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# Data file for mpc_sqr.
#
# Copyright (C) 2008, 2010, 2012 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:
#
# 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 nan 53 +inf 53 -inf 53 -inf N N
0 0 53 +inf 53 +inf 53 -inf 53 -1 N N
0 0 53 +inf 53 nan 53 -inf 53 -0 N N
0 0 53 +inf 53 nan 53 -inf 53 +0 N N
0 0 53 +inf 53 -inf 53 -inf 53 +1 N N
0 0 53 nan 53 -inf 53 -inf 53 +inf N N
0 0 53 nan 53 nan 53 -inf 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 nan 53 -0 53 -inf N N
0 0 53 -1 53 +0 53 -0 53 -1 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 -0 53 -0 53 +1 N N
0 0 53 -inf 53 nan 53 -0 53 +inf N N
0 0 53 nan 53 nan 53 -0 53 nan N N
0 0 53 -inf 53 nan 53 +0 53 -inf N N
0 0 53 -1 53 -0 53 +0 53 -1 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 +0 53 +0 53 +1 N N
0 0 53 -inf 53 nan 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 nan 53 -inf 53 +inf 53 -inf N N
0 0 53 +inf 53 -inf 53 +inf 53 -1 N N
0 0 53 +inf 53 nan 53 +inf 53 -0 N N
0 0 53 +inf 53 nan 53 +inf 53 +0 N N
0 0 53 +inf 53 +inf 53 +inf 53 +1 N N
0 0 53 nan 53 +inf 53 +inf 53 +inf N N
0 0 53 nan 53 nan 53 +inf 53 nan N N
0 0 53 nan 53 nan 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 nan 53 nan 53 nan 53 +inf N N
0 0 53 nan 53 nan 53 nan 53 nan N N
# pure real argument
+ 0 53 0x12345676543230p+52 2 +0 53 0x1111111000000f 17 +0 N N
- 0 53 0x1234567654322fp+52 3 -0 54 -0x1111111000000f 16 +0 Z N
+ 0 53 0x12345676543230p+52 4 -0 55 0x1111111000000f 15 -0 U N
- 0 53 0x1234567654322fp+52 5 +0 56 -0x1111111000000f 14 -0 D N
- 0 53 0x1234567654322fp+52 6 +0 57 0x1111111000000f 13 +0 Z Z
+ 0 53 0x12345676543230p+52 7 -0 58 -0x1111111000000f 12 +0 U Z
- 0 53 0x1234567654322fp+52 8 -0 59 0x1111111000000f 11 -0 D Z
+ 0 53 0x12345676543230p+52 9 +0 60 -0x1111111000000f 10 -0 N Z
+ 0 53 0x12345676543230p+52 10 +0 61 0x1111111000000f 9 +0 U U
- 0 53 0x1234567654322fp+52 11 -0 62 -0x1111111000000f 8 +0 D U
+ 0 53 0x12345676543230p+52 12 -0 63 0x1111111000000f 7 -0 N U
- 0 53 0x1234567654322fp+52 13 +0 64 -0x1111111000000f 6 -0 Z U
- 0 53 0x1234567654322fp+52 14 +0 65 0x1111111000000f 5 +0 D D
+ 0 53 0x12345676543230p+52 15 -0 66 -0x1111111000000f 4 +0 N D
- 0 53 0x1234567654322fp+52 16 -0 67 0x1111111000000f 3 -0 Z D
+ 0 53 0x12345676543230p+52 17 +0 68 -0x1111111000000f 2 -0 U D
# pure imaginary argument
- 0 53 -0xE1000002000000p+56 53 +0 53 +0 53 0xf0000001111111 N N
+ 0 53 -0xe1000001fffff8p+56 52 -0 51 -0 54 0xf0000001111111 Z N
