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        .file "reg_round.S"
/*---------------------------------------------------------------------------+
 |  reg_round.S                                                              |
 |                                                                           |
 | Rounding/truncation/etc for FPU basic arithmetic functions.               |
 |                                                                           |
 | Copyright (C) 1993,1995                                                   |
 |                       W. Metzenthen, 22 Parker St, Ormond, Vic 3163,      |
 |                       Australia.  E-mail billm@jacobi.maths.monash.edu.au |
 |                                                                           |
 | This code has four possible entry points.                                 |
 | The following must be entered by a jmp instruction:                       |
 |   fpu_reg_round, fpu_reg_round_sqrt, and fpu_Arith_exit.                  |
 |                                                                           |
 | The _round_reg entry point is intended to be used by C code.              |
 | From C, call as:                                                          |
 | void round_reg(FPU_REG *arg, unsigned int extent, unsigned int control_w) |
 |                                                                           |
 | For correct "up" and "down" rounding, the argument must have the correct  |
 | sign.                                                                     |
 |                                                                           |
 +---------------------------------------------------------------------------*/

/*---------------------------------------------------------------------------+
 | Four entry points.                                                        |
 |                                                                           |
 | Needed by both the fpu_reg_round and fpu_reg_round_sqrt entry points:     |
 |  %eax:%ebx  64 bit significand                                            |
 |  %edx       32 bit extension of the significand                           |
 |  %edi       pointer to an FPU_REG for the result to be stored             |
 |  stack      calling function must have set up a C stack frame and         |
 |             pushed %esi, %edi, and %ebx                                   |
 |                                                                           |
 | Needed just for the fpu_reg_round_sqrt entry point:                       |
 |  %cx  A control word in the same format as the FPU control word.          |
 | Otherwise, PARAM4 must give such a value.                                 |
 |                                                                           |
 |                                                                           |
 | The significand and its extension are assumed to be exact in the          |
 | following sense:                                                          |
 |   If the significand by itself is the exact result then the significand   |
 |   extension (%edx) must contain 0, otherwise the significand extension    |
 |   must be non-zero.                                                       |
 |   If the significand extension is non-zero then the significand is        |
 |   smaller than the magnitude of the correct exact result by an amount     |
 |   greater than zero and less than one ls bit of the significand.          |
 |   The significand extension is only required to have three possible       |
 |   non-zero values:                                                        |
 |       less than 0x80000000  <=> the significand is less than 1/2 an ls    |
 |                                 bit smaller than the magnitude of the     |
 |                                 true exact result.                        |
 |         exactly 0x80000000  <=> the significand is exactly 1/2 an ls bit  |
 |                                 smaller than the magnitude of the true    |
 |                                 exact result.                             |
 |    greater than 0x80000000  <=> the significand is more than 1/2 an ls    |
 |                                 bit smaller than the magnitude of the     |
 |                                 true exact result.                        |
 |                                                                           |
 +---------------------------------------------------------------------------*/

/*---------------------------------------------------------------------------+
 |  The code in this module has become quite complex, but it should handle   |
 |  all of the FPU flags which are set at this stage of the basic arithmetic |
 |  computations.                                                            |
 |  There are a few rare cases where the results are not set identically to  |
 |  a real FPU. These require a bit more thought because at this stage the   |
 |  results of the code here appear to be more consistent...                 |
 |  This may be changed in a future version.                                 |
 +---------------------------------------------------------------------------*/


#include "fpu_emu.h"
#include "exception.h"
#include "control_w.h"

/* Flags for FPU_bits_lost */
#define LOST_DOWN       $1
#define LOST_UP         $2

/* Flags for FPU_denormal */
#define DENORMAL        $1
#define UNMASKED_UNDERFLOW $2


#ifndef NON_REENTRANT_FPU
/*      Make the code re-entrant by putting
        local storage on the stack: */
#define FPU_bits_lost   (%esp)
#define FPU_denormal    1(%esp)

#else
/*      Not re-entrant, so we can gain speed by putting
        local storage in a static area: */
.data
        .align 2,0
FPU_bits_lost:
        .byte   0
FPU_denormal:
        .byte   0
#endif NON_REENTRANT_FPU


