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Diffstat (limited to 'complex.c')
| -rw-r--r-- | complex.c | 2850 |
1 files changed, 2850 insertions, 0 deletions
diff --git a/complex.c b/complex.c new file mode 100644 index 0000000000..85d724f273 --- /dev/null +++ b/complex.c @@ -0,0 +1,2850 @@ +/* + 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> + +#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 "internal/string.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 + +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 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 bool +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 rb_equal(x, ZERO) != 0; +} + +#define f_nonzero_p(x) (!f_zero_p(x)) + +static inline bool +always_finite_type_p(VALUE x) +{ + if (FIXNUM_P(x)) return true; + if (FLONUM_P(x)) return true; /* Infinity can't be a flonum */ + return (RB_INTEGER_TYPE_P(x) || RB_TYPE_P(x, T_RATIONAL)); +} + +inline static int +f_finite_p(VALUE x) +{ + if (always_finite_type_p(x)) { + return TRUE; + } + else if (RB_FLOAT_TYPE_P(x)) { + return isfinite(RFLOAT_VALUE(x)); + } + return RTEST(rb_funcallv(x, id_finite_p, 0, 0)); +} + +inline static int +f_infinite_p(VALUE x) +{ + if (always_finite_type_p(x)) { + return FALSE; + } + else if (RB_FLOAT_TYPE_P(x)) { + return isinf(RFLOAT_VALUE(x)); + } + return RTEST(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), sizeof(struct RComplex), 0); + + RCOMPLEX_SET_REAL(obj, real); + RCOMPLEX_SET_IMAG(obj, imag); + OBJ_FREEZE((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) +{ + RUBY_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) +{ + RUBY_ASSERT(!RB_TYPE_P(x, T_COMPLEX)); + RUBY_ASSERT(!RB_TYPE_P(y, T_COMPLEX)); + return nucomp_s_new_internal(klass, x, y); +} + +WARN_UNUSED_RESULT(inline static VALUE nucomp_real_check(VALUE num)); +inline static VALUE +nucomp_real_check(VALUE num) +{ + if (!RB_INTEGER_TYPE_P(num) && + !RB_FLOAT_TYPE_P(num) && + !RB_TYPE_P(num, T_RATIONAL)) { + if (RB_TYPE_P(num, T_COMPLEX) && nucomp_real_p(num)) { + VALUE real = RCOMPLEX(num)->real; + RUBY_ASSERT(!RB_TYPE_P(real, T_COMPLEX)); + return real; + } + if (!k_numeric_p(num) || !f_real_p(num)) + rb_raise(rb_eTypeError, "not a real"); + } + return num; +} + +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 = 0) -> complex + * + * Returns a new \Complex object formed from the arguments, + * each of which must be an instance of Numeric, + * or an instance of one of its subclasses: + * \Complex, Float, Integer, Rational; + * see {Rectangular Coordinates}[rdoc-ref:Complex@Rectangular+Coordinates]: + * + * Complex.rect(3) # => (3+0i) + * Complex.rect(3, Math::PI) # => (3+3.141592653589793i) + * Complex.rect(-3, -Math::PI) # => (-3-3.141592653589793i) + * + * \Complex.rectangular is an alias for \Complex.rect. + */ +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: + real = nucomp_real_check(real); + imag = ZERO; + break; + default: + real = nucomp_real_check(real); + imag = nucomp_real_check(imag); + break; + } + + return nucomp_s_new_internal(klass, real, imag); +} + +inline static VALUE +f_complex_new2(VALUE klass, VALUE x, VALUE y) +{ + if (RB_TYPE_P(x, T_COMPLEX)) { + get_dat1(x); + x = dat->real; + y = f_add(dat->imag, y); + } + 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(real, imag = 0, exception: true) -> complex or nil + * Complex(s, exception: true) -> complex or nil + * + * Returns a new \Complex object if the arguments are valid; + * otherwise raises an exception if +exception+ is +true+; + * otherwise returns +nil+. + * + * With Numeric arguments +real+ and +imag+, + * returns <tt>Complex.rect(real, imag)</tt> if the arguments are valid. + * + * With string argument +s+, returns a new \Complex object if the argument is valid; + * the string may have: + * + * - One or two numeric substrings, + * each of which specifies a Complex, Float, Integer, Numeric, or Rational value, + * specifying {rectangular coordinates}[rdoc-ref:Complex@Rectangular+Coordinates]: + * + * - Sign-separated real and imaginary numeric substrings + * (with trailing character <tt>'i'</tt>): + * + * Complex('1+2i') # => (1+2i) + * Complex('+1+2i') # => (1+2i) + * Complex('+1-2i') # => (1-2i) + * Complex('-1+2i') # => (-1+2i) + * Complex('-1-2i') # => (-1-2i) + * + * - Real-only numeric string (without trailing character <tt>'i'</tt>): + * + * Complex('1') # => (1+0i) + * Complex('+1') # => (1+0i) + * Complex('-1') # => (-1+0i) + * + * - Imaginary-only numeric string (with trailing character <tt>'i'</tt>): + * + * Complex('1i') # => (0+1i) + * Complex('+1i') # => (0+1i) + * Complex('-1i') # => (0-1i) + * + * - At-sign separated real and imaginary rational substrings, + * each of which specifies a Rational value, + * specifying {polar coordinates}[rdoc-ref:Complex@Polar+Coordinates]: + * + * Complex('1/2@3/4') # => (0.36584443443691045+0.34081938001166706i) + * Complex('+1/2@+3/4') # => (0.36584443443691045+0.34081938001166706i) + * Complex('+1/2@-3/4') # => (0.36584443443691045-0.34081938001166706i) + * Complex('-1/2@+3/4') # => (-0.36584443443691045-0.34081938001166706i) + * Complex('-1/2@-3/4') # => (-0.36584443443691045+0.34081938001166706i) + * + */ +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 && UNDEF_P(a2)) { + 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_real(VALUE klass, VALUE x, VALUE y) +{ + 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))); +} + +static VALUE +f_complex_polar(VALUE klass, VALUE x, VALUE y) +{ + x = nucomp_real_check(x); + y = nucomp_real_check(y); + return f_complex_polar_real(klass, x, 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 = 0) -> complex + * + * Returns a new \Complex object formed from the arguments, + * each of which must be an instance of Numeric, + * or an instance of one of its subclasses: + * \Complex, Float, Integer, Rational. + * Argument +arg+ is given in radians; + * see {Polar Coordinates}[rdoc-ref:Complex@Polar+Coordinates]: + * + * Complex.polar(3) # => (3+0i) + * Complex.polar(3, 2.0) # => (-1.2484405096414273+2.727892280477045i) + * Complex.polar(-3, -2.0) # => (1.2484405096414273+2.727892280477045i) + * + */ +static VALUE +nucomp_s_polar(int argc, VALUE *argv, VALUE klass) +{ + VALUE abs, arg; + + argc = rb_scan_args(argc, argv, "11", &abs, &arg); + abs = nucomp_real_check(abs); + if (argc == 2) { + arg = nucomp_real_check(arg); + } + else { + arg = ZERO; + } + return f_complex_polar_real(klass, abs, arg); +} + +/* + * call-seq: + * real -> numeric + * + * Returns the real value for +self+: + * + * Complex.rect(7).real # => 7 + * Complex.rect(9, -4).real # => 9 + * + * If +self+ was created with + * {polar coordinates}[rdoc-ref:Complex@Polar+Coordinates], the returned value + * is computed, and may be inexact: + * + * Complex.polar(1, Math::PI/4).real # => 0.7071067811865476 # Square root of 2. + * + */ +VALUE +rb_complex_real(VALUE self) +{ + get_dat1(self); + return dat->real; +} + +/* + * call-seq: + * imag -> numeric + * + * Returns the imaginary value for +self+: + * + * Complex.rect(7).imag # => 0 + * Complex.rect(9, -4).imag # => -4 + * + * If +self+ was created with + * {polar coordinates}[rdoc-ref:Complex@Polar+Coordinates], the returned value + * is computed, and may be inexact: + * + * Complex.polar(1, Math::PI/4).imag # => 0.7071067811865476 # Square root of 2. + * + */ +VALUE +rb_complex_imag(VALUE self) +{ + get_dat1(self); + return dat->imag; +} + +/* + * call-seq: + * -self -> complex + * + * Returns +self+, negated, which is the negation of each of its parts: + * + * -Complex.rect(1, 2) # => (-1-2i) + * -Complex.rect(-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: + * self + other -> numeric + * + * Returns the sum of +self+ and +other+: + * + * Complex(1, 2) + 0 # => (1+2i) + * Complex(1, 2) + 1 # => (2+2i) + * Complex(1, 2) + -1 # => (0+2i) + * + * Complex(1, 2) + 1.0 # => (2.0+2i) + * + * Complex(1, 2) + Complex(2, 1) # => (3+3i) + * Complex(1, 2) + Complex(2.0, 1.0) # => (3.0+3.0i) + * + * Complex(1, 2) + Rational(1, 1) # => ((2/1)+2i) + * Complex(1, 2) + Rational(1, 2) # => ((3/2)+2i) + * + * For a computation involving Floats, the result may be inexact (see Float#+): + * + * Complex(1, 2) + 3.14 # => (4.140000000000001+2i) + */ +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: + * self - other -> complex + * + * Returns the difference of +self+ and +other+: + * + * Complex.rect(2, 3) - Complex.rect(2, 3) # => (0+0i) + * Complex.rect(900) - Complex.rect(1) # => (899+0i) + * Complex.rect(-2, 9) - Complex.rect(-9, 2) # => (7+7i) + * Complex.rect(9, 8) - 4 # => (5+8i) + * Complex.rect(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, bool az, bool 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) +{ + bool arzero = f_zero_p(areal); + bool aizero = f_zero_p(aimag); + bool brzero = f_zero_p(breal); + bool 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: + * self * other -> numeric + * + * Returns the numeric product of +self+ and +other+: + * + * Complex.rect(9, 8) * 4 # => (36+32i) + * Complex.rect(20, 9) * 9.8 # => (196.0+88.2i) + * Complex.rect(2, 3) * Complex.rect(2, 3) # => (-5+12i) + * Complex.rect(900) * Complex.rect(1) # => (900+0i) + * Complex.rect(-2, 9) * Complex.rect(-9, 2) # => (0-85i) + * Complex.rect(9, 8) * Rational(2, 3) # => ((6/1)+(16/3)*i) + * + */ +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: + * self / other -> complex + * + * Returns the quotient of +self+ and +other+: + * + * Complex.rect(2, 3) / Complex.rect(2, 3) # => (1+0i) + * Complex.rect(900) / Complex.rect(1) # => (900+0i) + * Complex.rect(-2, 9) / Complex.rect(-9, 2) # => ((36/85)-(77/85)*i) + * Complex.rect(9, 8) / 4 # => ((9/4)+2i) + * Complex.rect(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: + * fdiv(numeric) -> new_complex + * + * Returns <tt>Complex.rect(self.real/numeric, self.imag/numeric)</tt>: + * + * Complex.rect(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); +} + +static VALUE +zero_for(VALUE x) +{ + if (RB_FLOAT_TYPE_P(x)) + return DBL2NUM(0); + if (RB_TYPE_P(x, T_RATIONAL)) + return rb_rational_new(INT2FIX(0), INT2FIX(1)); + + return INT2FIX(0); +} + +static VALUE +complex_pow_for_special_angle(VALUE self, VALUE other) +{ + if (!rb_integer_type_p(other)) { + return Qundef; + } + + get_dat1(self); + VALUE x = Qundef; + int dir; + if (f_zero_p(dat->imag)) { + x = dat->real; + dir = 0; + } + else if (f_zero_p(dat->real)) { + x = dat->imag; + dir = 2; + } + else if (f_eqeq_p(dat->real, dat->imag)) { + x = dat->real; + dir = 1; + } + else if (f_eqeq_p(dat->real, f_negate(dat->imag))) { + x = dat->imag; + dir = 3; + } + else { + dir = 0; + } + + if (UNDEF_P(x)) return x; + + if (f_negative_p(x)) { + x = f_negate(x); + dir += 4; + } + + VALUE zx; + if (dir % 2 == 0) { + zx = rb_num_pow(x, other); + } + else { + zx = rb_num_pow( + rb_funcall(rb_int_mul(TWO, x), '*', 1, x), + rb_int_div(other, TWO) + ); + if (rb_int_odd_p(other)) { + zx = rb_funcall(zx, '*', 1, x); + } + } + static const int dirs[][2] = { + {1, 0}, {1, 1}, {0, 1}, {-1, 1}, {-1, 0}, {-1, -1}, {0, -1}, {1, -1} + }; + int z_dir = FIX2INT(rb_int_modulo(rb_int_mul(INT2FIX(dir), other), INT2FIX(8))); + + VALUE zr = Qfalse, zi = Qfalse; + switch (dirs[z_dir][0]) { + case 0: zr = zero_for(zx); break; + case 1: zr = zx; break; + case -1: zr = f_negate(zx); break; + } + switch (dirs[z_dir][1]) { + case 0: zi = zero_for(zx); break; + case 1: zi = zx; break; + case -1: zi = f_negate(zx); break; + } + return nucomp_s_new_internal(CLASS_OF(self), zr, zi); +} + + +/* + * call-seq: + * self ** exponent -> complex + * + * Returns +self+ raised to the power +exponent+: + * + * Complex.rect(0, 1) ** 2 # => (-1+0i) + * Complex.rect(-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 (other == ONE) { + get_dat1(self); + return nucomp_s_new_internal(CLASS_OF(self), dat->real, dat->imag); + } + + VALUE result = complex_pow_for_special_angle(self, other); + if (!UNDEF_P(result)) return result; + + 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_BIGNUM_TYPE_P(other)) + 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: + * self == other -> true or false + * + * Returns whether both <tt>self.real == other.real</tt> + * and <tt>self.imag == other.imag</tt>: + * + * Complex.rect(2, 3) == Complex.rect(2.0, 3.0) # => true + * + */ +static VALUE +nucomp_eqeq_p(VALUE self, VALUE other) +{ + if (RB_TYPE_P(other, T_COMPLEX)) { + get_dat2(self, other); + + return RBOOL(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 RBOOL(f_eqeq_p(dat->real, other) && f_zero_p(dat->imag)); + } + return RBOOL(f_eqeq_p(other, self)); +} + +static bool +nucomp_real_p(VALUE self) +{ + get_dat1(self); + return f_zero_p(dat->imag); +} + +/* + * call-seq: + * self <=> other -> -1, 0, 1, or nil + * + * Compares +self+ and +other+. + * + * Returns: + * + * - <tt>self.real <=> other.real</tt> if both of the following are true: + * + * - <tt>self.imag == 0</tt>. + * - <tt>other.imag == 0</tt> (always true if +other+ is numeric but not complex). + * + * - +nil+ otherwise. + * + * Examples: + * + * Complex.rect(2) <=> 3 # => -1 + * Complex.rect(2) <=> 2 # => 0 + * Complex.rect(2) <=> 1 # => 1 + * Complex.rect(2, 1) <=> 1 # => nil # self.imag not zero. + * Complex.rect(1) <=> Complex.rect(1, 1) # => nil # object.imag not zero. + * Complex.rect(1) <=> 'Foo' # => nil # object.imag not defined. + * + * \Class \Complex includes module Comparable, + * each of whose methods uses Complex#<=> for comparison. + */ +static VALUE +nucomp_cmp(VALUE self, VALUE other) +{ + if (!k_numeric_p(other)) { + return rb_num_coerce_cmp(self, other, idCmp); + } + if (!nucomp_real_p(self)) { + return Qnil; + } + if (RB_TYPE_P(other, T_COMPLEX)) { + if (nucomp_real_p(other)) { + get_dat2(self, other); + return rb_funcall(adat->real, idCmp, 1, bdat->real); + } + } + else { + get_dat1(self); + if (f_real_p(other)) { + return rb_funcall(dat->real, idCmp, 1, other); + } + else { + return rb_num_coerce_cmp(dat->real, other, idCmp); + } + } + 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: + * abs -> float + * + * Returns the absolute value (magnitude) for +self+; + * see {polar coordinates}[rdoc-ref:Complex@Polar+Coordinates]: + * + * Complex.polar(-1, 0).abs # => 1.0 + * + * If +self+ was created with + * {rectangular coordinates}[rdoc-ref:Complex@Rectangular+Coordinates], the returned value + * is computed, and may be inexact: + * + * Complex.rectangular(1, 1).abs # => 1.4142135623730951 # The square root of 2. + * + */ +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: + * abs2 -> float + * + * Returns square of the absolute value (magnitude) for +self+; + * see {polar coordinates}[rdoc-ref:Complex@Polar+Coordinates]: + * + * Complex.polar(2, 2).abs2 # => 4.0 + * + * If +self+ was created with + * {rectangular coordinates}[rdoc-ref:Complex@Rectangular+Coordinates], the returned value + * is computed, and may be inexact: + * + * Complex.rectangular(1.0/3, 1.0/3).abs2 # => 0.2222222222222222 + * + */ +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: + * arg -> float + * + * Returns the argument (angle) for +self+ in radians; + * see {polar coordinates}[rdoc-ref:Complex@Polar+Coordinates]: + * + * Complex.polar(3, Math::PI/2).arg # => 1.57079632679489660 + * + * If +self+ was created with + * {rectangular coordinates}[rdoc-ref:Complex@Rectangular+Coordinates], the returned value + * is computed, and may be inexact: + * + * Complex.polar(1, 1.0/3).arg # => 0.33333333333333326 + * + */ +VALUE +rb_complex_arg(VALUE self) +{ + get_dat1(self); + return rb_math_atan2(dat->imag, dat->real); +} + +/* + * call-seq: + * rect -> array + * + * Returns the array <tt>[self.real, self.imag]</tt>: + * + * Complex.rect(1, 2).rect # => [1, 2] + * + * See {Rectangular Coordinates}[rdoc-ref:Complex@Rectangular+Coordinates]. + * + * If +self+ was created with + * {polar coordinates}[rdoc-ref:Complex@Polar+Coordinates], the returned value + * is computed, and may be inexact: + * + * Complex.polar(1.0, 1.0).rect # => [0.5403023058681398, 0.8414709848078965] + * + * + * Complex#rectangular is an alias for Complex#rect. + */ +static VALUE +nucomp_rect(VALUE self) +{ + get_dat1(self); + return rb_assoc_new(dat->real, dat->imag); +} + +/* + * call-seq: + * polar -> array + * + * Returns the array <tt>[self.abs, self.arg]</tt>: + * + * Complex.polar(1, 2).polar # => [1.0, 2.0] + * + * See {Polar Coordinates}[rdoc-ref:Complex@Polar+Coordinates]. + * + * If +self+ was created with + * {rectangular coordinates}[rdoc-ref:Complex@Rectangular+Coordinates], the returned value + * is computed, and may be inexact: + * + * Complex.rect(1, 1).polar # => [1.4142135623730951, 0.7853981633974483] + * + */ +static VALUE +nucomp_polar(VALUE self) +{ + return rb_assoc_new(f_abs(self), f_arg(self)); +} + +/* + * call-seq: + * conj -> complex + * + * Returns the conjugate of +self+, <tt>Complex.rect(self.imag, self.real)</tt>: + * + * Complex.rect(1, 2).conj # => (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: + * real? -> false + * + * Returns +false+; for compatibility with Numeric#real?. + */ +static VALUE +nucomp_real_p_m(VALUE self) +{ + return Qfalse; +} + +/* + * call-seq: + * denominator -> integer + * + * Returns the denominator of +self+, which is + * the {least common multiple}[https://en.wikipedia.org/wiki/Least_common_multiple] + * of <tt>self.real.denominator</tt> and <tt>self.imag.denominator</tt>: + * + * Complex.rect(Rational(1, 2), Rational(2, 3)).denominator # => 6 + * + * Note that <tt>n.denominator</tt> of a non-rational numeric is +1+. + * + * Related: Complex#numerator. + */ +static VALUE +nucomp_denominator(VALUE self) +{ + get_dat1(self); + return rb_lcm(f_denominator(dat->real), f_denominator(dat->imag)); +} + +/* + * call-seq: + * numerator -> new_complex + * + * Returns the \Complex object created from the numerators + * of the real and imaginary parts of +self+, + * after converting each part to the + * {lowest common denominator}[https://en.wikipedia.org/wiki/Lowest_common_denominator] + * of the two: + * + * c = Complex.rect(Rational(2, 3), Rational(3, 4)) # => ((2/3)+(3/4)*i) + * c.numerator # => (8+9i) + * + * In this example, the lowest common denominator of the two parts is 12; + * the two converted parts may be thought of as \Rational(8, 12) and \Rational(9, 12), + * whose numerators, respectively, are 8 and 9; + * so the returned value of <tt>c.numerator</tt> is <tt>Complex.rect(8, 9)</tt>. + * + * Related: Complex#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; +} + +/* + * :call-seq: + * hash -> integer + * + * Returns the integer hash value for +self+. + * + * Two \Complex objects created from the same values will have the same hash value + * (and will compare using #eql?): + * + * Complex.rect(1, 2).hash == Complex.rect(1, 2).hash # => true + * + */ +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 RBOOL((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 s, VALUE (*func)(VALUE)) +{ + int impos; + + get_dat1(self); + + impos = f_tpositive_p(dat->imag); + + rb_str_concat(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: + * to_s -> string + * + * Returns a string representation of +self+: + * + * Complex.rect(2).to_s # => "2+0i" + * Complex.rect(-8, 6).to_s # => "-8+6i" + * Complex.rect(0, Rational(1, 2)).to_s # => "0+1/2i" + * Complex.rect(0, Float::INFINITY).to_s # => "0+Infinity*i" + * Complex.rect(Float::NAN, Float::NAN).to_s # => "NaN+NaN*i" + * + */ +static VALUE +nucomp_to_s(VALUE self) +{ + return f_format(self, rb_usascii_str_new2(""), rb_String); +} + +/* + * call-seq: + * inspect -> string + * + * Returns a string representation of +self+: + * + * Complex.rect(2).inspect # => "(2+0i)" + * Complex.rect(-8, 6).inspect # => "(-8+6i)" + * Complex.rect(0, Rational(1, 2)).inspect # => "(0+(1/2)*i)" + * Complex.rect(0, Float::INFINITY).inspect # => "(0+Infinity*i)" + * Complex.rect(Float::NAN, Float::NAN).inspect # => "(NaN+NaN*i)" + * + */ +static VALUE +nucomp_inspect(VALUE self) +{ + VALUE s; + + s = rb_usascii_str_new2("("); + f_format(self, s, 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: + * finite? -> true or false + * + * Returns +true+ if both <tt>self.real.finite?</tt> and <tt>self.imag.finite?</tt> + * are true, +false+ otherwise: + * + * Complex.rect(1, 1).finite? # => true + * Complex.rect(Float::INFINITY, 0).finite? # => false + * + * Related: Numeric#finite?, Float#finite?. + */ +static VALUE +rb_complex_finite_p(VALUE self) +{ + get_dat1(self); + + return RBOOL(f_finite_p(dat->real) && f_finite_p(dat->imag)); +} + +/* + * call-seq: + * infinite? -> 1 or nil + * + * Returns +1+ if either <tt>self.real.infinite?</tt> or <tt>self.imag.infinite?</tt> + * is true, +nil+ otherwise: + * + * Complex.rect(Float::INFINITY, 0).infinite? # => 1 + * Complex.rect(1, 1).infinite? # => nil + * + * Related: Numeric#infinite?, Float#infinite?. + */ +static VALUE +rb_complex_infinite_p(VALUE self) +{ + get_dat1(self); + + if (!f_infinite_p(dat->real) && !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(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(VALUE x, VALUE y) +{ + VALUE a[2]; + a[0] = x; + a[1] = y; + return nucomp_s_convert(2, a, rb_cComplex); +} + +VALUE +rb_dbl_complex_new(double real, double imag) +{ + return rb_complex_raw(DBL2NUM(real), DBL2NUM(imag)); +} + +/* + * call-seq: + * to_i -> integer + * + * Returns the value of <tt>self.real</tt> as an Integer, if possible: + * + * Complex.rect(1, 0).to_i # => 1 + * Complex.rect(1, Rational(0, 1)).to_i # => 1 + * + * Raises RangeError if <tt>self.imag</tt> is not exactly zero + * (either <tt>Integer(0)</tt> or <tt>Rational(0, n)</tt>). + */ +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: + * to_f -> float + * + * Returns the value of <tt>self.real</tt> as a Float, if possible: + * + * Complex.rect(1, 0).to_f # => 1.0 + * Complex.rect(1, Rational(0, 1)).to_f # => 1.0 + * + * Raises RangeError if <tt>self.imag</tt> is not exactly zero + * (either <tt>Integer(0)</tt> or <tt>Rational(0, n)</tt>). + */ +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: + * to_r -> rational + * + * Returns the value of <tt>self.real</tt> as a Rational, if possible: + * + * Complex.rect(1, 0).to_r # => (1/1) + * Complex.rect(1, Rational(0, 1)).to_r # => (1/1) + * Complex.rect(1, 0.0).to_r # => (1/1) + * + * Raises RangeError if <tt>self.imag</tt> is not exactly zero + * (either <tt>Integer(0)</tt> or <tt>Rational(0, n)</tt>) + * and <tt>self.imag.to_r</tt> is not exactly zero. + * + * Related: Complex#rationalize. + */ +static VALUE +nucomp_to_r(VALUE self) +{ + get_dat1(self); + + if (RB_FLOAT_TYPE_P(dat->imag) && FLOAT_ZERO_P(dat->imag)) { + /* Do nothing here */ + } + else if (!k_exact_zero_p(dat->imag)) { + VALUE imag = rb_check_convert_type_with_id(dat->imag, T_RATIONAL, "Rational", idTo_r); + if (NIL_P(imag) || !k_exact_zero_p(imag)) { + rb_raise(rb_eRangeError, "can't convert %"PRIsVALUE" into Rational", + self); + } + } + return f_to_r(dat->real); +} + +/* + * call-seq: + * rationalize(epsilon = nil) -> rational + * + * Returns a Rational object whose value is exactly or approximately + * equivalent to that of <tt>self.real</tt>. + * + * With no argument +epsilon+ given, returns a \Rational object + * whose value is exactly equal to that of <tt>self.real.rationalize</tt>: + * + * Complex.rect(1, 0).rationalize # => (1/1) + * Complex.rect(1, Rational(0, 1)).rationalize # => (1/1) + * Complex.rect(3.14159, 0).rationalize # => (314159/100000) + * + * With argument +epsilon+ given, returns a \Rational object + * whose value is exactly or approximately equal to that of <tt>self.real</tt> + * to the given precision: + * + * Complex.rect(3.14159, 0).rationalize(0.1) # => (16/5) + * Complex.rect(3.14159, 0).rationalize(0.01) # => (22/7) + * Complex.rect(3.14159, 0).rationalize(0.001) # => (201/64) + * Complex.rect(3.14159, 0).rationalize(0.0001) # => (333/106) + * Complex.rect(3.14159, 0).rationalize(0.00001) # => (355/113) + * Complex.rect(3.14159, 0).rationalize(0.000001) # => (7433/2366) + * Complex.rect(3.14159, 0).rationalize(0.0000001) # => (9208/2931) + * Complex.rect(3.14159, 0).rationalize(0.00000001) # => (47460/15107) + * Complex.rect(3.14159, 0).rationalize(0.000000001) # => (76149/24239) + * Complex.rect(3.14159, 0).rationalize(0.0000000001) # => (314159/100000) + * Complex.rect(3.14159, 0).rationalize(0.0) # => (3537115888337719/1125899906842624) + * + * Related: Complex#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: + * to_c -> self + * + * Returns +self+. + */ +static VALUE +nucomp_to_c(VALUE self) +{ + return self; +} + +/* + * call-seq: + * to_c -> complex + * + * Returns +self+ as a Complex object. + */ +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 (us) { + if (strict) return 0; + break; + } + 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); + + if (raise) { + s = StringValueCStr(self); + } + else if (!