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-rw-r--r--complex.c2459
1 files changed, 2459 insertions, 0 deletions
diff --git a/complex.c b/complex.c
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index 0000000000..27c1f131e3
--- /dev/null
+++ b/complex.c
@@ -0,0 +1,2459 @@
+/*
+ complex.c: Coded by Tadayoshi Funaba 2008-2012
+
+ This implementation is based on Keiju Ishitsuka's Complex library
+ which is written in ruby.
+*/
+
+#include "ruby/internal/config.h"
+
+#if defined _MSC_VER
+/* Microsoft Visual C does not define M_PI and others by default */
+# define _USE_MATH_DEFINES 1
+#endif
+
+#include <ctype.h>
+#include <math.h>
+
+#undef NDEBUG
+#define NDEBUG
+#include "id.h"
+#include "internal.h"
+#include "internal/array.h"
+#include "internal/class.h"
+#include "internal/complex.h"
+#include "internal/math.h"
+#include "internal/numeric.h"
+#include "internal/object.h"
+#include "internal/rational.h"
+#include "ruby_assert.h"
+
+#define ZERO INT2FIX(0)
+#define ONE INT2FIX(1)
+#define TWO INT2FIX(2)
+#if USE_FLONUM
+#define RFLOAT_0 DBL2NUM(0)
+#else
+static VALUE RFLOAT_0;
+#endif
+#if defined(HAVE_SIGNBIT) && defined(__GNUC__) && defined(__sun) && \
+ !defined(signbit)
+extern int signbit(double);
+#endif
+
+VALUE rb_cComplex;
+
+static ID id_abs, id_arg,
+ id_denominator, id_numerator,
+ id_real_p, id_i_real, id_i_imag,
+ id_finite_p, id_infinite_p, id_rationalize,
+ id_PI;
+#define id_to_i idTo_i
+#define id_to_r idTo_r
+#define id_negate idUMinus
+#define id_expt idPow
+#define id_to_f idTo_f
+#define id_quo idQuo
+#define id_fdiv idFdiv
+
+#define f_boolcast(x) ((x) ? Qtrue : Qfalse)
+
+#define fun1(n) \
+inline static VALUE \
+f_##n(VALUE x)\
+{\
+ return rb_funcall(x, id_##n, 0);\
+}
+
+#define fun2(n) \
+inline static VALUE \
+f_##n(VALUE x, VALUE y)\
+{\
+ return rb_funcall(x, id_##n, 1, y);\
+}
+
+#define PRESERVE_SIGNEDZERO
+
+inline static VALUE
+f_add(VALUE x, VALUE y)
+{
+ if (RB_INTEGER_TYPE_P(x) &&
+ LIKELY(rb_method_basic_definition_p(rb_cInteger, idPLUS))) {
+ if (FIXNUM_ZERO_P(x))
+ return y;
+ if (FIXNUM_ZERO_P(y))
+ return x;
+ return rb_int_plus(x, y);
+ }
+ else if (RB_FLOAT_TYPE_P(x) &&
+ LIKELY(rb_method_basic_definition_p(rb_cFloat, idPLUS))) {
+ if (FIXNUM_ZERO_P(y))
+ return x;
+ return rb_float_plus(x, y);
+ }
+ else if (RB_TYPE_P(x, T_RATIONAL) &&
+ LIKELY(rb_method_basic_definition_p(rb_cRational, idPLUS))) {
+ if (FIXNUM_ZERO_P(y))
+ return x;
+ return rb_rational_plus(x, y);
+ }
+
+ return rb_funcall(x, '+', 1, y);
+}
+
+inline static VALUE
+f_div(VALUE x, VALUE y)
+{
+ if (FIXNUM_P(y) && FIX2LONG(y) == 1)
+ return x;
+ return rb_funcall(x, '/', 1, y);
+}
+
+inline static int
+f_gt_p(VALUE x, VALUE y)
+{
+ if (RB_INTEGER_TYPE_P(x)) {
+ if (FIXNUM_P(x) && FIXNUM_P(y))
+ return (SIGNED_VALUE)x > (SIGNED_VALUE)y;
+ return RTEST(rb_int_gt(x, y));
+ }
+ else if (RB_FLOAT_TYPE_P(x))
+ return RTEST(rb_float_gt(x, y));
+ else if (RB_TYPE_P(x, T_RATIONAL)) {
+ int const cmp = rb_cmpint(rb_rational_cmp(x, y), x, y);
+ return cmp > 0;
+ }
+ return RTEST(rb_funcall(x, '>', 1, y));
+}
+
+inline static VALUE
+f_mul(VALUE x, VALUE y)
+{
+ if (RB_INTEGER_TYPE_P(x) &&
+ LIKELY(rb_method_basic_definition_p(rb_cInteger, idMULT))) {
+ if (FIXNUM_ZERO_P(y))
+ return ZERO;
+ if (FIXNUM_ZERO_P(x) && RB_INTEGER_TYPE_P(y))
+ return ZERO;
+ if (x == ONE) return y;
+ if (y == ONE) return x;
+ return rb_int_mul(x, y);
+ }
+ else if (RB_FLOAT_TYPE_P(x) &&
+ LIKELY(rb_method_basic_definition_p(rb_cFloat, idMULT))) {
+ if (y == ONE) return x;
+ return rb_float_mul(x, y);
+ }
+ else if (RB_TYPE_P(x, T_RATIONAL) &&
+ LIKELY(rb_method_basic_definition_p(rb_cRational, idMULT))) {
+ if (y == ONE) return x;
+ return rb_rational_mul(x, y);
+ }
+ else if (LIKELY(rb_method_basic_definition_p(CLASS_OF(x), idMULT))) {
+ if (y == ONE) return x;
+ }
+ return rb_funcall(x, '*', 1, y);
+}
+
+inline static VALUE
+f_sub(VALUE x, VALUE y)
+{
+ if (FIXNUM_ZERO_P(y) &&
+ LIKELY(rb_method_basic_definition_p(CLASS_OF(x), idMINUS))) {
+ return x;
+ }
+ return rb_funcall(x, '-', 1, y);
+}
+
+inline static VALUE
+f_abs(VALUE x)
+{
+ if (RB_INTEGER_TYPE_P(x)) {
+ return rb_int_abs(x);
+ }
+ else if (RB_FLOAT_TYPE_P(x)) {
+ return rb_float_abs(x);
+ }
+ else if (RB_TYPE_P(x, T_RATIONAL)) {
+ return rb_rational_abs(x);
+ }
+ else if (RB_TYPE_P(x, T_COMPLEX)) {
+ return rb_complex_abs(x);
+ }
+ return rb_funcall(x, id_abs, 0);
+}
+
+static VALUE numeric_arg(VALUE self);
+static VALUE float_arg(VALUE self);
+
+inline static VALUE
+f_arg(VALUE x)
+{
+ if (RB_INTEGER_TYPE_P(x)) {
+ return numeric_arg(x);
+ }
+ else if (RB_FLOAT_TYPE_P(x)) {
+ return float_arg(x);
+ }
+ else if (RB_TYPE_P(x, T_RATIONAL)) {
+ return numeric_arg(x);
+ }
+ else if (RB_TYPE_P(x, T_COMPLEX)) {
+ return rb_complex_arg(x);
+ }
+ return rb_funcall(x, id_arg, 0);
+}
+
+inline static VALUE
+f_numerator(VALUE x)
+{
+ if (RB_TYPE_P(x, T_RATIONAL)) {
+ return RRATIONAL(x)->num;
+ }
+ if (RB_FLOAT_TYPE_P(x)) {
+ return rb_float_numerator(x);
+ }
+ return x;
+}
+
+inline static VALUE
+f_denominator(VALUE x)
+{
+ if (RB_TYPE_P(x, T_RATIONAL)) {
+ return RRATIONAL(x)->den;
+ }
+ if (RB_FLOAT_TYPE_P(x)) {
+ return rb_float_denominator(x);
+ }
+ return INT2FIX(1);
+}
+
+inline static VALUE
+f_negate(VALUE x)
+{
+ if (RB_INTEGER_TYPE_P(x)) {
+ return rb_int_uminus(x);
+ }
+ else if (RB_FLOAT_TYPE_P(x)) {
+ return rb_float_uminus(x);
+ }
+ else if (RB_TYPE_P(x, T_RATIONAL)) {
+ return rb_rational_uminus(x);
+ }
+ else if (RB_TYPE_P(x, T_COMPLEX)) {
+ return rb_complex_uminus(x);
+ }
+ return rb_funcall(x, id_negate, 0);
+}
+
+static bool nucomp_real_p(VALUE self);
+
+static inline bool
+f_real_p(VALUE x)
+{
+ if (RB_INTEGER_TYPE_P(x)) {
+ return true;
+ }
+ else if (RB_FLOAT_TYPE_P(x)) {
+ return true;
+ }
+ else if (RB_TYPE_P(x, T_RATIONAL)) {
+ return true;
+ }
+ else if (RB_TYPE_P(x, T_COMPLEX)) {
+ return nucomp_real_p(x);
+ }
+ return rb_funcall(x, id_real_p, 0);
+}
+
+inline static VALUE
+f_to_i(VALUE x)
+{
+ if (RB_TYPE_P(x, T_STRING))
+ return rb_str_to_inum(x, 10, 0);
+ return rb_funcall(x, id_to_i, 0);
+}
+
+inline static VALUE
+f_to_f(VALUE x)
+{
+ if (RB_TYPE_P(x, T_STRING))
