/*-
 * Copyright (c) 2008-2013 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-invctrig.c,v 1.1 2013/05/31 00:27:55 svnexp Exp $
 */

/*
 * Tests for casin[h](), cacos[h](), and catan[h]().
 */

#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 OPT_INVALID     (ALL_STD_EXCEPT & ~FE_INVALID)
#define OPT_INEXACT     (ALL_STD_EXCEPT & ~FE_INEXACT)
#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)

#pragma STDC FENV_ACCESS        ON
#pragma STDC CX_LIMITED_RANGE   OFF

/* Flags that determine whether to check the signs of the result. */
#define CS_REAL 1
#define CS_IMAG 2
#define CS_BOTH (CS_REAL | CS_IMAG)

#ifdef  DEBUG
#define debug(...)      printf(__VA_ARGS__)
#else
#define debug(...)      (void)0
#endif

/*
 * 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.
 *
 * 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_p(func, z, result, exceptmask, excepts, checksign) do {    \
        volatile long double complex _d = z;                            \
        debug("  testing %s(%Lg + %Lg I) == %Lg + %Lg I\n", #func,      \
            creall(_d), cimagl(_d), creall(result), cimagl(result));    \
        assert(feclearexcept(FE_ALL_EXCEPT) == 0);                      \
        assert(cfpequal((func)(_d), (result), (checksign)));            \
        assert(((func), fetestexcept(exceptmask) == (excepts)));        \
} while (0)

/*
 * Test within a given tolerance.  The tolerance indicates relative error
 * in ulps.
 */
#define test_p_tol(func, z, result, tol)                        do {    \
        volatile long double complex _d = z;                            \
        debug("  testing %s(%Lg + %Lg I) ~= %Lg + %Lg I\n", #func,      \
            creall(_d), cimagl(_d), creall(result), cimagl(result));    \
        assert(cfpequal_tol((func)(_d), (result), (tol)));              \
} while (0)

/* These wrappers apply the identities f(conj(z)) = conj(f(z)). */
#define test(func, z, result, exceptmask, excepts, checksign)   do {    \
        test_p(func, z, result, exceptmask, excepts, checksign);        \
        test_p(func, conjl(z), conjl(result), exceptmask, excepts, checksign); \
} while (0)
#define test_tol(func, z, result, tol)                          do {    \
        test_p_tol(func, z, result, tol);                               \
        test_p_tol(func, conjl(z), conjl(result), tol);                 \
} while (0)

/* Test the given function in all precisions. */
#define testall(func, x, result, exceptmask, excepts, checksign) do {   \
        test(func, x, result, exceptmask, excepts, checksign);          \
        test(func##f, x, result, exceptmask, excepts, checksign);       \
} while (0)
#define testall_odd(func, x, result, exceptmask, excepts, checksign) do { \
        testall(func, x, result, exceptmask, excepts, checksign);       \
        testall(func, -(x), -result, exceptmask, excepts, checksign);   \
} while (0)
#define testall_even(func, x, result, exceptmask, excepts, checksign) do { \
        testall(func, x, result, exceptmask, excepts, checksign);       \
        testall(func, -(x), result, exceptmask, excepts, checksign);    \
} while (0)

/*
 * Test the given function in all precisions, within a given tolerance.
 * The tolerance is specified in ulps.
 */
#define testall_tol(func, x, result, tol)                          do { \
        test_tol(func, x, result, (tol) * DBL_ULP());                   \
        test_tol(func##f, x, result, (tol) * FLT_ULP());                \
} while (0)
#define testall_odd_tol(func, x, result, tol)                      do { \
        testall_tol(func, x, result, tol);                              \
        testall_tol(func, -(x), -result, tol);                          \
} while (0)
#define testall_even_tol(func, x, result, tol)                     do { \
        testall_tol(func, x, result, tol);                              \
        testall_tol(func, -(x), result, tol);                           \
} while (0)

