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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.
*/
/*
tan.S is part of FPlib V 0.3.0 ported to avr-as
for details see readme.fplib
*----------------------------------------------------------------------------------------
* A = tan(A)
*
* tan( x ) = tan( fmod(x,PI) )
* tan(-x ) = - tan(x)
*
* since the power series of tangens converts quite slow for bigger values
* the formula tan(x) = 1/tan(PI/2 - x) is used for values > PI/4
*/
#if !defined(DOXYGEN)
#include "gasava.inc"
#include "fplib.inc"
TEXT_SEG(fplib, tan)
FUNCTION(tan)
GLOBAL(tan)
PUSH rSI0
MOV rSI0,rA3 ; keep sign tan(x) = -tan(-x)
ANDI rSI0,0x80 ; assume inversion flag zero
ANDI rA3,0x7F
CPI rA3,0x39
BRCS _tan_100 ; (tan(A < 0x39000000)=A)
LDI rB3,0x40
LDI rB2,0x49
LDI rB1,0x0F
LDI rB0,0xDB ; load PI
RCALL _U(fmod) ; X = x [0..PI[
LDI rB3,0x3F
LDI rB2,0xC9
LDI rB1,0x0F
LDI rB0,0xDB ; load PI/2
CP rB0,rA0
CPC rB1,rA1
CPC rB2,rA2
CPC rB3,rA3 ; B(=PI/2) - A
BREQ _tan_INF
BRCC _tan_10
LDI rB3,0x40
LDI rB2,0x49 ; load PI
ORI rA3,0x80 ; A = -A
RCALL _U(__addsf3) ; A = A+B = B + (-A)
LDI rB3,0x80
EOR rSI0,rB3
_tan_10:
LDI rB3,0x3F
LDI rB2,0x49
LDI rB1,0x0F
LDI rB0,0xDB ; load PI/4
CP rB0,rA0
CPC rB1,rA1
CPC rB2,rA2
CPC rB3,rA3 ; B(=PI/4) - A
BRCC _tan_00
INC rSI0
ORI rA3,0x80 ; negate A
LDI rB2,0xC9 ; P/4 -> PI/2
RCALL _U(__addsf3) ; PI/2 - A
_tan_00:
PUSH rA3
PUSH rA2
PUSH rA1
PUSH rA0
RCALL _U(square) ; x
ORI rA3,0x80 ; -x
LDI ZL,LOW(table_tan)
LDI ZH,HIGH(table_tan)
RCALL _U(__fp_powerseries)
POP rB0
POP rB1
POP rB2
POP rB3
RCALL _U(__mulsf3)
SBRS rSI0,0
RJMP _tan_100
RCALL _U(__fp_inverse)
_tan_100:
SBRC rSI0,7
ORI rA3,0x80
POP rSI0
RET
_tan_INF:
POP rSI0
RJMP _U(__fp_nan)
ENDFUNC
/*
*
* see cephes22: tan.c
* and FPlib doc
* 1 - x(f1 - x(f2 - xf3))
* tan(x) = x * --------------------------
* 1 - x(h1 - x(h2 - xh3))
*
* f3 : 1.09079E-5
* f2 : 0.00310705
* f1 : 0.130906
* 1.0 :
*
* h3 : 0.000253971
* h2 : 0.0245202
* h1 : 0.464239
*/
PGM_SECTION
/* these constants are *no* IEEE float values: exponent unpacked allready
* first byte : exponent
* 2nd byte : msb of mantissa with sign as bit 7
* 3rd & 4th byte : mantissa
*/
table_tan: DCB 3 ; no of table entries - 1 (preload value)
DCB 0x73, 0x05, 0x27, 0x60 ; h - first calculate denominator
DCB 0x79, 0x48, 0xDE, 0x92
DCB 0x7D, 0x6D, 0xB0, 0xCA
DCB 0x7F, 0x00, 0x00, 0x00
DCB 3 ; no of table entries - 1 (preload value)
DCB 0x6E, 0x37, 0x00, 0xF3 ; f
DCB 0x76, 0x4B, 0x9F, 0xB8
DCB 0x7C, 0x06, 0x0C, 0x3E
DCB 0x7F, 0x00, 0x00, 0x00
#endif /* not DOXYGEN */
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