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linux/arch/x86/math-emu/wm_sqrt.S
Greg Kroah-Hartman b24413180f License cleanup: add SPDX GPL-2.0 license identifier to files with no license 
Many source files in the tree are missing licensing information, which
makes it harder for compliance tools to determine the correct license.

By default all files without license information are under the default
license of the kernel, which is GPL version 2.

Update the files which contain no license information with the 'GPL-2.0'
SPDX license identifier.  The SPDX identifier is a legally binding
shorthand, which can be used instead of the full boiler plate text.

This patch is based on work done by Thomas Gleixner and Kate Stewart and
Philippe Ombredanne.

How this work was done:

Patches were generated and checked against linux-4.14-rc6 for a subset of
the use cases:
 - file had no licensing information it it.
 - file was a */uapi/* one with no licensing information in it,
 - file was a */uapi/* one with existing licensing information,

Further patches will be generated in subsequent months to fix up cases
where non-standard license headers were used, and references to license
had to be inferred by heuristics based on keywords.

The analysis to determine which SPDX License Identifier to be applied to
a file was done in a spreadsheet of side by side results from of the
output of two independent scanners (ScanCode & Windriver) producing SPDX
tag:value files created by Philippe Ombredanne.  Philippe prepared the
base worksheet, and did an initial spot review of a few 1000 files.

The 4.13 kernel was the starting point of the analysis with 60,537 files
assessed.  Kate Stewart did a file by file comparison of the scanner
results in the spreadsheet to determine which SPDX license identifier(s)
to be applied to the file. She confirmed any determination that was not
immediately clear with lawyers working with the Linux Foundation.

Criteria used to select files for SPDX license identifier tagging was:
 - Files considered eligible had to be source code files.
 - Make and config files were included as candidates if they contained >5
   lines of source
 - File already had some variant of a license header in it (even if <5
   lines).

All documentation files were explicitly excluded.

The following heuristics were used to determine which SPDX license
identifiers to apply.

 - when both scanners couldn't find any license traces, file was
   considered to have no license information in it, and the top level
   COPYING file license applied.

   For non */uapi/* files that summary was:

   SPDX license identifier                            # files
   ---------------------------------------------------|-------
   GPL-2.0                                              11139

   and resulted in the first patch in this series.

   If that file was a */uapi/* path one, it was "GPL-2.0 WITH
   Linux-syscall-note" otherwise it was "GPL-2.0".  Results of that was:

   SPDX license identifier                            # files
   ---------------------------------------------------|-------
   GPL-2.0 WITH Linux-syscall-note                        930

   and resulted in the second patch in this series.

 - if a file had some form of licensing information in it, and was one
   of the */uapi/* ones, it was denoted with the Linux-syscall-note if
   any GPL family license was found in the file or had no licensing in
   it (per prior point).  Results summary:

   SPDX license identifier                            # files
   ---------------------------------------------------|------
   GPL-2.0 WITH Linux-syscall-note                       270
   GPL-2.0+ WITH Linux-syscall-note                      169
   ((GPL-2.0 WITH Linux-syscall-note) OR BSD-2-Clause)    21
   ((GPL-2.0 WITH Linux-syscall-note) OR BSD-3-Clause)    17
   LGPL-2.1+ WITH Linux-syscall-note                      15
   GPL-1.0+ WITH Linux-syscall-note                       14
   ((GPL-2.0+ WITH Linux-syscall-note) OR BSD-3-Clause)    5
   LGPL-2.0+ WITH Linux-syscall-note                       4
   LGPL-2.1 WITH Linux-syscall-note                        3
   ((GPL-2.0 WITH Linux-syscall-note) OR MIT)              3
   ((GPL-2.0 WITH Linux-syscall-note) AND MIT)             1

   and that resulted in the third patch in this series.

 - when the two scanners agreed on the detected license(s), that became
   the concluded license(s).

