/* $OpenBSD: poly_sin.c,v 1.1 1996/08/27 10:32:55 downsj Exp $ */ /* * poly_sin.c * * Computation of an approximation of the sin function by a polynomial * * * 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_sin.c,v 1.5 1994/08/31 04:45:22 davidg Exp $ * */ #include #include #include #include #define HIPOWER 5 static unsigned short lterms[HIPOWER][4] = { {0x846a, 0x42d1, 0xb544, 0x921f}, {0xe110, 0x75aa, 0xbc67, 0x1466}, {0x503d, 0xa43f, 0x83c1, 0x000a}, {0x8f9d, 0x7a19, 0x00f4, 0x0000}, {0xda03, 0x06aa, 0x0000, 0x0000}, }; static unsigned short negterms[HIPOWER][4] = { {0x95ed, 0x2df2, 0xe731, 0xa55d}, {0xd159, 0xe62b, 0xd2cc, 0x0132}, {0x6342, 0xe9fb, 0x3c60, 0x0000}, {0x6256, 0xdf5a, 0x0002, 0x0000}, {0xf279, 0x000b, 0x0000, 0x0000}, }; /*--- poly_sine() -----------------------------------------------------------+ | | +---------------------------------------------------------------------------*/ void poly_sine(FPU_REG * arg, FPU_REG * result) { short exponent; FPU_REG Xx, Xx2, Xx4, accum, negaccum; exponent = arg->exp - EXP_BIAS; if (arg->tag == TW_Zero) { /* Return 0.0 */ reg_move(&CONST_Z, result); return; } #ifdef PARANOID if (arg->sign != 0) { /* Can't hack a number < 0.0 */ EXCEPTION(EX_Invalid); reg_move(&CONST_QNaN, result); return; } if (exponent >= 0) { /* Can't hack a number > 1.0 */ if ((exponent == 0) && (arg->sigl == 0) && (arg->sigh == 0x80000000)) { reg_move(&CONST_1, result); return; } EXCEPTION(EX_Invalid); reg_move(&CONST_QNaN, result); return; } #endif /* PARANOID */ Xx.sigl = arg->sigl; Xx.sigh = arg->sigh; if (exponent < -1) { /* shift the argument right by the required places */ if (shrx(&(Xx.sigl), -1 - exponent) >= (unsigned)0x80000000) (*((long long *) (&(Xx.sigl))))++; /* round up */ } mul64((long long *) &(Xx.sigl), (long long *) &(Xx.sigl), (long long *) &(Xx2.sigl)); mul64((long long *) &(Xx2.sigl), (long long *) &(Xx2.sigl), (long long *) &(Xx4.sigl)); /* will be a valid positive nr with expon = 0 */ *(short *) &(accum.sign) = 0; accum.exp = 0; /* Do the basic fixed point polynomial evaluation */ polynomial((u_int *) &(accum.sigl), (u_int *)&(Xx4.sigl), lterms, HIPOWER - 1); /* will be a valid positive nr with expon = 0 */ *(short *) &(negaccum.sign) = 0; negaccum.exp = 0; /* Do the basic fixed point polynomial evaluation */ polynomial((u_int *) &(negaccum.sigl), (u_int *)&(Xx4.sigl), negterms, HIPOWER - 1); mul64((long long *) &(Xx2.sigl), (long long *) &(negaccum.sigl), (long long *) &(negaccum.sigl)); /* Subtract the mantissas */ *((long long *) (&(accum.sigl))) -= *((long long *) (&(negaccum.sigl))); /* Convert to 64 bit signed-compatible */ accum.exp = EXP_BIAS - 1 + accum.exp; *(short *) &(result->sign) = *(short *) &(accum.sign); result->exp = accum.exp; result->sigl = accum.sigl; result->sigh = accum.sigh; normalize(result); reg_mul(result, arg, result, FULL_PRECISION); reg_u_add(result, arg, result, FULL_PRECISION); /* A small overflow may be possible... but an illegal result. */ if (result->exp >= EXP_BIAS) { if ((result->exp > EXP_BIAS) /* Larger or equal 2.0 */ ||(result->sigl > 1) /* Larger than 1.0+msb */ ||(result->sigh != 0x80000000) /* Much > 1.0 */ ) { #ifdef DEBUGGING RE_ENTRANT_CHECK_OFF printk("\nEXP=%d, MS=%08x, LS=%08x\n", result->exp, result->sigh, result->sigl); RE_ENTRANT_CHECK_ON #endif /* DEBUGGING */ EXCEPTION(EX_INTERNAL | 0x103); } #ifdef DEBUGGING RE_ENTRANT_CHECK_OFF printk("\n***CORRECTING ILLEGAL RESULT*** in poly_sin() computation\n"); printk("EXP=%d, MS=%08x, LS=%08x\n", result->exp, result->sigh, result->sigl); RE_ENTRANT_CHECK_ON #endif /* DEBUGGING */ result->sigl = 0; /* Truncate the result to 1.00 */ } }