+ return DBL2NUM(rb_str_to_dbl(x, 0));
+ return rb_funcall(x, id_to_f, 0);
+}
+
+fun1(to_r)
+
+inline static int
+f_eqeq_p(VALUE x, VALUE y)
+{
+ if (FIXNUM_P(x) && FIXNUM_P(y))
+ return x == y;
+ else if (RB_FLOAT_TYPE_P(x) || RB_FLOAT_TYPE_P(y))
+ return NUM2DBL(x) == NUM2DBL(y);
+ return (int)rb_equal(x, y);
+}
+
+fun2(expt)
+fun2(fdiv)
+
+static VALUE
+f_quo(VALUE x, VALUE y)
+{
+ if (RB_INTEGER_TYPE_P(x))
+ return rb_numeric_quo(x, y);
+ if (RB_FLOAT_TYPE_P(x))
+ return rb_float_div(x, y);
+ if (RB_TYPE_P(x, T_RATIONAL))
+ return rb_numeric_quo(x, y);
+
+ return rb_funcallv(x, id_quo, 1, &y);
+}
+
+inline static int
+f_negative_p(VALUE x)
+{
+ if (RB_INTEGER_TYPE_P(x))
+ return INT_NEGATIVE_P(x);
+ else if (RB_FLOAT_TYPE_P(x))
+ return RFLOAT_VALUE(x) < 0.0;
+ else if (RB_TYPE_P(x, T_RATIONAL))
+ return INT_NEGATIVE_P(RRATIONAL(x)->num);
+ return rb_num_negative_p(x);
+}
+
+#define f_positive_p(x) (!f_negative_p(x))
+
+inline static int
+f_zero_p(VALUE x)
+{
+ if (RB_FLOAT_TYPE_P(x)) {
+ return FLOAT_ZERO_P(x);
+ }
+ else if (RB_INTEGER_TYPE_P(x)) {
+ return FIXNUM_ZERO_P(x);
+ }
+ else if (RB_TYPE_P(x, T_RATIONAL)) {
+ const VALUE num = RRATIONAL(x)->num;
+ return FIXNUM_ZERO_P(num);
+ }
+ return (int)rb_equal(x, ZERO);
+}
+
+#define f_nonzero_p(x) (!f_zero_p(x))
+
+VALUE rb_flo_is_finite_p(VALUE num);
+inline static int
+f_finite_p(VALUE x)
+{
+ if (RB_INTEGER_TYPE_P(x)) {
+ return TRUE;
+ }
+ else if (RB_FLOAT_TYPE_P(x)) {
+ return (int)rb_flo_is_finite_p(x);
+ }
+ else if (RB_TYPE_P(x, T_RATIONAL)) {
+ return TRUE;
+ }
+ return RTEST(rb_funcallv(x, id_finite_p, 0, 0));
+}
+
+VALUE rb_flo_is_infinite_p(VALUE num);
+inline static VALUE
+f_infinite_p(VALUE x)
+{
+ if (RB_INTEGER_TYPE_P(x)) {
+ return Qnil;
+ }
+ else if (RB_FLOAT_TYPE_P(x)) {
+ return rb_flo_is_infinite_p(x);
+ }
+ else if (RB_TYPE_P(x, T_RATIONAL)) {
+ return Qnil;
+ }
+ return rb_funcallv(x, id_infinite_p, 0, 0);
+}
+
+inline static int
+f_kind_of_p(VALUE x, VALUE c)
+{
+ return (int)rb_obj_is_kind_of(x, c);
+}
+
+inline static int
+k_numeric_p(VALUE x)
+{
+ return f_kind_of_p(x, rb_cNumeric);
+}
+
+#define k_exact_p(x) (!RB_FLOAT_TYPE_P(x))
+
+#define k_exact_zero_p(x) (k_exact_p(x) && f_zero_p(x))
+
+#define get_dat1(x) \
+ struct RComplex *dat = RCOMPLEX(x)
+
+#define get_dat2(x,y) \
+ struct RComplex *adat = RCOMPLEX(x), *bdat = RCOMPLEX(y)
+
+inline static VALUE
+nucomp_s_new_internal(VALUE klass, VALUE real, VALUE imag)
+{
+ NEWOBJ_OF(obj, struct RComplex, klass, T_COMPLEX | (RGENGC_WB_PROTECTED_COMPLEX ? FL_WB_PROTECTED : 0));
+
+ RCOMPLEX_SET_REAL(obj, real);
+ RCOMPLEX_SET_IMAG(obj, imag);
+ OBJ_FREEZE_RAW((VALUE)obj);
+
+ return (VALUE)obj;
+}
+
+static VALUE
+nucomp_s_alloc(VALUE klass)
+{
+ return nucomp_s_new_internal(klass, ZERO, ZERO);
+}
+
+inline static VALUE
+f_complex_new_bang1(VALUE klass, VALUE x)
+{
+ assert(!RB_TYPE_P(x, T_COMPLEX));
+ return nucomp_s_new_internal(klass, x, ZERO);
+}
+
+inline static VALUE
+f_complex_new_bang2(VALUE klass, VALUE x, VALUE y)
+{
+ assert(!RB_TYPE_P(x, T_COMPLEX));
+ assert(!RB_TYPE_P(y, T_COMPLEX));
+ return nucomp_s_new_internal(klass, x, y);
+}
+
+inline static void
+nucomp_real_check(VALUE num)
+{
+ if (!RB_INTEGER_TYPE_P(num) &&
+ !RB_FLOAT_TYPE_P(num) &&
+ !RB_TYPE_P(num, T_RATIONAL)) {
+ if (!k_numeric_p(num) || !f_real_p(num))
+ rb_raise(rb_eTypeError, "not a real");
+ }
+}
+
+inline static VALUE
+nucomp_s_canonicalize_internal(VALUE klass, VALUE real, VALUE imag)
+{
+ int complex_r, complex_i;
+ complex_r = RB_TYPE_P(real, T_COMPLEX);
+ complex_i = RB_TYPE_P(imag, T_COMPLEX);
+ if (!complex_r && !complex_i) {
+ return nucomp_s_new_internal(klass, real, imag);
+ }
+ else if (!complex_r) {
+ get_dat1(imag);
+
+ return nucomp_s_new_internal(klass,
+ f_sub(real, dat->imag),
+ f_add(ZERO, dat->real));
+ }
+ else if (!complex_i) {
+ get_dat1(real);
+
+ return nucomp_s_new_internal(klass,
+ dat->real,
+ f_add(dat->imag, imag));
+ }
+ else {
+ get_dat2(real, imag);
+
+ return nucomp_s_new_internal(klass,
+ f_sub(adat->real, bdat->imag),
+ f_add(adat->imag, bdat->real));
+ }
+}
+
+/*
+ * call-seq:
+ * Complex.rect(real[, imag]) -> complex
+ * Complex.rectangular(real[, imag]) -> complex
+ *
+ * Returns a complex object which denotes the given rectangular form.
+ *
+ * Complex.rectangular(1, 2) #=> (1+2i)
+ */
+static VALUE
+nucomp_s_new(int argc, VALUE *argv, VALUE klass)
+{
+ VALUE real, imag;
+
+ switch (rb_scan_args(argc, argv, "11", &real, &imag)) {
+ case 1:
+ nucomp_real_check(real);
+ imag = ZERO;
+ break;
+ default:
+ nucomp_real_check(real);
+ nucomp_real_check(imag);
+ break;
+ }
+
+ return nucomp_s_canonicalize_internal(klass, real, imag);
+}
+
+inline static VALUE
+f_complex_new2(VALUE klass, VALUE x, VALUE y)
+{
+ assert(!RB_TYPE_P(x, T_COMPLEX));
+ return nucomp_s_canonicalize_internal(klass, x, y);
+}
+
+static VALUE nucomp_convert(VALUE klass, VALUE a1, VALUE a2, int raise);
+static VALUE nucomp_s_convert(int argc, VALUE *argv, VALUE klass);
+
+/*
+ * call-seq:
+ * Complex(x[, y], exception: true) -> numeric or nil
+ *
+ * Returns x+i*y;
+ *
+ * Complex(1, 2) #=> (1+2i)
+ * Complex('1+2i') #=> (1+2i)
+ * Complex(nil) #=> TypeError
+ * Complex(1, nil) #=> TypeError
+ *
+ * Complex(1, nil, exception: false) #=> nil
+ * Complex('1+2', exception: false) #=> nil
+ *
+ * Syntax of string form:
+ *
+ * string form = extra spaces , complex , extra spaces ;
+ * complex = real part | [ sign ] , imaginary part
+ * | real part , sign , imaginary part
+ * | rational , "@" , rational ;
+ * real part = rational ;
+ * imaginary part = imaginary unit | unsigned rational , imaginary unit ;
+ * rational = [ sign ] , unsigned rational ;
+ * unsigned rational = numerator | numerator , "/" , denominator ;
+ * numerator = integer part | fractional part | integer part , fractional part ;
+ * denominator = digits ;
+ * integer part = digits ;
+ * fractional part = "." , digits , [ ( "e" | "E" ) , [ sign ] , digits ] ;
+ * imaginary unit = "i" | "I" | "j" | "J" ;
+ * sign = "-" | "+" ;
+ * digits = digit , { digit | "_" , digit };
+ * digit = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9" ;
+ * extra spaces = ? \s* ? ;
+ *
+ * See String#to_c.
