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if ( count == 64 ) { |
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z1 = a0 | ( 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 128-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 128, the result will be 0. The result is broken into two 64-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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shift128Right( |
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uint64_t a0, uint64_t a1, int16 count, uint64_t *z0Ptr, uint64_t *z1Ptr ) |
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{ |
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uint64_t z0, z1; |
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int8 negCount = ( - count ) & 63;
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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 < 64 ) { |
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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 & 63 ) ) : 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 128-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 128, the result will be either
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| 0 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 64-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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shift128RightJamming( |
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uint64_t a0, uint64_t a1, int16 count, uint64_t *z0Ptr, uint64_t *z1Ptr ) |
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{ |
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uint64_t z0, z1; |
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int8 negCount = ( - count ) & 63;
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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 < 64 ) { |
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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 == 64 ) { |
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z1 = a0 | ( a1 != 0 );
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} |
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else if ( count < 128 ) { |
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z1 = ( a0>>( count & 63 ) ) | ( ( ( 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 192-bit value formed by concatenating `a0', `a1', and `a2' right
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| by 64 _plus_ the number of bits given in `count'. The shifted result is
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| at most 128 nonzero bits; these are broken into two 64-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 64-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 63 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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shift128ExtraRightJamming( |
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uint64_t a0, |
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uint64_t a1, |
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uint64_t a2, |
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int16 count, |
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uint64_t *z0Ptr, |
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uint64_t *z1Ptr, |
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uint64_t *z2Ptr |
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) |
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{ |
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uint64_t z0, z1, z2; |
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int8 negCount = ( - count ) & 63;
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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 < 64 ) { |
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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 == 64 ) { |
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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 < 128 ) { |
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z2 = a0<<negCount; |
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z1 = a0>>( count & 63 );
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} |
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else {
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z2 = ( count == 128 ) ? 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 128-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 64. The result is broken into two 64-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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shortShift128Left( |
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uint64_t a0, uint64_t a1, int16 count, uint64_t *z0Ptr, uint64_t *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 ) & 63 ) ); |
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} |
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/*----------------------------------------------------------------------------
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| Shifts the 192-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 64. The result is broken into three
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| 64-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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shortShift192Left( |
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uint64_t a0, |
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uint64_t a1, |
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uint64_t a2, |
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int16 count, |
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uint64_t *z0Ptr, |
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uint64_t *z1Ptr, |
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uint64_t *z2Ptr |
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) |
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{ |
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uint64_t 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 ) & 63 );
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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 128-bit value formed by concatenating `a0' and `a1' to the 128-bit
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| value formed by concatenating `b0' and `b1'. Addition is modulo 2^128, so
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| any carry out is lost. The result is broken into two 64-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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add128( |
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uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1, uint64_t *z0Ptr, uint64_t *z1Ptr ) |
345 |
{ |
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uint64_t z1; |
347 |
|
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z1 = a1 + b1; |
349 |
*z1Ptr = z1; |
350 |
*z0Ptr = a0 + b0 + ( z1 < a1 ); |
351 |
|
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} |
353 |
|
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/*----------------------------------------------------------------------------
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| Adds the 192-bit value formed by concatenating `a0', `a1', and `a2' to the
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| 192-bit value formed by concatenating `b0', `b1', and `b2'. Addition is
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| modulo 2^192, so any carry out is lost. The result is broken into three
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| 64-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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add192( |
364 |
uint64_t a0, |
365 |
uint64_t a1, |
366 |
uint64_t a2, |
367 |
uint64_t b0, |
368 |
uint64_t b1, |
369 |
uint64_t b2, |
370 |
uint64_t *z0Ptr, |
371 |
uint64_t *z1Ptr, |
372 |
uint64_t *z2Ptr |
373 |
) |
374 |
{ |
375 |
uint64_t z0, z1, z2; |
376 |
int8 carry0, carry1; |
377 |
|
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z2 = a2 + b2; |
379 |
carry1 = ( z2 < a2 ); |
380 |
z1 = a1 + b1; |
381 |
carry0 = ( z1 < a1 ); |
382 |
z0 = a0 + b0; |
383 |
z1 += carry1; |
384 |
z0 += ( z1 < carry1 ); |
385 |
z0 += carry0; |
386 |
*z2Ptr = z2; |
387 |
*z1Ptr = z1; |
388 |
*z0Ptr = z0; |
389 |
|
390 |
} |
391 |
|
392 |
/*----------------------------------------------------------------------------
|
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| Subtracts the 128-bit value formed by concatenating `b0' and `b1' from the
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394 |
| 128-bit value formed by concatenating `a0' and `a1'. Subtraction is modulo
|
395 |
| 2^128, so any borrow out (carry out) is lost. The result is broken into two
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396 |
| 64-bit pieces which are stored at the locations pointed to by `z0Ptr' and
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397 |
| `z1Ptr'.
