mirror of
https://github.com/opnsense/src.git
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Add some tests for cexp() and cexpf(). (I need to clean up all of
these tests some day, but in the mean time, they're a useful sanity check for future changes.)
This commit is contained in:
David Schultz
parent
97a539be1f
commit
2dc9da4376
3 changed files with 391 additions and 1 deletions
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@ -1,6 +1,6 @@
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# $FreeBSD$
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TESTS= test-conj test-csqrt test-exponential test-fenv test-fma \
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TESTS= test-cexp test-conj test-csqrt test-exponential test-fenv test-fma \
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test-fmaxmin test-ilogb test-invtrig test-logarithm test-lrint \
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test-lround test-nan test-nearbyint test-next test-rem test-trig
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CFLAGS+= -O0 -lm
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380
tools/regression/lib/msun/test-cexp.c
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380
tools/regression/lib/msun/test-cexp.c
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/*-
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* Copyright (c) 2008-2011 David Schultz <das@FreeBSD.org>
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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*
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* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*/
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/*
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* Tests for corner cases in cexp*().
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*/
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#include <sys/cdefs.h>
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__FBSDID("$FreeBSD$");
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#include <assert.h>
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#include <complex.h>
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#include <fenv.h>
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#include <float.h>
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#include <math.h>
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#include <stdio.h>
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#define ALL_STD_EXCEPT (FE_DIVBYZERO | FE_INEXACT | FE_INVALID | \
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FE_OVERFLOW | FE_UNDERFLOW)
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#define FLT_ULP() ldexpl(1.0, 1 - FLT_MANT_DIG)
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#define DBL_ULP() ldexpl(1.0, 1 - DBL_MANT_DIG)
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#define LDBL_ULP() ldexpl(1.0, 1 - LDBL_MANT_DIG)
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#define N(i) (sizeof(i) / sizeof((i)[0]))
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#pragma STDC FENV_ACCESS ON
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#pragma STDC CX_LIMITED_RANGE OFF
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/*
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* XXX gcc implements complex multiplication incorrectly. In
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* particular, it implements it as if the CX_LIMITED_RANGE pragma
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* were ON. Consequently, we need this function to form numbers
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* such as x + INFINITY * I, since gcc evalutes INFINITY * I as
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* NaN + INFINITY * I.
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*/
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static inline long double complex
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cpackl(long double x, long double y)
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{
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long double complex z;
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__real__ z = x;
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__imag__ z = y;
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return (z);
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}
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/*
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* Test that a function returns the correct value and sets the
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* exception flags correctly. The exceptmask specifies which
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* exceptions we should check. We need to be lenient for several
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* reasons, but mainly because on some architectures it's impossible
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* to raise FE_OVERFLOW without raising FE_INEXACT. In some cases,
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* whether cexp() raises an invalid exception is unspecified.
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*
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* These are macros instead of functions so that assert provides more
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* meaningful error messages.
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*
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* XXX The volatile here is to avoid gcc's bogus constant folding and work
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* around the lack of support for the FENV_ACCESS pragma.
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*/
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#define test(func, z, result, exceptmask, excepts, checksign) do { \
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volatile long double complex _d = z; \
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assert(feclearexcept(FE_ALL_EXCEPT) == 0); \
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assert(cfpequal((func)(_d), (result), (checksign))); \
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assert(((func), fetestexcept(exceptmask) == (excepts))); \
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} while (0)
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/* Test within a given tolerance. */
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#define test_tol(func, z, result, tol) do { \
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volatile long double complex _d = z; \
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assert(cfpequal_tol((func)(_d), (result), (tol))); \
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} while (0)
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/* Test all the functions that compute cexp(x). */
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#define testall(x, result, exceptmask, excepts, checksign) do { \
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test(cexp, x, result, exceptmask, excepts, checksign); \
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test(cexpf, x, result, exceptmask, excepts, checksign); \
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} while (0)
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/*
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* Test all the functions that compute cexp(x), within a given tolerance.
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* The tolerance is specified in ulps.
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*/
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#define testall_tol(x, result, tol) do { \
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test_tol(cexp, x, result, tol * DBL_ULP()); \
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test_tol(cexpf, x, result, tol * FLT_ULP()); \
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} while (0)
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/* Various finite non-zero numbers to test. */
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static const float finites[] =
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{ -42.0e20, -1.0 -1.0e-10, -0.0, 0.0, 1.0e-10, 1.0, 42.0e20 };
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/*
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* Determine whether x and y are equal, with two special rules:
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* +0.0 != -0.0
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* NaN == NaN
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* If checksign is 0, we compare the absolute values instead.