+ */
+static VALUE
+nucomp_f_complex(int argc, VALUE *argv, VALUE klass)
+{
+ VALUE a1, a2, opts = Qnil;
+ int raise = TRUE;
+
+ if (rb_scan_args(argc, argv, "11:", &a1, &a2, &opts) == 1) {
+ a2 = Qundef;
+ }
+ if (!NIL_P(opts)) {
+ raise = rb_opts_exception_p(opts, raise);
+ }
+ if (argc > 0 && CLASS_OF(a1) == rb_cComplex && a2 == Qundef) {
+ return a1;
+ }
+ return nucomp_convert(rb_cComplex, a1, a2, raise);
+}
+
+#define imp1(n) \
+inline static VALUE \
+m_##n##_bang(VALUE x)\
+{\
+ return rb_math_##n(x);\
+}
+
+imp1(cos)
+imp1(cosh)
+imp1(exp)
+
+static VALUE
+m_log_bang(VALUE x)
+{
+ return rb_math_log(1, &x);
+}
+
+imp1(sin)
+imp1(sinh)
+
+static VALUE
+m_cos(VALUE x)
+{
+ if (!RB_TYPE_P(x, T_COMPLEX))
+ return m_cos_bang(x);
+ {
+ get_dat1(x);
+ return f_complex_new2(rb_cComplex,
+ f_mul(m_cos_bang(dat->real),
+ m_cosh_bang(dat->imag)),
+ f_mul(f_negate(m_sin_bang(dat->real)),
+ m_sinh_bang(dat->imag)));
+ }
+}
+
+static VALUE
+m_sin(VALUE x)
+{
+ if (!RB_TYPE_P(x, T_COMPLEX))
+ return m_sin_bang(x);
+ {
+ get_dat1(x);
+ return f_complex_new2(rb_cComplex,
+ f_mul(m_sin_bang(dat->real),
+ m_cosh_bang(dat->imag)),
+ f_mul(m_cos_bang(dat->real),
+ m_sinh_bang(dat->imag)));
+ }
+}
+
+static VALUE
+f_complex_polar(VALUE klass, VALUE x, VALUE y)
+{
+ assert(!RB_TYPE_P(x, T_COMPLEX));
+ assert(!RB_TYPE_P(y, T_COMPLEX));
+ if (f_zero_p(x) || f_zero_p(y)) {
+ return nucomp_s_new_internal(klass, x, RFLOAT_0);
+ }
+ if (RB_FLOAT_TYPE_P(y)) {
+ const double arg = RFLOAT_VALUE(y);
+ if (arg == M_PI) {
+ x = f_negate(x);
+ y = RFLOAT_0;
+ }
+ else if (arg == M_PI_2) {
+ y = x;
+ x = RFLOAT_0;
+ }
+ else if (arg == M_PI_2+M_PI) {
+ y = f_negate(x);
+ x = RFLOAT_0;
+ }
+ else if (RB_FLOAT_TYPE_P(x)) {
+ const double abs = RFLOAT_VALUE(x);
+ const double real = abs * cos(arg), imag = abs * sin(arg);
+ x = DBL2NUM(real);
+ y = DBL2NUM(imag);
+ }
+ else {
+ const double ax = sin(arg), ay = cos(arg);
+ y = f_mul(x, DBL2NUM(ax));
+ x = f_mul(x, DBL2NUM(ay));
+ }
+ return nucomp_s_new_internal(klass, x, y);
+ }
+ return nucomp_s_canonicalize_internal(klass,
+ f_mul(x, m_cos(y)),
+ f_mul(x, m_sin(y)));
+}
+
+#ifdef HAVE___COSPI
+# define cospi(x) __cospi(x)
+#else
+# define cospi(x) cos((x) * M_PI)
+#endif
+#ifdef HAVE___SINPI
+# define sinpi(x) __sinpi(x)
+#else
+# define sinpi(x) sin((x) * M_PI)
+#endif
+/* returns a Complex or Float of ang*PI-rotated abs */
+VALUE
+rb_dbl_complex_new_polar_pi(double abs, double ang)
+{
+ double fi;
+ const double fr = modf(ang, &fi);
+ int pos = fr == +0.5;
+
+ if (pos || fr == -0.5) {
+ if ((modf(fi / 2.0, &fi) != fr) ^ pos) abs = -abs;
+ return rb_complex_new(RFLOAT_0, DBL2NUM(abs));
+ }
+ else if (fr == 0.0) {
+ if (modf(fi / 2.0, &fi) != 0.0) abs = -abs;
+ return DBL2NUM(abs);
+ }
+ else {
+ const double real = abs * cospi(ang), imag = abs * sinpi(ang);
+ return rb_complex_new(DBL2NUM(real), DBL2NUM(imag));
+ }
+}
+
+/*
+ * call-seq:
+ * Complex.polar(abs[, arg]) -> complex
+ *
+ * Returns a complex object which denotes the given polar form.
+ *
+ * Complex.polar(3, 0) #=> (3.0+0.0i)
+ * Complex.polar(3, Math::PI/2) #=> (1.836909530733566e-16+3.0i)
+ * Complex.polar(3, Math::PI) #=> (-3.0+3.673819061467132e-16i)
+ * Complex.polar(3, -Math::PI/2) #=> (1.836909530733566e-16-3.0i)
+ */
+static VALUE
+nucomp_s_polar(int argc, VALUE *argv, VALUE klass)
+{
+ VALUE abs, arg;
+
+ switch (rb_scan_args(argc, argv, "11", &abs, &arg)) {
+ case 1:
+ nucomp_real_check(abs);
+ return nucomp_s_new_internal(klass, abs, ZERO);
+ default:
+ nucomp_real_check(abs);
+ nucomp_real_check(arg);
+ break;
+ }
+ if (RB_TYPE_P(abs, T_COMPLEX)) {
+ get_dat1(abs);
+ abs = dat->real;
+ }
+ if (RB_TYPE_P(arg, T_COMPLEX)) {
+ get_dat1(arg);
+ arg = dat->real;
+ }
+ return f_complex_polar(klass, abs, arg);
+}
+
+/*
+ * call-seq:
+ * cmp.real -> real
+ *
+ * Returns the real part.
+ *
+ * Complex(7).real #=> 7
+ * Complex(9, -4).real #=> 9
+ */
+VALUE
+rb_complex_real(VALUE self)
+{
+ get_dat1(self);
+ return dat->real;
+}
+
+/*
+ * call-seq:
+ * cmp.imag -> real
+ * cmp.imaginary -> real
+ *
+ * Returns the imaginary part.
+ *
+ * Complex(7).imaginary #=> 0
+ * Complex(9, -4).imaginary #=> -4
+ */
+VALUE
+rb_complex_imag(VALUE self)
+{
+ get_dat1(self);
+ return dat->imag;
+}
+
+/*
+ * call-seq:
+ * -cmp -> complex
+ *
+ * Returns negation of the value.
+ *
+ * -Complex(1, 2) #=> (-1-2i)
+ */
+VALUE
+rb_complex_uminus(VALUE self)
+{
+ get_dat1(self);
+ return f_complex_new2(CLASS_OF(self),
+ f_negate(dat->real), f_negate(dat->imag));
+}
+
+/*
+ * call-seq:
+ * cmp + numeric -> complex
+ *
+ * Performs addition.
+ *
+ * Complex(2, 3) + Complex(2, 3) #=> (4+6i)
+ * Complex(900) + Complex(1) #=> (901+0i)
+ * Complex(-2, 9) + Complex(-9, 2) #=> (-11+11i)
+ * Complex(9, 8) + 4 #=> (13+8i)
+ * Complex(20, 9) + 9.8 #=> (29.8+9i)
+ */
+VALUE
+rb_complex_plus(VALUE self, VALUE other)
+{
+ if (RB_TYPE_P(other, T_COMPLEX)) {
+ VALUE real, imag;
+
+ get_dat2(self, other);
+
+ real = f_add(adat->real, bdat->real);
+ imag = f_add(adat->imag, bdat->imag);
+
+ return f_complex_new2(CLASS_OF(self), real, imag);
+ }
+ if (k_numeric_p(other) && f_real_p(other)) {
+ get_dat1(self);
+
+ return f_complex_new2(CLASS_OF(self),
+ f_add(dat->real, other), dat->imag);
+ }
+ return rb_num_coerce_bin(self, other, '+');
+}
+
+/*
+ * call-seq:
+ * cmp - numeric -> complex
+ *
+ * Performs subtraction.
+ *
+ * Complex(2, 3) - Complex(2, 3) #=> (0+0i)
+ * Complex(900) - Complex(1) #=> (899+0i)
+ * Complex(-2, 9) - Complex(-9, 2) #=> (7+7i)
+ * Complex(9, 8) - 4 #=> (5+8i)
+ * Complex(20, 9) - 9.8 #=> (10.2+9i)
+ */
+VALUE
+rb_complex_minus(VALUE self, VALUE other)
+{
+ if (RB_TYPE_P(other, T_COMPLEX)) {
+ VALUE real, imag;
+
+ get_dat2(self, other);
+
+ real = f_sub(adat->real, bdat->real);
+ imag = f_sub(adat->imag, bdat->imag);
+
+ return f_complex_new2(CLASS_OF(self), real, imag);
+ }
+ if (k_numeric_p(other) && f_real_p(other)) {
+ get_dat1(self);
+
+ return f_complex_new2(CLASS_OF(self),
+ f_sub(dat->real, other), dat->imag);
+ }
+ return rb_num_coerce_bin(self, other, '-');
+}
+
+static VALUE
+safe_mul(VALUE a, VALUE b, int az, int bz)
+{
+ double v;
+ if (!az && bz && RB_FLOAT_TYPE_P(a) && (v = RFLOAT_VALUE(a), !isnan(v))) {
+ a = signbit(v) ? DBL2NUM(-1.0) : DBL2NUM(1.0);
+ }
+ if (!bz && az && RB_FLOAT_TYPE_P(b) && (v = RFLOAT_VALUE(b), !isnan(v))) {
+ b = signbit(v) ? DBL2NUM(-1.0) : DBL2NUM(1.0);
+ }
+ return f_mul(a, b);
+}
+
+static void
+comp_mul(VALUE areal, VALUE aimag, VALUE breal, VALUE bimag, VALUE *real, VALUE *imag)
+{
+ int arzero = f_zero_p(areal);
+ int aizero = f_zero_p(aimag);
+ int brzero = f_zero_p(breal);
+ int bizero = f_zero_p(bimag);
+ *real = f_sub(safe_mul(areal, breal, arzero, brzero),
+ safe_mul(aimag, bimag, aizero, bizero));
+ *imag = f_add(safe_mul(areal, bimag, arzero, bizero),
+ safe_mul(aimag, breal, aizero, brzero));
+}
+
+/*
+ * call-seq:
+ * cmp * numeric -> complex
+ *
+ * Performs multiplication.
