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Filename : REG_ROUN.S

.file "reg_round.S"
/*---------------------------------------------------------------------------+
| reg_round.S |
| |
| Rounding/truncation/etc for FPU basic arithmetic functions. |
| |
| Copyright (C) 1993 |
| W. Metzenthen, 22 Parker St, Ormond, Vic 3163, |
| Australia. E-mail [email protected] |
| |
| This code has four possible entry points. |
| The following must be entered by a jmp intruction: |
| 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_asm.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


#ifdef 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 REENTRANT_FPU


.text
.align 2,144
.globl fpu_reg_round
.globl fpu_reg_round_sqrt
.globl fpu_Arith_exit
.globl _round_reg

/* Entry point when called from C */
_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 */

#ifdef REENTRANT_FPU
pushl %ebx /* adjust the stack pointer */
#endif 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:
#ifdef REENTRANT_FPU
popl %ebx /* adjust the stack pointer */
#endif 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 _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 _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 _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 _set_precision_flag_down
popl %eax

push %eax
pushl EX_Underflow
call _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 _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