diff options
Diffstat (limited to 'complex.c')
| -rw-r--r-- | complex.c | 2511 |
1 files changed, 1067 insertions, 1444 deletions
@@ -5,51 +5,47 @@ which is written in ruby. */ -#include "ruby/internal/config.h" - +#include "ruby/config.h" #if defined _MSC_VER /* Microsoft Visual C does not define M_PI and others by default */ # define _USE_MATH_DEFINES 1 #endif - -#include <ctype.h> #include <math.h> - -#include "id.h" #include "internal.h" -#include "internal/array.h" -#include "internal/class.h" -#include "internal/complex.h" -#include "internal/math.h" -#include "internal/numeric.h" -#include "internal/object.h" -#include "internal/rational.h" -#include "internal/string.h" + +#define NDEBUG #include "ruby_assert.h" #define ZERO INT2FIX(0) #define ONE INT2FIX(1) #define TWO INT2FIX(2) -#if USE_FLONUM #define RFLOAT_0 DBL2NUM(0) -#else -static VALUE RFLOAT_0; +#if defined(HAVE_SIGNBIT) && defined(__GNUC__) && defined(__sun) && \ + !defined(signbit) +extern int signbit(double); #endif VALUE rb_cComplex; +static VALUE nucomp_abs(VALUE self); +static VALUE nucomp_arg(VALUE self); + static ID id_abs, id_arg, - id_denominator, id_numerator, - id_real_p, id_i_real, id_i_imag, + id_denominator, id_expt, id_fdiv, + id_negate, id_numerator, id_quo, + id_real_p, id_to_f, id_to_i, id_to_r, + id_i_real, id_i_imag, id_finite_p, id_infinite_p, id_rationalize, id_PI; -#define id_to_i idTo_i -#define id_to_r idTo_r -#define id_negate idUMinus -#define id_expt idPow -#define id_to_f idTo_f -#define id_quo idQuo -#define id_fdiv idFdiv + +#define 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 \ @@ -65,32 +61,31 @@ 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) { - if (RB_INTEGER_TYPE_P(x) && - LIKELY(rb_method_basic_definition_p(rb_cInteger, idPLUS))) { - if (FIXNUM_ZERO_P(x)) - return y; - if (FIXNUM_ZERO_P(y)) - return x; - return rb_int_plus(x, y); - } - else if (RB_FLOAT_TYPE_P(x) && - LIKELY(rb_method_basic_definition_p(rb_cFloat, idPLUS))) { - if (FIXNUM_ZERO_P(y)) - return x; - return rb_float_plus(x, y); - } - else if (RB_TYPE_P(x, T_RATIONAL) && - LIKELY(rb_method_basic_definition_p(rb_cRational, idPLUS))) { - if (FIXNUM_ZERO_P(y)) - return x; - return rb_rational_plus(x, y); - } - +#ifndef PRESERVE_SIGNEDZERO + if (FIXNUM_P(y) && FIXNUM_ZERO_P(y)) + return x; + else if (FIXNUM_P(x) && FIXNUM_ZERO_P(x)) + return y; +#endif return rb_funcall(x, '+', 1, y); } @@ -98,7 +93,7 @@ inline static VALUE f_div(VALUE x, VALUE y) { if (FIXNUM_P(y) && FIX2LONG(y) == 1) - return x; + return x; return rb_funcall(x, '/', 1, y); } @@ -122,104 +117,44 @@ f_gt_p(VALUE x, VALUE y) inline static VALUE f_mul(VALUE x, VALUE y) { - if (RB_INTEGER_TYPE_P(x) && - LIKELY(rb_method_basic_definition_p(rb_cInteger, idMULT))) { - if (FIXNUM_ZERO_P(y)) - return ZERO; - if (FIXNUM_ZERO_P(x) && RB_INTEGER_TYPE_P(y)) - return ZERO; - if (x == ONE) return y; - if (y == ONE) return x; - return rb_int_mul(x, y); - } - else if (RB_FLOAT_TYPE_P(x) && - LIKELY(rb_method_basic_definition_p(rb_cFloat, idMULT))) { - if (y == ONE) return x; - return rb_float_mul(x, y); - } - else if (RB_TYPE_P(x, T_RATIONAL) && - LIKELY(rb_method_basic_definition_p(rb_cRational, idMULT))) { - if (y == ONE) return x; - return rb_rational_mul(x, y); - } - else if (LIKELY(rb_method_basic_definition_p(CLASS_OF(x), idMULT))) { - if (y == ONE) return x; +#ifndef PRESERVE_SIGNEDZERO + if (FIXNUM_P(y)) { + long iy = FIX2LONG(y); + if (iy == 0) { + if (RB_INTEGER_TYPE_P(x)) + return ZERO; + } + else if (iy == 1) + return x; + } + else if (FIXNUM_P(x)) { + long ix = FIX2LONG(x); + if (ix == 0) { + if (RB_INTEGER_TYPE_P(y)) + return ZERO; + } + else if (ix == 1) + return y; } +#endif return rb_funcall(x, '*', 1, y); } inline static VALUE f_sub(VALUE x, VALUE y) { - if (FIXNUM_ZERO_P(y) && - LIKELY(rb_method_basic_definition_p(CLASS_OF(x), idMINUS))) { - return x; - } +#ifndef PRESERVE_SIGNEDZERO + if (FIXNUM_P(y) && FIXNUM_ZERO_P(y)) + return x; +#endif return rb_funcall(x, '-', 1, y); } -inline static VALUE -f_abs(VALUE x) -{ - if (RB_INTEGER_TYPE_P(x)) { - return rb_int_abs(x); - } - else if (RB_FLOAT_TYPE_P(x)) { - return rb_float_abs(x); - } - else if (RB_TYPE_P(x, T_RATIONAL)) { - return rb_rational_abs(x); - } - else if (RB_TYPE_P(x, T_COMPLEX)) { - return rb_complex_abs(x); - } - return rb_funcall(x, id_abs, 0); -} +fun1(abs) +fun1(arg) +fun1(denominator) -static VALUE numeric_arg(VALUE self); -static VALUE float_arg(VALUE self); - -inline static VALUE -f_arg(VALUE x) -{ - if (RB_INTEGER_TYPE_P(x)) { - return numeric_arg(x); - } - else if (RB_FLOAT_TYPE_P(x)) { - return float_arg(x); - } - else if (RB_TYPE_P(x, T_RATIONAL)) { - return numeric_arg(x); - } - else if (RB_TYPE_P(x, T_COMPLEX)) { - return rb_complex_arg(x); - } - return rb_funcall(x, id_arg, 0); -} - -inline static VALUE -f_numerator(VALUE x) -{ - if (RB_TYPE_P(x, T_RATIONAL)) { - return RRATIONAL(x)->num; - } - if (RB_FLOAT_TYPE_P(x)) { - return rb_float_numerator(x); - } - return x; -} - -inline static VALUE -f_denominator(VALUE x) -{ - if (RB_TYPE_P(x, T_RATIONAL)) { - return RRATIONAL(x)->den; - } - if (RB_FLOAT_TYPE_P(x)) { - return rb_float_denominator(x); - } - return INT2FIX(1); -} +static VALUE nucomp_negate(VALUE self); inline static VALUE f_negate(VALUE x) @@ -234,44 +169,26 @@ f_negate(VALUE x) return rb_rational_uminus(x); } else if (RB_TYPE_P(x, T_COMPLEX)) { - return rb_complex_uminus(x); + return nucomp_negate(x); } return rb_funcall(x, id_negate, 0); } -static bool nucomp_real_p(VALUE self); - -static inline bool -f_real_p(VALUE x) -{ - if (RB_INTEGER_TYPE_P(x)) { - return true; - } - else if (RB_FLOAT_TYPE_P(x)) { - return true; - } - else if (RB_TYPE_P(x, T_RATIONAL)) { - return true; - } - else if (RB_TYPE_P(x, T_COMPLEX)) { - return nucomp_real_p(x); - } - return rb_funcall(x, id_real_p, 0); -} +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_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 DBL2NUM(rb_str_to_dbl(x, 0)); return rb_funcall(x, id_to_f, 0); } @@ -281,27 +198,15 @@ inline static int f_eqeq_p(VALUE x, VALUE y) { if (FIXNUM_P(x) && FIXNUM_P(y)) - return x == y; + return x == y; else if (RB_FLOAT_TYPE_P(x) || RB_FLOAT_TYPE_P(y)) - return NUM2DBL(x) == NUM2DBL(y); + return NUM2DBL(x) == NUM2DBL(y); return (int)rb_equal(x, y); } fun2(expt) fun2(fdiv) - -static VALUE -f_quo(VALUE x, VALUE y) -{ - if (RB_INTEGER_TYPE_P(x)) - return rb_numeric_quo(x, y); - if (RB_FLOAT_TYPE_P(x)) - return rb_float_div(x, y); - if (RB_TYPE_P(x, T_RATIONAL)) - return rb_numeric_quo(x, y); - - return rb_funcallv(x, id_quo, 1, &y); -} +fun2(quo) inline static int f_negative_p(VALUE x) @@ -317,54 +222,51 @@ f_negative_p(VALUE x) #define f_positive_p(x) (!f_negative_p(x)) -inline static bool +inline static int f_zero_p(VALUE x) { - if (RB_FLOAT_TYPE_P(x)) { - return FLOAT_ZERO_P(x); - } - else if (RB_INTEGER_TYPE_P(x)) { + if (RB_INTEGER_TYPE_P(x)) { return FIXNUM_ZERO_P(x); } else if (RB_TYPE_P(x, T_RATIONAL)) { const VALUE num = RRATIONAL(x)->num; return FIXNUM_ZERO_P(num); } - return rb_equal(x, ZERO) != 0; + return (int)rb_equal(x, ZERO); } #define f_nonzero_p(x) (!f_zero_p(x)) -static inline bool -always_finite_type_p(VALUE x) -{ - if (FIXNUM_P(x)) return true; - if (FLONUM_P(x)) return true; /* Infinity can't be a flonum */ - return (RB_INTEGER_TYPE_P(x) || RB_TYPE_P(x, T_RATIONAL)); -} - +VALUE rb_flo_is_finite_p(VALUE num); inline static int f_finite_p(VALUE x) { - if (always_finite_type_p(x)) { + if (RB_INTEGER_TYPE_P(x)) { return TRUE; } else if (RB_FLOAT_TYPE_P(x)) { - return isfinite(RFLOAT_VALUE(x)); + return (int)rb_flo_is_finite_p(x); + } + else if (RB_TYPE_P(x, T_RATIONAL)) { + return TRUE; } return RTEST(rb_funcallv(x, id_finite_p, 0, 0)); } -inline static int +VALUE rb_flo_is_infinite_p(VALUE num); +inline static VALUE f_infinite_p(VALUE x) { - if (always_finite_type_p(x)) { - return FALSE; + if (RB_INTEGER_TYPE_P(x)) { + return Qnil; } else if (RB_FLOAT_TYPE_P(x)) { - return isinf(RFLOAT_VALUE(x)); + return rb_flo_is_infinite_p(x); } - return RTEST(rb_funcallv(x, id_infinite_p, 0, 0)); + else if (RB_TYPE_P(x, T_RATIONAL)) { + return Qnil; + } + return rb_funcallv(x, id_infinite_p, 0, 0); } inline static int @@ -392,12 +294,11 @@ k_numeric_p(VALUE x) inline static VALUE nucomp_s_new_internal(VALUE klass, VALUE real, VALUE imag) { - NEWOBJ_OF(obj, struct RComplex, klass, - T_COMPLEX | (RGENGC_WB_PROTECTED_COMPLEX ? FL_WB_PROTECTED : 0), sizeof(struct RComplex), 0); + 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); - OBJ_FREEZE((VALUE)obj); + OBJ_FREEZE_RAW(obj); return (VALUE)obj; } @@ -408,86 +309,118 @@ 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) { - RUBY_ASSERT(!RB_TYPE_P(x, T_COMPLEX)); + assert(!RB_TYPE_P(x, T_COMPLEX)); return nucomp_s_new_internal(klass, x, ZERO); } inline static VALUE f_complex_new_bang2(VALUE klass, VALUE x, VALUE y) { - RUBY_ASSERT(!RB_TYPE_P(x, T_COMPLEX)); - RUBY_ASSERT(!RB_TYPE_P(y, T_COMPLEX)); + assert(!RB_TYPE_P(x, T_COMPLEX)); + assert(!RB_TYPE_P(y, T_COMPLEX)); return nucomp_s_new_internal(klass, x, y); } -WARN_UNUSED_RESULT(inline static VALUE nucomp_real_check(VALUE num)); -inline static VALUE +#ifdef CANONICALIZATION_FOR_MATHN +#define CANON +#endif + +#ifdef CANON +static int canonicalization = 0; + +RUBY_FUNC_EXPORTED void +nucomp_canonicalization(int f) +{ + canonicalization = f; +} +#else +#define canonicalization 0 +#endif + +inline static void nucomp_real_check(VALUE num) { if (!RB_INTEGER_TYPE_P(num) && - !RB_FLOAT_TYPE_P(num) && - !RB_TYPE_P(num, T_RATIONAL)) { - if (RB_TYPE_P(num, T_COMPLEX) && nucomp_real_p(num)) { - VALUE real = RCOMPLEX(num)->real; - RUBY_ASSERT(!RB_TYPE_P(real, T_COMPLEX)); - return real; - } - if (!k_numeric_p(num) || !f_real_p(num)) - rb_raise(rb_eTypeError, "not a real"); + !RB_FLOAT_TYPE_P(num) && + !RB_TYPE_P(num, T_RATIONAL)) { + if (!k_numeric_p(num) || !f_real_p(num)) + rb_raise(rb_eTypeError, "not a real"); } - return num; } inline static VALUE nucomp_s_canonicalize_internal(VALUE klass, VALUE real, VALUE imag) { - int complex_r, complex_i; - complex_r = RB_TYPE_P(real, T_COMPLEX); - complex_i = RB_TYPE_P(imag, T_COMPLEX); - if (!complex_r && !complex_i) { - return nucomp_s_new_internal(klass, real, imag); - } - else if (!complex_r) { - get_dat1(imag); +#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)); + return nucomp_s_new_internal(klass, + f_sub(real, dat->imag), + f_add(ZERO, dat->real)); } - else if (!complex_i) { - get_dat1(real); + else if (f_real_p(imag)) { + get_dat1(real); - return nucomp_s_new_internal(klass, - dat->real, - f_add(dat->imag, imag)); + return nucomp_s_new_internal(klass, + dat->real, + f_add(dat->imag, imag)); } else { - get_dat2(real, imag); + get_dat2(real, imag); - return nucomp_s_new_internal(klass, - f_sub(adat->real, bdat->imag), - f_add(adat->imag, bdat->real)); + return nucomp_s_new_internal(klass, + f_sub(adat->real, bdat->imag), + f_add(adat->imag, bdat->real)); } } /* * call-seq: - * Complex.rect(real, imag = 0) -> complex - * - * Returns a new \Complex object formed from the arguments, - * each of which must be an instance of Numeric, - * or an instance of one of its subclasses: - * \Complex, Float, Integer, Rational; - * see {Rectangular Coordinates}[rdoc-ref:Complex@Rectangular+Coordinates]: + * Complex.rect(real[, imag]) -> complex + * Complex.rectangular(real[, imag]) -> complex * - * Complex.rect(3) # => (3+0i) - * Complex.rect(3, Math::PI) # => (3+3.141592653589793i) - * Complex.rect(-3, -Math::PI) # => (-3-3.141592653589793i) + * Returns a complex object which denotes the given rectangular form. * - * \Complex.rectangular is an alias for \Complex.rect. + * Complex.rectangular(1, 2) #=> (1+2i) */ static VALUE nucomp_s_new(int argc, VALUE *argv, VALUE klass) @@ -496,99 +429,64 @@ nucomp_s_new(int argc, VALUE *argv, VALUE klass) switch (rb_scan_args(argc, argv, "11", &real, &imag)) { case 1: - real = nucomp_real_check(real); - imag = ZERO; - break; + nucomp_real_check(real); + imag = ZERO; + break; default: - real = nucomp_real_check(real); - imag = nucomp_real_check(imag); - break; + nucomp_real_check(real); + nucomp_real_check(imag); + break; } - return nucomp_s_new_internal(klass, real, imag); + return nucomp_s_canonicalize_internal(klass, real, imag); } inline static VALUE f_complex_new2(VALUE klass, VALUE x, VALUE y) { - if (RB_TYPE_P(x, T_COMPLEX)) { - get_dat1(x); - x = dat->real; - y = f_add(dat->imag, y); - } + assert(!RB_TYPE_P(x, T_COMPLEX)); return nucomp_s_canonicalize_internal(klass, x, y); } -static VALUE nucomp_convert(VALUE klass, VALUE a1, VALUE a2, int raise); static VALUE nucomp_s_convert(int argc, VALUE *argv, VALUE klass); /* * call-seq: - * Complex(real, imag = 0, exception: true) -> complex or nil - * Complex(s, exception: true) -> complex or nil - * - * Returns a new \Complex object if the arguments are valid; - * otherwise raises an exception if +exception+ is +true+; - * otherwise returns +nil+. - * - * With Numeric arguments +real+ and +imag+, - * returns <tt>Complex.rect(real, imag)</tt> if the arguments are valid. - * - * With string argument +s+, returns a new \Complex object if the argument is valid; - * the string may have: - * - * - One or two numeric substrings, - * each of which specifies a Complex, Float, Integer, Numeric, or Rational value, - * specifying {rectangular coordinates}[rdoc-ref:Complex@Rectangular+Coordinates]: - * - * - Sign-separated real and imaginary numeric substrings - * (with trailing character <tt>'i'</tt>): - * - * Complex('1+2i') # => (1+2i) - * Complex('+1+2i') # => (1+2i) - * Complex('+1-2i') # => (1-2i) - * Complex('-1+2i') # => (-1+2i) - * Complex('-1-2i') # => (-1-2i) - * - * - Real-only numeric string (without trailing character <tt>'i'</tt>): - * - * Complex('1') # => (1+0i) - * Complex('+1') # => (1+0i) - * Complex('-1') # => (-1+0i) - * - * - Imaginary-only numeric string (with trailing character <tt>'i'</tt>): - * - * Complex('1i') # => (0+1i) - * Complex('+1i') # => (0+1i) - * Complex('-1i') # => (0-1i) - * - * - At-sign separated real and imaginary rational substrings, - * each of which specifies a Rational value, - * specifying {polar coordinates}[rdoc-ref:Complex@Polar+Coordinates]: - * - * Complex('1/2@3/4') # => (0.36584443443691045+0.34081938001166706i) - * Complex('+1/2@+3/4') # => (0.36584443443691045+0.34081938001166706i) - * Complex('+1/2@-3/4') # => (0.36584443443691045-0.34081938001166706i) - * Complex('-1/2@+3/4') # => (-0.36584443443691045-0.34081938001166706i) - * Complex('-1/2@-3/4') # => (-0.36584443443691045+0.34081938001166706i) - * + * 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) { - VALUE a1, a2, opts = Qnil; - int raise = TRUE; - - if (rb_scan_args(argc, argv, "11:", &a1, &a2, &opts) == 1) { - a2 = Qundef; - } - if (!NIL_P(opts)) { - raise = rb_opts_exception_p(opts, raise); - } - if (argc > 0 && CLASS_OF(a1) == rb_cComplex && UNDEF_P(a2)) { - return a1; - } - return nucomp_convert(rb_cComplex, a1, a2, raise); + return nucomp_s_convert(argc, argv, rb_cComplex); } #define imp1(n) \ @@ -614,161 +512,146 @@ imp1(sinh) static VALUE m_cos(VALUE x) { - if (!RB_TYPE_P(x, T_COMPLEX)) - return m_cos_bang(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))); + get_dat1(x); + return f_complex_new2(rb_cComplex, + f_mul(m_cos_bang(dat->real), + m_cosh_bang(dat->imag)), + f_mul(f_negate(m_sin_bang(dat->real)), + m_sinh_bang(dat->imag))); } } static VALUE m_sin(VALUE x) { - if (!RB_TYPE_P(x, T_COMPLEX)) - return m_sin_bang(x); + 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))); + get_dat1(x); + return f_complex_new2(rb_cComplex, + f_mul(m_sin_bang(dat->real), + m_cosh_bang(dat->imag)), + f_mul(m_cos_bang(dat->real), + m_sinh_bang(dat->imag))); } } -static VALUE -f_complex_polar_real(VALUE klass, VALUE x, VALUE y) +#if 0 +imp1(sqrt) + +VALUE +rb_complex_sqrt(VALUE x) { - if (f_zero_p(x) || f_zero_p(y)) { - return nucomp_s_new_internal(klass, x, RFLOAT_0); - } - if (RB_FLOAT_TYPE_P(y)) { - const double arg = RFLOAT_VALUE(y); - if (arg == M_PI) { - x = f_negate(x); - y = RFLOAT_0; - } - else if (arg == M_PI_2) { - y = x; - x = RFLOAT_0; - } - else if (arg == M_PI_2+M_PI) { - y = f_negate(x); - x = RFLOAT_0; - } - else if (RB_FLOAT_TYPE_P(x)) { - const double abs = RFLOAT_VALUE(x); - const double real = abs * cos(arg), imag = abs * sin(arg); - x = DBL2NUM(real); - y = DBL2NUM(imag); - } - else { - const double ax = sin(arg), ay = cos(arg); - y = f_mul(x, DBL2NUM(ax)); - x = f_mul(x, DBL2NUM(ay)); - } - return nucomp_s_new_internal(klass, x, y); - } - return nucomp_s_canonicalize_internal(klass, - f_mul(x, m_cos(y)), - f_mul(x, m_sin(y))); + int pos; + VALUE a, re, im; + get_dat1(x); + + pos = f_positive_p(dat->imag); + a = f_abs(x); + re = m_sqrt_bang(f_div(f_add(a, dat->real), TWO)); + im = m_sqrt_bang(f_div(f_sub(a, dat->real), TWO)); + if (!pos) im = f_negate(im); + return f_complex_new2(rb_cComplex, re, im); } static VALUE -f_complex_polar(VALUE klass, VALUE x, VALUE y) +m_sqrt(VALUE x) { - x = nucomp_real_check(x); - y = nucomp_real_check(y); - return f_complex_polar_real(klass, x, y); + if (f_real_p(x)) { + if (f_positive_p(x)) + return m_sqrt_bang(x); + return f_complex_new2(rb_cComplex, ZERO, m_sqrt_bang(f_negate(x))); + } + return rb_complex_sqrt(x); } - -#ifdef HAVE___COSPI -# define cospi(x) __cospi(x) -#else -# define cospi(x) cos((x) * M_PI) -#endif -#ifdef HAVE___SINPI -# define sinpi(x) __sinpi(x) -#else -# define sinpi(x) sin((x) * M_PI) #endif -/* returns a Complex or Float of ang*PI-rotated abs */ -VALUE -rb_dbl_complex_new_polar_pi(double abs, double ang) -{ - double fi; - const double fr = modf(ang, &fi); - int pos = fr == +0.5; - if (pos || fr == -0.5) { - if ((modf(fi / 2.0, &fi) != fr) ^ pos) abs = -abs; - return rb_complex_new(RFLOAT_0, DBL2NUM(abs)); - } - else if (fr == 0.0) { - if (modf(fi / 2.0, &fi) != 0.0) abs = -abs; - return DBL2NUM(abs); +static VALUE +f_complex_polar(VALUE klass, VALUE x, VALUE y) +{ + assert(!RB_TYPE_P(x, T_COMPLEX)); + assert(!RB_TYPE_P(y, T_COMPLEX)); + if (f_zero_p(x) || f_zero_p(y)) { + if (canonicalization) return x; + return nucomp_s_new_internal(klass, x, RFLOAT_0); } - else { - const double real = abs * cospi(ang), imag = abs * sinpi(ang); - return rb_complex_new(DBL2NUM(real), DBL2NUM(imag)); + if (RB_FLOAT_TYPE_P(y)) { + const double arg = RFLOAT_VALUE(y); + if (arg == M_PI) { + x = f_negate(x); + if (canonicalization) return x; + y = RFLOAT_0; + } + else if (arg == M_PI_2) { + y = x; + x = RFLOAT_0; + } + else if (arg == M_PI_2+M_PI) { + y = f_negate(x); + x = RFLOAT_0; + } + else if (RB_FLOAT_TYPE_P(x)) { + const double abs = RFLOAT_VALUE(x); + const double real = abs * cos(arg), imag = abs * sin(arg); + x = DBL2NUM(real); + if (canonicalization && imag == 0.0) return x; + y = DBL2NUM(imag); + } + else { + y = f_mul(x, DBL2NUM(sin(arg))); + x = f_mul(x, DBL2NUM(cos(arg))); + if (canonicalization && f_zero_p(y)) return x; + } + return