/*
 * This file is part of the MicroPython project, http://micropython.org/
 *
 * The MIT License (MIT)
 *
 * SPDX-FileCopyrightText: Copyright (c) 2013, 2014 Damien P. George
 * Copyright (c) 2017 Michael McWethy
 *
 * Permission is hereby granted, free of charge, to any person obtaining a copy
 * of this software and associated documentation files (the "Software"), to deal
 * in the Software without restriction, including without limitation the rights
 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 * copies of the Software, and to permit persons to whom the Software is
 * furnished to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice shall be included in
 * all copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
 * THE SOFTWARE.
 */

#include "py/builtin.h"
#include "py/runtime.h"

#if MICROPY_PY_BUILTINS_FLOAT

#include <math.h>

// M_PI is not part of the math.h standard and may not be defined
// And by defining our own we can ensure it uses the correct const format.
#define MP_PI MICROPY_FLOAT_CONST(3.14159265358979323846)


//| """mathematical functions
//|
//| The `math` module provides some basic mathematical functions for
//| working with floating-point numbers.
//|
//| |see_cpython_module| :mod:`cpython:math`.
//| """

STATIC NORETURN void math_error(void) {
    mp_raise_ValueError(translate("math domain error"));
}

#define MATH_FUN_1(py_name, c_name) \
    STATIC mp_obj_t mp_math_##py_name(mp_obj_t x_obj) { return mp_obj_new_float(MICROPY_FLOAT_C_FUN(c_name)(mp_obj_get_float(x_obj))); } \
    STATIC MP_DEFINE_CONST_FUN_OBJ_1(mp_math_##py_name##_obj, mp_math_##py_name);

#define MATH_FUN_2(py_name, c_name) \
    STATIC mp_obj_t mp_math_##py_name(mp_obj_t x_obj, mp_obj_t y_obj) { return mp_obj_new_float(MICROPY_FLOAT_C_FUN(c_name)(mp_obj_get_float(x_obj), mp_obj_get_float(y_obj))); } \
    STATIC MP_DEFINE_CONST_FUN_OBJ_2(mp_math_##py_name##_obj, mp_math_##py_name);

#define MATH_FUN_1_TO_BOOL(py_name, c_name) \
    STATIC mp_obj_t mp_math_##py_name(mp_obj_t x_obj) { return mp_obj_new_bool(c_name(mp_obj_get_float(x_obj))); } \
    STATIC MP_DEFINE_CONST_FUN_OBJ_1(mp_math_##py_name##_obj, mp_math_##py_name);

#define MATH_FUN_1_TO_INT(py_name, c_name) \
    STATIC mp_obj_t mp_math_##py_name(mp_obj_t x_obj) { return mp_obj_new_int_from_float(MICROPY_FLOAT_C_FUN(c_name)(mp_obj_get_float(x_obj))); } \
    STATIC MP_DEFINE_CONST_FUN_OBJ_1(mp_math_##py_name##_obj, mp_math_##py_name);

#define MATH_FUN_1_ERRCOND(py_name, c_name, error_condition) \
    STATIC mp_obj_t mp_math_##py_name(mp_obj_t x_obj) { \
        mp_float_t x = mp_obj_get_float(x_obj); \
        if (error_condition) { \
            math_error(); \
        } \
        return mp_obj_new_float(MICROPY_FLOAT_C_FUN(c_name)(x)); \
    } \
    STATIC MP_DEFINE_CONST_FUN_OBJ_1(mp_math_##py_name##_obj, mp_math_##py_name);

#ifdef MP_NEED_LOG2
// 1.442695040888963407354163704 is 1/_M_LN2
#define log2(x) (log(x) * 1.442695040888963407354163704)
#endif

//| e: float
//| """base of the natural logarithm"""
//|
//| pi: float
//| """the ratio of a circle's circumference to its diameter"""
//|

