mp_obj_t mp_cmath_sqrt(mp_obj_t z_obj) {
mp_float_t real, imag;
mp_obj_get_complex(z_obj, &real, &imag);
mp_float_t sqrt_abs = MICROPY_FLOAT_C_FUN(pow)(real*real + imag*imag, 0.25);
mp_float_t theta = 0.5 * MICROPY_FLOAT_C_FUN(atan2)(imag, real);
return mp_obj_new_complex(sqrt_abs * cos(theta), sqrt_abs * sin(theta));
}
mp_obj_t mp_obj_complex_binary_op(int 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 RT_BINARY_OP_ADD:
case RT_BINARY_OP_INPLACE_ADD:
lhs_real += rhs_real;
lhs_imag += rhs_imag;
break;
case RT_BINARY_OP_SUBTRACT:
case RT_BINARY_OP_INPLACE_SUBTRACT:
lhs_real -= rhs_real;
lhs_imag -= rhs_imag;
break;
case RT_BINARY_OP_MULTIPLY:
case RT_BINARY_OP_INPLACE_MULTIPLY:
{
mp_float_t real = lhs_real * rhs_real - lhs_imag * rhs_imag;
lhs_imag = lhs_real * rhs_imag + lhs_imag * rhs_real;
lhs_real = real;
break;
}
/* TODO floor(?) the value
case RT_BINARY_OP_FLOOR_DIVIDE:
case RT_BINARY_OP_INPLACE_FLOOR_DIVIDE: val = lhs_val / rhs_val; break;
*/
/* TODO
case RT_BINARY_OP_TRUE_DIVIDE:
case RT_BINARY_OP_INPLACE_TRUE_DIVIDE: val = lhs_val / rhs_val; break;
*/
return NULL; // op not supported
}
return mp_obj_new_complex(lhs_real, lhs_imag);
}
static mp_obj_t complex_unary_op(int op, mp_obj_t o_in) {
mp_obj_complex_t *o = o_in;
switch (op) {
case RT_UNARY_OP_NOT: if (o->real != 0 || o->imag != 0) { return mp_const_true;} else { return mp_const_false; }
case RT_UNARY_OP_POSITIVE: return o_in;
case RT_UNARY_OP_NEGATIVE: return mp_obj_new_complex(-o->real, -o->imag);
default: return MP_OBJ_NULL; // op not supported
}
}
STATIC mp_obj_t complex_unary_op(int op, mp_obj_t o_in) {
mp_obj_complex_t *o = o_in;
switch (op) {
case MP_UNARY_OP_BOOL: return MP_BOOL(o->real != 0 || o->imag != 0);
case MP_UNARY_OP_POSITIVE: return o_in;
case MP_UNARY_OP_NEGATIVE: return mp_obj_new_complex(-o->real, -o->imag);
default: return MP_OBJ_NULL; // op not supported
}
}
STATIC mp_obj_t complex_make_new(mp_obj_t type_in, uint n_args, uint n_kw, const mp_obj_t *args) {
// TODO check n_kw == 0
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
uint l;
const char *s = mp_obj_str_get_data(args[0], &l);
return mp_parse_num_decimal(s, l, true, true);
} 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: {
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);
}
default:
nlr_raise(mp_obj_new_exception_msg_varg(&mp_type_TypeError, "complex takes at most 2 arguments, %d given", n_args));
}
}
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_make_new(mp_obj_t type_in, uint n_args, uint n_kw, const mp_obj_t *args) {
// TODO check n_kw == 0
switch (n_args) {
case 0:
return mp_obj_new_complex(0, 0);
case 1:
// TODO allow string as first arg and parse it
if (MP_OBJ_IS_TYPE(args[0], &complex_type)) {
return args[0];
} else {
return mp_obj_new_complex(mp_obj_get_float(args[0]), 0);
}
case 2:
{
mp_float_t real, imag;
if (MP_OBJ_IS_TYPE(args[0], &complex_type)) {
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], &complex_type)) {
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);
}
default:
