windows-server-2003/base/wow64/mscpu/fraglib/fputrig.c

/*++

Copyright (c) 1995-2000 Microsoft Corporation

Module Name:

    fputrig.c

Abstract:

    Floating point trig and transcendental functions

Author:

    05-Oct-1995 BarryBo

Revision History:

--*/

#include <nt.h>
#include <ntrtl.h>
#include <nturtl.h>
#include <windows.h>
#include <float.h>
#include <math.h>
#include <stdio.h>
#include "wx86.h"
#include "cpuassrt.h"
#include "fragp.h"
#include "fpufragp.h"

ASSERTNAME;

//
// Forward declarations
//
NPXFUNC1(FCOS_VALID);
NPXFUNC1(FCOS_ZERO);
NPXFUNC1(FCOS_SPECIAL);
NPXFUNC1(FCOS_EMPTY);
NPXFUNC2(FPATAN_VALID_VALID);
NPXFUNC2(FPATAN_VALID_SPECIAL);
NPXFUNC2(FPATAN_SPECIAL_VALID);
NPXFUNC2(FPATAN_SPECIAL_SPECIAL);
NPXFUNC2(FPATAN_EMPTY_ALL);
NPXFUNC2(FPATAN_ALL_EMPTY);
NPXFUNC0(FPTAN_VALID);
NPXFUNC0(FPTAN_ZERO);
NPXFUNC0(FPTAN_SPECIAL);
NPXFUNC0(FSIN_VALID);
NPXFUNC0(FSIN_ZERO);
NPXFUNC0(FSIN_SPECIAL);
NPXFUNC0(FSIN_EMPTY);
NPXFUNC0(FSINCOS_VALID);
NPXFUNC0(FSINCOS_ZERO);
NPXFUNC0(FSINCOS_SPECIAL);
NPXFUNC2(FYL2X_VALID_VALID);
NPXFUNC2(FYL2X_VALID_ZERO);
NPXFUNC2(FYL2X_ZERO_VALID);
NPXFUNC2(FYL2X_ZERO_ZERO);
NPXFUNC2(FYL2X_SPECIAL_VALIDORZERO);
NPXFUNC2(FYL2X_VALIDORZERO_SPECIAL);
NPXFUNC2(FYL2X_SPECIAL_SPECIAL);
NPXFUNC2(FYL2X_ANY_EMPTY);
NPXFUNC2(FYL2X_EMPTY_ANY);
NPXFUNC2(FYL2XP1_VALIDORZERO_ZERO);
NPXFUNC2(FYL2XP1_VALIDORZERO_VALID);
NPXFUNC2(FYL2XP1_SPECIAL_VALIDORZERO);
NPXFUNC2(FYL2XP1_VALIDORZERO_SPECIAL);
NPXFUNC2(FYL2XP1_SPECIAL_SPECIAL);
NPXFUNC2(FYL2XP1_ANY_EMPTY);
NPXFUNC2(FYL2XP1_EMPTY_ANY);
NPXFUNC1(F2XM1_VALID);
NPXFUNC1(F2XM1_ZERO);
NPXFUNC1(F2XM1_SPECIAL);
NPXFUNC1(F2XM1_EMPTY);


//
// Jump tables
//
const NpxFunc1 FCOSTable[TAG_MAX] = {
    FCOS_VALID,
    FCOS_ZERO,
    FCOS_SPECIAL,
    FCOS_EMPTY
};

const NpxFunc2 FPATANTable[TAG_MAX][TAG_MAX] = {
    // left = TAG_VALID, right is ...
    { FPATAN_VALID_VALID, FPATAN_VALID_VALID, FPATAN_VALID_SPECIAL, FPATAN_ALL_EMPTY },
    // left = TAG_ZERO, right is ...
    { FPATAN_VALID_VALID, FPATAN_VALID_VALID, FPATAN_VALID_SPECIAL, FPATAN_ALL_EMPTY },
    // left = TAG_SPECIAL, right is ...
    { FPATAN_SPECIAL_VALID, FPATAN_SPECIAL_VALID, FPATAN_SPECIAL_SPECIAL, FPATAN_ALL_EMPTY },
    // left = TAG_EMPTY, right is ...
    { FPATAN_EMPTY_ALL, FPATAN_EMPTY_ALL, FPATAN_EMPTY_ALL, FPATAN_EMPTY_ALL }
};