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*/
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static int
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fpequal(long double x, long double y, int checksign)
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{
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if (isnan(x) || isnan(y))
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return (1);
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if (checksign)
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return (x == y && !signbit(x) == !signbit(y));
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else
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return (fabsl(x) == fabsl(y));
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}
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static int
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fpequal_tol(long double x, long double y, long double tol)
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{
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fenv_t env;
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int ret;
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if (isnan(x) && isnan(y))
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return (1);
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if (!signbit(x) != !signbit(y))
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return (0);
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if (x == y)
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return (1);
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if (tol == 0)
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return (0);
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/* Hard case: need to check the tolerance. */
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feholdexcept(&env);
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/*
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* For our purposes here, if y=0, we interpret tol as an absolute
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* tolerance. This is to account for roundoff in the input, e.g.,
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* cos(Pi/2) ~= 0.
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*/
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if (y == 0.0)
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ret = fabsl(x - y) <= fabsl(tol);
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else
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ret = fabsl(x - y) <= fabsl(y * tol);
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fesetenv(&env);
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return (ret);
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}
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static int
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cfpequal(long double complex x, long double complex y, int checksign)
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{
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return (fpequal(creal(x), creal(y), checksign)
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&& fpequal(cimag(x), cimag(y), checksign));
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}
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static int
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cfpequal_tol(long double complex x, long double complex y, long double tol)
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{
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return (fpequal_tol(creal(x), creal(y), tol)
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&& fpequal_tol(cimag(x), cimag(y), tol));
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}
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/* Tests for 0 */
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void
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test_zero(void)
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{
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/* cexp(0) = 1, no exceptions raised */
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testall(0.0, 1.0, ALL_STD_EXCEPT, 0, 1);
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testall(-0.0, 1.0, ALL_STD_EXCEPT, 0, 1);
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testall(cpackl(0.0, -0.0), cpackl(1.0, -0.0), ALL_STD_EXCEPT, 0, 1);
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testall(cpackl(-0.0, -0.0), cpackl(1.0, -0.0), ALL_STD_EXCEPT, 0, 1);
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}
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/*
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* Tests for NaN. The signs of the results are indeterminate unless the
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* imaginary part is 0.
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*/
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void
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test_nan()
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{
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int i;
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/* cexp(x + NaNi) = NaN + NaNi and optionally raises invalid */
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/* cexp(NaN + yi) = NaN + NaNi and optionally raises invalid (|y|>0) */
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for (i = 0; i < N(finites); i++) {
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testall(cpackl(finites[i], NAN), cpackl(NAN, NAN),
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ALL_STD_EXCEPT & ~FE_INVALID, 0, 0);
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if (finites[i] == 0.0)
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continue;
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/* XXX FE_INEXACT shouldn't be raised here */
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testall(cpackl(NAN, finites[i]), cpackl(NAN, NAN),
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ALL_STD_EXCEPT & ~(FE_INVALID | FE_INEXACT), 0, 0);
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}
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/* cexp(NaN +- 0i) = NaN +- 0i */
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testall(cpackl(NAN, 0.0), cpackl(NAN, 0.0), ALL_STD_EXCEPT, 0, 1);
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testall(cpackl(NAN, -0.0), cpackl(NAN, -0.0), ALL_STD_EXCEPT, 0, 1);
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/* cexp(inf + NaN i) = inf + nan i */
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testall(cpackl(INFINITY, NAN), cpackl(INFINITY, NAN),
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ALL_STD_EXCEPT, 0, 0);
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/* cexp(-inf + NaN i) = 0 */
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testall(cpackl(-INFINITY, NAN), cpackl(0.0, 0.0),
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ALL_STD_EXCEPT, 0, 0);
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/* cexp(NaN + NaN i) = NaN + NaN i */
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testall(cpackl(NAN, NAN), cpackl(NAN, NAN),
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ALL_STD_EXCEPT, 0, 0);
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}
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void
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test_inf(void)
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{
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int i;
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/* cexp(x + inf i) = NaN + NaNi and raises invalid */
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/* cexp(inf + yi) = 0 + 0yi */
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/* cexp(-inf + yi) = inf + inf yi (except y=0) */
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for (i = 0; i < N(finites); i++) {
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testall(cpackl(finites[i], INFINITY), cpackl(NAN, NAN),
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ALL_STD_EXCEPT, FE_INVALID, 1);
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/* XXX shouldn't raise an inexact exception */
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testall(cpackl(-INFINITY, finites[i]),
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cpackl(0.0, 0.0 * finites[i]),
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ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
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if (finites[i] == 0)
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continue;
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testall(cpackl(INFINITY, finites[i]),
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cpackl(INFINITY, INFINITY * finites[i]),
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ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
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}
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testall(cpackl(INFINITY, 0.0), cpackl(INFINITY, 0.0),
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ALL_STD_EXCEPT, 0, 1);
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testall(cpackl(INFINITY, -0.0), cpackl(INFINITY, -0.0),
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ALL_STD_EXCEPT, 0, 1);
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}
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void
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test_reals(void)
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{