+ *
+ * Complex(2, 3) * Complex(2, 3) #=> (-5+12i)
+ * Complex(900) * Complex(1) #=> (900+0i)
+ * Complex(-2, 9) * Complex(-9, 2) #=> (0-85i)
+ * Complex(9, 8) * 4 #=> (36+32i)
+ * Complex(20, 9) * 9.8 #=> (196.0+88.2i)
+ */
+VALUE
+rb_complex_mul(VALUE self, VALUE other)
+{
+ if (RB_TYPE_P(other, T_COMPLEX)) {
+ VALUE real, imag;
+ get_dat2(self, other);
+
+ comp_mul(adat->real, adat->imag, bdat->real, bdat->imag, &real, &imag);
+
+ return f_complex_new2(CLASS_OF(self), real, imag);
+ }
+ if (k_numeric_p(other) && f_real_p(other)) {
+ get_dat1(self);
+
+ return f_complex_new2(CLASS_OF(self),
+ f_mul(dat->real, other),
+ f_mul(dat->imag, other));
+ }
+ return rb_num_coerce_bin(self, other, '*');
+}
+
+inline static VALUE
+f_divide(VALUE self, VALUE other,
+ VALUE (*func)(VALUE, VALUE), ID id)
+{
+ if (RB_TYPE_P(other, T_COMPLEX)) {
+ VALUE r, n, x, y;
+ int flo;
+ get_dat2(self, other);
+
+ flo = (RB_FLOAT_TYPE_P(adat->real) || RB_FLOAT_TYPE_P(adat->imag) ||
+ RB_FLOAT_TYPE_P(bdat->real) || RB_FLOAT_TYPE_P(bdat->imag));
+
+ if (f_gt_p(f_abs(bdat->real), f_abs(bdat->imag))) {
+ r = (*func)(bdat->imag, bdat->real);
+ n = f_mul(bdat->real, f_add(ONE, f_mul(r, r)));
+ x = (*func)(f_add(adat->real, f_mul(adat->imag, r)), n);
+ y = (*func)(f_sub(adat->imag, f_mul(adat->real, r)), n);
+ }
+ else {
+ r = (*func)(bdat->real, bdat->imag);
+ n = f_mul(bdat->imag, f_add(ONE, f_mul(r, r)));
+ x = (*func)(f_add(f_mul(adat->real, r), adat->imag), n);
+ y = (*func)(f_sub(f_mul(adat->imag, r), adat->real), n);
+ }
+ if (!flo) {
+ x = rb_rational_canonicalize(x);
+ y = rb_rational_canonicalize(y);
+ }
+ return f_complex_new2(CLASS_OF(self), x, y);
+ }
+ if (k_numeric_p(other) && f_real_p(other)) {
+ VALUE x, y;
+ get_dat1(self);
+ x = rb_rational_canonicalize((*func)(dat->real, other));
+ y = rb_rational_canonicalize((*func)(dat->imag, other));
+ return f_complex_new2(CLASS_OF(self), x, y);
+ }
+ return rb_num_coerce_bin(self, other, id);
+}
+
+#define rb_raise_zerodiv() rb_raise(rb_eZeroDivError, "divided by 0")
+
+/*
+ * call-seq:
+ * cmp / numeric -> complex
+ * cmp.quo(numeric) -> complex
+ *
+ * Performs division.
+ *
+ * Complex(2, 3) / Complex(2, 3) #=> ((1/1)+(0/1)*i)
+ * Complex(900) / Complex(1) #=> ((900/1)+(0/1)*i)
+ * Complex(-2, 9) / Complex(-9, 2) #=> ((36/85)-(77/85)*i)
+ * Complex(9, 8) / 4 #=> ((9/4)+(2/1)*i)
+ * Complex(20, 9) / 9.8 #=> (2.0408163265306123+0.9183673469387754i)
+ */
+VALUE
+rb_complex_div(VALUE self, VALUE other)
+{
+ return f_divide(self, other, f_quo, id_quo);
+}
+
+#define nucomp_quo rb_complex_div
+
+/*
+ * call-seq:
+ * cmp.fdiv(numeric) -> complex
+ *
+ * Performs division as each part is a float, never returns a float.
+ *
+ * Complex(11, 22).fdiv(3) #=> (3.6666666666666665+7.333333333333333i)
+ */
+static VALUE
+nucomp_fdiv(VALUE self, VALUE other)
+{
+ return f_divide(self, other, f_fdiv, id_fdiv);
+}
+
+inline static VALUE
+f_reciprocal(VALUE x)
+{
+ return f_quo(ONE, x);
+}
+
+/*
+ * call-seq:
+ * cmp ** numeric -> complex
+ *
+ * Performs exponentiation.
+ *
+ * Complex('i') ** 2 #=> (-1+0i)
+ * Complex(-8) ** Rational(1, 3) #=> (1.0000000000000002+1.7320508075688772i)
+ */
+VALUE
+rb_complex_pow(VALUE self, VALUE other)
+{
+ if (k_numeric_p(other) && k_exact_zero_p(other))
+ return f_complex_new_bang1(CLASS_OF(self), ONE);
+
+ if (RB_TYPE_P(other, T_RATIONAL) && RRATIONAL(other)->den == LONG2FIX(1))
+ other = RRATIONAL(other)->num; /* c14n */
+
+ if (RB_TYPE_P(other, T_COMPLEX)) {
+ get_dat1(other);
+
+ if (k_exact_zero_p(dat->imag))
+ other = dat->real; /* c14n */
+ }
+
+ if (RB_TYPE_P(other, T_COMPLEX)) {
+ VALUE r, theta, nr, ntheta;
+
+ get_dat1(other);
+
+ r = f_abs(self);
+ theta = f_arg(self);
+
+ nr = m_exp_bang(f_sub(f_mul(dat->real, m_log_bang(r)),
+ f_mul(dat->imag, theta)));
+ ntheta = f_add(f_mul(theta, dat->real),
+ f_mul(dat->imag, m_log_bang(r)));
+ return f_complex_polar(CLASS_OF(self), nr, ntheta);
+ }
+ if (FIXNUM_P(other)) {
+ long n = FIX2LONG(other);
+ if (n == 0) {
+ return nucomp_s_new_internal(CLASS_OF(self), ONE, ZERO);
+ }
+ if (n < 0) {
+ self = f_reciprocal(self);
+ other = rb_int_uminus(other);
+ n = -n;
+ }
+ {
+ get_dat1(self);
+ VALUE xr = dat->real, xi = dat->imag, zr = xr, zi = xi;
+
+ if (f_zero_p(xi)) {
+ zr = rb_num_pow(zr, other);
+ }
+ else if (f_zero_p(xr)) {
+ zi = rb_num_pow(zi, other);
+ if (n & 2) zi = f_negate(zi);
+ if (!(n & 1)) {
+ VALUE tmp = zr;
+ zr = zi;
+ zi = tmp;
+ }
+ }
+ else {
+ while (--n) {
+ long q, r;
+
+ for (; q = n / 2, r = n % 2, r == 0; n = q) {
+ VALUE tmp = f_sub(f_mul(xr, xr), f_mul(xi, xi));
+ xi = f_mul(f_mul(TWO, xr), xi);
+ xr = tmp;
+ }
+ comp_mul(zr, zi, xr, xi, &zr, &zi);
+ }
+ }
+ return nucomp_s_new_internal(CLASS_OF(self), zr, zi);
+ }
+ }
+ if (k_numeric_p(other) && f_real_p(other)) {
+ VALUE r, theta;
+
+ if (RB_TYPE_P(other, T_BIGNUM))
+ rb_warn("in a**b, b may be too big");
+
+ r = f_abs(self);
+ theta = f_arg(self);
+
+ return f_complex_polar(CLASS_OF(self), f_expt(r, other),
+ f_mul(theta, other));
+ }
+ return rb_num_coerce_bin(self, other, id_expt);
+}
+
+/*
+ * call-seq:
+ * cmp == object -> true or false
+ *
+ * Returns true if cmp equals object numerically.
+ *
+ * Complex(2, 3) == Complex(2, 3) #=> true
+ * Complex(5) == 5 #=> true
+ * Complex(0) == 0.0 #=> true
+ * Complex('1/3') == 0.33 #=> false
+ * Complex('1/2') == '1/2' #=> false
+ */
+static VALUE
+nucomp_eqeq_p(VALUE self, VALUE other)
+{
+ if (RB_TYPE_P(other, T_COMPLEX)) {
+ get_dat2(self, other);
+
+ return f_boolcast(f_eqeq_p(adat->real, bdat->real) &&
+ f_eqeq_p(adat->imag, bdat->imag));
+ }
+ if (k_numeric_p(other) && f_real_p(other)) {
+ get_dat1(self);
+
+ return f_boolcast(f_eqeq_p(dat->real, other) && f_zero_p(dat->imag));
+ }
+ return f_boolcast(f_eqeq_p(other, self));
+}
+
+static bool
+nucomp_real_p(VALUE self)
+{
+ get_dat1(self);
+ return(f_zero_p(dat->imag) ? true : false);
+}
+
+/*
+ * call-seq:
+ * cmp <=> object -> 0, 1, -1, or nil
+ *
+ * If +cmp+'s imaginary part is zero, and +object+ is also a
+ * real number (or a Complex number where the imaginary part is zero),
+ * compare the real part of +cmp+ to object. Otherwise, return nil.
+ *
+ * Complex(2, 3) <=> Complex(2, 3) #=> nil
+ * Complex(2, 3) <=> 1 #=> nil
+ * Complex(2) <=> 1 #=> 1
+ * Complex(2) <=> 2 #=> 0
+ * Complex(2) <=> 3 #=> -1
+ */
+static VALUE
+nucomp_cmp(VALUE self, VALUE other)
+{
+ if (nucomp_real_p(self) && k_numeric_p(other)) {
+ if (RB_TYPE_P(other, T_COMPLEX) && nucomp_real_p(other)) {
+ get_dat2(self, other);
+ return rb_funcall(adat->real, idCmp, 1, bdat->real);
+ }
+ else if (f_real_p(other)) {
+ get_dat1(self);
+ return rb_funcall(dat->real, idCmp, 1, other);
+ }
+ }
+ return Qnil;
+}
+
+/* :nodoc: */
+static VALUE
+nucomp_coerce(VALUE self, VALUE other)
+{
+ if (RB_TYPE_P(other, T_COMPLEX))
+ return rb_assoc_new(other, self);
+ if (k_numeric_p(other) && f_real_p(other))
+ return rb_assoc_new(f_complex_new_bang1(CLASS_OF(self), other), self);
+
+ rb_raise(rb_eTypeError, "%"PRIsVALUE" can't be coerced into %"PRIsVALUE,
+ rb_obj_class(other), rb_obj_class(self));
+ return Qnil;
+}
+
+/*
+ * call-seq:
+ * cmp.abs -> real
+ * cmp.magnitude -> real
+ *
+ * Returns the absolute part of its polar form.
