/*-
 * Copyright (c) 2008-2011 David Schultz <das@FreeBSD.org>
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 *
 * $FreeBSD: src/tools/regression/lib/msun/test-cexp.c,v 1.3 2013/05/29 00:27:12 svnexp Exp $
 */

/*
 * Tests for corner cases in cexp*().
 */

#include <assert.h>
#include <complex.h>
#include <fenv.h>
#include <float.h>
#include <math.h>
#include <stdio.h>

#define ALL_STD_EXCEPT  (FE_DIVBYZERO | FE_INEXACT | FE_INVALID | \
                         FE_OVERFLOW | FE_UNDERFLOW)
#define FLT_ULP()       ldexpl(1.0, 1 - FLT_MANT_DIG)
#define DBL_ULP()       ldexpl(1.0, 1 - DBL_MANT_DIG)
#define LDBL_ULP()      ldexpl(1.0, 1 - LDBL_MANT_DIG)

#define N(i)    (sizeof(i) / sizeof((i)[0]))

#pragma STDC FENV_ACCESS        ON
#pragma STDC CX_LIMITED_RANGE   OFF

/*
 * XXX gcc implements complex multiplication incorrectly. In
 * particular, it implements it as if the CX_LIMITED_RANGE pragma
 * were ON. Consequently, we need this function to form numbers
 * such as x + INFINITY * I, since gcc evalutes INFINITY * I as
 * NaN + INFINITY * I.
 */
static inline long double complex
cpackl(long double x, long double y)
{
        long double complex z;

        __real__ z = x;
        __imag__ z = y;
        return (z);
}

/*
 * Test that a function returns the correct value and sets the
 * exception flags correctly. The exceptmask specifies which
 * exceptions we should check. We need to be lenient for several
 * reasons, but mainly because on some architectures it's impossible
 * to raise FE_OVERFLOW without raising FE_INEXACT. In some cases,
 * whether cexp() raises an invalid exception is unspecified.
 *
 * These are macros instead of functions so that assert provides more
 * meaningful error messages.
 *
 * XXX The volatile here is to avoid gcc's bogus constant folding and work
 *     around the lack of support for the FENV_ACCESS pragma.
 */
#define test(func, z, result, exceptmask, excepts, checksign)   do {    \
        volatile long double complex _d = z;                            \
        assert(feclearexcept(FE_ALL_EXCEPT) == 0);                      \
        assert(cfpequal((func)(_d), (result), (checksign)));            \
        assert(((func), fetestexcept(exceptmask) == (excepts)));        \
} while (0)

/* Test within a given tolerance. */
#define test_tol(func, z, result, tol)                          do {    \
        volatile long double complex _d = z;                            \
        assert(cfpequal_tol((func)(_d), (result), (tol)));              \
} while (0)

/* Test all the functions that compute cexp(x). */
#define testall(x, result, exceptmask, excepts, checksign)      do {    \
        test(cexp, x, result, exceptmask, excepts, checksign);          \
        test(cexpf, x, result, exceptmask, excepts, checksign);         \
} while (0)

/*
 * Test all the functions that compute cexp(x), within a given tolerance.
 * The tolerance is specified in ulps.
 */
#define testall_tol(x, result, tol)                             do {    \
        test_tol(cexp, x, result, tol * DBL_ULP());                     \
        test_tol(cexpf, x, result, tol * FLT_ULP());                    \
} while (0)

/* Various finite non-zero numbers to test. */
static const float finites[] =
{ -42.0e20, -1.0, -1.0e-10, -0.0, 0.0, 1.0e-10, 1.0, 42.0e20 };

/*
 * Determine whether x and y are equal, with two special rules:
 *      +0.0 != -0.0
 *       NaN == NaN
 * If checksign is 0, we compare the absolute values instead.
 */
static int
fpequal(long double x, long double y, int checksign)
{
        if (isnan(x) || isnan(y))
                return (1);
        if (checksign)
                return (x == y && !signbit(x) == !signbit(y));
        else
                return (fabsl(x) == fabsl(y));
}

static int
fpequal_tol(long double x, long double y, long double tol)
{
        fenv_t env;
        int ret;

        if (isnan(x) && isnan(y))
                return (1);
        if (!signbit(x) != !signbit(y))
                return (0);
        if (x == y)
                return (1);
        if (tol == 0)
                return (0);

        /* Hard case: need to check the tolerance. */
        feholdexcept(&env);
        /*
         * For our purposes here, if y=0, we interpret tol as an absolute
         * tolerance. This is to account for roundoff in the input, e.g.,
         * cos(Pi/2) ~= 0.
         */
        if (y == 0.0)
                ret = fabsl(x - y) <= fabsl(tol);
        else
                ret = fabsl(x - y) <= fabsl(y * tol);
        fesetenv(&env);
        return (ret);
}

static int
cfpequal(long double complex x, long double complex y, int checksign)
{
        return (fpequal(creal(x), creal(y), checksign)
                && fpequal(cimag(x), cimag(y), checksign));
}

static int
cfpequal_tol(long double complex x, long double complex y, long double tol)
{
        return (fpequal_tol(creal(x), creal(y), tol)
                && fpequal_tol(cimag(x), cimag(y), tol));
}


