py/modmath.c

/*
 * This file is part of the MicroPython project, http://micropython.org/
 *
 * The MIT License (MIT)
 *
 * Copyright (c) 2013-2017 Damien P. George
 *
 * 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 && MICROPY_PY_MATH

#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)
#define MP_PI_4 MICROPY_FLOAT_CONST(0.78539816339744830962)
#define MP_3_PI_4 MICROPY_FLOAT_CONST(2.35619449019234492885)

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

STATIC mp_obj_t math_generic_1(mp_obj_t x_obj, mp_float_t (*f)(mp_float_t)) {
    mp_float_t x = mp_obj_get_float(x_obj);
    mp_float_t ans = f(x);
    if ((isnan(ans) && !isnan(x)) || (isinf(ans) && !isinf(x))) {
        math_error();
    }
    return mp_obj_new_float(ans);
}

STATIC mp_obj_t math_generic_2(mp_obj_t x_obj, mp_obj_t y_obj, mp_float_t (*f)(mp_float_t, mp_float_t)) {
    mp_float_t x = mp_obj_get_float(x_obj);
    mp_float_t y = mp_obj_get_float(y_obj);
    mp_float_t ans = f(x, y);
    if ((isnan(ans) && !isnan(x) && !isnan(y)) || (isinf(ans) && !isinf(x))) {
        math_error();
    }
    return mp_obj_new_float(ans);
}

#define MATH_FUN_1(py_name, c_name) \
    STATIC mp_obj_t mp_math_##py_name(mp_obj_t x_obj) { \
        return math_generic_1(x_obj, MICROPY_FLOAT_C_FUN(c_name)); \
    } \
    STATIC MP_DEFINE_CONST_FUN_OBJ_1(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_2(py_name, c_name) \
    STATIC mp_obj_t mp_math_##py_name(mp_obj_t x_obj, mp_obj_t y_obj) { \
        return math_generic_2(x_obj, y_obj, MICROPY_FLOAT_C_FUN(c_name)); \
    } \
    STATIC MP_DEFINE_CONST_FUN_OBJ_2(mp_math_##py_name##_obj, mp_math_##py_name);

#define MATH_FUN_2_FLT_INT(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_int(y_obj))); \
    } \
    STATIC MP_DEFINE_CONST_FUN_OBJ_2(mp_math_##py_name##_obj, mp_math_##py_name);

#if MP_NEED_LOG2
#undef log2
#undef log2f
// 1.442695040888963407354163704 is 1/_M_LN2
mp_float_t MICROPY_FLOAT_C_FUN(log2)(mp_float_t x) {
    return MICROPY_FLOAT_C_FUN(log)(x) * MICROPY_FLOAT_CONST(1.442695040888963407354163704);
}
#endif

