summaryrefslogtreecommitdiff
path: root/complex.c
diff options
context:
space:
mode:
Diffstat (limited to 'complex.c')
-rw-r--r--complex.c1699
1 files changed, 998 insertions, 701 deletions
diff --git a/complex.c b/complex.c
index ea3c137461..4e2bff5df4 100644
--- a/complex.c
+++ b/complex.c
@@ -24,6 +24,7 @@
#include "internal/numeric.h"
#include "internal/object.h"
#include "internal/rational.h"
+#include "internal/string.h"
#include "ruby_assert.h"
#define ZERO INT2FIX(0)
@@ -97,7 +98,7 @@ 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);
}
@@ -152,7 +153,7 @@ f_sub(VALUE x, VALUE y)
{
if (FIXNUM_ZERO_P(y) &&
LIKELY(rb_method_basic_definition_p(CLASS_OF(x), idMINUS))) {
- return x;
+ return x;
}
return rb_funcall(x, '-', 1, y);
}
@@ -262,7 +263,7 @@ 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);
}
@@ -270,7 +271,7 @@ 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);
}
@@ -280,9 +281,9 @@ 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);
}
@@ -316,7 +317,7 @@ f_negative_p(VALUE x)
#define f_positive_p(x) (!f_negative_p(x))
-inline static int
+inline static bool
f_zero_p(VALUE x)
{
if (RB_FLOAT_TYPE_P(x)) {
@@ -329,7 +330,7 @@ f_zero_p(VALUE x)
const VALUE num = RRATIONAL(x)->num;
return FIXNUM_ZERO_P(num);
}
- return (int)rb_equal(x, ZERO);
+ return rb_equal(x, ZERO) != 0;
}
#define f_nonzero_p(x) (!f_zero_p(x))
@@ -342,7 +343,6 @@ always_finite_type_p(VALUE x)
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)
{
@@ -350,12 +350,11 @@ f_finite_p(VALUE x)
return TRUE;
}
else if (RB_FLOAT_TYPE_P(x)) {
- return isfinite(RFLOAT_VALUE(x));
+ return isfinite(RFLOAT_VALUE(x));
}
return RTEST(rb_funcallv(x, id_finite_p, 0, 0));
}
-VALUE rb_flo_is_infinite_p(VALUE num);
inline static int
f_infinite_p(VALUE x)
{
@@ -363,7 +362,7 @@ f_infinite_p(VALUE x)
return FALSE;
}
else if (RB_FLOAT_TYPE_P(x)) {
- return isinf(RFLOAT_VALUE(x));
+ return isinf(RFLOAT_VALUE(x));
}
return RTEST(rb_funcallv(x, id_infinite_p, 0, 0));
}
@@ -393,7 +392,8 @@ 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));
+ NEWOBJ_OF(obj, struct RComplex, klass,
+ T_COMPLEX | (RGENGC_WB_PROTECTED_COMPLEX ? FL_WB_PROTECTED : 0), sizeof(struct RComplex), 0);
RCOMPLEX_SET_REAL(obj, real);
RCOMPLEX_SET_IMAG(obj, imag);
@@ -411,27 +411,34 @@ nucomp_s_alloc(VALUE klass)
inline static VALUE
f_complex_new_bang1(VALUE klass, VALUE x)
{
- assert(!RB_TYPE_P(x, T_COMPLEX));
+ RUBY_ASSERT(!RB_TYPE_P(x, T_COMPLEX));
return nucomp_s_new_internal(klass, x, ZERO);
}
inline static VALUE
f_complex_new_bang2(VALUE klass, VALUE x, VALUE y)
{
- assert(!RB_TYPE_P(x, T_COMPLEX));
- assert(!RB_TYPE_P(y, T_COMPLEX));
+ RUBY_ASSERT(!RB_TYPE_P(x, T_COMPLEX));
+ RUBY_ASSERT(!RB_TYPE_P(y, T_COMPLEX));
return nucomp_s_new_internal(klass, x, y);
}
-inline static void
+WARN_UNUSED_RESULT(inline static VALUE nucomp_real_check(VALUE num));
+inline static VALUE
nucomp_real_check(VALUE num)
{
if (!RB_INTEGER_TYPE_P(num) &&
- !RB_FLOAT_TYPE_P(num) &&
- !RB_TYPE_P(num, T_RATIONAL)) {
- if (!k_numeric_p(num) || !f_real_p(num))
- rb_raise(rb_eTypeError, "not a real");
+ !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");
}
+ return num;
}
inline static VALUE
@@ -441,39 +448,46 @@ nucomp_s_canonicalize_internal(VALUE klass, VALUE real, VALUE imag)
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);
+ return nucomp_s_new_internal(klass, real, imag);
}
else if (!complex_r) {
- get_dat1(imag);
+ 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);
+ 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]) -> complex
- * Complex.rectangular(real[, imag]) -> complex
+ * 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]:
*
- * Returns a complex object which denotes the given rectangular form.