 - when there was disagreement between the two scanners (one detected a
   license but the other didn't, or they both detected different
   licenses) a manual inspection of the file occurred.

 - In most cases a manual inspection of the information in the file
   resulted in a clear resolution of the license that should apply (and
   which scanner probably needed to revisit its heuristics).

 - When it was not immediately clear, the license identifier was
   confirmed with lawyers working with the Linux Foundation.

 - If there was any question as to the appropriate license identifier,
   the file was flagged for further research and to be revisited later
   in time.

In total, over 70 hours of logged manual review was done on the
spreadsheet to determine the SPDX license identifiers to apply to the
source files by Kate, Philippe, Thomas and, in some cases, confirmation
by lawyers working with the Linux Foundation.

Kate also obtained a third independent scan of the 4.13 code base from
FOSSology, and compared selected files where the other two scanners
disagreed against that SPDX file, to see if there was new insights.  The
Windriver scanner is based on an older version of FOSSology in part, so
they are related.

Thomas did random spot checks in about 500 files from the spreadsheets
for the uapi headers and agreed with SPDX license identifier in the
files he inspected. For the non-uapi files Thomas did random spot checks
in about 15000 files.

In initial set of patches against 4.14-rc6, 3 files were found to have
copy/paste license identifier errors, and have been fixed to reflect the
correct identifier.

Additionally Philippe spent 10 hours this week doing a detailed manual
inspection and review of the 12,461 patched files from the initial patch
version early this week with:
 - a full scancode scan run, collecting the matched texts, detected
   license ids and scores
 - reviewing anything where there was a license detected (about 500+
   files) to ensure that the applied SPDX license was correct
 - reviewing anything where there was no detection but the patch license
   was not GPL-2.0 WITH Linux-syscall-note to ensure that the applied
   SPDX license was correct

This produced a worksheet with 20 files needing minor correction.  This
worksheet was then exported into 3 different .csv files for the
different types of files to be modified.

These .csv files were then reviewed by Greg.  Thomas wrote a script to
parse the csv files and add the proper SPDX tag to the file, in the
format that the file expected.  This script was further refined by Greg
based on the output to detect more types of files automatically and to
distinguish between header and source .c files (which need different
comment types.)  Finally Greg ran the script using the .csv files to
generate the patches.

Reviewed-by: Kate Stewart <kstewart@linuxfoundation.org>
Reviewed-by: Philippe Ombredanne <pombredanne@nexb.com>
Reviewed-by: Thomas Gleixner <tglx@linutronix.de>
Signed-off-by: Greg Kroah-Hartman <gregkh@linuxfoundation.org>
2017-11-02 11:10:55 +01:00