(s = rb_str_to_cstr(self))) { + return Qnil; + } + + if (!parse_comp(s, TRUE, &num)) { + if (!raise) return Qnil; + rb_raise(rb_eArgError, "invalid value for convert(): %+"PRIsVALUE, + self); + } + + return num; +} + +/* + * call-seq: + * to_c -> complex + * + * Returns a Complex object: + * parses the leading substring of +self+ + * to extract two numeric values that become the coordinates of the complex object. + * + * The substring is interpreted as containing + * either rectangular coordinates (real and imaginary parts) + * or polar coordinates (magnitude and angle parts), + * depending on an included or implied "separator" character: + * + * - <tt>'+'</tt>, <tt>'-'</tt>, or no separator: rectangular coordinates. + * - <tt>'@'</tt>: polar coordinates. + * + * <b>In Brief</b> + * + * In these examples, we use method Complex#rect to display rectangular coordinates, + * and method Complex#polar to display polar coordinates. + * + * # Rectangular coordinates. + * + * # Real-only: no separator; imaginary part is zero. + * '9'.to_c.rect # => [9, 0] # Integer. + * '-9'.to_c.rect # => [-9, 0] # Integer (negative). + * '2.5'.to_c.rect # => [2.5, 0] # Float. + * '1.23e-14'.to_c.rect # => [1.23e-14, 0] # Float with exponent. + * '2.5/1'.to_c.rect # => [(5/2), 0] # Rational. + * + * # Some things are ignored. + * 'foo1'.to_c.rect # => [0, 0] # Unparsed entire substring. + * '1foo'.to_c.rect # => [1, 0] # Unparsed trailing substring. + * ' 1 '.to_c.rect # => [1, 0] # Leading and trailing whitespace. + * * + * # Imaginary only: trailing 'i' required; real part is zero. + * '9i'.to_c.rect # => [0, 9] + * '-9i'.to_c.rect # => [0, -9] + * '2.5i'.to_c.rect # => [0, 2.5] + * '1.23e-14i'.to_c.rect # => [0, 1.23e-14] + * '2.5/1i'.to_c.rect # => [0, (5/2)] + * + * # Real and imaginary; '+' or '-' separator; trailing 'i' required. + * '2+3i'.to_c.rect # => [2, 3] + * '-2-3i'.to_c.rect # => [-2, -3] + * '2.5+3i'.to_c.rect # => [2.5, 3] + * '2.5+3/2i'.to_c.rect # => [2.5, (3/2)] + * + * # Polar coordinates; '@' separator; magnitude required. + * '1.0@0'.to_c.polar # => [1.0, 0.0] + * '1.0@'.to_c.polar # => [1.0, 0.0] + * "1.0@#{Math::PI}".to_c.polar # => [1.0, 3.141592653589793] + * "1.0@#{Math::PI/2}".to_c.polar # => [1.0, 1.5707963267948966] + * + * <b>Parsed Values</b> + * + * The parsing may be thought of as searching for numeric literals + * embedded in the substring. + * + * This section shows how the method parses numeric values from leading substrings. + * The examples show real-only or imaginary-only parsing; + * the parsing is the same for each part. + * + * '1foo'.to_c # => (1+0i) # Ignores trailing unparsed characters. + * ' 1 '.to_c # => (1+0i) # Ignores leading and trailing whitespace. + * 'x1'.to_c # => (0+0i) # Finds no leading numeric. + * + * # Integer literal embedded in the substring. + * '1'.to_c # => (1+0i) + * '-1'.to_c # => (-1+0i) + * '1i'.to_c # => (0+1i) + * + * # Integer literals that don't work. + * '0b100'.to_c # => (0+0i) # Not parsed as binary. + * '0o100'.to_c # => (0+0i) # Not parsed as octal. + * '0d100'.to_c # => (0+0i) # Not parsed as decimal. + * '0x100'.to_c # => (0+0i) # Not parsed as hexadecimal. + * '010'.to_c # => (10+0i) # Not parsed as octal. + * + * # Float literals: + * '3.14'.to_c # => (3.14+0i) + * '3.14i'.to_c # => (0+3.14i) + * '1.23e4'.to_c # => (12300.0+0i) + * '1.23e+4'.to_c # => (12300.0+0i) + * '1.23e-4'.to_c # => (0.000123+0i) + * + * # Rational literals: + * '1/2'.to_c # => ((1/2)+0i) + * '-1/2'.to_c # => ((-1/2)+0i) + * '1/2r'.to_c # => ((1/2)+0i) + * '-1/2r'.to_c # => ((-1/2)+0i) + * + * <b>Rectangular Coordinates</b> + * + * With separator <tt>'+'</tt> or <tt>'-'</tt>, + * or with no separator, + * interprets the values as rectangular coordinates: real and imaginary. + * + * With no separator, assigns a single value to either the real or the imaginary part: + * + * ''.to_c # => (0+0i) # Defaults to zero. + * '1'.to_c # => (1+0i) # Real (no trailing 'i'). + * '1i'.to_c # => (0+1i) # Imaginary (trailing 'i'). + * 'i'.to_c # => (0+1i) # Special case (imaginary 1). + * + * With separator <tt>'+'</tt>, both parts positive (or zero): + * + * # Without trailing 'i'. + * '+'.to_c # => (0+0i) # No values: