diff options
Diffstat (limited to 'ruby_2_2/complex.c')
| -rw-r--r-- | ruby_2_2/complex.c | 2217 |
1 files changed, 0 insertions, 2217 deletions
diff --git a/ruby_2_2/complex.c b/ruby_2_2/complex.c deleted file mode 100644 index 4548c5e2a5..0000000000 --- a/ruby_2_2/complex.c +++ /dev/null @@ -1,2217 +0,0 @@ -/* - complex.c: Coded by Tadayoshi Funaba 2008-2012 - - This implementation is based on Keiju Ishitsuka's Complex library - which is written in ruby. -*/ - -#include "internal.h" -#include <math.h> - -#define NDEBUG -#include <assert.h> - -#define ZERO INT2FIX(0) -#define ONE INT2FIX(1) -#define TWO INT2FIX(2) - -VALUE rb_cComplex; - -static ID id_abs, id_arg, id_convert, - id_denominator, id_eqeq_p, 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; - -#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) && FIX2LONG(y) == 0) - return x; - else if (FIXNUM_P(x) && FIX2LONG(x) == 0) - 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 VALUE -f_gt_p(VALUE x, VALUE y) -{ - if (FIXNUM_P(x) && FIXNUM_P(y)) - return f_boolcast(FIX2LONG(x) > FIX2LONG(y)); - return 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 (FIXNUM_P(x) || RB_TYPE_P(x, T_BIGNUM)) - return ZERO; - } - else if (iy == 1) - return x; - } - else if (FIXNUM_P(x)) { - long ix = FIX2LONG(x); - if (ix == 0) { - if (FIXNUM_P(y) || RB_TYPE_P(y, T_BIGNUM)) - 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) && FIX2LONG(y) == 0) - return x; -#endif - return rb_funcall(x, '-', 1, y); -} - -fun1(abs) -fun1(arg) -fun1(denominator) -fun1(negate) -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 VALUE -f_eqeq_p(VALUE x, VALUE y) -{ - if (FIXNUM_P(x) && FIXNUM_P(y)) - return f_boolcast(FIX2LONG(x) == FIX2LONG(y)); - return rb_funcall(x, id_eqeq_p, 1, y); -} - -fun2(expt) -fun2(fdiv) -fun2(quo) - -inline static VALUE -f_negative_p(VALUE x) -{ - if (FIXNUM_P(x)) - return f_boolcast(FIX2LONG(x) < 0); - return rb_funcall(x, '<', 1, ZERO); -} - -#define f_positive_p(x) (!f_negative_p(x)) - -inline static VALUE -f_zero_p(VALUE x) -{ - if (RB_TYPE_P(x, T_FIXNUM)) { - return f_boolcast(FIX2LONG(x) == 0); - } - else if (RB_TYPE_P(x, T_BIGNUM)) { - return Qfalse; - } - else if (RB_TYPE_P(x, T_RATIONAL)) { - VALUE num = RRATIONAL(x)->num; - - return f_boolcast(FIXNUM_P(num) && FIX2LONG(num) == 0); - } - return rb_funcall(x, id_eqeq_p, 1, ZERO); -} - -#define f_nonzero_p(x) (!f_zero_p(x)) - -inline static VALUE -f_one_p(VALUE x) -{ - if (RB_TYPE_P(x, T_FIXNUM)) { - return f_boolcast(FIX2LONG(x) == 1); - } - else if (RB_TYPE_P(x, T_BIGNUM)) { - return Qfalse; - } - else if (RB_TYPE_P(x, T_RATIONAL)) { - VALUE num = RRATIONAL(x)->num; - VALUE den = RRATIONAL(x)->den; - - return f_boolcast(FIXNUM_P(num) && FIX2LONG(num) == 1 && - FIXNUM_P(den) && FIX2LONG(den) == 1); - } - return rb_funcall(x, id_eqeq_p, 1, ONE); -} - -inline static VALUE -f_kind_of_p(VALUE x, VALUE c) -{ - return rb_obj_is_kind_of(x, c); -} - -inline static VALUE -k_numeric_p(VALUE x) -{ - return f_kind_of_p(x, rb_cNumeric); -} - -inline static VALUE -k_fixnum_p(VALUE x) -{ - return f_kind_of_p(x, rb_cFixnum); -} - -inline static VALUE -k_bignum_p(VALUE x) -{ - return f_kind_of_p(x, rb_cBignum); -} - -inline static VALUE -k_float_p(VALUE x) -{ - return f_kind_of_p(x, rb_cFloat); -} - -inline static VALUE -k_rational_p(VALUE x) -{ - return f_kind_of_p(x, rb_cRational); -} - -inline static VALUE -k_complex_p(VALUE x) -{ - return f_kind_of_p(x, rb_cComplex); -} - -#define k_exact_p(x) (!k_float_p(x)) -#define k_inexact_p(x) k_float_p(x) - -#define k_exact_zero_p(x) (k_exact_p(x) && f_zero_p(x)) -#define k_exact_one_p(x) (k_exact_p(x) && f_one_p(x)) - -#define get_dat1(x) \ - struct RComplex *dat;\ - dat = ((struct RComplex *)(x)) - -#define get_dat2(x,y) \ - struct RComplex *adat, *bdat;\ - adat = ((struct RComplex *)(x));\ - bdat = ((struct 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(!k_complex_p(x)); - return nucomp_s_new_internal(klass, x, ZERO); -} - -inline static VALUE -f_complex_new_bang2(VALUE klass, VALUE x, VALUE y) -{ - assert(!k_complex_p(x)); - assert(!k_complex_p(y)); - 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; -} -#endif - -inline static void -nucomp_real_check(VALUE num) -{ - if (!RB_TYPE_P(num, T_FIXNUM) && - !RB_TYPE_P(num, T_BIGNUM) && - !RB_TYPE_P(num, T_FLOAT) && - !