/* $OpenBSD: poly_tan.c,v 1.1 1996/08/27 10:32:55 downsj Exp $ */ /* * poly_tan.c * * Compute the tan of a FPU_REG, using a polynomial approximation. * * * Copyright (C) 1992,1993,1994 * W. Metzenthen, 22 Parker St, Ormond, Vic 3163, * Australia. E-mail billm@vaxc.cc.monash.edu.au * All rights reserved. * * This copyright notice covers the redistribution and use of the * FPU emulator developed by W. Metzenthen. It covers only its use * in the 386BSD, FreeBSD and NetBSD operating systems. Any other * use is not permitted under this copyright. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * 2. Redistributions in binary form must include information specifying * that source code for the emulator is freely available and include * either: * a) an offer to provide the source code for a nominal distribution * fee, or * b) list at least two alternative methods whereby the source * can be obtained, e.g. a publically accessible bulletin board * and an anonymous ftp site from which the software can be * downloaded. * 3. All advertising materials specifically mentioning features or use of * this emulator must acknowledge that it was developed by W. Metzenthen. * 4. The name of W. Metzenthen may not be used to endorse or promote * products derived from this software without specific prior written * permission. * * THIS SOFTWARE IS PROVIDED ``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 * W. METZENTHEN 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. * * * The purpose of this copyright, based upon the Berkeley copyright, is to * ensure that the covered software remains freely available to everyone. * * The software (with necessary differences) is also available, but under * the terms of the GNU copyleft, for the Linux operating system and for * the djgpp ms-dos extender. * * W. Metzenthen June 1994. * * * $FreeBSD: poly_tan.c,v 1.5 1995/05/30 07:57:52 rgrimes Exp $ * */ #include #include #include #include #define HIPOWERop 3 /* odd poly, positive terms */ static unsigned short oddplterms[HIPOWERop][4] = { {0x846a, 0x42d1, 0xb544, 0x921f}, {0x6fb2, 0x0215, 0x95c0, 0x099c}, {0xfce6, 0x0cc8, 0x1c9a, 0x0000} }; #define HIPOWERon 2 /* odd poly, negative terms */ static unsigned short oddnegterms[HIPOWERon][4] = { {0x6906, 0xe205, 0x25c8, 0x8838}, {0x1dd7, 0x3fe3, 0x944e, 0x002c} }; #define HIPOWERep 2 /* even poly, positive terms */ static unsigned short evenplterms[HIPOWERep][4] = { {0xdb8f, 0x3761, 0x1432, 0x2acf}, {0x16eb, 0x13c1, 0x3099, 0x0003} }; #define HIPOWERen 2 /* even poly, negative terms */ static unsigned short evennegterms[HIPOWERen][4] = { {0x3a7c, 0xe4c5, 0x7f87, 0x2945}, {0x572b, 0x664c, 0xc543, 0x018c} }; /*--- poly_tan() ------------------------------------------------------------+ | | +---------------------------------------------------------------------------*/ void poly_tan(FPU_REG * arg, FPU_REG * y_reg) { char invert = 0; short exponent; FPU_REG odd_poly, even_poly, pos_poly, neg_poly; FPU_REG argSq; long long arg_signif, argSqSq; exponent = arg->exp - EXP_BIAS; if (arg->tag == TW_Zero) { /* Return 0.0 */ reg_move(&CONST_Z, y_reg); return; } if (exponent >= -1) { /* argument is in the range [0.5 .. 