litex/software/libbase/softfloat-macros.h

/*
===============================================================================

This C source fragment is part of the SoftFloat IEC/IEEE Floating-point
Arithmetic Package, Release 2.

Written by John R. Hauser.  This work was made possible in part by the
International Computer Science Institute, located at Suite 600, 1947 Center
Street, Berkeley, California 94704.  Funding was partially provided by the
National Science Foundation under grant MIP-9311980.  The original version
of this code was written as part of a project to build a fixed-point vector
processor in collaboration with the University of California at Berkeley,
overseen by Profs. Nelson Morgan and John Wawrzynek.  More information
is available through the web page `http://HTTP.CS.Berkeley.EDU/~jhauser/
arithmetic/softfloat.html'.

THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE.  Although reasonable effort
has been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT
TIMES RESULT IN INCORRECT BEHAVIOR.  USE OF THIS SOFTWARE IS RESTRICTED TO
PERSONS AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ANY
AND ALL LOSSES, COSTS, OR OTHER PROBLEMS ARISING FROM ITS USE.

Derivative works are acceptable, even for commercial purposes, so long as
(1) they include prominent notice that the work is derivative, and (2) they
include prominent notice akin to these three paragraphs for those parts of
this code that are retained.

===============================================================================
*/

/*
-------------------------------------------------------------------------------
Shifts `a' right by the number of bits given in `count'.  If any nonzero
bits are shifted off, they are ``jammed'' into the least significant bit of
the result by setting the least significant bit to 1.  The value of `count'
can be arbitrarily large; in particular, if `count' is greater than 32, the
result will be either 0 or 1, depending on whether `a' is zero or nonzero.
The result is stored in the location pointed to by `zPtr'.
-------------------------------------------------------------------------------
*/
INLINE void shift32RightJamming( bits32 a, int16 count, bits32 *zPtr )
{
    bits32 z;

    if ( count == 0 ) {
        z = a;
    }
    else if ( count < 32 ) {
        z = ( a>>count ) | ( ( a<<( ( - count ) & 31 ) ) != 0 );
    }
    else {
        z = ( a != 0 );
    }
    *zPtr = z;

}

/*
-------------------------------------------------------------------------------
Shifts the 64-bit value formed by concatenating `a0' and `a1' right by the
number of bits given in `count'.  Any bits shifted off are lost.  The value
of `count' can be arbitrarily large; in particular, if `count' is greater
than 64, the result will be 0.  The result is broken into two 32-bit pieces
which are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
-------------------------------------------------------------------------------
*/
INLINE void
 shift64Right(
     bits32 a0, bits32 a1, int16 count, bits32 *z0Ptr, bits32 *z1Ptr )
{
    bits32 z0, z1;
    int8 negCount = ( - count ) & 31;

    if ( count == 0 ) {
        z1 = a1;
        z0 = a0;
    }
    else if ( count < 32 ) {
        z1 = ( a0<<negCount ) | ( a1>>count );
        z0 = a0>>count;
    }
    else {
        z1 = ( count < 64 ) ? ( a0>>( count & 31 ) ) : 0;
        z0 = 0;
    }
    *z1Ptr = z1;
    *z0Ptr = z0;

}

/*
-------------------------------------------------------------------------------
Shifts the 64-bit value formed by concatenating `a0' and `a1' right by the
number of bits given in `count'.  If any nonzero bits are shifted off, they
are ``jammed'' into the least significant bit of the result by setting the
least significant bit to 1.  The value of `count' can be arbitrarily large;
in particular, if `count' is greater than 64, the result will be either 0
or 1, depending on whether the concatenation of `a0' and `a1' is zero or
nonzero.  The result is broken into two 32-bit pieces which are stored at
the locations pointed to by `z0Ptr' and `z1Ptr'.
-------------------------------------------------------------------------------
*/
INLINE void
 shift64RightJamming(
     bits32 a0, bits32 a1, int16 count, bits32 *z0Ptr, bits32 *z1Ptr )
{
    bits32 z0, z1;
    int8 negCount = ( - count ) & 31;