const NpxFunc0 FPTANTable[TAG_MAX-1] = {
    FPTAN_VALID,
    FPTAN_ZERO,
    FPTAN_SPECIAL
};

const NpxFunc0 FSINTable[TAG_MAX] = {
    FSIN_VALID,
    FSIN_ZERO,
    FSIN_SPECIAL,
    FSIN_EMPTY
};

const NpxFunc0 FSINCOSTable[TAG_MAX-1] = {
    FSINCOS_VALID,
    FSINCOS_ZERO,
    FSINCOS_SPECIAL
};

// In the functions, l == ST(0), r = ST(1)
// r = r*log(l), l must be > 0
const NpxFunc2 FYL2XTable[TAG_MAX][TAG_MAX] = {
    // left is TAG_VALID, right is ...
    { FYL2X_VALID_VALID, FYL2X_VALID_ZERO, FYL2X_VALIDORZERO_SPECIAL, FYL2X_ANY_EMPTY },
    // left is TAG_ZERO, right is ...
    { FYL2X_ZERO_VALID, FYL2X_ZERO_ZERO, FYL2X_VALIDORZERO_SPECIAL, FYL2X_ANY_EMPTY },
    // left is TAG_SPECIAL, right is ...
    { FYL2X_SPECIAL_VALIDORZERO, FYL2X_SPECIAL_VALIDORZERO, FYL2X_SPECIAL_SPECIAL, FYL2X_ANY_EMPTY },
    // left is TAG_EMPTY, right is ...
    { FYL2X_EMPTY_ANY, FYL2X_EMPTY_ANY, FYL2X_EMPTY_ANY, FYL2X_EMPTY_ANY}
};

// In the functions, l == ST(0), r = ST(1)
// r = r*(logl+1), l must be > 1
const NpxFunc2 FYL2XP1Table[TAG_MAX][TAG_MAX] = {
    // left is TAG_VALID, right is ...
    { FYL2XP1_VALIDORZERO_VALID, FYL2XP1_VALIDORZERO_ZERO, FYL2XP1_VALIDORZERO_SPECIAL, FYL2XP1_ANY_EMPTY },
    // left is TAG_ZERO, right is ...
    { FYL2XP1_VALIDORZERO_VALID, FYL2XP1_VALIDORZERO_ZERO, FYL2XP1_VALIDORZERO_SPECIAL, FYL2X_ANY_EMPTY },
    // left is TAG_SPECIAL, right is ...
    { FYL2XP1_SPECIAL_VALIDORZERO, FYL2XP1_SPECIAL_VALIDORZERO, FYL2XP1_SPECIAL_SPECIAL, FYL2XP1_ANY_EMPTY },
    // left is TAG_EMPTY, right is ...
    { FYL2XP1_EMPTY_ANY, FYL2XP1_EMPTY_ANY, FYL2XP1_EMPTY_ANY, FYL2XP1_EMPTY_ANY}
};

const NpxFunc1 F2XM1Table[TAG_MAX] = {
    F2XM1_VALID,
    F2XM1_ZERO,
    F2XM1_SPECIAL,
    F2XM1_EMPTY
};



