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711 lines
18 KiB
711 lines
18 KiB
/* SPDX-License-Identifier: GPL-2.0 */ |
|
.file "reg_round.S" |
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/*---------------------------------------------------------------------------+ |
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| reg_round.S | |
|
| | |
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| Rounding/truncation/etc for FPU basic arithmetic functions. | |
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| | |
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| Copyright (C) 1993,1995,1997 | |
|
| W. Metzenthen, 22 Parker St, Ormond, Vic 3163, | |
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| Australia. E-mail billm@suburbia.net | |
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| | |
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| This code has four possible entry points. | |
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| The following must be entered by a jmp instruction: | |
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| fpu_reg_round, fpu_reg_round_sqrt, and fpu_Arith_exit. | |
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| | |
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| The FPU_round entry point is intended to be used by C code. | |
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| From C, call as: | |
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| int FPU_round(FPU_REG *arg, unsigned int extent, unsigned int control_w) | |
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| | |
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| Return value is the tag of the answer, or-ed with FPU_Exception if | |
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| one was raised, or -1 on internal error. | |
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| | |
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| For correct "up" and "down" rounding, the argument must have the correct | |
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| sign. | |
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| | |
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+---------------------------------------------------------------------------*/ |
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|
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/*---------------------------------------------------------------------------+ |
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| Four entry points. | |
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| | |
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| Needed by both the fpu_reg_round and fpu_reg_round_sqrt entry points: | |
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| %eax:%ebx 64 bit significand | |
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| %edx 32 bit extension of the significand | |
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| %edi pointer to an FPU_REG for the result to be stored | |
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| stack calling function must have set up a C stack frame and | |
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| pushed %esi, %edi, and %ebx | |
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| | |
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| Needed just for the fpu_reg_round_sqrt entry point: | |
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| %cx A control word in the same format as the FPU control word. | |
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| Otherwise, PARAM4 must give such a value. | |
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| | |
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| | |
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| The significand and its extension are assumed to be exact in the | |
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| following sense: | |
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| If the significand by itself is the exact result then the significand | |
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| extension (%edx) must contain 0, otherwise the significand extension | |
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| must be non-zero. | |
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| If the significand extension is non-zero then the significand is | |
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| smaller than the magnitude of the correct exact result by an amount | |
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| greater than zero and less than one ls bit of the significand. | |
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| The significand extension is only required to have three possible | |
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| non-zero values: | |
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| less than 0x80000000 <=> the significand is less than 1/2 an ls | |
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| bit smaller than the magnitude of the | |
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| true exact result. | |
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| exactly 0x80000000 <=> the significand is exactly 1/2 an ls bit | |
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| smaller than the magnitude of the true | |
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| exact result. | |
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| greater than 0x80000000 <=> the significand is more than 1/2 an ls | |
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| bit smaller than the magnitude of the | |
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| true exact result. | |
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| | |
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+---------------------------------------------------------------------------*/ |
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|
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/*---------------------------------------------------------------------------+ |
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| The code in this module has become quite complex, but it should handle | |
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| all of the FPU flags which are set at this stage of the basic arithmetic | |
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| computations. | |
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| There are a few rare cases where the results are not set identically to | |
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| a real FPU. These require a bit more thought because at this stage the | |
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| results of the code here appear to be more consistent... | |
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| This may be changed in a future version. | |
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+---------------------------------------------------------------------------*/ |
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|
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|
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#include "fpu_emu.h" |
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#include "exception.h" |
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#include "control_w.h" |
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|
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/* Flags for FPU_bits_lost */ |
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#define LOST_DOWN $1 |
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#define LOST_UP $2 |
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|
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/* Flags for FPU_denormal */ |
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#define DENORMAL $1 |
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#define UNMASKED_UNDERFLOW $2 |
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|
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#ifndef NON_REENTRANT_FPU |
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/* Make the code re-entrant by putting |
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local storage on the stack: */ |
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#define FPU_bits_lost (%esp) |
