1# Data file for mpc_sqrt. 2# 3# Copyright (C) 2008, 2010 INRIA 4# 5# This file is part of GNU MPC. 6# 7# GNU MPC is free software; you can redistribute it and/or modify it under 8# the terms of the GNU Lesser General Public License as published by the 9# Free Software Foundation; either version 3 of the License, or (at your 10#o ption) any later version. 11# 12# GNU MPC is distributed in the hope that it will be useful, but WITHOUT ANY 13# WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS 14# FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for 15# more details. 16# 17# You should have received a copy of the GNU Lesser General Public License 18# along with this program. If not, see http://www.gnu.org/licenses/ . 19# 20# The line format respects the parameter order in function prototype as 21# follow: 22# 23# INEX_RE INEX_IM PREC_ROP_RE ROP_RE PREC_ROP_IM ROP_IM PREC_OP_RE OP_RE PREC_OP_IM OP_IM RND_RE RND_IM 24# 25# see sin.dat for precisions 26 27# special values (following ISO C99 standard) 280 0 53 +inf 53 -inf 53 -inf 53 -inf N N 290 0 53 +0 53 -inf 53 -inf 53 -1 N N 300 0 53 +0 53 -inf 53 -inf 53 -0 N N 310 0 53 +0 53 +inf 53 -inf 53 +0 N N 320 0 53 +0 53 +inf 53 -inf 53 +1 N N 330 0 53 +inf 53 +inf 53 -inf 53 +inf N N 340 0 53 nan 53 inf 53 -inf 53 nan N N 350 0 53 +inf 53 -inf 53 -1 53 -inf N N 360 0 53 +0 53 -1 53 -1 53 -0 N N 370 0 53 +0 53 +1 53 -1 53 +0 N N 380 0 53 +inf 53 +inf 53 -1 53 +inf N N 390 0 53 nan 53 nan 53 -1 53 nan N N 400 0 53 +inf 53 -inf 53 -0 53 -inf N N 410 0 53 +1 53 -1 53 -0 53 -2 N N 420 0 53 +0 53 -0 53 -0 53 -0 N N 430 0 53 +0 53 +0 53 -0 53 +0 N N 440 0 53 +1 53 +1 53 -0 53 +2 N N 450 0 53 +inf 53 +inf 53 -0 53 +inf N N 460 0 53 nan 53 nan 53 -0 53 nan N N 470 0 53 +inf 53 -inf 53 +0 53 -inf N N 480 0 53 +1 53 -1 53 +0 53 -2 N N 490 0 53 +0 53 -0 53 +0 53 -0 N N 500 0 53 +0 53 +0 53 +0 53 +0 N N 510 0 53 +1 53 +1 53 +0 53 +2 N N 520 0 53 +inf 53 +inf 53 +0 53 +inf N N 530 0 53 nan 53 nan 53 +0 53 nan N N 540 0 53 +inf 53 -inf 53 +1 53 -inf N N 550 0 53 +1 53 -0 53 +1 53 -0 N N 560 0 53 +1 53 +0 53 +1 53 +0 N N 570 0 53 +inf 53 +inf 53 +1 53 +inf N N 580 0 53 nan 53 nan 53 +1 53 nan N N 590 0 53 +inf 53 -inf 53 +inf 53 -inf N N 600 0 53 +inf 53 -0 53 +inf 53 -1 N N 610 0 53 +inf 53 -0 53 +inf 53 -0 N N 620 0 53 +inf 53 +0 53 +inf 53 +0 N N 630 0 53 +inf 53 +0 53 +inf 53 +1 N N 640 0 53 +inf 53 +inf 53 +inf 53 +inf N N 650 0 53 +inf 53 nan 53 +inf 53 nan N N 660 0 53 +inf 53 -inf 53 nan 53 -inf N N 670 0 53 nan 53 nan 53 nan 53 -1 N N 680 0 53 nan 53 nan 53 nan 53 -0 N N 690 0 53 nan 53 nan 53 nan 53 +0 N N 700 0 53 nan 53 nan 53 nan 53 +1 N N 710 0 53 +inf 53 +inf 53 nan 53 +inf N N 720 0 53 nan 53 nan 53 nan 53 nan N N 73 74# purely real argument 75# sqrt(x +i*0) = sqrt(x) +i*0, when x>0 76# sqrt(x -i*0) = sqrt(x) -i*0, when x>0 77# sqrt(x +i*0) = +0 +i*sqrt(-x) +i*0, when x<0 78# sqrt(x -i*0) = +0 -i*sqrt(-x) +i*0, when x<0 79+ 0 53 0x16a09e667f3bcdp-52 53 +0 53 2 17 +0 N N 800 + 53 +0 53 0x16a09e667f3bcdp-52 54 -2 16 +0 Z N 81+ 0 53 0x16a09e667f3bcdp-52 53 -0 55 2 15 -0 U N 820 - 53 +0 53 -0x16a09e667f3bcdp-52 56 -2 14 -0 D N 83- 0 53 0x5a827999fcef30p-54 53 +0 57 2 13 +0 Z Z 840 - 53 +0 53 0x5a827999fcef30p-54 58 -2 12 +0 U Z 85- 0 53 0x5a827999fcef30p-54 53 -0 59 2 11 -0 D Z 860 + 53 +0 53 -0x5a827999fcef30p-54 60 -2 10 -0 N Z 87+ 0 53 0x16a09e667f3bcdp-52 53 +0 61 2 9 +0 U U 880 + 53 +0 53 0x16a09e667f3bcdp-52 62 -2 8 +0 D U 89+ 0 53 0x16a09e667f3bcdp-52 53 -0 63 2 7 -0 N U 900 + 53 +0 53 -0x5a827999fcef30p-54 64 -2 6 -0 Z U 91- 0 53 0x5a827999fcef30p-54 53 +0 65 2 5 +0 D D 920 - 53 +0 53 0x5a827999fcef30p-54 66 -2 4 +0 N D 93- 0 53 0x5a827999fcef30p-54 53 -0 67 2 3 -0 Z D 940 - 53 +0 53 -0x16a09e667f3bcdp-52 68 -2 2 -0 U D 95 96# purely imaginary argument 97# sqrt(+/-0 +i*y) = sqrt(y/2) * (1 +i), when y >0 98# sqrt(+/-0 +i*y) = sqrt(-y/2) * (1 -i), when y < 0 99+ + 53 0x16a09e667f3bcdp-52 53 0x16a09e667f3bcdp-52 53 +0 53 4 N N 100- + 53 0x5a827999fcef30p-54 53 0x16a09e667f3bcdp-52 51 -0 54 4 Z N 101+ - 53 0x16a09e667f3bcdp-52 53 -0x16a09e667f3bcdp-52 49 +0 55 -4 U N 102- - 53 0x5a827999fcef30p-54 53 -0x16a09e667f3bcdp-52 47 -0 56 -4 D N 