NPXFUNC1(FCOS_VALID)
{
    Fp->r64 = cos(Fp->r64);
    SetTag(Fp);
}

NPXFUNC1(FCOS_ZERO)
{
    Fp->Tag = TAG_VALID;
    Fp->r64 = 1.0;
}

NPXFUNC1(FCOS_SPECIAL)
{
    switch (Fp->TagSpecial) {
    case TAG_SPECIAL_DENORM:
        FCOS_VALID(cpu, Fp);
        break;

    case TAG_SPECIAL_INFINITY:
        cpu->FpStatusC2 = 1;
        SetIndefinite(Fp);
        break;

    case TAG_SPECIAL_SNAN:
        HandleSnan(cpu, Fp);
        break;

    case TAG_SPECIAL_QNAN:
    case TAG_SPECIAL_INDEF:
        HandleInvalidOp(cpu);
        break;
    }
}

NPXFUNC1(FCOS_EMPTY)
{
    HandleStackEmpty(cpu, Fp);
}

FRAG0(FCOS)
{
    PFPREG ST0;
    FpArithPreamble(cpu);

    cpu->FpStatusC2 = 0;
    ST0 = cpu->FpST0;
    (*FCOSTable[ST0->Tag])(cpu, ST0);
}

NPXFUNC2(FPATAN_VALID_VALID)
{
    l->r64 = Proxyatan2(l->r64, r->r64);
    SetTag(l);
    POPFLT;
}

NPXFUNC2(FPATAN_VALID_SPECIAL)
{
    switch (r->TagSpecial) {
    case TAG_SPECIAL_DENORM:
    case TAG_SPECIAL_INFINITY:
        FPATAN_VALID_VALID(cpu, l, r);
        break;

    case TAG_SPECIAL_SNAN:
        if (HandleSnan(cpu, r)) {
            break;
        }
        // else fall into QNAN

    case TAG_SPECIAL_QNAN:
    case TAG_SPECIAL_INDEF:
        // return the QNAN as the result
        l->r64 = r->r64;
        l->Tag = TAG_SPECIAL;
        l->TagSpecial = r->TagSpecial;
        POPFLT;
        break;
    }
}

NPXFUNC2(FPATAN_SPECIAL_VALID)
{
    switch (l->TagSpecial) {
    case TAG_SPECIAL_DENORM:
    case TAG_SPECIAL_INFINITY:
        FPATAN_VALID_VALID(cpu, l, r);
        break;

    case TAG_SPECIAL_SNAN:
        if (HandleSnan(cpu, l)) {
            break;
        }
        // else fall into QNAN

    case TAG_SPECIAL_QNAN:
    case TAG_SPECIAL_INDEF:
        // The QNAN is already in l, so nothing to do.
        POPFLT;
        break;
    }
}

NPXFUNC2(FPATAN_SPECIAL_SPECIAL)
{
    if (l->TagSpecial == TAG_SPECIAL_SNAN && HandleSnan(cpu, l)) {
        return;
    }
    if (r->TagSpecial == TAG_SPECIAL_SNAN && HandleSnan(cpu, r)) {
        return;
    }
    if (IS_TAG_NAN(l)) {
        if (IS_TAG_NAN(r)) {
            //
            // Return the larger of the two NANs
            //
            l->r64 = l->r64 + r->r64;
            SetTag(l);
        }
        //
        // else l is a NAN and r isn't - return the NAN in l
        //
        POPFLT;
        return;
    }
    if (IS_TAG_NAN(r)) {
        // r is a NAN and l isn't - return the NAN in l
        l->r64 = r->r64;
        l->Tag = TAG_SPECIAL;
        l->TagSpecial = r->TagSpecial;
        POPFLT;
    }

    // Otherwise, l and r are both INFINITY.  Return INDEFINITE
    CPUASSERT(l->TagSpecial == TAG_SPECIAL_INFINITY &&
              r->TagSpecial == TAG_SPECIAL_INFINITY);
    SetIndefinite(l);
    POPFLT;
}

NPXFUNC2(FPATAN_EMPTY_ALL)
{
    if (!HandleStackEmpty(cpu, l)) {
        (*FPATANTable[TAG_SPECIAL][r->Tag])(cpu, l, r);
    }
}