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/* SPDX-License-Identifier: GPL-2.0 */
.file "wm_sqrt.S"
/*---------------------------------------------------------------------------+
| wm_sqrt.S |
| |
| Fixed point arithmetic square root evaluation. |
| |
| Copyright (C) 1992,1993,1995,1997 |
| W. Metzenthen, 22 Parker St, Ormond, Vic 3163, |
| Australia. E-mail billm@suburbia.net |
| |
| Call from C as: |
| int wm_sqrt(FPU_REG *n, unsigned int control_word) |
| |
+---------------------------------------------------------------------------*/
/*---------------------------------------------------------------------------+
| wm_sqrt(FPU_REG *n, unsigned int control_word) |
| returns the square root of n in n. |
| |
| Use Newton's method to compute the square root of a number, which must |
| be in the range [1.0 .. 4.0), to 64 bits accuracy. |
| Does not check the sign or tag of the argument. |
| Sets the exponent, but not the sign or tag of the result. |
| |
| The guess is kept in %esi:%edi |
+---------------------------------------------------------------------------*/
#include "exception.h"
#include "fpu_emu.h"
#ifndef NON_REENTRANT_FPU
/* Local storage on the stack: */
#define FPU_accum_3 -4(%ebp) /* ms word */
#define FPU_accum_2 -8(%ebp)
#define FPU_accum_1 -12(%ebp)
#define FPU_accum_0 -16(%ebp)
/*
* The de-normalised argument:
* sq_2 sq_1 sq_0
* b b b b b b b ... b b b b b b .... b b b b 0 0 0 ... 0
* ^ binary point here
*/
#define FPU_fsqrt_arg_2 -20(%ebp) /* ms word */
#define FPU_fsqrt_arg_1 -24(%ebp)
#define FPU_fsqrt_arg_0 -28(%ebp) /* ls word, at most the ms bit is set */
#else
/* Local storage in a static area: */
.data
.align 4,0
FPU_accum_3:
.long 0 /* ms word */
FPU_accum_2:
.long 0
FPU_accum_1:
.long 0
FPU_accum_0:
.long 0
/* The de-normalised argument:
sq_2 sq_1 sq_0
b b b b b b b ... b b b b b b .... b b b b 0 0 0 ... 0
^ binary point here
*/
FPU_fsqrt_arg_2:
.long 0 /* ms word */
FPU_fsqrt_arg_1:
.long 0
FPU_fsqrt_arg_0:
.long 0 /* ls word, at most the ms bit is set */
#endif /* NON_REENTRANT_FPU */
.text
ENTRY(wm_sqrt)
pushl %ebp
movl %esp,%ebp
#ifndef NON_REENTRANT_FPU
subl $28,%esp
#endif /* NON_REENTRANT_FPU */
pushl %esi
pushl %edi
pushl %ebx
movl PARAM1,%esi
movl SIGH(%esi),%eax
movl SIGL(%esi),%ecx
xorl %edx,%edx
/* We use a rough linear estimate for the first guess.. */
cmpw EXP_BIAS,EXP(%esi)
jnz sqrt_arg_ge_2
shrl $1,%eax /* arg is in the range [1.0 .. 2.0) */
rcrl $1,%ecx
rcrl $1,%edx
sqrt_arg_ge_2:
/* From here on, n is never accessed directly again until it is
replaced by the answer. */
movl %eax,FPU_fsqrt_arg_2 /* ms word of n */
movl %ecx,FPU_fsqrt_arg_1
movl %edx,FPU_fsqrt_arg_0
/* Make a linear first estimate */
shrl $1,%eax
addl $0x40000000,%eax
movl $0xaaaaaaaa,%ecx
mull %ecx
shll %edx /* max result was 7fff... */
testl $0x80000000,%edx /* but min was 3fff... */
jnz sqrt_prelim_no_adjust
movl $0x80000000,%edx /* round up */
sqrt_prelim_no_adjust:
movl %edx,%esi /* Our first guess */
/* We have now computed (approx) (2 + x) / 3, which forms the basis
for a few iterations of Newton's method */
movl FPU_fsqrt_arg_2,%ecx /* ms word */
/*
* From our initial estimate, three iterations are enough to get us