+ 0 53 -0xe1000001fffff8p+56 51 -0 49 +0 55 -0xf0000001111111 U N
- 0 53 -0xe1000002000000p+56 50 +0 47 -0 56 -0xf0000001111111 D N
+ 0 53 -0xe1000001fffff8p+56 49 +0 45 +0 57 0xf0000001111111 Z Z
+ 0 53 -0xe1000001fffff8p+56 48 -0 43 -0 58 0xf0000001111111 U Z
- 0 53 -0xe1000002000000p+56 47 -0 41 +0 59 -0xf0000001111111 D Z
- 0 53 -0xe1000002000000p+56 46 +0 39 -0 60 -0xf0000001111111 N Z
+ 0 53 -0xe1000001fffff8p+56 45 +0 37 +0 61 0xf0000001111111 U U
- 0 53 -0xe1000002000000p+56 44 -0 35 -0 62 0xf0000001111111 D U
- 0 53 -0xe1000002000000p+56 43 -0 33 +0 63 -0xf0000001111111 N U
+ 0 53 -0xe1000001fffff8p+56 42 +0 31 -0 64 -0xf0000001111111 Z U
- 0 53 -0xe1000002000000p+56 41 +0 29 +0 65 0xf0000001111111 D D
- 0 53 -0xe1000002000000p+56 40 -0 27 -0 66 0xf0000001111111 N D
+ 0 53 -0xe1000001fffff8p+56 39 -0 25 +0 67 -0xf0000001111111 Z D
+ 0 53 -0xe1000001fffff8p+56 38 +0 23 -0 68 -0xf0000001111111 U D
# IEEE-754 double precision
- + 53 0x10000000020000p+04 53 0x10000000effff 53 0x400008000180fp-22 53 0x7ffff0077efcbp-32 N N
- - 53 0x3ffffffffffffd 53 0x7ffffffffffff4p+52 53 0x1fffffffffffff 53 0x1ffffffffffffe Z N
+ + 53 0x1c16e5d4c4d5e7p-45 53 -0x7ffffff800007p-47 53 0xf 53 -0x1111111000000fp-53 U N
- + 53 0xfdbac097c8dc50p+2096 53 0x7f6e5d4c3b2a2p+1036 53 0xfedcba9876543p+1024 53 0x10000000000001p-42 D N
+ - 53 -0x10000000020000p+04 53 0x10000000efffefp-04 53 0x7ffff0077efcbp-32 53 0x400008000180fp-22 Z Z
+ + 53 0x3ffffffffffffe 53 -0x7ffffffffffff4p+52 53 0x1fffffffffffff 53 -0x1ffffffffffffe U Z
- - 53 0xe0b72ea626af3p-44 53 0x7ffffff800007p-47 53 0xf 53 0x1111111000000fp-53 D Z
- - 53 -0xfdbac097c8dc58p+2096 53 0x7f6e5d4c3b2a1cp+1032 53 -0x10000000000001p-42 53 -0xfedcba9876543p+1024 N Z
+ + 53 0x10000000020001p+04 53 -0x10000000efffefp-04 53 0x400008000180fp-22 53 -0x7ffff0077efcbp-32 U U
- + 53 -0x3ffffffffffffe 53 -0x7ffffffffffff4p+52 53 -0x1ffffffffffffe 53 0x1fffffffffffff D U
- + 53 -0x1C16E5D4C4D5E7p-45 53 0x1ffffffe00001dp-49 53 -0x1111111000000fp-53 53 -0xf N U
+ + 53 -0xfdbac097c8dc50p+2096 53 -0x7f6e5d4c3b2a1cp+1032 53 0x10000000000001p-42 53 -0xfedcba9876543p+1024 Z U
- - 53 -0x10000000020001p+04 53 -0x10000000effff 53 -0x7ffff0077efcbp-32 53 0x400008000180fp-22 D D
- - 53 0x3ffffffffffffd 53 -0x7ffffffffffff8p+52 53 -0x1fffffffffffff 53 0x1ffffffffffffe N D
+ - 53 -0xE0B72EA626AF3p-44 53 -0x1FFFFFFE00001Dp-49 53 0x1111111000000fp-53 53 -0xf Z D
+ - 53 0xfdbac097c8dc58p+2096 53 -0x7f6e5d4c3b2a2p+1036 53 -0xfedcba9876543p+1024 53 0x10000000000001p-42 U D