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(!k_complex_p(x)); - return nucomp_s_canonicalize_internal(klass, x, y); -} - -/* - * 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 rb_funcall2(rb_cComplex, id_convert, argc, argv); -} - -#define imp1(n) \ -inline static VALUE \ -m_##n##_bang(VALUE x)\ -{\ - return rb_math_##n(x);\ -} - -#define imp2(n) \ -inline static VALUE \ -m_##n##_bang(VALUE x, VALUE y)\ -{\ - return rb_math_##n(x, y);\ -} - -imp2(atan2) -imp1(cos) -imp1(cosh) -imp1(exp) -imp2(hypot) - -#define m_hypot(x,y) m_hypot_bang((x),(y)) - -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) - -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))); - } - } -} -#endif - -inline static VALUE -f_complex_polar(VALUE klass, VALUE x, VALUE y) -{ - assert(!k_complex_p(x)); - assert(!k_complex_p(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); - arg = ZERO; - break; - 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)); -} - -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); -} - -/* - * 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) - */ -static VALUE -nucomp_add(VALUE self, VALUE other) -{ - return f_addsub(self, other, f_add, '+'); -} - -/* - * 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) -{ - return f_addsub(self, other, f_sub, '-'); -} - -/* - * 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) - */ -static VALUE -nucomp_mul(VALUE self, VALUE other) -{ - if (k_complex_p(other)) { - VALUE real, imag; - - get_dat2(self, other); - - real = f_sub(f_mul(adat->real, bdat->real), - f_mul(adat->imag, bdat->imag)); - imag = f_add(f_mul(adat->real, bdat->imag), - f_mul(adat->imag, bdat->real)); - - 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 (k_complex_p(other)) { - int flo; - get_dat2(self, other); - - flo = (k_float_p(adat->real) || k_float_p(adat->imag) || - k_float_p(bdat->real) || k_float_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 (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); -} - -/* - * 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); -} - -/* :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, "%s can't be coerced into %s", - rb_obj_classname(other), rb_obj_classname(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 (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); -} - -/* - * 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 m_atan2_bang(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 (k_complex_p(other)) { - 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 VALUE -f_signbit(VALUE x) -{ -#if defined(HAVE_SIGNBIT) && defined(__GNUC__) && defined(__sun) && \ - !defined(signbit) - extern int signbit(double); -#endif - if (RB_TYPE_P(x, T_FLOAT)) { - double f = RFLOAT_VALUE(x); - return f_boolcast(!isnan(f) && signbit(f)); - } - return f_negative_p(x); -} - -inline static VALUE -f_tpositive_p(VALUE x) -{ - return f_boolcast(!f_signbit(x)); -} - -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.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; -} - -/* :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); -} - -static VALUE nucomp_s_convert(int argc, VALUE *argv, VALUE klass); - -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_set_real(VALUE cmp, VALUE r) -{ - RCOMPLEX_SET_REAL(cmp, r); - return cmp; -} - -VALUE -rb_complex_set_imag(VALUE cmp, VALUE i) -{ - RCOMPLEX_SET_IMAG(cmp, i); - return 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_inexact_p(dat->imag) || f_nonzero_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_inexact_p(dat->imag) || f_nonzero_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_inexact_p(dat->imag) || f_nonzero_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_inexact_p(dat->imag) || f_nonzero_p(dat->imag)) { - rb_raise(rb_eRangeError, "can't convert %"PRIsVALUE" into Rational", - self); - } - return rb_funcall2(dat->real, rb_intern("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 <ctype.h> - -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); -} - -#define id_PI rb_intern("PI") - -/* - * 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 rb_const_get(rb_mMath, id_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)); -} - -/* - * call-seq: - * num.polar -> array - * - * Returns an array; [num.abs, num.arg]. - */ -static VALUE -numeric_polar(VALUE self) -{ - return rb_assoc_new(f_abs(self), f_arg(self)); -} - -/* - * 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. - * - * In ruby, you can create complex object with Complex, Complex::rect, - * Complex::polar or to_c method. - * - * 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_convert = rb_intern("convert"); - id_denominator = rb_intern("denominator"); - id_eqeq_p = rb_intern("=="); - 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 */ - - 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_method(rb_cComplex, "%"); - rb_undef_method(rb_cComplex, "<"); - rb_undef_method(rb_cComplex, "<="); - rb_undef_method(rb_cComplex, "<=>"); - rb_undef_method(rb_cComplex, ">"); - rb_undef_method(rb_cComplex, ">="); - rb_undef_method(rb_cComplex, "between?"); - 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"); - -#if 0 /* NUBY */ - rb_undef_method(rb_cComplex, "//"); -#endif - - 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, "+", nucomp_add, 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_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: -*/ |