CbC/CbC_gcc: libquadmath/math/j1q.c annotate

annotate libquadmath/math/j1q.c @ 158:494b0b89df80 default tip

...

author	Shinji KONO <kono@ie.u-ryukyu.ac.jp>
date	Mon, 25 May 2020 18:13:55 +0900
parents	1830386684a0
children

rev	line source
68 561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	1 /* j1l.c
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 * Bessel function of order one
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 *
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	6 *
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	7 * SYNOPSIS:
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	8 *
145 1830386684a0 gcc-9.2.0 anatofuz parents: 111 diff changeset	9 * long double x, y, j1l();
68 561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	10 *
145 1830386684a0 gcc-9.2.0 anatofuz parents: 111 diff changeset	11 * y = j1l( x );
68 561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	12 *
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	13 *
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	14 *
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	15 * DESCRIPTION:
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	16 *
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	17 * Returns Bessel function of first kind, order one of the argument.
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 * The domain is divided into two major intervals [0, 2] and
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	20 * (2, infinity). In the first interval the rational approximation is
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	21 * J1(x) = .5x + x x^2 R(x^2)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	22 *
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	23 * The second interval is further partitioned into eight equal segments
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	24 * of 1/x.
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	25 * J1(x) = sqrt(2/(pi x)) (P1(x) cos(X) - Q1(x) sin(X)),
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	26 * X = x - 3 pi / 4,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	27 *
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	28 * and the auxiliary functions are given by
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	29 *
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	30 * J1(x)cos(X) + Y1(x)sin(X) = sqrt( 2/(pi x)) P1(x),
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	31 * P1(x) = 1 + 1/x^2 R(1/x^2)
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 * Y1(x)cos(X) - J1(x)sin(X) = sqrt( 2/(pi x)) Q1(x),
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	34 * Q1(x) = 1/x (.375 + 1/x^2 R(1/x^2)).
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	35 *
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	36 *
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	37 *
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	38 * ACCURACY:
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	39 *
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	40 * Absolute error:
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	41 * arithmetic domain # trials peak rms
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	42 * IEEE 0, 30 100000 2.8e-34 2.7e-35
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 *
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	45 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	46
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	47 /* y1l.c
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	48 *
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	49 * Bessel function of the second kind, order one
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	50 *
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	51 *
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	52 *
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	53 * SYNOPSIS:
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	54 *
145 1830386684a0 gcc-9.2.0 anatofuz parents: 111 diff changeset	55 * double x, y, y1l();
68 561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	56 *
145 1830386684a0 gcc-9.2.0 anatofuz parents: 111 diff changeset	57 * y = y1l( x );
68 561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	58 *
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	59 *
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	60 *
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	61 * DESCRIPTION:
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	62 *
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	63 * Returns Bessel function of the second kind, of order
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	64 * one, of the argument.
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 * The domain is divided into two major intervals [0, 2] and
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	67 * (2, infinity). In the first interval the rational approximation is
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	68 * Y1(x) = 2/pi * (log(x) * J1(x) - 1/x) + x R(x^2) .
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	69 * In the second interval the approximation is the same as for J1(x), and
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	70 * Y1(x) = sqrt(2/(pi x)) (P1(x) sin(X) + Q1(x) cos(X)),
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	71 * X = x - 3 pi / 4.
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 * ACCURACY:
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	74 *
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	75 * Absolute error, when y0(x) < 1; else relative error:
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	76 *
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	77 * arithmetic domain # trials peak rms
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	78 * IEEE 0, 30 100000 2.7e-34 2.9e-35
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 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	81
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	82 /* Copyright 2001 by Stephen L. Moshier (moshier@na-net.onrl.gov).
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	83
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	84 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	85 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	86 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	87 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	88
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	89 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	90 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	91 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	92 Lesser General Public License for more details.
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	93
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	94 You should have received a copy of the GNU Lesser General Public
145 1830386684a0 gcc-9.2.0 anatofuz parents: 111 diff changeset	95 License along with this library; if not, see
1830386684a0 gcc-9.2.0 anatofuz parents: 111 diff changeset	96 <http://www.gnu.org/licenses/>. */
68 561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	97
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	98 #include "quadmath-imp.h"
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	99
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	100 /* 1 / sqrt(pi) */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	101 static const __float128 ONEOSQPI = 5.6418958354775628694807945156077258584405E-1Q;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	102 /* 2 / pi */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	103 static const __float128 TWOOPI = 6.3661977236758134307553505349005744813784E-1Q;
145 1830386684a0 gcc-9.2.0 anatofuz parents: 111 diff changeset	104 static const __float128 zero = 0;
68 561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	105
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	106 /* J1(x) = .5x + x x^2 R(x^2)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	107 Peak relative error 1.9e-35
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	108 0 <= x <= 2 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	109 #define NJ0_2N 6
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	110 static const __float128 J0_2N[NJ0_2N + 1] = {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	111 -5.943799577386942855938508697619735179660E16Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	112 1.812087021305009192259946997014044074711E15Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	113 -2.761698314264509665075127515729146460895E13Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	114 2.091089497823600978949389109350658815972E11Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	115 -8.546413231387036372945453565654130054307E8Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	116 1.797229225249742247475464052741320612261E6Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	117 -1.559552840946694171346552770008812083969E3Q
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	118 };
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	119 #define NJ0_2D 6
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	120 static const __float128 J0_2D[NJ0_2D + 1] = {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	121 9.510079323819108569501613916191477479397E17Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	122 1.063193817503280529676423936545854693915E16Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	123 5.934143516050192600795972192791775226920E13Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	124 2.168000911950620999091479265214368352883E11Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	125 5.673775894803172808323058205986256928794E8Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	126 1.080329960080981204840966206372671147224E6Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	127 1.411951256636576283942477881535283304912E3Q,
145 1830386684a0 gcc-9.2.0 anatofuz parents: 111 diff changeset	128 /* 1.000000000000000000000000000000000000000E0L */
68 561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	129 };
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	130
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	131 /* J1(x)cosX + Y1(x)sinX = sqrt( 2/(pi x)) P1(x), P1(x) = 1 + 1/x^2 R(1/x^2),
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	132 0 <= 1/x <= .0625
