713 lines
21 KiB
NASM
713 lines
21 KiB
NASM
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subttl emround.asm - Rounding and Precision Control and FRNDINT
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page
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;*******************************************************************************
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;emround.asm - Rounding and Precision Control
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;
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; Microsoft Confidential
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;
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; Copyright (c) Microsoft Corporation 1991
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; All Rights Reserved
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;
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;Purpose:
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; Rounding and precision control. The correct routine is jumped
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; to through the [RoundMode] vector.
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;
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;Revision History:
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;
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; [] 09/05/91 TP Initial 32-bit version.
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; 02/28/92 JWM Minor bug fix in NotNearLow
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;
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;*******************************************************************************
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RndIntSpcl:
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cmp cl,bTAG_INF
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jz RndIntX ;Leave infinity unchanged
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cmp cl,bTAG_DEN
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jnz SpclDestNotDen ;Handle NAN & empty - in emarith.asm
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;Handle denormal
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mov EMSEG:[CURerr],Denormal
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test EMSEG:[CWmask],Denormal ;Is it masked?
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jnz NormRndInt ;If so, ignore denormalization
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RndIntX:
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ret
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;********
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EM_ENTRY eFRNDINT
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eFRNDINT:
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;********
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;edi points to top of stack
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mov ecx,EMSEG:[edi].ExpSgn
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cmp cl,bTAG_ZERO
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.erre bTAG_VALID lt bTAG_ZERO
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.erre bTAG_SNGL lt bTAG_ZERO
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jz RndIntX
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ja RndIntSpcl
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cmp ecx,63 shl 16 ;Is it already integer?
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jge RndIntX
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NormRndInt:
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mov ebx,EMSEG:[edi].lManHi
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mov esi,EMSEG:[edi].lManLo
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mov EMSEG:[Result],edi ;Save result pointer
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xor eax,eax ;Extend mantissa
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push offset SaveResult
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jmp RoundToBit
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;*******************************************************************************
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ResultOverflow:
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;mantissa in ebx:esi, exponent in high ecx, sign in ch bit 7, tag in cl.
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;We were all ready to save the rounded result, but the exponent turned out
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;to be too large.
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or EMSEG:[CURerr],Overflow
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sub ecx,UnderBias shl 16 ;Unmasked response
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test EMSEG:[CWmask],Overflow ;Is exception unmasked?
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jz SaveResult ;If so, we're ready
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;Produce masked overflow response
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mov ebx,1 shl 31 ;Assume infinity
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xor esi,esi
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mov cl,bTAG_INF
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mov al,EMSEG:[CWcntl] ;Get rounding control
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mov ah,al
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and ah,RCchop ;Rounding control only
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;Return max value if RCup bit = 1 and -, or RCdown bit = 1 and +
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;i.e., RCup & sign OR RCdown & not sign
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.erre RCchop eq RCup + RCdown ;Always return max value
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.erre RCnear eq 0 ;Never return max value
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sar ch,7 ;Expand sign through whole byte
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.erre (RCdown and bSign) eq 0 ;Don't want to change real sign
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xor ch,RCdown ;Flip sign for RCdown bit
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and ah,ch ;RCup & sign OR RCdown & not sign
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jnz SaveMax
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and ecx,0FFFFH
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or ecx,TexpMax shl 16
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jmp SaveResult ;Save Infinity
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SaveMax:
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;Get max value for current precision
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mov ebx,0FFFFFF00H ;Max value for 24 bits
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and ecx,bSign shl 8 ;Preserve only sign
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or ecx,(IexpMax-IexpBias-1) shl 16 + bTAG_VALID ;Set up max value
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and al,PrecisionControl
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.erre PC24 eq 0
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jz SaveResult ;Save 24-bit max value
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dec esi ;esi == -1
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mov ebx,esi
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cmp al,PC53
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jnz SaveResult ;Save 64-bit max value
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mov esi,0FFFFF800H
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jmp SaveResult ;Save 53-bit max value
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;*******************************************************************************
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;
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;64-bit rounding routines
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;
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;***********
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Round64down:
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;***********
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cmp ecx,(IexpMin-IexpBias+1) shl 16 ;Test for Underflow
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jl RndDenorm64
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or eax,eax ;Exact result?
