diff options
author | Jari Vetoniemi <jari.vetoniemi@indooratlas.com> | 2020-03-16 18:49:26 +0900 |
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committer | Jari Vetoniemi <jari.vetoniemi@indooratlas.com> | 2020-03-30 00:39:06 +0900 |
commit | fcbf63e62c627deae76c1b8cb8c0876c536ed811 (patch) | |
tree | 64cb17de3f41a2b6fef2368028fbd00349946994 /jni/ruby/complex.c |
Fresh start
Diffstat (limited to 'jni/ruby/complex.c')
-rw-r--r-- | jni/ruby/complex.c | 2217 |
1 files changed, 2217 insertions, 0 deletions
diff --git a/jni/ruby/complex.c b/jni/ruby/complex.c new file mode 100644 index 0000000..11a394c --- /dev/null +++ b/jni/ruby/complex.c @@ -0,0 +1,2217 @@ +/* + 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_REAL(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: +*/ |