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	133 Peak relative error 3.6e-36 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	134 #define NP16_IN 9
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	135 static const __float128 P16_IN[NP16_IN + 1] = {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	136 5.143674369359646114999545149085139822905E-16Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	137 4.836645664124562546056389268546233577376E-13Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	138 1.730945562285804805325011561498453013673E-10Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	139 3.047976856147077889834905908605310585810E-8Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	140 2.855227609107969710407464739188141162386E-6Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	141 1.439362407936705484122143713643023998457E-4Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	142 3.774489768532936551500999699815873422073E-3Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	143 4.723962172984642566142399678920790598426E-2Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	144 2.359289678988743939925017240478818248735E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	145 3.032580002220628812728954785118117124520E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	146 };
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	147 #define NP16_ID 9
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	148 static const __float128 P16_ID[NP16_ID + 1] = {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	149 4.389268795186898018132945193912677177553E-15Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	150 4.132671824807454334388868363256830961655E-12Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	151 1.482133328179508835835963635130894413136E-9Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	152 2.618941412861122118906353737117067376236E-7Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	153 2.467854246740858470815714426201888034270E-5Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	154 1.257192927368839847825938545925340230490E-3Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	155 3.362739031941574274949719324644120720341E-2Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	156 4.384458231338934105875343439265370178858E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	157 2.412830809841095249170909628197264854651E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	158 4.176078204111348059102962617368214856874E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	159 /* 1.000000000000000000000000000000000000000E0 */
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
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	162 /* J1(x)cosX + Y1(x)sinX = sqrt( 2/(pi x)) P1(x), P1(x) = 1 + 1/x^2 R(1/x^2),
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	163 0.0625 <= 1/x <= 0.125
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	164 Peak relative error 1.9e-36 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	165 #define NP8_16N 11
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	166 static const __float128 P8_16N[NP8_16N + 1] = {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	167 2.984612480763362345647303274082071598135E-16Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	168 1.923651877544126103941232173085475682334E-13Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	169 4.881258879388869396043760693256024307743E-11Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	170 6.368866572475045408480898921866869811889E-9Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	171 4.684818344104910450523906967821090796737E-7Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	172 2.005177298271593587095982211091300382796E-5Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	173 4.979808067163957634120681477207147536182E-4Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	174 6.946005761642579085284689047091173581127E-3Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	175 5.074601112955765012750207555985299026204E-2Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	176 1.698599455896180893191766195194231825379E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	177 1.957536905259237627737222775573623779638E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	178 2.991314703282528370270179989044994319374E-2Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	179 };
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	180 #define NP8_16D 10
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	181 static const __float128 P8_16D[NP8_16D + 1] = {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	182 2.546869316918069202079580939942463010937E-15Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	183 1.644650111942455804019788382157745229955E-12Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	184 4.185430770291694079925607420808011147173E-10Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	185 5.485331966975218025368698195861074143153E-8Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	186 4.062884421686912042335466327098932678905E-6Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	187 1.758139661060905948870523641319556816772E-4Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	188 4.445143889306356207566032244985607493096E-3Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	189 6.391901016293512632765621532571159071158E-2Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	190 4.933040207519900471177016015718145795434E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	191 1.839144086168947712971630337250761842976E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	192 2.715120873995490920415616716916149586579E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	193 /* 1.000000000000000000000000000000000000000E0 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	194 };
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	195
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	196 /* J1(x)cosX + Y1(x)sinX = sqrt( 2/(pi x)) P1(x), P1(x) = 1 + 1/x^2 R(1/x^2),
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	197 0.125 <= 1/x <= 0.1875
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	198 Peak relative error 1.3e-36 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	199 #define NP5_8N 10
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	200 static const __float128 P5_8N[NP5_8N + 1] = {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	201 2.837678373978003452653763806968237227234E-12Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	202 9.726641165590364928442128579282742354806E-10Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	203 1.284408003604131382028112171490633956539E-7Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	204 8.524624695868291291250573339272194285008E-6Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	205 3.111516908953172249853673787748841282846E-4Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	206 6.423175156126364104172801983096596409176E-3Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	207 7.430220589989104581004416356260692450652E-2Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	208 4.608315409833682489016656279567605536619E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	209 1.396870223510964882676225042258855977512E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	210 1.718500293904122365894630460672081526236E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	211 5.465927698800862172307352821870223855365E-1Q
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	212 };
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	213 #define NP5_8D 10
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	214 static const __float128 P5_8D[NP5_8D + 1] = {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	215 2.421485545794616609951168511612060482715E-11Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	216 8.329862750896452929030058039752327232310E-9Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	217 1.106137992233383429630592081375289010720E-6Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	218 7.405786153760681090127497796448503306939E-5Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	219 2.740364785433195322492093333127633465227E-3Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	220 5.781246470403095224872243564165254652198E-2Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	221 6.927711353039742469918754111511109983546E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	222 4.558679283460430281188304515922826156690E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	223 1.534468499844879487013168065728837900009E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	224 2.313927430889218597919624843161569422745E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	225 1.194506341319498844336768473218382828637E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	226 /* 1.000000000000000000000000000000000000000E0 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	227 };
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 /* J1(x)cosX + Y1(x)sinX = sqrt( 2/(pi x)) P1(x), P1(x) = 1 + 1/x^2 R(1/x^2),
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	230 Peak relative error 1.4e-36
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	231 0.1875 <= 1/x <= 0.25 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	232 #define NP4_5N 10
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	233 static const __float128 P4_5N[NP4_5N + 1] = {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	234 1.846029078268368685834261260420933914621E-10Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	235 3.916295939611376119377869680335444207768E-8Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	236 3.122158792018920627984597530935323997312E-6Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	237 1.218073444893078303994045653603392272450E-4Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	238 2.536420827983485448140477159977981844883E-3Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	239 2.883011322006690823959367922241169171315E-2Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	240 1.755255190734902907438042414495469810830E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	241 5.379317079922628599870898285488723736599E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	242 7.284904050194300773890303361501726561938E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	243 3.270110346613085348094396323925000362813E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	244 1.804473805689725610052078464951722064757E-2Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	245 };