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int i;
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for (i = 0; i < N(finites); i++) {
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/* XXX could check exceptions more meticulously */
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test(cexp, cpackl(finites[i], 0.0),
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cpackl(exp(finites[i]), 0.0),
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FE_INVALID | FE_DIVBYZERO, 0, 1);
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test(cexp, cpackl(finites[i], -0.0),
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cpackl(exp(finites[i]), -0.0),
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FE_INVALID | FE_DIVBYZERO, 0, 1);
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test(cexpf, cpackl(finites[i], 0.0),
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cpackl(expf(finites[i]), 0.0),
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FE_INVALID | FE_DIVBYZERO, 0, 1);
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test(cexpf, cpackl(finites[i], -0.0),
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cpackl(expf(finites[i]), -0.0),
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FE_INVALID | FE_DIVBYZERO, 0, 1);
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}
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}
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void
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test_imaginaries(void)
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{
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int i;
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for (i = 0; i < N(finites); i++) {
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test(cexp, cpackl(0.0, finites[i]),
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cpackl(cos(finites[i]), sin(finites[i])),
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ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
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test(cexp, cpackl(-0.0, finites[i]),
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cpackl(cos(finites[i]), sin(finites[i])),
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ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
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test(cexpf, cpackl(0.0, finites[i]),
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cpackl(cosf(finites[i]), sinf(finites[i])),
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ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
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test(cexpf, cpackl(-0.0, finites[i]),
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cpackl(cosf(finites[i]), sinf(finites[i])),
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ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
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}
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}
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void
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test_small(void)
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{
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static const double tests[] = {
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/* csqrt(a + bI) = x + yI */
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/* a b x y */
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1.0, M_PI_4, M_SQRT2 * 0.5 * M_E, M_SQRT2 * 0.5 * M_E,
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-1.0, M_PI_4, M_SQRT2 * 0.5 / M_E, M_SQRT2 * 0.5 / M_E,
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2.0, M_PI_2, 0.0, M_E * M_E,
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M_LN2, M_PI, -2.0, 0.0,
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};
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double a, b;
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double x, y;
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int i;
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for (i = 0; i < N(tests); i += 4) {
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a = tests[i];
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b = tests[i + 1];
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x = tests[i + 2];
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y = tests[i + 3];
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test_tol(cexp, cpackl(a, b), cpackl(x, y), 3 * DBL_ULP());
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/* float doesn't have enough precision to pass these tests */
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if (x == 0 || y == 0)
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continue;
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test_tol(cexpf, cpackl(a, b), cpackl(x, y), 1 * FLT_ULP());
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}
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}
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/* Test inputs with a real part r that would overflow exp(r). */
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void
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test_large(void)
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{
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test_tol(cexp, cpackl(709.79, 0x1p-1074),
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cpackl(INFINITY, 8.94674309915433533273e-16), DBL_ULP());
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test_tol(cexp, cpackl(1000, 0x1p-1074),
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cpackl(INFINITY, 9.73344457300016401328e+110), DBL_ULP());
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test_tol(cexp, cpackl(1400, 0x1p-1074),
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cpackl(INFINITY, 5.08228858149196559681e+284), DBL_ULP());
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test_tol(cexp, cpackl(900, 0x1.23456789abcdep-1020),
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cpackl(INFINITY, 7.42156649354218408074e+83), DBL_ULP());
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test_tol(cexp, cpackl(1300, 0x1.23456789abcdep-1020),
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cpackl(INFINITY, 3.87514844965996756704e+257), DBL_ULP());
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test_tol(cexpf, cpackl(88.73, 0x1p-149),
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cpackl(INFINITY, 4.80265603e-07), 2 * FLT_ULP());
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test_tol(cexpf, cpackl(90, 0x1p-149),
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cpackl(INFINITY, 1.7101492622e-06f), 2 * FLT_ULP());
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test_tol(cexpf, cpackl(192, 0x1p-149),
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cpackl(INFINITY, 3.396809344e+38f), 2 * FLT_ULP());
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test_tol(cexpf, cpackl(120, 0x1.234568p-120),
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cpackl(INFINITY, 1.1163382522e+16f), 2 * FLT_ULP());
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test_tol(cexpf, cpackl(170, 0x1.234568p-120),
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cpackl(INFINITY, 5.7878851079e+37f), 2 * FLT_ULP());
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}
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int
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main(int argc, char *argv[])
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{
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printf("1..7\n");
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test_zero();
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printf("ok 1 - cexp zero\n");
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test_nan();
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printf("ok 2 - cexp nan\n");
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test_inf();
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printf("ok 3 - cexp inf\n");
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test_reals();
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printf("ok 4 - cexp reals\n");
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test_imaginaries();
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printf("ok 5 - cexp imaginaries\n");
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test_small();
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printf("ok 6 - cexp small\n");
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test_large();
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printf("ok 7 - cexp large\n");
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return (0);
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}
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10
tools/regression/lib/msun/test-cexp.t
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10
tools/regression/lib/msun/test-cexp.t
Normal file
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@ -0,0 +1,10 @@
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#!/bin/sh
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# $FreeBSD$
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cd `dirname $0`
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executable=`basename $0 .t`
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make $executable 2>&1 > /dev/null
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exec ./$executable
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