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#define FPU_denormal 1(%esp) |
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|
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#else |
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/* Not re-entrant, so we can gain speed by putting |
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local storage in a static area: */ |
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.data |
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.align 4,0 |
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FPU_bits_lost: |
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.byte 0 |
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FPU_denormal: |
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.byte 0 |
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#endif /* NON_REENTRANT_FPU */ |
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|
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|
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.text |
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.globl fpu_reg_round |
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.globl fpu_Arith_exit |
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|
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/* Entry point when called from C */ |
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SYM_FUNC_START(FPU_round) |
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pushl %ebp |
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movl %esp,%ebp |
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pushl %esi |
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pushl %edi |
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pushl %ebx |
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|
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movl PARAM1,%edi |
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movl SIGH(%edi),%eax |
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movl SIGL(%edi),%ebx |
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movl PARAM2,%edx |
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|
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fpu_reg_round: /* Normal entry point */ |
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movl PARAM4,%ecx |
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|
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#ifndef NON_REENTRANT_FPU |
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pushl %ebx /* adjust the stack pointer */ |
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#endif /* NON_REENTRANT_FPU */ |
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|
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#ifdef PARANOID |
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/* Cannot use this here yet */ |
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/* orl %eax,%eax */ |
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/* jns L_entry_bugged */ |
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#endif /* PARANOID */ |
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|
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cmpw EXP_UNDER,EXP(%edi) |
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jle L_Make_denorm /* The number is a de-normal */ |
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|
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movb $0,FPU_denormal /* 0 -> not a de-normal */ |
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|
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Denorm_done: |
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movb $0,FPU_bits_lost /* No bits yet lost in rounding */ |
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|
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movl %ecx,%esi |
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andl CW_PC,%ecx |
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cmpl PR_64_BITS,%ecx |
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je LRound_To_64 |
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cmpl PR_53_BITS,%ecx |
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je LRound_To_53 |
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cmpl PR_24_BITS,%ecx |
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je LRound_To_24 |
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|
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#ifdef PECULIAR_486 |
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/* With the precision control bits set to 01 "(reserved)", a real 80486 |
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behaves as if the precision control bits were set to 11 "64 bits" */ |
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cmpl PR_RESERVED_BITS,%ecx |
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je LRound_To_64 |
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#ifdef PARANOID |
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jmp L_bugged_denorm_486 |
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#endif /* PARANOID */ |
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#else |
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#ifdef PARANOID |
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jmp L_bugged_denorm /* There is no bug, just a bad control word */ |
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#endif /* PARANOID */ |
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#endif /* PECULIAR_486 */ |
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/* Round etc to 24 bit precision */ |
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LRound_To_24: |
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movl %esi,%ecx |
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andl CW_RC,%ecx |
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cmpl RC_RND,%ecx |
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je LRound_nearest_24 |
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|
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cmpl RC_CHOP,%ecx |
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je LCheck_truncate_24 |
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|
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cmpl RC_UP,%ecx /* Towards +infinity */ |
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je LUp_24 |
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cmpl RC_DOWN,%ecx /* Towards -infinity */ |
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je LDown_24 |
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#ifdef PARANOID |
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jmp L_bugged_round24 |
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#endif /* PARANOID */ |
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LUp_24: |
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cmpb SIGN_POS,PARAM5 |
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jne LCheck_truncate_24 /* If negative then up==truncate */ |
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|
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jmp LCheck_24_round_up |
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LDown_24: |
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cmpb SIGN_POS,PARAM5 |
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je LCheck_truncate_24 /* If positive then down==truncate */ |
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LCheck_24_round_up: |
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movl %eax,%ecx |
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andl $0x000000ff,%ecx |
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orl %ebx,%ecx |
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orl %edx,%ecx |
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jnz LDo_24_round_up |
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jmp L_Re_normalise |
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LRound_nearest_24: |
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/* Do rounding of the 24th bit if needed (nearest or even) */ |
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movl %eax,%ecx |
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andl $0x000000ff,%ecx |
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cmpl $0x00000080,%ecx |
