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/* Copyright (c) 2002 Michael Stumpf <mistumpf@de.pepperl-fuchs.com>
Copyright (c) 2006 Dmitry Xmelkov
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. */
/* $Id: tan.S,v 1.10 2007/01/14 15:13:39 dmix Exp $ */
#include "fp32def.h"
#include "asmdef.h"
/* float tan (float A);
The tan() function returns the tangent of A, where A is given
in radians.
*/
/* Calculation:
0 <= x <= Pi/4 --> tan(x) fmod
Pi/4 < x < Pi/2 --> 1/tan(Pi/2-x) fmod, Pi/2-x, 1/x
Pi/2 <= x <= 3*Pi/4 --> -1/tan(x-Pi/2) fmod, 1/x, -x
3*Pi/4 < x < Pi --> -tan(Pi-x) fmod, Pi/2-x, -x
*/
#define HI40_PIO4 0x3F490FDA /* (flt40_t) Pi/4 */
#define LO40_PIO4 0xA2 /* --"-- */
#define HI40_PIO2 0x3FC90FDA /* (flt40_t) Pi/2 */
#define LO40_PIO2 0xA2 /* --"-- */
#define rsign YH
ENTRY tan
; save sign
push rsign
mov rsign, rA3
; fmod by Pi/2
rcall _U(__fp_rempio2)
; save perion number
lsr ZL
ror rsign
; is A <= Pi/4 ?
#if LO40_PIO4 == 0xFF /* HI40_PIO4: increment is not needed */
# error
#endif
ldi rB0, lo8(HI40_PIO4)
ldi rB1, hi8(HI40_PIO4)
ldi rB2, hlo8(HI40_PIO4)
ldi rB3, hhi8(HI40_PIO4)
cpi rAE, LO40_PIO4 + 1
cpc rA0, rB0
cpc rA1, rB1
cpc rA2, rB2
cpc rA3, rB3
ror rsign ; save comparison result
brmi 1f ; N == C flag after comparison
; for A > Pi/4: tan(A) == 1/tan(Pi/2 - A)
#if (HI40_PIO4 ^ HI40_PIO2) & 0xFF00FFFF /* 'ldi' optimization */
# error
#endif
ldi rBE, LO40_PIO2
ldi rB2, hlo8(HI40_PIO2)
ori rA3, 0x80
rcall _U(__addsf3x)
rcall _U(__fp_round)
; calculate tan(A) for 0 <= A <= Pi/4
1: ldi ZL, lo8(.L_table)
ldi ZH, hi8(.L_table)
rcall _U(__fp_powsodd)
; correct result
lsl rsign
brvs 2f
rcall _U(inverse)
2: lsl rsign
brvc 3f
subi rA3, 0x80
3: pop rsign
ret
ENDFUNC
PGM_SECTION
.L_table:
.byte 6
.byte 0x64,0xec,0x1b,0x3c ; 0.0095168091
.byte 0x04,0xbc,0x16,0x3e,0x3b ; 0.0029005250
.byte 0xe5,0xb9,0x3c,0xc9,0x3c ; 0.0245650893
.byte 0x37,0xc2,0x9e,0x5a,0x3d ; 0.0533740603
.byte 0x66,0x04,0x98,0x08,0x3e ; 0.1333923995
.byte 0xea,0x69,0xaa,0xaa,0x3e ; 0.3333314036
.byte 0x00,0x00,0x00,0x80,0x3f ; 1.0000000000
.end
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