    if ( count == 0 ) {
        z1 = a1;
        z0 = a0;
    }
    else if ( count < 32 ) {
        z1 = ( a0<<negCount ) | ( a1>>count ) | ( ( a1<<negCount ) != 0 );
        z0 = a0>>count;
    }
    else {
        if ( count == 32 ) {
            z1 = a0 | ( a1 != 0 );
        }
        else if ( count < 64 ) {
            z1 = ( a0>>( count & 31 ) ) | ( ( ( a0<<negCount ) | a1 ) != 0 );
        }
        else {
            z1 = ( ( a0 | a1 ) != 0 );
        }
        z0 = 0;
    }
    *z1Ptr = z1;
    *z0Ptr = z0;

}

/*
-------------------------------------------------------------------------------
Shifts the 96-bit value formed by concatenating `a0', `a1', and `a2' right
by 32 _plus_ the number of bits given in `count'.  The shifted result is
at most 64 nonzero bits; these are broken into two 32-bit pieces which are
stored at the locations pointed to by `z0Ptr' and `z1Ptr'.  The bits shifted
off form a third 32-bit result as follows:  The _last_ bit shifted off is
the most-significant bit of the extra result, and the other 31 bits of the
extra result are all zero if and only if _all_but_the_last_ bits shifted off
were all zero.  This extra result is stored in the location pointed to by
`z2Ptr'.  The value of `count' can be arbitrarily large.
    (This routine makes more sense if `a0', `a1', and `a2' are considered
to form a fixed-point value with binary point between `a1' and `a2'.  This
fixed-point value is shifted right by the number of bits given in `count',
and the integer part of the result is returned at the locations pointed to
by `z0Ptr' and `z1Ptr'.  The fractional part of the result may be slightly
corrupted as described above, and is returned at the location pointed to by
`z2Ptr'.)
-------------------------------------------------------------------------------
*/
INLINE void
 shift64ExtraRightJamming(
     bits32 a0,
     bits32 a1,
     bits32 a2,
     int16 count,
     bits32 *z0Ptr,
     bits32 *z1Ptr,
     bits32 *z2Ptr
 )
{
    bits32 z0, z1, z2;
    int8 negCount = ( - count ) & 31;

    if ( count == 0 ) {
        z2 = a2;
        z1 = a1;
        z0 = a0;
    }
    else {
        if ( count < 32 ) {
            z2 = a1<<negCount;
            z1 = ( a0<<negCount ) | ( a1>>count );
            z0 = a0>>count;
        }
        else {
            if ( count == 32 ) {
                z2 = a1;
                z1 = a0;
            }
            else {
                a2 |= a1;
                if ( count < 64 ) {
                    z2 = a0<<negCount;
                    z1 = a0>>( count & 31 );
                }
                else {
                    z2 = ( count == 64 ) ? a0 : ( a0 != 0 );
                    z1 = 0;
                }
            }
            z0 = 0;
        }
        z2 |= ( a2 != 0 );
    }
    *z2Ptr = z2;
    *z1Ptr = z1;
    *z0Ptr = z0;

}

/*
-------------------------------------------------------------------------------
Shifts the 64-bit value formed by concatenating `a0' and `a1' left by the
number of bits given in `count'.  Any bits shifted off are lost.  The value
of `count' must be less than 32.  The result is broken into two 32-bit
pieces which are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
-------------------------------------------------------------------------------
*/
INLINE void
 shortShift64Left(
     bits32 a0, bits32 a1, int16 count, bits32 *z0Ptr, bits32 *z1Ptr )
{

    *z1Ptr = a1<<count;
    *z0Ptr =
        ( count == 0 ) ? a0 : ( a0<<count ) | ( a1>>( ( - count ) & 31 ) );

