Bochs/bochs/cpu/softfloat-macros.h

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

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://www.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 ALL LOSSES,
COSTS, OR OTHER PROBLEMS THEY INCUR DUE TO THE SOFTWARE, AND WHO FURTHERMORE
EFFECTIVELY INDEMNIFY JOHN HAUSER AND THE INTERNATIONAL COMPUTER SCIENCE
INSTITUTE (possibly via similar legal notice) AGAINST ALL LOSSES, COSTS, OR
OTHER PROBLEMS INCURRED BY THEIR CUSTOMERS AND CLIENTS DUE TO THE SOFTWARE.

Derivative works are acceptable, even for commercial purposes, so long as
(1) the source code for the derivative work includes prominent notice that
the work is derivative, and (2) the source code includes prominent notice with
these four paragraphs for those parts of this code that are retained.
=============================================================================*/

/*============================================================================
 * Adapted for Bochs (x86 achitecture simulator) by
 *            Stanislav Shwartsman (gate@fidonet.org.il)
 * ==========================================================================*/ 

/*----------------------------------------------------------------------------
| 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'.
*----------------------------------------------------------------------------*/

BX_CPP_INLINE void shift32RightJamming(Bit32u a, Bit16s count, Bit32u *zPtr)
{
    Bit32u z;

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

/*----------------------------------------------------------------------------
| Shifts `a' right by the number of bits given in `count'.  If any nonzero
| bits are shifted off, they are ``jammed'' into the least significant bit of
| the result by setting the least significant bit to 1.  The value of `count'
| can be arbitrarily large; in particular, if `count' is greater than 64, the
| result will be either 0 or 1, depending on whether `a' is zero or nonzero.
| The result is stored in the location pointed to by `zPtr'.
*----------------------------------------------------------------------------*/

BX_CPP_INLINE void shift64RightJamming(Bit64u a, Bit16s count, Bit64u *zPtr)
{
    Bit64u z;

    if (count == 0) {
        z = a;
    }
    else if (count < 64) {
        z = (a>>count) | ((a<<((-count) & 63)) != 0);
    }
    else {
        z = (a != 0);
    }
    *zPtr = z;
}

/*----------------------------------------------------------------------------
| Shifts the 128-bit value formed by concatenating `a0' and `a1' right by 64
| _plus_ the number of bits given in `count'.  The shifted result is at most
| 64 nonzero bits; this is stored at the location pointed to by `z0Ptr'.  The
| bits shifted off form a second 64-bit result as follows:  The _last_ bit
| shifted off is the most-significant bit of the extra result, and the other
| 63 bits of the extra result are all zero if and only if _all_but_the_last_
| bits shifted off were all zero.  This extra result is stored in the location
| pointed to by `z1Ptr'.  The value of `count' can be arbitrarily large.
|     (This routine makes more sense if `a0' and `a1' are considered to form
| a fixed-point value with binary point between `a0' and `a1'.  This fixed-
| point value is shifted right by the number of bits given in `count', and
| the integer part of the result is returned at the location pointed to by
| `z0Ptr'.  The fractional part of the result may be slightly corrupted as
| described above, and is returned at the location pointed to by `z1Ptr'.)
*----------------------------------------------------------------------------*/

BX_CPP_INLINE void
 shift64ExtraRightJamming(
     Bit64u a0, Bit64u a1, Bit16s count, Bit64u *z0Ptr, Bit64u *z1Ptr)
{
    Bit64u z0, z1;
    Bit8s negCount = (-count) & 63;

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

/*----------------------------------------------------------------------------
| Adds the 128-bit value formed by concatenating `a0' and `a1' to the 128-bit
| value formed by concatenating `b0' and `b1'.  Addition is modulo 2^128, so
| any carry out is lost.  The result is broken into two 64-bit pieces which
| are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
*----------------------------------------------------------------------------*/