/* XXX static const long double */
#define pi 3.14159265358979323846264338327950280L
#define c3pi  9.42477796076937971538793014983850839L

/*
 * 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 || y == 0.0)
                return (0);

        /* Hard case: need to check the tolerance. */
        feholdexcept(&env);
        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 & CS_REAL)
                && fpequal(cimag(x), cimag(y), checksign & CS_IMAG));
}

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)
{
        long double complex zero = CMPLXL(0.0, 0.0);

        testall_tol(cacosh, zero, CMPLXL(0.0, pi / 2), 1);
        testall_tol(cacosh, -zero, CMPLXL(0.0, -pi / 2), 1);
        testall_tol(cacos, zero, CMPLXL(pi / 2, -0.0), 1);
        testall_tol(cacos, -zero, CMPLXL(pi / 2, 0.0), 1);

        testall_odd(casinh, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
        testall_odd(casin, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);

        testall_odd(catanh, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
        testall_odd(catan, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
}

/*
 * Tests for NaN inputs.
 */
void
test_nan()
{
        long double complex nan_nan = CMPLXL(NAN, NAN);
        long double complex z;

        /*
         * IN           CACOSH      CACOS       CASINH      CATANH
         * NaN,NaN      NaN,NaN     NaN,NaN     NaN,NaN     NaN,NaN
         * finite,NaN   NaN,NaN*    NaN,NaN*    NaN,NaN*    NaN,NaN*
         * NaN,finite   NaN,NaN*    NaN,NaN*    NaN,NaN*    NaN,NaN*
         * NaN,Inf      Inf,NaN     NaN,-Inf    ?Inf,NaN    ?0,pi/2     
         * +-Inf,NaN    Inf,NaN     NaN,?Inf    +-Inf,NaN   +-0,NaN
         * +-0,NaN      NaN,NaN*    pi/2,NaN    NaN,NaN*    +-0,NaN
         * NaN,0        NaN,NaN*    NaN,NaN*    NaN,0       NaN,NaN*
         *
         *  * = raise invalid
         */
        z = nan_nan;
        testall(cacosh, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
        testall(cacos, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
        testall(casinh, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
        testall(casin, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
        testall(catanh, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
        testall(catan, z, nan_nan, ALL_STD_EXCEPT, 0, 0);

        z = CMPLXL(0.5, NAN);
        testall(cacosh, z, nan_nan, OPT_INVALID, 0, 0);
        testall(cacos, z, nan_nan, OPT_INVALID, 0, 0);
        testall(casinh, z, nan_nan, OPT_INVALID, 0, 0);
        testall(casin, z, nan_nan, OPT_INVALID, 0, 0);
        testall(catanh, z, nan_nan, OPT_INVALID, 0, 0);
        testall(catan, z, nan_nan, OPT_INVALID, 0, 0);

        z = CMPLXL(NAN, 0.5);
        testall(cacosh, z, nan_nan, OPT_INVALID, 0, 0);
        testall(cacos, z, nan_nan, OPT_INVALID, 0, 0);
        testall(casinh, z, nan_nan, OPT_INVALID, 0, 0);
        testall(casin, z, nan_nan, OPT_INVALID, 0, 0);
        testall(catanh, z, nan_nan, OPT_INVALID, 0, 0);
        testall(catan, z, nan_nan, OPT_INVALID, 0, 0);

        z = CMPLXL(NAN, INFINITY);
        testall(cacosh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, CS_REAL);
        testall(cacosh, -z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, CS_REAL);
        testall(cacos, z, CMPLXL(NAN, -INFINITY), ALL_STD_EXCEPT, 0, CS_IMAG);
        testall(casinh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, 0);
        testall(casin, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, CS_IMAG);
        testall_tol(catanh, z, CMPLXL(0.0, pi / 2), 1);
        testall(catan, z, CMPLXL(NAN, 0.0), ALL_STD_EXCEPT, 0, CS_IMAG);