NPXFUNC2(FPATAN_ALL_EMPTY)
{
    if (!HandleStackEmpty(cpu, r)) {
        (*FPATANTable[l->Tag][TAG_SPECIAL])(cpu, l, r);
    }
}

FRAG0(FPATAN)
{
    PFPREG l = &cpu->FpStack[ST(1)];
    PFPREG r = cpu->FpST0;

    FpArithPreamble(cpu);
    (*FPATANTable[l->Tag][r->Tag])(cpu, l, r);
}


NPXFUNC0(FPTAN_VALID)
{
    int Exponent;
    PFPREG ST0;

    // get the exponent and make sure it is < 63
    ST0 = cpu->FpST0;
    Exponent = (int)((ST0->rdw[1] >> 20) & 0x7ff) - 1023;
    if (Exponent >= 63) {
        cpu->FpStatusC2 = 1;
        return;
    }
    ST0->r64 = tan(ST0->r64);
    SetTag(ST0);
    PUSHFLT(ST0);
    ST0->Tag = TAG_VALID;
    ST0->r64 = 1.0;
}

NPXFUNC0(FPTAN_ZERO)
{
    PFPREG ST0;

    ST0=cpu->FpST0;
    ST0->r64 = 0.0;
    ST0->Tag = TAG_ZERO;
    PUSHFLT(ST0);
    ST0->r64 = 1.0;
    ST0->Tag = TAG_VALID;
}

NPXFUNC0(FPTAN_SPECIAL)
{
    if (cpu->FpST0->TagSpecial == TAG_SPECIAL_SNAN && HandleSnan(cpu, cpu->FpST0)) {
        return;
    } else if (cpu->FpST0->TagSpecial == TAG_SPECIAL_DENORM) {
        FPTAN_VALID(cpu);
    }
    cpu->FpStatusC2 = 1;
}

FRAG0(FPTAN)
{
    PFPREG ST0;

    FpArithPreamble(cpu);

    ST0 = cpu->FpST0;

    //
    // TAG_EMPTY is handled first so that we can check ST(7) before
    // anything else has a chance to raise an exception.
    //
    if (ST0->Tag == TAG_EMPTY && HandleStackEmpty(cpu, ST0)) {
        return;
    }

    if (cpu->FpStack[ST(7)].Tag != TAG_EMPTY) {
        HandleStackFull(cpu, &cpu->FpStack[ST(7)]);
        return;
    }

    // assume no error
    cpu->FpStatusC2 = 0;

    // calculate the value
    CPUASSERT(ST0->Tag < TAG_EMPTY); // EMPTY was already handled
    (*FPTANTable[ST0->Tag])(cpu);
}

NPXFUNC0(FSIN_VALID)
{
    PFPREG ST0;

    ST0 = cpu->FpST0;
    ST0->r64 = sin(ST0->r64);
    SetTag(ST0);
}

NPXFUNC0(FSIN_ZERO)
{
    // sin(0.0) == 0.0, so there is nothing to do
}

NPXFUNC0(FSIN_SPECIAL)
{
    if (cpu->FpST0->TagSpecial == TAG_SPECIAL_SNAN && HandleSnan(cpu, cpu->FpST0)) {
        return;
    } else if (cpu->FpST0->TagSpecial == TAG_SPECIAL_DENORM) {
        FSIN_VALID(cpu);
    }
    cpu->FpStatusC2 = 1;
}

NPXFUNC0(FSIN_EMPTY)
{
    if (!HandleStackEmpty(cpu, cpu->FpST0)) {
        cpu->FpStatusC2 = 1;
    }
}

FRAG0(FSIN)
{
    FpArithPreamble(cpu);

    // assume no error
    cpu->FpStatusC2 = 0;

    // calculate the value
    (*FSINTable[cpu->FpST0->Tag])(cpu);
}

NPXFUNC0(FSINCOS_VALID)
{
    DOUBLE Val;
    PFPREG ST0;

