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317 lines
9.4 KiB
C
317 lines
9.4 KiB
C
/*
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* poly_l2.c
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*
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* Compute the base 2 log 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 HIPOWER 9
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static unsigned short lterms[HIPOWER][4] =
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{
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/* Ideal computation with these coeffs gives about 64.6 bit rel
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* accuracy. */
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{0xe177, 0xb82f, 0x7652, 0x7154},
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{0xee0f, 0xe80f, 0x2770, 0x7b1c},
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{0x0fc0, 0xbe87, 0xb143, 0x49dd},
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{0x78b9, 0xdadd, 0xec54, 0x34c2},
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{0x003a, 0x5de9, 0x628b, 0x2909},
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{0x5588, 0xed16, 0x4abf, 0x2193},
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{0xb461, 0x85f7, 0x347a, 0x1c6a},
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{0x0975, 0x87b3, 0xd5bf, 0x1876},
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{0xe85c, 0xcec9, 0x84e7, 0x187d}
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};
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/*--- poly_l2() -------------------------------------------------------------+
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| Base 2 logarithm by a polynomial approximation. |
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+---------------------------------------------------------------------------*/
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void
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poly_l2(FPU_REG * arg, FPU_REG * result)
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{
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short exponent;
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char zero; /* flag for an Xx == 0 */
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unsigned short bits, shift;
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long long Xsq;
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FPU_REG accum, denom, num, Xx;
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exponent = arg->exp - EXP_BIAS;
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accum.tag = TW_Valid; /* set the tags to Valid */
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if (arg->sigh > (unsigned) 0xb504f334) {
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/* This is good enough for the computation of the polynomial
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* sum, but actually results in a loss of precision for the
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* computation of Xx. This will matter only if exponent
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* becomes zero. */
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exponent++;
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accum.sign = 1; /* sign to negative */
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num.exp = EXP_BIAS; /* needed to prevent errors in div
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* routine */
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reg_u_div(&CONST_1, arg, &num, FULL_PRECISION);
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} else {
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accum.sign = 0; /* set the sign to positive */
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num.sigl = arg->sigl; /* copy the mantissa */
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num.sigh = arg->sigh;
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}
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/* shift num left, lose the ms bit */
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num.sigh <<= 1;
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if (num.sigl & 0x80000000)
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num.sigh |= 1;
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num.sigl <<= 1;
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denom.sigl = num.sigl;
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denom.sigh = num.sigh;
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poly_div4((long long *) &(denom.sigl));
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denom.sigh += 0x80000000; /* set the msb */
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Xx.exp = EXP_BIAS; /* needed to prevent errors in div routine */
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reg_u_div(&num, &denom, &Xx, FULL_PRECISION);
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zero = !(Xx.sigh | Xx.sigl);
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mul64((long long *) &Xx.sigl, (long long *) &Xx.sigl, &Xsq);
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poly_div16(&Xsq);
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accum.exp = -1; /* exponent of accum */
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/* Do the basic fixed point polynomial evaluation */
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polynomial((unsigned *) &accum.sigl, (unsigned *) &Xsq, lterms, HIPOWER - 1);
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if (!exponent) {
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/* If the exponent is zero, then we would lose precision by
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* sticking to fixed point computation here */
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/* We need to re-compute Xx because of loss of precision. */
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FPU_REG lXx;
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char sign;
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sign = accum.sign;
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accum.sign = 0;
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/* make accum compatible and normalize */
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accum.exp = EXP_BIAS + accum.exp;
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normalize(&accum);
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if (zero) {
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reg_move(&CONST_Z, result);
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} else {
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/* we need to re-compute lXx to better accuracy */
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num.tag = TW_Valid; /* set the tags to Vaild */
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num.sign = 0; /* set the sign to positive */
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num.exp = EXP_BIAS - 1;
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if (sign) {
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/* The argument is of the form 1-x */
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/* Use 1-1/(1-x) = x/(1-x) */
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*((long long *) &num.sigl) = -*((long long *) &(arg->sigl));
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normalize(&num);
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reg_div(&num, arg, &num, FULL_PRECISION);
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} else {
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normalize(&num);
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}
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denom.tag = TW_Valid; /* set the tags to Valid */
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denom.sign = SIGN_POS; /* set the sign to positive */
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denom.exp = EXP_BIAS;
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reg_div(&num, &denom, &lXx, FULL_PRECISION);
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reg_u_mul(&lXx, &accum, &accum, FULL_PRECISION);
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reg_u_add(&lXx, &accum, result, FULL_PRECISION);
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normalize(result);
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}
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result->sign = sign;