+ * Complex.rect(3) # => (3+0i)
+ * Complex.rect(3, Math::PI) # => (3+3.141592653589793i)
+ * Complex.rect(-3, -Math::PI) # => (-3-3.141592653589793i)
*
- * Complex.rectangular(1, 2) #=> (1+2i)
+ * \Complex.rectangular is an alias for \Complex.rect.
*/
static VALUE
nucomp_s_new(int argc, VALUE *argv, VALUE klass)
@@ -482,22 +496,26 @@ nucomp_s_new(int argc, VALUE *argv, VALUE klass)
switch (rb_scan_args(argc, argv, "11", &real, &imag)) {
case 1:
- nucomp_real_check(real);
- imag = ZERO;
- break;
+ real = nucomp_real_check(real);
+ imag = ZERO;
+ break;
default:
- nucomp_real_check(real);
- nucomp_real_check(imag);
- break;
+ real = nucomp_real_check(real);
+ imag = nucomp_real_check(imag);
+ break;
}
- return nucomp_s_canonicalize_internal(klass, real, imag);
+ return nucomp_s_new_internal(klass, real, imag);
}
inline static VALUE
f_complex_new2(VALUE klass, VALUE x, VALUE y)
{
- assert(!RB_TYPE_P(x, T_COMPLEX));
+ if (RB_TYPE_P(x, T_COMPLEX)) {
+ get_dat1(x);
+ x = dat->real;
+ y = f_add(dat->imag, y);
+ }
return nucomp_s_canonicalize_internal(klass, x, y);
}
@@ -506,39 +524,54 @@ static VALUE nucomp_s_convert(int argc, VALUE *argv, VALUE klass);
/*
* call-seq:
- * Complex(x[, y], exception: true) -> numeric or nil
- *
- * Returns x+i*y;
- *
- * Complex(1, 2) #=> (1+2i)
- * Complex('1+2i') #=> (1+2i)
- * Complex(nil) #=> TypeError
- * Complex(1, nil) #=> TypeError
- *
- * Complex(1, nil, exception: false) #=> nil
- * Complex('1+2', exception: false) #=> nil
- *
- * 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.