103- - 53 0x5a827999fcef30p-54 53 0x5a827999fcef30p-54 45 +0 57 4 Z Z 104+ - 53 0x16a09e667f3bcdp-52 53 0x5a827999fcef30p-54 43 -0 58 4 U Z 105- + 53 0x5a827999fcef30p-54 53 -0x5a827999fcef30p-54 41 +0 59 -4 D Z 106+ + 53 0x16a09e667f3bcdp-52 53 -0x5a827999fcef30p-54 39 -0 60 -4 N Z 107+ + 53 0x16a09e667f3bcdp-52 53 0x16a09e667f3bcdp-52 37 +0 61 4 U U 108- + 53 0x5a827999fcef30p-54 53 0x16a09e667f3bcdp-52 35 -0 62 4 D U 109+ + 53 0x16a09e667f3bcdp-52 53 -0x5a827999fcef30p-54 33 +0 63 -4 N U 110- + 53 0x5a827999fcef30p-54 53 -0x5a827999fcef30p-54 31 -0 64 -4 Z U 111- - 53 0x5a827999fcef30p-54 53 0x5a827999fcef30p-54 29 +0 65 4 D D 112+ - 53 0x16a09e667f3bcdp-52 53 0x5a827999fcef30p-54 27 -0 66 4 N D 113- - 53 0x5a827999fcef30p-54 53 -0x16a09e667f3bcdp-52 25 +0 67 -4 Z D 114+ - 53 0x16a09e667f3bcdp-52 53 -0x16a09e667f3bcdp-52 23 -0 68 -4 U D 115 116# bugs fixed in r160 2008-07-15 117- + 19 0b11101001001001001100p+39 19 -0b1010110101100111011p-236 19 0b1.101010001010100000p+117 19 -0b1.001110111101100001p-158 N Z 118- + 2 0b11p+100 2 -0b11p+100 2 -0 2 -0b11p+203 N Z 1190 + 2 0 2 -0b10p+117 2 -0b11p+235 2 -0 N Z 120 121# close to infinite loop reported by Emmanuel Thome, 22 Oct 2010, 122# and all its variants of signs and directed roundings 123- + 375 1 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281177 375 1 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 N N 124+ + 375 0x1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281177 375 1 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 U U 125- - 375 1 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef5fffffffffffffffffffffffffffffffffffffffffffep-202281177 375 1 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 D D 126- + 375 1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef5fffffffffffffffffffffffffffffffffffffffffffep-202281177 375 1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 D U 127- - 375 1 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef5fffffffffffffffffffffffffffffffffffffffffffep-202281177 375 1 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 Z Z 128- - 375 1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281177 375 1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 N N 129+ + 375 0x1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef5fffffffffffffffffffffffffffffffffffffffffffep-202281177 375 1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 U U 130- - 375 1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281177 375 1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 D D 131- + 375 1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef5fffffffffffffffffffffffffffffffffffffffffffep-202281177 375 1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 Z Z 132+ - 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281177 375 1 375 -1 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 N N 133+ + 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281177 375 0x1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004 375 -1 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 U U 134- - 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef5fffffffffffffffffffffffffffffffffffffffffffep-202281177 375 1 375 -1 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 D D 135- - 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef5fffffffffffffffffffffffffffffffffffffffffffep-202281177 375 1 375 -1 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 Z Z 136+ + 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281177 375 -1 375 -1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 N N 137+ + 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281177 375 -1 375 -1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 U U 138- - 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef5fffffffffffffffffffffffffffffffffffffffffffep-202281177 375 -0x1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004 375 -1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 D D 139- + 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef5fffffffffffffffffffffffffffffffffffffffffffep-202281177 375 -1 375 -1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 Z Z 140