|
398 |
*----------------------------------------------------------------------------*/
|
399 |
|
400 |
INLINE void
|
401 |
sub128( |
402 |
uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1, uint64_t *z0Ptr, uint64_t *z1Ptr ) |
403 |
{ |
404 |
|
405 |
*z1Ptr = a1 - b1; |
406 |
*z0Ptr = a0 - b0 - ( a1 < b1 ); |
407 |
|
408 |
} |
409 |
|
410 |
/*----------------------------------------------------------------------------
|
411 |
| Subtracts the 192-bit value formed by concatenating `b0', `b1', and `b2'
|
412 |
| from the 192-bit value formed by concatenating `a0', `a1', and `a2'.
|
413 |
| Subtraction is modulo 2^192, so any borrow out (carry out) is lost. The
|
414 |
| result is broken into three 64-bit pieces which are stored at the locations
|
415 |
| pointed to by `z0Ptr', `z1Ptr', and `z2Ptr'.
|
416 |
*----------------------------------------------------------------------------*/
|
417 |
|
418 |
INLINE void
|
419 |
sub192( |
420 |
uint64_t a0, |
421 |
uint64_t a1, |
422 |
uint64_t a2, |
423 |
uint64_t b0, |
424 |
uint64_t b1, |
425 |
uint64_t b2, |
426 |
uint64_t *z0Ptr, |
427 |
uint64_t *z1Ptr, |
428 |
uint64_t *z2Ptr |
429 |
) |
430 |
{ |
431 |
uint64_t z0, z1, z2; |
432 |
int8 borrow0, borrow1; |
433 |
|
434 |
z2 = a2 - b2; |
435 |
borrow1 = ( a2 < b2 ); |
436 |
z1 = a1 - b1; |
437 |
borrow0 = ( a1 < b1 ); |
438 |
z0 = a0 - b0; |
439 |
z0 -= ( z1 < borrow1 ); |
440 |
z1 -= borrow1; |
441 |
z0 -= borrow0; |
442 |
*z2Ptr = z2; |
443 |
*z1Ptr = z1; |
444 |
*z0Ptr = z0; |
445 |
|
446 |
} |
447 |
|
448 |
/*----------------------------------------------------------------------------
|
449 |
| Multiplies `a' by `b' to obtain a 128-bit product. The product is broken
|
450 |
| into two 64-bit pieces which are stored at the locations pointed to by
|
451 |
| `z0Ptr' and `z1Ptr'.
|
452 |
*----------------------------------------------------------------------------*/
|
453 |
|
454 |
INLINE void mul64To128( uint64_t a, uint64_t b, uint64_t *z0Ptr, uint64_t *z1Ptr )
|
455 |
{ |
456 |
uint32_t aHigh, aLow, bHigh, bLow; |
457 |
uint64_t z0, zMiddleA, zMiddleB, z1; |
458 |
|
459 |
aLow = a; |
460 |
aHigh = a>>32;
|
461 |
bLow = b; |
462 |
bHigh = b>>32;
|
463 |
z1 = ( (uint64_t) aLow ) * bLow; |
464 |
zMiddleA = ( (uint64_t) aLow ) * bHigh; |
465 |
zMiddleB = ( (uint64_t) aHigh ) * bLow; |
466 |
z0 = ( (uint64_t) aHigh ) * bHigh; |
467 |
zMiddleA += zMiddleB; |
468 |
z0 += ( ( (uint64_t) ( zMiddleA < zMiddleB ) )<<32 ) + ( zMiddleA>>32 ); |
469 |
zMiddleA <<= 32;
|
470 |
z1 += zMiddleA; |
471 |
z0 += ( z1 < zMiddleA ); |
472 |
*z1Ptr = z1; |
473 |
*z0Ptr = z0; |
474 |
|
475 |
} |
476 |
|
477 |
/*----------------------------------------------------------------------------
|
478 |
| Multiplies the 128-bit value formed by concatenating `a0' and `a1' by
|
479 |
| `b' to obtain a 192-bit product. The product is broken into three 64-bit
|
480 |
| pieces which are stored at the locations pointed to by `z0Ptr', `z1Ptr', and
|
481 |
| `z2Ptr'.