/* Tests for 0 */
void
test_zero(void)
{

        /* cexp(0) = 1, no exceptions raised */
        testall(0.0, 1.0, ALL_STD_EXCEPT, 0, 1);
        testall(-0.0, 1.0, ALL_STD_EXCEPT, 0, 1);
        testall(cpackl(0.0, -0.0), cpackl(1.0, -0.0), ALL_STD_EXCEPT, 0, 1);
        testall(cpackl(-0.0, -0.0), cpackl(1.0, -0.0), ALL_STD_EXCEPT, 0, 1);
}

/*
 * Tests for NaN.  The signs of the results are indeterminate unless the
 * imaginary part is 0.
 */
void
test_nan()
{
        int i;

        /* cexp(x + NaNi) = NaN + NaNi and optionally raises invalid */
        /* cexp(NaN + yi) = NaN + NaNi and optionally raises invalid (|y|>0) */
        for (i = 0; i < N(finites); i++) {
                testall(cpackl(finites[i], NAN), cpackl(NAN, NAN),
                        ALL_STD_EXCEPT & ~FE_INVALID, 0, 0);
                if (finites[i] == 0.0)
                        continue;
                /* XXX FE_INEXACT shouldn't be raised here */
                testall(cpackl(NAN, finites[i]), cpackl(NAN, NAN),
                        ALL_STD_EXCEPT & ~(FE_INVALID | FE_INEXACT), 0, 0);
        }

        /* cexp(NaN +- 0i) = NaN +- 0i */
        testall(cpackl(NAN, 0.0), cpackl(NAN, 0.0), ALL_STD_EXCEPT, 0, 1);
        testall(cpackl(NAN, -0.0), cpackl(NAN, -0.0), ALL_STD_EXCEPT, 0, 1);

        /* cexp(inf + NaN i) = inf + nan i */
        testall(cpackl(INFINITY, NAN), cpackl(INFINITY, NAN),
                ALL_STD_EXCEPT, 0, 0);
        /* cexp(-inf + NaN i) = 0 */
        testall(cpackl(-INFINITY, NAN), cpackl(0.0, 0.0),
                ALL_STD_EXCEPT, 0, 0);
        /* cexp(NaN + NaN i) = NaN + NaN i */
        testall(cpackl(NAN, NAN), cpackl(NAN, NAN),
                ALL_STD_EXCEPT, 0, 0);
}

void
test_inf(void)
{
        int i;

        /* cexp(x + inf i) = NaN + NaNi and raises invalid */
        for (i = 0; i < N(finites); i++) {
                testall(cpackl(finites[i], INFINITY), cpackl(NAN, NAN),
                        ALL_STD_EXCEPT, FE_INVALID, 1);
        }
        /* cexp(-inf + yi) = 0 * (cos(y) + sin(y)i) */
                /* XXX shouldn't raise an inexact exception */
        testall(cpackl(-INFINITY, M_PI_4), cpackl(0.0, 0.0),
                        ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
        testall(cpackl(-INFINITY, 3 * M_PI_4), cpackl(-0.0, 0.0),
                        ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
        testall(cpackl(-INFINITY, 5 * M_PI_4), cpackl(-0.0, -0.0),
                ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
        testall(cpackl(-INFINITY, 7 * M_PI_4), cpackl(0.0, -0.0),
                ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
        testall(cpackl(-INFINITY, 0.0), cpackl(0.0, 0.0),
                ALL_STD_EXCEPT, 0, 1);
        testall(cpackl(-INFINITY, -0.0), cpackl(0.0, -0.0),
                ALL_STD_EXCEPT, 0, 1);
        /* cexp(inf + yi) = inf * (cos(y) + sin(y)i) (except y=0) */
        /* XXX shouldn't raise an inexact exception */
        testall(cpackl(INFINITY, M_PI_4), cpackl(INFINITY, INFINITY),
                ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
        testall(cpackl(INFINITY, 3 * M_PI_4), cpackl(-INFINITY, INFINITY),
                ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
        testall(cpackl(INFINITY, 5 * M_PI_4), cpackl(-INFINITY, -INFINITY),
                ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
        testall(cpackl(INFINITY, 7 * M_PI_4), cpackl(INFINITY, -INFINITY),
                ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
        /* cexp(inf + 0i) = inf + 0i */
        testall(cpackl(INFINITY, 0.0), cpackl(INFINITY, 0.0),
                ALL_STD_EXCEPT, 0, 1);
        testall(cpackl(INFINITY, -0.0), cpackl(INFINITY, -0.0),
                ALL_STD_EXCEPT, 0, 1);
}

void
test_reals(void)
{
        int i;