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jz SaveValidResult
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or EMSEG:[CURerr],Precision ;Set flag on inexact result
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;Chop if positive, increase mantissa if negative
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test ch,bSign
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jz SaveValidResult ;Positive, so chop
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jmp RoundUp64 ;Round up if negative
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RndDenorm64:
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test EMSEG:[CWmask],Underflow ;Is exception unmasked?
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jz RndSetUnder
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Denormalize:
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;We don't really store in denormalized format, but we need the number
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;to be rounded as if we do. If the exponent were -IexpBias, we would
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;lose 1 bit of precision; as it gets more negative, we lose more bits.
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;We'll do this by adjusting the exponent so that the bits we want to
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;keep look like integer bits, and performing round-to-integer.
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add ecx,(IexpBias+62) shl 16 ;Adjust exponent so we're integer
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call RoundToBit
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;Set underflow exception if precision exception is set
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mov al,EMSEG:[CURerr]
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and al,Precision
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ror al,Precision-Underflow ;Move Precision bit to Underflow pos.
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or EMSEG:[CURerr],al ;Signal Underflow if inexact
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cmp cl,bTAG_ZERO
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jz SaveResult
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sub ecx,(IexpBias+62) shl 16;Restore unbiased exponent
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cmp ecx,TexpMin shl 16 ;Did we round out of denorm?
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jae SaveResult
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mov cl,bTAG_DEN
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jmp SaveResult
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RndSetUnder:
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;Underflow exception not masked. Adjust exponent and try again.
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or EMSEG:[CURerr],Underflow
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add ecx,UnderBias shl 16
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jmp EMSEG:[RoundMode] ;Try again with revised exponent
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;***********
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Round64near:
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;***********
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;mantissa in ebx:esi:eax, exponent in high ecx, sign in ch bit 7
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cmp ecx,TexpMin shl 16 ;Test for Underflow
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jl RndDenorm64
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or eax,eax ;Exact result?
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jz short SaveValidResult
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or EMSEG:[CURerr],Precision ;Set flag on inexact result
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;To perform "round even" when the round bit is set and the sticky bits
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;are zero, we treat the LSB as if it were a sticky bit. Thus if the LSB
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;is set, that will always force a round up (to even) if the round bit is
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;set. If the LSB is zero, then the sticky bits remain zero and we always
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;round down. This rounding rule is implemented by adding RoundBit-1
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;(7F..FFH), setting CY if round up.
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bt esi,0 ;Is mantissa even or odd? (set CY)
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adc eax,(1 shl 31)-1 ;Sum LSB & sticky bits--CY if round up
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jnc SaveValidResult
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RoundUp64:
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mov EMSEG:[SWcc],RoundUp
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add esi,1
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adc ebx,0
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jc BumpExponent ;Overflowed, increment exponent
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SaveValidResult: ;A jump to here requires 9 clocks
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or esi,esi ;Any bits in low half?
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.erre bTAG_VALID eq 1
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.erre bTAG_SNGL eq 0
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setnz cl ;if low half==0 then cl=0 else cl=1
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cmp ecx,TexpMax shl 16 ;Test for overflow
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jge ResultOverflow
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SaveResult: ;A jump to here requires 10 clocks
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;mantissa in ebx:esi, exponent in high ecx, sign in ch bit 7, tag in cl
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mov edi,EMSEG:[Result]
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SaveResultEdi:
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mov EMSEG:[edi].lManLo,esi
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mov EMSEG:[edi].lManHi,ebx
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SaveExpSgn:
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mov EMSEG:[edi].ExpSgn,ecx
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ret
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;***********
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Round64up:
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;***********
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cmp ecx,TexpMin shl 16 ;Test for Underflow
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jl RndDenorm64
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or eax,eax ;Exact result?
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jz short SaveValidResult
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or EMSEG:[CURerr],Precision;Set flag on inexact result
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;Chop if negative, increase mantissa if positive
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cmp ch,bSign ;No CY iff sign bit is set
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jc RoundUp64 ;Round up if positive
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jmp short SaveValidResult
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;***********
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Round64chop:
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;***********
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cmp ecx,TexpMin shl 16 ;Test for Underflow
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jl RndDenorm64
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or eax,eax ;Exact result?
