/* 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/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 #include "internal.h" #define NDEBUG #include "ruby_assert.h" #define ZERO INT2FIX(0) #define ONE INT2FIX(1) #define TWO INT2FIX(2) #define RFLOAT_0 DBL2NUM(0) #if defined(HAVE_SIGNBIT) && defined(__GNUC__) && defined(__sun) && \ !defined(signbit) extern int signbit(double); #endif VALUE rb_cComplex; static VALUE nucomp_abs(VALUE self); static VALUE nucomp_arg(VALUE self); static ID id_abs, id_arg, id_denominator, id_expt, id_fdiv, id_negate, id_numerator, id_quo, id_real_p, id_to_f, id_to_i, id_to_r, id_i_real, id_i_imag, id_finite_p, id_infinite_p, id_rationalize, id_PI; #define f_boolcast(x) ((x) ? Qtrue : Qfalse) #define binop(n,op) \ inline static VALUE \ f_##n(VALUE x, VALUE y)\ {\ return rb_funcall(x, (op), 1, y);\ } #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 math1(n) \ inline static VALUE \ m_##n(VALUE x)\ {\ return rb_funcall(rb_mMath, id_##n, 1, x);\ } #define math2(n) \ inline static VALUE \ m_##n(VALUE x, VALUE y)\ {\ return rb_funcall(rb_mMath, id_##n, 2, x, y);\ } #define PRESERVE_SIGNEDZERO inline static VALUE f_add(VALUE x, VALUE y) { #ifndef PRESERVE_SIGNEDZERO if (FIXNUM_P(y) && FIXNUM_ZERO_P(y)) return x; else if (FIXNUM_P(x) && FIXNUM_ZERO_P(x)) return y; #endif 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) { #ifndef PRESERVE_SIGNEDZERO if (FIXNUM_P(y)) { long iy = FIX2LONG(y); if (iy == 0) { if (RB_INTEGER_TYPE_P(x)) return ZERO; } else if (iy == 1) return x; } else if (FIXNUM_P(x)) { long ix = FIX2LONG(x); if (ix == 0) { if (RB_INTEGER_TYPE_P(y)) return ZERO; } else if (ix == 1) return y; } #endif return rb_funcall(x, '*', 1, y); } inline static VALUE f_sub(VALUE x, VALUE y) { #ifndef PRESERVE_SIGNEDZERO if (FIXNUM_P(y) && FIXNUM_ZERO_P(y)) return x; #endif return rb_funcall(x, '-', 1, y); } fun1(abs) fun1(arg) fun1(denominator) static VALUE nucomp_negate(VALUE self); 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 nucomp_negate(x); } return rb_funcall(x, id_negate, 0); } fun1(numerator) fun1(real_p) 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) fun2(quo) 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_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)) 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); return (VALUE)obj; } static VALUE nucomp_s_alloc(VALUE klass) { return nucomp_s_new_internal(klass, ZERO, ZERO); } #if 0 static VALUE nucomp_s_new_bang(int argc, VALUE *argv, VALUE klass) { VALUE real, imag; switch (rb_scan_args(argc, argv, "11", &real, &imag)) { case 1: if (!k_numeric_p(real)) real = f_to_i(real); imag = ZERO; break; default: if (!k_numeric_p(real)) real = f_to_i(real); if (!k_numeric_p(imag)) imag = f_to_i(imag); break; } return nucomp_s_new_internal(klass, real, imag); } #endif 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); } #ifdef CANONICALIZATION_FOR_MATHN #define CANON #endif #ifdef CANON static int canonicalization = 0; RUBY_FUNC_EXPORTED void nucomp_canonicalization(int f) { canonicalization = f; } #else #define canonicalization 0 #endif 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) { #ifdef CANON #define CL_CANON #ifdef CL_CANON if (k_exact_zero_p(imag) && canonicalization) return real; #else if (f_zero_p(imag) && canonicalization) return real; #endif #endif if (f_real_p(real) && f_real_p(imag)) return nucomp_s_new_internal(klass, real, imag); else if (f_real_p(real)) { get_dat1(imag); return nucomp_s_new_internal(klass, f_sub(real, dat->imag), f_add(ZERO, dat->real)); } else if (f_real_p(imag)) { 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_s_convert(int argc, VALUE *argv, VALUE klass); /* * call-seq: * Complex(x[, y]) -> numeric * * Returns x+i*y; * * Complex(1, 2) #=> (1+2i) * Complex('1+2i') #=> (1+2i) * Complex(nil) #=> TypeError * Complex(1, nil) #=> TypeError * * 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) { return nucomp_s_convert(argc, argv, rb_cComplex); } #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 (f_real_p(x)) 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 (f_real_p(x)) 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))); } } #if 0 imp1(sqrt) VALUE rb_complex_sqrt(VALUE x) { int pos; VALUE a, re, im; get_dat1(x); pos = f_positive_p(dat->imag); a = f_abs(x); re = m_sqrt_bang(f_div(f_add(a, dat->real), TWO)); im = m_sqrt_bang(f_div(f_sub(a, dat->real), TWO)); if (!pos) im = f_negate(im); return f_complex_new2(rb_cComplex, re, im); } static VALUE m_sqrt(VALUE x) { if (f_real_p(x)) { if (f_positive_p(x)) return m_sqrt_bang(x); return f_complex_new2(rb_cComplex, ZERO, m_sqrt_bang(f_negate(x))); } return rb_complex_sqrt(x); } #endif 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)) { if (canonicalization) return x; 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); if (canonicalization) return 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); if (canonicalization && imag == 0.0) return x; y = DBL2NUM(imag); } else { y = f_mul(x, DBL2NUM(sin(arg))); x = f_mul(x, DBL2NUM(cos(arg))); if (canonicalization && f_zero_p(y)) return x; } 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))); } /* * 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); if (canonicalization) return abs; return nucomp_s_new_internal(klass, abs, ZERO); default: nucomp_real_check(abs); nucomp_real_check(arg); break; } 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 */ static VALUE nucomp_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 */ static VALUE nucomp_imag(VALUE self) { get_dat1(self); return dat->imag; } /* * call-seq: * -cmp -> complex * * Returns negation of the value. * * -Complex(1, 2) #=> (-1-2i) */ static VALUE nucomp_negate(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) */ static VALUE nucomp_sub(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); } /* * 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; VALUE areal, aimag, breal, bimag; int arzero, aizero, brzero, bizero; get_dat2(self, other); arzero = f_zero_p(areal = adat->real); aizero = f_zero_p(aimag = adat->imag); brzero = f_zero_p(breal = bdat->real); bizero = f_zero_p(bimag = bdat->imag); 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)); 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, '*'); } #define nucomp_mul rb_complex_mul inline static VALUE f_divide(VALUE self, VALUE other, VALUE (*func)(VALUE, VALUE), ID id) { if (RB_TYPE_P(other, T_COMPLEX)) { 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))) { VALUE r, n; r = (*func)(bdat->imag, bdat->real); n = f_mul(bdat->real, f_add(ONE, f_mul(r, r))); if (flo) return f_complex_new2(CLASS_OF(self), (*func)(self, n), (*func)(f_negate(f_mul(self, r)), n)); return f_complex_new2(CLASS_OF(self), (*func)(f_add(adat->real, f_mul(adat->imag, r)), n), (*func)(f_sub(adat->imag, f_mul(adat->real, r)), n)); } else { VALUE r, n; r = (*func)(bdat->real, bdat->imag); n = f_mul(bdat->imag, f_add(ONE, f_mul(r, r))); if (flo) return f_complex_new2(CLASS_OF(self), (*func)(f_mul(self, r), n), (*func)(f_negate(self), n)); return f_complex_new2(CLASS_OF(self), (*func)(f_add(f_mul(adat->real, r), adat->imag), n), (*func)(f_sub(f_mul(adat->imag, r), adat->real), n)); } } if (k_numeric_p(other) && f_real_p(other)) { get_dat1(self); return f_complex_new2(CLASS_OF(self), (*func)(dat->real, other), (*func)(dat->imag, other)); } 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) */ static VALUE nucomp_div(VALUE self, VALUE other) { return f_divide(self, other, f_quo, id_quo); } #define nucomp_quo nucomp_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) */ static VALUE nucomp_expt(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)) { if (f_gt_p(other, ZERO)) { VALUE x, z; long n; x = self; z = x; n = FIX2LONG(other) - 1; while (n) { long q, r; while (1) { get_dat1(x); q = n / 2; r = n % 2; if (r) break; x = nucomp_s_new_internal(CLASS_OF(self), f_sub(f_mul(dat->real, dat->real), f_mul(dat->imag, dat->imag)), f_mul(f_mul(TWO, dat->real), dat->imag)); n = q; } z = f_mul(z, x); n--; } return z; } return f_expt(f_reciprocal(self), rb_int_uminus(other)); } 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)); } /* :nodoc: */ static VALUE nucomp_coerce(VALUE self, VALUE other) { if (k_numeric_p(other) && f_real_p(other)) return rb_assoc_new(f_complex_new_bang1(CLASS_OF(self), other), self); if (RB_TYPE_P(other, T_COMPLEX)) return rb_assoc_new(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 */ static VALUE nucomp_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 */ static VALUE nucomp_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) */ static VALUE nucomp_conj(VALUE self) { get_dat1(self); return f_complex_new2(CLASS_OF(self), dat->real, f_negate(dat->imag)); } #if 0 /* :nodoc: */ static VALUE nucomp_true(VALUE self) { return Qtrue; } #endif /* * call-seq: * cmp.real? -> false * * Returns false. */ static VALUE nucomp_false(VALUE self) { return Qfalse; } #if 0 /* :nodoc: */ static VALUE nucomp_exact_p(VALUE self) { get_dat1(self); return f_boolcast(k_exact_p(dat->real) && k_exact_p(dat->imag)); } /* :nodoc: */ static VALUE nucomp_inexact_p(VALUE self) { return f_boolcast(!nucomp_exact_p(self)); } #endif /* * 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 = f_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: */ static VALUE nucomp_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 LONG2FIX(v); } /* :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 magnitude is finite number, * oterwise returns +false+. */ static VALUE rb_complex_finite_p(VALUE self) { VALUE magnitude = nucomp_abs(self); if (FINITE_TYPE_P(magnitude)) { return Qtrue; } else if (RB_FLOAT_TYPE_P(magnitude)) { const double f = RFLOAT_VALUE(magnitude); return isinf(f) ? Qfalse : Qtrue; } else { return rb_funcall(magnitude, id_finite_p, 0); } } /* * call-seq: * cmp.infinite? -> nil or 1 * * Returns values corresponding to the value of +cmp+'s magnitude: * * +finite+:: +nil+ * ++Infinity+:: ++1+ * * For example: * * (1+1i).infinite? #=> nil * (Float::INFINITY + 1i).infinite? #=> 1 */ static VALUE rb_complex_infinite_p(VALUE self) { VALUE magnitude = nucomp_abs(self); if (FINITE_TYPE_P(magnitude)) { return Qnil; } if (RB_FLOAT_TYPE_P(magnitude)) { const double f = RFLOAT_VALUE(magnitude); if (isinf(f)) { return ONE; } return Qnil; } else { return rb_funcall(magnitude, id_infinite_p, 0); } } /* :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)); 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_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_complex_abs(VALUE cmp) { return nucomp_abs(cmp); } /* * 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_scan_args(argc, argv, "01", NULL); 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); } #include 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_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) { char *s; VALUE num; rb_must_asciicompat(self); s = RSTRING_PTR(self); if (!s || memchr(s, '\0', RSTRING_LEN(self))) 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)) { 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 nucomp_s_convert(int argc, VALUE *argv, VALUE klass) { VALUE a1, a2, backref; rb_scan_args(argc, argv, "11", &a1, &a2); if (NIL_P(a1) || (argc == 2 && NIL_P(a2))) rb_raise(rb_eTypeError, "can't convert nil into Complex"); backref = rb_backref_get(); rb_match_busy(backref); if (RB_TYPE_P(a1, T_STRING)) { a1 = string_to_c_strict(a1); } if (RB_TYPE_P(a2, T_STRING)) { a2 = string_to_c_strict(a2); } rb_backref_set(backref); 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 (argc == 1 || (k_exact_zero_p(a2))) return a1; } if (argc == 1) { if (k_numeric_p(a1) && !f_real_p(a1)) return a1; /* should raise exception for consistency */ if (!k_numeric_p(a1)) return rb_convert_type(a1, T_COMPLEX, "Complex", "to_c"); } 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))); } { VALUE argv2[2]; argv2[0] = a1; argv2[1] = a2; return nucomp_s_new(argc, argv2, klass); } } /* --- */ /* * 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; #undef rb_intern #define rb_intern(str) rb_intern_const(str) assert(fprintf(stderr, "assert() is now active\n")); id_abs = rb_intern("abs"); id_arg = rb_intern("arg"); id_denominator = rb_intern("denominator"); id_expt = rb_intern("**"); id_fdiv = rb_intern("fdiv"); id_negate = rb_intern("-@"); id_numerator = rb_intern("numerator"); id_quo = rb_intern("quo"); id_real_p = rb_intern("real?"); id_to_f = rb_intern("to_f"); id_to_i = rb_intern("to_i"); id_to_r = rb_intern("to_r"); id_i_real = rb_intern("@real"); id_i_imag = rb_intern("@image"); /* @image, not @imag */ id_finite_p = rb_intern("finite?"); id_infinite_p = rb_intern("infinite?"); id_rationalize = rb_intern("rationalize"); id_PI = rb_intern("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"); #if 0 rb_define_private_method(CLASS_OF(rb_cComplex), "new!", nucomp_s_new_bang, -1); rb_define_private_method(CLASS_OF(rb_cComplex), "new", nucomp_s_new, -1); #else rb_undef_method(CLASS_OF(rb_cComplex), "new"); #endif 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, rb_mComparable); rb_undef_method(rb_cComplex, "%"); 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", nucomp_real, 0); rb_define_method(rb_cComplex, "imaginary", nucomp_imag, 0); rb_define_method(rb_cComplex, "imag", nucomp_imag, 0); rb_define_method(rb_cComplex, "-@", nucomp_negate, 0); rb_define_method(rb_cComplex, "+", rb_complex_plus, 1); rb_define_method(rb_cComplex, "-", nucomp_sub, 1); rb_define_method(rb_cComplex, "*", nucomp_mul, 1); rb_define_method(rb_cComplex, "/", nucomp_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, "**", nucomp_expt, 1); rb_define_method(rb_cComplex, "==", nucomp_eqeq_p, 1); rb_define_method(rb_cComplex, "coerce", nucomp_coerce, 1); rb_define_method(rb_cComplex, "abs", nucomp_abs, 0); rb_define_method(rb_cComplex, "magnitude", nucomp_abs, 0); rb_define_method(rb_cComplex, "abs2", nucomp_abs2, 0); rb_define_method(rb_cComplex, "arg", nucomp_arg, 0); rb_define_method(rb_cComplex, "angle", nucomp_arg, 0); rb_define_method(rb_cComplex, "phase", nucomp_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", nucomp_conj, 0); rb_define_method(rb_cComplex, "conj", nucomp_conj, 0); #if 0 rb_define_method(rb_cComplex, "~", nucomp_conj, 0); /* gcc */ #endif rb_define_method(rb_cComplex, "real?", nucomp_false, 0); #if 0 rb_define_method(rb_cComplex, "complex?", nucomp_true, 0); rb_define_method(rb_cComplex, "exact?", nucomp_exact_p, 0); rb_define_method(rb_cComplex, "inexact?", nucomp_inexact_p, 0); #endif 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); compat = rb_define_class_under(rb_cComplex, "compatible", rb_cObject); /* :nodoc: */ 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)); rb_provide("complex.so"); /* for backward compatibility */ } /* Local variables: c-file-style: "ruby" End: */