//| def acos(x: float) -> float:
//|     """Return the inverse cosine of ``x``."""
//|     ...
//|
//| def asin(x: float) -> float:
//|     """Return the inverse sine of ``x``."""
//|     ...
//|
//| def atan(x: float) -> float:
//|     """Return the inverse tangent of ``x``."""
//|     ...
//|
//| def atan2(y: float, x: float) -> float:
//|     """Return the principal value of the inverse tangent of ``y/x``."""
//|     ...
//|
//| def ceil(x: float) -> int:
//|     """Return an integer, being ``x`` rounded towards positive infinity."""
//|     ...
//|
//| def copysign(x: float, y: float) -> float:
//|     """Return ``x`` with the sign of ``y``."""
//|     ...
//|
//| def cos(x: float) -> float:
//|     """Return the cosine of ``x``."""
//|     ...
//|
//| def degrees(x: float) -> float:
//|     """Return radians ``x`` converted to degrees."""
//|     ...
//|
//| def exp(x: float) -> float:
//|     """Return the exponential of ``x``."""
//|     ...
//|
//| def fabs(x: float) -> float:
//|     """Return the absolute value of ``x``."""
//|     ...
//|
//| def floor(x: float) -> int:
//|     """Return an integer, being ``x`` rounded towards negative infinity."""
//|     ...
//|
//| def fmod(x: float, y: float) -> int:
//|     """Return the remainder of ``x/y``."""
//|     ...
//|
//| def frexp(x: float) -> Tuple[int, int]:
//|     """Decomposes a floating-point number into its mantissa and exponent.
//|     The returned value is the tuple ``(m, e)`` such that ``x == m * 2**e``
//|     exactly.  If ``x == 0`` then the function returns ``(0.0, 0)``, otherwise
//|     the relation ``0.5 <= abs(m) < 1`` holds."""
//|     ...
//|
//| def isfinite(x: float) -> bool:
//|     """Return ``True`` if ``x`` is finite."""
//|     ...
//|
//| def isinf(x: float) -> bool:
//|     """Return ``True`` if ``x`` is infinite."""
//|     ...
//|
//| def isnan(x: float) -> bool:
//|     """Return ``True`` if ``x`` is not-a-number"""
//|     ...
//|
//| def ldexp(x: float, exp: float) -> float:
//|     """Return ``x * (2**exp)``."""
//|     ...
//|
//| def log(x: float, base: float = e) -> float:
//|     """Return the logarithm of x to the given base. If base is not specified,
//|     returns the natural logarithm (base e) of x"""
//|     ...
//|
//| def modf(x: float) -> Tuple[float, float]:
//|     """Return a tuple of two floats, being the fractional and integral parts of
//|     ``x``.  Both return values have the same sign as ``x``."""
//|     ...
//|
//| def pow(x: float, y: float) -> float:
//|     """Returns ``x`` to the power of ``y``."""
//|
//| def radians(x: float) -> float:
//|     """Return degrees ``x`` converted to radians."""
//|
//| def sin(x: float) -> float:
//|     """Return the sine of ``x``."""
//|     ...
//|
//| def sqrt(x: float) -> float:
//|     """Returns the square root of ``x``."""
//|     ...
//|
//| def tan(x: float) -> float:
//|     """Return the tangent of ``x``."""
//|     ...
//|
//| def trunc(x: float) -> int:
//|     """Return an integer, being ``x`` rounded towards 0."""
//|     ...
//|
MATH_FUN_1_ERRCOND(sqrt, sqrt, (x < (mp_float_t)0.0))

MATH_FUN_2(pow, pow)

MATH_FUN_1(exp, exp)
#if MICROPY_PY_MATH_SPECIAL_FUNCTIONS
//| def expm1(x: float) -> float:
//|     """Return ``exp(x) - 1``.
//|
//|     May not be available on some boards.
//|     """
//|     ...
//|
MATH_FUN_1(expm1, expm1)

//| def log2(x: float) -> float:
//|     """Return the base-2 logarithm of ``x``.
//|
//|     May not be available on some boards.
//|     """
//|     ...
//|
MATH_FUN_1_ERRCOND(log2, log2, (x <= (mp_float_t)0.0))

//| def log10(x: float) -> float:
//|     """Return the base-10 logarithm of ``x``.
//|
//|     May not be available on some boards.
//|     """
//|     ...
//|
MATH_FUN_1_ERRCOND(log10, log10, (x <= (mp_float_t)0.0))

