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tests/mul.dat
189 строк
13 KB
Andreas Enge
Correct signs of 0 parts in exact Karatsuba multiplication.
01 дек 2022, 12:02
01 дек 2022, 12:02
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# Data file for mpc_mul # # Copyright (C) 2008, 2010, 2011, 2012, 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_OP1_RE OP1_RE PREC_OP1_IM OP1_IM PREC_OP2_RE OP2_RE PREC_OP2_IM OP2_IM RND_RE RND_IM # # See add.dat for more details. # special values (following ISO C99 standard, G.5.1) 0 0 53 nan 53 +inf 53 -inf 53 -inf 53 -inf 53 -inf N Z 0 0 53 nan 53 +inf 53 -inf 53 +inf 53 +1 53 -inf Z U 0 0 53 +inf 53 -inf 53 +inf 53 -inf 53 +inf 53 +0 U D 0 0 53 +inf 53 -inf 53 +inf 53 +inf 53 -0 53 -1 D N 0 0 53 -inf 53 +inf 53 -inf 53 -inf 53 -0 53 -1 N U 0 0 53 -inf 53 +inf 53 -inf 53 +inf 53 +inf 53 nan Z D 0 0 53 -inf 53 -inf 53 +inf 53 -inf 53 nan 53 -1 U N 0 0 53 nan 53 nan 53 +inf 53 +inf 53 -0 53 nan D Z 0 0 53 nan 53 nan 53 -inf 53 -inf 53 nan 53 nan N D 0 0 53 -inf 53 -inf 53 -1 53 -inf 53 +inf 53 -1 N D 0 0 53 -inf 53 nan 53 -inf 53 +1 53 +inf 53 -0 Z N 0 0 53 +inf 53 nan 53 +1 53 -inf 53 -0 53 +1 U Z 0 0 53 nan 53 nan 53 +inf 53 +1 53 -0 53 -0 D U 0 0 53 nan 53 -inf 53 -1 53 -inf 53 +inf 53 nan N N 0 0 53 nan 53 -inf 53 -inf 53 +1 53 nan 53 +1 Z Z 0 0 53 nan 53 nan 53 +1 53 -inf 53 -0 53 nan U U 0 0 53 nan 53 nan 53 +inf 53 +1 53 nan 53 nan D D 0 0 53 +inf 53 nan 53 -0 53 -inf 53 +0 53 +inf D D 0 0 53 -inf 53 nan 53 -inf 53 +0 53 +1 53 -0 N Z 0 0 53 nan 53 nan 53 +0 53 -inf 53 -0 53 -0 Z U 0 0 53 -inf 53 nan 53 +inf 53 +0 53 -inf 53 nan U D 0 0 53 -inf 53 nan 53 -0 53 -inf 53 nan 53 -1 D N 0 0 53 nan 53 nan 53 -inf 53 +0 53 +0 53 nan N U 0 0 53 nan 53 nan 53 +0 53 -inf 53 nan 53 nan Z D 0 0 53 +1 53 -0 53 +0 53 +1 53 -0 53 -1 Z D 0 0 53 -0 53 +0 53 -1 53 -0 53 +0 53 -0 U N 0 0 53 -inf 53 nan 53 -0 53 +1 53 nan 53 +inf D Z 0 0 53 nan 53 nan 53 +1 53 -0 53 -1 53 nan N D 0 0 53 nan 53 nan 53 +0 53 +1 53 nan 53 -0 Z N 0 0 53 nan 53 nan 53 -1 53 -0 53 nan 53 nan U Z 0 0 53 +0 53 +0 53 -0 53 +0 53 +0 53 -0 U Z 0 0 53 nan 53 nan 53 +0 53 -0 53 nan 53 -inf D U 0 0 53 nan 53 nan 53 +0 53 +0 53 -1 53 nan N N 0 0 53 nan 53 nan 53 -0 53 -0 53 nan 53 -0 Z Z 0 0 53 nan 53 nan 53 -0 53 +0 53 nan 53 nan U U 0 0 53 +inf 53 nan 53 nan 53 -inf 53 nan 53 +inf U U 0 0 53 -inf 53 nan 53 +inf 53 nan 53 -1 53 nan D D 0 0 53 nan 53 nan 53 nan 53 -inf 53 nan 53 -0 N Z 0 0 53 