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/* Copyright (c) 2002, Reiner Patommel
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.
* ----------------------------------------------------------------------------
* asin.S
*-----------------------------------------------------------------------------
Contributors:
Created by Reiner Patommel, 01 Dec 2002
-*- Mode: Asm -*-
* Accuracy: 0.00000 <= |x| <= 0.99999: better than +/-3*10^-7
* 0.99999 <= |x| < 1.00000: better than +/-5*10^-5
* ----------------------------------------------------------------------------
* A = asin(A)
*--------------------------------------------------------------------------*/
/* $Id: asin.S,v 1.4.2.1 2005/01/07 21:27:14 joerg_wunsch Exp $ */
#if !defined(DOXYGEN)
#include "gasava.inc"
#include "fplib.inc"
#define sign r26
TEXT_SEG(fplib, asin)
FUNCTION(asin)
GLOBAL(asin)
CLR sign
SBRC rA3, 7
ORI sign, 1
PUSH sign ; remember sign of x (bit 0 set: x < 0)
ANDI rA3, 0x7F ; x = |x|
LDI rB3, 0x3F
LDI rB2, 0x80
CPI rA0, 0x01
CPC rA1, __zero_reg__
CPC rA2, rB2
CPC rA3, rB3 ; A - 1.0000001192092896
BRCS _asin_calc ; A <= 1.0
XCALL (__fp_nanEDOM) ; A > 1.0 -> argument range error
POP sign ; clean-up
RET ; return with NAN
_asin_calc: ; here x <= 1.0
PUSH rA3
PUSH rA2
PUSH rA1
PUSH rA0 ; save x
LDI ZL,LOW(table_asin)
LDI ZH,HIGH(table_asin) ; point to table
XCALL _U(__fp_powerseries) ; A = P0 + x(P1 + x(P2 + x(P3 + x(P4 +
; x(P5 + x(P6 + x(P7)))))))
POP rB0
POP rB1
POP rB2
POP rB3 ; get x again
PUSH rA3
PUSH rA2
PUSH rA1
PUSH rA0 ; save A
LDI rA3, 0x3F
LDI rA2, 0x80
CLR rA1
CLR rA0 ; A = 1.0
ORI rB3, 0x80 ; B = -x
XCALL _U(__addsf3) ; A = 1 + (-x)
XCALL _U(sqrt) ; A = sqrt(1-x)
POP rB0
POP rB1
POP rB2
POP rB3 ; get A again
XCALL _U(__mulsf3) ; A = (1 - x)^2 (P0 + x(P1 + x(P2 + x(P3 +
; x(P4 + x(P5 + x(P6 + x(P7))))))))
LDI rB3, 0x3F
LDI rB2, 0xC9
LDI rB1, 0x0F
LDI rB0, 0xDB ; B = PI/2
ORI rA3, 0x80 ; A = -A
XCALL _U(__addsf3) ; A = pi/2 - (1 - x)^2 (P0 + x(P1 + x(P2 +
; x(P3 + x(P4 + x(P5 + x(P6 + x(P7))))))))
POP sign ; get sign of x again
SBRC sign, 0
ORI rA3, 0x80 ; asin(x) = -asin(-x)
RET
ENDFUNC
/*----------------------------------------------------------------------------
asin(x) = pi/2 - (1 - x)^2 (P0 + x(P1 + x(P2 + x(P3 + x(P4 + x(P5 +
x(P6 + x(P7))))))))
*
* P0 : 1.57079 63050 [3FC90FDA]
* P1 : -0,21459 88016 [BE5BBFCA]
* P2 : 0.08897 89874 [3DB63A9E]
* P3 : -0.05017 43046 [BD4D8392]
* P4 : 0.03089 18810 [3CFD10F8]
* P5 : -0.01708 81256 [BC8BFC66]
* P6 : 0.00667 00901 [3BDA90C5]
* P7 : -0.00126 24911 [BAA57A2C]
*/
PGM_SECTION
table_asin: DCB 7
DCB 0x75, 0xA5, 0x7A, 0x2C ; P7
DCB 0x77, 0x5A, 0x90, 0xC5 ; P6
DCB 0x79, 0x8B, 0xFC, 0x66 ; P5
DCB 0x79, 0x7D, 0x10, 0xF8 ; P4
DCB 0x7A, 0xCD, 0x83, 0x92 ; P3
DCB 0x7B, 0x36, 0x3A, 0x9E ; P2
DCB 0x7C, 0xDB, 0xBF, 0xCA ; P1
DCB 0x7F, 0x49, 0x0F, 0xDA ; P0
DCB 0x00 ; 0.0
/*--------------------------------------------------------------------------*/
#endif /* not DOXYGEN */
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