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jc LCheck_truncate_24 /* less than half, no increment needed */ |
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|
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jne LGreater_Half_24 /* greater than half, increment needed */ |
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|
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/* Possibly half, we need to check the ls bits */ |
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orl %ebx,%ebx |
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jnz LGreater_Half_24 /* greater than half, increment needed */ |
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orl %edx,%edx |
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jnz LGreater_Half_24 /* greater than half, increment needed */ |
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|
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/* Exactly half, increment only if 24th bit is 1 (round to even) */ |
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testl $0x00000100,%eax |
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jz LDo_truncate_24 |
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LGreater_Half_24: /* Rounding: increment at the 24th bit */ |
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LDo_24_round_up: |
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andl $0xffffff00,%eax /* Truncate to 24 bits */ |
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xorl %ebx,%ebx |
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movb LOST_UP,FPU_bits_lost |
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addl $0x00000100,%eax |
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jmp LCheck_Round_Overflow |
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LCheck_truncate_24: |
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movl %eax,%ecx |
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andl $0x000000ff,%ecx |
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orl %ebx,%ecx |
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orl %edx,%ecx |
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jz L_Re_normalise /* No truncation needed */ |
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|
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LDo_truncate_24: |
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andl $0xffffff00,%eax /* Truncate to 24 bits */ |
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xorl %ebx,%ebx |
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movb LOST_DOWN,FPU_bits_lost |
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jmp L_Re_normalise |
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/* Round etc to 53 bit precision */ |
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LRound_To_53: |
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movl %esi,%ecx |
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andl CW_RC,%ecx |
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cmpl RC_RND,%ecx |
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je LRound_nearest_53 |
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cmpl RC_CHOP,%ecx |
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je LCheck_truncate_53 |
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cmpl RC_UP,%ecx /* Towards +infinity */ |
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je LUp_53 |
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cmpl RC_DOWN,%ecx /* Towards -infinity */ |
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je LDown_53 |
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#ifdef PARANOID |
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jmp L_bugged_round53 |
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#endif /* PARANOID */ |
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LUp_53: |
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cmpb SIGN_POS,PARAM5 |
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jne LCheck_truncate_53 /* If negative then up==truncate */ |
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jmp LCheck_53_round_up |
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LDown_53: |
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cmpb SIGN_POS,PARAM5 |
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je LCheck_truncate_53 /* If positive then down==truncate */ |
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LCheck_53_round_up: |
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movl %ebx,%ecx |
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andl $0x000007ff,%ecx |
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orl %edx,%ecx |
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jnz LDo_53_round_up |
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jmp L_Re_normalise |
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LRound_nearest_53: |
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/* Do rounding of the 53rd bit if needed (nearest or even) */ |
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movl %ebx,%ecx |
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andl $0x000007ff,%ecx |
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cmpl $0x00000400,%ecx |
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jc LCheck_truncate_53 /* less than half, no increment needed */ |
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jnz LGreater_Half_53 /* greater than half, increment needed */ |
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/* Possibly half, we need to check the ls bits */ |
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orl %edx,%edx |
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jnz LGreater_Half_53 /* greater than half, increment needed */ |
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/* Exactly half, increment only if 53rd bit is 1 (round to even) */ |
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testl $0x00000800,%ebx |
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jz LTruncate_53 |
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LGreater_Half_53: /* Rounding: increment at the 53rd bit */ |
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LDo_53_round_up: |
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movb LOST_UP,FPU_bits_lost |
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andl $0xfffff800,%ebx /* Truncate to 53 bits */ |
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addl $0x00000800,%ebx |
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adcl $0,%eax |
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jmp LCheck_Round_Overflow |
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LCheck_truncate_53: |
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movl %ebx,%ecx |
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andl $0x000007ff,%ecx |
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orl %edx,%ecx |
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jz L_Re_normalise |
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LTruncate_53: |
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movb LOST_DOWN,FPU_bits_lost |
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andl $0xfffff800,%ebx /* Truncate to 53 bits */ |
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jmp L_Re_normalise |
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/* Round etc to 64 bit precision */ |
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LRound_To_64: |
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movl %esi,%ecx |
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andl CW_RC,%ecx |
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cmpl RC_RND,%ecx |
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je LRound_nearest_64 |
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cmpl RC_CHOP,%ecx |
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je LCheck_truncate_64 |
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cmpl RC_UP,%ecx /* Towards +infinity */ |
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je LUp_64 |
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cmpl RC_DOWN,%ecx /* Towards -infinity */ |
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je LDown_64 |
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#ifdef PARANOID |
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jmp L_bugged_round64 |