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	246 #define NP4_5D 9
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	247 static const __float128 P4_5D[NP4_5D + 1] = {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	248 1.575278146806816970152174364308980863569E-9Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	249 3.361289173657099516191331123405675054321E-7Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	250 2.704692281550877810424745289838790693708E-5Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	251 1.070854930483999749316546199273521063543E-3Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	252 2.282373093495295842598097265627962125411E-2Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	253 2.692025460665354148328762368240343249830E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	254 1.739892942593664447220951225734811133759E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	255 5.890727576752230385342377570386657229324E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	256 9.517442287057841500750256954117735128153E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	257 6.100616353935338240775363403030137736013E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	258 /* 1.000000000000000000000000000000000000000E0 */
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
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	261 /* J1(x)cosX + Y1(x)sinX = sqrt( 2/(pi x)) P1(x), P1(x) = 1 + 1/x^2 R(1/x^2),
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	262 Peak relative error 3.0e-36
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	263 0.25 <= 1/x <= 0.3125 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	264 #define NP3r2_4N 9
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	265 static const __float128 P3r2_4N[NP3r2_4N + 1] = {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	266 8.240803130988044478595580300846665863782E-8Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	267 1.179418958381961224222969866406483744580E-5Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	268 6.179787320956386624336959112503824397755E-4Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	269 1.540270833608687596420595830747166658383E-2Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	270 1.983904219491512618376375619598837355076E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	271 1.341465722692038870390470651608301155565E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	272 4.617865326696612898792238245990854646057E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	273 7.435574801812346424460233180412308000587E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	274 4.671327027414635292514599201278557680420E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	275 7.299530852495776936690976966995187714739E-1Q,
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 #define NP3r2_4D 9
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	278 static const __float128 P3r2_4D[NP3r2_4D + 1] = {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	279 7.032152009675729604487575753279187576521E-7Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	280 1.015090352324577615777511269928856742848E-4Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	281 5.394262184808448484302067955186308730620E-3Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	282 1.375291438480256110455809354836988584325E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	283 1.836247144461106304788160919310404376670E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	284 1.314378564254376655001094503090935880349E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	285 4.957184590465712006934452500894672343488E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	286 9.287394244300647738855415178790263465398E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	287 7.652563275535900609085229286020552768399E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	288 2.147042473003074533150718117770093209096E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	289 /* 1.000000000000000000000000000000000000000E0 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	290 };
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	291
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	292 /* J1(x)cosX + Y1(x)sinX = sqrt( 2/(pi x)) P1(x), P1(x) = 1 + 1/x^2 R(1/x^2),
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	293 Peak relative error 1.0e-35
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	294 0.3125 <= 1/x <= 0.375 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	295 #define NP2r7_3r2N 9
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	296 static const __float128 P2r7_3r2N[NP2r7_3r2N + 1] = {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	297 4.599033469240421554219816935160627085991E-7Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	298 4.665724440345003914596647144630893997284E-5Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	299 1.684348845667764271596142716944374892756E-3Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	300 2.802446446884455707845985913454440176223E-2Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	301 2.321937586453963310008279956042545173930E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	302 9.640277413988055668692438709376437553804E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	303 1.911021064710270904508663334033003246028E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	304 1.600811610164341450262992138893970224971E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	305 4.266299218652587901171386591543457861138E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	306 1.316470424456061252962568223251247207325E-2Q,
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 #define NP2r7_3r2D 8
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	309 static const __float128 P2r7_3r2D[NP2r7_3r2D + 1] = {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	310 3.924508608545520758883457108453520099610E-6Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	311 4.029707889408829273226495756222078039823E-4Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	312 1.484629715787703260797886463307469600219E-2Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	313 2.553136379967180865331706538897231588685E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	314 2.229457223891676394409880026887106228740E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	315 1.005708903856384091956550845198392117318E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	316 2.277082659664386953166629360352385889558E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	317 2.384726835193630788249826630376533988245E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	318 9.700989749041320895890113781610939632410E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	319 /* 1.000000000000000000000000000000000000000E0 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	320 };
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	321
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	322 /* J1(x)cosX + Y1(x)sinX = sqrt( 2/(pi x)) P1(x), P1(x) = 1 + 1/x^2 R(1/x^2),
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	323 Peak relative error 1.7e-36
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	324 0.3125 <= 1/x <= 0.4375 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	325 #define NP2r3_2r7N 9
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	326 static const __float128 P2r3_2r7N[NP2r3_2r7N + 1] = {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	327 3.916766777108274628543759603786857387402E-6Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	328 3.212176636756546217390661984304645137013E-4Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	329 9.255768488524816445220126081207248947118E-3Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	330 1.214853146369078277453080641911700735354E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	331 7.855163309847214136198449861311404633665E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	332 2.520058073282978403655488662066019816540E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	333 3.825136484837545257209234285382183711466E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	334 2.432569427554248006229715163865569506873E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	335 4.877934835018231178495030117729800489743E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	336 1.109902737860249670981355149101343427885E-2Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	337 };
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	338 #define NP2r3_2r7D 8
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	339 static const __float128 P2r3_2r7D[NP2r3_2r7D + 1] = {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	340 3.342307880794065640312646341190547184461E-5Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	341 2.782182891138893201544978009012096558265E-3Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	342 8.221304931614200702142049236141249929207E-2Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	343 1.123728246291165812392918571987858010949E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	344 7.740482453652715577233858317133423434590E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	345 2.737624677567945952953322566311201919139E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	346 4.837181477096062403118304137851260715475E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	347 3.941098643468580791437772701093795299274E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	348 1.245821247166544627558323920382547533630E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	349 /* 1.000000000000000000000000000000000000000E0 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	350 };
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	351
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	352 /* J1(x)cosX + Y1(x)sinX = sqrt( 2/(pi x)) P1(x), P1(x) = 1 + 1/x^2 R(1/x^2),