nucomp_s_new_internal(klass, x, y); } + return nucomp_s_canonicalize_internal(klass, + f_mul(x, m_cos(y)), + f_mul(x, m_sin(y))); } /* * call-seq: - * Complex.polar(abs, arg = 0) -> complex - * - * Returns a new \Complex object formed from the arguments, - * each of which must be an instance of Numeric, - * or an instance of one of its subclasses: - * \Complex, Float, Integer, Rational. - * Argument +arg+ is given in radians; - * see {Polar Coordinates}[rdoc-ref:Complex@Polar+Coordinates]: + * Complex.polar(abs[, arg]) -> complex * - * Complex.polar(3) # => (3+0i) - * Complex.polar(3, 2.0) # => (-1.2484405096414273+2.727892280477045i) - * Complex.polar(-3, -2.0) # => (1.2484405096414273+2.727892280477045i) + * 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; - argc = rb_scan_args(argc, argv, "11", &abs, &arg); - abs = nucomp_real_check(abs); - if (argc == 2) { - arg = nucomp_real_check(arg); - } - else { - arg = ZERO; + switch (rb_scan_args(argc, argv, "11", &abs, &arg)) { + case 1: + nucomp_real_check(abs); + if (canonicalization) return abs; + return nucomp_s_new_internal(klass, abs, ZERO); + default: + nucomp_real_check(abs); + nucomp_real_check(arg); + break; } - return f_complex_polar_real(klass, abs, arg); + return f_complex_polar(klass, abs, arg); } /* * call-seq: - * real -> numeric - * - * Returns the real value for +self+: - * - * Complex.rect(7).real # => 7 - * Complex.rect(9, -4).real # => 9 - * - * If +self+ was created with - * {polar coordinates}[rdoc-ref:Complex@Polar+Coordinates], the returned value - * is computed, and may be inexact: + * cmp.real -> real * - * Complex.polar(1, Math::PI/4).real # => 0.7071067811865476 # Square root of 2. + * Returns the real part. * + * Complex(7).real #=> 7 + * Complex(9, -4).real #=> 9 */ -VALUE -rb_complex_real(VALUE self) +static VALUE +nucomp_real(VALUE self) { get_dat1(self); return dat->real; @@ -776,22 +659,16 @@ rb_complex_real(VALUE self) /* * call-seq: - * imag -> numeric - * - * Returns the imaginary value for +self+: - * - * Complex.rect(7).imag # => 0 - * Complex.rect(9, -4).imag # => -4 + * cmp.imag -> real + * cmp.imaginary -> real * - * If +self+ was created with - * {polar coordinates}[rdoc-ref:Complex@Polar+Coordinates], the returned value - * is computed, and may be inexact: - * - * Complex.polar(1, Math::PI/4).imag # => 0.7071067811865476 # Square root of 2. + * Returns the imaginary part. * + * Complex(7).imaginary #=> 0 + * Complex(9, -4).imaginary #=> -4 */ -VALUE -rb_complex_imag(VALUE self) +static VALUE +nucomp_imag(VALUE self) { get_dat1(self); return dat->imag; @@ -799,188 +676,193 @@ rb_complex_imag(VALUE self) /* * call-seq: - * -complex -> new_complex + * -cmp -> complex * - * Returns the negation of +self+, which is the negation of each of its parts: - * - * -Complex.rect(1, 2) # => (-1-2i) - * -Complex.rect(-1, -2) # => (1+2i) + * Returns negation of the value. * + * -Complex(1, 2) #=> (-1-2i) */ -VALUE -rb_complex_uminus(VALUE self) +static VALUE +nucomp_negate(VALUE self) { - get_dat1(self); - return f_complex_new2(CLASS_OF(self), - f_negate(dat->real), f_negate(dat->imag)); + get_dat1(self); + return f_complex_new2(CLASS_OF(self), + f_negate(dat->real), f_negate(dat->imag)); } /* * call-seq: - * complex + numeric -> new_complex - * - * Returns the sum of +self+ and +numeric+: + * cmp + numeric -> complex * - * Complex.rect(2, 3) + Complex.rect(2, 3) # => (4+6i) - * Complex.rect(900) + Complex.rect(1) # => (901+0i) - * Complex.rect(-2, 9) + Complex.rect(-9, 2) # => (-11+11i) - * Complex.rect(9, 8) + 4 # => (13+8i) - * Complex.rect(20, 9) + 9.8 # => (29.8+9i) + * Performs addition. * + * Complex(2, 3) + Complex(2, 3) #=> (4+6i) + * Complex(900) + Complex(1) #=> (901+0i) + * Complex(-2, 9) + Complex(-9, 2) #=> (-11+11i) + * Complex(9, 8) + 4 #=> (13+8i) + * Complex(20, 9) + 9.8 #=> (29.8+9i) */ VALUE rb_complex_plus(VALUE self, VALUE other) { if (RB_TYPE_P(other, T_COMPLEX)) { - VALUE real, imag; + VALUE real, imag; - get_dat2(self, other); + get_dat2(self, other); - real = f_add(adat->real, bdat->real); - imag = f_add(adat->imag, bdat->imag); + real = f_add(adat->real, bdat->real); + imag = f_add(adat->imag, bdat->imag); - return f_complex_new2(CLASS_OF(self), real, imag); + return f_complex_new2(CLASS_OF(self), real, imag); } if (k_numeric_p(other) && f_real_p(other)) { - get_dat1(self); + get_dat1(self); - return f_complex_new2(CLASS_OF(self), - f_add(dat->real, other), dat->imag); + return f_complex_new2(CLASS_OF(self), + f_add(dat->real, other), dat->imag); } return rb_num_coerce_bin(self, other, '+'); } /* * call-seq: - * complex - numeric -> new_complex - * - * Returns the difference of +self+ and +numeric+: + * cmp - numeric -> complex * - * Complex.rect(2, 3) - Complex.rect(2, 3) # => (0+0i) - * Complex.rect(900) - Complex.rect(1) # => (899+0i) - * Complex.rect(-2, 9) - Complex.rect(-9, 2) # => (7+7i) - * Complex.rect(9, 8) - 4 # => (5+8i) - * Complex.rect(20, 9) - 9.8 # => (10.2+9i) + * 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) */ -VALUE -rb_complex_minus(VALUE self, VALUE other) +static VALUE +nucomp_sub(VALUE self, VALUE other) { if (RB_TYPE_P(other, T_COMPLEX)) { - VALUE real, imag; + VALUE real, imag; - get_dat2(self, other); + get_dat2(self, other); - real = f_sub(adat->real, bdat->real); - imag = f_sub(adat->imag, bdat->imag); + real = f_sub(adat->real, bdat->real); + imag = f_sub(adat->imag, bdat->imag); - return f_complex_new2(CLASS_OF(self), real, imag); + return f_complex_new2(CLASS_OF(self), real, imag); } if (k_numeric_p(other) && f_real_p(other)) { - get_dat1(self); + get_dat1(self); - return f_complex_new2(CLASS_OF(self), - f_sub(dat->real, other), dat->imag); + return f_complex_new2(CLASS_OF(self), + f_sub(dat->real, other), dat->imag); } return rb_num_coerce_bin(self, other, '-'); } static VALUE -safe_mul(VALUE a, VALUE b, bool az, bool bz) +safe_mul(VALUE a, VALUE b, int az, int bz) { double v; if (!az && bz && RB_FLOAT_TYPE_P(a) && (v = RFLOAT_VALUE(a), !isnan(v))) { - a = signbit(v) ? DBL2NUM(-1.0) : DBL2NUM(1.0); + a = signbit(v) ? DBL2NUM(-1.0) : DBL2NUM(1.0); } if (!bz && az && RB_FLOAT_TYPE_P(b) && (v = RFLOAT_VALUE(b), !isnan(v))) { - b = signbit(v) ? DBL2NUM(-1.0) : DBL2NUM(1.0); + b = signbit(v) ? DBL2NUM(-1.0) : DBL2NUM(1.0); } return f_mul(a, b); } -static void -comp_mul(VALUE areal, VALUE aimag, VALUE breal, VALUE bimag, VALUE *real, VALUE *imag) -{ - bool arzero = f_zero_p(areal); - bool aizero = f_zero_p(aimag); - bool brzero = f_zero_p(breal); - bool bizero = f_zero_p(bimag); - *real = f_sub(safe_mul(areal, breal, arzero, brzero), - safe_mul(aimag, bimag, aizero, bizero)); - *imag = f_add(safe_mul(areal, bimag, arzero, bizero), - safe_mul(aimag, breal, aizero, brzero)); -} - /* * call-seq: - * complex * numeric -> new_complex - * - * Returns the product of +self+ and +numeric+: + * cmp * numeric -> complex * - * Complex.rect(2, 3) * Complex.rect(2, 3) # => (-5+12i) - * Complex.rect(900) * Complex.rect(1) # => (900+0i) - * Complex.rect(-2, 9) * Complex.rect(-9, 2) # => (0-85i) - * Complex.rect(9, 8) * 4 # => (36+32i) - * Complex.rect(20, 9) * 9.8 # => (196.0+88.2i) + * Performs multiplication. * + * Complex(2, 3) * Complex(2, 3) #=> (-5+12i) + * Complex(900) * Complex(1) #=> (900+0i) + * Complex(-2, 9) * Complex(-9, 2) #=> (0-85i) + * Complex(9, 8) * 4 #=> (36+32i) + * Complex(20, 9) * 9.8 #=> (196.0+88.2i) */ VALUE rb_complex_mul(VALUE self, VALUE other) { if (RB_TYPE_P(other, T_COMPLEX)) { - VALUE real, imag; - get_dat2(self, other); + VALUE real, imag; + VALUE areal, aimag, breal, bimag; + int arzero, aizero, brzero, bizero; + + get_dat2(self, other); - comp_mul(adat->real, adat->imag, bdat->real, bdat->imag, &real, &imag); + arzero = f_zero_p(areal = adat->real); + aizero = f_zero_p(aimag = adat->imag); + brzero = f_zero_p(breal = bdat->real); + bizero = f_zero_p(bimag = bdat->imag); + real = f_sub(safe_mul(areal, breal, arzero, brzero), + safe_mul(aimag, bimag, aizero, bizero)); + imag = f_add(safe_mul(areal, bimag, arzero, bizero), + safe_mul(aimag, breal, aizero, brzero)); - return f_complex_new2(CLASS_OF(self), real, imag); + return f_complex_new2(CLASS_OF(self), real, imag); } if (k_numeric_p(other) && f_real_p(other)) { - get_dat1(self); + get_dat1(self); - return f_complex_new2(CLASS_OF(self), - f_mul(dat->real, other), - f_mul(dat->imag, other)); + return f_complex_new2(CLASS_OF(self), + f_mul(dat->real, other), + f_mul(dat->imag, other)); } return rb_num_coerce_bin(self, other, '*'); } +#define nucomp_mul rb_complex_mul inline static VALUE f_divide(VALUE self, VALUE other, - VALUE (*func)(VALUE, VALUE), ID id) + VALUE (*func)(VALUE, VALUE), ID id) { if (RB_TYPE_P(other, T_COMPLEX)) { - VALUE r, n, x, y; - int flo; - get_dat2(self, other); - - flo = (RB_FLOAT_TYPE_P(adat->real) || RB_FLOAT_TYPE_P(adat->imag) || - RB_FLOAT_TYPE_P(bdat->real) || RB_FLOAT_TYPE_P(bdat->imag)); - - if (f_gt_p(f_abs(bdat->real), f_abs(bdat->imag))) { - r = (*func)(bdat->imag, bdat->real); - n = f_mul(bdat->real, f_add(ONE, f_mul(r, r))); - x = (*func)(f_add(adat->real, f_mul(adat->imag, r)), n); - y = (*func)(f_sub(adat->imag, f_mul(adat->real, r)), n); - } - else { - r = (*func)(bdat->real, bdat->imag); - n = f_mul(bdat->imag, f_add(ONE, f_mul(r, r))); - x = (*func)(f_add(f_mul(adat->real, r), adat->imag), n); - y = (*func)(f_sub(f_mul(adat->imag, r), adat->real), n); - } - if (!flo) { - x = rb_rational_canonicalize(x); - y = rb_rational_canonicalize(y); - } - return