1# Data file for mpc_mul 2# 3# Copyright (C) 2008, 2010, 2011, 2012 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_OP1_RE OP1_RE PREC_OP1_IM OP1_IM PREC_OP2_RE OP2_RE PREC_OP2_IM OP2_IM RND_RE RND_IM 24# 25# See add.dat for more details. 26 27# special values (following ISO C99 standard, G.5.1) 280 0 53 nan 53 +inf 53 -inf 53 -inf 53 -inf 53 -inf N Z 290 0 53 nan 53 +inf 53 -inf 53 +inf 53 +1 53 -inf Z U 300 0 53 +inf 53 -inf 53 +inf 53 -inf 53 +inf 53 +0 U D 310 0 53 +inf 53 -inf 53 +inf 53 +inf 53 -0 53 -1 D N 320 0 53 -inf 53 +inf 53 -inf 53 -inf 53 -0 53 -1 N U 330 0 53 -inf 53 +inf 53 -inf 53 +inf 53 +inf 53 nan Z D 340 0 53 -inf 53 -inf 53 +inf 53 -inf 53 nan 53 -1 U N 350 0 53 nan 53 nan 53 +inf 53 +inf 53 -0 53 nan D Z 360 0 53 nan 53 nan 53 -inf 53 -inf 53 nan 53 nan N D 37 380 0 53 -inf 53 -inf 53 -1 53 -inf 53 +inf 53 -1 N D 390 0 53 -inf 53 nan 53 -inf 53 +1 53 +inf 53 -0 Z N 400 0 53 +inf 53 nan 53 +1 53 -inf 53 -0 53 +1 U Z 410 0 53 nan 53 nan 53 +inf 53 +1 53 -0 53 -0 D U 420 0 53 nan 53 -inf 53 -1 53 -inf 53 +inf 53 nan N N 430 0 53 nan 53 -inf 53 -inf 53 +1 53 nan 53 +1 Z Z 440 0 53 nan 53 nan 53 +1 53 -inf 53 -0 53 nan U U 450 0 53 nan 53 nan 53 +inf 53 +1 53 nan 53 nan D D 46 470 0 53 +inf 53 nan 53 -0 53 -inf 53 +0 53 +inf D D 480 0 53 -inf 53 nan 53 -inf 53 +0 53 +1 53 -0 N Z 490 0 53 nan 53 nan 53 +0 53 -inf 53 -0 53 -0 Z U 500 0 53 -inf 53 nan 53 +inf 53 +0 53 -inf 53 nan U D 510 0 53 -inf 53 nan 53 -0 53 -inf 53 nan 53 -1 D N 520 0 53 nan 53 nan 53 -inf 53 +0 53 +0 53 nan N U 530 0 53 nan 53 nan 53 +0 53 -inf 53 nan 53 nan Z D 54 550 0 53 +1 53 -0 53 +0 53 +1 53 -0 53 -1 Z D 560 0 53 -0 53 +0 53 -1 53 -0 53 +0 53 -0 U N 570 0 53 -inf 53 nan 53 -0 53 +1 53 nan 53 +inf D Z 580 0 53 nan 53 nan 53 +1 53 -0 53 -1 53 nan N D 590 0 53 nan 53 nan 53 +0 53 +1 53 nan 53 -0 Z N 600 0 53 nan 53 nan 53 -1 53 -0 53 nan 53 nan U Z 61 620 0 53 +0 53 +0 53 -0 53 +0 53 +0 53 -0 U Z 630 0 53 nan 53 nan 53 +0 53 -0 53 nan 53 -inf D U 640 0 53 nan 53 nan 53 +0 53 +0 53 -1 53 nan N N 650 0 53 nan 53 nan 53 -0 53 -0 53 nan 53 -0 Z Z 660 0 53 nan 53 nan 53 -0 53 +0 53 nan 53 nan U U 67 680 0 53 +inf 53 nan 53 nan 53 -inf 53 nan 53 +inf U U 690 0 53 -inf 53 nan 53 +inf 53 nan 53 -1 53 nan D D 700 0 53 nan 53 nan 53 nan 53 -inf 53 nan 53 -0 N Z 710 0 53 nan 53 nan 53 -inf 53 nan 53 nan 53 nan Z U 72 730 0 53 nan 53 nan 53 +1 53 nan 53 nan 53 -1 Z U 740 0 53 nan 53 nan 53 nan 53 +1 53 -0 53 nan U D 750 0 53 nan 53 nan 53 -1 53 nan 53 nan 53 nan D N 76 770 0 53 nan 53 nan 53 nan 53 +0 53 +0 53 nan D N 780 0 53 nan 53 nan 53 +0 53 nan 53 nan 53 nan N U 79 800 0 53 nan 53 nan 53 nan 53 nan 53 nan 53 nan N U 81 82# pure real arguments 830 0 53 0x10000000000001p-52 53 -0 53 +1 53 -0 53 0x10000000000001p-52 53 -0 N N 840 0 53 0x10000000000001p-52 53 -0 53 +1 53 -0 53 0x10000000000001p-52 53 -0 Z Z 