|
482 |
*----------------------------------------------------------------------------*/
|
483 |
|
484 |
INLINE void
|
485 |
mul128By64To192( |
486 |
uint64_t a0, |
487 |
uint64_t a1, |
488 |
uint64_t b, |
489 |
uint64_t *z0Ptr, |
490 |
uint64_t *z1Ptr, |
491 |
uint64_t *z2Ptr |
492 |
) |
493 |
{ |
494 |
uint64_t z0, z1, z2, more1; |
495 |
|
496 |
mul64To128( a1, b, &z1, &z2 ); |
497 |
mul64To128( a0, b, &z0, &more1 ); |
498 |
add128( z0, more1, 0, z1, &z0, &z1 );
|
499 |
*z2Ptr = z2; |
500 |
*z1Ptr = z1; |
501 |
*z0Ptr = z0; |
502 |
|
503 |
} |
504 |
|
505 |
/*----------------------------------------------------------------------------
|
506 |
| Multiplies the 128-bit value formed by concatenating `a0' and `a1' to the
|
507 |
| 128-bit value formed by concatenating `b0' and `b1' to obtain a 256-bit
|
508 |
| product. The product is broken into four 64-bit pieces which are stored at
|
509 |
| the locations pointed to by `z0Ptr', `z1Ptr', `z2Ptr', and `z3Ptr'.
|
510 |
*----------------------------------------------------------------------------*/
|
511 |
|
512 |
INLINE void
|
513 |
mul128To256( |
514 |
uint64_t a0, |
515 |
uint64_t a1, |
516 |
uint64_t b0, |
517 |
uint64_t b1, |
518 |
uint64_t *z0Ptr, |
519 |
uint64_t *z1Ptr, |
520 |
uint64_t *z2Ptr, |
521 |
uint64_t *z3Ptr |
522 |
) |
523 |
{ |
524 |
uint64_t z0, z1, z2, z3; |
525 |
uint64_t more1, more2; |
526 |
|
527 |
mul64To128( a1, b1, &z2, &z3 ); |
528 |
mul64To128( a1, b0, &z1, &more2 ); |
529 |
add128( z1, more2, 0, z2, &z1, &z2 );
|
530 |
mul64To128( a0, b0, &z0, &more1 ); |
531 |
add128( z0, more1, 0, z1, &z0, &z1 );
|
532 |
mul64To128( a0, b1, &more1, &more2 ); |
533 |
add128( more1, more2, 0, z2, &more1, &z2 );
|
534 |
add128( z0, z1, 0, more1, &z0, &z1 );
|
535 |
*z3Ptr = z3; |
536 |
*z2Ptr = z2; |
537 |
*z1Ptr = z1; |
538 |
*z0Ptr = z0; |
539 |
|
540 |
} |
541 |
|
542 |
/*----------------------------------------------------------------------------
|
543 |
| Returns an approximation to the 64-bit integer quotient obtained by dividing
|
544 |
| `b' into the 128-bit value formed by concatenating `a0' and `a1'. The
|
545 |
| divisor `b' must be at least 2^63. If q is the exact quotient truncated
|
546 |
| toward zero, the approximation returned lies between q and q + 2 inclusive.
|
547 |
| If the exact quotient q is larger than 64 bits, the maximum positive 64-bit
|
548 |
| unsigned integer is returned.
