/* Copyright (c) 2002 Michael Stumpf 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