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#endif /* PARANOID */ |
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LUp_64: |
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cmpb SIGN_POS,PARAM5 |
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jne LCheck_truncate_64 /* If negative then up==truncate */ |
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orl %edx,%edx |
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jnz LDo_64_round_up |
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jmp L_Re_normalise |
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LDown_64: |
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cmpb SIGN_POS,PARAM5 |
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je LCheck_truncate_64 /* If positive then down==truncate */ |
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orl %edx,%edx |
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jnz LDo_64_round_up |
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jmp L_Re_normalise |
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LRound_nearest_64: |
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cmpl $0x80000000,%edx |
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jc LCheck_truncate_64 |
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jne LDo_64_round_up |
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/* Now test for round-to-even */ |
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testb $1,%bl |
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jz LCheck_truncate_64 |
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LDo_64_round_up: |
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movb LOST_UP,FPU_bits_lost |
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addl $1,%ebx |
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adcl $0,%eax |
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LCheck_Round_Overflow: |
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jnc L_Re_normalise |
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/* Overflow, adjust the result (significand to 1.0) */ |
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rcrl $1,%eax |
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rcrl $1,%ebx |
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incw EXP(%edi) |
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jmp L_Re_normalise |
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LCheck_truncate_64: |
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orl %edx,%edx |
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jz L_Re_normalise |
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LTruncate_64: |
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movb LOST_DOWN,FPU_bits_lost |
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L_Re_normalise: |
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testb $0xff,FPU_denormal |
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jnz Normalise_result |
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L_Normalised: |
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movl TAG_Valid,%edx |
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L_deNormalised: |
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cmpb LOST_UP,FPU_bits_lost |
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je L_precision_lost_up |
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cmpb LOST_DOWN,FPU_bits_lost |
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je L_precision_lost_down |
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L_no_precision_loss: |
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/* store the result */ |
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L_Store_significand: |
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movl %eax,SIGH(%edi) |
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movl %ebx,SIGL(%edi) |
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cmpw EXP_OVER,EXP(%edi) |
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jge L_overflow |
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movl %edx,%eax |
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/* Convert the exponent to 80x87 form. */ |
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addw EXTENDED_Ebias,EXP(%edi) |
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andw $0x7fff,EXP(%edi) |
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fpu_reg_round_signed_special_exit: |
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cmpb SIGN_POS,PARAM5 |
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je fpu_reg_round_special_exit |
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orw $0x8000,EXP(%edi) /* Negative sign for the result. */ |
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fpu_reg_round_special_exit: |
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#ifndef NON_REENTRANT_FPU |
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popl %ebx /* adjust the stack pointer */ |
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#endif /* NON_REENTRANT_FPU */ |
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fpu_Arith_exit: |
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popl %ebx |
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popl %edi |
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popl %esi |
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leave |
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ret |
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/* |
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* Set the FPU status flags to represent precision loss due to |
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* round-up. |
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*/ |
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L_precision_lost_up: |
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push %edx |
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push %eax |
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call set_precision_flag_up |
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popl %eax |
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popl %edx |
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jmp L_no_precision_loss |
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|
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/* |
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* Set the FPU status flags to represent precision loss due to |
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* truncation. |
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*/ |
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L_precision_lost_down: |
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push %edx |
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push %eax |
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call set_precision_flag_down |
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popl %eax |
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popl %edx |
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jmp L_no_precision_loss |
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/* |
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* The number is a denormal (which might get rounded up to a normal) |
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* Shift the number right the required number of bits, which will |
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* have to be undone later... |
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*/ |
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L_Make_denorm: |
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/* The action to be taken depends upon whether the underflow |
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exception is masked */ |
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testb CW_Underflow,%cl /* Underflow mask. */ |
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jz Unmasked_underflow /* Do not make a denormal. */ |
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movb DENORMAL,FPU_denormal |
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pushl %ecx /* Save */ |
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movw EXP_UNDER+1,%cx |
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subw EXP(%edi),%cx |