+ * 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)
+ *
*/
static VALUE
nucomp_f_complex(int argc, VALUE *argv, VALUE klass)
@@ -552,7 +585,7 @@ nucomp_f_complex(int argc, VALUE *argv, VALUE klass)
if (!NIL_P(opts)) {
raise = rb_opts_exception_p(opts, raise);
}
- if (argc > 0 && CLASS_OF(a1) == rb_cComplex && a2 == Qundef) {
+ if (argc > 0 && CLASS_OF(a1) == rb_cComplex && UNDEF_P(a2)) {
return a1;
}
return nucomp_convert(rb_cComplex, a1, a2, raise);
@@ -582,14 +615,14 @@ static VALUE
m_cos(VALUE x)
{
if (!RB_TYPE_P(x, T_COMPLEX))
- return m_cos_bang(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)));
}
}
@@ -597,55 +630,61 @@ static VALUE
m_sin(VALUE x)
{
if (!RB_TYPE_P(x, T_COMPLEX))
- return m_sin_bang(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(VALUE klass, VALUE x, VALUE y)
+f_complex_polar_real(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)) {
- return nucomp_s_new_internal(klass, x, RFLOAT_0);
+ 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 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_new_internal(klass, x, y);
}
return nucomp_s_canonicalize_internal(klass,
- f_mul(x, m_cos(y)),
- f_mul(x, m_sin(y)));
+ f_mul(x, m_cos(y)),
+ f_mul(x, m_sin(y)));
+}
+
+static VALUE
+f_complex_polar(VALUE klass, VALUE x, VALUE y)
+{
+ x = nucomp_real_check(x);
+ y = nucomp_real_check(y);
+ return f_complex_polar_real(klass, x, y);
}
#ifdef HAVE___COSPI
@@ -667,12 +706,12 @@ rb_dbl_complex_new_polar_pi(double abs, double ang)
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));
+ 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);
+ if (modf(fi / 2.0, &fi) != 0.0) abs = -abs;
+ return DBL2NUM(abs);
}
else {
const double real = abs * cospi(ang), imag = abs * sinpi(ang);
@@ -682,48 +721,51 @@ rb_dbl_complex_new_polar_pi(double abs, double ang)
/*
* call-seq:
- * Complex.polar(abs[, arg]) -> complex
+ * Complex.polar(abs, arg = 0) -> complex
*
- * Returns a complex object which denotes the given polar form.
+ * 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(3) # => (3+0i)
+ * Complex.polar(3, 2.0) # => (-1.2484405096414273+2.727892280477045i)
+ * Complex.polar(-3, -2.0) # => (1.2484405096414273+2.727892280477045i)
*
- * 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);
- return nucomp_s_new_internal(klass, abs, ZERO);
- default:
- nucomp_real_check(abs);
- nucomp_real_check(arg);
- break;
- }
- if (RB_TYPE_P(abs, T_COMPLEX)) {
- get_dat1(abs);
- abs = dat->real;
+ argc = rb_scan_args(argc, argv, "11", &abs, &arg);
+ abs = nucomp_real_check(abs);
+ if (argc == 2) {
+ arg = nucomp_real_check(arg);
}
- if (RB_TYPE_P(arg, T_COMPLEX)) {
- get_dat1(arg);
- arg = dat->real;
+ else {
+ arg = ZERO;
}
- return f_complex_polar(klass, abs, arg);
+ return f_complex_polar_real(klass, abs, arg);
}
/*
* call-seq:
- * cmp.real -> real
+ * 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:
*
- * Returns the real part.
+ * Complex.polar(1, Math::PI/4).real # => 0.7071067811865476 # Square root of 2.
*
- * Complex(7).real #=> 7
- * Complex(9, -4).real #=> 9
*/
VALUE
rb_complex_real(VALUE self)
@@ -734,13 +776,19 @@ rb_complex_real(VALUE self)
/*
* call-seq:
- * cmp.imag -> real
- * cmp.imaginary -> real
+ * imag -> numeric
+ *
+ * Returns the imaginary value for +self+:
+ *
+ * Complex.rect(7).imag # => 0
+ * Complex.rect(9, -4).imag # => -4
+ *
+ * If +self+ was created with
+ * {polar coordinates}[rdoc-ref:Complex@Polar+Coordinates], the returned value
+ * is computed, and may be inexact:
*
- * Returns the imaginary part.
+ * Complex.polar(1, Math::PI/4).imag # => 0.7071067811865476 # Square root of 2.
*
- * Complex(7).imaginary #=> 0
- * Complex(9, -4).imaginary #=> -4
*/
VALUE
rb_complex_imag(VALUE self)
@@ -751,97 +799,101 @@ rb_complex_imag(VALUE self)
/*
* call-seq:
- * -cmp -> complex
+ * -complex -> new_complex
*
- * Returns negation of the value.