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	353 Peak relative error 1.7e-35
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	354 0.4375 <= 1/x <= 0.5 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	355 #define NP2_2r3N 8
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	356 static const __float128 P2_2r3N[NP2_2r3N + 1] = {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	357 3.397930802851248553545191160608731940751E-4Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	358 2.104020902735482418784312825637833698217E-2Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	359 4.442291771608095963935342749477836181939E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	360 4.131797328716583282869183304291833754967E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	361 1.819920169779026500146134832455189917589E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	362 3.781779616522937565300309684282401791291E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	363 3.459605449728864218972931220783543410347E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	364 1.173594248397603882049066603238568316561E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	365 9.455702270242780642835086549285560316461E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	366 };
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	367 #define NP2_2r3D 8
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	368 static const __float128 P2_2r3D[NP2_2r3D + 1] = {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	369 2.899568897241432883079888249845707400614E-3Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	370 1.831107138190848460767699919531132426356E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	371 3.999350044057883839080258832758908825165E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	372 3.929041535867957938340569419874195303712E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	373 1.884245613422523323068802689915538908291E2Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	374 4.461469948819229734353852978424629815929E2Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	375 5.004998753999796821224085972610636347903E2Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	376 2.386342520092608513170837883757163414100E2Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	377 3.791322528149347975999851588922424189957E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	378 /* 1.000000000000000000000000000000000000000E0 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	379 };
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	380
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	381 /* Y1(x)cosX - J1(x)sinX = sqrt( 2/(pi x)) Q1(x),
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	382 Q1(x) = 1/x (.375 + 1/x^2 R(1/x^2)),
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	383 Peak relative error 8.0e-36
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	384 0 <= 1/x <= .0625 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	385 #define NQ16_IN 10
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	386 static const __float128 Q16_IN[NQ16_IN + 1] = {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	387 -3.917420835712508001321875734030357393421E-18Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	388 -4.440311387483014485304387406538069930457E-15Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	389 -1.951635424076926487780929645954007139616E-12Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	390 -4.318256438421012555040546775651612810513E-10Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	391 -5.231244131926180765270446557146989238020E-8Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	392 -3.540072702902043752460711989234732357653E-6Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	393 -1.311017536555269966928228052917534882984E-4Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	394 -2.495184669674631806622008769674827575088E-3Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	395 -2.141868222987209028118086708697998506716E-2Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	396 -6.184031415202148901863605871197272650090E-2Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	397 -1.922298704033332356899546792898156493887E-2Q,
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 #define NQ16_ID 9
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	400 static const __float128 Q16_ID[NQ16_ID + 1] = {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	401 3.820418034066293517479619763498400162314E-17Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	402 4.340702810799239909648911373329149354911E-14Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	403 1.914985356383416140706179933075303538524E-11Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	404 4.262333682610888819476498617261895474330E-9Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	405 5.213481314722233980346462747902942182792E-7Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	406 3.585741697694069399299005316809954590558E-5Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	407 1.366513429642842006385029778105539457546E-3Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	408 2.745282599850704662726337474371355160594E-2Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	409 2.637644521611867647651200098449903330074E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	410 1.006953426110765984590782655598680488746E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	411 /* 1.000000000000000000000000000000000000000E0 */
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
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	414 /* Y1(x)cosX - J1(x)sinX = sqrt( 2/(pi x)) Q1(x),
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	415 Q1(x) = 1/x (.375 + 1/x^2 R(1/x^2)),
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	416 Peak relative error 1.9e-36
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	417 0.0625 <= 1/x <= 0.125 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	418 #define NQ8_16N 11
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	419 static const __float128 Q8_16N[NQ8_16N + 1] = {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	420 -2.028630366670228670781362543615221542291E-17Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	421 -1.519634620380959966438130374006858864624E-14Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	422 -4.540596528116104986388796594639405114524E-12Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	423 -7.085151756671466559280490913558388648274E-10Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	424 -6.351062671323970823761883833531546885452E-8Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	425 -3.390817171111032905297982523519503522491E-6Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	426 -1.082340897018886970282138836861233213972E-4Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	427 -2.020120801187226444822977006648252379508E-3Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	428 -2.093169910981725694937457070649605557555E-2Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	429 -1.092176538874275712359269481414448063393E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	430 -2.374790947854765809203590474789108718733E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	431 -1.365364204556573800719985118029601401323E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	432 };
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	433 #define NQ8_16D 11
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	434 static const __float128 Q8_16D[NQ8_16D + 1] = {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	435 1.978397614733632533581207058069628242280E-16Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	436 1.487361156806202736877009608336766720560E-13Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	437 4.468041406888412086042576067133365913456E-11Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	438 7.027822074821007443672290507210594648877E-9Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	439 6.375740580686101224127290062867976007374E-7Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	440 3.466887658320002225888644977076410421940E-5Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	441 1.138625640905289601186353909213719596986E-3Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	442 2.224470799470414663443449818235008486439E-2Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	443 2.487052928527244907490589787691478482358E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	444 1.483927406564349124649083853892380899217E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	445 4.182773513276056975777258788903489507705E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	446 4.419665392573449746043880892524360870944E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	447 /* 1.000000000000000000000000000000000000000E0 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	448 };
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	449
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	450 /* Y1(x)cosX - J1(x)sinX = sqrt( 2/(pi x)) Q1(x),
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	451 Q1(x) = 1/x (.375 + 1/x^2 R(1/x^2)),
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	452 Peak relative error 1.5e-35
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	453 0.125 <= 1/x <= 0.1875 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	454 #define NQ5_8N 10
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	455 static const __float128 Q5_8N[NQ5_8N + 1] = {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	456 -3.656082407740970534915918390488336879763E-13Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	457 -1.344660308497244804752334556734121771023E-10Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	458 -1.909765035234071738548629788698150760791E-8Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	459 -1.366668038160120210269389551283666716453E-6Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	460 -5.392327355984269366895210704976314135683E-5Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	461 -1.206268245713024564674432357634540343884E-3Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	462 -1.515456784370354374066417703736088291287E-2Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	463 -1.022454301137286306933217746545237098518E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	464 -3.373438906472495080504907858424251082240E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	465 -4.510782522110845697262323973549178453405E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	466 -1.549000892545288676809660828213589804884E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	467 };