* to 30 bits or so. This will then allow two iterations at better
* precision to complete the process.
*/
/* Compute (g + n/g)/2 at each iteration (g is the guess). */
shrl %ecx /* Doing this first will prevent a divide */
/* overflow later. */
movl %ecx,%edx /* msw of the arg / 2 */
divl %esi /* current estimate */
shrl %esi /* divide by 2 */
addl %eax,%esi /* the new estimate */
movl %ecx,%edx
divl %esi
shrl %esi
addl %eax,%esi
movl %ecx,%edx
divl %esi
shrl %esi
addl %eax,%esi
/*
* Now that an estimate accurate to about 30 bits has been obtained (in %esi),
* we improve it to 60 bits or so.
*
* The strategy from now on is to compute new estimates from
* guess := guess + (n - guess^2) / (2 * guess)
*/
/* First, find the square of the guess */
movl %esi,%eax
mull %esi
/* guess^2 now in %edx:%eax */
movl FPU_fsqrt_arg_1,%ecx
subl %ecx,%eax
movl FPU_fsqrt_arg_2,%ecx /* ms word of normalized n */
sbbl %ecx,%edx
jnc sqrt_stage_2_positive
/* Subtraction gives a negative result,
negate the result before division. */
notl %edx
notl %eax
addl $1,%eax
adcl $0,%edx
divl %esi
movl %eax,%ecx
movl %edx,%eax
divl %esi
jmp sqrt_stage_2_finish
sqrt_stage_2_positive:
divl %esi
movl %eax,%ecx
movl %edx,%eax
divl %esi
notl %ecx
notl %eax
addl $1,%eax
adcl $0,%ecx
sqrt_stage_2_finish:
sarl $1,%ecx /* divide by 2 */
rcrl $1,%eax
/* Form the new estimate in %esi:%edi */
movl %eax,%edi
addl %ecx,%esi
jnz sqrt_stage_2_done /* result should be [1..2) */
#ifdef PARANOID
/* It should be possible to get here only if the arg is ffff....ffff */
cmp $0xffffffff,FPU_fsqrt_arg_1
jnz sqrt_stage_2_error
#endif /* PARANOID */
/* The best rounded result. */
xorl %eax,%eax
decl %eax
movl %eax,%edi
movl %eax,%esi
movl $0x7fffffff,%eax
jmp sqrt_round_result
#ifdef PARANOID
sqrt_stage_2_error:
pushl EX_INTERNAL|0x213
call EXCEPTION
#endif /* PARANOID */
sqrt_stage_2_done:
/* Now the square root has been computed to better than 60 bits. */
/* Find the square of the guess. */
movl %edi,%eax /* ls word of guess */
mull %edi
movl %edx,FPU_accum_1
movl %esi,%eax
mull %esi
movl %edx,FPU_accum_3
movl %eax,FPU_accum_2
movl %edi,%eax
mull %esi
addl %eax,FPU_accum_1
adcl %edx,FPU_accum_2
adcl $0,FPU_accum_3
/* movl %esi,%eax */
/* mull %edi */
addl %eax,FPU_accum_1
adcl %edx,FPU_accum_2
adcl $0,FPU_accum_3
/* guess^2 now in FPU_accum_3:FPU_accum_2:FPU_accum_1 */
movl FPU_fsqrt_arg_0,%eax /* get normalized n */
subl %eax,FPU_accum_1
movl FPU_fsqrt_arg_1,%eax
sbbl %eax,FPU_accum_2
movl FPU_fsqrt_arg_2,%eax /* ms word of normalized n */
sbbl %eax,FPU_accum_3
jnc sqrt_stage_3_positive
/* Subtraction gives a negative result,
negate the result before division */
notl FPU_accum_1
notl FPU_accum_2
notl FPU_accum_3
addl $1,FPU_accum_1
adcl $0,FPU_accum_2
#ifdef PARANOID
adcl $0,FPU_accum_3 /* This must be zero */
jz sqrt_stage_3_no_error
sqrt_stage_3_error:
pushl EX_INTERNAL|0x207
call EXCEPTION
sqrt_stage_3_no_error:
#endif /* PARANOID */
movl FPU_accum_2,%edx
movl FPU_accum_1,%eax
divl %esi
movl %eax,%ecx
movl %edx,%eax
divl %esi
sarl $1,%ecx /* divide by 2 */
rcrl $1,%eax
/* prepare to round the result */
addl %ecx,%edi
adcl $0,%esi
jmp sqrt_stage_3_finished
sqrt_stage_3_positive:
movl FPU_accum_2,%edx
movl FPU_accum_1,%eax
divl %esi
