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|
.file "reg_round.S"
/*---------------------------------------------------------------------------+
| reg_round.S |
| |
| Rounding/truncation/etc for FPU basic arithmetic functions. |
| |
| Copyright (C) 1993,1995,1997 |
| W. Metzenthen, 22 Parker St, Ormond, Vic 3163, |
| Australia. E-mail billm@suburbia.net |
| |
| 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 FPU_round entry point is intended to be used by C code. |
| From C, call as: |
| int FPU_round(FPU_REG *arg, unsigned int extent, unsigned int control_w) |
| |
| Return value is the tag of the answer, or-ed with FPU_Exception if |
| one was raised, or -1 on internal error. |
| |
| 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 4,0
FPU_bits_lost:
.byte 0
FPU_denormal:
.byte 0
#endif /* NON_REENTRANT_FPU */
.text
.globl fpu_reg_round
.globl fpu_Arith_exit
/* Entry point when called from C */
ENTRY(FPU_round)
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
fpu_reg_round: /* Normal entry point */
movl PARAM4,%ecx
#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 */
cmpw EXP_UNDER,EXP(%edi)
jle L_Make_denorm /* The number is a de-normal */
movb $0,FPU_denormal /* 0 -> not a de-normal */
Denorm_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,PARAM5
jne LCheck_truncate_24 /* If negative then up==truncate */
jmp LCheck_24_round_up
LDown_24:
cmpb SIGN_POS,PARAM5
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 L_Re_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 L_Re_normalise /* No truncation needed */
LDo_truncate_24:
andl $0xffffff00,%eax /* Truncate to 24 bits */
xorl %ebx,%ebx
movb LOST_DOWN,FPU_bits_lost
jmp L_Re_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,PARAM5
jne LCheck_truncate_53 /* If negative then up==truncate */
jmp LCheck_53_round_up
LDown_53:
cmpb SIGN_POS,PARAM5
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 L_Re_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 L_Re_normalise
LTruncate_53:
movb LOST_DOWN,FPU_bits_lost
andl $0xfffff800,%ebx /* Truncate to 53 bits */
jmp L_Re_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,PARAM5
jne LCheck_truncate_64 /* If negative then up==truncate */
orl %edx,%edx
jnz LDo_64_round_up
jmp L_Re_normalise
LDown_64:
cmpb SIGN_POS,PARAM5
je LCheck_truncate_64 /* If positive then down==truncate */
orl %edx,%edx
jnz LDo_64_round_up
jmp L_Re_normalise
LRound_nearest_64:
cmpl $0x80000000,%edx
jc LCheck_truncate_64
jne LDo_64_round_up
/* Now test for round-to-even */
testb $1,%bl
jz LCheck_truncate_64
LDo_64_round_up:
movb LOST_UP,FPU_bits_lost
addl $1,%ebx
adcl $0,%eax
LCheck_Round_Overflow:
jnc L_Re_normalise
/* Overflow, adjust the result (significand to 1.0) */
rcrl $1,%eax
rcrl $1,%ebx
incw EXP(%edi)
jmp L_Re_normalise
LCheck_truncate_64:
orl %edx,%edx
jz L_Re_normalise
LTruncate_64:
movb LOST_DOWN,FPU_bits_lost
L_Re_normalise:
testb $0xff,FPU_denormal
jnz Normalise_result
L_Normalised:
movl TAG_Valid,%edx
L_deNormalised:
cmpb LOST_UP,FPU_bits_lost
je L_precision_lost_up
cmpb LOST_DOWN,FPU_bits_lost
je L_precision_lost_down
L_no_precision_loss:
/* store the result */
L_Store_significand:
movl %eax,SIGH(%edi)
movl %ebx,SIGL(%edi)
cmpw EXP_OVER,EXP(%edi)
jge L_overflow
movl %edx,%eax
/* Convert the exponent to 80x87 form. */
addw EXTENDED_Ebias,EXP(%edi)
andw $0x7fff,EXP(%edi)
fpu_reg_round_signed_special_exit:
cmpb SIGN_POS,PARAM5
je fpu_reg_round_special_exit
orw $0x8000,EXP(%edi) /* Negative sign for the result. */
fpu_reg_round_special_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.
*/
L_precision_lost_up:
push %edx
push %eax
call set_precision_flag_up
popl %eax
popl %edx
jmp L_no_precision_loss
/*
* Set the FPU status flags to represent precision loss due to
* truncation.
*/
L_precision_lost_down:
push %edx
push %eax
call set_precision_flag_down
popl %eax
popl %edx
jmp L_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...
*/
L_Make_denorm:
/* The action to be taken depends upon whether the underflow
exception is masked */
testb CW_Underflow,%cl /* Underflow mask. */
jz Unmasked_underflow /* Do not make a denormal. */
movb DENORMAL,FPU_denormal
pushl %ecx /* Save */
movw EXP_UNDER+1,%cx
subw EXP(%edi),%cx
cmpw $64,%cx /* shrd only works for 0..31 bits */
jnc Denorm_shift_more_than_63
cmpw $32,%cx /* shrd only works for 0..31 bits */
jnc Denorm_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
*/
addw %cx,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 Denorm_done
/* Shift by [32..63] bits */
Denorm_shift_more_than_32:
addw %cx,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 Denorm_done
/* Shift by [64..) bits */
Denorm_shift_more_than_63:
cmpw $64,%cx
jne Denorm_shift_more_than_64
/* Exactly 64 bit shift */
addw %cx,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 Denorm_done
Denorm_shift_more_than_64:
movw 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 Denorm_done
Unmasked_underflow:
movb UNMASKED_UNDERFLOW,FPU_denormal
jmp Denorm_done
/* Undo the de-normalisation. */
Normalise_result:
cmpb UNMASKED_UNDERFLOW,FPU_denormal
je Signal_underflow
/* The number must be a denormal if we got here. */
#ifdef PARANOID
/* But check it... just in case. */
cmpw 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 LPseudoDenormal /* Will be masked underflow */
#else
orl %eax,%eax /* ms bits */
js L_Normalised /* No longer a denormal */
#endif /* PECULIAR_486 */
jnz LDenormal_adj_exponent
orl %ebx,%ebx
jz L_underflow_to_zero /* The contents are zero */
LDenormal_adj_exponent:
decw EXP(%edi)
LPseudoDenormal:
testb $0xff,FPU_bits_lost /* bits lost == underflow */
movl TAG_Special,%edx
jz L_deNormalised
/* There must be a masked underflow */
push %eax
pushl EX_Underflow
call EXCEPTION
popl %eax
popl %eax
movl TAG_Special,%edx
jmp L_deNormalised
/*
* 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 */
movw EXP_UNDER,EXP(%edi)
movl TAG_Zero,%edx
jmp L_Store_significand
/* The operations resulted in a number too large to represent. */
L_overflow:
addw EXTENDED_Ebias,EXP(%edi) /* Set for unmasked response. */
push %edi
call arith_overflow
pop %edi
jmp fpu_reg_round_signed_special_exit
Signal_underflow:
/* The number may have been changed to a non-denormal */
/* by the rounding operations. */
cmpw EXP_UNDER,EXP(%edi)
jle Do_unmasked_underflow
jmp L_Normalised
Do_unmasked_underflow:
/* Increase the exponent by the magic number */
addw $(3*(1<<13)),EXP(%edi)
push %eax
pushl EX_Underflow
call EXCEPTION
popl %eax
popl %eax
jmp L_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_special_exit
#endif /* PARANOID */
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