tests/sqrt.dat - master - niceSOFT/mpc

tests/sqrt.dat
160 строк11 KB
Paul Zimmermann
added a comment and a test for mpc_sqrt
11 сен 2024, 18:58
11 сен 2024, 18:58bdf4a0e
# Data file for mpc_sqrt.
#
# Copyright (C) 2008, 2010, 2022 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  0x16a09e667f3bcdp-52 53                    -0    55  2 15 -0 A 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  0x16a09e667f3bcdp-52 53                    +0    61  2  9 +0 A A
0 + 53                    +0 53  0x16a09e667f3bcdp-52    62 -2  8 +0 D U
0 + 53                    +0 53  0x16a09e667f3bcdp-52    62 -2  8 +0 A A
+ 0 53  0x16a09e667f3bcdp-52 53                    -0    63  2  7 -0 N U
+ 0 53  0x16a09e667f3bcdp-52 53                    -0    63  2  7 -0 N A
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
0 - 53                    +0 53 -0x16a09e667f3bcdp-52    68 -2  2 -0 A A

# 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 0x16a09e667f3bcdp-52 53 -0x16a09e667f3bcdp-52    49 +0 55 -4 A 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 0x16a09e667f3bcdp-52 53  0x5a827999fcef30p-54    43 -0 58  4 A 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 0x16a09e667f3bcdp-52 53  0x16a09e667f3bcdp-52    37 +0 61  4 A A
- + 53 0x5a827999fcef30p-54 53  0x16a09e667f3bcdp-52    35 -0 62  4 D U
- + 53 0x5a827999fcef30p-54 53  0x16a09e667f3bcdp-52    35 -0 62  4 D A
+ + 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 0x5a827999fcef30p-54 53 -0x16a09e667f3bcdp-52    25 +0 67 -4 Z A
+ - 53 0x16a09e667f3bcdp-52 53 -0x16a09e667f3bcdp-52    23 -0 68 -4 U D
+ - 53 0x16a09e667f3bcdp-52 53 -0x16a09e667f3bcdp-52    23 -0 68 -4 A A

# z=(-1.95050937e+25,-2.65087379e-39)
+ - 24 0x7.2fb038p-164 24 -0x1.011258p32 24 -0x1.0225d4p64 24 -0xe.6ec760p-132 N N
# z=(-1.89432151e+24,-1.06397210e+09)
? ? 24 0x0.001954c04p0 24 -0x1.407478p40 24 -0x1.912360p80 24 -0x3.f6aed0p28 N N

# 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.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281177 375 1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 D A
- + 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.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281177 375 0x1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004 375 -1 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 A A
- - 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.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281177 375 -1 375 -1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 A Z
- - 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef5fffffffffffffffffffffffffffffffffffffffffffep-202281177 375 -0x1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004 375 -1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 Z A
- + 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef5fffffffffffffffffffffffffffffffffffffffffffep-202281177 375 -1 375 -1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 Z Z

- + 117 0xf.ac581f15b0c7dadc9b637dba98cb8p+396 117 -0xf.ac581f15b0c7dadc9b637dba98cb8p+396 53 -0x1.2bc0ca9f6bf0fp-376 53 -0x1.eb4cb4594a7f5p+800 N N