diff options
Diffstat (limited to 'arch/x86/math-emu/reg_round.S')
| -rw-r--r-- | arch/x86/math-emu/reg_round.S | 711 |
1 files changed, 711 insertions, 0 deletions
diff --git a/arch/x86/math-emu/reg_round.S b/arch/x86/math-emu/reg_round.S new file mode 100644 index 000000000..04563421e --- /dev/null +++ b/arch/x86/math-emu/reg_round.S @@ -0,0 +1,711 @@ +/* SPDX-License-Identifier: GPL-2.0 */ + .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 */ + +ENDPROC(FPU_round) |