850 0 53 0x10000000000001p-52 53 -0 53 +1 53 -0 53 0x10000000000001p-52 53 -0 U U 860 0 53 -0x10000000000001p-52 53 -0 53 -1 53 -0 53 0x10000000000001p-52 53 -0 D D 87 88# one pure real argument 890 0 53 0x10000000000001p-52 53 0x10000000000001p-52 53 +1 53 +1 53 0x10000000000001p-52 53 -0 N N 900 0 53 0x10000000000001p-52 53 -0x10000000000001p-51 53 +1 53 -2 53 0x10000000000001p-52 53 -0 Z Z 91- + 53 -0x30000000000004p-52 53 0x30000000000004p-52 53 -3 53 +3 53 0x10000000000001p-52 53 +0 N N 92+ - 53 -0x30000000000002p-52 53 0x30000000000002p-52 53 -3 53 +3 53 0x10000000000001p-52 53 +0 Z Z 93+ + 53 -0x30000000000002p-52 53 0x30000000000004p-52 53 -3 53 +3 53 0x10000000000001p-52 53 +0 U U 94- - 53 -0x30000000000004p-52 53 0x30000000000002p-52 53 -3 53 +3 53 0x10000000000001p-52 53 +0 D D 950 0 53 -0x10000000000001p-52 53 -0x10000000000001p-50 53 -1 53 -4 53 0x10000000000001p-52 53 +0 D D 960 0 53 +0 53 +0 53 +0 53 +0 53 0x10000000000001p-52 53 -1 N N 970 0 53 +0 53 -0 53 +0 53 -0 53 0x10000000000001p-52 53 -2 Z Z 980 0 53 +0 53 +0 53 +0 53 +0 53 0x10000000000001p-52 53 +3 U U 990 0 53 -0 53 -0 53 -0 53 -0 53 0x10000000000001p-52 53 +4 D D 100 101# pure imaginary arguments 1020 0 53 -0x10000000000001p-52 53 -0 53 -0 53 0x10000000000001p-52 53 -0 53 +1 N N 1030 0 53 -0x10000000000001p-52 53 +0 53 +0 53 0x10000000000001p-52 53 -0 53 +1 Z Z 1040 0 53 -0x10000000000001p-52 53 +0 53 +0 53 0x10000000000001p-52 53 -0 53 +1 U U 1050 0 53 -0x10000000000001p-52 53 -0 53 -0 53 0x10000000000001p-52 53 -0 53 +1 D D 106 107# one pure imaginary argument 1080 0 53 -0x10000000000001p-52 53 -0x10000000000001p-52 53 -0 53 0x10000000000001p-52 53 -1 53 +1 N N 1090 0 53 +0x10000000000001p-52 53 -0x10000000000001p-51 53 +0 53 0x10000000000001p-52 53 -2 53 -1 Z Z 110+ - 53 0x30000000000004p-52 53 -0x30000000000004p-52 53 +0 53 0x10000000000001p-52 53 -3 53 -3 N N 111- + 53 0x30000000000002p-52 53 -0x30000000000002p-52 53 +0 53 0x10000000000001p-52 53 -3 53 -3 Z Z 112+ + 53 0x30000000000004p-52 53 -0x30000000000002p-52 53 +0 53 0x10000000000001p-52 53 -3 53 -3 U U 113- - 53 0x30000000000002p-52 53 -0x30000000000004p-52 53 +0 53 0x10000000000001p-52 53 -3 53 -3 D D 1140 0 53 +0x10000000000001p-52 53 -0x10000000000001p-50 53 -0 53 0x10000000000001p-52 53 -4 53 -1 D D 115 116# big precision uses Karatsuba method 1170 0 4096 0x1420176785BD601FC018AD36471p-96 4096 -0x1ECCDBDA38B2611A32848E7ADF43p-100 53 0x6B2E363676587p-44 53 0x1AC20AAC49ED37p-47 53 0x12264C57B44C6Bp-53 53 -0x138639A4B8D8B3p-50 N N 118 119# Karatsuba case where x=0 since ad=bc: (1+i)^2 at artificially high 120# precision so that Karatsuba is actually used. 1210 0 4096 0 4096 2 4096 1 4096 1 4096 1 4096 1 N N 122# trigger the line reducing prec_x to prec_u 1230 0 4096 0 4096 2 40960 1 40960 1 40960 1 40960 1 N N 124# another particular cases 125+ + 6 -0x9p-497 