1.0] */ if (exponent >= 0) { #ifdef PARANOID if ((exponent == 0) && (arg->sigl == 0) && (arg->sigh == 0x80000000)) #endif /* PARANOID */ { arith_overflow(y_reg); return; } #ifdef PARANOID EXCEPTION(EX_INTERNAL | 0x104); /* There must be a logic * error */ return; #endif /* PARANOID */ } /* The argument is in the range [0.5 .. 1.0) */ /* Convert the argument to a number in the range (0.0 .. 0.5] */ *((long long *) (&arg->sigl)) = -*((long long *) (&arg->sigl)); normalize(arg); /* Needed later */ exponent = arg->exp - EXP_BIAS; invert = 1; } #ifdef PARANOID if (arg->sign != 0) { /* Can't hack a number < 0.0 */ arith_invalid(y_reg); return; } /* Need a positive number */ #endif /* PARANOID */ *(long long *) &arg_signif = *(long long *) &(arg->sigl); if (exponent < -1) { /* shift the argument right by the required places */ if (shrx(&arg_signif, -1 - exponent) >= (unsigned)0x80000000) arg_signif++; /* round up */ } mul64(&arg_signif, &arg_signif, (long long *) (&argSq.sigl)); mul64((long long *) (&argSq.sigl), (long long *) (&argSq.sigl), &argSqSq); /* will be a valid positive nr with expon = 0 */ *(short *) &(pos_poly.sign) = 0; pos_poly.exp = EXP_BIAS; /* Do the basic fixed point polynomial evaluation */ polynomial((u_int *) &pos_poly.sigl, (unsigned *) &argSqSq, oddplterms, HIPOWERop - 1); /* will be a valid positive nr with expon = 0 */ *(short *) &(neg_poly.sign) = 0; neg_poly.exp = EXP_BIAS; /* Do the basic fixed point polynomial evaluation */ polynomial((u_int *) &neg_poly.sigl, (unsigned *) &argSqSq, oddnegterms, HIPOWERon - 1); mul64((long long *) (&argSq.sigl), (long long *) (&neg_poly.sigl), (long long *) (&neg_poly.sigl)); /* Subtract the mantissas */ *((long long *) (&pos_poly.sigl)) -= *((long long *) (&neg_poly.sigl)); /* Convert to 64 bit signed-compatible */ pos_poly.exp -= 1; reg_move(&pos_poly, &odd_poly); normalize(&odd_poly); reg_mul(&odd_poly, arg, &odd_poly, FULL_PRECISION); reg_u_add(&odd_poly, arg, &odd_poly, FULL_PRECISION); /* This is just the odd * polynomial */ /* will be a valid positive nr with expon = 0 */ *(short *) &(pos_poly.sign) = 0; pos_poly.exp = EXP_BIAS; /* Do the basic fixed point polynomial evaluation */ polynomial((u_int *) &pos_poly.sigl, (unsigned *) &argSqSq, evenplterms, HIPOWERep - 1); mul64((long long *) (&argSq.sigl), (long long *) (&pos_poly.sigl), (long long *) (&pos_poly.sigl)); /* will be a valid positive nr with expon = 0 */ *(short *) &(neg_poly.sign) = 0; neg_poly.exp = EXP_BIAS; /* Do the basic fixed point polynomial evaluation */ polynomial((u_int *) &neg_poly.sigl, (unsigned *) &argSqSq, evennegterms, HIPOWERen - 1); /* Subtract the mantissas */ *((long long *) (&neg_poly.sigl)) -= *((long long *) (&pos_poly.sigl)); /* and multiply by argSq */ /* Convert argSq to a valid reg number */ *(short *) &(argSq.sign) = 0; argSq.exp = EXP_BIAS - 1; normalize(&argSq); /* Convert to 64 bit signed-compatible */ neg_poly.exp -= 1; reg_move(&neg_poly, &even_poly); normalize(&even_poly); reg_mul(&even_poly, &argSq, &even_poly, FULL_PRECISION); reg_add(&even_poly, &argSq, &even_poly, FULL_PRECISION); reg_sub(&CONST_1, &even_poly, &even_poly, FULL_PRECISION); /* This is just the even * polynomial */ /* Now ready to copy the results */ if (invert) { reg_div(&even_poly, &odd_poly, y_reg, FULL_PRECISION); } else { reg_div(&odd_poly, &even_poly, y_reg, FULL_PRECISION); } }