text: /*
   * This file is part of the MicroPython project, http://micropython.org/
   *
   * The MIT License (MIT)
   *
   * Copyright (c) 2013, 2014 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 <stdlib.h>
  #include <stdio.h>
  #include <assert.h>
  
  #include "py/parsenum.h"
  #include "py/runtime.h"
  
  #if MICROPY_PY_BUILTINS_COMPLEX
  
  #include <math.h>
  #include "py/formatfloat.h"
  
  typedef struct _mp_obj_complex_t {
      mp_obj_base_t base;
      mp_float_t real;
      mp_float_t imag;
  } mp_obj_complex_t;
  
  STATIC void complex_print(const mp_print_t *print, mp_obj_t o_in, mp_print_kind_t kind) {
      (void)kind;
      mp_obj_complex_t *o = MP_OBJ_TO_PTR(o_in);
      #if MICROPY_FLOAT_IMPL == MICROPY_FLOAT_IMPL_FLOAT
      char buf[16];
      #if MICROPY_OBJ_REPR == MICROPY_OBJ_REPR_C
      const int precision = 6;
      #else
      const int precision = 7;
      #endif
      #else
      char buf[32];
      const int precision = 16;
      #endif
      if (o->real == 0) {
          mp_format_float(o->imag, buf, sizeof(buf), 'g', precision, '\0');
          mp_printf(print, "%sj", buf);
      } else {
          mp_format_float(o->real, buf, sizeof(buf), 'g', precision, '\0');
          mp_printf(print, "(%s", buf);
          if (o->imag >= 0 || isnan(o->imag)) {
              mp_print_str(print, "+");
          }
          mp_format_float(o->imag, buf, sizeof(buf), 'g', precision, '\0');
          mp_printf(print, "%sj)", buf);
      }
  }
  
  STATIC mp_obj_t complex_make_new(const mp_obj_type_t *type_in, size_t n_args, size_t n_kw, const mp_obj_t *args) {
      (void)type_in;
      mp_arg_check_num(n_args, n_kw, 0, 2, false);
  
      switch (n_args) {
          case 0:
              return mp_obj_new_complex(0, 0);
  
          case 1:
              if (mp_obj_is_str(args[0])) {
                  // a string, parse it
                  size_t l;
                  const char *s = mp_obj_str_get_data(args[0], &l);
                  return mp_parse_num_decimal(s, l, true, true, NULL);
              } else if (mp_obj_is_type(args[0], &mp_type_complex)) {
                  // a complex, just return it
                  return args[0];
              } else {
                  // something else, try to cast it to a complex
                  return mp_obj_new_complex(mp_obj_get_float(args[0]), 0);
              }
  
          case 2:
          default: {
              mp_float_t real, imag;
              if (mp_obj_is_type(args[0], &mp_type_complex)) {
                  mp_obj_complex_get(args[0], &real, &imag);
              } else {
                  real = mp_obj_get_float(args[0]);
                  imag = 0;
              }
              if (mp_obj_is_type(args[1], &mp_type_complex)) {
                  mp_float_t real2, imag2;
                  mp_obj_complex_get(args[1], &real2, &imag2);
                  real -= imag2;
                  imag += real2;
              } else {
                  imag += mp_obj_get_float(args[1]);
              }
              return mp_obj_new_complex(real, imag);
          }
      }
  }
  
  STATIC mp_obj_t complex_unary_op(mp_unary_op_t op, mp_obj_t o_in) {
      mp_obj_complex_t *o = MP_OBJ_TO_PTR(o_in);
      switch (op) {
          case MP_UNARY_OP_BOOL:
              return mp_obj_new_bool(o->real != 0 || o->imag != 0);
          case MP_UNARY_OP_HASH:
              return MP_OBJ_NEW_SMALL_INT(mp_float_hash(o->real) ^ mp_float_hash(o->imag));
          case MP_UNARY_OP_POSITIVE:
              return o_in;
          case MP_UNARY_OP_NEGATIVE:
              return mp_obj_new_complex(-o->real, -o->imag);
          case MP_UNARY_OP_ABS:
              return mp_obj_new_float(MICROPY_FLOAT_C_FUN(sqrt)(o->real * o->real + o->imag * o->imag));
          default:
              return MP_OBJ_NULL;      // op not supported
      }
  }
  
  STATIC mp_obj_t complex_binary_op(mp_binary_op_t op, mp_obj_t lhs_in, mp_obj_t rhs_in) {
      mp_obj_complex_t *lhs = MP_OBJ_TO_PTR(lhs_in);
      return mp_obj_complex_binary_op(op, lhs->real, lhs->imag, rhs_in);
  }
  