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jz short SaveValidResult
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or EMSEG:[CURerr],Precision;Set flag on inexact result
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jmp short SaveValidResult
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;*******************************************************************************
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;
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;53-bit rounding routines
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;
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;***********
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Round53down:
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;***********
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cmp ecx,TexpMin shl 16 ;Test for Underflow
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jl RndDenorm53
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mov edx,esi ;Get low bits
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and edx,(1 shl 11) - 1 ;Mask to last 11 bits
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or edx,eax ;Throwing away any bits?
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jz SaveValidResult
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or EMSEG:[CURerr],Precision;Set flag on inexact result
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;Chop if positive, increase mantissa if negative
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and esi,not ((1 shl 11)-1) ;Mask off low 11 bits
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test ch,bSign
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jz SaveValidResult ;Positive, go chop
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jmp RoundUp53
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RndDenorm53:
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test EMSEG:[CWmask],Underflow;Is exception unmasked?
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jz RndSetUnder
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;We don't really store in denormalized format, but we need the number
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;to be rounded as if we do. If the exponent were -IexpBias, we would
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;lose 1 bit of precision; as it gets more negative, we lose more bits.
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;We'll do this by adjusting the exponent so that the bits we want to
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;keep look like integer bits, and performing round-to-integer.
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add ecx,(IexpBias+51) shl 16 ;Adjust exponent so we're integer
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call RoundToBit
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;Set underflow exception if precision exception is set
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mov al,EMSEG:[CURerr]
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and al,Precision
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ror al,Precision-Underflow ;Move Precision bit to Underflow pos.
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or EMSEG:[CURerr],al ;Signal Underflow if inexact
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cmp cl,bTAG_ZERO
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jz SaveResult
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sub ecx,(IexpBias+51) shl 16;Restore unbiased exponent
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cmp ecx,(IexpMin-IexpBias+1) shl 16 ;Did we round out of denorm?
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jae SaveResult
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mov cl,bTAG_DEN
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jmp SaveResult
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;***********
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Round53near:
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;***********
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;mantissa in ebx:esi:eax, exponent in high ecx, sign in ch bit 7
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cmp ecx,TexpMin shl 16 ;Test for Underflow
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jl RndDenorm53
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mov edx,esi ;Get low bits
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and edx,(1 shl 11) - 1 ;Mask to last 11 bits
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or edx,eax ;Throwing away any bits?
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jz SaveValidResult
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or EMSEG:[CURerr],Precision;Set flag on inexact result
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;To perform "round even" when the round bit is set and the sticky bits
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;are zero, we treat the LSB as if it were a sticky bit. Thus if the LSB
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;is set, that will always force a round up (to even) if the round bit is
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;set. If the LSB is zero, then the sticky bits remain zero and we always
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;round down.
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mov edx,esi
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and esi,not ((1 shl 11)-1) ;Mask off low 11 bits
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test edx,1 shl 10 ;Is round bit set?
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jz SaveValidResult
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and edx,(3 shl 10)-1 ;Keep only sticky bits and LSB
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or eax,edx ;Combine with other sticky bits
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jz SaveValidResult
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RoundUp53:
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mov EMSEG:[SWcc],RoundUp
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add esi,1 shl 11 ;Round
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adc ebx,0
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jnc SaveValidResult
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BumpExponent:
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add ecx,1 shl 16 ;Mantissa overflowed, bump exponent
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or ebx,1 shl 31 ;Set MSB
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jmp SaveValidResult
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;***********
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Round53up:
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;***********
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cmp ecx,TexpMin shl 16 ;Test for Underflow
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jl RndDenorm53
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mov edx,esi ;Get low bits
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and edx,(1 shl 11) - 1 ;Mask to last 11 bits
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or edx,eax ;Throwing away any bits?
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jz SaveValidResult
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or EMSEG:[CURerr],Precision;Set flag on inexact result
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;Chop if negative, increase mantissa if positive
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and esi,not ((1 shl 11)-1) ;Mask off low 11 bits
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test ch,bSign
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jz RoundUp53 ;Round up if positive
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jmp SaveValidResult
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;***********
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Round53chop:
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;***********
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cmp ecx,TexpMin shl 16 ;Test for Underflow
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jl RndDenorm53
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mov edx,esi ;Get low bits
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and edx,(1 shl 11) - 1 ;Mask to last 11 bits
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or edx,eax ;Throwing away any bits?