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return;
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}
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mul64((long long *) &accum.sigl,
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(long long *) &Xx.sigl, (long long *) &accum.sigl);
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*((long long *) (&accum.sigl)) += *((long long *) (&Xx.sigl));
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if (Xx.sigh > accum.sigh) {
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/* There was an overflow */
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poly_div2((long long *) &accum.sigl);
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accum.sigh |= 0x80000000;
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accum.exp++;
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}
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/* When we add the exponent to the accum result later, we will require
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* that their signs are the same. Here we ensure that this is so. */
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if (exponent && ((exponent < 0) ^ (accum.sign))) {
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/* signs are different */
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accum.sign = !accum.sign;
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/* An exceptional case is when accum is zero */
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if (accum.sigl | accum.sigh) {
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/* find 1-accum */
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/* Shift to get exponent == 0 */
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if (accum.exp < 0) {
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poly_div2((long long *) &accum.sigl);
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accum.exp++;
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}
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/* Just negate, but throw away the sign */
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*((long long *) &(accum.sigl)) = -*((long long *) &(accum.sigl));
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if (exponent < 0)
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exponent++;
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else
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exponent--;
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}
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}
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shift = exponent >= 0 ? exponent : -exponent;
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bits = 0;
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if (shift) {
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if (accum.exp) {
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accum.exp++;
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poly_div2((long long *) &accum.sigl);
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}
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while (shift) {
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poly_div2((long long *) &accum.sigl);
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if (shift & 1)
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accum.sigh |= 0x80000000;
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shift >>= 1;
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bits++;
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}
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}
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/* Convert to 64 bit signed-compatible */
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accum.exp += bits + EXP_BIAS - 1;
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reg_move(&accum, result);
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normalize(result);
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return;
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}
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/*--- poly_l2p1() -----------------------------------------------------------+
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| Base 2 logarithm by a polynomial approximation. |
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| log2(x+1) |
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+---------------------------------------------------------------------------*/
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int
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poly_l2p1(FPU_REG * arg, FPU_REG * result)
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{
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char sign = 0;
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long long Xsq;
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FPU_REG arg_pl1, denom, accum, local_arg, poly_arg;
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sign = arg->sign;
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reg_add(arg, &CONST_1, &arg_pl1, FULL_PRECISION);
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if ((arg_pl1.sign) | (arg_pl1.tag)) { /* We need a valid positive
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* number! */
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return 1;
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}
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reg_add(&CONST_1, &arg_pl1, &denom, FULL_PRECISION);
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reg_div(arg, &denom, &local_arg, FULL_PRECISION);
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local_arg.sign = 0; /* Make the sign positive */
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/* Now we need to check that |local_arg| is less than 3-2*sqrt(2) =
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* 0.17157.. = .0xafb0ccc0 * 2^-2 */
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if (local_arg.exp >= EXP_BIAS - 3) {
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if ((local_arg.exp > EXP_BIAS - 3) ||
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(local_arg.sigh > (unsigned) 0xafb0ccc0)) {
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/* The argument is large */
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poly_l2(&arg_pl1, result);
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return 0;
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}
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}
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/* Make a copy of local_arg */
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reg_move(&local_arg, &poly_arg);
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/* Get poly_arg bits aligned as required */
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shrx((unsigned *) &(poly_arg.sigl), -(poly_arg.exp - EXP_BIAS + 3));
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mul64((long long *) &(poly_arg.sigl), (long long *) &(poly_arg.sigl), &Xsq);
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poly_div16(&Xsq);
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/* Do the basic fixed point polynomial evaluation */
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polynomial((u_int *) &accum.sigl, (unsigned *) &Xsq, lterms, HIPOWER - 1);
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accum.tag = TW_Valid; /* set the tags to Valid */
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accum.sign = SIGN_POS; /* and make accum positive */
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/* make accum compatible and normalize */
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accum.exp = EXP_BIAS - 1;
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normalize(&accum);
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reg_u_mul(&local_arg, &accum, &accum, FULL_PRECISION);
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reg_u_add(&local_arg, &accum, result, FULL_PRECISION);
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/* Multiply the result by 2 */
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result->exp++;
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result->sign = sign;
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return 0;
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}
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