6 0x33p-315 6 -0x1dp-73 6 0x3p148 6 0x11p-463 6 0x3p-645 N N 126+ - 6 0x33p-315 6 0x9p-497 6 0x3p148 6 0x1dp-73 6 0x11p-463 6 0x3p-645 N N 1270 0 4 0x1p-1902 4 0x3p-1085 4 -0x1p-892 4 -0x3p-75 4 -0x1p-1010 4 0 N N 128 129# a few particular values 1300 0 8 10 8 -5 8 4 8 3 8 1 8 -2 N N 131+ + 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 1320 0 15 2 15 0 15 -1 15 -1 15 -1 15 1 N N 133 134# check squares, copied from sqr.dat 135+ - 53 0xfdbac097c8dc58p+2096 53 -0x7f6e5d4c3b2a2p+1036 53 -0xfedcba9876543p+1024 53 0x10000000000001p-42 53 -0xfedcba9876543p+1024 53 0x10000000000001p-42 U D 136+ 0 30 309485009533114692573069312 30 18889465966662952943616 30 17592186044416 30 536870913 30 17592186044416 30 536870913 N N 1370 0 4 0 4 2 4 1 4 1 4 1 4 1 N N 138+ + 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 139? + 3464 inf 3464 inf 866 -0x2.5763c6519ef1510f8afa101a210b8030b1909cc17004db561a25d9b53e2c08c41c01e8bbac5af6299b9d8786030aa14943d841798c8c369287942e4d4cec42a60ab0922af931159805e631128e97f973754ad53972d5d320a651a3b4a667f0ef2b92dbd698d159c3642675140@192158913 866 -0xd.15f2d530934dd930d66e89d70762d2337a8f973dd6915eb6b532fd372fcc955df1d852632d4e46fe64154ceda991a1302caf1b0ec622497e3e5724dd05b1c89a06e28d7e18e8af58f5ff4c9998cb31714688867524f41e0b31e847c1bf40de5127f858069998efd7c3e599080@192158893 866 -0x2.5763c6519ef1510f8afa101a210b8030b1909cc17004db561a25d9b53e2c08c41c01e8bbac5af6299b9d8786030aa14943d841798c8c369287942e4d4cec42a60ab0922af931159805e631128e97f973754ad53972d5d320a651a3b4a667f0ef2b92dbd698d159c3642675140@192158913 866 -0xd.15f2d530934dd930d66e89d70762d2337a8f973dd6915eb6b532fd372fcc955df1d852632d4e46fe64154ceda991a1302caf1b0ec622497e3e5724dd05b1c89a06e28d7e18e8af58f5ff4c9998cb31714688867524f41e0b31e847c1bf40de5127f858069998efd7c3e599080@192158893 N N 140? + 2256 0 2256 -0 564 0xc.87999bfd1cb1a64288881e214b7cf1af979863b23c030b79c4a8bebb39177967608388a2e4df527977e7755a25df8af8f72fdd6dd2f42bd00de83088b4e9b59ce85caf2e6b0c0@-184298749 564 -0x2.5109af459d4daf357e09475ec991cdc9b02c8f7dfacdc060d2a24710d09c997f8aea6dbd46f10828c30b583fdcc90d7dcbb895689d594d3813db40784d2309e450d1fb6e38da8@-184298726 564 0xc.87999bfd1cb1a64288881e214b7cf1af979863b23c030b79c4a8bebb39177967608388a2e4df527977e7755a25df8af8f72fdd6dd2f42bd00de83088b4e9b59ce85caf2e6b0c0@-184298749 564 -0x2.5109af459d4daf357e09475ec991cdc9b02c8f7dfacdc060d2a24710d09c997f8aea6dbd46f10828c30b583fdcc90d7dcbb895689d594d3813db40784d2309e450d1fb6e38da8@-184298726 N N 141 142# intermediate over- and underflows 143- + 100 -inf 100 +inf 100 0x1@125000750 100 0x3@125000750 100 0x1@225000750 100 0x2@225000750 N N 144- + 100 -inf 100 +inf 100 0x1@225000750 100 0x2@225000750 100 0x1@125000750 100 0x3@125000750 N N 145- - 100 -inf 100 -inf 100 0x1@225000750 100 -0x2@225000750 100 0x1@125000750 100 -0x3@125000750 N N 146+ - 100 -0 100 +0 100 