.file "reg_round.S" /* $OpenBSD: reg_round.s,v 1.4 2004/01/13 18:08:48 espie Exp $ */ /* * reg_round.S * * Rounding/truncation/etc for FPU basic arithmetic functions. * * This code has four possible entry points. * The following must be entered by a jmp intruction: * FPU_round, FPU_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) * * * Copyright (C) 1992,1993,1994 * W. Metzenthen, 22 Parker St, Ormond, Vic 3163, * Australia. E-mail billm@vaxc.cc.monash.edu.au * All rights reserved. * * This copyright notice covers the redistribution and use of the * FPU emulator developed by W. Metzenthen. It covers only its use * in the 386BSD, FreeBSD and NetBSD operating systems. Any other * use is not permitted under this copyright. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * 2. Redistributions in binary form must include information specifying * that source code for the emulator is freely available and include * either: * a) an offer to provide the source code for a nominal distribution * fee, or * b) list at least two alternative methods whereby the source * can be obtained, e.g. a publically accessible bulletin board * and an anonymous ftp site from which the software can be * downloaded. * 3. All advertising materials specifically mentioning features or use of * this emulator must acknowledge that it was developed by W. Metzenthen. * 4. The name of W. Metzenthen may not be used to endorse or promote * products derived from this software without specific prior written * permission. * * THIS SOFTWARE IS PROVIDED ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, * INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY * AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL * W. METZENTHEN BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. * * * The purpose of this copyright, based upon the Berkeley copyright, is to * ensure that the covered software remains freely available to everyone. * * The software (with necessary differences) is also available, but under * the terms of the GNU copyleft, for the Linux operating system and for * the djgpp ms-dos extender. * * W. Metzenthen June 1994. * * * $FreeBSD: reg_round.s,v 1.3 1994/06/10 07:44:55 rich Exp $ * */ /*---------------------------------------------------------------------------+ | Four entry points. | | | | Needed by both the FPU_round and FPU_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_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 #include #include #include #define LOST_DOWN $1 #define LOST_UP $2 #define DENORMAL $1 #define UNMASKED_UNDERFLOW $2 .data #ifdef __ELF__ .align 4,0 #else .align 2,0 #endif FPU_bits_lost: .byte 0 FPU_denormal: .byte 0 .text #ifdef __ELF__ .align 4,144 #else .align 2,144 #endif .globl FPU_round .globl FPU_round_sqrt .globl FPU_Arith_exit .globl _C_LABEL(round_reg) /* Entry point when called from C */ _C_LABEL(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_round_sqrt FPU_round: /* Normal entry point */ movl PARAM4,%ecx FPU_round_sqrt: /* Entry point from wm_sqrt.S */ #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 PARANOID jmp L_bugged /* There is no bug, just a bad control word */ #endif /* PARANOID */ /* 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 #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 #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 #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,%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 LRe_normalise /* Rounding done, no overflow */ /* Overflow, adjust the result (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: cmpl EXP_OVER,EXP(%edi) jge L_overflow /* store the result */ movb TW_Valid,TAG(%edi) xL_Store_significand: movl %eax,SIGH(%edi) movl %ebx,SIGL(%edi) 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 _C_LABEL(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 _C_LABEL(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(%edi),%ecx subl EXP_UNDER+1,%ecx negl %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 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: /* Increase the exponent by the magic number*/ addl $(3*(1<<13)),EXP(%edi) 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 */ orl %eax,%eax /* ms bits*/ 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 _C_LABEL(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 _C_LABEL(set_precision_flag_down) popl %eax push %eax pushl EX_Underflow call _C_LABEL(exception) popl %eax popl %eax movb TW_Zero,TAG(%edi) jmp xL_Store_significand /* The operations resulted in a number too large to represent.*/ L_overflow: push %edi call _C_LABEL(arith_overflow) pop %edi jmp FPU_Arith_exit xSignal_underflow: push %eax pushl EX_Underflow call EXCEPTION popl %eax popl %eax jmp xL_Normalised #ifdef PARANOID /* If we ever get here then we have problems! */ L_bugged: pushl EX_INTERNAL|0x201 call EXCEPTION popl %ebx jmp FPU_Arith_exit L_norm_bugged: pushl EX_INTERNAL|0x216 call EXCEPTION popl %ebx jmp FPU_Arith_exit L_entry_bugged: pushl EX_INTERNAL|0x217 call EXCEPTION popl %ebx jmp FPU_Arith_exit #endif /* PARANOID */