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	468 #define NQ5_8D 10
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	469 static const __float128 Q5_8D[NQ5_8D + 1] = {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	470 3.565550843359501079050699598913828460036E-12Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	471 1.321016015556560621591847454285330528045E-9Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	472 1.897542728662346479999969679234270605975E-7Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	473 1.381720283068706710298734234287456219474E-5Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	474 5.599248147286524662305325795203422873725E-4Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	475 1.305442352653121436697064782499122164843E-2Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	476 1.750234079626943298160445750078631894985E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	477 1.311420542073436520965439883806946678491E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	478 5.162757689856842406744504211089724926650E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	479 9.527760296384704425618556332087850581308E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	480 6.604648207463236667912921642545100248584E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	481 /* 1.000000000000000000000000000000000000000E0 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	482 };
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	483
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	484 /* Y1(x)cosX - J1(x)sinX = sqrt( 2/(pi x)) Q1(x),
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	485 Q1(x) = 1/x (.375 + 1/x^2 R(1/x^2)),
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	486 Peak relative error 1.3e-35
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	487 0.1875 <= 1/x <= 0.25 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	488 #define NQ4_5N 10
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	489 static const __float128 Q4_5N[NQ4_5N + 1] = {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	490 -4.079513568708891749424783046520200903755E-11Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	491 -9.326548104106791766891812583019664893311E-9Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	492 -8.016795121318423066292906123815687003356E-7Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	493 -3.372350544043594415609295225664186750995E-5Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	494 -7.566238665947967882207277686375417983917E-4Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	495 -9.248861580055565402130441618521591282617E-3Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	496 -6.033106131055851432267702948850231270338E-2Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	497 -1.966908754799996793730369265431584303447E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	498 -2.791062741179964150755788226623462207560E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	499 -1.255478605849190549914610121863534191666E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	500 -4.320429862021265463213168186061696944062E-3Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	501 };
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	502 #define NQ4_5D 9
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	503 static const __float128 Q4_5D[NQ4_5D + 1] = {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	504 3.978497042580921479003851216297330701056E-10Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	505 9.203304163828145809278568906420772246666E-8Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	506 8.059685467088175644915010485174545743798E-6Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	507 3.490187375993956409171098277561669167446E-4Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	508 8.189109654456872150100501732073810028829E-3Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	509 1.072572867311023640958725265762483033769E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	510 7.790606862409960053675717185714576937994E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	511 3.016049768232011196434185423512777656328E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	512 5.722963851442769787733717162314477949360E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	513 4.510527838428473279647251350931380867663E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	514 /* 1.000000000000000000000000000000000000000E0 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	515 };
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	516
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	517 /* Y1(x)cosX - J1(x)sinX = sqrt( 2/(pi x)) Q1(x),
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	518 Q1(x) = 1/x (.375 + 1/x^2 R(1/x^2)),
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	519 Peak relative error 2.1e-35
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	520 0.25 <= 1/x <= 0.3125 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	521 #define NQ3r2_4N 9
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	522 static const __float128 Q3r2_4N[NQ3r2_4N + 1] = {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	523 -1.087480809271383885936921889040388133627E-8Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	524 -1.690067828697463740906962973479310170932E-6Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	525 -9.608064416995105532790745641974762550982E-5Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	526 -2.594198839156517191858208513873961837410E-3Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	527 -3.610954144421543968160459863048062977822E-2Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	528 -2.629866798251843212210482269563961685666E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	529 -9.709186825881775885917984975685752956660E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	530 -1.667521829918185121727268867619982417317E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	531 -1.109255082925540057138766105229900943501E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	532 -1.812932453006641348145049323713469043328E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	533 };
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	534 #define NQ3r2_4D 9
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	535 static const __float128 Q3r2_4D[NQ3r2_4D + 1] = {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	536 1.060552717496912381388763753841473407026E-7Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	537 1.676928002024920520786883649102388708024E-5Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	538 9.803481712245420839301400601140812255737E-4Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	539 2.765559874262309494758505158089249012930E-2Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	540 4.117921827792571791298862613287549140706E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	541 3.323769515244751267093378361930279161413E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	542 1.436602494405814164724810151689705353670E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	543 3.163087869617098638064881410646782408297E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	544 3.198181264977021649489103980298349589419E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	545 1.203649258862068431199471076202897823272E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	546 /* 1.000000000000000000000000000000000000000E0 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	547 };
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	548
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	549 /* Y1(x)cosX - J1(x)sinX = sqrt( 2/(pi x)) Q1(x),
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	550 Q1(x) = 1/x (.375 + 1/x^2 R(1/x^2)),
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	551 Peak relative error 1.6e-36
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	552 0.3125 <= 1/x <= 0.375 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	553 #define NQ2r7_3r2N 9
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	554 static const __float128 Q2r7_3r2N[NQ2r7_3r2N + 1] = {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	555 -1.723405393982209853244278760171643219530E-7Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	556 -2.090508758514655456365709712333460087442E-5Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	557 -9.140104013370974823232873472192719263019E-4Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	558 -1.871349499990714843332742160292474780128E-2Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	559 -1.948930738119938669637865956162512983416E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	560 -1.048764684978978127908439526343174139788E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	561 -2.827714929925679500237476105843643064698E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	562 -3.508761569156476114276988181329773987314E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	563 -1.669332202790211090973255098624488308989E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	564 -1.930796319299022954013840684651016077770E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	565 };
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	566 #define NQ2r7_3r2D 9