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jz SaveValidResult
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or EMSEG:[CURerr],Precision;Set flag on inexact result
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and esi,not ((1 shl 11)-1) ;Mask off low 11 bits
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jmp SaveValidResult
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;*******************************************************************************
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;
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;24-bit rounding routines
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;
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;***********
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Round24down:
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;***********
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cmp ecx,TexpMin shl 16 ;Test for Underflow
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jl RndDenorm24
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or eax,esi ;Low dword is just sticky bits
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mov edx,ebx ;Get low bits
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and edx,(1 shl 8) - 1 ;Mask to last 8 bits
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or edx,eax ;Throwing away any bits?
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jz SaveValidResult
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or EMSEG:[CURerr],Precision;Set flag on inexact result
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;Chop if positive, increase mantissa if negative
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xor esi,esi
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and ebx,not ((1 shl 8)-1) ;Mask off low 8 bits
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test ch,bSign
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jz SaveValidResult ;Chop if positive
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jmp RoundUp24
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RndDenorm24:
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test EMSEG:[CWmask],Underflow;Is exception unmasked?
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jz RndSetUnder
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;We don't really store in denormalized format, but we need the number
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;to be rounded as if we do. If the exponent were -IexpBias, we would
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;lose 1 bit of precision; as it gets more negative, we lose more bits.
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;We'll do this by adjusting the exponent so that the bits we want to
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;keep look like integer bits, and performing round-to-integer.
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add ecx,(IexpBias+22) shl 16 ;Adjust exponent so we're integer
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call RoundToBit
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|
|
;Set underflow exception if precision exception is set
|
||
|
|
mov al,EMSEG:[CURerr]
|
||
|
|
and al,Precision
|
||
|
|
ror al,Precision-Underflow ;Move Precision bit to Underflow pos.
|
||
|
|
or EMSEG:[CURerr],al ;Signal Underflow if inexact
|
||
|
|
cmp cl,bTAG_ZERO
|
||
|
|
jz SaveResult
|
||
|
|
sub ecx,(IexpBias+22) shl 16;Restore unbiased exponent
|
||
|
|
cmp ecx,(IexpMin-IexpBias+1) shl 16 ;Did we round out of denorm?
|
||
|
|
jae SaveResult
|
||
|
|
mov cl,bTAG_DEN
|
||
|
|
jmp SaveResult
|
||
|
|
|
||
|
|
;***********
|
||
|
|
Round24near:
|
||
|
|
;***********
|
||
|
|
;mantissa in ebx:esi:eax, exponent in high ecx, sign in ch bit 7
|
||
|
|
cmp ecx,TexpMin shl 16 ;Test for Underflow
|
||
|
|
jl RndDenorm24
|
||
|
|
or eax,esi ;Low dword is just sticky bits
|
||
|
|
mov edx,ebx ;Get low bits
|
||
|
|
and edx,(1 shl 8) - 1 ;Mask to last 8 bits
|
||
|
|
or edx,eax ;Throwing away any bits?
|
||
|
|
jz SaveValidResult
|
||
|
|
or EMSEG:[CURerr],Precision;Set flag on inexact result
|
||
|
|
xor esi,esi
|
||
|
|
|
||
|
|
;To perform "round even" when the round bit is set and the sticky bits
|
||
|
|
;are zero, we treat the LSB as if it were a sticky bit. Thus if the LSB
|
||
|
|
;is set, that will always force a round up (to even) if the round bit is
|
||
|
|
;set. If the LSB is zero, then the sticky bits remain zero and we always
|
||
|
|
;round down.
|
||
|
|
|
||
|
|
mov edx,ebx
|
||
|
|
and ebx,not ((1 shl 8)-1) ;Mask off low 8 bits
|
||
|
|
test dl,1 shl 7 ;Round bit set?
|
||
|
|
jz SaveValidResult
|
||
|
|
and edx,(3 shl 7)-1 ;Mask to LSB and sticky bits
|
||
|
|
or eax,edx ;Combine all sticky bits
|
||
|
|
jz SaveValidResult
|
||
|
|
RoundUp24:
|
||
|
|
mov EMSEG:[SWcc],RoundUp
|
||
|
|
add ebx,1 shl 8
|
||
|
|
jnc SaveValidResult
|
||
|
|
jmp BumpExponent ;Overflowed, increment exponent
|
||
|
|
|
||
|
|
;***********
|
||
|
|
Round24up:
|
||
|
|
;***********
|
||
|
|
cmp ecx,TexpMin shl 16 ;Test for Underflow
|
||
|
|
jl RndDenorm24
|
||
|
|
or eax,esi ;Low dword is just sticky bits
|
||
|
|
mov edx,ebx ;Get low bits
|
||
|
|
and edx,(1 shl 8) - 1 ;Mask to last 8 bits
|
||
|
|
or edx,eax ;Throwing away any bits?