f_complex_new2(CLASS_OF(self), x, y); + int flo; + get_dat2(self, other); + + flo = (RB_FLOAT_TYPE_P(adat->real) || RB_FLOAT_TYPE_P(adat->imag) || + RB_FLOAT_TYPE_P(bdat->real) || RB_FLOAT_TYPE_P(bdat->imag)); + + if (f_gt_p(f_abs(bdat->real), f_abs(bdat->imag))) { + VALUE r, n; + + r = (*func)(bdat->imag, bdat->real); + n = f_mul(bdat->real, f_add(ONE, f_mul(r, r))); + if (flo) + return f_complex_new2(CLASS_OF(self), + (*func)(self, n), + (*func)(f_negate(f_mul(self, r)), n)); + return f_complex_new2(CLASS_OF(self), + (*func)(f_add(adat->real, + f_mul(adat->imag, r)), n), + (*func)(f_sub(adat->imag, + f_mul(adat->real, r)), n)); + } + else { + VALUE r, n; + + r = (*func)(bdat->real, bdat->imag); + n = f_mul(bdat->imag, f_add(ONE, f_mul(r, r))); + if (flo) + return f_complex_new2(CLASS_OF(self), + (*func)(f_mul(self, r), n), + (*func)(f_negate(self), n)); + return f_complex_new2(CLASS_OF(self), + (*func)(f_add(f_mul(adat->real, r), + adat->imag), n), + (*func)(f_sub(f_mul(adat->imag, r), + adat->real), n)); + } } if (k_numeric_p(other) && f_real_p(other)) { - VALUE x, y; - get_dat1(self); - x = rb_rational_canonicalize((*func)(dat->real, other)); - y = rb_rational_canonicalize((*func)(dat->imag, other)); - return f_complex_new2(CLASS_OF(self), x, y); + 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); } @@ -989,33 +871,32 @@ f_divide(VALUE self, VALUE other, /* * call-seq: - * complex / numeric -> new_complex - * - * Returns the quotient of +self+ and +numeric+: + * cmp / numeric -> complex + * cmp.quo(numeric) -> complex * - * Complex.rect(2, 3) / Complex.rect(2, 3) # => (1+0i) - * Complex.rect(900) / Complex.rect(1) # => (900+0i) - * Complex.rect(-2, 9) / Complex.rect(-9, 2) # => ((36/85)-(77/85)*i) - * Complex.rect(9, 8) / 4 # => ((9/4)+2i) - * Complex.rect(20, 9) / 9.8 # => (2.0408163265306123+0.9183673469387754i) + * 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) */ -VALUE -rb_complex_div(VALUE self, VALUE other) +static VALUE +nucomp_div(VALUE self, VALUE other) { return f_divide(self, other, f_quo, id_quo); } -#define nucomp_quo rb_complex_div +#define nucomp_quo nucomp_div /* * call-seq: - * fdiv(numeric) -> new_complex + * cmp.fdiv(numeric) -> complex * - * Returns <tt>Complex.rect(self.real/numeric, self.imag/numeric)</tt>: - * - * Complex.rect(11, 22).fdiv(3) # => (3.6666666666666665+7.333333333333333i) + * 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) @@ -1029,366 +910,196 @@ f_reciprocal(VALUE x) return f_quo(ONE, x); } -static VALUE -zero_for(VALUE x) -{ - if (RB_FLOAT_TYPE_P(x)) - return DBL2NUM(0); - if (RB_TYPE_P(x, T_RATIONAL)) - return rb_rational_new(INT2FIX(0), INT2FIX(1)); - - return INT2FIX(0); -} - -static VALUE -complex_pow_for_special_angle(VALUE self, VALUE other) -{ - if (!rb_integer_type_p(other)) { - return Qundef; - } - - get_dat1(self); - VALUE x = Qundef; - int dir; - if (f_zero_p(dat->imag)) { - x = dat->real; - dir = 0; - } - else if (f_zero_p(dat->real)) { - x = dat->imag; - dir = 2; - } - else if (f_eqeq_p(dat->real, dat->imag)) { - x = dat->real; - dir = 1; - } - else if (f_eqeq_p(dat->real, f_negate(dat->imag))) { - x = dat->imag; - dir = 3; - } else { - dir = 0; - } - - if (UNDEF_P(x)) return x; - - if (f_negative_p(x)) { - x = f_negate(x); - dir += 4; - } - - VALUE zx; - if (dir % 2 == 0) { - zx = rb_num_pow(x, other); - } - else { - zx = rb_num_pow( - rb_funcall(rb_int_mul(TWO, x), '*', 1, x), - rb_int_div(other, TWO) - ); - if (rb_int_odd_p(other)) { - zx = rb_funcall(zx, '*', 1, x); - } - } - static const int dirs[][2] = { - {1, 0}, {1, 1}, {0, 1}, {-1, 1}, {-1, 0}, {-1, -1}, {0, -1}, {1, -1} - }; - int z_dir = FIX2INT(rb_int_modulo(rb_int_mul(INT2FIX(dir), other), INT2FIX(8))); - - VALUE zr = Qfalse, zi = Qfalse; - switch (dirs[z_dir][0]) { - case 0: zr = zero_for(zx); break; - case 1: zr = zx; break; - case -1: zr = f_negate(zx); break; - } - switch (dirs[z_dir][1]) { - case 0: zi = zero_for(zx); break; - case 1: zi = zx; break; - case -1: zi = f_negate(zx); break; - } - return nucomp_s_new_internal(CLASS_OF(self), zr, zi); -} - - /* * call-seq: - * complex ** numeric -> new_complex - * - * Returns +self+ raised to power +numeric+: + * cmp ** numeric -> complex * - * Complex.rect(0, 1) ** 2 # => (-1+0i) - * Complex.rect(-8) ** Rational(1, 3) # => (1.0000000000000002+1.7320508075688772i) + * Performs exponentiation. * + * Complex('i') ** 2 #=> (-1+0i) + * Complex(-8) ** Rational(1, 3) #=> (1.0000000000000002+1.7320508075688772i) */ -VALUE -rb_complex_pow(VALUE self, VALUE other) +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); + return f_complex_new_bang1(CLASS_OF(self), ONE); if (RB_TYPE_P(other, T_RATIONAL) && RRATIONAL(other)->den == LONG2FIX(1)) - other = RRATIONAL(other)->num; /* c14n */ + other = RRATIONAL(other)->num; /* c14n */ if (RB_TYPE_P(other, T_COMPLEX)) { - get_dat1(other); - - if (k_exact_zero_p(dat->imag)) - other = dat->real; /* c14n */ - } + get_dat1(other); - if (other == ONE) { - get_dat1(self); - return nucomp_s_new_internal(CLASS_OF(self), dat->real, dat->imag); + if (k_exact_zero_p(dat->imag)) + other = dat->real; /* c14n */ } - VALUE result = complex_pow_for_special_angle(self, other); - if (!UNDEF_P(result)) return result; - if (RB_TYPE_P(other, T_COMPLEX)) { - VALUE r, theta, nr, ntheta; + VALUE r, theta, nr, ntheta; - get_dat1(other); + get_dat1(other); - r = f_abs(self); - theta = f_arg(self); + 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); + nr = m_exp_bang(f_sub(f_mul(dat->real, m_log_bang(r)), + f_mul(dat->imag, theta))); + ntheta = f_add(f_mul(theta, dat->real), + f_mul(dat->imag, m_log_bang(r))); + return f_complex_polar(CLASS_OF(self), nr, ntheta); } if (FIXNUM_P(other)) { - long n = FIX2LONG(other); - if (n == 0) { - return nucomp_s_new_internal(CLASS_OF(self), ONE, ZERO); - } - if (n < 0) { - self = f_reciprocal(self); - other = rb_int_uminus(other); - n = -n; - } - { - get_dat1(self); - VALUE xr = dat->real, xi = dat->imag, zr = xr, zi = xi; - - if (f_zero_p(xi)) { - zr = rb_num_pow(zr, other); - } - else if (f_zero_p(xr)) { - zi = rb_num_pow(zi, other); - if (n & 2) zi = f_negate(zi); - if (!(n & 1)) { - VALUE tmp = zr; - zr = zi; - zi = tmp; - } - } - else { - while (--n) { - long q, r; - - for (; q = n / 2, r = n % 2, r == 0; n = q) { - VALUE tmp = f_sub(f_mul(xr, xr), f_mul(xi, xi)); - xi = f_mul(f_mul(TWO, xr), xi); - xr = tmp; - } - comp_mul(zr, zi, xr, xi, &zr, &zi); - } - } - return nucomp_s_new_internal(CLASS_OF(self), zr, zi); - } + if (f_gt_p(other, ZERO)) { + VALUE x, z; + long n; + + x = self; + z = x; + n = FIX2LONG(other) - 1; + + while (n) { + long q, r; + + while (1) { + get_dat1(x); + + q = n / 2; + r = n % 2; + + if (r) + break; + + x = nucomp_s_new_internal(CLASS_OF(self), + f_sub(f_mul(dat->real, dat->real), + f_mul(dat->imag, dat->imag)), + f_mul(f_mul(TWO, dat->real), dat->imag)); + n = q; + } + z = f_mul(z, x); + n--; + } + return z; + } + return f_expt(f_reciprocal(self), rb_int_uminus(other)); } if (k_numeric_p(other) && f_real_p(other)) { - VALUE r, theta; + VALUE r, theta; - if (RB_BIGNUM_TYPE_P(other)) - rb_warn("in a**b, b may be too big"); + if (RB_TYPE_P(other, T_BIGNUM)) + rb_warn("in a**b, b may be too big"); - r = f_abs(self); - theta = f_arg(self); + r = f_abs(self); + theta = f_arg(self); - return f_complex_polar(CLASS_OF(self), f_expt(r, other), - f_mul(theta, other)); + 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: - * complex == object -> true or false + * cmp == object -> true or false * - * Returns +true+ if <tt>self.real == object.real</tt> - * and <tt>self.imag == object.imag</tt>: - * - * Complex.rect(2, 3) == Complex.rect(2.0, 3.0) # => true + * Returns true if cmp equals object numerically. * + * Complex(2, 3) == Complex(2, 3) #=> true + * Complex(5) == 5 #=> true + * Complex(0) == 0.0 #=> true + * Complex('1/3') == 0.33 #=> false + * Complex('1/2') == '1/2' #=> false */ static VALUE nucomp_eqeq_p(VALUE self, VALUE other) { if (RB_TYPE_P(other, T_COMPLEX)) { - get_dat2(self, other); + get_dat2(self, other); - return RBOOL(f_eqeq_p(adat->real, bdat->real) && - f_eqeq_p(adat->imag, bdat->imag)); + 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); + get_dat1(self); - return RBOOL(f_eqeq_p(dat->real, other) && f_zero_p(dat->imag)); + return f_boolcast(f_eqeq_p(dat->real, other) && f_zero_p(dat->imag)); } - return RBOOL(f_eqeq_p(other, self)); -} - -static bool -nucomp_real_p(VALUE self) -{ - get_dat1(self); - return f_zero_p(dat->imag); -} - -/* - * call-seq: - * complex <=> object -> -1, 0, 1, or nil - * - * Returns: - * - * - <tt>self.real <=> object.real</tt> if both of the following are true: - * - * - <tt>self.imag == 0</tt>. - * - <tt>object.imag == 0</tt>. # Always true if object is numeric but not complex. - * - * - +nil+ otherwise. - * - * Examples: - * - * Complex.rect(2) <=> 3 # => -1 - * Complex.rect(2) <=> 2 # => 0 - * Complex.rect(2) <=> 1 # => 1 - * Complex.rect(2, 1) <=> 1 # => nil # self.imag not zero. - * Complex.rect(1) <=> Complex.rect(1, 1) # => nil # object.imag not zero. - * Complex.rect(1) <=> 'Foo' # => nil # object.imag not defined. - * - */ -static VALUE -nucomp_cmp(VALUE self, VALUE other) -{ - if (!k_numeric_p(other)) { - return rb_num_coerce_cmp(self, other, idCmp); - } - if (!nucomp_real_p(self)) { - return Qnil; - } - if (RB_TYPE_P(other, T_COMPLEX)) { - if (nucomp_real_p(other)) { - get_dat2(self, other); - return rb_funcall(adat->real, idCmp, 1, bdat->real); - } - } - else { - get_dat1(self); - if (f_real_p(other)) { - return rb_funcall(dat->real, idCmp, 1, other); - } - else { - return rb_num_coerce_cmp(dat->real, other, idCmp); - } - } - return Qnil; + return f_boolcast(f_eqeq_p(other, self)); } /* :nodoc: */ static VALUE nucomp_coerce(VALUE self, VALUE other) { - if (RB_TYPE_P(other, T_COMPLEX)) - return rb_assoc_new(other, self); if (k_numeric_p(other) && f_real_p(other)) - return rb_assoc_new(f_complex_new_bang1(CLASS_OF(self), other), self); + return rb_assoc_new(f_complex_new_bang1(CLASS_OF(self), other), self); + if (RB_TYPE_P(other, T_COMPLEX)) + return rb_assoc_new(other, self); rb_raise(rb_eTypeError, "%"PRIsVALUE" can't be coerced into %"PRIsVALUE, - rb_obj_class(other), rb_obj_class(self)); + rb_obj_class(other), rb_obj_class(self)); return Qnil; } /* * call-seq: - * abs -> float - * - * Returns the absolute value (magnitude) for +self+; - * see {polar coordinates}[rdoc-ref:Complex@Polar+Coordinates]: - * - * Complex.polar(-1, 0).abs # => 1.0 + * cmp.abs -> real + * cmp.magnitude -> real * - * If +self+ was created with - * {rectangular coordinates}[rdoc-ref:Complex@Rectangular+Coordinates], the returned value - * is computed, and may be inexact: - * - * Complex.rectangular(1, 1).abs # => 1.4142135623730951 # The square root of 2. + * Returns the absolute part of its polar form. * + * Complex(-1).abs #=> 1 + * Complex(3.0, -4.0).abs #=> 5.0 */ -VALUE -rb_complex_abs(VALUE self) +static VALUE +nucomp_abs(VALUE self) { get_dat1(self); if (f_zero_p(dat->real)) { - VALUE a = f_abs(dat->imag); - if (RB_FLOAT_TYPE_P(dat->real) && !RB_FLOAT_TYPE_P(dat->imag)) - a = f_to_f(a); - return a; + VALUE a = f_abs(dat->imag); + if (RB_FLOAT_TYPE_P(dat->real) && !RB_FLOAT_TYPE_P(dat->imag)) + a = f_to_f(a); + return a; } if (f_zero_p(dat->imag)) { - VALUE a = f_abs(dat->real); - if (!RB_FLOAT_TYPE_P(dat->real) && RB_FLOAT_TYPE_P(dat->imag)) - a = f_to_f(a); - return a; + VALUE a = f_abs(dat->real); + if (!RB_FLOAT_TYPE_P(dat->real) && RB_FLOAT_TYPE_P(dat->imag)) + a = f_to_f(a); + return a; } return rb_math_hypot(dat->real, dat->imag); } /* * call-seq: - * abs2 -> float - * - * Returns square of the absolute value (magnitude) for +self+; - * see {polar coordinates}[rdoc-ref:Complex@Polar+Coordinates]: + * cmp.abs2 -> real * - * Complex.polar(2, 2).abs2 # => 4.0 - * - * If +self+ was created with - * {rectangular coordinates}[rdoc-ref:Complex@Rectangular+Coordinates], the returned value - * is computed, and may be inexact: - * - * Complex.rectangular(1.0/3, 1.0/3).abs2 # => 0.2222222222222222 + * 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)); + f_mul(dat->imag, dat->imag)); } /* * call-seq: - * arg -> float - * - * Returns the argument (angle) for +self+ in radians; - * see {polar coordinates}[rdoc-ref:Complex@Polar+Coordinates]: + * cmp.arg -> float + * cmp.angle -> float + * cmp.phase -> float * - * Complex.polar(3, Math::PI/2).arg # => 1.57079632679489660 - * - * If +self+ was created with - * {rectangular coordinates}[rdoc-ref:Complex@Rectangular+Coordinates], the returned value - * is computed, and may be inexact: - * - * Complex.polar(1, 1.0/3).arg # => 0.33333333333333326 + * Returns the angle part of its polar form. * + * Complex.polar(3, Math::PI/2).arg #=> 1.5707963267948966 */ -VALUE -rb_complex_arg(VALUE self) +static VALUE +nucomp_arg(VALUE self) { get_dat1(self); return rb_math_atan2(dat->imag, dat->real); @@ -1396,22 +1107,12 @@ rb_complex_arg(VALUE self) /* * call-seq: - * rect -> array - * - * Returns the array <tt>[self.real, self.imag]</tt>: - * - * Complex.rect(1, 2).rect # => [1, 2] - * - * See {Rectangular Coordinates}[rdoc-ref:Complex@Rectangular+Coordinates]. + * cmp.rect -> array + * cmp.rectangular -> array * - * If +self+ was created with - * {polar coordinates}[rdoc-ref:Complex@Polar+Coordinates], the returned value - * is computed, and may be inexact: + * Returns an array; [cmp.real, cmp.imag]. * - * Complex.polar(1.0, 1.0).rect # => [0.5403023058681398, 0.8414709848078965] - * - * - * Complex#rectangular is an alias for Complex#rect. + * Complex(1, 2).rectangular #=> [1, 2] */ static VALUE nucomp_rect(VALUE self) @@ -1422,20 +1123,11 @@ nucomp_rect(VALUE self) /* * call-seq: - * polar -> array - * - * Returns the array <tt>[self.abs, self.arg]</tt>: - * - * Complex.polar(1, 2).polar # => [1.0, 2.0] + * cmp.polar -> array * - * See {Polar Coordinates}[rdoc-ref:Complex@Polar+Coordinates]. - * - * If +self+ was created with - * {rectangular coordinates}[rdoc-ref:Complex@Rectangular+Coordinates], the returned value - * is computed, and may be inexact: - * - * Complex.rect(1, 1).polar # => [1.4142135623730951, 0.7853981633974483] + * Returns an array; [cmp.abs, cmp.arg]. * + * Complex(1, 2).polar #=> [2.23606797749979, 1.1071487177940904] */ static VALUE nucomp_polar(VALUE self) @@ -1445,45 +1137,65 @@ nucomp_polar(VALUE self) /* * call-seq: - * conj -> complex - * - * Returns the conjugate of +self+, <tt>Complex.rect(self.imag, self.real)</tt>: + * cmp.conj -> complex + * cmp.conjugate -> complex * - * Complex.rect(1, 2).conj # => (1-2i) + * Returns the complex conjugate. * + * Complex(1, 2).conjugate #=> (1-2i) */ -VALUE -rb_complex_conjugate(VALUE self) +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: - * real? -> false + * cmp.real? -> false * - * Returns +false+; for compatibility with Numeric#real?. + * Returns false. */ static VALUE -nucomp_real_p_m(VALUE self) +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: - * denominator -> integer - * - * Returns the denominator of +self+, which is - * the {least common multiple}[https://en.wikipedia.org/wiki/Least_common_multiple] - * of <tt>self.real.denominator</tt> and <tt>self.imag.denominator</tt>: + * cmp.denominator -> integer * - * Complex.rect(Rational(1, 2), Rational(2, 3)).denominator # => 6 + * Returns the denominator (lcm of both denominator - real and imag). * - * Note that <tt>n.denominator</tt> of a non-rational numeric is +1+. - * - * Related: Complex#numerator. + * See numerator. */ static VALUE nucomp_denominator(VALUE self) @@ -1494,23 +1206,21 @@ nucomp_denominator(VALUE self) /* * call-seq: - * numerator -> new_complex - * - * Returns the \Complex object created from the numerators - * of the real and imaginary parts of +self+, - * after converting each part to the - * {lowest common denominator}[https://en.wikipedia.org/wiki/Lowest_common_denominator] - * of the two: + * cmp.numerator -> numeric * - * c = Complex.rect(Rational(2, 3), Rational(3, 4)) # => ((2/3)+(3/4)*i) - * c.numerator # => (8+9i) + * Returns the numerator. * - * In this example, the lowest common denominator of the two parts is 12; - * the two converted parts may be thought of as \Rational(8, 12) and \Rational(9, 12), - * whose numerators, respectively, are 8 and 9; - * so the returned value of <tt>c.numerator</tt> is <tt>Complex.rect(8, 9)</tt>. + * 1 2 3+4i <- numerator + * - + -i -> ---- + * 2 3 6 <- denominator * - * Related: Complex#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) @@ -1519,17 +1229,17 @@ nucomp_numerator(VALUE self) get_dat1(self); - cd = nucomp_denominator(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)))); + f_mul(f_numerator(dat->real), + f_div(cd, f_denominator(dat->real))), + f_mul(f_numerator(dat->imag), + f_div(cd, f_denominator(dat->imag)))); } /* :nodoc: */ -st_index_t -rb_complex_hash(VALUE self) +static VALUE +nucomp_hash(VALUE self) { st_index_t v, h[2]; VALUE n; @@ -1540,25 +1250,7 @@ rb_complex_hash(VALUE self) n = rb_hash(dat->imag); h[1] = NUM2LONG(n); v = rb_memhash(h, sizeof(h)); - return v; -} - -/* - * :call-seq: - * hash -> integer - * - * Returns the integer hash value for +self+. - * - * Two \Complex objects created from the same values will have the same hash value - * (and will compare using #eql?): - * - * Complex.rect(1, 2).hash == Complex.rect(1, 2).hash # => true - * - */ -static VALUE -nucomp_hash(VALUE self) -{ - return ST2FIX(rb_complex_hash(self)); + return ST2FIX(v); } /* :nodoc: */ @@ -1566,11 +1258,11 @@ static VALUE nucomp_eql_p(VALUE self, VALUE other) { if (RB_TYPE_P(other, T_COMPLEX)) { - get_dat2(self, other); + get_dat2(self, other); - return RBOOL((CLASS_OF(adat->real) == CLASS_OF(bdat->real)) && - (CLASS_OF(adat->imag) == CLASS_OF(bdat->imag)) && - f_eqeq_p(self, other)); + return 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; @@ -1580,8 +1272,8 @@ inline static int f_signbit(VALUE x) { if (RB_FLOAT_TYPE_P(x)) { - double f = RFLOAT_VALUE(x); - return !isnan(f) && signbit(f); + double f = RFLOAT_VALUE(x); + return !isnan(f) && signbit(f); } return f_negative_p(x); } @@ -1593,20 +1285,21 @@ f_tpositive_p(VALUE x) } static VALUE -f_format(VALUE self, VALUE s, VALUE (*func)(VALUE)) +f_format(VALUE self, VALUE (*func)(VALUE)) { + VALUE s; int impos; get_dat1(self); impos = f_tpositive_p(dat->imag); - rb_str_concat(s, (*func)(dat->real)); + 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, "*"); rb_str_cat2(s, "i"); return s; @@ -1614,35 +1307,33 @@ f_format(VALUE self, VALUE s, VALUE (*func)(VALUE)) /* * call-seq: - * to_s -> string + * cmp.to_s -> string * - * Returns a string representation of +self+: - * - * Complex.rect(2).to_s # => "2+0i" - * Complex.rect(-8, 6).to_s # => "-8+6i" - * Complex.rect(0, Rational(1, 2)).to_s # => "0+1/2i" - * Complex.rect(0, Float::INFINITY).to_s # => "0+Infinity*i" - * Complex.rect(Float::NAN, Float::NAN).to_s # => "NaN+NaN*i" + * 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_usascii_str_new2(""), rb_String); + return f_format(self, rb_String); } /* * call-seq: - * inspect -> string - * - * Returns a string representation of +self+: + * cmp.inspect -> string * - * Complex.rect(2).inspect # => "(2+0i)" - * Complex.rect(-8, 6).inspect # => "(-8+6i)" - * Complex.rect(0, Rational(1, 2)).inspect # => "(0+(1/2)*i)" - * Complex.rect(0, Float::INFINITY).inspect # => "(0+Infinity*i)" - * Complex.rect(Float::NAN, Float::NAN).inspect # => "(NaN+NaN*i)" + * 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) @@ -1650,7 +1341,7 @@ nucomp_inspect(VALUE self) VALUE s; s = rb_usascii_str_new2("("); - f_format(self, s, rb_inspect); + rb_str_concat(s, f_format(self, rb_inspect)); rb_str_cat2(s, ")"); return s; @@ -1660,43 +1351,43 @@ nucomp_inspect(VALUE self) /* * call-seq: - * finite? -> true or false + * cmp.finite? -> true or false * - * Returns +true+ if both <tt>self.real.finite?