/** This file is part of the MicroPython project, http://micropython.org/** The MIT License (MIT)** Copyright (c) 2013-2017 Damien P. George* Copyright (c) Quectel Wireless Solution, Co., Ltd.All Rights Reserved.** 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_LN2mp_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 xMATH_FUN_1(sqrt, sqrt)// pow(x, y): returns x to the power of y#if MICROPY_PY_MATH_POW_FIX_NANmp_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 NaNif (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)#elseMATH_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_INFNANmp_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)#elseMATH_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_INFNANmp_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)#elseMATH_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 xMATH_FUN_1(erf, erf)// erfc(x): return the complementary error function of xMATH_FUN_1(erfc, erfc)// gamma(x): return the gamma function of xMATH_FUN_1(gamma, tgamma)// lgamma(x): return the natural logarithm of the gamma function of xMATH_FUN_1(lgamma, lgamma)#endif// TODO: fsum#if MICROPY_PY_MATH_ISCLOSESTATIC 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 infreturn 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 componentsSTATIC 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_NEGZEROif (fractional_part == MICROPY_FLOAT_CONST(0.0)) {fractional_part = copysign(fractional_part, x);}#endifmp_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 implementationSTATIC 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.htmlSTATIC 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;}#endifSTATIC MP_DEFINE_CONST_FUN_OBJ_1(mp_math_factorial_obj, mp_math_factorial);#endifSTATIC 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) },#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,};#endif // MICROPY_PY_BUILTINS_FLOAT && MICROPY_PY_MATH
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