|
||
|
|
jz SaveValidResult
|
||
|
|
or EMSEG:[CURerr],Precision;Set flag on inexact result
|
||
|
|
;Chop if negative, increase mantissa if positive
|
||
|
|
xor esi,esi
|
||
|
|
and ebx,not ((1 shl 8)-1) ;Mask off low 8 bits
|
||
|
|
test ch,bSign
|
||
|
|
jz RoundUp24 ;Round up if positive
|
||
|
|
jmp SaveValidResult
|
||
|
|
|
||
|
|
;***********
|
||
|
|
Round24chop:
|
||
|
|
;***********
|
||
|
|
cmp ecx,TexpMin shl 16 ;Test for Underflow
|
||
|
|
jl RndDenorm24
|
||
|
|
or eax,esi ;Low dword is just sticky bits
|
||
|
|
mov edx,ebx ;Get low bits
|
||
|
|
and edx,(1 shl 8) - 1 ;Mask to last 8 bits
|
||
|
|
or edx,eax ;Throwing away any bits?
|
||
|
|
jz SaveValidResult
|
||
|
|
or EMSEG:[CURerr],Precision;Set flag on inexact result
|
||
|
|
xor esi,esi
|
||
|
|
and ebx,not ((1 shl 8)-1) ;Mask off low 8 bits
|
||
|
|
jmp SaveValidResult
|
||
|
|
|
||
|
|
;*******************************************************************************
|
||
|
|
|
||
|
|
;*** RoundToInteger
|
||
|
|
;
|
||
|
|
;This routine is used by FISTP Int64 and BSTP. Unlike RoundToBit, this
|
||
|
|
;unnormalizes the number into a 64-bit integer.
|
||
|
|
;
|
||
|
|
;Inputs:
|
||
|
|
; edi = pointer to number to round in stack
|
||
|
|
;Outputs:
|
||
|
|
; CY set if invalid operation
|
||
|
|
; ebx:edi = rounded integer if CY clear
|
||
|
|
; ch = sign if CY clear
|
||
|
|
;Note:
|
||
|
|
; FIST/FISTP/BSTP exception rules are used: If the number is too big,
|
||
|
|
; Invalid Operation occurs. Denormals are ignored.
|
||
|
|
;
|
||
|
|
;esi preserved
|
||
|
|
|
||
|
|
RoundSpcl64Int:
|
||
|
|
cmp cl,bTAG_DEN
|
||
|
|
jz NormRound64Int ;Ignore denormal
|
||
|
|
cmp cl,bTAG_EMPTY
|
||
|
|
jnz RoundInvalid ;All other specials are invalid
|
||
|
|
mov EMSEG:[CURerr],StackFlag+Invalid
|
||
|
|
stc ;Flag exception to caller
|
||
|
|
ret
|
||
|
|
|
||
|
|
RoundInvalid:
|
||
|
|
;Overflow on integer store is invalid according to IEEE
|
||
|
|
mov EMSEG:[CURerr],Invalid
|
||
|
|
stc ;Flag exception to caller
|
||
|
|
ret
|
||
|
|
|
||
|
|
RoundToInteger:
|
||
|
|
mov ebx,EMSEG:[edi].lManHi
|
||
|
|
mov ecx,EMSEG:[edi].ExpSgn
|
||
|
|
mov edi,EMSEG:[edi].lManLo
|
||
|
|
;mantissa in ebx:edi, exponent in high ecx, sign in ch bit 7, tag in cl
|
||
|
|
mov al,ch ;Save sign bit
|
||
|
|
cmp cl,bTAG_ZERO
|
||
|
|
.erre bTAG_VALID lt bTAG_ZERO
|
||
|
|
.erre bTAG_SNGL lt bTAG_ZERO
|
||
|
|
jz RoundIntX ;Just return zero
|
||
|
|
ja RoundSpcl64Int
|
||
|
|
NormRound64Int:
|
||
|
|
xor edx,edx
|
||
|
|
sar ecx,16 ;Bring exponent down
|
||
|
|
cmp ecx,-1 ;Is it less than 1?
