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# Data file for mpc_sqrt.
#
# Copyright (C) 2008, 2010 INRIA
#
# This file is part of GNU MPC.
#
# GNU MPC is free software; you can redistribute it and/or modify it under
# the terms of the GNU Lesser General Public License as published by the
# Free Software Foundation; either version 3 of the License, or (at your
#o ption) any later version.
#
# GNU MPC is distributed in the hope that it will be useful, but WITHOUT ANY
# WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
# FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for
# more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with this program. If not, see http://www.gnu.org/licenses/ .
#
# The line format respects the parameter order in function prototype as
# follow:
#
# 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
#
# see sin.dat for precisions
# special values (following ISO C99 standard)
0 0 53 +inf 53 -inf 53 -inf 53 -inf N N
0 0 53 +0 53 -inf 53 -inf 53 -1 N N
0 0 53 +0 53 -inf 53 -inf 53 -0 N N
0 0 53 +0 53 +inf 53 -inf 53 +0 N N
0 0 53 +0 53 +inf 53 -inf 53 +1 N N
0 0 53 +inf 53 +inf 53 -inf 53 +inf N N
0 0 53 nan 53 inf 53 -inf 53 nan N N
0 0 53 +inf 53 -inf 53 -1 53 -inf N N
0 0 53 +0 53 -1 53 -1 53 -0 N N
0 0 53 +0 53 +1 53 -1 53 +0 N N
0 0 53 +inf 53 +inf 53 -1 53 +inf N N
0 0 53 nan 53 nan 53 -1 53 nan N N
0 0 53 +inf 53 -inf 53 -0 53 -inf N N
0 0 53 +1 53 -1 53 -0 53 -2 N N
0 0 53 +0 53 -0 53 -0 53 -0 N N
0 0 53 +0 53 +0 53 -0 53 +0 N N
0 0 53 +1 53 +1 53 -0 53 +2 N N
0 0 53 +inf 53 +inf 53 -0 53 +inf N N
0 0 53 nan 53 nan 53 -0 53 nan N N
0 0 53 +inf 53 -inf 53 +0 53 -inf N N
0 0 53 +1 53 -1 53 +0 53 -2 N N
0 0 53 +0 53 -0 53 +0 53 -0 N N
0 0 53 +0 53 +0 53 +0 53 +0 N N
0 0 53 +1 53 +1 53 +0 53 +2 N N
0 0 53 +inf 53 +inf 53 +0 53 +inf N N
0 0 53 nan 53 nan 53 +0 53 nan N N
0 0 53 +inf 53 -inf 53 +1 53 -inf N N
0 0 53 +1 53 -0 53 +1 53 -0 N N
0 0 53 +1 53 +0 53 +1 53 +0 N N
0 0 53 +inf 53 +inf 53 +1 53 +inf N N
0 0 53 nan 53 nan 53 +1 53 nan N N
0 0 53 +inf 53 -inf 53 +inf 53 -inf N N
0 0 53 +inf 53 -0 53 +inf 53 -1 N N
0 0 53 +inf 53 -0 53 +inf 53 -0 N N
0 0 53 +inf 53 +0 53 +inf 53 +0 N N
0 0 53 +inf 53 +0 53 +inf 53 +1 N N
0 0 53 +inf 53 +inf 53 +inf 53 +inf N N
0 0 53 +inf 53 nan 53 +inf 53 nan N N
0 0 53 +inf 53 -inf 53 nan 53 -inf N N
0 0 53 nan 53 nan 53 nan 53 -1 N N
0 0 53 nan 53 nan 53 nan 53 -0 N N
0 0 53 nan 53 nan 53 nan 53 +0 N N
0 0 53 nan 53 nan 53 nan 53 +1 N N
0 0 53 +inf 53 +inf 53 nan 53 +inf N N
0 0 53 nan 53 nan 53 nan 53 nan N N
# purely real argument
# sqrt(x +i*0) = sqrt(x) +i*0, when x>0
# sqrt(x -i*0) = sqrt(x) -i*0, when x>0
# sqrt(x +i*0) = +0 +i*sqrt(-x) +i*0, when x<0
# sqrt(x -i*0) = +0 -i*sqrt(-x) +i*0, when x<0
+ 0 53 0x16a09e667f3bcdp-52 53 +0 53 2 17 +0 N N
0 + 53 +0 53 0x16a09e667f3bcdp-52 54 -2 16 +0 Z N
+ 0 53 0x16a09e667f3bcdp-52 53 -0 55 2 15 -0 U N
0 - 53 +0 53 -0x16a09e667f3bcdp-52 56 -2 14 -0 D N
- 0 53 0x5a827999fcef30p-54 53 +0 57 2 13 +0 Z Z
0 - 53 +0 53 0x5a827999fcef30p-54 58 -2 12 +0 U Z
- 0 53 0x5a827999fcef30p-54 53 -0 59 2 11 -0 D Z
0 + 53 +0 53 -0x5a827999fcef30p-54 60 -2 10 -0 N Z
+ 0 53 0x16a09e667f3bcdp-52 53 +0 61 2 9 +0 U U
0 + 53 +0 53 0x16a09e667f3bcdp-52 62 -2 8 +0 D U
+ 0 53 0x16a09e667f3bcdp-52 53 -0 63 2 7 -0 N U
0 + 53 +0 53 -0x5a827999fcef30p-54 64 -2 6 -0 Z U
- 0 53 0x5a827999fcef30p-54 53 +0 65 2 5 +0 D D
0 - 53 +0 53 0x5a827999fcef30p-54 66 -2 4 +0 N D
- 0 53 0x5a827999fcef30p-54 53 -0 67 2 3 -0 Z D
0 - 53 +0 53 -0x16a09e667f3bcdp-52 68 -2 2 -0 U D
# purely imaginary argument
# sqrt(+/-0 +i*y) = sqrt(y/2) * (1 +i), when y >0
# sqrt(+/-0 +i*y) = sqrt(-y/2) * (1 -i), when y < 0
+ + 53 0x16a09e667f3bcdp-52 53 0x16a09e667f3bcdp-52 53 +0 53 4 N N
- + 53 0x5a827999fcef30p-54 53 0x16a09e667f3bcdp-52 51 -0 54 4 Z N
+ - 53 0x16a09e667f3bcdp-52 53 -0x16a09e667f3bcdp-52 49 +0 55 -4 U N
- - 53 0x5a827999fcef30p-54 53 -0x16a09e667f3bcdp-52 47 -0 56 -4 D N
- - 53 0x5a827999fcef30p-54 53 0x5a827999fcef30p-54 45 +0 57 4 Z Z