+ *
+ * Complex(-1).abs #=> 1
+ * Complex(3.0, -4.0).abs #=> 5.0
+ */
+VALUE
+rb_complex_abs(VALUE self)
+{
+ get_dat1(self);
+
+ if (f_zero_p(dat->real)) {
+ VALUE a = f_abs(dat->imag);
+ if (RB_FLOAT_TYPE_P(dat->real) && !RB_FLOAT_TYPE_P(dat->imag))
+ a = f_to_f(a);
+ return a;
+ }
+ if (f_zero_p(dat->imag)) {
+ VALUE a = f_abs(dat->real);
+ if (!RB_FLOAT_TYPE_P(dat->real) && RB_FLOAT_TYPE_P(dat->imag))
+ a = f_to_f(a);
+ return a;
+ }
+ return rb_math_hypot(dat->real, dat->imag);
+}
+
+/*
+ * call-seq:
+ * cmp.abs2 -> real
+ *
+ * Returns square of the absolute value.
+ *
+ * Complex(-1).abs2 #=> 1
+ * Complex(3.0, -4.0).abs2 #=> 25.0
+ */
+static VALUE
+nucomp_abs2(VALUE self)
+{
+ get_dat1(self);
+ return f_add(f_mul(dat->real, dat->real),
+ f_mul(dat->imag, dat->imag));
+}
+
+/*
+ * call-seq:
+ * cmp.arg -> float
+ * cmp.angle -> float
+ * cmp.phase -> float
+ *
+ * Returns the angle part of its polar form.
+ *
+ * Complex.polar(3, Math::PI/2).arg #=> 1.5707963267948966
+ */
+VALUE
+rb_complex_arg(VALUE self)
+{
+ get_dat1(self);
+ return rb_math_atan2(dat->imag, dat->real);
+}
+
+/*
+ * call-seq:
+ * cmp.rect -> array
+ * cmp.rectangular -> array
+ *
+ * Returns an array; [cmp.real, cmp.imag].
+ *
+ * Complex(1, 2).rectangular #=> [1, 2]
+ */
+static VALUE
+nucomp_rect(VALUE self)
+{
+ get_dat1(self);
+ return rb_assoc_new(dat->real, dat->imag);
+}
+
+/*
+ * call-seq:
+ * cmp.polar -> array
+ *
+ * Returns an array; [cmp.abs, cmp.arg].
+ *
+ * Complex(1, 2).polar #=> [2.23606797749979, 1.1071487177940904]
+ */
+static VALUE
+nucomp_polar(VALUE self)
+{
+ return rb_assoc_new(f_abs(self), f_arg(self));
+}
+
+/*
+ * call-seq:
+ * cmp.conj -> complex
+ * cmp.conjugate -> complex
+ *
+ * Returns the complex conjugate.
+ *
+ * Complex(1, 2).conjugate #=> (1-2i)
+ */
+VALUE
+rb_complex_conjugate(VALUE self)
+{
+ get_dat1(self);
+ return f_complex_new2(CLASS_OF(self), dat->real, f_negate(dat->imag));
+}
+
+/*
+ * call-seq:
+ * Complex(1).real? -> false
+ * Complex(1, 2).real? -> false
+ *
+ * Returns false, even if the complex number has no imaginary part.
+ */
+static VALUE
+nucomp_false(VALUE self)
+{
+ return Qfalse;
+}
+
+/*
+ * call-seq:
+ * cmp.denominator -> integer
+ *
+ * Returns the denominator (lcm of both denominator - real and imag).
+ *
+ * See numerator.
+ */
+static VALUE
+nucomp_denominator(VALUE self)
+{
+ get_dat1(self);
+ return rb_lcm(f_denominator(dat->real), f_denominator(dat->imag));
+}
+
+/*
+ * call-seq:
+ * cmp.numerator -> numeric
+ *
+ * Returns the numerator.
+ *
+ * 1 2 3+4i <- numerator
+ * - + -i -> ----
+ * 2 3 6 <- denominator
+ *
+ * c = Complex('1/2+2/3i') #=> ((1/2)+(2/3)*i)
+ * n = c.numerator #=> (3+4i)
+ * d = c.denominator #=> 6
+ * n / d #=> ((1/2)+(2/3)*i)
+ * Complex(Rational(n.real, d), Rational(n.imag, d))
+ * #=> ((1/2)+(2/3)*i)
+ * See denominator.
+ */
+static VALUE
+nucomp_numerator(VALUE self)
+{
+ VALUE cd;
+
+ get_dat1(self);
+
+ cd = nucomp_denominator(self);
+ return f_complex_new2(CLASS_OF(self),
+ f_mul(f_numerator(dat->real),
+ f_div(cd, f_denominator(dat->real))),
+ f_mul(f_numerator(dat->imag),
+ f_div(cd, f_denominator(dat->imag))));
+}
+
+/* :nodoc: */
+st_index_t
+rb_complex_hash(VALUE self)
+{
+ st_index_t v, h[2];
+ VALUE n;
+
+ get_dat1(self);
+ n = rb_hash(dat->real);
+ h[0] = NUM2LONG(n);
+ n = rb_hash(dat->imag);
+ h[1] = NUM2LONG(n);
+ v = rb_memhash(h, sizeof(h));
+ return v;
+}
+
+static VALUE
+nucomp_hash(VALUE self)
+{
+ return ST2FIX(rb_complex_hash(self));
+}
+
+/* :nodoc: */
+static VALUE
+nucomp_eql_p(VALUE self, VALUE other)
+{
+ if (RB_TYPE_P(other, T_COMPLEX)) {
+ get_dat2(self, other);
+
+ return f_boolcast((CLASS_OF(adat->real) == CLASS_OF(bdat->real)) &&
+ (CLASS_OF(adat->imag) == CLASS_OF(bdat->imag)) &&
+ f_eqeq_p(self, other));
+
+ }
+ return Qfalse;
+}
+
+inline static int
+f_signbit(VALUE x)
+{
+ if (RB_FLOAT_TYPE_P(x)) {
+ double f = RFLOAT_VALUE(x);
+ return !isnan(f) && signbit(f);
+ }
+ return f_negative_p(x);
+}
+
+inline static int
+f_tpositive_p(VALUE x)
+{
+ return !f_signbit(x);
+}
+
+static VALUE
+f_format(VALUE self, VALUE (*func)(VALUE))
+{
+ VALUE s;
+ int impos;
+
+ get_dat1(self);
+
+ impos = f_tpositive_p(dat->imag);
+
+ s = (*func)(dat->real);
+ rb_str_cat2(s, !impos ? "-" : "+");
+
+ rb_str_concat(s, (*func)(f_abs(dat->imag)));
+ if (!rb_isdigit(RSTRING_PTR(s)[RSTRING_LEN(s) - 1]))
+ rb_str_cat2(s, "*");
+ rb_str_cat2(s, "i");
+
+ return s;
+}
+
+/*
+ * call-seq:
+ * cmp.to_s -> string
+ *
+ * Returns the value as a string.
+ *
+ * Complex(2).to_s #=> "2+0i"
+ * Complex('-8/6').to_s #=> "-4/3+0i"
+ * Complex('1/2i').to_s #=> "0+1/2i"
+ * Complex(0, Float::INFINITY).to_s #=> "0+Infinity*i"
+ * Complex(Float::NAN, Float::NAN).to_s #=> "NaN+NaN*i"
+ */
+static VALUE
+nucomp_to_s(VALUE self)
+{
+ return f_format(self, rb_String);
+}
+
+/*
+ * call-seq:
+ * cmp.inspect -> string
+ *
+ * Returns the value as a string for inspection.
+ *
+ * Complex(2).inspect #=> "(2+0i)"
+ * Complex('-8/6').inspect #=> "((-4/3)+0i)"
+ * Complex('1/2i').inspect #=> "(0+(1/2)*i)"
+ * Complex(0, Float::INFINITY).inspect #=> "(0+Infinity*i)"
+ * Complex(Float::NAN, Float::NAN).inspect #=> "(NaN+NaN*i)"
+ */
+static VALUE
+nucomp_inspect(VALUE self)
+{
+ VALUE s;
+
+ s = rb_usascii_str_new2("(");
+ rb_str_concat(s, f_format(self, rb_inspect));
+ rb_str_cat2(s, ")");
+
+ return s;
+}
+
+#define FINITE_TYPE_P(v) (RB_INTEGER_TYPE_P(v) || RB_TYPE_P(v, T_RATIONAL))
+
+/*
+ * call-seq:
+ * cmp.finite? -> true or false
+ *
+ * Returns +true+ if +cmp+'s real and imaginary parts are both finite numbers,
+ * otherwise returns +false+.
+ */
+static VALUE
+rb_complex_finite_p(VALUE self)
+{
+ get_dat1(self);
+
+ if (f_finite_p(dat->real) && f_finite_p(dat->imag)) {
+ return Qtrue;
+ }
+ return Qfalse;
+}
+
+/*
+ * call-seq:
+ * cmp.infinite? -> nil or 1
+ *
+ * Returns +1+ if +cmp+'s real or imaginary part is an infinite number,
+ * otherwise returns +nil+.
