CbC/CbC_gcc: libquadmath/math/powq.c annotate

author	Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
date	Sun, 21 Aug 2011 07:07:55 +0900
parents
children	04ced10e8804

rev	line source
68 561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	1 /*
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	2 * ====================================================
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	4 *
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	5 * Developed at SunPro, a Sun Microsystems, Inc. business.
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	6 * Permission to use, copy, modify, and distribute this
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	7 * software is freely granted, provided that this notice
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	8 * is preserved.
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	9 * ====================================================
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	10 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	11
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	12 /* Expansions and modifications for 128-bit long double are
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	13 Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	14 and are incorporated herein by permission of the author. The author
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	15 reserves the right to distribute this material elsewhere under different
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	16 copying permissions. These modifications are distributed here under
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	17 the following terms:
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	18
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	19 This library is free software; you can redistribute it and/or
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	20 modify it under the terms of the GNU Lesser General Public
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	21 License as published by the Free Software Foundation; either
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	22 version 2.1 of the License, or (at your option) any later version.
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	23
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	24 This library is distributed in the hope that it will be useful,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	25 but WITHOUT ANY WARRANTY; without even the implied warranty of
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	26 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	27 Lesser General Public License for more details.
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	28
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	29 You should have received a copy of the GNU Lesser General Public
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	30 License along with this library; if not, write to the Free Software
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	31 Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	32
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	33 /* __ieee754_powl(x,y) return x**y
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	34 *
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	35 * n
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	36 * Method: Let x = 2 * (1+f)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	37 * 1. Compute and return log2(x) in two pieces:
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	38 * log2(x) = w1 + w2,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	39 * where w1 has 113-53 = 60 bit trailing zeros.
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	40 * 2. Perform y*log2(x) = n+y' by simulating muti-precision
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	41 * arithmetic, where \|y'\|<=0.5.
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	42 * 3. Return xy = 2nexp(y'log2)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	43 *
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	44 * Special cases:
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	45 * 1. (anything) ** 0 is 1
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	46 * 2. (anything) ** 1 is itself
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	47 * 3. (anything) ** NAN is NAN
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	48 * 4. NAN ** (anything except 0) is NAN
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	49 * 5. +-(\|x\| > 1) ** +INF is +INF
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	50 * 6. +-(\|x\| > 1) ** -INF is +0
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	51 * 7. +-(\|x\| < 1) ** +INF is +0
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	52 * 8. +-(\|x\| < 1) ** -INF is +INF
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	53 * 9. +-1 ** +-INF is NAN
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	54 * 10. +0 ** (+anything except 0, NAN) is +0
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	55 * 11. -0 ** (+anything except 0, NAN, odd integer) is +0
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	56 * 12. +0 ** (-anything except 0, NAN) is +INF
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	57 * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	58 * 14. -0 (odd integer) = -( +0 (odd integer) )
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	59 * 15. +INF ** (+anything except 0,NAN) is +INF
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	60 * 16. +INF ** (-anything except 0,NAN) is +0
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	61 * 17. -INF (anything) = -0 (-anything)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	62 * 18. (-anything) (integer) is (-1)(integer)(+anything*integer)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	63 * 19. (-anything except 0 and inf) ** (non-integer) is NAN
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	64 *
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	65 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	66
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	67 #include "quadmath-imp.h"
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	68
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	69 static const __float128 bp[] = {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	70 1.0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	71 1.5Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	72 };
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	73
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	74 /* log_2(1.5) */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	75 static const __float128 dp_h[] = {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	76 0.0,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	77 5.8496250072115607565592654282227158546448E-1Q
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	78 };
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	79
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	80 /* Low part of log_2(1.5) */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	81 static const __float128 dp_l[] = {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	82 0.0,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	83 1.0579781240112554492329533686862998106046E-16Q
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	84 };
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	85
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	86 static const __float128 zero = 0.0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	87 one = 1.0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	88 two = 2.0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	89 two113 = 1.0384593717069655257060992658440192E34Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	90 huge = 1.0e3000Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	91 tiny = 1.0e-3000Q;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	92
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	93 /* 3/2 log x = 3 z + z^3 + z^3 (z^2 R(z^2))
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	94 z = (x-1)/(x+1)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	95 1 <= x <= 1.25
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	96 Peak relative error 2.3e-37 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	97 static const __float128 LN[] =
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	98 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	99 -3.0779177200290054398792536829702930623200E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	100 6.5135778082209159921251824580292116201640E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	101 -4.6312921812152436921591152809994014413540E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	102 1.2510208195629420304615674658258363295208E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	103 -9.9266909031921425609179910128531667336670E-1Q