+ * 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)
*
- * -Complex(1, 2) #=> (-1-2i)
*/
VALUE
rb_complex_uminus(VALUE self)
{
get_dat1(self);
return f_complex_new2(CLASS_OF(self),
- f_negate(dat->real), f_negate(dat->imag));
+ f_negate(dat->real), f_negate(dat->imag));
}
/*
* call-seq:
- * cmp + numeric -> complex
+ * complex + numeric -> new_complex
+ *
+ * Returns the sum of +self+ and +numeric+:
*
- * Performs addition.
+ * 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)
*
- * 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:
- * cmp - numeric -> complex
+ * complex - numeric -> new_complex
*
- * Performs subtraction.
+ * Returns the difference of +self+ and +numeric+:
+ *
+ * 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)
*
- * 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)
{
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, int az, int bz)
+safe_mul(VALUE a, VALUE b, bool az, bool 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);
}
@@ -849,10 +901,10 @@ safe_mul(VALUE a, VALUE b, int az, int bz)
static void
comp_mul(VALUE areal, VALUE aimag, VALUE breal, VALUE bimag, VALUE *real, VALUE *imag)
{
- int arzero = f_zero_p(areal);
- int aizero = f_zero_p(aimag);
- int brzero = f_zero_p(breal);
- int bizero = f_zero_p(bimag);
+ 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),
@@ -861,61 +913,62 @@ comp_mul(VALUE areal, VALUE aimag, VALUE breal, VALUE bimag, VALUE *real, VALUE
/*
* call-seq:
- * cmp * numeric -> complex
+ * complex * numeric -> new_complex
+ *
+ * Returns the product of +self+ and +numeric+:
*
- * Performs multiplication.
+ * 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)
*
- * 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;
+ get_dat2(self, other);
comp_mul(adat->real, adat->imag, bdat->real, bdat->imag, &real, &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_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, '*');
}
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);
+ 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));
+ 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)));
+ 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)));
+ }
+ 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);
@@ -924,7 +977,7 @@ f_divide(VALUE self, VALUE other,
}
if (k_numeric_p(other) && f_real_p(other)) {
VALUE x, y;
- get_dat1(self);
+ 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);
@@ -936,16 +989,16 @@ f_divide(VALUE self, VALUE other,
/*
* call-seq:
- * cmp / numeric -> complex
- * cmp.quo(numeric) -> complex
+ * complex / numeric -> new_complex
*
- * Performs division.
+ * Returns the quotient of +self+ and +numeric+:
+ *
+ * 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)
*
- * 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)
@@ -957,11 +1010,12 @@ rb_complex_div(VALUE self, VALUE other)
/*
* call-seq:
- * cmp.fdiv(numeric) -> complex
+ * fdiv(numeric) -> new_complex
+ *
+ * Returns <tt>Complex.rect(self.real/numeric, self.imag/numeric)</tt>:
*
- * Performs division as each part is a float, never returns a float.
+ * Complex.rect(11, 22).fdiv(3) # => (3.6666666666666665+7.333333333333333i)
*
- * Complex(11, 22).fdiv(3) #=> (3.6666666666666665+7.333333333333333i)
*/
static VALUE
nucomp_fdiv(VALUE self, VALUE other)
@@ -975,44 +1029,133 @@ 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:
- * cmp ** numeric -> complex
+ * complex ** numeric -> new_complex
+ *
+ * Returns +self+ raised to power +numeric+:
*
- * Performs exponentiation.
+ * Complex.rect(0, 1) ** 2 # => (-1+0i)
+ * Complex.rect(-8) ** Rational(1, 3) # => (1.0000000000000002+1.7320508075688772i)
*
- * Complex('i') ** 2 #=> (-1+0i)
- * Complex(-8) ** Rational(1, 3) #=> (1.0000000000000002+1.7320508075688772i)
*/
VALUE
rb_complex_pow(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);
+ get_dat1(other);
+
+ if (k_exact_zero_p(dat->imag))
+ other = dat->real; /* c14n */
+ }
- if (k_exact_zero_p(dat->imag))
- other = dat->real; /* c14n */
+ if (other == ONE) {
+ get_dat1(self);
+ return nucomp_s_new_internal(CLASS_OF(self), dat->real, dat->imag);
}
+ 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);
@@ -1053,48 +1196,46 @@ rb_complex_pow(VALUE self, VALUE other)
}
}
return nucomp_s_new_internal(CLASS_OF(self), zr, zi);
- }
+ }
}
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_BIGNUM_TYPE_P(other))
+ 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:
- * cmp == object -> true or false
+ * complex == object -> true or false
+ *
+ * Returns +true+ if <tt>self.real == object.real</tt>
+ * and <tt>self.imag == object.imag</tt>:
*
- * Returns true if cmp equals object numerically.