    ST0 = cpu->FpST0;
    Val = ST0->r64;
    ST0->r64 = sin(Val);
    SetTag(ST0);
    PUSHFLT(ST0);
    ST0->r64 = cos(Val);
    SetTag(ST0);
}

NPXFUNC0(FSINCOS_ZERO)
{
    PFPREG ST0;

    ST0=cpu->FpST0;
    ST0->r64 = 0.0;
    ST0->Tag = TAG_ZERO;
    PUSHFLT(ST0);
    ST0->r64 = 1.0;
    ST0->Tag = TAG_VALID;
}

NPXFUNC0(FSINCOS_SPECIAL)
{
    switch (cpu->FpST0->TagSpecial) {
    case TAG_SPECIAL_DENORM:
        FSINCOS_VALID(cpu);
        break;

    case TAG_SPECIAL_INFINITY:
        cpu->FpStatusC2 = 1;
        SetIndefinite(cpu->FpST0);
        break;

    case TAG_SPECIAL_SNAN:
        if (HandleSnan(cpu, cpu->FpST0)) {
            return;
        }
        // else fall into TAG_SPECIAL_QNAN

    case TAG_SPECIAL_QNAN:
    case TAG_SPECIAL_INDEF:
        cpu->FpStatusC2 = 1;
        break;
    }
}

FRAG0(FSINCOS)
{
    PFPREG ST0;

    FpArithPreamble(cpu);

    // assume no errors
    cpu->FpStatusC2 = 0;

    ST0 = cpu->FpST0;
    if (ST0->Tag == TAG_EMPTY && HandleStackEmpty(cpu, ST0)) {
        return;
    }

    if (cpu->FpStack[ST(7)].Tag != TAG_EMPTY) {
        HandleStackFull(cpu, &cpu->FpStack[ST(7)]);
        return;
    }

    CPUASSERT(ST0->Tag < TAG_EMPTY); // EMPTY was already handled
    (*FSINCOSTable[ST0->Tag])(cpu);
}

NPXFUNC2(FYL2X_VALID_VALID)
{
    if (l->r64 < 0.0) {
        // ST0 is negative - invalid operation
        if (!HandleInvalidOp(cpu)) {
            SetIndefinite(r);
            POPFLT;
        }
        return;
    }
    // r = r * log10(l->r64) / log10(2)
    //
    r->r64 *= Proxylog10(l->r64) / (0.301029995664);
    SetTag(r);
    POPFLT;
}

NPXFUNC2(FYL2X_VALID_ZERO)
{
    if (l->r64 < 0.0) {
        // ST0 is negative - invalid operation
        if (!HandleInvalidOp(cpu)) {
            SetIndefinite(r);
            POPFLT;
        }
        return;
    }
    // r = r*log2(l), but r=0, so the answer is 0.
    r->r64 = 0;
    r->Tag = TAG_ZERO;
    POPFLT;
}

NPXFUNC2(FYL2X_ZERO_VALID)
{
    // Divide-by-zero error
    cpu->FpStatusExceptions |= FPCONTROL_ZM;
    if (cpu->FpControlMask & FPCONTROL_ZM) {
        // Zero-divide exception is masked - return -INFINITY
        r->r64 = R8NegativeInfinity;
        r->Tag = TAG_SPECIAL;
        r->TagSpecial = TAG_SPECIAL_INFINITY;
        POPFLT;
    } else {
        cpu->FpStatusES = 1;
    }
}

NPXFUNC2(FYL2X_ZERO_ZERO)
{
    if (!HandleInvalidOp(cpu)) {
        SetIndefinite(r);
        POPFLT;
    }
}