.text
.globl fpu_reg_round
.globl fpu_reg_round_sqrt
.globl fpu_Arith_exit

/* Entry point when called from C */
ENTRY(round_reg)
        pushl   %ebp
        movl    %esp,%ebp
        pushl   %esi
        pushl   %edi
        pushl   %ebx

        movl    PARAM1,%edi
        movl    SIGH(%edi),%eax
        movl    SIGL(%edi),%ebx
        movl    PARAM2,%edx
        movl    PARAM3,%ecx
        jmp     fpu_reg_round_sqrt

fpu_reg_round:                  /* Normal entry point */
        movl    PARAM4,%ecx

fpu_reg_round_sqrt:             /* Entry point from wm_sqrt.S */

#ifndef NON_REENTRANT_FPU
        pushl   %ebx            /* adjust the stack pointer */
#endif NON_REENTRANT_FPU

#ifdef PARANOID
/* Cannot use this here yet */
/*      orl     %eax,%eax */
/*      jns     L_entry_bugged */
#endif PARANOID

        cmpl    EXP_UNDER,EXP(%edi)
        jle     xMake_denorm                    /* The number is a de-normal */

        movb    $0,FPU_denormal                 /* 0 -> not a de-normal */

xDenorm_done:
        movb    $0,FPU_bits_lost                /* No bits yet lost in rounding */

        movl    %ecx,%esi
        andl    CW_PC,%ecx
        cmpl    PR_64_BITS,%ecx
        je      LRound_To_64

        cmpl    PR_53_BITS,%ecx
        je      LRound_To_53

        cmpl    PR_24_BITS,%ecx
        je      LRound_To_24

#ifdef PECULIAR_486
/* With the precision control bits set to 01 "(reserved)", a real 80486
   behaves as if the precision control bits were set to 11 "64 bits" */
        cmpl    PR_RESERVED_BITS,%ecx
        je      LRound_To_64
#ifdef PARANOID
        jmp     L_bugged_denorm_486
#endif PARANOID
#else
#ifdef PARANOID
        jmp     L_bugged_denorm /* There is no bug, just a bad control word */
#endif PARANOID
#endif PECULIAR_486


/* Round etc to 24 bit precision */
LRound_To_24:
        movl    %esi,%ecx
        andl    CW_RC,%ecx
        cmpl    RC_RND,%ecx
        je      LRound_nearest_24

        cmpl    RC_CHOP,%ecx
        je      LCheck_truncate_24

        cmpl    RC_UP,%ecx              /* Towards +infinity */
        je      LUp_24

        cmpl    RC_DOWN,%ecx            /* Towards -infinity */
        je      LDown_24

#ifdef PARANOID
        jmp     L_bugged_round24
#endif PARANOID

LUp_24:
        cmpb    SIGN_POS,SIGN(%edi)
        jne     LCheck_truncate_24      /* If negative then  up==truncate */

        jmp     LCheck_24_round_up

LDown_24:
        cmpb    SIGN_POS,SIGN(%edi)
        je      LCheck_truncate_24      /* If positive then  down==truncate */

LCheck_24_round_up:
        movl    %eax,%ecx
        andl    $0x000000ff,%ecx
        orl     %ebx,%ecx
        orl     %edx,%ecx
        jnz     LDo_24_round_up
        jmp     LRe_normalise

LRound_nearest_24:
        /* Do rounding of the 24th bit if needed (nearest or even) */
        movl    %eax,%ecx
        andl    $0x000000ff,%ecx
        cmpl    $0x00000080,%ecx
        jc      LCheck_truncate_24      /* less than half, no increment needed */

        jne     LGreater_Half_24        /* greater than half, increment needed */

        /* Possibly half, we need to check the ls bits */
        orl     %ebx,%ebx
        jnz     LGreater_Half_24        /* greater than half, increment needed */

        orl     %edx,%edx
        jnz     LGreater_Half_24        /* greater than half, increment needed */

        /* Exactly half, increment only if 24th bit is 1 (round to even) */
        testl   $0x00000100,%eax
        jz      LDo_truncate_24

LGreater_Half_24:                       /* Rounding: increment at the 24th bit */
LDo_24_round_up:
        andl    $0xffffff00,%eax        /* Truncate to 24 bits */
        xorl    %ebx,%ebx
        movb    LOST_UP,FPU_bits_lost
        addl    $0x00000100,%eax
        jmp     LCheck_Round_Overflow

LCheck_truncate_24:
        movl    %eax,%ecx
        andl    $0x000000ff,%ecx
        orl     %ebx,%ecx
        orl     %edx,%ecx
        jz      LRe_normalise           /* No truncation needed */

LDo_truncate_24:
        andl    $0xffffff00,%eax        /* Truncate to 24 bits */
        xorl    %ebx,%ebx
        movb    LOST_DOWN,FPU_bits_lost
        jmp     LRe_normalise