// sqrt(x): returns the square root of x
MATH_FUN_1(sqrt, sqrt)
// pow(x, y): returns x to the power of y
#if MICROPY_PY_MATH_POW_FIX_NAN
mp_float_t pow_func(mp_float_t x, mp_float_t y) {
    // pow(base, 0) returns 1 for any base, even when base is NaN
    // pow(+1, exponent) returns 1 for any exponent, even when exponent is NaN
    if (x == MICROPY_FLOAT_CONST(1.0) || y == MICROPY_FLOAT_CONST(0.0)) {
        return MICROPY_FLOAT_CONST(1.0);
    }
    return MICROPY_FLOAT_C_FUN(pow)(x, y);
}
MATH_FUN_2(pow, pow_func)
#else
MATH_FUN_2(pow, pow)
#endif
// exp(x)
MATH_FUN_1(exp, exp)
#if MICROPY_PY_MATH_SPECIAL_FUNCTIONS
// expm1(x)
MATH_FUN_1(expm1, expm1)
// log2(x)
MATH_FUN_1(log2, log2)
// log10(x)
MATH_FUN_1(log10, log10)
// cosh(x)
MATH_FUN_1(cosh, cosh)
// sinh(x)
MATH_FUN_1(sinh, sinh)
// tanh(x)
MATH_FUN_1(tanh, tanh)
// acosh(x)
MATH_FUN_1(acosh, acosh)
// asinh(x)
MATH_FUN_1(asinh, asinh)
// atanh(x)
MATH_FUN_1(atanh, atanh)
#endif
// cos(x)
MATH_FUN_1(cos, cos)
// sin(x)
MATH_FUN_1(sin, sin)
// tan(x)
MATH_FUN_1(tan, tan)
// acos(x)
MATH_FUN_1(acos, acos)
// asin(x)
MATH_FUN_1(asin, asin)
// atan(x)
MATH_FUN_1(atan, atan)
// atan2(y, x)
#if MICROPY_PY_MATH_ATAN2_FIX_INFNAN
mp_float_t atan2_func(mp_float_t x, mp_float_t y) {
    if (isinf(x) && isinf(y)) {
        return copysign(y < 0 ? MP_3_PI_4 : MP_PI_4, x);
    }
    return atan2(x, y);
}
MATH_FUN_2(atan2, atan2_func)
#else
MATH_FUN_2(atan2, atan2)
#endif
// ceil(x)
MATH_FUN_1_TO_INT(ceil, ceil)
// copysign(x, y)
STATIC mp_float_t MICROPY_FLOAT_C_FUN(copysign_func)(mp_float_t x, mp_float_t y) {
    return MICROPY_FLOAT_C_FUN(copysign)(x, y);
}
MATH_FUN_2(copysign, copysign_func)
// fabs(x)
STATIC mp_float_t MICROPY_FLOAT_C_FUN(fabs_func)(mp_float_t x) {
    return MICROPY_FLOAT_C_FUN(fabs)(x);
}
MATH_FUN_1(fabs, fabs_func)
// floor(x)
MATH_FUN_1_TO_INT(floor, floor) // TODO: delegate to x.__floor__() if x is not a float
// fmod(x, y)
#if MICROPY_PY_MATH_FMOD_FIX_INFNAN
mp_float_t fmod_func(mp_float_t x, mp_float_t y) {
    return (!isinf(x) && isinf(y)) ? x : fmod(x, y);
}
MATH_FUN_2(fmod, fmod_func)
#else
MATH_FUN_2(fmod, fmod)
#endif
// isfinite(x)
MATH_FUN_1_TO_BOOL(isfinite, isfinite)
// isinf(x)
MATH_FUN_1_TO_BOOL(isinf, isinf)
// isnan(x)
MATH_FUN_1_TO_BOOL(isnan, isnan)
// trunc(x)
MATH_FUN_1_TO_INT(trunc, trunc)
// ldexp(x, exp)
MATH_FUN_2_FLT_INT(ldexp, ldexp)
#if MICROPY_PY_MATH_SPECIAL_FUNCTIONS
// erf(x): return the error function of x
MATH_FUN_1(erf, erf)
// erfc(x): return the complementary error function of x
MATH_FUN_1(erfc, erfc)
// gamma(x): return the gamma function of x
MATH_FUN_1(gamma, tgamma)
// lgamma(x): return the natural logarithm of the gamma function of x
MATH_FUN_1(lgamma, lgamma)
#endif
// TODO: fsum

#if MICROPY_PY_MATH_ISCLOSE
STATIC mp_obj_t mp_math_isclose(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) {
    enum { ARG_rel_tol, ARG_abs_tol };
    static const mp_arg_t allowed_args[] = {
        {MP_QSTR_rel_tol, MP_ARG_KW_ONLY | MP_ARG_OBJ, {.u_obj = MP_OBJ_NULL}},
        {MP_QSTR_abs_tol, MP_ARG_KW_ONLY | MP_ARG_OBJ, {.u_obj = MP_OBJ_NEW_SMALL_INT(0)}},
    };
    mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)];
    mp_arg_parse_all(n_args - 2, pos_args + 2, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args);
    const mp_float_t a = mp_obj_get_float(pos_args[0]);
    const mp_float_t b = mp_obj_get_float(pos_args[1]);
    const mp_float_t rel_tol = args[ARG_rel_tol].u_obj == MP_OBJ_NULL
        ? (mp_float_t)1e-9 : mp_obj_get_float(args[ARG_rel_tol].u_obj);
    const mp_float_t abs_tol = mp_obj_get_float(args[ARG_abs_tol].u_obj);
    if (rel_tol < (mp_float_t)0.0 || abs_tol < (mp_float_t)0.0) {
        math_error();
    }
    if (a == b) {
        return mp_const_true;
    }
    const mp_float_t difference = MICROPY_FLOAT_C_FUN(fabs)(a - b);
    if (isinf(difference)) { // Either a or b is inf
        return mp_const_false;
    }
    if ((difference <= abs_tol) ||
        (difference <= MICROPY_FLOAT_C_FUN(fabs)(rel_tol * a)) ||
        (difference <= MICROPY_FLOAT_C_FUN(fabs)(rel_tol * b))) {
        return mp_const_true;
    }
    return mp_const_false;
}
MP_DEFINE_CONST_FUN_OBJ_KW(mp_math_isclose_obj, 2, mp_math_isclose);
#endif

// 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();
        } else if (base == (mp_float_t)1.0) {
            mp_raise_msg(&mp_type_ZeroDivisionError, MP_ERROR_TEXT("divide by zero"));
        }
        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