defaults to zero. + * '+1'.to_c # => (1+0i) # Value after '+': real only. + * '1+'.to_c # => (1+0i) # Value before '+': real only. + * '2+1'.to_c # => (2+0i) # Values before and after '+': real and imaginary. + * # With trailing 'i'. + * '+1i'.to_c # => (0+1i) # Value after '+': imaginary only. + * '2+i'.to_c # => (2+1i) # Value before '+': real and imaginary 1. + * '2+1i'.to_c # => (2+1i) # Values before and after '+': real and imaginary. + * + * With separator <tt>'-'</tt>, negative imaginary part: + * + * # Without trailing 'i'. + * '-'.to_c # => (0+0i) # No values: defaults to zero. + * '-1'.to_c # => (-1+0i) # Value after '-': negative real, zero imaginary. + * '1-'.to_c # => (1+0i) # Value before '-': positive real, zero imaginary. + * '2-1'.to_c # => (2+0i) # Values before and after '-': positive real, zero imaginary. + * # With trailing 'i'. + * '-1i'.to_c # => (0-1i) # Value after '-': negative real, zero imaginary. + * '2-i'.to_c # => (2-1i) # Value before '-': positive real, negative imaginary. + * '2-1i'.to_c # => (2-1i) # Values before and after '-': positive real, negative imaginary. + * + * Note that the suffixed character <tt>'i'</tt> + * may instead be one of <tt>'I'</tt>, <tt>'j'</tt>, or <tt>'J'</tt>, + * with the same effect. + * + * <b>Polar Coordinates</b> + * + * With separator <tt>'@'</tt>) + * interprets the values as polar coordinates: magnitude and angle. + * + * '2@'.to_c.polar # => [2, 0.0] # Value before '@': magnitude only. + * # Values before and after '@': magnitude and angle. + * '2@1'.to_c.polar # => [2.0, 1.0] + * "1.0@#{Math::PI/2}".to_c # => (0.0+1i) + * "1.0@#{Math::PI}".to_c # => (-1+0.0i) + * # Magnitude not given: defaults to zero. + * '@'.to_c.polar # => [0, 0.0] + * '@1'.to_c.polar # => [0, 0.0] + * + * '1.0@0'.to_c # => (1+0.0i) + * + * Note that in all cases, the suffixed character <tt>'i'</tt> + * may instead be one of <tt>'I'</tt>, <tt>'j'</tt>, <tt>'J'</tt>, + * with the same effect. + * + * See {Converting to Non-String}[rdoc-ref:String@Converting+to+Non--5CString]. + */ +static VALUE +string_to_c(VALUE self) +{ + VALUE num; + + rb_must_asciicompat(self); + + (void)parse_comp(rb_str_fill_terminator(self, 1), FALSE, &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 (UNDEF_P(a2) || (k_exact_zero_p(a2))) + return a1; + } + + if (UNDEF_P(a2)) { + if (k_numeric_p(a1) && !f_real_p(a1)) + return a1; + /* should raise exception for consistency */ + if (!k_numeric_p(a1)) { + if (!raise) { + a1 = rb_protect(to_complex, a1, NULL); + rb_set_errinfo(Qnil); + return a1; + } + 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 (UNDEF_P(a2)) { + 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: + * abs2 -> real + * + * Returns the square of +self+. + */ +static VALUE +numeric_abs2(VALUE self) +{ + return f_mul(self, self); +} + +/* + * call-seq: + * arg -> 0 or Math::PI + * + * Returns zero if +self+ is positive, Math::PI otherwise. + */ +static VALUE +numeric_arg(VALUE self) +{ + if (f_positive_p(self)) + return INT2FIX(0); + return DBL2NUM(M_PI); +} + +/* + * call-seq: + * rect -> array + * + * Returns array <tt>[self, 0]</tt>. + */ +static VALUE +numeric_rect(VALUE self) +{ + return rb_assoc_new(self, INT2FIX(0)); +} + +/* + * call-seq: + * polar -> array + * + * Returns array <tt>[self.abs, self.arg]</tt>. + */ +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: + * arg -> 0 or Math::PI + * + * Returns 0 if +self+ is positive, Math::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 object houses a pair of values, + * given when the object is created as either <i>rectangular coordinates</i> + * or <i>polar coordinates</i>. + * + * == Rectangular Coordinates + * + * The rectangular coordinates of a complex number + * are called the _real_ and _imaginary_ parts; + * see {Complex number definition}[https://en.wikipedia.org/wiki/Complex_number#Definition_and_basic_operations]. + * + * You can create a \Complex object from rectangular coordinates with: + * + * - A {complex literal}[rdoc-ref:syntax/literals.rdoc@Complex+Literals]. + * - Method Complex.rect. + * - Method Kernel#Complex, either with numeric arguments or with certain string arguments. + * - Method String#to_c, for certain strings. + * + * Note that each of the stored parts may be a an instance one of the classes + * Complex, Float, Integer, or Rational; + * they may be retrieved: + * + * - Separately, with methods Complex#real and Complex#imaginary. + * - Together, with method Complex#rect. + * + * The corresponding (computed) polar values may be retrieved: + * + * - Separately, with methods Complex#abs and Complex#arg. + * - Together, with method Complex#polar. + * + * == Polar Coordinates + * + * The polar coordinates of a complex number + * are called the _absolute_ and _argument_ parts; + * see {Complex polar plane}[https://en.wikipedia.org/wiki/Complex_number#Polar_form]. + * + * In