+ * Complex.rect(2, 3) == Complex.rect(2.0, 3.0) # => true
*
- * 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 RBOOL(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 RBOOL(f_eqeq_p(dat->real, other) && f_zero_p(dat->imag));
}
return RBOOL(f_eqeq_p(other, self));
}
@@ -1103,35 +1244,55 @@ static bool
nucomp_real_p(VALUE self)
{
get_dat1(self);
- return(f_zero_p(dat->imag) ? true : false);
+ return f_zero_p(dat->imag);
}
/*
* call-seq:
- * cmp <=> object -> 0, 1, -1, or nil
+ * 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.
*
- * If +cmp+'s imaginary part is zero, and +object+ is also a
- * real number (or a Complex number where the imaginary part is zero),
- * compare the real part of +cmp+ to object. Otherwise, return nil.
+ * 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.
*
- * Complex(2, 3) <=> Complex(2, 3) #=> nil
- * Complex(2, 3) <=> 1 #=> nil
- * Complex(2) <=> 1 #=> 1
- * Complex(2) <=> 2 #=> 0
- * Complex(2) <=> 3 #=> -1
*/
static VALUE
nucomp_cmp(VALUE self, VALUE other)
{
- if (nucomp_real_p(self) && k_numeric_p(other)) {
- if (RB_TYPE_P(other, T_COMPLEX) && nucomp_real_p(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 if (f_real_p(other)) {
- get_dat1(self);
+ }
+ 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;
}
@@ -1141,24 +1302,30 @@ static VALUE
nucomp_coerce(VALUE self, VALUE other)
{
if (RB_TYPE_P(other, T_COMPLEX))
- return rb_assoc_new(other, self);
+ 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);
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:
- * cmp.abs -> real
- * cmp.magnitude -> real
+ * abs -> float
+ *
+ * Returns the absolute value (magnitude) for +self+;
+ * see {polar coordinates}[rdoc-ref:Complex@Polar+Coordinates]:
+ *
+ * Complex.polar(-1, 0).abs # => 1.0
*
- * Returns the absolute part of its polar form.
+ * 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.
*
- * Complex(-1).abs #=> 1
- * Complex(3.0, -4.0).abs #=> 5.0
*/
VALUE
rb_complex_abs(VALUE self)
@@ -1166,46 +1333,59 @@ rb_complex_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:
- * cmp.abs2 -> real
+ * abs2 -> float
+ *
+ * Returns square of the absolute value (magnitude) for +self+;
+ * see {polar coordinates}[rdoc-ref:Complex@Polar+Coordinates]:
+ *
+ * Complex.polar(2, 2).abs2 # => 4.0
*
- * Returns square of the absolute value.
+ * 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
*
- * 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:
- * cmp.arg -> float
- * cmp.angle -> float
- * cmp.phase -> float
+ * arg -> float
+ *
+ * Returns the argument (angle) for +self+ in radians;
+ * see {polar coordinates}[rdoc-ref:Complex@Polar+Coordinates]:
+ *
+ * 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:
*
- * Returns the angle part of its polar form.
+ * Complex.polar(1, 1.0/3).arg # => 0.33333333333333326
*
- * Complex.polar(3, Math::PI/2).arg #=> 1.5707963267948966
*/
VALUE
rb_complex_arg(VALUE self)
@@ -1216,12 +1396,22 @@ rb_complex_arg(VALUE self)
/*
* call-seq:
- * cmp.rect -> array
- * cmp.rectangular -> array
+ * 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].
*
- * Returns an array; [cmp.real, cmp.imag].
