/* $OpenBSD: poly_atan.c,v 1.1 1996/08/27 10:32:53 downsj Exp $ */ /* * p_atan.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_atan.c,v 1.5 1995/12/14 09:50:24 phk Exp $ * */ #include #include #include #include #define HIPOWERon 6 /* odd poly, negative terms */ static unsigned oddnegterms[HIPOWERon][2] = { {0x00000000, 0x00000000}, /* for + 1.0 */ {0x763b6f3d, 0x1adc4428}, {0x20f0630b, 0x0502909d}, {0x4e825578, 0x0198ce38}, {0x22b7cb87, 0x008da6e3}, {0x9b30ca03, 0x00239c79} }; #define HIPOWERop 6 /* odd poly, positive terms */ static unsigned oddplterms[HIPOWERop][2] = { {0xa6f67cb8, 0x94d910bd}, {0xa02ffab4, 0x0a43cb45}, {0x04265e6b, 0x02bf5655}, {0x0a728914, 0x00f280f7}, {0x6d640e01, 0x004d6556}, {0xf1dd2dbf, 0x000a530a} }; static unsigned denomterm[2] = {0xfc4bd208, 0xea2e6612}; static void poly_add_1(FPU_REG * src); /*--- poly_atan() -----------------------------------------------------------+ | | +---------------------------------------------------------------------------*/ void poly_atan(FPU_REG * arg) { char recursions = 0; short exponent; FPU_REG odd_poly, even_poly, pos_poly, neg_poly; FPU_REG argSq; long long arg_signif, argSqSq; #ifdef PARANOID if (arg->sign != 0) { /* Can't hack a number < 0.0 */ arith_invalid(arg); return; } /* Need a positive number */ #endif /* PARANOID */ exponent = arg->exp - EXP_BIAS; if (arg->tag == TW_Zero) { /* Return 0.0 */ reg_move(&CONST_Z, arg); return; } if (exponent >= -2) { /* argument is in the range [0.25 .. 1.0] */ if (exponent >= 0) { #ifdef PARANOID if ((exponent == 0) && (arg->sigl == 0) && (arg->sigh == 0x80000000)) #endif /* PARANOID */ { reg_move(&CONST_PI4, arg); return; } #ifdef PARANOID EXCEPTION(EX_INTERNAL | 0x104); /* There must be a logic * error */ #endif /* PARANOID */ } /* If the argument is greater than sqrt(2)-1 (=0.414213562...) */ /* convert the argument by an identity for atan */ if ((exponent >= -1) || (arg->sigh > 0xd413ccd0)) { FPU_REG numerator, denom; recursions++; arg_signif = *(long long *) &(arg->sigl); if (exponent < -1) { if (shrx(&arg_signif, -1 - exponent) >= (unsigned)0x80000000) arg_signif++; /* round up */ } *(long long *) &(numerator.sigl) = -arg_signif; numerator.exp = EXP_BIAS - 1; normalize(&numerator); /* 1 - arg */ arg_signif = *(long long *) &(arg->sigl); if (shrx(&arg_signif, -exponent) >= (unsigned)0x80000000) arg_signif++; /* round up */ *(long long *) &(denom.sigl) = arg_signif; denom.sigh |= 0x80000000; /* 1 + arg */ arg->exp = numerator.exp; reg_u_div(&numerator, &denom, arg, FULL_PRECISION); exponent = arg->exp - EXP_BIAS; } } *(long long *) &arg_signif = *(long long *) &(arg->sigl); #ifdef PARANOID /* This must always be true */ if (exponent >= -1) { EXCEPTION(EX_INTERNAL | 0x120); /* There must be a logic error */ } #endif /* PARANOID */ /* shift the argument right by the required places */ if (shrx(&arg_signif, -1 - exponent) >= (unsigned)0x80000000) arg_signif++; /* round up */ /* Now have arg_signif with binary point at the left .1xxxxxxxx */ 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, (unsigned short (*)[4]) oddplterms, HIPOWERop - 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, (unsigned short (*)[4]) oddnegterms, HIPOWERon - 1); /* Subtract the mantissas */ *((long long *) (&pos_poly.sigl)) -= *((long long *) (&neg_poly.sigl)); reg_move(&pos_poly, &odd_poly); poly_add_1(&odd_poly); /* The complete odd polynomial */ reg_u_mul(&odd_poly, arg, &odd_poly, FULL_PRECISION); /* will be a valid positive nr with expon = 0 */ *(short *) &(even_poly.sign) = 0; mul64((long long *) (&argSq.sigl), (long long *) (&denomterm), (long long *) (&even_poly.sigl)); poly_add_1(&even_poly); reg_div(&odd_poly, &even_poly, arg, FULL_PRECISION); if (recursions) reg_sub(&CONST_PI4, arg, arg, FULL_PRECISION); } /* The argument to this function must be polynomial() compatible, i.e. have an exponent (not checked) of EXP_BIAS-1 but need not be normalized. This function adds 1.0 to the (assumed positive) argument. */ static void poly_add_1(FPU_REG * src) { /* Rounding in a consistent direction produces better results for the use of this function in poly_atan. Simple truncation is used here instead of round-to-nearest. */ #ifdef OBSOLETE char round = (src->sigl & 3) == 3; #endif /* OBSOLETE */ shrx(&src->sigl, 1); #ifdef OBSOLETE if (round) (*(long long *) &src->sigl)++; /* Round to even */ #endif /* OBSOLETE */ src->sigh |= 0x80000000; src->exp = EXP_BIAS; }