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/* -*- Mode: Asm -*- */
/* Copyright (c) 2002 Michael Stumpf <mistumpf@de.pepperl-fuchs.com>
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
* Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in
the documentation and/or other materials provided with the
distribution.
* Neither the name of the copyright holders nor the names of
contributors may be used to endorse or promote products derived
from this software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
POSSIBILITY OF SUCH DAMAGE.
*/
/*
fp_cosinus.S is part of FPlib V 0.3.0 ported to avr-as
for details see readme.fplib
*----------------------------------------------------------------------------------------
*
* A = cosinus(A) with A = [0...2PI[
*
* _ _ _ _ _ _
* |\ / \ | / | / |\ ;
* |a\ b c / d a \ b | c /d | / | \ ;
* +--\-----/-------- => ---\--+--/--- => +--/--- => +--X--- ;
* 0 \ / 2pi -pi \ | / pi 0| / pi | / pi/2 ;
* \_/ \_/ _/ _/ ;
* cos(x-PI) = cos(x) = cos(x) ;
* -cos(x) cos(-x)
* section sign
* a b c d a b c d a b c d a b c d
* + - - + - + + - - + + - + + + +
* sign complement for sections b + c
*/
#if !defined(DOXYGEN)
#include "gasava.inc"
#include "fplib.inc"
TEXT_SEG(fplib, __fp_cosinus)
FUNCTION(__fp_cosinus)
GLOBAL(__fp_cosinus) ; input A = [-2PI...2PI[
PUSH rSI0
ANDI rA3,0x7F ; input A = [0...2PI[
LDI rB3,0xC0
LDI rB2,0x49
LDI rB1,0x0F
LDI rB0,0xDB ; load -PI
RCALL _U(__addsf3) ; now A = [-PI..+PI[
LDI rSI0,0x80 ; assume sign complement (b,c)
ANDI rA3,0x7F ; positive cos(x-PI) = cos(-(x-PI)) = -cos(x)
LDI rB3,0x3F
LDI rB2,0xC9
LDI rB1,0x0F
LDI rB0,0xDB ; load PI/2
CP rA0,rB0 ;
CPC rA1,rB1 ;
CPC rA2,rB2
CPC rA3,rB3 ; cmp A to PI/2
BRCS fp_cosinus_00 ; branch if lower
; now (A = x) > PI/2, B = PI/2
LDI rB3,0xC0
LDI rB2,0x49 ; B = -PI
RCALL _U(__addsf3) ; PI-A = -(A+-PI)
CLR rSI0 ; no sign complement (a,d)
fp_cosinus_00:
RCALL _U(square) ; x
ORI rA3,0x80 ; -x
;
LDI ZL,LOW(table_cos) ;
LDI ZH,HIGH(table_cos) ;
RCALL _U(__fp_powerseries) ;
EOR rA3,rSI0 ; complement sign
POP rSI0
RET
ENDFUNC
PGM_SECTION
/* cos(x) = ( 1 - x(1/2! - x(1/4! - x(1/6! - x(1/8! - x(1/10! - x(1/12! - x(1/14!))
* these constants are *no* IEEE float values: exponet unpacked allready
* first byte : exponent
* 2nd byte : msb of mantissa with sign as bit 7
* 3rd & 4th byte : mantissa
*/
table_cos:
DCB 8 ; no of table entries - 1 (preload value)
; looks like 6 steps are sufficient
; 7 steps for sin(pi) == 0
;;DCB 0x4A, 0x34, 0x13, 0xC3 ;, 0x1E ; 1/18!
DCB 0x52, 0x57, 0x3F, 0x9F ;, 0x3A ; 1/16!
DCB 0x5A, 0x49, 0xCB, 0xA5 ;, 0x46 ; 1/14!
DCB 0x62, 0x0F, 0x76, 0xC7 ;, 0x80 ;C6 ; 1/12!
DCB 0x69, 0x13, 0xF2, 0x7E ;, 0xBC ; 1/10!
DCB 0x6F, 0x50, 0x0D, 0x01 ;, 0xD0 ; 1/8!
DCB 0x75, 0x36, 0x0B, 0x61 ;, 0xB6 ; 1/6!
DCB 0x7A, 0x2A, 0xAA, 0xAB ;, 0xAB ; 1/4! = 1/24
DCB 0x7E, 0x00, 0x00, 0x00 ;, 0x00 ; 1/2!
DCB 0x7F, 0x00, 0x00, 0x00 ;, 0x00 ; 1.0
DCB 0x00
#endif /* not DOXYGEN */
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