//| def cosh(x: float) -> float:
//|     """Return the hyperbolic cosine of ``x``.
//|
//|     May not be available on some boards.
//|     """
//|     ...
//|
MATH_FUN_1(cosh, cosh)

//| def sinh(x: float) -> float:
//|     """Return the hyperbolic sine of ``x``.
//|
//|     May not be available on some boards.
//|     """
//|     ...
//|
MATH_FUN_1(sinh, sinh)

//| def tanh(x: float) -> float:
//|     """Return the hyperbolic tangent of ``x``.
//|
//|     May not be available on some boards.
//|     """
//|     ...
//|
MATH_FUN_1(tanh, tanh)

//| def acosh(x: float) -> float:
//|     """Return the inverse hyperbolic cosine of ``x``.
//|
//|     May not be available on some boards.
//|     """
//|     ...
//|
MATH_FUN_1(acosh, acosh)

//| def asinh(x: float) -> float:
//|     """Return the inverse hyperbolic sine of ``x``.
//|
//|     May not be available on some boards.
//|     """
//|     ...
//|
MATH_FUN_1(asinh, asinh)

//| def atanh(x: float) -> float:
//|     """Return the inverse hyperbolic tangent of ``x``.
//|
//|     May not be available on some boards.
//|     """
//|     ...
//|
MATH_FUN_1(atanh, atanh)
#endif

MATH_FUN_1(cos, cos)

MATH_FUN_1(sin, sin)

MATH_FUN_1(tan, tan)

MATH_FUN_1(acos, acos)

MATH_FUN_1(asin, asin)

MATH_FUN_1(atan, atan)

MATH_FUN_2(atan2, atan2)

MATH_FUN_1_TO_INT(ceil, ceil)

MATH_FUN_2(copysign, copysign)

MATH_FUN_1(fabs, fabs)

MATH_FUN_1_TO_INT(floor, floor) // TODO: delegate to x.__floor__() if x is not a float

MATH_FUN_2(fmod, fmod)

MATH_FUN_1_TO_BOOL(isfinite, isfinite)

MATH_FUN_1_TO_BOOL(isinf, isinf)

MATH_FUN_1_TO_BOOL(isnan, isnan)

MATH_FUN_1_TO_INT(trunc, trunc)

MATH_FUN_2(ldexp, ldexp)
#if MICROPY_PY_MATH_SPECIAL_FUNCTIONS

//| def erf(x: float) -> float:
//|     """Return the error function of ``x``.
//|
//|     May not be available on some boards.
//|     """
//|     ...
//|
MATH_FUN_1(erf, erf)

//| def erfc(x: float) -> float:
//|     """Return the complementary error function of ``x``.
//|
//|     May not be available on some boards.
//|     """
//|     ...
//|
MATH_FUN_1(erfc, erfc)

//| def gamma(x: float) -> float:
//|     """Return the gamma function of ``x``.
//|
//|     May not be available on some boards.
//|     """
//|     ...
//|
MATH_FUN_1(gamma, tgamma)

//| def lgamma(x: float) -> float:
//|     """Return the natural logarithm of the gamma function of ``x``.
//|
//|     May not be available on some boards.
//|     """
//|     ...
//|
MATH_FUN_1(lgamma, lgamma)
#endif
// TODO: factorial, fsum

// Function that takes a variable number of arguments

// log(x[, base])
STATIC mp_obj_t mp_math_log(size_t n_args, const mp_obj_t *args) {
    mp_float_t x = mp_obj_get_float(args[0]);
    if (x <= (mp_float_t)0.0) {
        math_error();
    }
    mp_float_t l = MICROPY_FLOAT_C_FUN(log)(x);
    if (n_args == 1) {
        return mp_obj_new_float(l);
    } else {
        mp_float_t base = mp_obj_get_float(args[1]);
        if (base <= (mp_float_t)0.0) {
            math_error();
// Turn off warning when comparing exactly with integral value 1.0
            #pragma GCC diagnostic push
            #pragma GCC diagnostic ignored "-Wfloat-equal"
        } else if (base == (mp_float_t)1.0) {
            #pragma GCC diagnostic pop
            math_error();
        }
        return mp_obj_new_float(l / MICROPY_FLOAT_C_FUN(log)(base));
    }
}
STATIC MP_DEFINE_CONST_FUN_OBJ_VAR_BETWEEN(mp_math_log_obj, 1, 2, mp_math_log);

