755 lines
24 KiB
Plaintext
755 lines
24 KiB
Plaintext
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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 2.
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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
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http://www.jhauser.us/arithmetic/SoftFloat-2b/SoftFloat-source.txt
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THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort
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has been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT
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TIMES RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO
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PERSONS AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ANY
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AND ALL LOSSES, COSTS, OR OTHER PROBLEMS ARISING FROM ITS USE.
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Derivative works are acceptable, even for commercial purposes, so long as
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(1) they include prominent notice that the work is derivative, and (2) they
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include prominent notice akin to these three paragraphs for those parts of
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this code that are retained.
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===============================================================================
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*/
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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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*/
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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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-------------------------------------------------------------------------------
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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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*/
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INLINE void shift64RightJamming( bits64 a, int16 count, bits64 *zPtr )
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{
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bits64 z;
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__asm__("@shift64RightJamming -- start");
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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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__asm__("@shift64RightJamming -- end");
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*zPtr = z;
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}
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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 a
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fixed-point value with binary point between `a0' and `a1'. This fixed-point
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value is shifted right by the number of bits given in `count', and the
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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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*/
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INLINE void
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shift64ExtraRightJamming(
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bits64 a0, bits64 a1, int16 count, bits64 *z0Ptr, bits64 *z1Ptr )
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{
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bits64 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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-------------------------------------------------------------------------------
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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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*/
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INLINE void
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shift128Right(
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bits64 a0, bits64 a1, int16 count, bits64 *z0Ptr, bits64 *z1Ptr )
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{
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bits64 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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-------------------------------------------------------------------------------
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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 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 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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*/
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INLINE void
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shift128RightJamming(
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bits64 a0, bits64 a1, int16 count, bits64 *z0Ptr, bits64 *z1Ptr )
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{
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bits64 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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-------------------------------------------------------------------------------
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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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*/
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INLINE void
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shift128ExtraRightJamming(
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bits64 a0,
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bits64 a1,
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bits64 a2,
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int16 count,
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bits64 *z0Ptr,
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bits64 *z1Ptr,
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bits64 *z2Ptr
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)
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{
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bits64 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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-------------------------------------------------------------------------------
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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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*/
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INLINE void
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shortShift128Left(
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bits64 a0, bits64 a1, int16 count, bits64 *z0Ptr, bits64 *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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-------------------------------------------------------------------------------
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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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*/
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INLINE void
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shortShift192Left(
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bits64 a0,
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bits64 a1,
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bits64 a2,
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int16 count,
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bits64 *z0Ptr,
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bits64 *z1Ptr,
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bits64 *z2Ptr
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)
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{
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bits64 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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-------------------------------------------------------------------------------
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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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*/
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INLINE void
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add128(
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bits64 a0, bits64 a1, bits64 b0, bits64 b1, bits64 *z0Ptr, bits64 *z1Ptr )
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{
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bits64 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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-------------------------------------------------------------------------------
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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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*/
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INLINE void
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add192(
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bits64 a0,
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bits64 a1,
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||
|
|
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; /* hence b0 is 32 bits wide now */
|
||
|
|
if ( b0<<32 <= a0 ) {
|
||
|
|
z = LIT64( 0xFFFFFFFF00000000 );
|
||
|
|
} else {
|
||
|
|
z = a0;
|
||
|
|
do_div( z, b0 );
|
||
|
|
z <<= 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 );
|
||
|
|
if ( b0<<32 <= rem0 ) {
|
||
|
|
z |= 0xFFFFFFFF;
|
||
|
|
} else {
|
||
|
|
do_div( rem0, b0 );
|
||
|
|
z |= rem0;
|
||
|
|
}
|
||
|
|
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;
|
||
|
|
bits64 A;
|
||
|
|
|
||
|
|
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 );
|
||
|
|
}
|
||
|
|
A = ( (bits64) a )<<31;
|
||
|
|
do_div( A, z );
|
||
|
|
return ( (bits32) A ) + ( 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 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 );
|
||
|
|
|
||
|
|
}
|
||
|
|
|