/* Round etc to 53 bit precision */
LRound_To_53:
        movl    %esi,%ecx
        andl    CW_RC,%ecx
        cmpl    RC_RND,%ecx
        je      LRound_nearest_53

        cmpl    RC_CHOP,%ecx
        je      LCheck_truncate_53

        cmpl    RC_UP,%ecx              /* Towards +infinity */
        je      LUp_53

        cmpl    RC_DOWN,%ecx            /* Towards -infinity */
        je      LDown_53

#ifdef PARANOID
        jmp     L_bugged_round53
#endif PARANOID

LUp_53:
        cmpb    SIGN_POS,SIGN(%edi)
        jne     LCheck_truncate_53      /* If negative then  up==truncate */

        jmp     LCheck_53_round_up

LDown_53:
        cmpb    SIGN_POS,SIGN(%edi)
        je      LCheck_truncate_53      /* If positive then  down==truncate */

LCheck_53_round_up:
        movl    %ebx,%ecx
        andl    $0x000007ff,%ecx
        orl     %edx,%ecx
        jnz     LDo_53_round_up
        jmp     LRe_normalise

LRound_nearest_53:
        /* Do rounding of the 53rd bit if needed (nearest or even) */
        movl    %ebx,%ecx
        andl    $0x000007ff,%ecx
        cmpl    $0x00000400,%ecx
        jc      LCheck_truncate_53      /* less than half, no increment needed */

        jnz     LGreater_Half_53        /* greater than half, increment needed */

        /* Possibly half, we need to check the ls bits */
        orl     %edx,%edx
        jnz     LGreater_Half_53        /* greater than half, increment needed */

        /* Exactly half, increment only if 53rd bit is 1 (round to even) */
        testl   $0x00000800,%ebx
        jz      LTruncate_53

LGreater_Half_53:                       /* Rounding: increment at the 53rd bit */
LDo_53_round_up:
        movb    LOST_UP,FPU_bits_lost
        andl    $0xfffff800,%ebx        /* Truncate to 53 bits */
        addl    $0x00000800,%ebx
        adcl    $0,%eax
        jmp     LCheck_Round_Overflow

LCheck_truncate_53:
        movl    %ebx,%ecx
        andl    $0x000007ff,%ecx
        orl     %edx,%ecx
        jz      LRe_normalise

LTruncate_53:
        movb    LOST_DOWN,FPU_bits_lost
        andl    $0xfffff800,%ebx        /* Truncate to 53 bits */
        jmp     LRe_normalise


/* Round etc to 64 bit precision */
LRound_To_64:
        movl    %esi,%ecx
        andl    CW_RC,%ecx
        cmpl    RC_RND,%ecx
        je      LRound_nearest_64

        cmpl    RC_CHOP,%ecx
        je      LCheck_truncate_64

        cmpl    RC_UP,%ecx              /* Towards +infinity */
        je      LUp_64

        cmpl    RC_DOWN,%ecx            /* Towards -infinity */
        je      LDown_64

#ifdef PARANOID
        jmp     L_bugged_round64
#endif PARANOID

LUp_64:
        cmpb    SIGN_POS,SIGN(%edi)
        jne     LCheck_truncate_64      /* If negative then  up==truncate */

        orl     %edx,%edx
        jnz     LDo_64_round_up
        jmp     LRe_normalise

LDown_64:
        cmpb    SIGN_POS,SIGN(%edi)
        je      LCheck_truncate_64      /* If positive then  down==truncate */

        orl     %edx,%edx
        jnz     LDo_64_round_up
        jmp     LRe_normalise

LRound_nearest_64:
        cmpl    $0x80000000,%edx
        jc      LCheck_truncate_64

        jne     LDo_64_round_up

        /* Now test for round-to-even */
        testb   $1,%ebx
        jz      LCheck_truncate_64

LDo_64_round_up:
        movb    LOST_UP,FPU_bits_lost
        addl    $1,%ebx
        adcl    $0,%eax

LCheck_Round_Overflow:
        jnc     LRe_normalise

        /* Overflow, adjust the result (significand to 1.0) */
        rcrl    $1,%eax
        rcrl    $1,%ebx
        incl    EXP(%edi)
        jmp     LRe_normalise

