1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
|
; $Id: cos.asm $
;; @file
; IPRT - No-CRT cos - AMD64 & X86.
;
;
; Copyright (C) 2006-2023 Oracle and/or its affiliates.
;
; This file is part of VirtualBox base platform packages, as
; available from https://www.virtualbox.org.
;
; This program is free software; you can redistribute it and/or
; modify it under the terms of the GNU General Public License
; as published by the Free Software Foundation, in version 3 of the
; License.
;
; This program is distributed in the hope that it will be useful, but
; WITHOUT ANY WARRANTY; without even the implied warranty of
; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
; General Public License for more details.
;
; You should have received a copy of the GNU General Public License
; along with this program; if not, see <https://www.gnu.org/licenses>.
;
; The contents of this file may alternatively be used under the terms
; of the Common Development and Distribution License Version 1.0
; (CDDL), a copy of it is provided in the "COPYING.CDDL" file included
; in the VirtualBox distribution, in which case the provisions of the
; CDDL are applicable instead of those of the GPL.
;
; You may elect to license modified versions of this file under the
; terms and conditions of either the GPL or the CDDL or both.
;
; SPDX-License-Identifier: GPL-3.0-only OR CDDL-1.0
;
%define RT_ASM_WITH_SEH64
%include "iprt/asmdefs.mac"
%include "iprt/x86.mac"
BEGINCODE
;;
; Compute the cosine of rd, measured in radians.
;
; @returns st(0) / xmm0
; @param rd [rbp + xCB*2] / xmm0
;
RT_NOCRT_BEGINPROC cos
push xBP
SEH64_PUSH_xBP
mov xBP, xSP
SEH64_SET_FRAME_xBP 0
sub xSP, 20h
SEH64_ALLOCATE_STACK 20h
SEH64_END_PROLOGUE
%ifdef RT_OS_WINDOWS
;
; Make sure we use full precision and not the windows default of 53 bits.
;
;; @todo not sure if this makes any difference...
fnstcw [xBP - 20h]
mov ax, [xBP - 20h]
or ax, X86_FCW_PC_64 ; includes both bits, so no need to clear the mask.
mov [xBP - 1ch], ax
fldcw [xBP - 1ch]
%endif
;
; Load the input into st0.
;
%ifdef RT_ARCH_AMD64
movsd [xBP - 10h], xmm0
fld qword [xBP - 10h]
%else
fld qword [xBP + xCB*2]
%endif
;
; The FCOS instruction has a very narrow range (-3pi/8 to 3pi/8) where it
; works reliably, so outside that we'll use the FSIN instruction instead
; as it has a larger good range (-5pi/4 to 1pi/4 for cosine).
; Input conversion follows: cos(x) = sin(x + pi/2)
;
; We examin the input and weed out non-finit numbers first.
;
; We only do the range check on normal finite numbers.
fxam
fnstsw ax
and ax, X86_FSW_C3 | X86_FSW_C2 | X86_FSW_C0
cmp ax, X86_FSW_C2 ; Normal finite number (excluding zero)
je .finite
cmp ax, X86_FSW_C3 ; Zero
je .zero
cmp ax, X86_FSW_C3 | X86_FSW_C2 ; Denormals - treat them as zero.
je .zero
cmp ax, X86_FSW_C0 ; NaN - must handle it special,
je .nan
; Pass infinities and unsupported inputs to fcos, assuming it does the right thing.
; We also jump here if we get a finite number in the "good" range, see below.
.do_fcos:
fcos
jmp .return_val
;
; Finite number.
;
; First check if it's a very tiny number where we can simply return 1.
; Next check if it's in the range where FCOS is reasonable, otherwise
; go to FSIN to do the work.
;
.finite:
fld st0
fabs
fld qword [.s_r64TinyCosTo1 xWrtRIP]
fcomip st1
ja .zero_extra_pop
.not_that_tiny_input:
fld qword [.s_r64FCosOkay xWrtRIP]
fcomip st1
ffreep st0 ; pop fabs(input)
ja .do_fcos ; jmp if fabs(input) < .s_r64FCosOkay
;
; If we have a positive number we subtract 3pi/2, for negative we add pi/2.
; We still have the FXAM result in AX.
;
.outside_fcos_range:
test ax, X86_FSW_C1 ; The sign bit.
jnz .adjust_negative_to_sine
; Calc -3pi/2 using FPU-internal pi constant.
fldpi
fadd st0, st0 ; st0=2pi
fldpi
fdiv qword [.s_r64Two xWrtRIP] ; st1=2pi; st0=pi/2
fsubp st1, st0 ; st0=3pi/2
fchs ; st0=-3pi/2
jmp .make_sine_adjustment
.adjust_negative_to_sine:
; Calc +pi/2.
fldpi
fdiv qword [.s_r64Two xWrtRIP] ; st1=2pi; st0=pi/2
.make_sine_adjustment:
faddp st1, st0
;
; Call internal sine worker to calculate st0=sin(st0)
;
.do_sine:
mov ecx, 1 ; double
extern NAME(rtNoCrtMathSinCore)
call NAME(rtNoCrtMathSinCore)
;
; Return st0.
;
.return_val:
%ifdef RT_ARCH_AMD64
fstp qword [xBP - 10h]
movsd xmm0, [xBP - 10h]
%endif
%ifdef RT_OS_WINDOWS
fldcw [xBP - 20h] ; restore original
%endif
.return:
leave
ret
;
; cos(+/-0) = +1.0
;
.zero_extra_pop:
ffreep st0
.zero:
ffreep st0
fld1
jmp .return_val
;
; Input is NaN, output it unmodified as far as we can (FLD changes SNaN
; to QNaN when masked).
;
.nan:
%ifdef RT_ARCH_AMD64
ffreep st0
%endif
jmp .return
;
; Local constants.
;
ALIGNCODE(8)
; About 2**-27. When fabs(input) is below this limit we can consider cos(input) ~= 1.0.
.s_r64TinyCosTo1:
dq 7.4505806e-9
; The absolute limit for the range which FCOS is expected to produce reasonable results.
.s_r64FCosOkay:
dq 1.1780972450961724644225 ; 3*pi/8
.s_r64Two:
dq 2.0
ENDPROC RT_NOCRT(cos)
|