nan 53 nan 53 -inf 53 nan 53 nan 53 nan Z U 0 0 53 nan 53 nan 53 +1 53 nan 53 nan 53 -1 Z U 0 0 53 nan 53 nan 53 nan 53 +1 53 -0 53 nan U D 0 0 53 nan 53 nan 53 -1 53 nan 53 nan 53 nan D N 0 0 53 nan 53 nan 53 nan 53 +0 53 +0 53 nan D N 0 0 53 nan 53 nan 53 +0 53 nan 53 nan 53 nan N U 0 0 53 nan 53 nan 53 nan 53 nan 53 nan 53 nan N U # pure real arguments 0 0 53 0x10000000000001p-52 53 -0 53 +1 53 -0 53 0x10000000000001p-52 53 -0 N N 0 0 53 0x10000000000001p-52 53 -0 53 +1 53 -0 53 0x10000000000001p-52 53 -0 Z Z 0 0 53 0x10000000000001p-52 53 -0 53 +1 53 -0 53 0x10000000000001p-52 53 -0 U U 0 0 53 -0x10000000000001p-52 53 -0 53 -1 53 -0 53 0x10000000000001p-52 53 -0 D D # one pure real argument 0 0 53 0x10000000000001p-52 53 0x10000000000001p-52 53 +1 53 +1 53 0x10000000000001p-52 53 -0 N N 0 0 53 0x10000000000001p-52 53 -0x10000000000001p-51 53 +1 53 -2 53 0x10000000000001p-52 53 -0 Z Z - + 53 -0x30000000000004p-52 53 0x30000000000004p-52 53 -3 53 +3 53 0x10000000000001p-52 53 +0 N N + - 53 -0x30000000000002p-52 53 0x30000000000002p-52 53 -3 53 +3 53 0x10000000000001p-52 53 +0 Z Z + + 53 -0x30000000000002p-52 53 0x30000000000004p-52 53 -3 53 +3 53 0x10000000000001p-52 53 +0 U U - - 53 -0x30000000000004p-52 53 0x30000000000002p-52 53 -3 53 +3 53 0x10000000000001p-52 53 +0 D D 0 0 53 -0x10000000000001p-52 53 -0x10000000000001p-50 53 -1 53 -4 53 0x10000000000001p-52 53 +0 D D 0 0 53 +0 53 +0 53 +0 53 +0 53 0x10000000000001p-52 53 -1 N N 0 0 53 +0 53 -0 53 +0 53 -0 53 0x10000000000001p-52 53 -2 Z Z 0 0 53 +0 53 +0 53 +0 53 +0 53 0x10000000000001p-52 53 +3 U U 0 0 53 -0 53 -0 53 -0 53 -0 53 0x10000000000001p-52 53 +4 D D # pure imaginary arguments 0 0 53 -0x10000000000001p-52 53 -0 53 -0 53 0x10000000000001p-52 53 -0 53 +1 N N 0 0 53 -0x10000000000001p-52 53 +0 53 +0 53 0x10000000000001p-52 53 -0 53 +1 Z Z 0 0 53 -0x10000000000001p-52 53 +0 53 +0 53 0x10000000000001p-52 53 -0 53 +1 U U 0 0 53 -0x10000000000001p-52 53 -0 53 -0 53 0x10000000000001p-52 53 -0 53 +1 D D # one pure imaginary argument 0 0 53 -0x10000000000001p-52 53 -0x10000000000001p-52 53 -0 53 0x10000000000001p-52 53 -1 53 +1 N N 0 0 53 +0x10000000000001p-52 53 -0x10000000000001p-51 53 +0 53 0x10000000000001p-52 53 -2 53 -1 Z Z + - 53 0x30000000000004p-52 53 -0x30000000000004p-52 53 +0 53 0x10000000000001p-52 53 -3 53 -3 N N - + 53 0x30000000000002p-52 53 -0x30000000000002p-52 53 +0 53 0x10000000000001p-52 53 -3 53 -3 Z Z + + 53 