        for (i = 0; i < N(finites); i++) {
                /* XXX could check exceptions more meticulously */
                test(cexp, cpackl(finites[i], 0.0),
                     cpackl(exp(finites[i]), 0.0),
                     FE_INVALID | FE_DIVBYZERO, 0, 1);
                test(cexp, cpackl(finites[i], -0.0),
                     cpackl(exp(finites[i]), -0.0),
                     FE_INVALID | FE_DIVBYZERO, 0, 1);
                test(cexpf, cpackl(finites[i], 0.0),
                     cpackl(expf(finites[i]), 0.0),
                     FE_INVALID | FE_DIVBYZERO, 0, 1);
                test(cexpf, cpackl(finites[i], -0.0),
                     cpackl(expf(finites[i]), -0.0),
                     FE_INVALID | FE_DIVBYZERO, 0, 1);
        }
}

void
test_imaginaries(void)
{
        int i;

        for (i = 0; i < N(finites); i++) {
                test(cexp, cpackl(0.0, finites[i]),
                     cpackl(cos(finites[i]), sin(finites[i])),
                     ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
                test(cexp, cpackl(-0.0, finites[i]),
                     cpackl(cos(finites[i]), sin(finites[i])),
                     ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
                test(cexpf, cpackl(0.0, finites[i]),
                     cpackl(cosf(finites[i]), sinf(finites[i])),
                     ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
                test(cexpf, cpackl(-0.0, finites[i]),
                     cpackl(cosf(finites[i]), sinf(finites[i])),
                     ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
        }
}

void
test_small(void)
{
        static const double tests[] = {
             /* csqrt(a + bI) = x + yI */
             /* a       b       x                       y */
                 1.0,   M_PI_4, M_SQRT2 * 0.5 * M_E,    M_SQRT2 * 0.5 * M_E,
                -1.0,   M_PI_4, M_SQRT2 * 0.5 / M_E,    M_SQRT2 * 0.5 / M_E,
                 2.0,   M_PI_2, 0.0,                    M_E * M_E,
                 M_LN2, M_PI,   -2.0,                   0.0,
        };
        double a, b;
        double x, y;
        int i;

        for (i = 0; i < N(tests); i += 4) {
                a = tests[i];
                b = tests[i + 1];
                x = tests[i + 2];
                y = tests[i + 3];
                test_tol(cexp, cpackl(a, b), cpackl(x, y), 3 * DBL_ULP());

                /* float doesn't have enough precision to pass these tests */
                if (x == 0 || y == 0)
                        continue;
                test_tol(cexpf, cpackl(a, b), cpackl(x, y), 1 * FLT_ULP());
        }
}

/* Test inputs with a real part r that would overflow exp(r). */
void
test_large(void)
{

        test_tol(cexp, cpackl(709.79, 0x1p-1074),
                 cpackl(INFINITY, 8.94674309915433533273e-16), DBL_ULP());
        test_tol(cexp, cpackl(1000, 0x1p-1074),
                 cpackl(INFINITY, 9.73344457300016401328e+110), DBL_ULP());
        test_tol(cexp, cpackl(1400, 0x1p-1074),
                 cpackl(INFINITY, 5.08228858149196559681e+284), DBL_ULP());
        test_tol(cexp, cpackl(900, 0x1.23456789abcdep-1020),
                 cpackl(INFINITY, 7.42156649354218408074e+83), DBL_ULP());
        test_tol(cexp, cpackl(1300, 0x1.23456789abcdep-1020),
                 cpackl(INFINITY, 3.87514844965996756704e+257), DBL_ULP());

        test_tol(cexpf, cpackl(88.73, 0x1p-149),
                 cpackl(INFINITY, 4.80265603e-07), 2 * FLT_ULP());
        test_tol(cexpf, cpackl(90, 0x1p-149),
                 cpackl(INFINITY, 1.7101492622e-06f), 2 * FLT_ULP());
        test_tol(cexpf, cpackl(192, 0x1p-149),
                 cpackl(INFINITY, 3.396809344e+38f), 2 * FLT_ULP());
        test_tol(cexpf, cpackl(120, 0x1.234568p-120),
                 cpackl(INFINITY, 1.1163382522e+16f), 2 * FLT_ULP());
        test_tol(cexpf, cpackl(170, 0x1.234568p-120),
                 cpackl(INFINITY, 5.7878851079e+37f), 2 * FLT_ULP());
}

int
main(int argc, char *argv[])
{

        printf("1..7\n");

        test_zero();
        printf("ok 1 - cexp zero\n");

        test_nan();
        printf("ok 2 - cexp nan\n");

        test_inf();
        printf("ok 3 - cexp inf\n");

        test_reals();
        printf("ok 4 - cexp reals\n");

        test_imaginaries();
        printf("ok 5 - cexp imaginaries\n");

        test_small();
        printf("ok 6 - cexp small\n");

        test_large();
        printf("ok 7 - cexp large\n");

        return (0);
}