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	567 static const __float128 Q2r7_3r2D[NQ2r7_3r2D + 1] = {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	568 1.680730662300831976234547482334347983474E-6Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	569 2.084241442440551016475972218719621841120E-4Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	570 9.445316642108367479043541702688736295579E-3Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	571 2.044637889456631896650179477133252184672E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	572 2.316091982244297350829522534435350078205E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	573 1.412031891783015085196708811890448488865E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	574 4.583830154673223384837091077279595496149E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	575 7.549520609270909439885998474045974122261E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	576 5.697605832808113367197494052388203310638E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	577 1.601496240876192444526383314589371686234E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	578 /* 1.000000000000000000000000000000000000000E0 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	579 };
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	580
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	581 /* Y1(x)cosX - J1(x)sinX = sqrt( 2/(pi x)) Q1(x),
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	582 Q1(x) = 1/x (.375 + 1/x^2 R(1/x^2)),
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	583 Peak relative error 9.5e-36
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	584 0.375 <= 1/x <= 0.4375 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	585 #define NQ2r3_2r7N 9
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	586 static const __float128 Q2r3_2r7N[NQ2r3_2r7N + 1] = {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	587 -8.603042076329122085722385914954878953775E-7Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	588 -7.701746260451647874214968882605186675720E-5Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	589 -2.407932004380727587382493696877569654271E-3Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	590 -3.403434217607634279028110636919987224188E-2Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	591 -2.348707332185238159192422084985713102877E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	592 -7.957498841538254916147095255700637463207E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	593 -1.258469078442635106431098063707934348577E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	594 -8.162415474676345812459353639449971369890E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	595 -1.581783890269379690141513949609572806898E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	596 -1.890595651683552228232308756569450822905E-3Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	597 };
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	598 #define NQ2r3_2r7D 8
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	599 static const __float128 Q2r3_2r7D[NQ2r3_2r7D + 1] = {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	600 8.390017524798316921170710533381568175665E-6Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	601 7.738148683730826286477254659973968763659E-4Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	602 2.541480810958665794368759558791634341779E-2Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	603 3.878879789711276799058486068562386244873E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	604 3.003783779325811292142957336802456109333E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	605 1.206480374773322029883039064575464497400E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	606 2.458414064785315978408974662900438351782E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	607 2.367237826273668567199042088835448715228E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	608 9.231451197519171090875569102116321676763E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	609 /* 1.000000000000000000000000000000000000000E0 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	610 };
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	611
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	612 /* Y1(x)cosX - J1(x)sinX = sqrt( 2/(pi x)) Q1(x),
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	613 Q1(x) = 1/x (.375 + 1/x^2 R(1/x^2)),
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	614 Peak relative error 1.4e-36
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	615 0.4375 <= 1/x <= 0.5 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	616 #define NQ2_2r3N 9
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	617 static const __float128 Q2_2r3N[NQ2_2r3N + 1] = {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	618 -5.552507516089087822166822364590806076174E-6Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	619 -4.135067659799500521040944087433752970297E-4Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	620 -1.059928728869218962607068840646564457980E-2Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	621 -1.212070036005832342565792241385459023801E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	622 -6.688350110633603958684302153362735625156E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	623 -1.793587878197360221340277951304429821582E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	624 -2.225407682237197485644647380483725045326E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	625 -1.123402135458940189438898496348239744403E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	626 -1.679187241566347077204805190763597299805E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	627 -1.458550613639093752909985189067233504148E-3Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	628 };
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	629 #define NQ2_2r3D 8
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	630 static const __float128 Q2_2r3D[NQ2_2r3D + 1] = {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	631 5.415024336507980465169023996403597916115E-5Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	632 4.179246497380453022046357404266022870788E-3Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	633 1.136306384261959483095442402929502368598E-1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	634 1.422640343719842213484515445393284072830E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	635 8.968786703393158374728850922289204805764E0Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	636 2.914542473339246127533384118781216495934E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	637 4.781605421020380669870197378210457054685E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	638 3.693865837171883152382820584714795072937E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	639 1.153220502744204904763115556224395893076E1Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	640 /* 1.000000000000000000000000000000000000000E0 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	641 };
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	642
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	643
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	644 /* Evaluate P[n] x^n + P[n-1] x^(n-1) + ... + P[0] */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	645
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	646 static __float128
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	647 neval (__float128 x, const __float128 *p, int n)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	648 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	649 __float128 y;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	650
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	651 p += n;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	652 y = *p--;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	653 do
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	654 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	655 y = y * x + *p--;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	656 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	657 while (--n > 0);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	658 return y;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	659 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	660
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	661
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	662 /* Evaluate x^n+1 + P[n] x^(n) + P[n-1] x^(n-1) + ... + P[0] */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	663
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	664 static __float128
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	665 deval (__float128 x, const __float128 *p, int n)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	666 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	667 __float128 y;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	668
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	669 p += n;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	670 y = x + *p--;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	671 do
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	672 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	673 y = y * x + *p--;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	674 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	675 while (--n > 0);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	676 return y;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	677 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	678
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	679
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	680 /* Bessel function of the first kind, order one. */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	681
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	682 __float128
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	683 j1q (__float128 x)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	684 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	685 __float128 xx, xinv, z, p, q, c, s, cc, ss;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	686
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	687 if (! finiteq (x))
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	688 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	689 if (x != x)
111 04ced10e8804 gcc 7 kono parents: 68 diff changeset	690 return x + x;
68 561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	691 else
145 1830386684a0 gcc-9.2.0 anatofuz parents: 111 diff changeset	692 return 0;
68 561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	693 }
145 1830386684a0 gcc-9.2.0 anatofuz parents: 111 diff changeset	694 if (x == 0)