}

/*
-------------------------------------------------------------------------------
Shifts the 96-bit value formed by concatenating `a0', `a1', and `a2' left by
the number of bits given in `count'.  Any bits shifted off are lost.  The
value of `count' must be less than 32.  The result is broken into three
32-bit pieces which are stored at the locations pointed to by `z0Ptr',
`z1Ptr', and `z2Ptr'.
-------------------------------------------------------------------------------
*/
INLINE void
 shortShift96Left(
     bits32 a0,
     bits32 a1,
     bits32 a2,
     int16 count,
     bits32 *z0Ptr,
     bits32 *z1Ptr,
     bits32 *z2Ptr
 )
{
    bits32 z0, z1, z2;
    int8 negCount;

    z2 = a2<<count;
    z1 = a1<<count;
    z0 = a0<<count;
    if ( 0 < count ) {
        negCount = ( ( - count ) & 31 );
        z1 |= a2>>negCount;
        z0 |= a1>>negCount;
    }
    *z2Ptr = z2;
    *z1Ptr = z1;
    *z0Ptr = z0;

}

/*
-------------------------------------------------------------------------------
Adds the 64-bit value formed by concatenating `a0' and `a1' to the 64-bit
value formed by concatenating `b0' and `b1'.  Addition is modulo 2^64, so
any carry out is lost.  The result is broken into two 32-bit pieces which
are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
-------------------------------------------------------------------------------
*/
INLINE void
 add64(
     bits32 a0, bits32 a1, bits32 b0, bits32 b1, bits32 *z0Ptr, bits32 *z1Ptr )
{
    bits32 z1;

    z1 = a1 + b1;
    *z1Ptr = z1;
    *z0Ptr = a0 + b0 + ( z1 < a1 );

}

/*
-------------------------------------------------------------------------------
Adds the 96-bit value formed by concatenating `a0', `a1', and `a2' to the
96-bit value formed by concatenating `b0', `b1', and `b2'.  Addition is
modulo 2^96, so any carry out is lost.  The result is broken into three
32-bit pieces which are stored at the locations pointed to by `z0Ptr',
`z1Ptr', and `z2Ptr'.
-------------------------------------------------------------------------------
*/
INLINE void
 add96(
     bits32 a0,
     bits32 a1,
     bits32 a2,
     bits32 b0,
     bits32 b1,
     bits32 b2,
     bits32 *z0Ptr,
     bits32 *z1Ptr,
     bits32 *z2Ptr
 )
{
    bits32 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 64-bit value formed by concatenating `b0' and `b1' from the
64-bit value formed by concatenating `a0' and `a1'.  Subtraction is modulo
2^64, so any borrow out (carry out) is lost.  The result is broken into two
32-bit pieces which are stored at the locations pointed to by `z0Ptr' and
`z1Ptr'.
-------------------------------------------------------------------------------
*/
INLINE void
 sub64(
     bits32 a0, bits32 a1, bits32 b0, bits32 b1, bits32 *z0Ptr, bits32 *z1Ptr )
{

    *z1Ptr = a1 - b1;
    *z0Ptr = a0 - b0 - ( a1 < b1 );

}

/*
-------------------------------------------------------------------------------
Subtracts the 96-bit value formed by concatenating `b0', `b1', and `b2' from
the 96-bit value formed by concatenating `a0', `a1', and `a2'.  Subtraction
is modulo 2^96, so any borrow out (carry out) is lost.  The result is broken
into three 32-bit pieces which are stored at the locations pointed to by
`z0Ptr', `z1Ptr', and `z2Ptr'.
-------------------------------------------------------------------------------
*/
INLINE void
 sub96(
     bits32 a0,
     bits32 a1,
     bits32 a2,
     bits32 b0,
     bits32 b1,
     bits32 b2,
     bits32 *z0Ptr,
     bits32 *z1Ptr,
     bits32 *z2Ptr
 )
{
    bits32 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 64-bit product.  The product is broken
into two 32-bit pieces which are stored at the locations pointed to by
`z0Ptr' and `z1Ptr'.
-------------------------------------------------------------------------------
*/
INLINE void mul32To64( bits32 a, bits32 b, bits32 *z0Ptr, bits32 *z1Ptr )
{
    bits16 aHigh, aLow, bHigh, bLow;
    bits32 z0, zMiddleA, zMiddleB, z1;

    aLow = a;
    aHigh = a>>16;
    bLow = b;
    bHigh = b>>16;
    z1 = ( (bits32) aLow ) * bLow;
    zMiddleA = ( (bits32) aLow ) * bHigh;
    zMiddleB = ( (bits32) aHigh ) * bLow;
    z0 = ( (bits32) aHigh ) * bHigh;
    zMiddleA += zMiddleB;
    z0 += ( ( (bits32) ( zMiddleA < zMiddleB ) )<<16 ) + ( zMiddleA>>16 );
    zMiddleA <<= 16;
    z1 += zMiddleA;
    z0 += ( z1 < zMiddleA );
    *z1Ptr = z1;
    *z0Ptr = z0;