+ * If +self+ was created with
+ * {polar coordinates}[rdoc-ref:Complex@Polar+Coordinates], the returned value
+ * is computed, and may be inexact:
*
- * Complex(1, 2).rectangular #=> [1, 2]
+ * Complex.polar(1.0, 1.0).rect # => [0.5403023058681398, 0.8414709848078965]
+ *
+ *
+ * Complex#rectangular is an alias for Complex#rect.
*/
static VALUE
nucomp_rect(VALUE self)
@@ -1232,11 +1422,20 @@ nucomp_rect(VALUE self)
/*
* call-seq:
- * cmp.polar -> array
+ * polar -> array
+ *
+ * Returns the array <tt>[self.abs, self.arg]</tt>:
+ *
+ * Complex.polar(1, 2).polar # => [1.0, 2.0]
*
- * Returns an array; [cmp.abs, cmp.arg].
+ * 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]
*
- * Complex(1, 2).polar #=> [2.23606797749979, 1.1071487177940904]
*/
static VALUE
nucomp_polar(VALUE self)
@@ -1246,12 +1445,12 @@ nucomp_polar(VALUE self)
/*
* call-seq:
- * cmp.conj -> complex
- * cmp.conjugate -> complex
+ * conj -> complex
*
- * Returns the complex conjugate.
+ * Returns the conjugate of +self+, <tt>Complex.rect(self.imag, self.real)</tt>:
+ *
+ * Complex.rect(1, 2).conj # => (1-2i)
*
- * Complex(1, 2).conjugate #=> (1-2i)
*/
VALUE
rb_complex_conjugate(VALUE self)
@@ -1262,10 +1461,9 @@ rb_complex_conjugate(VALUE self)
/*
* call-seq:
- * Complex(1).real? -> false
- * Complex(1, 2).real? -> false
+ * real? -> false
*
- * Returns false, even if the complex number has no imaginary part.
+ * Returns +false+; for compatibility with Numeric#real?.
*/
static VALUE
nucomp_real_p_m(VALUE self)
@@ -1275,11 +1473,17 @@ nucomp_real_p_m(VALUE self)
/*
* call-seq:
- * cmp.denominator -> integer
+ * 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>:
*
- * Returns the denominator (lcm of both denominator - real and imag).
+ * Complex.rect(Rational(1, 2), Rational(2, 3)).denominator # => 6
*
- * See numerator.
+ * Note that <tt>n.denominator</tt> of a non-rational numeric is +1+.
+ *
+ * Related: Complex#numerator.
*/
static VALUE
nucomp_denominator(VALUE self)
@@ -1290,21 +1494,23 @@ nucomp_denominator(VALUE self)
/*
* call-seq:
- * cmp.numerator -> numeric
+ * 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:
*
- * Returns the numerator.
+ * c = Complex.rect(Rational(2, 3), Rational(3, 4)) # => ((2/3)+(3/4)*i)
+ * c.numerator # => (8+9i)
*
- * 1 2 3+4i <- numerator
- * - + -i -> ----
- * 2 3 6 <- denominator
+ * 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>.
*
- * 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.
+ * Related: Complex#denominator.
*/
static VALUE
nucomp_numerator(VALUE self)
@@ -1315,10 +1521,10 @@ nucomp_numerator(VALUE self)
cd = nucomp_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: */
@@ -1337,6 +1543,18 @@ rb_complex_hash(VALUE self)
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)
{
@@ -1348,11 +1566,11 @@ 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 RBOOL((CLASS_OF(adat->real) == CLASS_OF(bdat->real)) &&
+ (CLASS_OF(adat->imag) == CLASS_OF(bdat->imag)) &&
+ f_eqeq_p(self, other));
}
return Qfalse;
@@ -1362,8 +1580,8 @@ 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);
}
@@ -1389,7 +1607,7 @@ f_format(VALUE self, VALUE (*func)(VALUE))
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;
@@ -1397,15 +1615,16 @@ f_format(VALUE self, VALUE (*func)(VALUE))
/*
* call-seq:
- * cmp.to_s -> string
+ * to_s -> string
+ *
+ * Returns a string representation of +self+:
*
- * Returns the value as a string.