68 561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	695 return x;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	696 xx = fabsq (x);
111 04ced10e8804 gcc 7 kono parents: 68 diff changeset	697 if (xx <= 0x1p-58Q)
04ced10e8804 gcc 7 kono parents: 68 diff changeset	698 {
04ced10e8804 gcc 7 kono parents: 68 diff changeset	699 __float128 ret = x * 0.5Q;
04ced10e8804 gcc 7 kono parents: 68 diff changeset	700 math_check_force_underflow (ret);
04ced10e8804 gcc 7 kono parents: 68 diff changeset	701 if (ret == 0)
04ced10e8804 gcc 7 kono parents: 68 diff changeset	702 errno = ERANGE;
04ced10e8804 gcc 7 kono parents: 68 diff changeset	703 return ret;
04ced10e8804 gcc 7 kono parents: 68 diff changeset	704 }
145 1830386684a0 gcc-9.2.0 anatofuz parents: 111 diff changeset	705 if (xx <= 2)
68 561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	706 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	707 /* 0 <= x <= 2 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	708 z = xx * xx;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	709 p = xx * z * neval (z, J0_2N, NJ0_2N) / deval (z, J0_2D, NJ0_2D);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	710 p += 0.5Q * xx;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	711 if (x < 0)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	712 p = -p;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	713 return p;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	714 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	715
111 04ced10e8804 gcc 7 kono parents: 68 diff changeset	716 /* X = x - 3 pi/4
04ced10e8804 gcc 7 kono parents: 68 diff changeset	717 cos(X) = cos(x) cos(3 pi/4) + sin(x) sin(3 pi/4)
04ced10e8804 gcc 7 kono parents: 68 diff changeset	718 = 1/sqrt(2) * (-cos(x) + sin(x))
04ced10e8804 gcc 7 kono parents: 68 diff changeset	719 sin(X) = sin(x) cos(3 pi/4) - cos(x) sin(3 pi/4)
04ced10e8804 gcc 7 kono parents: 68 diff changeset	720 = -1/sqrt(2) * (sin(x) + cos(x))
04ced10e8804 gcc 7 kono parents: 68 diff changeset	721 cf. Fdlibm. */
04ced10e8804 gcc 7 kono parents: 68 diff changeset	722 sincosq (xx, &s, &c);
04ced10e8804 gcc 7 kono parents: 68 diff changeset	723 ss = -s - c;
04ced10e8804 gcc 7 kono parents: 68 diff changeset	724 cc = s - c;
145 1830386684a0 gcc-9.2.0 anatofuz parents: 111 diff changeset	725 if (xx <= FLT128_MAX / 2)
111 04ced10e8804 gcc 7 kono parents: 68 diff changeset	726 {
04ced10e8804 gcc 7 kono parents: 68 diff changeset	727 z = cosq (xx + xx);
04ced10e8804 gcc 7 kono parents: 68 diff changeset	728 if ((s * c) > 0)
04ced10e8804 gcc 7 kono parents: 68 diff changeset	729 cc = z / ss;
04ced10e8804 gcc 7 kono parents: 68 diff changeset	730 else
04ced10e8804 gcc 7 kono parents: 68 diff changeset	731 ss = z / cc;
04ced10e8804 gcc 7 kono parents: 68 diff changeset	732 }
04ced10e8804 gcc 7 kono parents: 68 diff changeset	733
04ced10e8804 gcc 7 kono parents: 68 diff changeset	734 if (xx > 0x1p256Q)
04ced10e8804 gcc 7 kono parents: 68 diff changeset	735 {
04ced10e8804 gcc 7 kono parents: 68 diff changeset	736 z = ONEOSQPI * cc / sqrtq (xx);
04ced10e8804 gcc 7 kono parents: 68 diff changeset	737 if (x < 0)
04ced10e8804 gcc 7 kono parents: 68 diff changeset	738 z = -z;
04ced10e8804 gcc 7 kono parents: 68 diff changeset	739 return z;
04ced10e8804 gcc 7 kono parents: 68 diff changeset	740 }
04ced10e8804 gcc 7 kono parents: 68 diff changeset	741
145 1830386684a0 gcc-9.2.0 anatofuz parents: 111 diff changeset	742 xinv = 1 / xx;
68 561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	743 z = xinv * xinv;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	744 if (xinv <= 0.25)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	745 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	746 if (xinv <= 0.125)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	747 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	748 if (xinv <= 0.0625)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	749 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	750 p = neval (z, P16_IN, NP16_IN) / deval (z, P16_ID, NP16_ID);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	751 q = neval (z, Q16_IN, NQ16_IN) / deval (z, Q16_ID, NQ16_ID);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	752 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	753 else
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	754 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	755 p = neval (z, P8_16N, NP8_16N) / deval (z, P8_16D, NP8_16D);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	756 q = neval (z, Q8_16N, NQ8_16N) / deval (z, Q8_16D, NQ8_16D);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	757 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	758 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	759 else if (xinv <= 0.1875)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	760 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	761 p = neval (z, P5_8N, NP5_8N) / deval (z, P5_8D, NP5_8D);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	762 q = neval (z, Q5_8N, NQ5_8N) / deval (z, Q5_8D, NQ5_8D);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	763 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	764 else
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	765 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	766 p = neval (z, P4_5N, NP4_5N) / deval (z, P4_5D, NP4_5D);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	767 q = neval (z, Q4_5N, NQ4_5N) / deval (z, Q4_5D, NQ4_5D);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	768 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	769 } /* .25 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	770 else /* if (xinv <= 0.5) */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	771 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	772 if (xinv <= 0.375)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	773 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	774 if (xinv <= 0.3125)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	775 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	776 p = neval (z, P3r2_4N, NP3r2_4N) / deval (z, P3r2_4D, NP3r2_4D);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	777 q = neval (z, Q3r2_4N, NQ3r2_4N) / deval (z, Q3r2_4D, NQ3r2_4D);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	778 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	779 else
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	780 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	781 p = neval (z, P2r7_3r2N, NP2r7_3r2N)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	782 / deval (z, P2r7_3r2D, NP2r7_3r2D);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	783 q = neval (z, Q2r7_3r2N, NQ2r7_3r2N)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	784 / deval (z, Q2r7_3r2D, NQ2r7_3r2D);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	785 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	786 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	787 else if (xinv <= 0.4375)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	788 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	789 p = neval (z, P2r3_2r7N, NP2r3_2r7N)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	790 / deval (z, P2r3_2r7D, NP2r3_2r7D);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	791 q = neval (z, Q2r3_2r7N, NQ2r3_2r7N)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	792 / deval (z, Q2r3_2r7D, NQ2r3_2r7D);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	793 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	794 else
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	795 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	796 p = neval (z, P2_2r3N, NP2_2r3N) / deval (z, P2_2r3D, NP2_2r3D);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	797 q = neval (z, Q2_2r3N, NQ2_2r3N) / deval (z, Q2_2r3D, NQ2_2r3D);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	798 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	799 }
145 1830386684a0 gcc-9.2.0 anatofuz parents: 111 diff changeset	800 p = 1 + z * p;
68 561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	801 q = z * q;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	802 q = q * xinv + 0.375Q * xinv;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	803 z = ONEOSQPI * (p * cc - q * ss) / sqrtq (xx);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	804 if (x < 0)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	805 z = -z;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	806 return z;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	807 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	808
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	809
145 1830386684a0 gcc-9.2.0 anatofuz parents: 111 diff changeset	810
68 561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	811 /* Y1(x) = 2/pi * (log(x) * J1(x) - 1/x) + x R(x^2)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	812 Peak relative error 6.2e-38
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	813 0 <= x <= 2 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	814 #define NY0_2N 7
145 1830386684a0 gcc-9.2.0 anatofuz parents: 111 diff changeset	815 static const __float128 Y0_2N[NY0_2N + 1] = {
68 561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	816 -6.804415404830253804408698161694720833249E19Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	817 1.805450517967019908027153056150465849237E19Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	818 -8.065747497063694098810419456383006737312E17Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	819 1.401336667383028259295830955439028236299E16Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	820 -1.171654432898137585000399489686629680230E14Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	821 5.061267920943853732895341125243428129150E11Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	822 -1.096677850566094204586208610960870217970E9Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	823 9.541172044989995856117187515882879304461E5Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	824 };
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	825 #define NY0_2D 7
145 1830386684a0 gcc-9.2.0 anatofuz parents: 111 diff changeset	826 static const __float128 Y0_2D[NY0_2D + 1] = {
