252 lines
7.8 KiB
C
252 lines
7.8 KiB
C
/*
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* p_atan.c
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*
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* Compute the tan of a FPU_REG, using a polynomial approximation.
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*
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*
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* Copyright (C) 1992,1993,1994
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* W. Metzenthen, 22 Parker St, Ormond, Vic 3163,
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* Australia. E-mail billm@vaxc.cc.monash.edu.au
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* All rights reserved.
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*
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* This copyright notice covers the redistribution and use of the
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* FPU emulator developed by W. Metzenthen. It covers only its use
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* in the 386BSD, FreeBSD and NetBSD operating systems. Any other
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* use is not permitted under this copyright.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must include information specifying
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* that source code for the emulator is freely available and include
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* either:
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* a) an offer to provide the source code for a nominal distribution
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* fee, or
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* b) list at least two alternative methods whereby the source
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* can be obtained, e.g. a publically accessible bulletin board
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* and an anonymous ftp site from which the software can be
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* downloaded.
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* 3. All advertising materials specifically mentioning features or use of
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* this emulator must acknowledge that it was developed by W. Metzenthen.
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* 4. The name of W. Metzenthen may not be used to endorse or promote
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* products derived from this software without specific prior written
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* permission.
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*
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* THIS SOFTWARE IS PROVIDED ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
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* INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY
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* AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL
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* W. METZENTHEN BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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* EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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* PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
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* LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
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* NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*
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*
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* The purpose of this copyright, based upon the Berkeley copyright, is to
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* ensure that the covered software remains freely available to everyone.
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*
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* The software (with necessary differences) is also available, but under
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* the terms of the GNU copyleft, for the Linux operating system and for
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* the djgpp ms-dos extender.
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*
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* W. Metzenthen June 1994.
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*
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*
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* $FreeBSD$
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*
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*/
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#include <gnu/i386/fpemul/reg_constant.h>
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#include <gnu/i386/fpemul/control_w.h>
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#define HIPOWERon 6 /* odd poly, negative terms */
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static unsigned oddnegterms[HIPOWERon][2] =
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{
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{0x00000000, 0x00000000}, /* for + 1.0 */
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{0x763b6f3d, 0x1adc4428},
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{0x20f0630b, 0x0502909d},
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{0x4e825578, 0x0198ce38},
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{0x22b7cb87, 0x008da6e3},
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{0x9b30ca03, 0x00239c79}
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};
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#define HIPOWERop 6 /* odd poly, positive terms */
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static unsigned oddplterms[HIPOWERop][2] =
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{
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{0xa6f67cb8, 0x94d910bd},
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{0xa02ffab4, 0x0a43cb45},
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{0x04265e6b, 0x02bf5655},
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{0x0a728914, 0x00f280f7},
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{0x6d640e01, 0x004d6556},
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{0xf1dd2dbf, 0x000a530a}
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};
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static unsigned denomterm[2] =
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{0xfc4bd208, 0xea2e6612};
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static void poly_add_1(FPU_REG * src);
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/*--- poly_atan() -----------------------------------------------------------+
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+---------------------------------------------------------------------------*/
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void
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poly_atan(FPU_REG * arg)
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{
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char recursions = 0;
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short exponent;
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FPU_REG odd_poly, even_poly, pos_poly, neg_poly;
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FPU_REG argSq;
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long long arg_signif, argSqSq;
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#ifdef PARANOID
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if (arg->sign != 0) { /* Can't hack a number < 0.0 */
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arith_invalid(arg);
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return;
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} /* Need a positive number */
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#endif /* PARANOID */
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exponent = arg->exp - EXP_BIAS;
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if (arg->tag == TW_Zero) {
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/* Return 0.0 */
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reg_move(&CONST_Z, arg);
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return;
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}
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if (exponent >= -2) {
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/* argument is in the range [0.25 .. 1.0] */
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if (exponent >= 0) {