// Functions that return a tuple


STATIC mp_obj_t mp_math_frexp(mp_obj_t x_obj) {
    int int_exponent = 0;
    mp_float_t significand = MICROPY_FLOAT_C_FUN(frexp)(mp_obj_get_float(x_obj), &int_exponent);
    mp_obj_t tuple[2];
    tuple[0] = mp_obj_new_float(significand);
    tuple[1] = mp_obj_new_int(int_exponent);
    return mp_obj_new_tuple(2, tuple);
}
STATIC MP_DEFINE_CONST_FUN_OBJ_1(mp_math_frexp_obj, mp_math_frexp);

STATIC mp_obj_t mp_math_modf(mp_obj_t x_obj) {
    mp_float_t int_part = 0.0;
    mp_float_t fractional_part = MICROPY_FLOAT_C_FUN(modf)(mp_obj_get_float(x_obj), &int_part);
    mp_obj_t tuple[2];
    tuple[0] = mp_obj_new_float(fractional_part);
    tuple[1] = mp_obj_new_float(int_part);
    return mp_obj_new_tuple(2, tuple);
}
STATIC MP_DEFINE_CONST_FUN_OBJ_1(mp_math_modf_obj, mp_math_modf);

// Angular conversions


STATIC mp_obj_t mp_math_radians(mp_obj_t x_obj) {
    return mp_obj_new_float(mp_obj_get_float(x_obj) * (MP_PI / MICROPY_FLOAT_CONST(180.0)));
}
STATIC MP_DEFINE_CONST_FUN_OBJ_1(mp_math_radians_obj, mp_math_radians);


STATIC mp_obj_t mp_math_degrees(mp_obj_t x_obj) {
    return mp_obj_new_float(mp_obj_get_float(x_obj) * (MICROPY_FLOAT_CONST(180.0) / MP_PI));
}
STATIC MP_DEFINE_CONST_FUN_OBJ_1(mp_math_degrees_obj, mp_math_degrees);