+ *
+ * For example:
+ *
+ * (1+1i).infinite? #=> nil
+ * (Float::INFINITY + 1i).infinite? #=> 1
+ */
+static VALUE
+rb_complex_infinite_p(VALUE self)
+{
+ get_dat1(self);
+
+ if (NIL_P(f_infinite_p(dat->real)) && NIL_P(f_infinite_p(dat->imag))) {
+ return Qnil;
+ }
+ return ONE;
+}
+
+/* :nodoc: */
+static VALUE
+nucomp_dumper(VALUE self)
+{
+ return self;
+}
+
+/* :nodoc: */
+static VALUE
+nucomp_loader(VALUE self, VALUE a)
+{
+ get_dat1(self);
+
+ RCOMPLEX_SET_REAL(dat, rb_ivar_get(a, id_i_real));
+ RCOMPLEX_SET_IMAG(dat, rb_ivar_get(a, id_i_imag));
+ OBJ_FREEZE_RAW(self);
+
+ return self;
+}
+
+/* :nodoc: */
+static VALUE
+nucomp_marshal_dump(VALUE self)
+{
+ VALUE a;
+ get_dat1(self);
+
+ a = rb_assoc_new(dat->real, dat->imag);
+ rb_copy_generic_ivar(a, self);
+ return a;
+}
+
+/* :nodoc: */
+static VALUE
+nucomp_marshal_load(VALUE self, VALUE a)
+{
+ Check_Type(a, T_ARRAY);
+ if (RARRAY_LEN(a) != 2)
+ rb_raise(rb_eArgError, "marshaled complex must have an array whose length is 2 but %ld", RARRAY_LEN(a));
+ rb_ivar_set(self, id_i_real, RARRAY_AREF(a, 0));
+ rb_ivar_set(self, id_i_imag, RARRAY_AREF(a, 1));
+ return self;
+}
+
+/* --- */
+
+VALUE
+rb_complex_raw(VALUE x, VALUE y)
+{
+ return nucomp_s_new_internal(rb_cComplex, x, y);
+}
+
+VALUE
+rb_complex_new(VALUE x, VALUE y)
+{
+ return nucomp_s_canonicalize_internal(rb_cComplex, x, y);
+}
+
+VALUE
+rb_complex_new_polar(VALUE x, VALUE y)
+{
+ return f_complex_polar(rb_cComplex, x, y);
+}
+
+VALUE
+rb_complex_polar(VALUE x, VALUE y)
+{
+ return rb_complex_new_polar(x, y);
+}
+
+VALUE
+rb_Complex(VALUE x, VALUE y)
+{
+ VALUE a[2];
+ a[0] = x;
+ a[1] = y;
+ return nucomp_s_convert(2, a, rb_cComplex);
+}
+
+/*!
+ * Creates a Complex object.
+ *
+ * \param real real part value
+ * \param imag imaginary part value
+ * \return a new Complex object
+ */
+VALUE
+rb_dbl_complex_new(double real, double imag)
+{
+ return rb_complex_raw(DBL2NUM(real), DBL2NUM(imag));
+}
+
+/*
+ * call-seq:
+ * cmp.to_i -> integer
+ *
+ * Returns the value as an integer if possible (the imaginary part
+ * should be exactly zero).
+ *
+ * Complex(1, 0).to_i #=> 1
+ * Complex(1, 0.0).to_i # RangeError
+ * Complex(1, 2).to_i # RangeError
+ */
+static VALUE
+nucomp_to_i(VALUE self)
+{
+ get_dat1(self);
+
+ if (!k_exact_zero_p(dat->imag)) {
+ rb_raise(rb_eRangeError, "can't convert %"PRIsVALUE" into Integer",
+ self);
+ }
+ return f_to_i(dat->real);
+}
+
+/*
+ * call-seq:
+ * cmp.to_f -> float
+ *
+ * Returns the value as a float if possible (the imaginary part should
+ * be exactly zero).
+ *
+ * Complex(1, 0).to_f #=> 1.0
+ * Complex(1, 0.0).to_f # RangeError
+ * Complex(1, 2).to_f # RangeError
+ */
+static VALUE
+nucomp_to_f(VALUE self)
+{
+ get_dat1(self);
+
+ if (!k_exact_zero_p(dat->imag)) {
+ rb_raise(rb_eRangeError, "can't convert %"PRIsVALUE" into Float",
+ self);
+ }
+ return f_to_f(dat->real);
+}
+
+/*
+ * call-seq:
+ * cmp.to_r -> rational
+ *
+ * Returns the value as a rational if possible (the imaginary part
+ * should be exactly zero).
+ *
+ * Complex(1, 0).to_r #=> (1/1)
+ * Complex(1, 0.0).to_r # RangeError
+ * Complex(1, 2).to_r # RangeError
+ *
+ * See rationalize.
+ */
+static VALUE
+nucomp_to_r(VALUE self)
+{
+ get_dat1(self);
+
+ if (!k_exact_zero_p(dat->imag)) {
+ rb_raise(rb_eRangeError, "can't convert %"PRIsVALUE" into Rational",
+ self);
+ }
+ return f_to_r(dat->real);
+}
+
+/*
+ * call-seq:
+ * cmp.rationalize([eps]) -> rational
+ *
+ * Returns the value as a rational if possible (the imaginary part
+ * should be exactly zero).
+ *
+ * Complex(1.0/3, 0).rationalize #=> (1/3)
+ * Complex(1, 0.0).rationalize # RangeError
+ * Complex(1, 2).rationalize # RangeError
+ *
+ * See to_r.
+ */
+static VALUE
+nucomp_rationalize(int argc, VALUE *argv, VALUE self)
+{
+ get_dat1(self);
+
+ rb_check_arity(argc, 0, 1);
+
+ if (!k_exact_zero_p(dat->imag)) {
+ rb_raise(rb_eRangeError, "can't convert %"PRIsVALUE" into Rational",
+ self);
+ }
+ return rb_funcallv(dat->real, id_rationalize, argc, argv);
+}
+
+/*
+ * call-seq:
+ * complex.to_c -> self
+ *
+ * Returns self.
+ *
+ * Complex(2).to_c #=> (2+0i)
+ * Complex(-8, 6).to_c #=> (-8+6i)
+ */
+static VALUE
+nucomp_to_c(VALUE self)
+{
+ return self;
+}
+
+/*
+ * call-seq:
+ * nil.to_c -> (0+0i)
+ *
+ * Returns zero as a complex.
+ */
+static VALUE
+nilclass_to_c(VALUE self)
+{
+ return rb_complex_new1(INT2FIX(0));
+}
+
+/*
+ * call-seq:
+ * num.to_c -> complex
+ *
+ * Returns the value as a complex.
+ */
+static VALUE
+numeric_to_c(VALUE self)
+{
+ return rb_complex_new1(self);
+}
+
+inline static int
+issign(int c)
+{
+ return (c == '-' || c == '+');
+}
+
+static int
+read_sign(const char **s,
+ char **b)
+{
+ int sign = '?';
+
+ if (issign(**s)) {
+ sign = **b = **s;
+ (*s)++;
+ (*b)++;
+ }
+ return sign;
+}
+
+inline static int
+isdecimal(int c)
+{
+ return isdigit((unsigned char)c);
+}
+
+static int
+read_digits(const char **s, int strict,
+ char **b)
+{
+ int us = 1;
+
+ if (!isdecimal(**s))
+ return 0;
+
+ while (isdecimal(**s) || **s == '_') {
+ if (**s == '_') {
+ if (strict) {
+ if (us)
+ return 0;
+ }
+ us = 1;
+ }
+ else {
+ **b = **s;
+ (*b)++;
+ us = 0;
+ }
+ (*s)++;
+ }
+ if (us)
+ do {
+ (*s)--;
+ } while (**s == '_');
+ return 1;
+}
+
+inline static int
+islettere(int c)
+{
+ return (c == 'e' || c == 'E');
+}
+
+static int
+read_num(const char **s, int strict,
+ char **b)
+{
+ if (**s != '.') {
+ if (!read_digits(s, strict, b))
+ return 0;
+ }
+
+ if (**s == '.') {
+ **b = **s;
+ (*s)++;
+ (*b)++;
+ if (!read_digits(s, strict, b)) {
+ (*b)--;
+ return 0;
+ }
+ }
+
+ if (islettere(**s)) {
+ **b = **s;
+ (*s)++;
+ (*b)++;
+ read_sign(s, b);
+ if (!read_digits(s, strict, b)) {
+ (*b)--;
+ return 0;
+ }
+ }
+ return 1;
+}
+
+inline static int
+read_den(const char **s, int strict,
+ char **b)
+{
+ if (!read_digits(s, strict, b))
+ return 0;
+ return 1;
+}
+
+static int
+read_rat_nos(const char **s, int strict,
+ char **b)
+{
+ if (!read_num(s, strict, b))
+ return 0;
+ if (**s == '/') {
+ **b = **s;
+ (*s)++;
+ (*b)++;
+ if (!read_den(s, strict, b)) {
+ (*b)--;
+ return 0;
+ }
+ }
+ return 1;
+}
+
+static int
+read_rat(const char **s, int strict,
+ char **b)
+{
+ read_sign(s, b);
+ if (!read_rat_nos(s, strict, b))
+ return 0;
+ return 1;
+}
+
+inline static int
+isimagunit(int c)
+{
+ return (c == 'i' || c == 'I' ||
+ c == 'j' || c == 'J');
+}
+
+static VALUE
+str2num(char *s)
+{
+ if (strchr(s, '/'))
+ return rb_cstr_to_rat(s, 0);
+ if (strpbrk(s, ".eE"))
+ return DBL2NUM(rb_cstr_to_dbl(s, 0));
+ return rb_cstr_to_inum(s, 10, 0);
+}
+
+static int
+read_comp(const char **s, int strict,
+ VALUE *ret, char **b)
+{
+ char *bb;
+ int sign;
+ VALUE num, num2;
+
+ bb = *b;
+
+ sign = read_sign(s, b);
+
+ if (isimagunit(**s)) {
+ (*s)++;
+ num = INT2FIX((sign == '-') ? -1 : + 1);
+ *ret = rb_complex_new2(ZERO, num);
+ return 1; /* e.g. "i" */
+ }