LCheck_truncate_64:
        orl     %edx,%edx
        jz      LRe_normalise

LTruncate_64:
        movb    LOST_DOWN,FPU_bits_lost

LRe_normalise:
        testb   $0xff,FPU_denormal
        jnz     xNormalise_result

xL_Normalised:
        cmpb    LOST_UP,FPU_bits_lost
        je      xL_precision_lost_up

        cmpb    LOST_DOWN,FPU_bits_lost
        je      xL_precision_lost_down

xL_no_precision_loss:
        /* store the result */
        movb    TW_Valid,TAG(%edi)

xL_Store_significand:
        movl    %eax,SIGH(%edi)
        movl    %ebx,SIGL(%edi)

        xorl    %eax,%eax       /* No errors detected. */

        cmpl    EXP_OVER,EXP(%edi)
        jge     L_overflow

fpu_reg_round_exit:
#ifndef NON_REENTRANT_FPU
        popl    %ebx            /* adjust the stack pointer */
#endif NON_REENTRANT_FPU

fpu_Arith_exit:
        popl    %ebx
        popl    %edi
        popl    %esi
        leave
        ret


/*
 * Set the FPU status flags to represent precision loss due to
 * round-up.
 */
xL_precision_lost_up:
        push    %eax
        call    SYMBOL_NAME(set_precision_flag_up)
        popl    %eax
        jmp     xL_no_precision_loss

/*
 * Set the FPU status flags to represent precision loss due to
 * truncation.
 */
xL_precision_lost_down:
        push    %eax
        call    SYMBOL_NAME(set_precision_flag_down)
        popl    %eax
        jmp     xL_no_precision_loss


/*
 * The number is a denormal (which might get rounded up to a normal)
 * Shift the number right the required number of bits, which will
 * have to be undone later...
 */
xMake_denorm:
        /* The action to be taken depends upon whether the underflow
           exception is masked */
        testb   CW_Underflow,%cl                /* Underflow mask. */
        jz      xUnmasked_underflow             /* Do not make a denormal. */

        movb    DENORMAL,FPU_denormal

        pushl   %ecx            /* Save */
        movl    EXP_UNDER+1,%ecx
        subl    EXP(%edi),%ecx

        cmpl    $64,%ecx        /* shrd only works for 0..31 bits */
        jnc     xDenorm_shift_more_than_63

        cmpl    $32,%ecx        /* shrd only works for 0..31 bits */
        jnc     xDenorm_shift_more_than_32

/*
 * We got here without jumps by assuming that the most common requirement
 *   is for a small de-normalising shift.
 * Shift by [1..31] bits
 */
        addl    %ecx,EXP(%edi)
        orl     %edx,%edx       /* extension */
        setne   %ch             /* Save whether %edx is non-zero */
        xorl    %edx,%edx
        shrd    %cl,%ebx,%edx
        shrd    %cl,%eax,%ebx
        shr     %cl,%eax
        orb     %ch,%dl
        popl    %ecx
        jmp     xDenorm_done

/* Shift by [32..63] bits */
xDenorm_shift_more_than_32:
        addl    %ecx,EXP(%edi)
        subb    $32,%cl
        orl     %edx,%edx
        setne   %ch
        orb     %ch,%bl
        xorl    %edx,%edx
        shrd    %cl,%ebx,%edx
        shrd    %cl,%eax,%ebx
        shr     %cl,%eax
        orl     %edx,%edx               /* test these 32 bits */
        setne   %cl
        orb     %ch,%bl
        orb     %cl,%bl
        movl    %ebx,%edx
        movl    %eax,%ebx
        xorl    %eax,%eax
        popl    %ecx
        jmp     xDenorm_done

/* Shift by [64..) bits */
xDenorm_shift_more_than_63:
        cmpl    $64,%ecx
        jne     xDenorm_shift_more_than_64

/* Exactly 64 bit shift */
        addl    %ecx,EXP(%edi)
        xorl    %ecx,%ecx
        orl     %edx,%edx
        setne   %cl
        orl     %ebx,%ebx
        setne   %ch
        orb     %ch,%cl
        orb     %cl,%al
        movl    %eax,%edx
        xorl    %eax,%eax
        xorl    %ebx,%ebx
        popl    %ecx
        jmp     xDenorm_done

xDenorm_shift_more_than_64:
        movl    EXP_UNDER+1,EXP(%edi)
/* This is easy, %eax must be non-zero, so.. */
        movl    $1,%edx
        xorl    %eax,%eax
        xorl    %ebx,%ebx
        popl    %ecx
        jmp     xDenorm_done


xUnmasked_underflow:
        movb    UNMASKED_UNDERFLOW,FPU_denormal
        jmp     xDenorm_done


