py/modmath.c - lite/micropython - Linaro Git Browser

 /*
  * 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)

 STATIC NORETURN void math_error(void) {
     mp_raise_ValueError("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
 MATH_FUN_2(pow, pow)
 // 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)
 MATH_FUN_2(atan2, atan2)
 // 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)
 MATH_FUN_2(fmod, fmod)
 // 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_a, ARG_b, ARG_rel_tol, ARG_abs_tol };
     static const mp_arg_t allowed_args[] = {
         {MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ},
         {MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ},
         {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, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args);
     const mp_float_t a = mp_obj_get_float(args[ARG_a].u_obj);
     const mp_float_t b = mp_obj_get_float(args[ARG_b].u_obj);
     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, "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 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

 // 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_msg(&mp_type_ValueError, "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_msg(&mp_type_ValueError, "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 },
     { 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
	/*
	* 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)

	STATIC NORETURN void math_error(void) {
	mp_raise_ValueError("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
	MATH_FUN_2(pow, pow)
	// 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)
	MATH_FUN_2(atan2, atan2)
	// 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)
	MATH_FUN_2(fmod, fmod)
	// 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_a, ARG_b, ARG_rel_tol, ARG_abs_tol };
	static const mp_arg_t allowed_args[] = {
	{MP_QSTR_, MP_ARG_REQUIRED \| MP_ARG_OBJ},
	{MP_QSTR_, MP_ARG_REQUIRED \| MP_ARG_OBJ},
	{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, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args);
	const mp_float_t a = mp_obj_get_float(args[ARG_a].u_obj);
	const mp_float_t b = mp_obj_get_float(args[ARG_b].u_obj);
	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, "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 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

	// 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_msg(&mp_type_ValueError, "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_msg(&mp_type_ValueError, "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 },
	{ 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