|
549 |
*----------------------------------------------------------------------------*/
|
550 |
|
551 |
static uint64_t estimateDiv128To64( uint64_t a0, uint64_t a1, uint64_t b )
|
552 |
{ |
553 |
uint64_t b0, b1; |
554 |
uint64_t rem0, rem1, term0, term1; |
555 |
uint64_t z; |
556 |
|
557 |
if ( b <= a0 ) return LIT64( 0xFFFFFFFFFFFFFFFF ); |
558 |
b0 = b>>32;
|
559 |
z = ( b0<<32 <= a0 ) ? LIT64( 0xFFFFFFFF00000000 ) : ( a0 / b0 )<<32; |
560 |
mul64To128( b, z, &term0, &term1 ); |
561 |
sub128( a0, a1, term0, term1, &rem0, &rem1 ); |
562 |
while ( ( (int64_t) rem0 ) < 0 ) { |
563 |
z -= LIT64( 0x100000000 );
|
564 |
b1 = b<<32;
|
565 |
add128( rem0, rem1, b0, b1, &rem0, &rem1 ); |
566 |
} |
567 |
rem0 = ( rem0<<32 ) | ( rem1>>32 ); |
568 |
z |= ( b0<<32 <= rem0 ) ? 0xFFFFFFFF : rem0 / b0; |
569 |
return z;
|
570 |
|
571 |
} |
572 |
|
573 |
/*----------------------------------------------------------------------------
|
574 |
| Returns an approximation to the square root of the 32-bit significand given
|
575 |
| by `a'. Considered as an integer, `a' must be at least 2^31. If bit 0 of
|
576 |
| `aExp' (the least significant bit) is 1, the integer returned approximates
|
577 |
| 2^31*sqrt(`a'/2^31), where `a' is considered an integer. If bit 0 of `aExp'
|
578 |
| is 0, the integer returned approximates 2^31*sqrt(`a'/2^30). In either
|
579 |
| case, the approximation returned lies strictly within +/-2 of the exact
|
580 |
| value.
|
581 |
*----------------------------------------------------------------------------*/
|
582 |
|
583 |
static uint32_t estimateSqrt32( int16 aExp, uint32_t a )
|
584 |
{ |
585 |
static const uint16_t sqrtOddAdjustments[] = { |
586 |
0x0004, 0x0022, 0x005D, 0x00B1, 0x011D, 0x019F, 0x0236, 0x02E0, |
587 |
0x039C, 0x0468, 0x0545, 0x0631, 0x072B, 0x0832, 0x0946, 0x0A67 |
588 |
}; |
589 |
static const uint16_t sqrtEvenAdjustments[] = { |
590 |
0x0A2D, 0x08AF, 0x075A, 0x0629, 0x051A, 0x0429, 0x0356, 0x029E, |
591 |
0x0200, 0x0179, 0x0109, 0x00AF, 0x0068, 0x0034, 0x0012, 0x0002 |
592 |
}; |
593 |
int8 index; |
594 |
uint32_t z; |
595 |
|
596 |
index = ( a>>27 ) & 15; |
597 |
if ( aExp & 1 ) { |
598 |
z = 0x4000 + ( a>>17 ) - sqrtOddAdjustments[ (int)index ]; |
599 |
z = ( ( a / z )<<14 ) + ( z<<15 ); |
600 |
a >>= 1;
|
601 |
} |
602 |
else {
|
603 |
z = 0x8000 + ( a>>17 ) - sqrtEvenAdjustments[ (int)index ]; |
604 |
z = a / z + z; |
605 |
z = ( 0x20000 <= z ) ? 0xFFFF8000 : ( z<<15 ); |
606 |
if ( z <= a ) return (uint32_t) ( ( (int32_t) a )>>1 ); |
607 |
} |
608 |
return ( (uint32_t) ( ( ( (uint64_t) a )<<31 ) / z ) ) + ( z>>1 ); |
609 |
|
610 |
} |
611 |
|
612 |
/*----------------------------------------------------------------------------
|
613 |
| Returns the number of leading 0 bits before the most-significant 1 bit of
|
614 |
| `a'. If `a' is zero, 32 is returned.