|
||
|
|
jle Under64Int
|
||
|
|
cmp ecx,63
|
||
|
|
jg RoundInvalid
|
||
|
|
sub ecx,63
|
||
|
|
neg ecx ;cl = amount to shift right
|
||
|
|
mov ch,al ;Get sign out of al
|
||
|
|
xor eax,eax
|
||
|
|
cmp cl,32 ;Too big for one shift?
|
||
|
|
jl ShortShft64
|
||
|
|
;32-bit shift right
|
||
|
|
xchg edx,edi
|
||
|
|
xchg ebx,edi ;ebx=0 now
|
||
|
|
shrd eax,edx,cl
|
||
|
|
;Max total shift is 63 bits, so we know that the LSB of eax is still zero.
|
||
|
|
;We can rotate this zero to the MSB so the sticky bits in eax can be combined
|
||
|
|
;with those in edx without affecting the rounding bit in the MSB of edx.
|
||
|
|
ror eax,1 ;MSB is now zero
|
||
|
|
ShortShft64:
|
||
|
|
;Shift count in cl is modulo-32
|
||
|
|
shrd edx,edi,cl
|
||
|
|
shrd edi,ebx,cl
|
||
|
|
shr ebx,cl
|
||
|
|
or edx,eax ;Collapse sticky bits into one dword
|
||
|
|
jz RoundIntX ;No sticky or round bits, so don't round
|
||
|
|
;Result will not be exact--check rounding mode
|
||
|
|
Round64Int:
|
||
|
|
mov EMSEG:[CURerr],Precision;Set flag on inexact result
|
||
|
|
test EMSEG:[CWcntl],RoundControl ;Check rounding control bits
|
||
|
|
.erre RCnear eq 0
|
||
|
|
jnz NotNearest64Int ;Not just round-to-nearest
|
||
|
|
|
||
|
|
;To perform "round even" when the round bit is set and the sticky bits
|
||
|
|
;are zero, we treat the LSB as if it were a sticky bit. Thus if the LSB
|
||
|
|
;is set, that will always force a round up (to even) if the round bit is
|
||
|
|
;set. If the LSB is zero, then the sticky bits remain zero and we always
|
||
|
|
;round down.
|
||
|
|
|
||
|
|
bt edi,0 ;Look at LSB (for round even)
|
||
|
|
adc edx,(1 shl 31)-1 ;CY set if round up
|
||
|
|
jnc RoundIntX
|
||
|
|
mov EMSEG:[SWcc],RoundUp
|
||
|
|
add edi,1 ;Round
|
||
|
|
adc ebx,0
|
||
|
|
jc RoundInvalid
|
||
|
|
RoundIntX:
|
||
|
|
ret ;CY clear, no Invalid exception
|
||
|
|
|
||
|
|
Shift64Round:
|
||
|
|
or edi,edi
|
||
|
|
setnz dl ;Set sticky bit in edx
|
||
|
|
xor edi,edi ;Mantissa is all zero
|
||
|
|
jmp Round64Int
|
||
|
|
|
||
|
|
Under64Int:
|
||
|
|
;ZF set if exponent is -1
|
||
|
|
xchg ebx,edx ;64-bit right shift
|
||
|
|
mov ch,al ;Restore sign to ch
|
||
|
|
jz Shift64Round ;Exp. is -1, could need to round up
|
||
|
|
xor edi,edi ;Mantissa is all zero
|
||
|
|
mov EMSEG:[CURerr],Precision;Set flag on inexact result
|
||
|
|
NotNearest64Int:
|
||
|
|
;We want to increase the magnitude if RCup and +, or RCdown and -
|
||
|
|
mov al,EMSEG:[CWcntl] ;Get rounding control
|
||
|
|
.erre (not RCup and RoundControl) eq RCdown
|
||
|
|
sar ch,7 ;Expand sign through whole byte
|
||
|
|
xor al,ch ;Flip round mode if -
|
||
|
|
and al,RoundControl
|
||
|
|
cmp al,RCup ;Rounding up?
|
||
|
|
jnz RoundIntOk ;No, chop it
|
||
|
|
mov EMSEG:[SWcc],RoundUp
|
||
|
|
add edi,1
|
||
|
|
adc ebx,0
|
||
|
|
jc RoundInvalid
|
||
|
|
RoundIntOk:
|
||
|
|
clc
|
||
|
|
ret
|
||
|
|
|
||
|
|
;*******************************************************************************
|
||
|
|
|
||
|
|
;*** RoundToBit
|
||
|
|
;
|
||
|
|
;This is a relatively low performance routine used by FRNDINT and to
|
||
|
|
;generate internal-format denormals. It can round to any bit position.