NPXFUNC2(FYL2X_SPECIAL_VALIDORZERO)
{
    switch (l->TagSpecial) {
    case TAG_SPECIAL_DENORM:
        (*FYL2XTable[TAG_VALID][r->Tag])(cpu, l, r);
        break;

    case TAG_SPECIAL_INFINITY:
        if (r->Tag == TAG_ZERO || r->rb[7] & 0x80) {
            // 0*infinity, or anything*-infinity
            SetIndefinite(r);
        } else {
            // return -infinity
            r->rb[7] |= 0x80;
        }
        POPFLT;
        break;

    case TAG_SPECIAL_SNAN:
        if (HandleSnan(cpu, l)) {
            return;
        }
        // else fall into TAG_SPECIAL_QNAN

    case TAG_SPECIAL_QNAN:
    case TAG_SPECIAL_INDEF:
        // l is a NAN and r is VALID or ZERO - return the NAN
        r->r64 = l->r64;
        r->Tag = l->Tag;
        r->TagSpecial = r->TagSpecial;
        POPFLT;
        break;
    }
}

NPXFUNC2(FYL2X_VALIDORZERO_SPECIAL)
{
    switch (r->TagSpecial) {
    case TAG_SPECIAL_DENORM:
        (*FYL2XTable[l->Tag][TAG_VALID])(cpu, l, r);
        break;

    case TAG_SPECIAL_INFINITY:
        // log(x)*infinity
        if (l->r64 > 1.0) {
            // return the original infinity - nothing to do
        } else if (l->r64 < 0.0 || l->r64 == 1.0) {
            if (HandleInvalidOp(cpu)) {
                return;
            }
            SetIndefinite(r);
        } else {
            // return infinity with sign flipped
            r->rb[7] ^= 0x80;
        }

        POPFLT;
        break;

    case TAG_SPECIAL_SNAN:
        if (HandleSnan(cpu, r)) {
            return;
        }
        // else fall into TAG_SPECIAL_QNAN

    case TAG_SPECIAL_QNAN:
    case TAG_SPECIAL_INDEF:
        // r is a NAN and l is VALID or ZERO - return the NAN
        POPFLT;
        break;
    }
}

NPXFUNC2(FYL2X_SPECIAL_SPECIAL)
{
    if (l->TagSpecial == TAG_SPECIAL_SNAN && HandleStackEmpty(cpu, l)) {
        return;
    }
    if (r->TagSpecial == TAG_SPECIAL_SNAN && HandleStackEmpty(cpu, r)) {
        return;
    }

    if (l->TagSpecial == TAG_SPECIAL_DENORM) {
        (*FYL2XTable[TAG_VALID][r->Tag])(cpu, l, r);
        return;
    }
    if (r->TagSpecial == TAG_SPECIAL_DENORM) {
        (*FYL2XTable[l->Tag][TAG_VALID])(cpu, l, r);
        return;
    }

    if (l->Tag == TAG_SPECIAL_INFINITY) {

        if (r->Tag == TAG_SPECIAL_INFINITY) {

            // two infinities - return INDEFINITE
            SetIndefinite(r);

        } else {
            CPUASSERT(IS_TAG_NAN(r));

            // r already has the NAN to return
        }
    } else {
        CPUASSERT(IS_TAG_NAN(l));

        if (r->Tag == TAG_SPECIAL_INFINITY) {
            //
            // Return the NAN from l
            //
            r->r64 = l->r64;
            r->TagSpecial = l->TagSpecial;
        } else {
            //
            // Return the largest of the two NANs
            //
            r->r64 = l->r64 + r->r64;
            SetTag(r);
        }
    }
    POPFLT;
}


NPXFUNC2(FYL2X_ANY_EMPTY)
{
    if (!HandleStackEmpty(cpu, r)) {
        (*FYL2XTable[l->Tag][TAG_SPECIAL])(cpu, l, r);
    }
}

NPXFUNC2(FYL2X_EMPTY_ANY)
{
    if (!HandleStackEmpty(cpu, l)) {
        (*FYL2XTable[TAG_SPECIAL][r->Tag])(cpu, l, r);
    }
}