// frexp(x): converts a floating-point number to fractional and integral components
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);

// modf(x)
STATIC mp_obj_t mp_math_modf(mp_obj_t x_obj) {
    mp_float_t int_part = 0.0;
    mp_float_t x = mp_obj_get_float(x_obj);
    mp_float_t fractional_part = MICROPY_FLOAT_C_FUN(modf)(x, &int_part);
    #if MICROPY_PY_MATH_MODF_FIX_NEGZERO
    if (fractional_part == MICROPY_FLOAT_CONST(0.0)) {
        fractional_part = copysign(fractional_part, x);
    }
    #endif
    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

// radians(x)
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);

// degrees(x)
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);

#if MICROPY_PY_MATH_FACTORIAL

#if MICROPY_OPT_MATH_FACTORIAL

// factorial(x): slightly efficient recursive implementation
STATIC mp_obj_t mp_math_factorial_inner(mp_uint_t start, mp_uint_t end) {
    if (start == end) {
        return mp_obj_new_int(start);
    } else if (end - start == 1) {
        return mp_binary_op(MP_BINARY_OP_MULTIPLY, MP_OBJ_NEW_SMALL_INT(start), MP_OBJ_NEW_SMALL_INT(end));
    } else if (end - start == 2) {
        mp_obj_t left = MP_OBJ_NEW_SMALL_INT(start);
        mp_obj_t middle = MP_OBJ_NEW_SMALL_INT(start + 1);
        mp_obj_t right = MP_OBJ_NEW_SMALL_INT(end);
        mp_obj_t tmp = mp_binary_op(MP_BINARY_OP_MULTIPLY, left, middle);
        return mp_binary_op(MP_BINARY_OP_MULTIPLY, tmp, right);
    } else {
        mp_uint_t middle = start + ((end - start) >> 1);
        mp_obj_t left = mp_math_factorial_inner(start, middle);
        mp_obj_t right = mp_math_factorial_inner(middle + 1, end);
        return mp_binary_op(MP_BINARY_OP_MULTIPLY, left, right);
    }
}
STATIC mp_obj_t mp_math_factorial(mp_obj_t x_obj) {
    mp_int_t max = mp_obj_get_int(x_obj);
    if (max < 0) {
        mp_raise_ValueError(MP_ERROR_TEXT("negative factorial"));
    } else if (max == 0) {
        return MP_OBJ_NEW_SMALL_INT(1);
    }
    return mp_math_factorial_inner(1, max);
}

#else

// factorial(x): squared difference implementation
// based on http://www.luschny.de/math/factorial/index.html
STATIC mp_obj_t mp_math_factorial(mp_obj_t x_obj) {
    mp_int_t max = mp_obj_get_int(x_obj);
    if (max < 0) {
        mp_raise_ValueError(MP_ERROR_TEXT("negative factorial"));
    } else if (max <= 1) {
        return MP_OBJ_NEW_SMALL_INT(1);
    }
    mp_int_t h = max >> 1;
    mp_int_t q = h * h;
    mp_int_t r = q << 1;
    if (max & 1) {
        r *= max;
    }
    mp_obj_t prod = MP_OBJ_NEW_SMALL_INT(r);
    for (mp_int_t num = 1; num < max - 2; num += 2) {
        q -= num;
        prod = mp_binary_op(MP_BINARY_OP_MULTIPLY, prod, MP_OBJ_NEW_SMALL_INT(q));
    }
    return prod;
}

#endif

STATIC MP_DEFINE_CONST_FUN_OBJ_1(mp_math_factorial_obj, mp_math_factorial);

#endif

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 },
    #if MICROPY_PY_MATH_CONSTANTS
    { MP_ROM_QSTR(MP_QSTR_tau), mp_const_float_tau },
    { MP_ROM_QSTR(MP_QSTR_inf), mp_const_float_inf },
    { MP_ROM_QSTR(MP_QSTR_nan), mp_const_float_nan },
    #endif
    { 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) },
    #if MICROPY_PY_MATH_ISCLOSE
    { MP_ROM_QSTR(MP_QSTR_isclose), MP_ROM_PTR(&mp_math_isclose_obj) },
    #endif
    { 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_FACTORIAL
    { MP_ROM_QSTR(MP_QSTR_factorial), MP_ROM_PTR(&mp_math_factorial_obj) },
    #endif
    #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 mp_module_math = {
    .base = { &mp_type_module },
    .globals = (mp_obj_dict_t *)&mp_module_math_globals,
};

MP_REGISTER_MODULE(MP_QSTR_math, mp_module_math);

#endif // MICROPY_PY_BUILTINS_FLOAT && MICROPY_PY_MATH