0x1@-125000750 100 0x3@-125000750 100 0x1@-225000750 100 0x2@-225000750 N N 147+ - 100 -0 100 +0 100 0x1@-225000750 100 0x2@-225000750 100 0x1@-125000750 100 0x3@-125000750 N N 148- - 100 +0 100 +0 100 0x3@-125000750 100 0x1@-125000750 100 0x1@-225000750 100 0x2@-225000750 N N 149- - 100 +0 100 +0 100 0x4@-125000750 100 0x1@-125000750 100 0x1@-225000750 100 0x2@-225000750 N N 150+ - 100 -0 100 +0 100 0x2@-225000750 100 0x1@-225000750 100 0x1@-125000750 100 0x3@-125000750 N N 1510 - 100 +0 100 +0 100 0x1@-225000750 100 0x1@-225000750 100 0x1@-125000750 100 0x1@-125000750 N N 1520 + 100 +0 100 +inf 100 0x1@125000750 100 0x1@125000750 100 0x1@225000750 100 0x1@225000750 N N 153+ 0 100 +inf 100 +0 100 0x1@125000750 100 0x1@125000750 100 0x1@225000750 100 -0x1@225000750 N N 154# the same with directed rounding 155- + 10 -inf 10 +inf 10 0x1@125000750 10 0x3@125000750 10 0x1@225000750 10 0x2@225000750 D U 156+ - 10 -0b1.111111111e1073741822 10 0b1.111111111e1073741822 10 0x1@125000750 10 0x3@125000750 10 0x1@225000750 10 0x2@225000750 U D 157+ - 10 -0 10 +0 10 0x1@-125000750 10 0x3@-125000750 10 0x1@-225000750 10 0x2@-225000750 U D 158- + 10 -0b1e-1073741824 10 0b1e-1073741824 10 0x1@-125000750 10 0x3@-125000750 10 0x1@-225000750 10 0x2@-225000750 D U 159# starting with Karatsuba 160- + 10000 -inf 100 +inf 100 0x1@125000750 100 0x3@125000750 100 0x1@225000750 100 0x2@225000750 N N 161- + 10000 -inf 100 +inf 100 0x1@225000750 100 0x2@225000750 100 0x1@125000750 100 0x3@125000750 N N 162- - 10000 -inf 100 -inf 100 0x1@225000750 100 -0x2@225000750 100 0x1@125000750 100 -0x3@125000750 N N 163+ - 10000 -0 100 +0 100 0x1@-125000750 100 0x3@-125000750 100 0x1@-225000750 100 0x2@-225000750 N N 164+ - 10000 -0 100 +0 100 0x1@-225000750 100 0x2@-225000750 100 0x1@-125000750 100 0x3@-125000750 N N 165- - 10000 +0 100 +0 100 0x3@-125000750 100 0x1@-125000750 100 0x1@-225000750 100 0x2@-225000750 N N 166- - 10000 +0 100 +0 100 0x4@-125000750 100 0x1@-125000750 100 0x1@-225000750 100 0x2@-225000750 N N 167+ - 10000 -0 100 +0 100 0x2@-225000750 100 0x1@-225000750 100 0x1@-125000750 100 0x3@-125000750 N N 1680 - 10000 +0 100 +0 100 0x1@-225000750 100 0x1@-225000750 100 0x1@-125000750 100 0x1@-125000750 N N 1690 + 10000 +0 100 +inf 100 0x1@125000750 100 0x1@125000750 100 0x1@225000750 100 0x1@225000750 N N 170+ 0 10000 +inf 100 +0 100 0x1@125000750 100 0x1@125000750 100 0x1@225000750 100 -0x1@225000750 N N 171+ + 10000 +inf 100 +inf 100 0x1@125000750 100 0x3@125000750 100 0x1@143434706 100 0x2@143434705 N N 172 173# improve code coverage: case where sign_x==0 in mpc_mul_karatsuba 1740 0 2000 6 2000 8 2000 4 2000 2 2000 2 2000 1 N N 1750 0 2000 0 2000 4 2000 2 2000 2 2000 1 2000 1 N N 176 177+ 0 2 1 2 0x2p-536870913 2 1 2 0x1p-536870913 2 1 2 0x1p-536870913 N N 1780 - 2 0 2 1 2 0x1p-536870913 2 1 2 1 2 0x1p-536870913 N N 179