|
||
|
|
;
|
||
|
|
;Inputs:
|
||
|
|
; mantissa in ebx:esi:eax, exponent in high ecx, sign in ch bit 7
|
||
|
|
;Purpose:
|
||
|
|
; Round number to integer. Zero exponent means number is in the
|
||
|
|
; range [1,2), so only the MSB will survive (MSB-1 is round bit).
|
||
|
|
; Larger exponents keep more bits; 63 would mean no rounding.
|
||
|
|
;Outputs:
|
||
|
|
; mantissa in ebx:esi, exponent in high ecx, sign in ch bit 7, tag in cl
|
||
|
|
;
|
||
|
|
;Does NOT detect overflow.
|
||
|
|
|
||
|
|
NoSigBits:
|
||
|
|
;Exponent was negative: no integer part
|
||
|
|
and ecx,bSign shl 8 ;Zero exponent, preserve sign
|
||
|
|
mov cl,bTAG_ZERO
|
||
|
|
or EMSEG:[CURerr],Precision;Set flag on inexact result
|
||
|
|
test EMSEG:[CWcntl],RoundControl ;Check rounding control bits
|
||
|
|
.erre RCnear eq 0
|
||
|
|
jnz NotNearNoSig ;Not just round-to-nearest
|
||
|
|
cmp edx,-1 ;Exponent of -1 ==> range [.5,1)
|
||
|
|
je HalfBitRound
|
||
|
|
RndIntToZero:
|
||
|
|
xor ebx,ebx
|
||
|
|
mov esi,ebx ;Just return zero
|
||
|
|
ret
|
||
|
|
|
||
|
|
NotNearNoSig:
|
||
|
|
;We want to increase the magnitude if RCup and +, or RCdown and -
|
||
|
|
mov al,EMSEG:[CWcntl] ;Get rounding control
|
||
|
|
sar ch,7 ;Expand sign through whole byte
|
||
|
|
xor al,ch ;Flip rounding bits if negative
|
||
|
|
and al,RoundControl
|
||
|
|
cmp al,RCup ;Rounding up?
|
||
|
|
jnz RndIntToZero ;No, chop it
|
||
|
|
RndIntToOne:
|
||
|
|
mov ebx,1 shl 31
|
||
|
|
xor esi,esi
|
||
|
|
mov cl,bTAG_SNGL
|
||
|
|
mov EMSEG:[SWcc],RoundUp
|
||
|
|
ret
|
||
|
|
|
||
|
|
HalfBitRound:
|
||
|
|
add ebx,ebx ;Shift off MSB (round bit)
|
||
|
|
or ebx,esi
|
||
|
|
or ebx,eax
|
||
|
|
jnz RndIntToOne
|
||
|
|
ret ;Return zero
|
||
|
|
|
||
|
|
;**********
|
||
|
|
RoundToBit:
|
||
|
|
;**********
|
||
|
|
mov edx,ecx ;Make copy of exponent
|
||
|
|
sar edx,16 ;Bring rounding exponent down
|
||
|
|
jl NoSigBits
|
||
|
|
mov cl,dl
|
||
|
|
cmp cl,32 ;Rounding in low word?
|
||
|
|
jae RoundLow
|
||
|
|
;When cl = 31, the RoundBit is in the low half while the LSB is in the
|
||
|
|
;high half. We must preserve the RoundBit when we move it to eax.
|
||
|
|
xchg eax,esi ;Low half becomes sticky bits
|
||
|
|
or ah,al ;Preserve lowest bits in ah
|
||
|
|
add esi,-1 ;Set CY if any original sticky bits
|
||
|
|
sbb al,al ;Put original sticky bits in al
|
||
|
|
mov esi,ebx
|
||
|
|
xor ebx,ebx ;Shift mantissa right 32 bits
|
||
|
|
RoundLow:
|
||
|
|
mov edx,(1 shl 31) - 1
|
||
|
|
shr edx,cl ;Make mask
|
||
|
|
;Note in the case of cl = 31, edx is now zero.