movl %eax,%ecx
movl %edx,%eax
divl %esi
sarl $1,%ecx /* divide by 2 */
rcrl $1,%eax
/* prepare to round the result */
notl %eax /* Negate the correction term */
notl %ecx
addl $1,%eax
adcl $0,%ecx /* carry here ==> correction == 0 */
adcl $0xffffffff,%esi
addl %ecx,%edi
adcl $0,%esi
sqrt_stage_3_finished:
/*
* The result in %esi:%edi:%esi should be good to about 90 bits here,
* and the rounding information here does not have sufficient accuracy
* in a few rare cases.
*/
cmpl $0xffffffe0,%eax
ja sqrt_near_exact_x
cmpl $0x00000020,%eax
jb sqrt_near_exact
cmpl $0x7fffffe0,%eax
jb sqrt_round_result
cmpl $0x80000020,%eax
jb sqrt_get_more_precision
sqrt_round_result:
/* Set up for rounding operations */
movl %eax,%edx
movl %esi,%eax
movl %edi,%ebx
movl PARAM1,%edi
movw EXP_BIAS,EXP(%edi) /* Result is in [1.0 .. 2.0) */
jmp fpu_reg_round
sqrt_near_exact_x:
/* First, the estimate must be rounded up. */
addl $1,%edi
adcl $0,%esi
sqrt_near_exact:
/*
* This is an easy case because x^1/2 is monotonic.
* We need just find the square of our estimate, compare it
* with the argument, and deduce whether our estimate is
* above, below, or exact. We use the fact that the estimate
* is known to be accurate to about 90 bits.
*/
movl %edi,%eax /* ls word of guess */
mull %edi
movl %edx,%ebx /* 2nd ls word of square */
movl %eax,%ecx /* ls word of square */
movl %edi,%eax
mull %esi
addl %eax,%ebx
addl %eax,%ebx
#ifdef PARANOID
cmp $0xffffffb0,%ebx
jb sqrt_near_exact_ok
cmp $0x00000050,%ebx
ja sqrt_near_exact_ok
pushl EX_INTERNAL|0x214
call EXCEPTION
sqrt_near_exact_ok:
#endif /* PARANOID */
or %ebx,%ebx
js sqrt_near_exact_small
jnz sqrt_near_exact_large
or %ebx,%edx
jnz sqrt_near_exact_large
/* Our estimate is exactly the right answer */
xorl %eax,%eax
jmp sqrt_round_result
sqrt_near_exact_small:
/* Our estimate is too small */
movl $0x000000ff,%eax
jmp sqrt_round_result
sqrt_near_exact_large:
/* Our estimate is too large, we need to decrement it */
subl $1,%edi
sbbl $0,%esi
movl $0xffffff00,%eax
jmp sqrt_round_result
sqrt_get_more_precision:
/* This case is almost the same as the above, except we start
with an extra bit of precision in the estimate. */
stc /* The extra bit. */
rcll $1,%edi /* Shift the estimate left one bit */
rcll $1,%esi
movl %edi,%eax /* ls word of guess */
mull %edi
movl %edx,%ebx /* 2nd ls word of square */
movl %eax,%ecx /* ls word of square */
movl %edi,%eax
mull %esi
addl %eax,%ebx
addl %eax,%ebx
/* Put our estimate back to its original value */
stc /* The ms bit. */
rcrl $1,%esi /* Shift the estimate left one bit */
rcrl $1,%edi
#ifdef PARANOID
cmp $0xffffff60,%ebx
jb sqrt_more_prec_ok
cmp $0x000000a0,%ebx
ja sqrt_more_prec_ok
pushl EX_INTERNAL|0x215
call EXCEPTION
sqrt_more_prec_ok:
#endif /* PARANOID */
or %ebx,%ebx
js sqrt_more_prec_small
jnz sqrt_more_prec_large
or %ebx,%ecx
jnz sqrt_more_prec_large
/* Our estimate is exactly the right answer */
movl $0x80000000,%eax
jmp sqrt_round_result
sqrt_more_prec_small:
/* Our estimate is too small */
movl $0x800000ff,%eax
jmp sqrt_round_result
sqrt_more_prec_large:
/* Our estimate is too large */
movl $0x7fffff00,%eax
jmp sqrt_round_result
ENDPROC(wm_sqrt)
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