STATIC const mp_rom_map_elem_t mp_module_math_globals_table[] = {
    { MP_ROM_QSTR(MP_QSTR___name__), MP_ROM_QSTR(MP_QSTR_math) },
    { MP_ROM_QSTR(MP_QSTR_e), mp_const_float_e },
    { MP_ROM_QSTR(MP_QSTR_pi), mp_const_float_pi },
    { MP_ROM_QSTR(MP_QSTR_sqrt), MP_ROM_PTR(&mp_math_sqrt_obj) },
    { MP_ROM_QSTR(MP_QSTR_pow), MP_ROM_PTR(&mp_math_pow_obj) },
    { MP_ROM_QSTR(MP_QSTR_exp), MP_ROM_PTR(&mp_math_exp_obj) },
    #if MICROPY_PY_MATH_SPECIAL_FUNCTIONS
    { MP_ROM_QSTR(MP_QSTR_expm1), MP_ROM_PTR(&mp_math_expm1_obj) },
    #endif
    { MP_ROM_QSTR(MP_QSTR_log), MP_ROM_PTR(&mp_math_log_obj) },
    #if MICROPY_PY_MATH_SPECIAL_FUNCTIONS
    { MP_ROM_QSTR(MP_QSTR_log2), MP_ROM_PTR(&mp_math_log2_obj) },
    { MP_ROM_QSTR(MP_QSTR_log10), MP_ROM_PTR(&mp_math_log10_obj) },
    { MP_ROM_QSTR(MP_QSTR_cosh), MP_ROM_PTR(&mp_math_cosh_obj) },
    { MP_ROM_QSTR(MP_QSTR_sinh), MP_ROM_PTR(&mp_math_sinh_obj) },
    { MP_ROM_QSTR(MP_QSTR_tanh), MP_ROM_PTR(&mp_math_tanh_obj) },
    { MP_ROM_QSTR(MP_QSTR_acosh), MP_ROM_PTR(&mp_math_acosh_obj) },
    { MP_ROM_QSTR(MP_QSTR_asinh), MP_ROM_PTR(&mp_math_asinh_obj) },
    { MP_ROM_QSTR(MP_QSTR_atanh), MP_ROM_PTR(&mp_math_atanh_obj) },
    #endif
    { MP_ROM_QSTR(MP_QSTR_cos), MP_ROM_PTR(&mp_math_cos_obj) },
    { MP_ROM_QSTR(MP_QSTR_sin), MP_ROM_PTR(&mp_math_sin_obj) },
    { MP_ROM_QSTR(MP_QSTR_tan), MP_ROM_PTR(&mp_math_tan_obj) },
    { MP_ROM_QSTR(MP_QSTR_acos), MP_ROM_PTR(&mp_math_acos_obj) },
    { MP_ROM_QSTR(MP_QSTR_asin), MP_ROM_PTR(&mp_math_asin_obj) },
    { MP_ROM_QSTR(MP_QSTR_atan), MP_ROM_PTR(&mp_math_atan_obj) },
    { MP_ROM_QSTR(MP_QSTR_atan2), MP_ROM_PTR(&mp_math_atan2_obj) },
    { MP_ROM_QSTR(MP_QSTR_ceil), MP_ROM_PTR(&mp_math_ceil_obj) },
    { MP_ROM_QSTR(MP_QSTR_copysign), MP_ROM_PTR(&mp_math_copysign_obj) },
    { MP_ROM_QSTR(MP_QSTR_fabs), MP_ROM_PTR(&mp_math_fabs_obj) },
    { MP_ROM_QSTR(MP_QSTR_floor), MP_ROM_PTR(&mp_math_floor_obj) },
    { MP_ROM_QSTR(MP_QSTR_fmod), MP_ROM_PTR(&mp_math_fmod_obj) },
    { MP_ROM_QSTR(MP_QSTR_frexp), MP_ROM_PTR(&mp_math_frexp_obj) },
    { MP_ROM_QSTR(MP_QSTR_ldexp), MP_ROM_PTR(&mp_math_ldexp_obj) },
    { MP_ROM_QSTR(MP_QSTR_modf), MP_ROM_PTR(&mp_math_modf_obj) },
    { MP_ROM_QSTR(MP_QSTR_isfinite), MP_ROM_PTR(&mp_math_isfinite_obj) },
    { MP_ROM_QSTR(MP_QSTR_isinf), MP_ROM_PTR(&mp_math_isinf_obj) },
    { MP_ROM_QSTR(MP_QSTR_isnan), MP_ROM_PTR(&mp_math_isnan_obj) },
    { MP_ROM_QSTR(MP_QSTR_trunc), MP_ROM_PTR(&mp_math_trunc_obj) },
    { MP_ROM_QSTR(MP_QSTR_radians), MP_ROM_PTR(&mp_math_radians_obj) },
    { MP_ROM_QSTR(MP_QSTR_degrees), MP_ROM_PTR(&mp_math_degrees_obj) },
    #if MICROPY_PY_MATH_SPECIAL_FUNCTIONS
    { MP_ROM_QSTR(MP_QSTR_erf), MP_ROM_PTR(&mp_math_erf_obj) },
    { MP_ROM_QSTR(MP_QSTR_erfc), MP_ROM_PTR(&mp_math_erfc_obj) },
    { MP_ROM_QSTR(MP_QSTR_gamma), MP_ROM_PTR(&mp_math_gamma_obj) },
    { MP_ROM_QSTR(MP_QSTR_lgamma), MP_ROM_PTR(&mp_math_lgamma_obj) },
    #endif
};

STATIC MP_DEFINE_CONST_DICT(mp_module_math_globals, mp_module_math_globals_table);

const mp_obj_module_t math_module = {
    .base = { &mp_type_module },
    .globals = (mp_obj_dict_t *)&mp_module_math_globals,
};

MP_REGISTER_MODULE(MP_QSTR_math, math_module);

#endif // MICROPY_PY_BUILTINS_FLOAT