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	104 };
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	105 static const __float128 LD[] =
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	106 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	107 -5.129862866715009066465422805058933131960E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	108 1.452015077564081884387441590064272782044E2Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	109 -1.524043275549860505277434040464085593165E2Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	110 7.236063513651544224319663428634139768808E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	111 -1.494198912340228235853027849917095580053E1Q
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	112 /* 1.0E0 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	113 };
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	114
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	115 /* exp(x) = 1 + x - x / (1 - 2 / (x - x^2 R(x^2)))
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	116 0 <= x <= 0.5
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	117 Peak relative error 5.7e-38 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	118 static const __float128 PN[] =
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	119 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	120 5.081801691915377692446852383385968225675E8Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	121 9.360895299872484512023336636427675327355E6Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	122 4.213701282274196030811629773097579432957E4Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	123 5.201006511142748908655720086041570288182E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	124 9.088368420359444263703202925095675982530E-3Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	125 };
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	126 static const __float128 PD[] =
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	127 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	128 3.049081015149226615468111430031590411682E9Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	129 1.069833887183886839966085436512368982758E8Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	130 8.259257717868875207333991924545445705394E5Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	131 1.872583833284143212651746812884298360922E3Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	132 /* 1.0E0 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	133 };
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	134
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	135 static const __float128
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	136 /* ln 2 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	137 lg2 = 6.9314718055994530941723212145817656807550E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	138 lg2_h = 6.9314718055994528622676398299518041312695E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	139 lg2_l = 2.3190468138462996154948554638754786504121E-17Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	140 ovt = 8.0085662595372944372e-0017Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	141 /* 2/(3log(2)) /
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	142 cp = 9.6179669392597560490661645400126142495110E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	143 cp_h = 9.6179669392597555432899980587535537779331E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	144 cp_l = 5.0577616648125906047157785230014751039424E-17Q;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	145
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	146 __float128
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	147 powq (__float128 x, __float128 y)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	148 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	149 __float128 z, ax, z_h, z_l, p_h, p_l;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	150 __float128 y1, t1, t2, r, s, t, u, v, w;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	151 __float128 s2, s_h, s_l, t_h, t_l;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	152 int32_t i, j, k, yisint, n;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	153 uint32_t ix, iy;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	154 int32_t hx, hy;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	155 ieee854_float128 o, p, q;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	156
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	157 p.value = x;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	158 hx = p.words32.w0;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	159 ix = hx & 0x7fffffff;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	160
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	161 q.value = y;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	162 hy = q.words32.w0;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	163 iy = hy & 0x7fffffff;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	164
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	165
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	166 /* y==zero: x*0 = 1 /
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	167 if ((iy \| q.words32.w1 \| q.words32.w2 \| q.words32.w3) == 0)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	168 return one;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	169
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	170 /* 1.0y = 1; -1.0+-Inf = 1 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	171 if (x == one)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	172 return one;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	173 if (x == -1.0Q && iy == 0x7fff0000
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	174 && (q.words32.w1 \| q.words32.w2 \| q.words32.w3) == 0)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	175 return one;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	176
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	177 /* +-NaN return x+y */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	178 if ((ix > 0x7fff0000)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	179 \|\| ((ix == 0x7fff0000)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	180 && ((p.words32.w1 \| p.words32.w2 \| p.words32.w3) != 0))
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	181 \|\| (iy > 0x7fff0000)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	182 \|\| ((iy == 0x7fff0000)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	183 && ((q.words32.w1 \| q.words32.w2 \| q.words32.w3) != 0)))
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	184 return x + y;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	185
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	186 /* determine if y is an odd int when x < 0
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	187 * yisint = 0 ... y is not an integer
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	188 * yisint = 1 ... y is an odd int
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	189 * yisint = 2 ... y is an even int
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	190 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	191 yisint = 0;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	192 if (hx < 0)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	193 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	194 if (iy >= 0x40700000) /* 2^113 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	195 yisint = 2; /* even integer y */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	196 else if (iy >= 0x3fff0000) /* 1.0 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	197 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	198 if (floorq (y) == y)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	199 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	200 z = 0.5 * y;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	201 if (floorq (z) == z)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	202 yisint = 2;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	203 else
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	204 yisint = 1;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	205 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	206 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	207 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	208
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	209 /* special value of y */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	210 if ((q.words32.w1 \| q.words32.w2 \| q.words32.w3) == 0)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	211 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	212 if (iy == 0x7fff0000) /* y is +-inf */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	213 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	214 if (((ix - 0x3fff0000) \| p.words32.w1 \| p.words32.w2 \| p.words32.w3)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	215 == 0)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	216 return y - y; /* +-1*inf is NaN /