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cmpw $64,%cx /* shrd only works for 0..31 bits */ |
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jnc Denorm_shift_more_than_63 |
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cmpw $32,%cx /* shrd only works for 0..31 bits */ |
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jnc Denorm_shift_more_than_32 |
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/* |
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* We got here without jumps by assuming that the most common requirement |
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* is for a small de-normalising shift. |
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* Shift by [1..31] bits |
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*/ |
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addw %cx,EXP(%edi) |
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orl %edx,%edx /* extension */ |
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setne %ch /* Save whether %edx is non-zero */ |
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xorl %edx,%edx |
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shrd %cl,%ebx,%edx |
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shrd %cl,%eax,%ebx |
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shr %cl,%eax |
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orb %ch,%dl |
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popl %ecx |
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jmp Denorm_done |
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|
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/* Shift by [32..63] bits */ |
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Denorm_shift_more_than_32: |
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addw %cx,EXP(%edi) |
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subb $32,%cl |
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orl %edx,%edx |
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setne %ch |
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orb %ch,%bl |
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xorl %edx,%edx |
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shrd %cl,%ebx,%edx |
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shrd %cl,%eax,%ebx |
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shr %cl,%eax |
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orl %edx,%edx /* test these 32 bits */ |
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setne %cl |
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orb %ch,%bl |
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orb %cl,%bl |
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movl %ebx,%edx |
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movl %eax,%ebx |
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xorl %eax,%eax |
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popl %ecx |
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jmp Denorm_done |
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|
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/* Shift by [64..) bits */ |
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Denorm_shift_more_than_63: |
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cmpw $64,%cx |
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jne Denorm_shift_more_than_64 |
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|
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/* Exactly 64 bit shift */ |
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addw %cx,EXP(%edi) |
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xorl %ecx,%ecx |
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orl %edx,%edx |
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setne %cl |
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orl %ebx,%ebx |
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setne %ch |
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orb %ch,%cl |
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orb %cl,%al |
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movl %eax,%edx |
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xorl %eax,%eax |
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xorl %ebx,%ebx |
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popl %ecx |
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jmp Denorm_done |
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Denorm_shift_more_than_64: |
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movw EXP_UNDER+1,EXP(%edi) |
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/* This is easy, %eax must be non-zero, so.. */ |
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movl $1,%edx |
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xorl %eax,%eax |
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xorl %ebx,%ebx |
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popl %ecx |
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jmp Denorm_done |
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Unmasked_underflow: |
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movb UNMASKED_UNDERFLOW,FPU_denormal |
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jmp Denorm_done |
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/* Undo the de-normalisation. */ |
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Normalise_result: |
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cmpb UNMASKED_UNDERFLOW,FPU_denormal |
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je Signal_underflow |
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/* The number must be a denormal if we got here. */ |
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#ifdef PARANOID |
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/* But check it... just in case. */ |
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cmpw EXP_UNDER+1,EXP(%edi) |
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jne L_norm_bugged |
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#endif /* PARANOID */ |
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|
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#ifdef PECULIAR_486 |
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/* |
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* This implements a special feature of 80486 behaviour. |
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* Underflow will be signalled even if the number is |
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* not a denormal after rounding. |
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* This difference occurs only for masked underflow, and not |
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* in the unmasked case. |
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* Actual 80486 behaviour differs from this in some circumstances. |
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*/ |
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orl %eax,%eax /* ms bits */ |
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js LPseudoDenormal /* Will be masked underflow */ |
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#else |
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orl %eax,%eax /* ms bits */ |
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js L_Normalised /* No longer a denormal */ |
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#endif /* PECULIAR_486 */ |
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jnz LDenormal_adj_exponent |
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orl %ebx,%ebx |
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jz L_underflow_to_zero /* The contents are zero */ |
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|
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LDenormal_adj_exponent: |
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decw EXP(%edi) |
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|
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LPseudoDenormal: |
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testb $0xff,FPU_bits_lost /* bits lost == underflow */ |
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movl TAG_Special,%edx |
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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 */ |
|
|
|
SYM_FUNC_END(FPU_round)
|
|
|