+
+ if (!read_rat_nos(s, strict, b)) {
+ **b = '\0';
+ num = str2num(bb);
+ *ret = rb_complex_new2(num, ZERO);
+ return 0; /* e.g. "-" */
+ }
+ **b = '\0';
+ num = str2num(bb);
+
+ if (isimagunit(**s)) {
+ (*s)++;
+ *ret = rb_complex_new2(ZERO, num);
+ return 1; /* e.g. "3i" */
+ }
+
+ if (**s == '@') {
+ int st;
+
+ (*s)++;
+ bb = *b;
+ st = read_rat(s, strict, b);
+ **b = '\0';
+ if (strlen(bb) < 1 ||
+ !isdecimal(*(bb + strlen(bb) - 1))) {
+ *ret = rb_complex_new2(num, ZERO);
+ return 0; /* e.g. "1@-" */
+ }
+ num2 = str2num(bb);
+ *ret = rb_complex_new_polar(num, num2);
+ if (!st)
+ return 0; /* e.g. "1@2." */
+ else
+ return 1; /* e.g. "1@2" */
+ }
+
+ if (issign(**s)) {
+ bb = *b;
+ sign = read_sign(s, b);
+ if (isimagunit(**s))
+ num2 = INT2FIX((sign == '-') ? -1 : + 1);
+ else {
+ if (!read_rat_nos(s, strict, b)) {
+ *ret = rb_complex_new2(num, ZERO);
+ return 0; /* e.g. "1+xi" */
+ }
+ **b = '\0';
+ num2 = str2num(bb);
+ }
+ if (!isimagunit(**s)) {
+ *ret = rb_complex_new2(num, ZERO);
+ return 0; /* e.g. "1+3x" */
+ }
+ (*s)++;
+ *ret = rb_complex_new2(num, num2);
+ return 1; /* e.g. "1+2i" */
+ }
+ /* !(@, - or +) */
+ {
+ *ret = rb_complex_new2(num, ZERO);
+ return 1; /* e.g. "3" */
+ }
+}
+
+inline static void
+skip_ws(const char **s)
+{
+ while (isspace((unsigned char)**s))
+ (*s)++;
+}
+
+static int
+parse_comp(const char *s, int strict, VALUE *num)
+{
+ char *buf, *b;
+ VALUE tmp;
+ int ret = 1;
+
+ buf = ALLOCV_N(char, tmp, strlen(s) + 1);
+ b = buf;
+
+ skip_ws(&s);
+ if (!read_comp(&s, strict, num, &b)) {
+ ret = 0;
+ }
+ else {
+ skip_ws(&s);
+
+ if (strict)
+ if (*s != '\0')
+ ret = 0;
+ }
+ ALLOCV_END(tmp);
+
+ return ret;
+}
+
+static VALUE
+string_to_c_strict(VALUE self, int raise)
+{
+ char *s;
+ VALUE num;
+
+ rb_must_asciicompat(self);
+
+ s = RSTRING_PTR(self);
+
+ if (!s || memchr(s, '\0', RSTRING_LEN(self))) {
+ if (!raise) return Qnil;
+ rb_raise(rb_eArgError, "string contains null byte");
+ }
+
+ if (s && s[RSTRING_LEN(self)]) {
+ rb_str_modify(self);
+ s = RSTRING_PTR(self);
+ s[RSTRING_LEN(self)] = '\0';
+ }
+
+ if (!s)
+ s = (char *)"";
+
+ if (!parse_comp(s, 1, &num)) {
+ if (!raise) return Qnil;
+ rb_raise(rb_eArgError, "invalid value for convert(): %+"PRIsVALUE,
+ self);
+ }
+
+ return num;
+}
+
+/*
+ * call-seq:
+ * str.to_c -> complex
+ *
+ * Returns a complex which denotes the string form. The parser
+ * ignores leading whitespaces and trailing garbage. Any digit
+ * sequences can be separated by an underscore. Returns zero for null
+ * or garbage string.
+ *
+ * '9'.to_c #=> (9+0i)
+ * '2.5'.to_c #=> (2.5+0i)
+ * '2.5/1'.to_c #=> ((5/2)+0i)
+ * '-3/2'.to_c #=> ((-3/2)+0i)
+ * '-i'.to_c #=> (0-1i)
+ * '45i'.to_c #=> (0+45i)
+ * '3-4i'.to_c #=> (3-4i)
+ * '-4e2-4e-2i'.to_c #=> (-400.0-0.04i)
+ * '-0.0-0.0i'.to_c #=> (-0.0-0.0i)
+ * '1/2+3/4i'.to_c #=> ((1/2)+(3/4)*i)
+ * 'ruby'.to_c #=> (0+0i)
+ *
+ * See Kernel.Complex.
+ */
+static VALUE
+string_to_c(VALUE self)
+{
+ char *s;
+ VALUE num;
+
+ rb_must_asciicompat(self);
+
+ s = RSTRING_PTR(self);
+
+ if (s && s[RSTRING_LEN(self)]) {
+ rb_str_modify(self);
+ s = RSTRING_PTR(self);
+ s[RSTRING_LEN(self)] = '\0';
+ }
+
+ if (!s)
+ s = (char *)"";
+
+ (void)parse_comp(s, 0, &num);
+
+ return num;
+}
+
+static VALUE
+to_complex(VALUE val)
+{
+ return rb_convert_type(val, T_COMPLEX, "Complex", "to_c");
+}
+
+static VALUE
+nucomp_convert(VALUE klass, VALUE a1, VALUE a2, int raise)
+{
+ if (NIL_P(a1) || NIL_P(a2)) {
+ if (!raise) return Qnil;
+ rb_raise(rb_eTypeError, "can't convert nil into Complex");
+ }
+
+ if (RB_TYPE_P(a1, T_STRING)) {
+ a1 = string_to_c_strict(a1, raise);
+ if (NIL_P(a1)) return Qnil;
+ }
+
+ if (RB_TYPE_P(a2, T_STRING)) {
+ a2 = string_to_c_strict(a2, raise);
+ if (NIL_P(a2)) return Qnil;
+ }
+
+ if (RB_TYPE_P(a1, T_COMPLEX)) {
+ {
+ get_dat1(a1);
+
+ if (k_exact_zero_p(dat->imag))
+ a1 = dat->real;
+ }
+ }
+
+ if (RB_TYPE_P(a2, T_COMPLEX)) {
+ {
+ get_dat1(a2);
+
+ if (k_exact_zero_p(dat->imag))
+ a2 = dat->real;
+ }
+ }
+
+ if (RB_TYPE_P(a1, T_COMPLEX)) {
+ if (a2 == Qundef || (k_exact_zero_p(a2)))
+ return a1;
+ }
+
+ if (a2 == Qundef) {
+ if (k_numeric_p(a1) && !f_real_p(a1))
+ return a1;
+ /* should raise exception for consistency */
+ if (!k_numeric_p(a1)) {
+ if (!raise)
+ return rb_protect(to_complex, a1, NULL);
+ return to_complex(a1);
+ }
+ }
+ else {
+ if ((k_numeric_p(a1) && k_numeric_p(a2)) &&
+ (!f_real_p(a1) || !f_real_p(a2)))
+ return f_add(a1,
+ f_mul(a2,
+ f_complex_new_bang2(rb_cComplex, ZERO, ONE)));
+ }
+
+ {
+ int argc;
+ VALUE argv2[2];
+ argv2[0] = a1;
+ if (a2 == Qundef) {
+ argv2[1] = Qnil;
+ argc = 1;
+ }
+ else {
+ if (!raise && !RB_INTEGER_TYPE_P(a2) && !RB_FLOAT_TYPE_P(a2) && !RB_TYPE_P(a2, T_RATIONAL))
+ return Qnil;
+ argv2[1] = a2;
+ argc = 2;
+ }
+ return nucomp_s_new(argc, argv2, klass);
+ }
+}
+
+static VALUE
+nucomp_s_convert(int argc, VALUE *argv, VALUE klass)
+{
+ VALUE a1, a2;
+
+ if (rb_scan_args(argc, argv, "11", &a1, &a2) == 1) {
+ a2 = Qundef;
+ }
+
+ return nucomp_convert(klass, a1, a2, TRUE);
+}
+
+/* --- */
+
+/*
+ * call-seq:
+ * num.real -> self
+ *
+ * Returns self.
+ */
+static VALUE
+numeric_real(VALUE self)
+{
+ return self;
+}
+
+/*
+ * call-seq:
+ * num.imag -> 0
+ * num.imaginary -> 0
+ *
+ * Returns zero.
+ */
+static VALUE
+numeric_imag(VALUE self)
+{
+ return INT2FIX(0);
+}
+
+/*
+ * call-seq:
+ * num.abs2 -> real
+ *
+ * Returns square of self.
+ */
+static VALUE
+numeric_abs2(VALUE self)
+{
+ return f_mul(self, self);
+}
+
+/*
+ * call-seq:
+ * num.arg -> 0 or float
+ * num.angle -> 0 or float
+ * num.phase -> 0 or float
+ *
+ * Returns 0 if the value is positive, pi otherwise.
+ */
+static VALUE
+numeric_arg(VALUE self)
+{
+ if (f_positive_p(self))
+ return INT2FIX(0);
+ return DBL2NUM(M_PI);
+}
+
+/*
+ * call-seq:
+ * num.rect -> array
+ * num.rectangular -> array
+ *
+ * Returns an array; [num, 0].
+ */
+static VALUE
+numeric_rect(VALUE self)
+{
+ return rb_assoc_new(self, INT2FIX(0));
+}
+
+static VALUE float_arg(VALUE self);
+
+/*
+ * call-seq:
+ * num.polar -> array
+ *
+ * Returns an array; [num.abs, num.arg].
+ */
+static VALUE
+numeric_polar(VALUE self)
+{
+ VALUE abs, arg;
+
+ if (RB_INTEGER_TYPE_P(self)) {
+ abs = rb_int_abs(self);
+ arg = numeric_arg(self);
+ }
+ else if (RB_FLOAT_TYPE_P(self)) {
+ abs = rb_float_abs(self);
+ arg = float_arg(self);
+ }
+ else if (RB_TYPE_P(self, T_RATIONAL)) {
+ abs = rb_rational_abs(self);
+ arg = numeric_arg(self);
+ }
+ else {
+ abs = f_abs(self);
+ arg = f_arg(self);
+ }
+ return rb_assoc_new(abs, arg);
+}
+
+/*
+ * call-seq:
+ * num.conj -> self
+ * num.conjugate -> self
+ *
+ * Returns self.
+ */
+static VALUE
+numeric_conj(VALUE self)
+{
+ return self;
+}
+
+/*
+ * call-seq:
+ * flo.arg -> 0 or float
+ * flo.angle -> 0 or float
+ * flo.phase -> 0 or float
+ *
+ * Returns 0 if the value is positive, pi otherwise.