BX_CPP_INLINE void
 add128(Bit64u a0, Bit64u a1, Bit64u b0, Bit64u b1, Bit64u *z0Ptr, Bit64u *z1Ptr)
{
    Bit64u z1;

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

/*----------------------------------------------------------------------------
| 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'.
*----------------------------------------------------------------------------*/

BX_CPP_INLINE void
 sub128(Bit64u a0, Bit64u a1, Bit64u b0, Bit64u b1, Bit64u *z0Ptr, Bit64u *z1Ptr)
{

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

/*----------------------------------------------------------------------------
| 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'.
*----------------------------------------------------------------------------*/

BX_CPP_INLINE void mul64To128(Bit64u a, Bit64u b, Bit64u *z0Ptr, Bit64u *z1Ptr)
{
    Bit32u aHigh, aLow, bHigh, bLow;
    Bit64u z0, zMiddleA, zMiddleB, z1;

    aLow = a;
    aHigh = a>>32;
    bLow = b;
    bHigh = b>>32;
    z1 = ((Bit64u) aLow) * bLow;
    zMiddleA = ((Bit64u) aLow) * bHigh;
    zMiddleB = ((Bit64u) aHigh) * bLow;
    z0 = ((Bit64u) aHigh) * bHigh;
    zMiddleA += zMiddleB;
    z0 += (((Bit64u) (zMiddleA < zMiddleB))<<32) + (zMiddleA>>32);
    zMiddleA <<= 32;
    z1 += zMiddleA;
    z0 += (z1 < zMiddleA);
    *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 Bit64u estimateDiv128To64(Bit64u a0, Bit64u a1, Bit64u b)
{
    Bit64u b0, b1;
    Bit64u rem0, rem1, term0, term1;
    Bit64u z;

    if (b <= a0) return BX_CONST64(0xFFFFFFFFFFFFFFFF);
    b0 = b>>32;
    z = (b0<<32 <= a0) ? BX_CONST64(0xFFFFFFFF00000000) : (a0 / b0)<<32;
    mul64To128(b, z, &term0, &term1);
    sub128(a0, a1, term0, term1, &rem0, &rem1);
    while (((Bit64s) rem0) < 0) {
        z -= BX_CONST64(0x100000000);
        b1 = b<<32;
        add128(rem0, rem1, b0, b1, &rem0, &rem1);
    }
    rem0 = (rem0<<32) | (rem1>>32);
    z |= (b0<<32 <= rem0) ? 0xFFFFFFFF : rem0 / b0;
    return z;
}

/*----------------------------------------------------------------------------
| 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 Bit32u estimateSqrt32(Bit16s aExp, Bit32u a)
{
    static const Bit16u sqrtOddAdjustments[] = {
        0x0004, 0x0022, 0x005D, 0x00B1, 0x011D, 0x019F, 0x0236, 0x02E0,
        0x039C, 0x0468, 0x0545, 0x0631, 0x072B, 0x0832, 0x0946, 0x0A67
    };
    static const Bit16u sqrtEvenAdjustments[] = {
        0x0A2D, 0x08AF, 0x075A, 0x0629, 0x051A, 0x0429, 0x0356, 0x029E,
        0x0200, 0x0179, 0x0109, 0x00AF, 0x0068, 0x0034, 0x0012, 0x0002
    };
    Bit8s index;
    Bit32u 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 (Bit32u) (((Bit32s) a)>>1);
    }
    return ((Bit32u) ((((Bit64u) a)<<31) / z)) + (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 int countLeadingZeros32(Bit32u a)
{
    static const Bit8s 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
    };
    Bit8s 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 int countLeadingZeros64(Bit64u a)
{
    Bit8s shiftCount;

    shiftCount = 0;
    if (a < ((Bit64u) 1)<<32) {
        shiftCount += 32;
    }
    else {
        a >>= 32;
    }
    shiftCount += countLeadingZeros32(a);
    return shiftCount;
}