        z = CMPLXL(INFINITY, NAN);
        testall_even(cacosh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0,
                     CS_REAL);
        testall_even(cacos, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, 0);
        testall_odd(casinh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0,
                    CS_REAL);
        testall_odd(casin, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, 0);
        testall_odd(catanh, z, CMPLXL(0.0, NAN), ALL_STD_EXCEPT, 0, CS_REAL);
        testall_odd_tol(catan, z, CMPLXL(pi / 2, 0.0), 1);

        z = CMPLXL(0.0, NAN);
        /* XXX We allow a spurious inexact exception here. */
        testall_even(cacosh, z, nan_nan, OPT_INVALID & ~FE_INEXACT, 0, 0);
        testall_even_tol(cacos, z, CMPLXL(pi / 2, NAN), 1);
        testall_odd(casinh, z, nan_nan, OPT_INVALID, 0, 0);
        testall_odd(casin, z, CMPLXL(0.0, NAN), ALL_STD_EXCEPT, 0, CS_REAL);
        testall_odd(catanh, z, CMPLXL(0.0, NAN), OPT_INVALID, 0, CS_REAL);
        testall_odd(catan, z, nan_nan, OPT_INVALID, 0, 0);

        z = CMPLXL(NAN, 0.0);
        testall(cacosh, z, nan_nan, OPT_INVALID, 0, 0);
        testall(cacos, z, nan_nan, OPT_INVALID, 0, 0);
        testall(casinh, z, CMPLXL(NAN, 0), ALL_STD_EXCEPT, 0, CS_IMAG);
        testall(casin, z, nan_nan, OPT_INVALID, 0, 0);
        testall(catanh, z, nan_nan, OPT_INVALID, 0, CS_IMAG);
        testall(catan, z, CMPLXL(NAN, 0.0), ALL_STD_EXCEPT, 0, 0);
}

void
test_inf(void)
{
        long double complex z;

        /*
         * IN           CACOSH      CACOS       CASINH      CATANH
         * Inf,Inf      Inf,pi/4    pi/4,-Inf   Inf,pi/4    0,pi/2
         * -Inf,Inf     Inf,3pi/4   3pi/4,-Inf  ---         ---
         * Inf,finite   Inf,0       0,-Inf      Inf,0       0,pi/2
         * -Inf,finite  Inf,pi      pi,-Inf     ---         ---
         * finite,Inf   Inf,pi/2    pi/2,-Inf   Inf,pi/2    0,pi/2
         */
        z = CMPLXL(INFINITY, INFINITY);
        testall_tol(cacosh, z, CMPLXL(INFINITY, pi / 4), 1);
        testall_tol(cacosh, -z, CMPLXL(INFINITY, -c3pi / 4), 1);
        testall_tol(cacos, z, CMPLXL(pi / 4, -INFINITY), 1);
        testall_tol(cacos, -z, CMPLXL(c3pi / 4, INFINITY), 1);
        testall_odd_tol(casinh, z, CMPLXL(INFINITY, pi / 4), 1);
        testall_odd_tol(casin, z, CMPLXL(pi / 4, INFINITY), 1);
        testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1);
        testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1);

        z = CMPLXL(INFINITY, 0.5);
        /* XXX We allow a spurious inexact exception here. */
        testall(cacosh, z, CMPLXL(INFINITY, 0), OPT_INEXACT, 0, CS_BOTH);
        testall_tol(cacosh, -z, CMPLXL(INFINITY, -pi), 1);
        testall(cacos, z, CMPLXL(0, -INFINITY), OPT_INEXACT, 0, CS_BOTH);
        testall_tol(cacos, -z, CMPLXL(pi, INFINITY), 1);
        testall_odd(casinh, z, CMPLXL(INFINITY, 0), OPT_INEXACT, 0, CS_BOTH);
        testall_odd_tol(casin, z, CMPLXL(pi / 2, INFINITY), 1);
        testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1);
        testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1);