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#ifdef PARANOID
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if ((exponent == 0) &&
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(arg->sigl == 0) && (arg->sigh == 0x80000000))
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#endif /* PARANOID */
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{
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reg_move(&CONST_PI4, arg);
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return;
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}
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#ifdef PARANOID
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EXCEPTION(EX_INTERNAL | 0x104); /* There must be a logic
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* error */
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#endif /* PARANOID */
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}
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/* If the argument is greater than sqrt(2)-1 (=0.414213562...) */
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/* convert the argument by an identity for atan */
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if ((exponent >= -1) || (arg->sigh > 0xd413ccd0)) {
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FPU_REG numerator, denom;
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recursions++;
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arg_signif = *(long long *) &(arg->sigl);
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if (exponent < -1) {
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if (shrx(&arg_signif, -1 - exponent) >= (unsigned)0x80000000)
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arg_signif++; /* round up */
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}
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*(long long *) &(numerator.sigl) = -arg_signif;
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numerator.exp = EXP_BIAS - 1;
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normalize(&numerator); /* 1 - arg */
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arg_signif = *(long long *) &(arg->sigl);
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if (shrx(&arg_signif, -exponent) >= (unsigned)0x80000000)
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arg_signif++; /* round up */
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*(long long *) &(denom.sigl) = arg_signif;
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denom.sigh |= 0x80000000; /* 1 + arg */
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arg->exp = numerator.exp;
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reg_u_div(&numerator, &denom, arg, FULL_PRECISION);
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exponent = arg->exp - EXP_BIAS;
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}
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}
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*(long long *) &arg_signif = *(long long *) &(arg->sigl);
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#ifdef PARANOID
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/* This must always be true */
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if (exponent >= -1) {
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EXCEPTION(EX_INTERNAL | 0x120); /* There must be a logic error */
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}
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#endif /* PARANOID */
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/* shift the argument right by the required places */
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if (shrx(&arg_signif, -1 - exponent) >= (unsigned)0x80000000)
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arg_signif++; /* round up */
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/* Now have arg_signif with binary point at the left .1xxxxxxxx */
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mul64(&arg_signif, &arg_signif, (long long *) (&argSq.sigl));
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mul64((long long *) (&argSq.sigl), (long long *) (&argSq.sigl), &argSqSq);
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/* will be a valid positive nr with expon = 0 */
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*(short *) &(pos_poly.sign) = 0;
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pos_poly.exp = EXP_BIAS;
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/* Do the basic fixed point polynomial evaluation */
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polynomial((u_int *) &pos_poly.sigl, (unsigned *) &argSqSq,
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(unsigned short (*)[4]) oddplterms, HIPOWERop - 1);
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mul64((long long *) (&argSq.sigl), (long long *) (&pos_poly.sigl),
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(long long *) (&pos_poly.sigl));
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/* will be a valid positive nr with expon = 0 */
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*(short *) &(neg_poly.sign) = 0;
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neg_poly.exp = EXP_BIAS;
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/* Do the basic fixed point polynomial evaluation */
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polynomial((u_int *) &neg_poly.sigl, (unsigned *) &argSqSq,
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(unsigned short (*)[4]) oddnegterms, HIPOWERon - 1);
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/* Subtract the mantissas */
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*((long long *) (&pos_poly.sigl)) -= *((long long *) (&neg_poly.sigl));
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reg_move(&pos_poly, &odd_poly);
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poly_add_1(&odd_poly);
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/* The complete odd polynomial */
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reg_u_mul(&odd_poly, arg, &odd_poly, FULL_PRECISION);
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/* will be a valid positive nr with expon = 0 */
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*(short *) &(even_poly.sign) = 0;
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mul64((long long *) (&argSq.sigl),
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(long long *) (&denomterm), (long long *) (&even_poly.sigl));
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poly_add_1(&even_poly);
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reg_div(&odd_poly, &even_poly, arg, FULL_PRECISION);
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if (recursions)
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reg_sub(&CONST_PI4, arg, arg, FULL_PRECISION);
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}
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/* The argument to this function must be polynomial() compatible,
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i.e. have an exponent (not checked) of EXP_BIAS-1 but need not
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be normalized.
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This function adds 1.0 to the (assumed positive) argument. */
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static void
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poly_add_1(FPU_REG * src)
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{
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/* Rounding in a consistent direction produces better results
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for the use of this function in poly_atan. Simple truncation
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is used here instead of round-to-nearest. */
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#ifdef OBSOLETE
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char round = (src->sigl & 3) == 3;
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#endif /* OBSOLETE */
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shrx(&src->sigl, 1);
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#ifdef OBSOLETE
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if (round)
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(*(long long *) &src->sigl)++; /* Round to even */
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#endif /* OBSOLETE */
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src->sigh |= 0x80000000;
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src->exp = EXP_BIAS;
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}
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