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	217 else if (ix >= 0x3fff0000) /* (\|x\|>1)*+-inf = inf,0 /
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	218 return (hy >= 0) ? y : zero;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	219 else /* (\|x\|<1)*-,+inf = inf,0 /
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	220 return (hy < 0) ? -y : zero;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	221 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	222 if (iy == 0x3fff0000)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	223 { /* y is +-1 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	224 if (hy < 0)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	225 return one / x;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	226 else
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	227 return x;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	228 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	229 if (hy == 0x40000000)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	230 return x * x; /* y is 2 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	231 if (hy == 0x3ffe0000)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	232 { /* y is 0.5 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	233 if (hx >= 0) /* x >= +0 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	234 return sqrtq (x);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	235 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	236 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	237
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	238 ax = fabsq (x);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	239 /* special value of x */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	240 if ((p.words32.w1 \| p.words32.w2 \| p.words32.w3) == 0)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	241 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	242 if (ix == 0x7fff0000 \|\| ix == 0 \|\| ix == 0x3fff0000)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	243 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	244 z = ax; /x is +-0,+-inf,+-1 /
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	245 if (hy < 0)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	246 z = one / z; /* z = (1/\|x\|) */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	247 if (hx < 0)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	248 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	249 if (((ix - 0x3fff0000) \| yisint) == 0)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	250 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	251 z = (z - z) / (z - z); /* (-1)*non-int is NaN /
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	252 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	253 else if (yisint == 1)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	254 z = -z; /* (x<0)odd = -(\|x\|odd) */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	255 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	256 return z;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	257 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	258 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	259
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	260 /* (x<0)*(non-int) is NaN /
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	261 if (((((uint32_t) hx >> 31) - 1) \| yisint) == 0)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	262 return (x - x) / (x - x);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	263
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	264 /* \|y\| is huge.
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	265 2^-16495 = 1/2 of smallest representable value.
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	266 If (1 - 1/131072)^y underflows, y > 1.4986e9 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	267 if (iy > 0x401d654b)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	268 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	269 /* if (1 - 2^-113)^y underflows, y > 1.1873e38 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	270 if (iy > 0x407d654b)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	271 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	272 if (ix <= 0x3ffeffff)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	273 return (hy < 0) ? huge * huge : tiny * tiny;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	274 if (ix >= 0x3fff0000)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	275 return (hy > 0) ? huge * huge : tiny * tiny;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	276 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	277 /* over/underflow if x is not close to one */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	278 if (ix < 0x3ffeffff)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	279 return (hy < 0) ? huge * huge : tiny * tiny;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	280 if (ix > 0x3fff0000)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	281 return (hy > 0) ? huge * huge : tiny * tiny;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	282 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	283
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	284 n = 0;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	285 /* take care subnormal number */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	286 if (ix < 0x00010000)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	287 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	288 ax *= two113;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	289 n -= 113;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	290 o.value = ax;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	291 ix = o.words32.w0;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	292 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	293 n += ((ix) >> 16) - 0x3fff;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	294 j = ix & 0x0000ffff;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	295 /* determine interval */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	296 ix = j \| 0x3fff0000; /* normalize ix */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	297 if (j <= 0x3988)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	298 k = 0; /* \|x\|<sqrt(3/2) */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	299 else if (j < 0xbb67)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	300 k = 1; /* \|x\|<sqrt(3) */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	301 else
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	302 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	303 k = 0;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	304 n += 1;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	305 ix -= 0x00010000;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	306 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	307
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	308 o.value = ax;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	309 o.words32.w0 = ix;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	310 ax = o.value;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	311
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	312 /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	313 u = ax - bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	314 v = one / (ax + bp[k]);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	315 s = u * v;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	316 s_h = s;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	317
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	318 o.value = s_h;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	319 o.words32.w3 = 0;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	320 o.words32.w2 &= 0xf8000000;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	321 s_h = o.value;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	322 /* t_h=ax+bp[k] High */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	323 t_h = ax + bp[k];
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	324 o.value = t_h;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	325 o.words32.w3 = 0;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	326 o.words32.w2 &= 0xf8000000;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	327 t_h = o.value;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	328 t_l = ax - (t_h - bp[k]);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	329 s_l = v * ((u - s_h * t_h) - s_h * t_l);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	330 /* compute log(ax) */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	331 s2 = s * s;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	332 u = LN[0] + s2 * (LN[1] + s2 * (LN[2] + s2 * (LN[3] + s2 * LN[4])));