+ - 53 0x16a09e667f3bcdp-52 53 0x5a827999fcef30p-54 43 -0 58 4 U Z
- + 53 0x5a827999fcef30p-54 53 -0x5a827999fcef30p-54 41 +0 59 -4 D Z
+ + 53 0x16a09e667f3bcdp-52 53 -0x5a827999fcef30p-54 39 -0 60 -4 N Z
+ + 53 0x16a09e667f3bcdp-52 53 0x16a09e667f3bcdp-52 37 +0 61 4 U U
- + 53 0x5a827999fcef30p-54 53 0x16a09e667f3bcdp-52 35 -0 62 4 D U
+ + 53 0x16a09e667f3bcdp-52 53 -0x5a827999fcef30p-54 33 +0 63 -4 N U
- + 53 0x5a827999fcef30p-54 53 -0x5a827999fcef30p-54 31 -0 64 -4 Z U
- - 53 0x5a827999fcef30p-54 53 0x5a827999fcef30p-54 29 +0 65 4 D D
+ - 53 0x16a09e667f3bcdp-52 53 0x5a827999fcef30p-54 27 -0 66 4 N D
- - 53 0x5a827999fcef30p-54 53 -0x16a09e667f3bcdp-52 25 +0 67 -4 Z D
+ - 53 0x16a09e667f3bcdp-52 53 -0x16a09e667f3bcdp-52 23 -0 68 -4 U D
# bugs fixed in r160 2008-07-15
- + 19 0b11101001001001001100p+39 19 -0b1010110101100111011p-236 19 0b1.101010001010100000p+117 19 -0b1.001110111101100001p-158 N Z
- + 2 0b11p+100 2 -0b11p+100 2 -0 2 -0b11p+203 N Z
0 + 2 0 2 -0b10p+117 2 -0b11p+235 2 -0 N Z
# close to infinite loop reported by Emmanuel Thome, 22 Oct 2010,
# and all its variants of signs and directed roundings
- + 375 1 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281177 375 1 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 N N
+ + 375 0x1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281177 375 1 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 U U
- - 375 1 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef5fffffffffffffffffffffffffffffffffffffffffffep-202281177 375 1 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 D D
- + 375 1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef5fffffffffffffffffffffffffffffffffffffffffffep-202281177 375 1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 D U
- - 375 1 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef5fffffffffffffffffffffffffffffffffffffffffffep-202281177 375 1 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 Z Z
- - 375 1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281177 375 1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 N N
+ + 375 0x1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef5fffffffffffffffffffffffffffffffffffffffffffep-202281177 375 1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 U U
- - 375 1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281177 375 1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 D D
- + 375 1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef5fffffffffffffffffffffffffffffffffffffffffffep-202281177 375 1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 Z Z
+ - 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281177 375 1 375 -1 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 N N
+ + 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281177 375 0x1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004 375 -1 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 U U
- - 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef5fffffffffffffffffffffffffffffffffffffffffffep-202281177 375 1 375 -1 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 D D
- - 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef5fffffffffffffffffffffffffffffffffffffffffffep-202281177 375 1 375 -1 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 Z Z
+ + 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281177 375 -1 375 -1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 N N
+ + 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281177 375 -1 375 -1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 U U
- - 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef5fffffffffffffffffffffffffffffffffffffffffffep-202281177 375 -0x1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004 375 -1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 D D
- + 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef5fffffffffffffffffffffffffffffffffffffffffffep-202281177 375 -1 375 -1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 Z Z
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