</tt> and <tt>self.imag.finite?</tt> - * are true, +false+ otherwise: - * - * Complex.rect(1, 1).finite? # => true - * Complex.rect(Float::INFINITY, 0).finite? # => false - * - * Related: Numeric#finite?, Float#finite?. + * Returns +true+ if +cmp+'s magnitude is a finite number, + * otherwise returns +false+. */ static VALUE rb_complex_finite_p(VALUE self) { get_dat1(self); - return RBOOL(f_finite_p(dat->real) && f_finite_p(dat->imag)); + if (f_finite_p(dat->real) && f_finite_p(dat->imag)) { + return Qtrue; + } + return Qfalse; } /* * call-seq: - * infinite? -> 1 or nil + * cmp.infinite? -> nil or 1 + * + * Returns values corresponding to the value of +cmp+'s magnitude: * - * Returns +1+ if either <tt>self.real.infinite?</tt> or <tt>self.imag.infinite?</tt> - * is true, +nil+ otherwise: + * +finite+:: +nil+ + * ++Infinity+:: ++1+ * - * Complex.rect(Float::INFINITY, 0).infinite? # => 1 - * Complex.rect(1, 1).infinite? # => nil + * For example: * - * Related: Numeric#infinite?, Float#infinite?. + * (1+1i).infinite? #=> nil + * (Float::INFINITY + 1i).infinite? #=> 1 */ static VALUE rb_complex_infinite_p(VALUE self) { get_dat1(self); - if (!f_infinite_p(dat->real) && !f_infinite_p(dat->imag)) { - return Qnil; + if (NIL_P(f_infinite_p(dat->real)) && NIL_P(f_infinite_p(dat->imag))) { + return Qnil; } return ONE; } @@ -1716,7 +1407,7 @@ nucomp_loader(VALUE self, VALUE a) RCOMPLEX_SET_REAL(dat, rb_ivar_get(a, id_i_real)); RCOMPLEX_SET_IMAG(dat, rb_ivar_get(a, id_i_imag)); - OBJ_FREEZE(self); + OBJ_FREEZE_RAW(self); return self; } @@ -1739,12 +1430,14 @@ 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_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) { @@ -1758,15 +1451,9 @@ rb_complex_new(VALUE x, VALUE y) } VALUE -rb_complex_new_polar(VALUE x, VALUE y) -{ - return f_complex_polar(rb_cComplex, x, y); -} - -VALUE rb_complex_polar(VALUE x, VALUE y) { - return rb_complex_new_polar(x, y); + return f_complex_polar(rb_cComplex, x, y); } VALUE @@ -1779,22 +1466,21 @@ rb_Complex(VALUE x, VALUE y) } VALUE -rb_dbl_complex_new(double real, double imag) +rb_complex_abs(VALUE cmp) { - return rb_complex_raw(DBL2NUM(real), DBL2NUM(imag)); + return nucomp_abs(cmp); } /* * call-seq: - * to_i -> integer - * - * Returns the value of <tt>self.real</tt> as an Integer, if possible: + * cmp.to_i -> integer * - * Complex.rect(1, 0).to_i # => 1 - * Complex.rect(1, Rational(0, 1)).to_i # => 1 + * Returns the value as an integer if possible (the imaginary part + * should be exactly zero). * - * Raises RangeError if <tt>self.imag</tt> is not exactly zero - * (either <tt>Integer(0)</tt> or <tt>Rational(0, _n_)</tt>). + * 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) @@ -1802,23 +1488,22 @@ nucomp_to_i(VALUE self) get_dat1(self); if (!k_exact_zero_p(dat->imag)) { - rb_raise(rb_eRangeError, "can't convert %"PRIsVALUE" into Integer", - self); + rb_raise(rb_eRangeError, "can't convert %"PRIsVALUE" into Integer", + self); } return f_to_i(dat->real); } /* * call-seq: - * to_f -> float + * cmp.to_f -> float * - * Returns the value of <tt>self.real</tt> as a Float, if possible: + * Returns the value as a float if possible (the imaginary part should + * be exactly zero). * - * Complex.rect(1, 0).to_f # => 1.0 - * Complex.rect(1, Rational(0, 1)).to_f # => 1.0 - * - * Raises RangeError if <tt>self.imag</tt> is not exactly zero - * (either <tt>Integer(0)</tt> or <tt>Rational(0, _n_)</tt>). + * 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) @@ -1826,84 +1511,56 @@ nucomp_to_f(VALUE self) get_dat1(self); if (!k_exact_zero_p(dat->imag)) { - rb_raise(rb_eRangeError, "can't convert %"PRIsVALUE" into Float", - self); + rb_raise(rb_eRangeError, "can't convert %"PRIsVALUE" into Float", + self); } return f_to_f(dat->real); } /* * call-seq: - * to_r -> rational - * - * Returns the value of <tt>self.real</tt> as a Rational, if possible: + * cmp.to_r -> rational * - * Complex.rect(1, 0).to_r # => (1/1) - * Complex.rect(1, Rational(0, 1)).to_r # => (1/1) - * Complex.rect(1, 0.0).to_r # => (1/1) + * Returns the value as a rational if possible (the imaginary part + * should be exactly zero). * - * Raises RangeError if <tt>self.imag</tt> is not exactly zero - * (either <tt>Integer(0)</tt> or <tt>Rational(0, _n_)</tt>) - * and <tt>self.imag.to_r</tt> is not exactly zero. + * Complex(1, 0).to_r #=> (1/1) + * Complex(1, 0.0).to_r # RangeError + * Complex(1, 2).to_r # RangeError * - * Related: Complex#rationalize. + * See rationalize. */ static VALUE nucomp_to_r(VALUE self) { get_dat1(self); - if (RB_FLOAT_TYPE_P(dat->imag) && FLOAT_ZERO_P(dat->imag)) { - /* Do nothing here */ - } - else if (!k_exact_zero_p(dat->imag)) { - VALUE imag = rb_check_convert_type_with_id(dat->imag, T_RATIONAL, "Rational", idTo_r); - if (NIL_P(imag) || !k_exact_zero_p(imag)) { - rb_raise(rb_eRangeError, "can't convert %"PRIsVALUE" into Rational", - self); - } + if (!k_exact_zero_p(dat->imag)) { + rb_raise(rb_eRangeError, "can't convert %"PRIsVALUE" into Rational", + self); } return f_to_r(dat->real); } /* * call-seq: - * rationalize(epsilon = nil) -> rational - * - * Returns a Rational object whose value is exactly or approximately - * equivalent to that of <tt>self.real</tt>. - * - * With no argument +epsilon+ given, returns a \Rational object - * whose value is exactly equal to that of <tt>self.real.rationalize</tt>: - * - * Complex.rect(1, 0).rationalize # => (1/1) - * Complex.rect(1, Rational(0, 1)).rationalize # => (1/1) - * Complex.rect(3.14159, 0).rationalize # => (314159/100000) - * - * With argument +epsilon+ given, returns a \Rational object - * whose value is exactly or approximately equal to that of <tt>self.real</tt> - * to the given precision: - * - * Complex.rect(3.14159, 0).rationalize(0.1) # => (16/5) - * Complex.rect(3.14159, 0).rationalize(0.01) # => (22/7) - * Complex.rect(3.14159, 0).rationalize(0.001) # => (201/64) - * Complex.rect(3.14159, 0).rationalize(0.0001) # => (333/106) - * Complex.rect(3.14159, 0).rationalize(0.00001) # => (355/113) - * Complex.rect(3.14159, 0).rationalize(0.000001) # => (7433/2366) - * Complex.rect(3.14159, 0).rationalize(0.0000001) # => (9208/2931) - * Complex.rect(3.14159, 0).rationalize(0.00000001) # => (47460/15107) - * Complex.rect(3.14159, 0).rationalize(0.000000001) # => (76149/24239) - * Complex.rect(3.14159, 0).rationalize(0.0000000001) # => (314159/100000) - * Complex.rect(3.14159, 0).rationalize(0.0) # => (3537115888337719/1125899906842624) - * - * Related: Complex#to_r. + * 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_check_arity(argc, 0, 1); + rb_scan_args(argc, argv, "01", NULL); if (!k_exact_zero_p(dat->imag)) { rb_raise(rb_eRangeError, "can't convert %"PRIsVALUE" into Rational", @@ -1914,9 +1571,12 @@ nucomp_rationalize(int argc, VALUE *argv, VALUE self) /* * call-seq: - * to_c -> self + * complex.to_c -> self * - * Returns +self+. + * Returns self. + * + * Complex(2).to_c #=> (2+0i) + * Complex(-8, 6).to_c #=> (-8+6i) */ static VALUE nucomp_to_c(VALUE self) @@ -1926,12 +1586,9 @@ nucomp_to_c(VALUE self) /* * call-seq: - * to_c -> (0+0i) - * - * Returns zero as a Complex: - * - * nil.to_c # => (0+0i) + * nil.to_c -> (0+0i) * + * Returns zero as a complex. */ static VALUE nilclass_to_c(VALUE self) @@ -1941,9 +1598,9 @@ nilclass_to_c(VALUE self) /* * call-seq: - * to_c -> complex + * num.to_c -> complex * - * Returns +self+ as a Complex object. + * Returns the value as a complex. */ static VALUE numeric_to_c(VALUE self) @@ -1951,6 +1608,8 @@ numeric_to_c(VALUE self) return rb_complex_new1(self); } +#include <ctype.h> + inline static int issign(int c) { @@ -1959,14 +1618,14 @@ issign(int c) static int read_sign(const char **s, - char **b) + char **b) { int sign = '?'; if (issign(**s)) { - sign = **b = **s; - (*s)++; - (*b)++; + sign = **b = **s; + (*s)++; + (*b)++; } return sign; } @@ -1979,32 +1638,32 @@ isdecimal(int c) static int read_digits(const char **s, int strict, - char **b) + char **b) { int us = 1; if (!isdecimal(**s)) - return 0; + return 0; while (isdecimal(**s) || **s == '_') { - if (**s == '_') { - if (us) { - if (strict) return 0; - break; - } - us = 1; - } - else { - **b = **s; - (*b)++; - us = 0; - } - (*s)++; + if (**s == '_') { + if (strict) { + if (us) + return 0; + } + us = 1; + } + else { + **b = **s; + (*b)++; + us = 0; + } + (*s)++; } if (us) - do { - (*s)--; - } while (**s == '_'); + do { + (*s)--; + } while (**s == '_'); return 1; } @@ -2016,70 +1675,70 @@ islettere(int c) static int read_num(const char **s, int strict, - char **b) + char **b) { if (**s != '.') { - if (!read_digits(s, strict, b)) - return 0; + if (!read_digits(s, strict, b)) + return 0; } if (**s == '.') { - **b = **s; - (*s)++; - (*b)++; - if (!read_digits(s, strict, b)) { - (*b)--; - return 0; - } + **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; - } + **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) + char **b) { if (!read_digits(s, strict, b)) - return 0; + return 0; return 1; } static int read_rat_nos(const char **s, int strict, - char **b) + char **b) { if (!read_num(s, strict, b)) - return 0; + return 0; if (**s == '/') { - **b = **s; - (*s)++; - (*b)++; - if (!read_den(s, strict, b)) { - (*b)--; - return 0; - } + **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) + char **b) { read_sign(s, b); if (!read_rat_nos(s, strict, b)) - return 0; + return 0; return 1; } @@ -2087,22 +1746,22 @@ inline static int isimagunit(int c) { return (c == 'i' || c == 'I' || - c == 'j' || c == 'J'); + c == 'j' || c == 'J'); } static VALUE str2num(char *s) { if (strchr(s, '/')) - return rb_cstr_to_rat(s, 0); + return rb_cstr_to_rat(s, 0); if (strpbrk(s, ".eE")) - return DBL2NUM(rb_cstr_to_dbl(s, 0)); + 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) + VALUE *ret, char **b) { char *bb; int sign; @@ -2113,72 +1772,72 @@ read_comp(const char **s, int strict, 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" */ + (*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); + *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" */ + (*s)++; + *ret = rb_complex_new2(ZERO, num); + return 1; /* e.g. "3i" */ } if (**s == '@') { - int st; - - (*s)++; - bb = *b; - st = read_rat(s, strict, b); - **b = '\0'; - if (strlen(bb) < 1 || - !isdecimal(*(bb + strlen(bb) - 1))) { - *ret = rb_complex_new2(num, ZERO); - return 0; /* e.g. "1@-" */ - } - num2 = str2num(bb); - *ret = rb_complex_new_polar(num, num2); - if (!st) - return 0; /* e.g. "1@2." */ - else - return 1; /* e.g. "1@2" */ + 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" */ + 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" */ + *ret = rb_complex_new2(num, ZERO); + return 1; /* e.g. "3" */ } } @@ -2186,11 +1845,12 @@ inline static void skip_ws(const char **s) { while (isspace((unsigned char)**s)) - (*s)++; + (*s)++; } static int -parse_comp(const char *s, int strict, VALUE *num) +parse_comp(const char *s, int strict, + VALUE *num) { char *buf, *b; VALUE tmp; @@ -2201,14 +1861,14 @@ parse_comp(const char *s, int strict, VALUE *num) skip_ws(&s); if (!read_comp(&s, strict, num, &b)) { - ret = 0; + ret = 0; } else { - skip_ws(&s); + skip_ws(&s); - if (strict) - if (*s != '\0') - ret = 0; + if (strict) + if (*s != '\0') + ret = 0; } ALLOCV_END(tmp); @@ -2216,24 +1876,30 @@ parse_comp(const char *s, int strict, VALUE *num) } static VALUE -string_to_c_strict(VALUE self, int raise) +string_to_c_strict(VALUE self) { char *s; VALUE num; rb_must_asciicompat(self); - if (raise) { - s = StringValueCStr(self); - } - else if (!(s = rb_str_to_cstr(self))) { - return Qnil; + 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 (!parse_comp(s, TRUE, &num)) { - if (!raise) return Qnil; - rb_raise(rb_eArgError, "invalid value for convert(): %+"PRIsVALUE, - self); + if (!s) + s = (char *)""; + + if (!parse_comp(s, 1, &num)) { + rb_raise(rb_eArgError, "invalid value for convert(): %+"PRIsVALUE, + self); } return num; @@ -2241,146 +1907,152 @@ string_to_c_strict(VALUE self, int raise) /* * call-seq: - * to_c -> complex - * - * Returns +self+ interpreted as a Complex object; - * leading whitespace and trailing garbage are ignored: - * - * '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) - * '1.0@0'.to_c # => (1+0.0i) - * "1.0@#{Math::PI/2}".to_c # => (0.0+1i) - * "1.0@#{Math::PI}".to_c # => (-1+0.0i) - * - * Returns \Complex zero if the string cannot be converted: - * - * 'ruby'.to_c # => (0+0i) - * - * See Kernel#Complex. + * 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); - (void)parse_comp(rb_str_fill_terminator(self, 1), FALSE, &num); + 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 -to_complex(VALUE val) +nucomp_s_convert(int argc, VALUE *argv, VALUE klass) { - return rb_convert_type(val, T_COMPLEX, "Complex", "to_c"); -} + VALUE a1, a2, backref; -static VALUE -nucomp_convert(VALUE klass, VALUE a1, VALUE a2, int raise) -{ - if (NIL_P(a1) || NIL_P(a2)) { - if (!raise) return Qnil; - rb_raise(rb_eTypeError, "can't convert nil into Complex"); - } + 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, raise); - if (NIL_P(a1)) return Qnil; + a1 = string_to_c_strict(a1); } if (RB_TYPE_P(a2, T_STRING)) { - a2 = string_to_c_strict(a2, raise); - if (NIL_P(a2)) return Qnil; + a2 = string_to_c_strict(a2); } + rb_backref_set(backref); + if (RB_TYPE_P(a1, T_COMPLEX)) { - { - get_dat1(a1); + { + get_dat1(a1); - if (k_exact_zero_p(dat->imag)) - a1 = dat->real; - } + if (k_exact_zero_p(dat->imag)) + a1 = dat->real; + } } if (RB_TYPE_P(a2, T_COMPLEX)) { - { - get_dat1(a2); + { + get_dat1(a2); - if (k_exact_zero_p(dat->imag)) - a2 = dat->real; - } + if (k_exact_zero_p(dat->imag)) + a2 = dat->real; + } } if (RB_TYPE_P(a1, T_COMPLEX)) { - if (UNDEF_P(a2) || (k_exact_zero_p(a2))) - return a1; - } - - if (UNDEF_P(a2)) { - if (k_numeric_p(a1) && !f_real_p(a1)) - return a1; - /* should raise exception for consistency */ - if (!k_numeric_p(a1)) { - if (!raise) { - a1 = rb_protect(to_complex, a1, NULL); - rb_set_errinfo(Qnil); - return a1; - } - return to_complex(a1); - } + 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))); + if ((k_numeric_p(a1) && k_numeric_p(a2)) && + (!f_real_p(a1) || !f_real_p(a2))) + return f_add(a1, + f_mul(a2, + f_complex_new_bang2(rb_cComplex, ZERO, ONE))); } { - int argc; - VALUE argv2[2]; - argv2[0] = a1; - if (UNDEF_P(a2)) { - argv2[1] = Qnil; - argc = 1; - } - else { - if (!raise && !RB_INTEGER_TYPE_P(a2) && !RB_FLOAT_TYPE_P(a2) && !RB_TYPE_P(a2, T_RATIONAL)) - return Qnil; - argv2[1] = a2; - argc = 2; - } - return nucomp_s_new(argc, argv2, klass); + 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 -nucomp_s_convert(int argc, VALUE *argv, VALUE klass) +numeric_real(VALUE self) { - VALUE a1, a2; - - if (rb_scan_args(argc, argv, "11", &a1, &a2) == 1) { - a2 = Qundef; - } + return self; +} - return nucomp_convert(klass, a1, a2, TRUE); +/* + * call-seq: + * num.imag -> 0 + * num.imaginary -> 0 + * + * Returns zero. + */ +static VALUE +numeric_imag(VALUE self) +{ + return INT2FIX(0); } /* * call-seq: - * abs2 -> real + * num.abs2 -> real * - * Returns the square of +self+. + * Returns square of self. */ static VALUE numeric_abs2(VALUE self) @@ -2390,9 +2062,11 @@ numeric_abs2(VALUE self) /* * call-seq: - * arg -> 0 or Math::PI + * num.arg -> 0 or float + * num.angle -> 0 or float + * num.phase -> 0 or float * - * Returns zero if +self+ is positive, Math::PI otherwise. + * Returns 0 if the value is positive, pi otherwise. */ static VALUE numeric_arg(VALUE self) @@ -2404,9 +2078,10 @@ numeric_arg(VALUE self) /* * call-seq: - * rect -> array + * num.rect -> array + * num.rectangular -> array * - * Returns array <tt>[self, 0]</tt>. + * Returns an array; [num, 0]. */ static VALUE numeric_rect(VALUE self) @@ -2414,11 +2089,13 @@ numeric_rect(VALUE self) return rb_assoc_new(self, INT2FIX(0)); } +static VALUE float_arg(VALUE self); + /* * call-seq: - * polar -> array + * num.polar -> array * - * Returns array <tt>[self.abs, self.arg]</tt>. + * Returns an array; [num.abs, num.arg]. */ static VALUE numeric_polar(VALUE self) @@ -2446,175 +2123,107 @@ numeric_polar(VALUE self) /* * call-seq: - * arg -> 0 or Math::PI + * 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 +self+ is positive, Math::PI otherwise. + * Returns 0 if the value is positive, pi otherwise. */ static VALUE float_arg(VALUE self) { if (isnan(RFLOAT_VALUE(self))) - return self; + return self; if (f_tpositive_p(self)) - return INT2FIX(0); + return INT2FIX(0); return rb_const_get(rb_mMath, id_PI); } /* - * A \Complex object houses a pair of values, - * given when the object is created as either <i>rectangular coordinates</i> - * or <i>polar coordinates</i>. - * - * == Rectangular Coordinates - * - * The rectangular coordinates of a complex number - * are called the _real_ and _imaginary_ parts; - * see {Complex number definition}[https://en.wikipedia.org/wiki/Complex_number#Definition_and_basic_operations]. - * - * You can create a \Complex object from rectangular coordinates with: - * - * - A {complex literal}[rdoc-ref:syntax/literals.rdoc@Complex+Literals]. - * - \Method Complex.rect. - * - \Method Kernel#Complex, either with numeric arguments or with certain string arguments. - * - \Method String#to_c, for certain strings. - * - * Note that each of the stored parts may be a an instance one of the classes - * Complex, Float, Integer, or Rational; - * they may be retrieved: - * - * - Separately, with methods Complex#real and Complex#imaginary. - * - Together, with method Complex#rect. - * - * The corresponding (computed) polar values may be retrieved: - * - * - Separately, with methods Complex#abs and Complex#arg. - * - Together, with method Complex#polar. - * - * == Polar Coordinates - * - * The polar coordinates of a complex number - * are called the _absolute_ and _argument_ parts; - * see {Complex polar plane}[https://en.wikipedia.org/wiki/Complex_number#Polar_form]. - * - * In this class, the argument part - * in expressed {radians}[https://en.wikipedia.org/wiki/Radian] - * (not {degrees}[https://en.wikipedia.org/wiki/Degree_(angle)]). - * - * You can create a \Complex object from polar coordinates with: + * 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. * - * - \Method Complex.polar. - * - \Method Kernel#Complex, with certain string arguments. - * - \Method String#to_c, for certain strings. + * Complex object can be created as literal, and also by using + * Kernel#Complex, Complex::rect, Complex::polar or to_c method. * - * Note that each of the stored parts may be a an instance one of the classes - * Complex, Float, Integer, or Rational; - * they may be retrieved: + * 2+1i #=> (2+1i) + * Complex(1) #=> (1+0i) + * Complex(2, 3) #=> (2+3i) + * Complex.polar(2, 3) #=> (-1.9799849932008908+0.2822400161197344i) + * 3.to_c #=> (3+0i) * - * - Separately, with methods Complex#abs and Complex#arg. - * - Together, with method Complex#polar. + * You can also create complex object from floating-point numbers or + * strings. * - * The corresponding (computed) rectangular values may be retrieved: + * 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) * - * - Separately, with methods Complex#real and Complex#imag. - * - Together, with method Complex#rect. + * 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) * - * == What's Here - * - * First, what's elsewhere: - * - * - \Class \Complex inherits (directly or indirectly) - * from classes {Numeric}[rdoc-ref:Numeric@What-27s+Here] - * and {Object}[rdoc-ref:Object@What-27s+Here]. - * - Includes (indirectly) module {Comparable}[rdoc-ref:Comparable@What-27s+Here]. - * - * Here, class \Complex has methods for: - * - * === Creating \Complex Objects - * - * - ::polar: Returns a new \Complex object based on given polar coordinates. - * - ::rect (and its alias ::rectangular): - * Returns a new \Complex object based on given rectangular coordinates. - * - * === Querying - * - * - #abs (and its alias #magnitude): Returns the absolute value for +self+. - * - #arg (and its aliases #angle and #phase): - * Returns the argument (angle) for +self+ in radians. - * - #denominator: Returns the denominator of +self+. - * - #finite?: Returns whether both +self.real+ and +self.image+ are finite. - * - #hash: Returns the integer hash value for +self+. - * - #imag (and its alias #imaginary): Returns the imaginary value for +self+. - * - #infinite?: Returns whether +self.real+ or +self.image+ is infinite. - * - #numerator: Returns the numerator of +self+. - * - #polar: Returns the array <tt>[self.abs, self.arg]</tt>. - * - #inspect: Returns a string representation of +self+. - * - #real: Returns the real value for +self+. - * - #real?: Returns +false+; for compatibility with Numeric#real?. - * - #rect (and its alias #rectangular): - * Returns the array <tt>[self.real, self.imag]</tt>. - * - * === Comparing - * - * - #<=>: Returns whether +self+ is less than, equal to, or greater than the given argument. - * - #==: Returns whether +self+ is equal to the given argument. - * - * === Converting - * - * - #rationalize: Returns a Rational object whose value is exactly - * or approximately equivalent to that of <tt>self.real</tt>. - * - #to_c: Returns +self+. - * - #to_d: Returns the value as a BigDecimal object. - * - #to_f: Returns the value of <tt>self.real</tt> as a Float, if possible. - * - #to_i: Returns the value of <tt>self.real</tt> as an Integer, if possible. - * - #to_r: Returns the value of <tt>self.real</tt> as a Rational, if possible. - * - #to_s: Returns a string representation of +self+. - * - * === Performing Complex Arithmetic - * - * - #*: Returns the product of +self+ and the given numeric. - * - #**: Returns +self+ raised to power of the given numeric. - * - #+: Returns the sum of +self+ and the given numeric. - * - #-: Returns the difference of +self+ and the given numeric. - * - #-@: Returns the negation of +self+. - * - #/: Returns the quotient of +self+ and the given numeric. - * - #abs2: Returns square of the absolute value (magnitude) for +self+. - * - #conj (and its alias #conjugate): Returns the conjugate of +self+. - * - #fdiv: Returns <tt>Complex.rect(self.real/numeric, self.imag/numeric)</tt>. - * - * === Working with JSON - * - * - ::json_create: Returns a new \Complex object, - * deserialized from the given serialized hash. - * - #as_json: Returns a serialized hash constructed from +self+. - * - #to_json: Returns a JSON string representing +self+. - * - * These methods are provided by the {JSON gem}[https://github.com/ruby/json]. To make these methods available: - * - * require 'json/add/complex' + * 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; - id_abs = rb_intern_const("abs"); - id_arg = rb_intern_const("arg"); - id_denominator = rb_intern_const("denominator"); - id_numerator = rb_intern_const("numerator"); - id_real_p = rb_intern_const("real?"); - id_i_real = rb_intern_const("@real"); - id_i_imag = rb_intern_const("@image"); /* @image, not @imag */ - id_finite_p = rb_intern_const("finite?"); - id_infinite_p = rb_intern_const("infinite?"); - id_rationalize = rb_intern_const("rationalize"); - id_PI = rb_intern_const("PI"); +#undef rb_intern +#define rb_intern(str) rb_intern_const(str) + + assert(fprintf(stderr, "assert() is now active\n")); + + id_abs = rb_intern("abs"); + id_arg = rb_intern("arg"); + id_denominator = rb_intern("denominator"); + id_expt = rb_intern("**"); + id_fdiv = rb_intern("fdiv"); + id_negate = rb_intern("-@"); + id_numerator = rb_intern("numerator"); + id_quo = rb_intern("quo"); + id_real_p = rb_intern("real?"); + id_to_f = rb_intern("to_f"); + id_to_i = rb_intern("to_i"); + id_to_r = rb_intern("to_r"); + id_i_real = rb_intern("@real"); + id_i_imag = rb_intern("@image"); /* @image, not @imag */ + id_finite_p = rb_intern("finite?"); + id_infinite_p = rb_intern("infinite?"); + id_rationalize = rb_intern("rationalize"); + id_PI = rb_intern("PI"); rb_cComplex = rb_define_class("Complex", rb_cNumeric); rb_define_alloc_func(rb_cComplex, nucomp_s_alloc); rb_undef_method(CLASS_OF(rb_cComplex), "allocate"); +#if 0 + rb_define_private_method(CLASS_OF(rb_cComplex), "new!", nucomp_s_new_bang, -1); + rb_define_private_method(CLASS_OF(rb_cComplex), "new", nucomp_s_new, -1); +#else rb_undef_method(CLASS_OF(rb_cComplex), "new"); +#endif rb_define_singleton_method(rb_cComplex, "rectangular", nucomp_s_new, -1); rb_define_singleton_method(rb_cComplex, "rect", nucomp_s_new, -1); @@ -2622,8 +2231,9 @@ Init_Complex(void) rb_define_global_function("Complex", nucomp_f_complex, -1); - rb_undef_methods_from(rb_cComplex, RCLASS_ORIGIN(rb_mComparable)); + rb_undef_methods_from(rb_cComplex, rb_mComparable); rb_undef_method(rb_cComplex, "%"); + rb_undef_method(rb_cComplex, "<=>"); rb_undef_method(rb_cComplex, "div"); rb_undef_method(rb_cComplex, "divmod"); rb_undef_method(rb_cComplex, "floor"); @@ -2635,36 +2245,43 @@ Init_Complex(void) rb_undef_method(rb_cComplex, "truncate"); rb_undef_method(rb_cComplex, "i"); - rb_define_method(rb_cComplex, "real", rb_complex_real, 0); - rb_define_method(rb_cComplex, "imaginary", rb_complex_imag, 0); - rb_define_method(rb_cComplex, "imag", rb_complex_imag, 0); + rb_define_method(rb_cComplex, "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, "-@", rb_complex_uminus, 0); + rb_define_method(rb_cComplex, "-@", nucomp_negate, 0); rb_define_method(rb_cComplex, "+", rb_complex_plus, 1); - rb_define_method(rb_cComplex, "-", rb_complex_minus, 1); - rb_define_method(rb_cComplex, "*", rb_complex_mul, 1); - rb_define_method(rb_cComplex, "/", rb_complex_div, 1); + rb_define_method(rb_cComplex, "-", 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, "**", rb_complex_pow, 1); + rb_define_method(rb_cComplex, "**", nucomp_expt, 1); rb_define_method(rb_cComplex, "==", nucomp_eqeq_p, 1); - rb_define_method(rb_cComplex, "<=>", nucomp_cmp, 1); rb_define_method(rb_cComplex, "coerce", nucomp_coerce, 1); - rb_define_method(rb_cComplex, "abs", rb_complex_abs, 0); - rb_define_method(rb_cComplex, "magnitude", rb_complex_abs, 0); + rb_define_method(rb_cComplex, "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", rb_complex_arg, 0); - rb_define_method(rb_cComplex, "angle", rb_complex_arg, 0); - rb_define_method(rb_cComplex, "phase", rb_complex_arg, 0); + rb_define_method(rb_cComplex, "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", rb_complex_conjugate, 0); - rb_define_method(rb_cComplex, "conj", rb_complex_conjugate, 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_real_p_m, 0); + 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); @@ -2682,11 +2299,12 @@ Init_Complex(void) rb_define_method(rb_cComplex, "infinite?", rb_complex_infinite_p, 0); rb_define_private_method(rb_cComplex, "marshal_dump", nucomp_marshal_dump, 0); - /* :nodoc: */ - compat = rb_define_class_under(rb_cComplex, "compatible", rb_cObject); + 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); @@ -2699,6 +2317,11 @@ Init_Complex(void) 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); @@ -2706,24 +2329,24 @@ Init_Complex(void) 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); /* - * Equivalent - * to <tt>Complex.rect(0, 1)</tt>: - * - * Complex::I # => (0+1i) - * + * The imaginary unit. */ rb_define_const(rb_cComplex, "I", - f_complex_new_bang2(rb_cComplex, ZERO, ONE)); - -#if !USE_FLONUM - rb_vm_register_global_object(RFLOAT_0 = DBL2NUM(0.0)); -#endif + f_complex_new_bang2(rb_cComplex, ZERO, ONE)); rb_provide("complex.so"); /* for backward compatibility */ } + +/* +Local variables: +c-file-style: "ruby" +End: +*/ |