}

/*
-------------------------------------------------------------------------------
Multiplies the 64-bit value formed by concatenating `a0' and `a1' by `b' to
obtain a 96-bit product.  The product is broken into three 32-bit pieces
which are stored at the locations pointed to by `z0Ptr', `z1Ptr', and
`z2Ptr'.
-------------------------------------------------------------------------------
*/
INLINE void
 mul64By32To96(
     bits32 a0,
     bits32 a1,
     bits32 b,
     bits32 *z0Ptr,
     bits32 *z1Ptr,
     bits32 *z2Ptr
 )
{
    bits32 z0, z1, z2, more1;

    mul32To64( a1, b, &z1, &z2 );
    mul32To64( a0, b, &z0, &more1 );
    add64( z0, more1, 0, z1, &z0, &z1 );
    *z2Ptr = z2;
    *z1Ptr = z1;
    *z0Ptr = z0;

}

/*
-------------------------------------------------------------------------------
Multiplies the 64-bit value formed by concatenating `a0' and `a1' to the
64-bit value formed by concatenating `b0' and `b1' to obtain a 128-bit
product.  The product is broken into four 32-bit pieces which are stored at
the locations pointed to by `z0Ptr', `z1Ptr', `z2Ptr', and `z3Ptr'.
-------------------------------------------------------------------------------
*/
INLINE void
 mul64To128(
     bits32 a0,
     bits32 a1,
     bits32 b0,
     bits32 b1,
     bits32 *z0Ptr,
     bits32 *z1Ptr,
     bits32 *z2Ptr,
     bits32 *z3Ptr
 )
{
    bits32 z0, z1, z2, z3;
    bits32 more1, more2;

    mul32To64( a1, b1, &z2, &z3 );
    mul32To64( a1, b0, &z1, &more2 );
    add64( z1, more2, 0, z2, &z1, &z2 );
    mul32To64( a0, b0, &z0, &more1 );
    add64( z0, more1, 0, z1, &z0, &z1 );
    mul32To64( a0, b1, &more1, &more2 );
    add64( more1, more2, 0, z2, &more1, &z2 );
    add64( z0, z1, 0, more1, &z0, &z1 );
    *z3Ptr = z3;
    *z2Ptr = z2;
    *z1Ptr = z1;
    *z0Ptr = z0;

}

/*
-------------------------------------------------------------------------------
Returns an approximation to the 32-bit integer quotient obtained by dividing
`b' into the 64-bit value formed by concatenating `a0' and `a1'.  The divisor
`b' must be at least 2^31.  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 32 bits, the maximum positive 32-bit
unsigned integer is returned.
-------------------------------------------------------------------------------
*/
static bits32 estimateDiv64To32( bits32 a0, bits32 a1, bits32 b )
{
    bits32 b0, b1;
    bits32 rem0, rem1, term0, term1;
    bits32 z;

    if ( b <= a0 ) return 0xFFFFFFFF;
    b0 = b>>16;
    z = ( b0<<16 <= a0 ) ? 0xFFFF0000 : ( a0 / b0 )<<16;
    mul32To64( b, z, &term0, &term1 );
    sub64( a0, a1, term0, term1, &rem0, &rem1 );
    while ( ( (sbits32) rem0 ) < 0 ) {
        z -= 0x10000;
        b1 = b<<16;
        add64( rem0, rem1, b0, b1, &rem0, &rem1 );
    }
    rem0 = ( rem0<<16 ) | ( rem1>>16 );
    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 );

}