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#include 

#ifndef M_E

 #define M_E     2.7182818284590452354

#endif

#ifndef M_PI

 #define M_PI    3.14159265358979323846

#endif

#include 

/*

 * template for tinypy math functions

 * with one parameter.

 *

 * @cfunc is the coresponding function name in C

 * math library.

 */

#define TP_MATH_FUNC1(cfunc)                        \

    static tp_obj math_##cfunc(TP) {                \

        double x = TP_NUM();                        \

        double r = 0.0;                             \

                                                    \

        errno = 0;                                  \

        r = cfunc(x);                               \

        if (errno == EDOM || errno == ERANGE) {     \

            tp_raise(tp_None, "%s(x): x=%f, "          \

                    "out of range", __func__, x);   \

        }                                           \

                                                    \

        return (tp_number(r));                      \

    }

/*

 * template for tinypy math functions

 * with two parameters.

 *

 * @cfunc is the coresponding function name in C

 * math library.

 */

#define TP_MATH_FUNC2(cfunc)                        \

    static tp_obj math_##cfunc(TP) {                \

        double x = TP_NUM();                        \

        double y = TP_NUM();                        \

        double r = 0.0;                             \

                                                    \

        errno = 0;                                  \

        r = cfunc(x, y);                            \

        if (errno == EDOM || errno == ERANGE) {     \

            tp_raise(tp_None, "%s(x, y): x=%f,y=%f "   \

                    "out of range", __func__, x, y);\

        }                                           \

                                                    \

        return (tp_number(r));                      \

    }

/*

 * PI definition: 3.1415926535897931

 */

static tp_obj   math_pi;

/*

 * E definition: 2.7182818284590451

 */

static tp_obj   math_e;

/*

 * acos(x)

 *

 * return arc cosine of x, return value is measured in radians.

 * if x falls out -1 to 1, raise out-of-range exception.

 */

TP_MATH_FUNC1(acos)

/*

 * asin(x)

 *

 * return arc sine of x, measured in radians, actually [-PI/2, PI/2]

 * if x falls out of -1 to 1, raise out-of-range exception

 */

TP_MATH_FUNC1(asin)

/*

 * atan(x)

 *

 * return arc tangent of x, measured in radians,

 */

TP_MATH_FUNC1(atan)

/*

 * atan2(x, y)

 *

 * return arc tangent of x/y, measured in radians.

 * unlike atan(x/y), both the signs of x and y

 * are considered to determine the quaderant of

 * the result.

 */

TP_MATH_FUNC2(atan2)

/*

 * ceil(x)

 *

 * return the ceiling of x, i.e, the smallest

 * integer >= x.

 */

TP_MATH_FUNC1(ceil)

/*

 * cos(x)

 *

 * return cosine of x. x is measured in radians.

 */

TP_MATH_FUNC1(cos)

/*

 * cosh(x)

 *

 * return hyperbolic cosine of x.

 */

TP_MATH_FUNC1(cosh)

/*

 * degrees(x)

 *

 * converts angle x from radians to degrees.

 * NOTE: this function is introduced by python,

 * so we cannot wrap it directly in TP_MATH_FUNC1(),

 * here the solution is defining a new

 * C function - degrees().

 */

static const double degToRad =

                3.141592653589793238462643383 / 180.0;

static double degrees(double x)

{

    return (x / degToRad);

}

TP_MATH_FUNC1(degrees)

/*

 * exp(x)

 *

 * return the value e raised to power of x.

 * e is the base of natural logarithms.

 */

TP_MATH_FUNC1(exp)

/*

 * fabs(x)

 *

 * return the absolute value of x.

 */

TP_MATH_FUNC1(fabs)

/*

 * floor(x)

 *

 * return the floor of x, i.e, the largest integer <= x

 */

TP_MATH_FUNC1(floor)

/*

 * fmod(x, y)

 *

 * return the remainder of dividing x by y. that is,

 * return x - n * y, where n is the quotient of x/y.

 * NOTE: this function relies on the underlying platform.

 */

TP_MATH_FUNC2(fmod)

/*

 * frexp(x)

 *

 * return a pair (r, y), which satisfies:

 * x = r * (2 ** y), and r is normalized fraction

 * which is laid between 1/2 <= abs(r) < 1.

 * if x = 0, the (r, y) = (0, 0).