  STATIC void complex_attr(mp_obj_t self_in, qstr attr, mp_obj_t *dest) {
      if (dest[0] != MP_OBJ_NULL) {
          // not load attribute
          return;
      }
      mp_obj_complex_t *self = MP_OBJ_TO_PTR(self_in);
      if (attr == MP_QSTR_real) {
          dest[0] = mp_obj_new_float(self->real);
      } else if (attr == MP_QSTR_imag) {
          dest[0] = mp_obj_new_float(self->imag);
      }
  }
  
  const mp_obj_type_t mp_type_complex = {
      { &mp_type_type },
      .flags = MP_TYPE_FLAG_EQ_NOT_REFLEXIVE | MP_TYPE_FLAG_EQ_CHECKS_OTHER_TYPE,
      .name = MP_QSTR_complex,
      .print = complex_print,
      .make_new = complex_make_new,
      .unary_op = complex_unary_op,
      .binary_op = complex_binary_op,
      .attr = complex_attr,
  };
  
  mp_obj_t mp_obj_new_complex(mp_float_t real, mp_float_t imag) {
      mp_obj_complex_t *o = m_new_obj(mp_obj_complex_t);
      o->base.type = &mp_type_complex;
      o->real = real;
      o->imag = imag;
      return MP_OBJ_FROM_PTR(o);
  }
  
  void mp_obj_complex_get(mp_obj_t self_in, mp_float_t *real, mp_float_t *imag) {
      assert(mp_obj_is_type(self_in, &mp_type_complex));
      mp_obj_complex_t *self = MP_OBJ_TO_PTR(self_in);
      *real = self->real;
      *imag = self->imag;
  }
  
  mp_obj_t mp_obj_complex_binary_op(mp_binary_op_t op, mp_float_t lhs_real, mp_float_t lhs_imag, mp_obj_t rhs_in) {
      mp_float_t rhs_real, rhs_imag;
      mp_obj_get_complex(rhs_in, &rhs_real, &rhs_imag); // can be any type, this function will convert to float (if possible)
      switch (op) {
          case MP_BINARY_OP_ADD:
          case MP_BINARY_OP_INPLACE_ADD:
              lhs_real += rhs_real;
              lhs_imag += rhs_imag;
              break;
          case MP_BINARY_OP_SUBTRACT:
          case MP_BINARY_OP_INPLACE_SUBTRACT:
              lhs_real -= rhs_real;
              lhs_imag -= rhs_imag;
              break;
          case MP_BINARY_OP_MULTIPLY:
          case MP_BINARY_OP_INPLACE_MULTIPLY: {
              mp_float_t real;
          multiply:
              real = lhs_real * rhs_real - lhs_imag * rhs_imag;
              lhs_imag = lhs_real * rhs_imag + lhs_imag * rhs_real;
              lhs_real = real;
              break;
          }
          case MP_BINARY_OP_FLOOR_DIVIDE:
          case MP_BINARY_OP_INPLACE_FLOOR_DIVIDE:
              mp_raise_TypeError("can't truncate-divide a complex number");
  
          case MP_BINARY_OP_TRUE_DIVIDE:
          case MP_BINARY_OP_INPLACE_TRUE_DIVIDE:
              if (rhs_imag == 0) {
                  if (rhs_real == 0) {
                      mp_raise_msg(&mp_type_ZeroDivisionError, "complex divide by zero");
                  }
                  lhs_real /= rhs_real;
                  lhs_imag /= rhs_real;
              } else if (rhs_real == 0) {
                  mp_float_t real = lhs_imag / rhs_imag;
                  lhs_imag = -lhs_real / rhs_imag;
                  lhs_real = real;
              } else {
                  mp_float_t rhs_len_sq = rhs_real * rhs_real + rhs_imag * rhs_imag;
                  rhs_real /= rhs_len_sq;
                  rhs_imag /= -rhs_len_sq;
                  goto multiply;
              }
              break;
  
          case MP_BINARY_OP_POWER:
          case MP_BINARY_OP_INPLACE_POWER: {
              // z1**z2 = exp(z2*ln(z1))
              //        = exp(z2*(ln(|z1|)+i*arg(z1)))
              //        = exp( (x2*ln1 - y2*arg1) + i*(y2*ln1 + x2*arg1) )
              //        = exp(x3 + i*y3)
              //        = exp(x3)*(cos(y3) + i*sin(y3))
              mp_float_t abs1 = MICROPY_FLOAT_C_FUN(sqrt)(lhs_real * lhs_real + lhs_imag * lhs_imag);
              if (abs1 == 0) {
                  if (rhs_imag == 0 && rhs_real >= 0) {
                      lhs_real = (rhs_real == 0);
                  } else {
                      mp_raise_msg(&mp_type_ZeroDivisionError, "0.0 to a complex power");
                  }
              } else {
                  mp_float_t ln1 = MICROPY_FLOAT_C_FUN(log)(abs1);
                  mp_float_t arg1 = MICROPY_FLOAT_C_FUN(atan2)(lhs_imag, lhs_real);
                  mp_float_t x3 = rhs_real * ln1 - rhs_imag * arg1;
                  mp_float_t y3 = rhs_imag * ln1 + rhs_real * arg1;
                  mp_float_t exp_x3 = MICROPY_FLOAT_C_FUN(exp)(x3);
                  lhs_real = exp_x3 * MICROPY_FLOAT_C_FUN(cos)(y3);
                  lhs_imag = exp_x3 * MICROPY_FLOAT_C_FUN(sin)(y3);
              }
              break;
          }
  
          case MP_BINARY_OP_EQUAL:
              return mp_obj_new_bool(lhs_real == rhs_real && lhs_imag == rhs_imag);
  
          default:
              return MP_OBJ_NULL; // op not supported
      }
      return mp_obj_new_complex(lhs_real, lhs_imag);
  }
  
  #endif
  