68 561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	827 3.470629591820267059538637461549677594549E20Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	828 4.120796439009916326855848107545425217219E18Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	829 2.477653371652018249749350657387030814542E16Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	830 9.954678543353888958177169349272167762797E13Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	831 2.957927997613630118216218290262851197754E11Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	832 6.748421382188864486018861197614025972118E8Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	833 1.173453425218010888004562071020305709319E6Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	834 1.450335662961034949894009554536003377187E3Q,
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	835 /* 1.000000000000000000000000000000000000000E0 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	836 };
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	837
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	838
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	839 /* Bessel function of the second kind, order one. */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	840
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	841 __float128
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	842 y1q (__float128 x)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	843 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	844 __float128 xx, xinv, z, p, q, c, s, cc, ss;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	845
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	846 if (! finiteq (x))
111 04ced10e8804 gcc 7 kono parents: 68 diff changeset	847 return 1 / (x + x * x);
145 1830386684a0 gcc-9.2.0 anatofuz parents: 111 diff changeset	848 if (x <= 0)
68 561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	849 {
145 1830386684a0 gcc-9.2.0 anatofuz parents: 111 diff changeset	850 if (x < 0)
68 561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	851 return (zero / (zero * x));
111 04ced10e8804 gcc 7 kono parents: 68 diff changeset	852 return -1 / zero; /* -inf and divide by zero exception. */
68 561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	853 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	854 xx = fabsq (x);
111 04ced10e8804 gcc 7 kono parents: 68 diff changeset	855 if (xx <= 0x1p-114)
68 561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	856 {
111 04ced10e8804 gcc 7 kono parents: 68 diff changeset	857 z = -TWOOPI / x;
04ced10e8804 gcc 7 kono parents: 68 diff changeset	858 if (isinfq (z))
04ced10e8804 gcc 7 kono parents: 68 diff changeset	859 errno = ERANGE;
04ced10e8804 gcc 7 kono parents: 68 diff changeset	860 return z;
04ced10e8804 gcc 7 kono parents: 68 diff changeset	861 }
145 1830386684a0 gcc-9.2.0 anatofuz parents: 111 diff changeset	862 if (xx <= 2)
1830386684a0 gcc-9.2.0 anatofuz parents: 111 diff changeset	863 {
68 561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	864 /* 0 <= x <= 2 */
145 1830386684a0 gcc-9.2.0 anatofuz parents: 111 diff changeset	865 SET_RESTORE_ROUNDF128 (FE_TONEAREST);
68 561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	866 z = xx * xx;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	867 p = xx * neval (z, Y0_2N, NY0_2N) / deval (z, Y0_2D, NY0_2D);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	868 p = -TWOOPI / xx + p;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	869 p = TWOOPI * logq (x) * j1q (x) + p;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	870 return p;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	871 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	872
111 04ced10e8804 gcc 7 kono parents: 68 diff changeset	873 /* X = x - 3 pi/4
04ced10e8804 gcc 7 kono parents: 68 diff changeset	874 cos(X) = cos(x) cos(3 pi/4) + sin(x) sin(3 pi/4)
04ced10e8804 gcc 7 kono parents: 68 diff changeset	875 = 1/sqrt(2) * (-cos(x) + sin(x))
04ced10e8804 gcc 7 kono parents: 68 diff changeset	876 sin(X) = sin(x) cos(3 pi/4) - cos(x) sin(3 pi/4)
04ced10e8804 gcc 7 kono parents: 68 diff changeset	877 = -1/sqrt(2) * (sin(x) + cos(x))
04ced10e8804 gcc 7 kono parents: 68 diff changeset	878 cf. Fdlibm. */
04ced10e8804 gcc 7 kono parents: 68 diff changeset	879 sincosq (xx, &s, &c);
04ced10e8804 gcc 7 kono parents: 68 diff changeset	880 ss = -s - c;
04ced10e8804 gcc 7 kono parents: 68 diff changeset	881 cc = s - c;
145 1830386684a0 gcc-9.2.0 anatofuz parents: 111 diff changeset	882 if (xx <= FLT128_MAX / 2)
111 04ced10e8804 gcc 7 kono parents: 68 diff changeset	883 {
04ced10e8804 gcc 7 kono parents: 68 diff changeset	884 z = cosq (xx + xx);
04ced10e8804 gcc 7 kono parents: 68 diff changeset	885 if ((s * c) > 0)
04ced10e8804 gcc 7 kono parents: 68 diff changeset	886 cc = z / ss;
04ced10e8804 gcc 7 kono parents: 68 diff changeset	887 else
04ced10e8804 gcc 7 kono parents: 68 diff changeset	888 ss = z / cc;
04ced10e8804 gcc 7 kono parents: 68 diff changeset	889 }
04ced10e8804 gcc 7 kono parents: 68 diff changeset	890
04ced10e8804 gcc 7 kono parents: 68 diff changeset	891 if (xx > 0x1p256Q)
04ced10e8804 gcc 7 kono parents: 68 diff changeset	892 return ONEOSQPI * ss / sqrtq (xx);
04ced10e8804 gcc 7 kono parents: 68 diff changeset	893
145 1830386684a0 gcc-9.2.0 anatofuz parents: 111 diff changeset	894 xinv = 1 / xx;
68 561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	895 z = xinv * xinv;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	896 if (xinv <= 0.25)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	897 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	898 if (xinv <= 0.125)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	899 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	900 if (xinv <= 0.0625)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	901 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	902 p = neval (z, P16_IN, NP16_IN) / deval (z, P16_ID, NP16_ID);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	903 q = neval (z, Q16_IN, NQ16_IN) / deval (z, Q16_ID, NQ16_ID);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	904 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	905 else
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	906 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	907 p = neval (z, P8_16N, NP8_16N) / deval (z, P8_16D, NP8_16D);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	908 q = neval (z, Q8_16N, NQ8_16N) / deval (z, Q8_16D, NQ8_16D);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	909 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	910 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	911 else if (xinv <= 0.1875)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	912 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	913 p = neval (z, P5_8N, NP5_8N) / deval (z, P5_8D, NP5_8D);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	914 q = neval (z, Q5_8N, NQ5_8N) / deval (z, Q5_8D, NQ5_8D);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	915 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	916 else
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	917 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	918 p = neval (z, P4_5N, NP4_5N) / deval (z, P4_5D, NP4_5D);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	919 q = neval (z, Q4_5N, NQ4_5N) / deval (z, Q4_5D, NQ4_5D);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	920 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	921 } /* .25 */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	922 else /* if (xinv <= 0.5) */
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	923 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	924 if (xinv <= 0.375)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	925 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	926 if (xinv <= 0.3125)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	927 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	928 p = neval (z, P3r2_4N, NP3r2_4N) / deval (z, P3r2_4D, NP3r2_4D);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	929 q = neval (z, Q3r2_4N, NQ3r2_4N) / deval (z, Q3r2_4D, NQ3r2_4D);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	930 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	931 else
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	932 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	933 p = neval (z, P2r7_3r2N, NP2r7_3r2N)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	934 / deval (z, P2r7_3r2D, NP2r7_3r2D);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	935 q = neval (z, Q2r7_3r2N, NQ2r7_3r2N)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	936 / deval (z, Q2r7_3r2D, NQ2r7_3r2D);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	937 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	938 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	939 else if (xinv <= 0.4375)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	940 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	941 p = neval (z, P2r3_2r7N, NP2r3_2r7N)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	942 / deval (z, P2r3_2r7D, NP2r3_2r7D);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	943 q = neval (z, Q2r3_2r7N, NQ2r3_2r7N)
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	944 / deval (z, Q2r3_2r7D, NQ2r3_2r7D);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	945 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	946 else
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	947 {
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	948 p = neval (z, P2_2r3N, NP2_2r3N) / deval (z, P2_2r3D, NP2_2r3D);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	949 q = neval (z, Q2_2r3N, NQ2_2r3N) / deval (z, Q2_2r3D, NQ2_2r3D);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	950 }
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	951 }
145 1830386684a0 gcc-9.2.0 anatofuz parents: 111 diff changeset	952 p = 1 + z * p;
68 561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	953 q = z * q;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	954 q = q * xinv + 0.375Q * xinv;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	955 z = ONEOSQPI * (p * ss + q * cc) / sqrtq (xx);
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	956 return z;
561a7518be6b update gcc-4.6 Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> parents: diff changeset	957 }

Mercurial > hg > CbC > CbC_gcc

annotate libquadmath/math/j1q.c @ 158:494b0b89df80 default tip