+ */
+static VALUE
+float_arg(VALUE self)
+{
+ if (isnan(RFLOAT_VALUE(self)))
+ return self;
+ if (f_tpositive_p(self))
+ return INT2FIX(0);
+ return rb_const_get(rb_mMath, id_PI);
+}
+
+/*
+ * A complex number can be represented as a paired real number with
+ * imaginary unit; a+bi. Where a is real part, b is imaginary part
+ * and i is imaginary unit. Real a equals complex a+0i
+ * mathematically.
+ *
+ * Complex object can be created as literal, and also by using
+ * Kernel#Complex, Complex::rect, Complex::polar or to_c method.
+ *
+ * 2+1i #=> (2+1i)
+ * Complex(1) #=> (1+0i)
+ * Complex(2, 3) #=> (2+3i)
+ * Complex.polar(2, 3) #=> (-1.9799849932008908+0.2822400161197344i)
+ * 3.to_c #=> (3+0i)
+ *
+ * You can also create complex object from floating-point numbers or
+ * strings.
+ *
+ * Complex(0.3) #=> (0.3+0i)
+ * Complex('0.3-0.5i') #=> (0.3-0.5i)
+ * Complex('2/3+3/4i') #=> ((2/3)+(3/4)*i)
+ * Complex('1@2') #=> (-0.4161468365471424+0.9092974268256817i)
+ *
+ * 0.3.to_c #=> (0.3+0i)
+ * '0.3-0.5i'.to_c #=> (0.3-0.5i)
+ * '2/3+3/4i'.to_c #=> ((2/3)+(3/4)*i)
+ * '1@2'.to_c #=> (-0.4161468365471424+0.9092974268256817i)
+ *
+ * A complex object is either an exact or an inexact number.
+ *
+ * Complex(1, 1) / 2 #=> ((1/2)+(1/2)*i)
+ * Complex(1, 1) / 2.0 #=> (0.5+0.5i)
+ */
+void
+Init_Complex(void)
+{
+ VALUE compat;
+ id_abs = rb_intern_const("abs");
+ id_arg = rb_intern_const("arg");
+ id_denominator = rb_intern_const("denominator");
+ id_numerator = rb_intern_const("numerator");
+ id_real_p = rb_intern_const("real?");
+ id_i_real = rb_intern_const("@real");
+ id_i_imag = rb_intern_const("@image"); /* @image, not @imag */
+ id_finite_p = rb_intern_const("finite?");
+ id_infinite_p = rb_intern_const("infinite?");
+ id_rationalize = rb_intern_const("rationalize");
+ id_PI = rb_intern_const("PI");
+
+ rb_cComplex = rb_define_class("Complex", rb_cNumeric);
+
+ rb_define_alloc_func(rb_cComplex, nucomp_s_alloc);
+ rb_undef_method(CLASS_OF(rb_cComplex), "allocate");
+
+ rb_undef_method(CLASS_OF(rb_cComplex), "new");
+
+ rb_define_singleton_method(rb_cComplex, "rectangular", nucomp_s_new, -1);
+ rb_define_singleton_method(rb_cComplex, "rect", nucomp_s_new, -1);
+ rb_define_singleton_method(rb_cComplex, "polar", nucomp_s_polar, -1);
+
+ rb_define_global_function("Complex", nucomp_f_complex, -1);
+
+ rb_undef_methods_from(rb_cComplex, RCLASS_ORIGIN(rb_mComparable));
+ rb_undef_method(rb_cComplex, "%");
+ rb_undef_method(rb_cComplex, "div");
+ rb_undef_method(rb_cComplex, "divmod");
+ rb_undef_method(rb_cComplex, "floor");
+ rb_undef_method(rb_cComplex, "ceil");
+ rb_undef_method(rb_cComplex, "modulo");
+ rb_undef_method(rb_cComplex, "remainder");
+ rb_undef_method(rb_cComplex, "round");
+ rb_undef_method(rb_cComplex, "step");
+ rb_undef_method(rb_cComplex, "truncate");
+ rb_undef_method(rb_cComplex, "i");
+
+ rb_define_method(rb_cComplex, "real", rb_complex_real, 0);
+ rb_define_method(rb_cComplex, "imaginary", rb_complex_imag, 0);
+ rb_define_method(rb_cComplex, "imag", rb_complex_imag, 0);
+
+ rb_define_method(rb_cComplex, "-@", rb_complex_uminus, 0);
+ rb_define_method(rb_cComplex, "+", rb_complex_plus, 1);
+ rb_define_method(rb_cComplex, "-", rb_complex_minus, 1);
+ rb_define_method(rb_cComplex, "*", rb_complex_mul, 1);
+ rb_define_method(rb_cComplex, "/", rb_complex_div, 1);
+ rb_define_method(rb_cComplex, "quo", nucomp_quo, 1);
+ rb_define_method(rb_cComplex, "fdiv", nucomp_fdiv, 1);
+ rb_define_method(rb_cComplex, "**", rb_complex_pow, 1);
+
+ rb_define_method(rb_cComplex, "==", nucomp_eqeq_p, 1);
+ rb_define_method(rb_cComplex, "<=>", nucomp_cmp, 1);
+ rb_define_method(rb_cComplex, "coerce", nucomp_coerce, 1);
+
+ rb_define_method(rb_cComplex, "abs", rb_complex_abs, 0);
+ rb_define_method(rb_cComplex, "magnitude", rb_complex_abs, 0);
+ rb_define_method(rb_cComplex, "abs2", nucomp_abs2, 0);
+ rb_define_method(rb_cComplex, "arg", rb_complex_arg, 0);
+ rb_define_method(rb_cComplex, "angle", rb_complex_arg, 0);
+ rb_define_method(rb_cComplex, "phase", rb_complex_arg, 0);
+ rb_define_method(rb_cComplex, "rectangular", nucomp_rect, 0);
+ rb_define_method(rb_cComplex, "rect", nucomp_rect, 0);
+ rb_define_method(rb_cComplex, "polar", nucomp_polar, 0);
+ rb_define_method(rb_cComplex, "conjugate", rb_complex_conjugate, 0);
+ rb_define_method(rb_cComplex, "conj", rb_complex_conjugate, 0);
+
+ rb_define_method(rb_cComplex, "real?", nucomp_false, 0);
+
+ rb_define_method(rb_cComplex, "numerator", nucomp_numerator, 0);
+ rb_define_method(rb_cComplex, "denominator", nucomp_denominator, 0);
+
+ rb_define_method(rb_cComplex, "hash", nucomp_hash, 0);
+ rb_define_method(rb_cComplex, "eql?", nucomp_eql_p, 1);
+
+ rb_define_method(rb_cComplex, "to_s", nucomp_to_s, 0);
+ rb_define_method(rb_cComplex, "inspect", nucomp_inspect, 0);
+
+ rb_undef_method(rb_cComplex, "positive?");
+ rb_undef_method(rb_cComplex, "negative?");
+
+ rb_define_method(rb_cComplex, "finite?", rb_complex_finite_p, 0);
+ rb_define_method(rb_cComplex, "infinite?", rb_complex_infinite_p, 0);
+
+ rb_define_private_method(rb_cComplex, "marshal_dump", nucomp_marshal_dump, 0);
+ /* :nodoc: */
+ compat = rb_define_class_under(rb_cComplex, "compatible", rb_cObject);
+ rb_define_private_method(compat, "marshal_load", nucomp_marshal_load, 1);
+ rb_marshal_define_compat(rb_cComplex, compat, nucomp_dumper, nucomp_loader);
+
+ /* --- */
+
+ rb_define_method(rb_cComplex, "to_i", nucomp_to_i, 0);
+ rb_define_method(rb_cComplex, "to_f", nucomp_to_f, 0);
+ rb_define_method(rb_cComplex, "to_r", nucomp_to_r, 0);
+ rb_define_method(rb_cComplex, "rationalize", nucomp_rationalize, -1);
+ rb_define_method(rb_cComplex, "to_c", nucomp_to_c, 0);
+ rb_define_method(rb_cNilClass, "to_c", nilclass_to_c, 0);
+ rb_define_method(rb_cNumeric, "to_c", numeric_to_c, 0);
+
+ rb_define_method(rb_cString, "to_c", string_to_c, 0);
+
+ rb_define_private_method(CLASS_OF(rb_cComplex), "convert", nucomp_s_convert, -1);
+
+ /* --- */
+
+ rb_define_method(rb_cNumeric, "real", numeric_real, 0);
+ rb_define_method(rb_cNumeric, "imaginary", numeric_imag, 0);
+ rb_define_method(rb_cNumeric, "imag", numeric_imag, 0);
+ rb_define_method(rb_cNumeric, "abs2", numeric_abs2, 0);
+ rb_define_method(rb_cNumeric, "arg", numeric_arg, 0);
+ rb_define_method(rb_cNumeric, "angle", numeric_arg, 0);
+ rb_define_method(rb_cNumeric, "phase", numeric_arg, 0);
+ rb_define_method(rb_cNumeric, "rectangular", numeric_rect, 0);
+ rb_define_method(rb_cNumeric, "rect", numeric_rect, 0);
+ rb_define_method(rb_cNumeric, "polar", numeric_polar, 0);
+ rb_define_method(rb_cNumeric, "conjugate", numeric_conj, 0);
+ rb_define_method(rb_cNumeric, "conj", numeric_conj, 0);
+
+ rb_define_method(rb_cFloat, "arg", float_arg, 0);
+ rb_define_method(rb_cFloat, "angle", float_arg, 0);
+ rb_define_method(rb_cFloat, "phase", float_arg, 0);
+
+ /*
+ * The imaginary unit.
+ */
+ rb_define_const(rb_cComplex, "I",
+ f_complex_new_bang2(rb_cComplex, ZERO, ONE));
+
+#if !USE_FLONUM
+ rb_gc_register_mark_object(RFLOAT_0 = DBL2NUM(0.0));
+#endif
+
+ rb_provide("complex.so"); /* for backward compatibility */
+}
generated by cgit v1.2.3 (git 2.25.1) at 2026-05-29 20:23:08 +0000