this class, the argument part + * in expressed {radians}[https://en.wikipedia.org/wiki/Radian] + * (not {degrees}[https://en.wikipedia.org/wiki/Degree_(angle)]). + * + * You can create a \Complex object from polar coordinates with: + * + * - Method Complex.polar. + * - Method Kernel#Complex, with certain string arguments. + * - Method String#to_c, for certain strings. + * + * Note that each of the stored parts may be a an instance one of the classes + * Complex, Float, Integer, or Rational; + * they may be retrieved: + * + * - Separately, with methods Complex#abs and Complex#arg. + * - Together, with method Complex#polar. + * + * The corresponding (computed) rectangular values may be retrieved: + * + * - Separately, with methods Complex#real and Complex#imag. + * - Together, with method Complex#rect. + * + * == What's Here + * + * First, what's elsewhere: + * + * - Class \Complex inherits (directly or indirectly) + * from classes {Numeric}[rdoc-ref:Numeric@What-27s+Here] + * and {Object}[rdoc-ref:Object@What-27s+Here]. + * - Includes (indirectly) module {Comparable}[rdoc-ref:Comparable@What-27s+Here]. + * + * Here, class \Complex has methods for: + * + * === Creating \Complex Objects + * + * - ::polar: Returns a new \Complex object based on given polar coordinates. + * - ::rect (and its alias ::rectangular): + * Returns a new \Complex object based on given rectangular coordinates. + * + * === Querying + * + * - #abs (and its alias #magnitude): Returns the absolute value for +self+. + * - #arg (and its aliases #angle and #phase): + * Returns the argument (angle) for +self+ in radians. + * - #denominator: Returns the denominator of +self+. + * - #finite?: Returns whether both +self.real+ and +self.image+ are finite. + * - #hash: Returns the integer hash value for +self+. + * - #imag (and its alias #imaginary): Returns the imaginary value for +self+. + * - #infinite?: Returns whether +self.real+ or +self.image+ is infinite. + * - #numerator: Returns the numerator of +self+. + * - #polar: Returns the array <tt>[self.abs, self.arg]</tt>. + * - #inspect: Returns a string representation of +self+. + * - #real: Returns the real value for +self+. + * - #real?: Returns +false+; for compatibility with Numeric#real?. + * - #rect (and its alias #rectangular): + * Returns the array <tt>[self.real, self.imag]</tt>. + * + * === Comparing + * + * - #<=>: Returns whether +self+ is less than, equal to, or greater than the given argument. + * - #==: Returns whether +self+ is equal to the given argument. + * + * === Converting + * + * - #rationalize: Returns a Rational object whose value is exactly + * or approximately equivalent to that of <tt>self.real</tt>. + * - #to_c: Returns +self+. + * - #to_d: Returns the value as a BigDecimal object. + * - #to_f: Returns the value of <tt>self.real</tt> as a Float, if possible. + * - #to_i: Returns the value of <tt>self.real</tt> as an Integer, if possible. + * - #to_r: Returns the value of <tt>self.real</tt> as a Rational, if possible. + * - #to_s: Returns a string representation of +self+. + * + * === Performing Complex Arithmetic + * + * - #*: Returns the product of +self+ and the given numeric. + * - #**: Returns +self+ raised to power of the given numeric. + * - #+: Returns the sum of +self+ and the given numeric. + * - #-: Returns the difference of +self+ and the given numeric. + * - #-@: Returns the negation of +self+. + * - #/: Returns the quotient of +self+ and the given numeric. + * - #abs2: Returns square of the absolute value (magnitude) for +self+. + * - #conj (and its alias #conjugate): Returns the conjugate of +self+. + * - #fdiv: Returns <tt>Complex.rect(self.real/numeric, self.imag/numeric)</tt>. + * + * === Working with JSON + * + * - ::json_create: Returns a new \Complex object, + * deserialized from the given serialized hash. + * - #as_json: Returns a serialized hash constructed from +self+. + * - #to_json: Returns a JSON string representing +self+. + * + * These methods are provided by the {JSON gem}[https://github.com/ruby/json]. To make these methods available: + * + * require 'json/add/complex' + * + */ +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_real_p_m, 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_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, "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_cFloat, "arg", float_arg, 0); + rb_define_method(rb_cFloat, "angle", float_arg, 0); + rb_define_method(rb_cFloat, "phase", float_arg, 0); + + /* + * Equivalent + * to <tt>Complex.rect(0, 1)</tt>: + * + * Complex::I # => (0+1i) + * + */ + rb_define_const(rb_cComplex, "I", + f_complex_new_bang2(rb_cComplex, ZERO, ONE)); + +#if !USE_FLONUM + rb_vm_register_global_object(RFLOAT_0 = DBL2NUM(0.0)); +#endif + + rb_provide("complex.so"); /* for backward compatibility */ +} |