/* Undo the de-normalisation. */
xNormalise_result:
        cmpb    UNMASKED_UNDERFLOW,FPU_denormal
        je      xSignal_underflow

/* The number must be a denormal if we got here. */
#ifdef PARANOID
        /* But check it... just in case. */
        cmpl    EXP_UNDER+1,EXP(%edi)
        jne     L_norm_bugged
#endif PARANOID

#ifdef PECULIAR_486
        /*
         * This implements a special feature of 80486 behaviour.
         * Underflow will be signalled even if the number is
         * not a denormal after rounding.
         * This difference occurs only for masked underflow, and not
         * in the unmasked case.
         * Actual 80486 behaviour differs from this in some circumstances.
         */
        orl     %eax,%eax               /* ms bits */
        js      LNormalise_shift_done   /* Will be masked underflow */
#endif PECULIAR_486

        orl     %eax,%eax               /* ms bits */
        js      xL_Normalised           /* No longer a denormal */

        jnz     LNormalise_shift_up_to_31       /* Shift left 0 - 31 bits */

        orl     %ebx,%ebx
        jz      L_underflow_to_zero     /* The contents are zero */

/* Shift left 32 - 63 bits */
        movl    %ebx,%eax
        xorl    %ebx,%ebx
        subl    $32,EXP(%edi)

LNormalise_shift_up_to_31:
        bsrl    %eax,%ecx       /* get the required shift in %ecx */
        subl    $31,%ecx
        negl    %ecx
        shld    %cl,%ebx,%eax
        shl     %cl,%ebx
        subl    %ecx,EXP(%edi)

LNormalise_shift_done:
        testb   $0xff,FPU_bits_lost     /* bits lost == underflow */
        jz      xL_Normalised

        /* There must be a masked underflow */
        push    %eax
        pushl   EX_Underflow
        call    SYMBOL_NAME(exception)
        popl    %eax
        popl    %eax
        jmp     xL_Normalised


/*
 * The operations resulted in a number too small to represent.
 * Masked response.
 */
L_underflow_to_zero:
        push    %eax
        call    SYMBOL_NAME(set_precision_flag_down)
        popl    %eax

        push    %eax
        pushl   EX_Underflow
        call    SYMBOL_NAME(exception)
        popl    %eax
        popl    %eax

/* Reduce the exponent to EXP_UNDER */
        movl    EXP_UNDER,EXP(%edi)
        movb    TW_Zero,TAG(%edi)
        jmp     xL_Store_significand


/* The operations resulted in a number too large to represent. */
L_overflow:
        push    %edi
        call    SYMBOL_NAME(arith_overflow)
        pop     %edi
        jmp     fpu_reg_round_exit


xSignal_underflow:
        /* The number may have been changed to a non-denormal */
        /* by the rounding operations. */
        cmpl    EXP_UNDER,EXP(%edi)
        jle     xDo_unmasked_underflow

        jmp     xL_Normalised

xDo_unmasked_underflow:
        /* Increase the exponent by the magic number */
        addl    $(3*(1<<13)),EXP(%edi)
        push    %eax
        pushl   EX_Underflow
        call    EXCEPTION
        popl    %eax
        popl    %eax
        jmp     xL_Normalised


#ifdef PARANOID
#ifdef PECULIAR_486
L_bugged_denorm_486:
        pushl   EX_INTERNAL|0x236
        call    EXCEPTION
        popl    %ebx
        jmp     L_exception_exit
#else
L_bugged_denorm:
        pushl   EX_INTERNAL|0x230
        call    EXCEPTION
        popl    %ebx
        jmp     L_exception_exit
#endif PECULIAR_486

L_bugged_round24:
        pushl   EX_INTERNAL|0x231
        call    EXCEPTION
        popl    %ebx
        jmp     L_exception_exit

L_bugged_round53:
        pushl   EX_INTERNAL|0x232
        call    EXCEPTION
        popl    %ebx
        jmp     L_exception_exit

L_bugged_round64:
        pushl   EX_INTERNAL|0x233
        call    EXCEPTION
        popl    %ebx
        jmp     L_exception_exit

L_norm_bugged:
        pushl   EX_INTERNAL|0x234
        call    EXCEPTION
        popl    %ebx
        jmp     L_exception_exit

L_entry_bugged:
        pushl   EX_INTERNAL|0x235
        call    EXCEPTION
        popl    %ebx
L_exception_exit:
        mov     $1,%eax
        jmp     fpu_reg_round_exit
#endif PARANOID