/* :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 nurat_hash(VALUE self, SEL sel) { long v, h[2]; VALUE n; get_dat1(self); n = rb_hash(dat->num); h[0] = NUM2LONG(n); n = rb_hash(dat->den); h[1] = NUM2LONG(n); v = rb_memhash(h, sizeof(h)); return LONG2FIX(v); }
/* * 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)))); }
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))); } }
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: * 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 (k_complex_p(other)) { 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_eqeq_p(other, self); }
static VALUE nurat_round(VALUE self) { get_dat1(self); if (f_negative_p(dat->num)) { VALUE num, den; num = f_negate(dat->num); num = f_add(f_mul(num, TWO), dat->den); den = f_mul(dat->den, TWO); return f_negate(f_idiv(num, den)); } else { VALUE num = f_add(f_mul(dat->num, TWO), dat->den); VALUE den = f_mul(dat->den, TWO); return f_idiv(num, den); } }
static VALUE f_format(VALUE self, VALUE (*func)(VALUE)) { VALUE s, 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.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 (k_float_p(dat->real) && !k_float_p(dat->imag)) a = f_to_f(a); return a; } if (f_zero_p(dat->imag)) { VALUE a = f_abs(dat->real); if (!k_float_p(dat->real) && k_float_p(dat->imag)) a = f_to_f(a); return a; } return m_hypot(dat->real, dat->imag); }
static VALUE nucomp_sub(VALUE self, VALUE other) { if (k_complex_p(other)) { 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 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))); } else { get_dat1(x); if (f_negative_p(dat->imag)) return f_conj(m_sqrt(f_conj(x))); else { VALUE a = f_abs(x); return f_complex_new2(rb_cComplex, m_sqrt_bang(f_div(f_add(a, dat->real), TWO)), m_sqrt_bang(f_div(f_sub(a, dat->real), TWO))); } } }
inline static VALUE f_addsub(VALUE self, VALUE other, VALUE (*func)(VALUE, VALUE), ID id) { if (k_complex_p(other)) { VALUE real, imag; get_dat2(self, other); real = (*func)(adat->real, bdat->real); imag = (*func)(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), (*func)(dat->real, other), dat->imag); } return rb_num_coerce_bin(self, other, id); }
static VALUE nurat_round(VALUE self, SEL sel) { VALUE num, den, neg; get_dat1(self); num = dat->num; den = dat->den; neg = f_negative_p(num); if (neg) num = f_negate(num); num = f_add(f_mul(num, TWO), den); den = f_mul(den, TWO); num = f_idiv(num, den); if (neg) num = f_negate(num); return num; }
static VALUE nurat_cmp(VALUE self, VALUE other) { switch (TYPE(other)) { case T_FIXNUM: case T_BIGNUM: { get_dat1(self); if (FIXNUM_P(dat->den) && FIX2LONG(dat->den) == 1) return f_cmp(dat->num, other); else return f_cmp(self, f_rational_new_bang1(CLASS_OF(self), other)); } case T_FLOAT: return f_cmp(f_to_f(self), other); case T_RATIONAL: { VALUE num1, num2; get_dat2(self, other); if (FIXNUM_P(adat->num) && FIXNUM_P(adat->den) && FIXNUM_P(bdat->num) && FIXNUM_P(bdat->den)) { num1 = f_imul(FIX2LONG(adat->num), FIX2LONG(bdat->den)); num2 = f_imul(FIX2LONG(bdat->num), FIX2LONG(adat->den)); } else { num1 = f_mul(adat->num, bdat->den); num2 = f_mul(bdat->num, adat->den); } return f_cmp(f_sub(num1, num2), ZERO); } default: return rb_num_coerce_bin(self, other, id_cmp); } }
/* * call-seq: * rat == object -> true or false * * Returns true if rat equals object numerically. * * For example: * * Rational(2, 3) == Rational(2, 3) #=> true * Rational(5) == 5 #=> true * Rational(0) == 0.0 #=> true * Rational('1/3') == 0.33 #=> false * Rational('1/2') == '1/2' #=> false */ static VALUE nurat_eqeq_p(VALUE self, SEL sel, VALUE other) { switch (TYPE(other)) { case T_FIXNUM: case T_BIGNUM: { get_dat1(self); if (f_zero_p(dat->num) && f_zero_p(other)) return Qtrue; if (!FIXNUM_P(dat->den)) return Qfalse; if (FIX2LONG(dat->den) != 1) return Qfalse; if (f_eqeq_p(dat->num, other)) return Qtrue; return Qfalse; } case T_FLOAT: return f_eqeq_p(f_to_f(self), other); case T_RATIONAL: { get_dat2(self, other); if (f_zero_p(adat->num) && f_zero_p(bdat->num)) return Qtrue; return f_boolcast(f_eqeq_p(adat->num, bdat->num) && f_eqeq_p(adat->den, bdat->den)); } default: return f_eqeq_p(other, self); } }
/* * 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.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; }
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: * rat.denominator -> integer * * Returns the denominator (always positive). * * For example: * * Rational(7).denominator #=> 1 * Rational(7, 1).denominator #=> 1 * Rational(9, -4).denominator #=> 4 * Rational(-2, -10).denominator #=> 5 * rat.numerator.gcd(rat.denominator) #=> 1 */ static VALUE nurat_denominator(VALUE self, SEL sel) { get_dat1(self); return dat->den; }
/* :nodoc: */ static VALUE nucomp_exact_p(VALUE self) { get_dat1(self); return f_boolcast(k_exact_p(dat->real) && k_exact_p(dat->imag)); }
/* * 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)); }
/* * 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); }
static VALUE nurat_ceil(VALUE self, SEL sel) { get_dat1(self); return f_negate(f_idiv(f_negate(dat->num), dat->den)); }
/* * call-seq: * rat.to_f -> float * * Return the value as a float. * * For example: * * Rational(2).to_f #=> 2.0 * Rational(9, 4).to_f #=> 2.25 * Rational(-3, 4).to_f #=> -0.75 * Rational(20, 3).to_f #=> 6.666666666666667 */ static VALUE nurat_to_f(VALUE self, SEL sel) { get_dat1(self); return f_fdiv(dat->num, dat->den); }
VALUE rb_rational_reciprocal(VALUE x, SEL sel) { get_dat1(x); return f_rational_new_no_reduce2(CLASS_OF(x), dat->den, dat->num); }
/* * 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 ** 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 (k_rational_p(other) && f_one_p(f_denominator(other))) other = f_numerator(other); /* c14n */ if (k_complex_p(other)) { get_dat1(other); if (k_exact_zero_p(dat->imag)) other = dat->real; /* c14n */ } if (k_complex_p(other)) { 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 (k_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), f_negate(other)); } if (k_numeric_p(other) && f_real_p(other)) { VALUE r, theta; if (k_bignum_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); }
static VALUE nurat_floor(VALUE self, SEL sel) { get_dat1(self); return f_idiv(dat->num, dat->den); }
/* * 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 m_atan2_bang(dat->imag, dat->real); }
/* * call-seq: * rat.numerator -> integer * * Returns the numerator. * * For example: * * Rational(7).numerator #=> 7 * Rational(7, 1).numerator #=> 7 * Rational(9, -4).numerator #=> -9 * Rational(-2, -10).numerator #=> 1 */ static VALUE nurat_numerator(VALUE self, SEL sel) { get_dat1(self); return dat->num; }