text: /*
   * 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
  