# improve test coverage:
# For op=x+i*y, we need a case where x+y and x-y are inexact at the
# higher computing precision, and where x and y do not have too
# distinct exponents so that Karatsuba gets triggered...
# (2^44 + i*(2^29 + 1))^2 \approx (2^88-2^58) + i*2^45*(2^29+1)
+ 0 30 309485009533114692573069312 30 18889465966662952943616 30 17592186044416 30 536870913 N N
# ...and a case where x+y or x-y are 0.
0 0 4 0 4 2 4 1 4 1 N N
# a few values, previously hard-coded in tsqr.c
0 0 8 7 8 24 8 4 8 3 N N
+ + 8 0b1.1000111e-3 8 0b1.1100111e-3 27 0b1.11111011011000010101000000e-2 27 0b1.11010001010110111001110001e-3 N N
# bug 20090930, infinite loop
+ + 3464 inf 3464 inf 866 -0x2.5763c6519ef1510f8afa101a210b8030b1909cc17004db561a25d9b53e2c08c41c01e8bbac5af6299b9d8786030aa14943d841798c8c369287942e4d4cec42a60ab0922af931159805e631128e97f973754ad53972d5d320a651a3b4a667f0ef2b92dbd698d159c3642675140@192158913 866 -0xd.15f2d530934dd930d66e89d70762d2337a8f973dd6915eb6b532fd372fcc955df1d852632d4e46fe64154ceda991a1302caf1b0ec622497e3e5724dd05b1c89a06e28d7e18e8af58f5ff4c9998cb31714688867524f41e0b31e847c1bf40de5127f858069998efd7c3e599080@192158893 N N
# bug 20091001, infinite loop
? + 2256 0 2256 -0 564 0xc.87999bfd1cb1a64288881e214b7cf1af979863b23c030b79c4a8bebb39177967608388a2e4df527977e7755a25df8af8f72fdd6dd2f42bd00de83088b4e9b59ce85caf2e6b0c0@-184298749 564 -0x2.5109af459d4daf357e09475ec991cdc9b02c8f7dfacdc060d2a24710d09c997f8aea6dbd46f10828c30b583fdcc90d7dcbb895689d594d3813db40784d2309e450d1fb6e38da8@-184298726 N N
# (x+x*i)^2 = 0+2*x^2*i with exact real part
0 0 100 0 100 304831530559368 100 12345678 100 12345678 N N
0 0 1000 0 100 304831530559368 100 12345678 100 12345678 N N
# intermediate overflow- and underflows
0 + 100 0 100 +inf 100 0x1@225000750 100 0x1@225000750 N N
0 + 10000 0 10000 +inf 100 0x1@225000750 100 0x1@225000750 N N
0 - 100 0 100 +0 100 0x1@-225000750 100 0x1@-225000750 N N
0 + 100 0 100 -0 100 0x1@-225000750 100 -0x1@-225000750 N N
0 - 10000 0 10000 +0 100 0x1@-225000750 100 0x1@-225000750 N N
0 + 10000 0 10000 -0 100 0x1@-225000750 100 -0x1@-225000750 N N
# intermediate overflow in Karatsuba found by hydra, simplified test case
- - 100 -inf 100 -inf 593 -0xf@192058806 593 0x1@192058873 N N
# another interesting one with not exactly the same behaviour
- - 100 -inf 100 -inf 100 -0xf@192058806 100 0x1@192058873 N N
0 + 100 0 100 inf 100 0x1@192058806 100 0x1@192058806 N N
# Re(op)*Im(op) can be computed, but multiplication by 2 triggers overflow
0 + 100 0 100 inf 100 0b1@536870911 100 0b1@536870911 N N
0 - 10 0 10 0b1.111111111e1073741822 100 0b1@536870911 100 0b1@536870911 N D
0 - 10 0 10 0b1.111111111e1073741822 100 0b1@536870912 100 0b1@536870912 N D
0 0 10 0 10 0b1e-1073741823 100 0b1@-536870912 100 0b1@-536870912 N N
0 - 10 0 10 0 100 0b1@-536870913 100 0b1@-536870913 N N
0 + 10 0 10 0b1@-1073741824 100 0b1@-536870913 100 0b1@-536870913 N U
+ - 10 0b1e-1073741824 10 0 100 0b1@-536870912 100 0b1@-536870913 N N
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