        z = CMPLXL(0.5, INFINITY);
        testall_tol(cacosh, z, CMPLXL(INFINITY, pi / 2), 1);
        testall_tol(cacosh, -z, CMPLXL(INFINITY, -pi / 2), 1);
        testall_tol(cacos, z, CMPLXL(pi / 2, -INFINITY), 1);
        testall_tol(cacos, -z, CMPLXL(pi / 2, INFINITY), 1);
        testall_odd_tol(casinh, z, CMPLXL(INFINITY, pi / 2), 1);
        /* XXX We allow a spurious inexact exception here. */
        testall_odd(casin, z, CMPLXL(0.0, INFINITY), OPT_INEXACT, 0, CS_BOTH);
        testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1);
        testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1);
}

/* Tests along the real and imaginary axes. */
void
test_axes(void)
{
        static const long double nums[] = {
                -2, -1, -0.5, 0.5, 1, 2
        };
        long double complex z;
        int i;

        for (i = 0; i < sizeof(nums) / sizeof(nums[0]); i++) {
                /* Real axis */
                z = CMPLXL(nums[i], 0.0);
                if (fabs(nums[i]) <= 1) {
                        testall_tol(cacosh, z, CMPLXL(0.0, acos(nums[i])), 1);
                        testall_tol(cacos, z, CMPLXL(acosl(nums[i]), -0.0), 1);
                        testall_tol(casin, z, CMPLXL(asinl(nums[i]), 0.0), 1);
                        testall_tol(catanh, z, CMPLXL(atanh(nums[i]), 0.0), 1);
                } else {
                        testall_tol(cacosh, z,
                                    CMPLXL(acosh(fabs(nums[i])),
                                           (nums[i] < 0) ? pi : 0), 1);
                        testall_tol(cacos, z,
                                    CMPLXL((nums[i] < 0) ? pi : 0,
                                           -acosh(fabs(nums[i]))), 1);
                        testall_tol(casin, z,
                                    CMPLXL(copysign(pi / 2, nums[i]),
                                           acosh(fabs(nums[i]))), 1);
                        testall_tol(catanh, z,
                                    CMPLXL(atanh(1 / nums[i]), pi / 2), 1);
                }
                testall_tol(casinh, z, CMPLXL(asinh(nums[i]), 0.0), 1);
                testall_tol(catan, z, CMPLXL(atan(nums[i]), 0), 1);

                /* TODO: Test the imaginary axis. */
        }
}

void
test_small(void)
{
        /*
         * z =  0.75 + i 0.25
         *     acos(z) = Pi/4 - i ln(2)/2
         *     asin(z) = Pi/4 + i ln(2)/2
         *     atan(z) = atan(4)/2 + i ln(17/9)/4
         */
        static const struct {
                complex long double z;
                complex long double acos_z;
                complex long double asin_z;
                complex long double atan_z;
        } tests[] = {
                { CMPLXL(0.75L, 0.25L),
                  CMPLXL(pi / 4, -0.34657359027997265470861606072908828L),
                  CMPLXL(pi / 4, 0.34657359027997265470861606072908828L),
                  CMPLXL(0.66290883183401623252961960521423782L,
                         0.15899719167999917436476103600701878L) },
        };
        int i;

        for (i = 0; i < sizeof(tests) / sizeof(tests[0]); i++) {
                testall_tol(cacos, tests[i].z, tests[i].acos_z, 2);
                testall_odd_tol(casin, tests[i].z, tests[i].asin_z, 2);
                testall_odd_tol(catan, tests[i].z, tests[i].atan_z, 2);
        }
}

/* Test inputs that might cause overflow in a sloppy implementation. */
void
test_large(void)
{

        /* TODO: Write these tests */
}

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

        printf("1..6\n");

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

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

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

        test_axes();
        printf("ok 4 - invctrig axes\n");

        test_small();
        printf("ok 5 - invctrig small\n");

        test_large();
        printf("ok 6 - invctrig large\n");

        return (0);
}