FRAG0(FYL2X)
{
    PFPREG l, r;

    FpArithPreamble(cpu);

    l = cpu->FpST0;
    r = &cpu->FpStack[ST(1)];

    // In the functions, l == ST(0), r = ST(1)
    (*FYL2XTable[l->Tag][r->Tag])(cpu, l, r);
}



NPXFUNC2(FYL2XP1_VALIDORZERO_VALID)
{
    if (l->r64 < -1.0) {
        if (!HandleInvalidOp(cpu)) {
            SetIndefinite(r);
            POPFLT;
        }
        return;
    } else if (l->r64 == -1.0) {
        // Divide-by-zero error
        cpu->FpStatusExceptions |= FPCONTROL_ZM;
        if (cpu->FpControlMask & FPCONTROL_ZM) {
            // Zero-divide exception is masked - return -INFINITY
            r->r64 = R8NegativeInfinity;
            r->Tag = TAG_SPECIAL;
            r->TagSpecial = TAG_SPECIAL_INFINITY;
            POPFLT;
        } else {
           cpu->FpStatusES = 1;
        }
        return;
    }
    // r = r * log10(l+1) / log10(2)
    //
    r->r64 *= Proxylog10(l->r64 + 1.0) / (0.301029995664);
    SetTag(r);
    POPFLT;
}

NPXFUNC2(FYL2XP1_VALIDORZERO_ZERO)
{
    if (l->r64 < -1.0) {
        if (!HandleInvalidOp(cpu)) {
            SetIndefinite(r);
            POPFLT;
        }
        return;
    }
    // r = r*log2(l), but r=0, so the answer is 0.
    r->r64 = 0;
    r->Tag = TAG_ZERO;
    POPFLT;
}

NPXFUNC2(FYL2XP1_SPECIAL_VALIDORZERO)
{
    switch (l->TagSpecial) {
    case TAG_SPECIAL_DENORM:
        (*FYL2XP1Table[TAG_VALID][r->Tag])(cpu, l, r);
        break;

    case TAG_SPECIAL_INFINITY:
        if (r->Tag == TAG_ZERO || r->rb[7] & 0x80) {
            if (HandleInvalidOp(cpu)) {
                return;
            }

            // 0*infinity, or anything*-infinity
            SetIndefinite(r);
        } else {
            // return -infinity
            r->rb[7] |= 0x80;
        }
        POPFLT;
        break;

    case TAG_SPECIAL_SNAN:
        if (HandleSnan(cpu, l)) {
            return;
        }
        // else fall into TAG_SPECIAL_QNAN

    case TAG_SPECIAL_QNAN:
    case TAG_SPECIAL_INDEF:
        // l is a NAN and r is VALID or ZERO - return the NAN
        r->r64 = l->r64;
        r->Tag = l->Tag;
        r->TagSpecial = r->TagSpecial;
        POPFLT;
        break;
    }
}

NPXFUNC2(FYL2XP1_VALIDORZERO_SPECIAL)
{
    switch (r->TagSpecial) {
    case TAG_SPECIAL_DENORM:
        (*FYL2XP1Table[l->Tag][TAG_VALID])(cpu, l, r);
        break;

    case TAG_SPECIAL_INFINITY:
        // log(x)*infinity
        if (l->r64 > 1.0) {
            // return the original infinity - nothing to do
        } else if (l->r64 < 0.0 || l->r64 == 1.0) {
            if (HandleInvalidOp(cpu)) {
                return;
            }
            SetIndefinite(r);
        } else {
            // return infinity with sign flipped
            r->rb[7] ^= 0x80;
        }

        POPFLT;
        break;

    case TAG_SPECIAL_SNAN:
        if (HandleSnan(cpu, r)) {
            return;
        }
        // else fall into TAG_SPECIAL_QNAN

    case TAG_SPECIAL_QNAN:
    case TAG_SPECIAL_INDEF:
        // r is a NAN and l is VALID or ZERO - return the NAN
        POPFLT;
        break;
    }
}