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	333 v = LD[0] + s2 * (LD[1] + s2 * (LD[2] + s2 * (LD[3] + s2 * (LD[4] + s2))));
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	334 r = s2 * s2 * u / v;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	335 r += s_l * (s_h + s);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	336 s2 = s_h * s_h;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	337 t_h = 3.0 + s2 + r;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	338 o.value = t_h;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	339 o.words32.w3 = 0;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	340 o.words32.w2 &= 0xf8000000;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	341 t_h = o.value;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	342 t_l = r - ((t_h - 3.0) - s2);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	343 /* u+v = s(1+...) /
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	344 u = s_h * t_h;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	345 v = s_l * t_h + t_l * s;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	346 /* 2/(3log2)(s+...) /
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	347 p_h = u + v;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	348 o.value = p_h;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	349 o.words32.w3 = 0;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	350 o.words32.w2 &= 0xf8000000;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	351 p_h = o.value;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	352 p_l = v - (p_h - u);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	353 z_h = cp_h * p_h; /* cp_h+cp_l = 2/(3log2) /
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	354 z_l = cp_l * p_h + p_l * cp + dp_l[k];
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	355 /* log2(ax) = (s+..)2/(3log2) = n + dp_h + z_h + z_l */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	356 t = (__float128) n;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	357 t1 = (((z_h + z_l) + dp_h[k]) + t);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	358 o.value = t1;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	359 o.words32.w3 = 0;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	360 o.words32.w2 &= 0xf8000000;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	361 t1 = o.value;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	362 t2 = z_l - (((t1 - t) - dp_h[k]) - z_h);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	363
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	364 /* s (sign of result -ve*odd) = -1 else = 1 /
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	365 s = one;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	366 if (((((uint32_t) hx >> 31) - 1) \| (yisint - 1)) == 0)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	367 s = -one; /* (-ve)*(odd int) /
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	368
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	369 /* split up y into y1+y2 and compute (y1+y2)(t1+t2) /
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	370 y1 = y;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	371 o.value = y1;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	372 o.words32.w3 = 0;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	373 o.words32.w2 &= 0xf8000000;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	374 y1 = o.value;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	375 p_l = (y - y1) * t1 + y * t2;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	376 p_h = y1 * t1;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	377 z = p_l + p_h;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	378 o.value = z;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	379 j = o.words32.w0;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	380 if (j >= 0x400d0000) /* z >= 16384 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	381 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	382 /* if z > 16384 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	383 if (((j - 0x400d0000) \| o.words32.w1 \| o.words32.w2 \| o.words32.w3) != 0)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	384 return s * huge * huge; /* overflow */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	385 else
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	386 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	387 if (p_l + ovt > z - p_h)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	388 return s * huge * huge; /* overflow */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	389 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	390 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	391 else if ((j & 0x7fffffff) >= 0x400d01b9) /* z <= -16495 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	392 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	393 /* z < -16495 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	394 if (((j - 0xc00d01bc) \| o.words32.w1 \| o.words32.w2 \| o.words32.w3)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	395 != 0)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	396 return s * tiny * tiny; /* underflow */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	397 else
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	398 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	399 if (p_l <= z - p_h)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	400 return s * tiny * tiny; /* underflow */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	401 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	402 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	403 /* compute 2*(p_h+p_l) /
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	404 i = j & 0x7fffffff;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	405 k = (i >> 16) - 0x3fff;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	406 n = 0;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	407 if (i > 0x3ffe0000)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	408 { /* if \|z\| > 0.5, set n = [z+0.5] */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	409 n = floorq (z + 0.5Q);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	410 t = n;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	411 p_h -= t;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	412 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	413 t = p_l + p_h;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	414 o.value = t;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	415 o.words32.w3 = 0;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	416 o.words32.w2 &= 0xf8000000;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	417 t = o.value;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	418 u = t * lg2_h;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	419 v = (p_l - (t - p_h)) * lg2 + t * lg2_l;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	420 z = u + v;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	421 w = v - (z - u);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	422 /* exp(z) */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	423 t = z * z;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	424 u = PN[0] + t * (PN[1] + t * (PN[2] + t * (PN[3] + t * PN[4])));
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	425 v = PD[0] + t * (PD[1] + t * (PD[2] + t * (PD[3] + t)));
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	426 t1 = z - t * u / v;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	427 r = (z * t1) / (t1 - two) - (w + z * w);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	428 z = one - (r - z);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	429 o.value = z;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	430 j = o.words32.w0;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	431 j += (n << 16);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	432 if ((j >> 16) <= 0)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	433 z = scalbnq (z, n); /* subnormal output */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	434 else
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	435 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	436 o.words32.w0 = j;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	437 z = o.value;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	438 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	439 return s * z;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	440 }

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561a7518be6b update gcc-4.6