 */

static tp_obj math_frexp(TP) {

    double x = TP_NUM();

    int    y = 0;

    double r = 0.0;

    tp_obj rList = tp_list(tp);

    errno = 0;

    r = frexp(x, &y);

    if (errno == EDOM || errno == ERANGE) {

        tp_raise(tp_None, "%s(x): x=%f, "

                "out of range", __func__, x);

    }

    _tp_list_append(tp, rList.list.val, tp_number(r));

    _tp_list_append(tp, rList.list.val, tp_number((tp_num)y));

    return (rList);

}

/*

 * hypot(x, y)

 *

 * return Euclidean distance, namely,

 * sqrt(x*x + y*y)

 */

TP_MATH_FUNC2(hypot)

/*

 * ldexp(x, y)

 *

 * return the result of multiplying x by 2

 * raised to y.

 */

TP_MATH_FUNC2(ldexp)

/*

 * log(x, [base])

 *

 * return logarithm of x to given base. If base is

 * not given, return the natural logarithm of x.

 * Note: common logarithm(log10) is used to compute

 * the denominator and numerator. based on fomula:

 * log(x, base) = log10(x) / log10(base).

 */

static tp_obj math_log(TP) {

    double x = TP_NUM();

    tp_obj b = TP_DEFAULT(tp_None);

    double y = 0.0;

    double den = 0.0;   /* denominator */

    double num = 0.0;   /* numinator */

    double r = 0.0;     /* result */

    if (b.type == TP_NONE)

        y = M_E;

    else if (b.type == TP_NUMBER)

        y = (double)b.number.val;

    else

        tp_raise(tp_None, "%s(x, [base]): base invalid", __func__);

    errno = 0;

    num = log10(x);

    if (errno == EDOM || errno == ERANGE)

        goto excep;

    errno = 0;

    den = log10(y);

    if (errno == EDOM || errno == ERANGE)

        goto excep;

    r = num / den;

    return (tp_number(r));

excep:

    tp_raise(tp_None, "%s(x, y): x=%f,y=%f "

            "out of range", __func__, x, y);

}

/*

 * log10(x)

 *

 * return 10-based logarithm of x.

 */

TP_MATH_FUNC1(log10)

/*

 * modf(x)

 *

 * return a pair (r, y). r is the integral part of

 * x and y is the fractional part of x, both holds

 * the same sign as x.

 */

static tp_obj math_modf(TP) {

    double x = TP_NUM();

    double y = 0.0;

    double r = 0.0;

    tp_obj rList = tp_list(tp);

    errno = 0;

    r = modf(x, &y);

    if (errno == EDOM || errno == ERANGE) {

        tp_raise(tp_None, "%s(x): x=%f, "

                "out of range", __func__, x);

    }

    _tp_list_append(tp, rList.list.val, tp_number(r));

    _tp_list_append(tp, rList.list.val, tp_number(y));

    return (rList);

}

/*

 * pow(x, y)

 *

 * return value of x raised to y. equivalence of x ** y.

 * NOTE: conventionally, tp_pow() is the implementation

 * of builtin function pow(); whilst, math_pow() is an

 * alternative in math module.

 */

static tp_obj math_pow(TP) {

    double x = TP_NUM();

    double y = TP_NUM();

    double r = 0.0;

    errno = 0;

    r = pow(x, y);

    if (errno == EDOM || errno == ERANGE) {

        tp_raise(tp_None, "%s(x, y): x=%f,y=%f "

                "out of range", __func__, x, y);

    }

    return (tp_number(r));

}

/*

 * radians(x)

 *

 * converts angle x from degrees to radians.

 * NOTE: this function is introduced by python,

 * adopt same solution as degrees(x).

 */

static double radians(double x)

{

    return (x * degToRad);

}

TP_MATH_FUNC1(radians)

/*

 * sin(x)

 *

 * return sine of x, x is measured in radians.

 */

TP_MATH_FUNC1(sin)

/*

 * sinh(x)

 *

 * return hyperbolic sine of x.

 * mathematically, sinh(x) = (exp(x) - exp(-x)) / 2.

 */

TP_MATH_FUNC1(sinh)

/*

 * sqrt(x)

 *

 * return square root of x.

 * if x is negtive, raise out-of-range exception.

 */

TP_MATH_FUNC1(sqrt)

/*

 * tan(x)

 *

 * return tangent of x, x is measured in radians.

 */

TP_MATH_FUNC1(tan)

/*

 * tanh(x)

 *

 * return hyperbolic tangent of x.

 * mathematically, tanh(x) = sinh(x) / cosh(x).

 */

TP_MATH_FUNC1(tanh)