NPXFUNC2(FYL2XP1_SPECIAL_SPECIAL)
{
    if (l->TagSpecial == TAG_SPECIAL_SNAN && HandleStackEmpty(cpu, l)) {
        return;
    }
    if (r->TagSpecial == TAG_SPECIAL_SNAN && HandleStackEmpty(cpu, r)) {
        return;
    }

    if (l->TagSpecial == TAG_SPECIAL_DENORM) {
        (*FYL2XP1Table[TAG_VALID][r->Tag])(cpu, l, r);
        return;
    }
    if (r->TagSpecial == TAG_SPECIAL_DENORM) {
        (*FYL2XP1Table[l->Tag][TAG_VALID])(cpu, l, r);
        return;
    }

    if (l->Tag == TAG_SPECIAL_INFINITY) {

        if (r->Tag == TAG_SPECIAL_INFINITY) {

            if (l->rb[7] & 0x80) {
                // l is negative infinity.  Invalid op
                if (HandleInvalidOp(cpu)) {
                    return;
                }
                SetIndefinite(r);
            }


        } else {
            CPUASSERT(IS_TAG_NAN(r));

            // r already has the NAN to return
        }
    } else {
        CPUASSERT(IS_TAG_NAN(l));

        if (r->Tag == TAG_SPECIAL_INFINITY) {
            //
            // Return the NAN from l
            //
            r->r64 = l->r64;
            r->TagSpecial = l->TagSpecial;
        } else {
            //
            // Return the largest of the two NANs
            //
            r->r64 = l->r64 + r->r64;
            SetTag(r);
        }
    }
    POPFLT;
}


NPXFUNC2(FYL2XP1_ANY_EMPTY)
{
    if (!HandleStackEmpty(cpu, r)) {
        (*FYL2XP1Table[l->Tag][TAG_SPECIAL])(cpu, l, r);
    }
}

NPXFUNC2(FYL2XP1_EMPTY_ANY)
{
    if (!HandleStackEmpty(cpu, l)) {
        (*FYL2XP1Table[TAG_SPECIAL][r->Tag])(cpu, l, r);
    }
}

FRAG0(FYL2XP1)
{
    PFPREG l, r;

    FpArithPreamble(cpu);

    l = cpu->FpST0;
    r = &cpu->FpStack[ST(1)];

    // In the functions, l == ST(0), r = ST(1)
    (*FYL2XP1Table[l->Tag][r->Tag])(cpu, l, r);
}



NPXFUNC1(F2XM1_VALID)
{
    Fp->r64 = pow(2.0, Fp->r64) - 1.0;
    SetTag(Fp);
}

NPXFUNC1(F2XM1_ZERO)
{
    // nothing to do - return the same zero
}

NPXFUNC1(F2XM1_SPECIAL)
{
    switch (Fp->TagSpecial) {
    case TAG_SPECIAL_DENORM:
        F2XM1_VALID(cpu, Fp);
        break;

    case TAG_SPECIAL_INFINITY:
        if (Fp->rb[7] & 0x80) {
            // -infinity - return 1
            Fp->r64 = 1.0;
            Fp->Tag = TAG_VALID;
        }
        // else +infinity - return +infinity
        break;

    case TAG_SPECIAL_SNAN:
        HandleSnan(cpu, Fp);
        // fall into TAG_SPECIAL_QNAN

    case TAG_SPECIAL_QNAN:
    case TAG_SPECIAL_INDEF:
        // return the NAN
        break;
    }
}

NPXFUNC1(F2XM1_EMPTY)
{
    HandleStackEmpty(cpu, Fp);
}

FRAG0(F2XM1)
{
    PFPREG ST0;

    FpArithPreamble(cpu);
    ST0 = cpu->FpST0;
    (*F2XM1Table[ST0->Tag])(cpu, ST0);
}