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|
; $Id: cosf.asm $
;; @file
; IPRT - No-CRT cosf - 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 rf, measured in radians.
;
; @returns st(0) / xmm0
; @param rf [rbp + xCB*2] / xmm0
;
RT_NOCRT_BEGINPROC cosf
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
movss [xBP - 10h], xmm0
fld dword [xBP - 10h]
%else
fld dword [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: cosf(x) = sinf(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, 0 ; double
extern NAME(rtNoCrtMathSinCore)
call NAME(rtNoCrtMathSinCore)
;
; Return st0.
;
.return_val:
%ifdef RT_ARCH_AMD64
fstp dword [xBP - 10h]
movss xmm0, [xBP - 10h]
%endif
%ifdef RT_OS_WINDOWS
fldcw [xBP - 20h] ; restore original
%endif
.return:
leave
ret
;
; cosf(+/-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**-18. When fabs(input) is below this limit we can consider cosf(input) ~= 1.0.
.s_r64TinyCosTo1:
dq 0.000244140625
; 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(cosf)
|
