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master
tests/asin.dat
151 строка
8 KB
Paul Zimmermann
improved error analysis of mpc_asin_large_pos()
13 сен 2024, 12:51
13 сен 2024, 12:51
9274b6b
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# Data file for mpc_asin. # # Copyright (C) 2009, 2011, 2013, 2014, 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 # # where op = op_re + i * op_im, rop = rop_re + i * rop_im, # rop_re is ROP_RE rounded to nearest to the precision of PREC_ROP_RE # rop_im is ROP_IM rounded to nearest to the precision of PREC_ROP_IM # op_re is OP_RE rounded to nearest to the precision of PREC_OP_RE # op_im is OP_IM rounded to nearest to the precision of PREC_OP_IM # ROP_RE is checked against Re(asin op) rounded to the precision PREC_ROP_RE # in the direction RND_RE # ROP_IM is checked against Im(asin op) rounded to the precision PREC_ROP_IM # in the direction RND_IM # INEX_RE is the ternary value for the real part with the following notation: # "?" ternary value not checked # "+" if ROP_RE is greater than the exact mathematical result # "0" if ROP_RE is exactly the mathematical result # "-" if ROP_RE is less than the exact mathematical result # (m.m. INEX_IM) # rounding modes notation: # "N" is rounding to nearest # "Z" is rounding towards zero # "U" is rounding towards plus infinity # "D" is rounding towards minus infinity # Use prefixes "0b" for values in base two, "0x" for values in base sixteen, # no prefix for value in base ten. # In all bases, "nan" is NaN, "inf" is infinity; # The sign of the result is checked with "+inf", "-inf", "-0", or "+0". # special values (following ISO C99 standard) + 0 53 -0x1921FB54442D18p-53 53 -inf 53 -inf 53 -inf N N + 0 53 -0x1921FB54442D18p-52 53 -inf 53 -inf 53 -1 N N + 0 53 -0x1921FB54442D18p-52 53 -inf 53 -inf 53 -0 N N + 0 53 -0x1921FB54442D18p-52 53 +inf 53 -inf 53 +0 N N + 0 53 -0x1921FB54442D18p-52 53 +inf 53 -inf 53 +1 N N + 0 53 -0x1921FB54442D18p-53 53 +inf 53 -inf 53 +inf N N 0 0 53 nan 53 inf 53 -inf 53 nan N N 0 0 53 -0 53 -inf 53 -6 53 -inf N N 0 0 53 -0 53 +inf 53 -6 53 +inf N N 0 0 53 nan 53 nan 53 -6 53 nan N N 0 0 53 -0 53 -inf 53 -0.5 53 -inf N N 0 0 53 -0 53 +inf 53 -0.5 53 +inf N N 0 0 53 nan 53 nan 53 -0.5 53 nan N N 0 0 53 -0 53 -inf 53 -0 53 -inf 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 -0 53 +inf 53 -0 53 +inf N N 0 0 53 -0 53 nan 53 -0 53 nan N N 0 0 53 +0 53 -inf 53 +0 53 -inf 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 +0 53 +inf 53 +0 53 +inf N N 0 0 53 +0 53 nan 53 +0 53 nan N N 0 0 53 +0 53 -inf 53 +0.5 53 -inf N N 0 0 53 +0 53 +inf 53 +0.5 53 +inf N N 0 0 53 nan 53 nan 53 +0.5 53 nan N N 0 0 53 +0 53 -inf 53 +6 53 -inf N N 0 0 53 +0 53 +inf 53 +6 53 +inf N N 0 0 53 nan 53 nan 53 +6 53 nan N N - 0 53 0x1921FB54442D18p-53 53 -inf 53 +inf 53 -inf N N - 0 53 0x1921FB54442D18p-52 53 -inf 53 +inf 53 -1 N N - 0 53 0x1921FB54442D18p-52 53 -inf 53 +inf 53 -0 N N - 0 53 0x1921FB54442D18p-52 53 +inf 53 +inf 53 +0 N N - 0 53 0x1921FB54442D18p-52 53 +inf 53 +inf 53 +1 N N - 0 53 0x1921FB54442D18p-53 53 +inf 53 +inf 53 +inf N N 0 0 53 nan 53 inf 53 +inf 53 nan N N 0 0 53 