|
615 |
*----------------------------------------------------------------------------*/
|
616 |
|
617 |
static int8 countLeadingZeros32( uint32_t a )
|
618 |
{ |
619 |
static const int8 countLeadingZerosHigh[] = { |
620 |
8, 7, 6, 6, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, |
621 |
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, |
622 |
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, |
623 |
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, |
624 |
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, |
625 |
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, |
626 |
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, |
627 |
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, |
628 |
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, |
629 |
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, |
630 |
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, |
631 |
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, |
632 |
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, |
633 |
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, |
634 |
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, |
635 |
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
636 |
}; |
637 |
int8 shiftCount; |
638 |
|
639 |
shiftCount = 0;
|
640 |
if ( a < 0x10000 ) { |
641 |
shiftCount += 16;
|
642 |
a <<= 16;
|
643 |
} |
644 |
if ( a < 0x1000000 ) { |
645 |
shiftCount += 8;
|
646 |
a <<= 8;
|
647 |
} |
648 |
shiftCount += countLeadingZerosHigh[ a>>24 ];
|
649 |
return shiftCount;
|
650 |
|
651 |
} |
652 |
|
653 |
/*----------------------------------------------------------------------------
|
654 |
| Returns the number of leading 0 bits before the most-significant 1 bit of
|
655 |
| `a'. If `a' is zero, 64 is returned.
|
656 |
*----------------------------------------------------------------------------*/
|
657 |
|
658 |
static int8 countLeadingZeros64( uint64_t a )
|
659 |
{ |
660 |
int8 shiftCount; |
661 |
|
662 |
shiftCount = 0;
|
663 |
if ( a < ( (uint64_t) 1 )<<32 ) { |
664 |
shiftCount += 32;
|
665 |
} |
666 |
else {
|
667 |
a >>= 32;
|
668 |
} |
669 |
shiftCount += countLeadingZeros32( a ); |
670 |
return shiftCount;
|
671 |
|
672 |
} |
673 |
|
674 |
/*----------------------------------------------------------------------------
|
675 |
| Returns 1 if the 128-bit value formed by concatenating `a0' and `a1'
|
676 |
| is equal to the 128-bit value formed by concatenating `b0' and `b1'.
|
677 |
| Otherwise, returns 0.
|
678 |
*----------------------------------------------------------------------------*/
|
679 |
|
680 |
INLINE flag eq128( uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1 ) |
681 |
{ |
682 |
|
683 |
return ( a0 == b0 ) && ( a1 == b1 );
|
684 |
|
685 |
} |
686 |
|
687 |
/*----------------------------------------------------------------------------
|
688 |
| Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is less
|
689 |
| than or equal to the 128-bit value formed by concatenating `b0' and `b1'.
|
690 |
| Otherwise, returns 0.
|
691 |
*----------------------------------------------------------------------------*/
|
692 |
|
693 |
INLINE flag le128( uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1 ) |
694 |
{ |
695 |
|
696 |
return ( a0 < b0 ) || ( ( a0 == b0 ) && ( a1 <= b1 ) );
|
697 |
|
698 |
} |
699 |
|
700 |
/*----------------------------------------------------------------------------
|
701 |
| Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is less
|
702 |
| than the 128-bit value formed by concatenating `b0' and `b1'. Otherwise,
|
703 |
| returns 0.
|
704 |
*----------------------------------------------------------------------------*/
|
705 |
|
706 |
INLINE flag lt128( uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1 ) |
707 |
{ |
708 |
|
709 |
return ( a0 < b0 ) || ( ( a0 == b0 ) && ( a1 < b1 ) );
|
710 |
|
711 |
} |
712 |
|
713 |
/*----------------------------------------------------------------------------
|
714 |
| Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is
|
715 |
| not equal to the 128-bit value formed by concatenating `b0' and `b1'.
|
716 |
| Otherwise, returns 0.
|
717 |
*----------------------------------------------------------------------------*/
|
718 |
|
719 |
INLINE flag ne128( uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1 ) |
720 |
{ |
721 |
|
722 |
return ( a0 != b0 ) || ( a1 != b1 );
|
723 |
|
724 |
} |