nlr_jump(mp_obj_new_exception_msg_1_arg(MP_QSTR_TypeError, "complex takes at most 2 arguments, %d given", (void*)(machine_int_t)n_args));
}
}
mp_obj_t mp_obj_complex_binary_op(int 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:
nlr_raise(mp_obj_new_exception_msg_varg(&mp_type_TypeError, "can't do truncated division of a complex number"));
case MP_BINARY_OP_TRUE_DIVIDE:
case MP_BINARY_OP_INPLACE_TRUE_DIVIDE:
if (rhs_imag == 0) {
if (rhs_real == 0) {
nlr_raise(mp_obj_new_exception_msg(&mp_type_ZeroDivisionError, "complex division 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) {
lhs_real = 1;
rhs_real = 0;
} else {
nlr_raise(mp_obj_new_exception_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_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);
}
mp_obj_t mp_cmath_sin(mp_obj_t z_obj) {
mp_float_t real, imag;
mp_obj_get_complex(z_obj, &real, &imag);
return mp_obj_new_complex(MICROPY_FLOAT_C_FUN(sin)(real) * MICROPY_FLOAT_C_FUN(cosh)(imag), MICROPY_FLOAT_C_FUN(cos)(real) * MICROPY_FLOAT_C_FUN(sinh)(imag));
}
mp_obj_t mp_cmath_log10(mp_obj_t z_obj) {
mp_float_t real, imag;
mp_obj_get_complex(z_obj, &real, &imag);
return mp_obj_new_complex(0.5 * MICROPY_FLOAT_C_FUN(log10)(real*real + imag*imag), MICROPY_FLOAT_C_FUN(atan2)(imag, real));
}
mp_obj_t mp_cmath_exp(mp_obj_t z_obj) {
mp_float_t real, imag;
mp_obj_get_complex(z_obj, &real, &imag);
mp_float_t exp_real = MICROPY_FLOAT_C_FUN(exp)(real);
return mp_obj_new_complex(exp_real * MICROPY_FLOAT_C_FUN(cos)(imag), exp_real * MICROPY_FLOAT_C_FUN(sin)(imag));
}
mp_obj_t mp_cmath_rect(mp_obj_t r_obj, mp_obj_t phi_obj) {
mp_float_t r = mp_obj_get_float(r_obj);
mp_float_t phi = mp_obj_get_float(phi_obj);
return mp_obj_new_complex(r * MICROPY_FLOAT_C_FUN(cos)(phi), r * MICROPY_FLOAT_C_FUN(sin)(phi));
}
mp_obj_t rt_load_const_dec(qstr qstr) {
#if MICROPY_ENABLE_FLOAT
DEBUG_OP_printf("load '%s'\n", qstr_str(qstr));
const char *s = qstr_str(qstr);
int in = PARSE_DEC_IN_INTG;
mp_float_t dec_val = 0;
bool exp_neg = false;
int exp_val = 0;
int exp_extra = 0;
bool imag = false;
for (; *s; s++) {
int dig = *s;
if ('0' <= dig && dig <= '9') {
dig -= '0';
if (in == PARSE_DEC_IN_EXP) {
exp_val = 10 * exp_val + dig;
} else {
dec_val = 10 * dec_val + dig;
if (in == PARSE_DEC_IN_FRAC) {
exp_extra -= 1;
}
}
} else if (in == PARSE_DEC_IN_INTG && dig == '.') {
in = PARSE_DEC_IN_FRAC;
} else if (in != PARSE_DEC_IN_EXP && (dig == 'E' || dig == 'e')) {
in = PARSE_DEC_IN_EXP;
if (s[1] == '+') {
s++;
} else if (s[1] == '-') {
s++;
exp_neg = true;
}
} else if (dig == 'J' || dig == 'j') {
s++;
imag = true;
break;
} else {
// unknown character
break;
}
}
if (*s != 0) {
nlr_jump(mp_obj_new_exception_msg(MP_QSTR_SyntaxError, "invalid syntax for number"));
}
if (exp_neg) {
exp_val = -exp_val;
}
exp_val += exp_extra;
for (; exp_val > 0; exp_val--) {
dec_val *= 10;
}
for (; exp_val < 0; exp_val++) {
dec_val *= 0.1;
}
if (imag) {
return mp_obj_new_complex(0, dec_val);
} else {
return mp_obj_new_float(dec_val);
}
#else
nlr_jump(mp_obj_new_exception_msg(MP_QSTR_SyntaxError, "decimal numbers not supported"));
#endif
}