|
||
|
|
mov edi,esi
|
||
|
|
and edi,edx
|
||
|
|
or edi,eax ;Any bits being lost?
|
||
|
|
jz RndSetTag ;All done
|
||
|
|
inc edx ;Mask for LSB
|
||
|
|
or EMSEG:[CURerr],Precision;Set flag on inexact result
|
||
|
|
test EMSEG:[CWcntl],RoundControl ;Check rounding control bits
|
||
|
|
.erre RCnear eq 0
|
||
|
|
jnz NotNearLow ;Not just round-to-nearest
|
||
|
|
mov edi,edx ;Save LSB mask
|
||
|
|
shr edi,1 ;Mask for round bit
|
||
|
|
jc SplitRound ;Round bit in eax?
|
||
|
|
test esi,edi ;Round bit set?
|
||
|
|
jz MaskOffLow
|
||
|
|
dec edi ;Mask for sticky bits
|
||
|
|
or edi,edx ;Sticky bits + LSB
|
||
|
|
and edi,esi
|
||
|
|
or edi,eax ;Any sticky bits set?
|
||
|
|
jz MaskOffLow
|
||
|
|
RoundUpThenMask:
|
||
|
|
mov EMSEG:[SWcc],RoundUp
|
||
|
|
add esi,edx ;Round up
|
||
|
|
adc ebx,0
|
||
|
|
jc RoundBumpExp
|
||
|
|
MaskOffLow:
|
||
|
|
dec edx ;Mask for round & sticky bits
|
||
|
|
not edx
|
||
|
|
and esi,edx ;Zero out low bits
|
||
|
|
RndSetTag:
|
||
|
|
or ebx,ebx ;Is it normalized?
|
||
|
|
jns RoundedHighHalf
|
||
|
|
or esi,esi ;Any bits in low half?
|
||
|
|
.erre bTAG_VALID eq 1
|
||
|
|
.erre bTAG_SNGL eq 0
|
||
|
|
setnz cl ;if low half==0 then cl=0 else cl=1
|
||
|
|
ret
|
||
|
|
|
||
|
|
SplitRound:
|
||
|
|
;Rounding high half in esi on rounding bit in eax
|
||
|
|
bt esi,0 ;Look at LSB
|
||
|
|
adc eax,(1 shl 31) - 1 ;Set CY if round up
|
||
|
|
jc RoundUpThenMask
|
||
|
|
or ebx,ebx ;Will set ZF for jnz below
|
||
|
|
RoundedHighHalf:
|
||
|
|
;Rounding occured in high half, which had been moved low.
|
||
|
|
;Move it back up high.
|
||
|
|
;
|
||
|
|
;ZF set here on content of ebx. If not zero, rounding high half in esi
|
||
|
|
;rippled forward into zero in ebx.
|
||
|
|
mov cl,bTAG_SNGL
|
||
|
|
jnz RndIntNorm ;Present high half should be zero
|
||
|
|
xchg ebx,esi ;Shift left 32 bits
|
||
|
|
ret
|
||
|
|
|
||
|
|
RndIntNorm:
|
||
|
|
;Rounded up high half of mantissa, which rolled over to 0.
|
||
|
|
add ecx,1 shl 16 ;Increase exponent
|
||
|
|
mov ebx,1 shl 31 ;Restore MSB
|
||
|
|
ret ;Tag already set to SNGL
|
||
|
|
|
||
|
|
RoundBumpExp:
|
||
|
|
;Mantissa was FFFFF... and rolled over to 0 when we rounded
|
||
|
|
add ecx,1 shl 16 ;Increase exponent
|
||
|
|
mov ebx,1 shl 31 ;Restore MSB
|
||
|
|
jmp MaskOffLow
|
||
|
|
|
||
|
|
NotNearLow:
|
||
|
|
;We want to increase the magnitude if RCup and +, or RCdown and -
|
||
|
|
mov al,EMSEG:[CWcntl] ;Get rounding control
|
||
|
|
sar ch,7 ;Expand sign through whole byte
|
||
|
|
.erre (not RCup and RoundControl) eq RCdown
|
||
|
|
xor al,ch ;Flip rounding bits if negative
|
||
|
|
and al,RoundControl
|
||
|
|
cmp al,RCup ;Rounding up?
|
||
|
|
jz RoundUpThenMask ;yes
|
||
|
|
jmp MaskOffLow ;No, chop it
|