nan 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 nan 53 +inf 53 nan 53 +inf N N 0 0 53 nan 53 nan 53 nan 53 nan N N # pure real argument + - 53 -0x1921FB54442D18p-52 53 -0x1ECC2CAEC5160Ap-53 53 -1.5 53 -0 N N + + 53 -0x1921FB54442D18p-52 53 0x1ECC2CAEC5160Ap-53 53 -1.5 53 +0 N N + 0 53 -0x1921FB54442D18p-52 53 -0 53 -1 53 -0 N N + 0 53 -0x1921FB54442D18p-52 53 +0 53 -1 53 +0 N N - 0 53 -0x10C152382D7366p-53 53 -0 53 -0.5 53 -0 N N - 0 53 -0x10C152382D7366p-53 53 +0 53 -0.5 53 +0 N N + 0 53 0x10C152382D7366p-53 53 -0 53 +0.5 53 -0 N N + 0 53 0x10C152382D7366p-53 53 +0 53 +0.5 53 +0 N N - 0 53 0x1921FB54442D18p-52 53 -0 53 +1 53 -0 N N - 0 53 0x1921FB54442D18p-52 53 +0 53 +1 53 +0 N N - - 53 0x1921FB54442D18p-52 53 -0x1ECC2CAEC5160Ap-53 53 +1.5 53 -0 N N - + 53 0x1921FB54442D18p-52 53 0x1ECC2CAEC5160Ap-53 53 +1.5 53 +0 N N # pure imaginary argument 0 + 53 -0 53 -0x131DC0090B63D8p-52 53 -0 53 -1.5 N N 0 + 53 +0 53 -0x131DC0090B63D8p-52 53 +0 53 -1.5 N N 0 - 53 -0 53 -0x1C34366179D427p-53 53 -0 53 -1 N N 0 - 53 +0 53 -0x1C34366179D427p-53 53 +0 53 -1 N N 0 - 53 -0 53 -0x1ECC2CAEC5160Ap-54 53 -0 53 -0.5 N N 0 - 53 +0 53 -0x1ECC2CAEC5160Ap-54 53 +0 53 -0.5 N N 0 + 53 -0 53 0x1ECC2CAEC5160Ap-54 53 -0 53 +0.5 N N 0 + 53 +0 53 0x1ECC2CAEC5160Ap-54 53 +0 53 +0.5 N N 0 + 53 -0 53 0x1C34366179D427p-53 53 -0 53 +1 N N 0 + 53 +0 53 0x1C34366179D427p-53 53 +0 53 +1 N N 0 - 53 -0 53 0x131DC0090B63D8p-52 53 -0 53 +1.5 N N 0 - 53 +0 53 0x131DC0090B63D8p-52 53 +0 53 +1.5 N N # IEEE-754 double precision and other precisions + - 53 0x189BF9EC7FCD5Bp-54 53 0x1206ECFA94614Bp-50 53 17 53 42 N N - + 2 1.5 2 6 2 96 2 0x1p-8 N N - - 8 0xC9p-7 8 0x15p-2 2 96 2 0x1p-8 N N # special cases 1 + i*y with tiny y - - 53 0x3243f6a8885a3p-49 53 0x1p-500 53 1 53 0x1p-1000 N N - + 53 0x3243f6a8885a3p-49 53 -0x1p-500 53 1 53 -0x1p-1000 N N - - 11 0xc9p-7 11 0xb5p-28 11 1 11 0x1p-41 N N - + 53 0x3243f6a8885a3p-49 53 0x16a09e667f3bcdp-552 53 1 53 0x1p-999 N N - + 2 1.5 2 0x1p-40 2 1 20 0xff802p-100 N N - - 24 -0x1p-148 24 -0xc.75cp-20 24 -0x1p-148 24 -0xc.75cp-20 N N # this test failed before the 1.3.0 release ? ? 9 -0x1.72p+0 9 -0x1.e4p-5 9 -0x1.fdp-1 9 -0x1.dcp-8 Z N # test case for asin_taylor1 + - 7 0b1.000001p-2 4 0b1p-9 2 0b1p-2 2 0b1p-9 N N - + 26 -0b1.0000001010111110100111010p-2 15 -0b1.00001000011001p-20 2 -0b1p-2 2 -0b1p-20 N N # test cases that required >= 5 Ziv loops - + 109 0x1.91f28721152dc8689c478af3c45p+0 88 0x4.f415ad0f62c5f350cc2288p+4 24 0x2.889d3p+112 24 0x7.27888p+100 N N - + 2 0x1.8p+0 2 0x1p-40 2 0x1p+0 20 0xf.f802p-84 N N # test case that required 8 Ziv loops (up to precision of 2947 bits) - + 117 0x1.63c2a68f7672dc51c5533e7204abap+0 117 0x2.c67c415afa0f8efb5a4ca99cdc946p+8 53 0xf.e38444d37e158p+1020 53 0x2.e8d198e14e25ep+1020 N N # test case that required 7 Ziv loops + + 117 -0x1.9178210c692ab7e8fe73e93224145p+0 117 -0x5.bec0f4d5d9b98027de86848bfea98p+0 53 -0x9.c556066fe22bp+4 53 -0x6.655bac2f12f08p-4 N N # test case that required precision up to 9379 bits - + 117 0x2.44b6d15aa7e1f505da03b77225f1ep-2032 117 0x2.c53e9823468d2845b483befae017cp+8 53 0xa.9825deeb1c41p-1012 53 0x4.ab9d26976257p+1020 N N