0x30000000000004p-52 53 -0x30000000000002p-52 53 +0 53 0x10000000000001p-52 53 -3 53 -3 U U - - 53 0x30000000000002p-52 53 -0x30000000000004p-52 53 +0 53 0x10000000000001p-52 53 -3 53 -3 D D 0 0 53 +0x10000000000001p-52 53 -0x10000000000001p-50 53 -0 53 0x10000000000001p-52 53 -4 53 -1 D D # big precision uses Karatsuba method 0 0 4096 0x1420176785BD601FC018AD36471p-96 4096 -0x1ECCDBDA38B2611A32848E7ADF43p-100 53 0x6B2E363676587p-44 53 0x1AC20AAC49ED37p-47 53 0x12264C57B44C6Bp-53 53 -0x138639A4B8D8B3p-50 N N # Karatsuba case where x=0 since ad=bc: (1+i)^2 at artificially high # precision so that Karatsuba is actually used. 0 0 4096 0 4096 2 4096 1 4096 1 4096 1 4096 1 N N # trigger the line reducing prec_x to prec_u 0 0 4096 0 4096 2 40960 1 40960 1 40960 1 40960 1 N N # another particular cases + + 6 -0x9p-497 6 0x33p-315 6 -0x1dp-73 6 0x3p148 6 0x11p-463 6 0x3p-645 N N + - 6 0x33p-315 6 0x9p-497 6 0x3p148 6 0x1dp-73 6 0x11p-463 6 0x3p-645 N N 0 0 4 0x1p-1902 4 0x3p-1085 4 -0x1p-892 4 -0x3p-75 4 -0x1p-1010 4 0 N N # a few particular values 0 0 8 10 8 -5 8 4 8 3 8 1 8 -2 N N + + 27 0b1.10110000001100010010000000e-3 27 0b1.00111100000010100001011001e-1 27 0b1.11111011011000010101000000e-2 27 0b1.11010001010110111001110001e-3 27 0b1.10100101110110011011100100e-1 27 0b1.10111100011000001100110011e-1 N N 0 0 15 2 15 0 15 -1 15 -1 15 -1 15 1 N N # check squares, copied from sqr.dat + - 53 0xfdbac097c8dc58p+2096 53 -0x7f6e5d4c3b2a2p+1036 53 -0xfedcba9876543p+1024 53 0x10000000000001p-42 53 -0xfedcba9876543p+1024 53 0x10000000000001p-42 U D + 0 30 309485009533114692573069312 30 18889465966662952943616 30 17592186044416 30 536870913 30 17592186044416 30 536870913 N N 0 0 4 0 4 2 4 1 4 1 4 1 4 1 N N + + 8 0b1.1000111e-3 8 0b1.1100111e-3 27 0b1.11111011011000010101000000e-2 27 0b1.11010001010110111001110001e-3 27 0b1.11111011011000010101000000e-2 27 0b1.11010001010110111001110001e-3 N N # the following is the square (x+i*y)^2 where |x| >= 2.34*2^768635652 and # |y| <= 13.09*2^768635572, thus x^2 >= 5.47*2^1537271304 and # y^2 <= 171.34*2^1537271144 < x*2^(-155) thus x^2-y^2 should overflow # with the default emax = 1073741821 ? + 3464 inf 3464 inf 866 -0x2.5763c6519ef1510f8afa101a210b8030b1909cc17004db561a25d9b53e2c08c41c01e8bbac5af6299b9d8786030aa14943d841798c8c369287942e4d4cec42a60ab0922af931159805e631128e97f973754ad53972d5d320a651a3b4a667f0ef2b92dbd698d159c3642675140@192158913 866 -0xd.15f2d530934dd930d66e89d70762d2337a8f973dd6915eb6b532fd372fcc955df1d852632d4e46fe64154ceda991a1302caf1b0ec622497e3e5724dd05b1c89a06e28d7e18e8af58f5ff4c9998cb31714688867524f41e0b31e847c1bf40de5127f858069998efd7c3e599080@192158893 866 -0x2.5763c6519ef1510f8afa101a210b8030b1909cc17004db561a25d9b53e2c08c41c01e8bbac5af6299b9d8786030aa14943d841798c8c369287942e4d4cec42a60ab0922af931159805e631128e97f973754ad53972d5d320a651a3b4a667f0ef2b92dbd698d159c3642675140@192158913 866 -0xd.15f2d530934dd930d66e89d70762d2337a8f973dd6915eb6b532fd372fcc955df1d852632d4e46fe64154ceda991a1302caf1b0ec622497e3e5724dd05b1c89a06e28d7e18e8af58f5ff4c9998cb31714688867524f41e0b31e847c1bf40de5127f858069998efd7c3e599080@192158893 N N ? + 2256 0 2256 -0 564 0xc.87999bfd1cb1a64288881e214b7cf1af979863b23c030b79c4a8bebb39177967608388a2e4df527977e7755a25df8af8f72fdd6dd2f42bd00de83088b4e9b59ce85caf2e6b0c0@-184298749 564 -0x2.5109af459d4daf357e09475ec991cdc9b02c8f7dfacdc060d2a24710d09c997f8aea6dbd46f10828c30b583fdcc90d7dcbb895689d594d3813db40784d2309e450d1fb6e38da8@-184298726 564 0xc.87999bfd1cb1a64288881e214b7cf1af979863b23c030b79c4a8bebb39177967608388a2e4df527977e7755a25df8af8f72fdd6dd2f42bd00de83088b4e9b59ce85caf2e6b0c0@-184298749 564 -0x2.5109af459d4daf357e09475ec991cdc9b02c8f7dfacdc060d2a24710d09c997f8aea6dbd46f10828c30b583fdcc90d7dcbb895689d594d3813db40784d2309e450d1fb6e38da8@-184298726 N N # intermediate over- and underflows - + 100 -inf 100 +inf 100 0x1@125000750 100 0x3@125000750 100 0x1@225000750 100 0x2@225000750 N N - + 100 -inf 100 +inf 100 0x1@225000750 100 0x2@225000750 100 0x1@125000750 100 0x3@125000750 N N - - 100 -inf 100 -inf 100 0x1@225000750 100 -0x2@225000750 100 0x1@125000750 100 -0x3@125000750 N N + - 100 -0 100 +0 100 0x1@-125000750 100 0x3@-125000750 100 0x1@-225000750 100 0x2@-225000750 N N + - 100 -0 100 +0 100 0x1@-225000750 100 0x2@-225000750 100 0x1@-125000750 100 0x3@-125000750 N N - - 100 +0 100 +0 100 0x3@-125000750 100 0x1@-125000750 100 0x1@-225000750 100 0x2@-225000750 N N - - 100 +0 100 +0 100 0x4@-125000750 100 0x1@-125000750 100 0x1@-225000750 100 0x2@-225000750 N N + - 100 -0 100 +0 100 0x2@-225000750 100 0x1@-225000750 100 0x1@-125000750 100 0x3@-125000750 N N 0 - 100 +0 100 +0 100 0x1@-225000750 100 0x1@-225000750 100 0x1@-125000750 100 0x1@-125000750 N N 0 + 100 +0 100 +inf 100 0x1@125000750 100 0x1@125000750 100 0x1@225000750 100 0x1@225000750 N N + 0 100 +inf 100 +0 100 0x1@125000750 100 0x1@125000750 100 0x1@225000750 100 -0x1@225000750 N N # the same with directed rounding - + 10 -inf 10 +inf 10 0x1@125000750 10 0x3@125000750 10 0x1@225000750 10 0x2@225000750 D U - + 10 -inf 10 +inf 10 0x1@125000750 10 0x3@125000750 10 0x1@225000750 10 0x2@225000750 A A # the following test assumes the maximum MPFR exponent is 1073741821 # and the minimum exponent is -1073741821 + - 10 -0b1.111111111e1073741820 10 0b1.111111111e1073741820 10 0x1@125000750 10 0x3@125000750 10 0x1@225000750 10 0x2@225000750 U D + - 10 -0 10 +0 10 0x1@-125000750 10 0x3@-125000750 10 0x1@-225000750 10 0x2@-225000750 U D - + 10 -0b1e-1073741822 10 0b1e-1073741822 10 0x1@-125000750 10 0x3@-125000750 10 0x1@-225000750 10 0x2@-225000750 D U - + 10 -0b1e-1073741822 10 0b1e-1073741822 10 0x1@-125000750 10 0x3@-125000750 10 0x1@-225000750 10 0x2@-225000750 A A # starting with Karatsuba - + 10000 -inf 100 +inf 100 0x1@125000750 100 0x3@125000750 100 0x1@225000750 100 0x2@225000750 N N - + 10000 -inf 100 +inf 100 0x1@225000750 100 0x2@225000750 100 0x1@125000750 100 0x3@125000750 N N - - 10000 -inf 100 -inf 100 0x1@225000750 100 -0x2@225000750 100 0x1@125000750 100 -0x3@125000750 N N + - 10000 -0 100 +0 100 0x1@-125000750 100 0x3@-125000750 100 0x1@-225000750 100 0x2@-225000750 N N + - 10000 -0 100 +0 100 0x1@-225000750 100 0x2@-225000750 100 0x1@-125000750 100 0x3@-125000750 N N - - 10000 +0 100 +0 100 0x3@-125000750 100 0x1@-125000750 100 0x1@-225000750 100 0x2@-225000750 N N - - 10000 +0 100 +0 100 0x4@-125000750 100 0x1@-125000750 100 0x1@-225000750 100 0x2@-225000750 N N + - 10000 -0 100 +0 100 0x2@-225000750 100 0x1@-225000750 100 0x1@-125000750 100 0x3@-125000750 N N 0 - 10000 +0 100 +0 100 0x1@-225000750 100 0x1@-225000750 100 0x1@-125000750 100 0x1@-125000750 N N 0 + 10000 +0 100 +inf 100 0x1@125000750 100 0x1@125000750 100 0x1@225000750 100 0x1@225000750 N N + 0 10000 +inf 100 +0 100 0x1@125000750 100 0x1@125000750 100 0x1@225000750 100 -0x1@225000750 N N + + 10000 +inf 100 +inf 100 0x1@125000750 100 0x3@125000750 100 0x1@143434706 100 0x2@143434705 N N # improve code coverage: case where sign_x==0 in mpc_mul_karatsuba 0 0 2000 6 2000 8 2000 4 2000 2 2000 2 2000 1 N N 0 0 2000 0 2000 4 2000 2 2000 2 2000 1 2000 1 N N + 0 2 1 2 0x2p-536870913 2 1 2 0x1p-536870913 2 1 2 0x1p-536870913 N N 0 - 2 0 2 1 2 0x1p-536870913 2 1 2 1 2 0x1p-536870913 N N # error in sign of 0 with exact Karatsuba found on 2022-11-30 0 0 1473 -50 1473 +0 20 1 20 2 20 -10 20 20 N N