+ * 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"
*
- * 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)
@@ -1415,15 +1634,16 @@ nucomp_to_s(VALUE self)
/*
* call-seq:
- * cmp.inspect -> string
+ * inspect -> string
*
- * Returns the value as a string for inspection.
+ * Returns a string representation of +self+:
+ *
+ * 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)"
*
- * 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)
@@ -1441,10 +1661,15 @@ nucomp_inspect(VALUE self)
/*
* call-seq:
- * cmp.finite? -> true or false
+ * finite? -> true or false
+ *
+ * Returns +true+ if both <tt>self.real.finite?</tt> and <tt>self.imag.finite?</tt>
+ * are true, +false+ otherwise:
*
- * Returns +true+ if +cmp+'s real and imaginary parts are both finite numbers,
- * otherwise returns +false+.
+ * Complex.rect(1, 1).finite? # => true
+ * Complex.rect(Float::INFINITY, 0).finite? # => false
+ *
+ * Related: Numeric#finite?, Float#finite?.
*/
static VALUE
rb_complex_finite_p(VALUE self)
@@ -1456,15 +1681,15 @@ rb_complex_finite_p(VALUE self)
/*
* call-seq:
- * cmp.infinite? -> nil or 1
+ * infinite? -> 1 or nil
*
- * Returns +1+ if +cmp+'s real or imaginary part is an infinite number,
- * otherwise returns +nil+.
+ * Returns +1+ if either <tt>self.real.infinite?</tt> or <tt>self.imag.infinite?</tt>
+ * is true, +nil+ otherwise:
*
- * For example:
+ * Complex.rect(Float::INFINITY, 0).infinite? # => 1
+ * Complex.rect(1, 1).infinite? # => nil
*
- * (1+1i).infinite? #=> nil
- * (Float::INFINITY + 1i).infinite? #=> 1
+ * Related: Numeric#infinite?, Float#infinite?.
*/
static VALUE
rb_complex_infinite_p(VALUE self)
@@ -1472,7 +1697,7 @@ rb_complex_infinite_p(VALUE self)
get_dat1(self);
if (!f_infinite_p(dat->real) && !f_infinite_p(dat->imag)) {
- return Qnil;
+ return Qnil;
}
return ONE;
}
@@ -1515,7 +1740,7 @@ 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;
@@ -1562,14 +1787,15 @@ rb_dbl_complex_new(double real, double imag)
/*
* call-seq:
- * cmp.to_i -> integer
+ * to_i -> integer
+ *
+ * Returns the value of <tt>self.real</tt> as an Integer, if possible:
*
- * Returns the value as an integer if possible (the imaginary part
- * should be exactly zero).
+ * Complex.rect(1, 0).to_i # => 1
+ * Complex.rect(1, Rational(0, 1)).to_i # => 1
*
- * Complex(1, 0).to_i #=> 1
- * Complex(1, 0.0).to_i # RangeError
- * Complex(1, 2).to_i # RangeError
+ * Raises RangeError if <tt>self.imag</tt> is not exactly zero
+ * (either <tt>Integer(0)</tt> or <tt>Rational(0, _n_)</tt>).
*/
static VALUE
nucomp_to_i(VALUE self)
@@ -1577,22 +1803,23 @@ 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:
- * cmp.to_f -> float
+ * to_f -> float
*
- * Returns the value as a float if possible (the imaginary part should
- * be exactly zero).
+ * Returns the value of <tt>self.real</tt> as a Float, if possible:
*
- * Complex(1, 0).to_f #=> 1.0
- * Complex(1, 0.0).to_f # RangeError
- * Complex(1, 2).to_f # RangeError
+ * 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>).
*/
static VALUE
nucomp_to_f(VALUE self)
@@ -1600,49 +1827,77 @@ 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:
- * cmp.to_r -> rational
+ * to_r -> rational
+ *
+ * Returns the value of <tt>self.real</tt> as a Rational, if possible:
*
- * Returns the value as a rational if possible (the imaginary part
- * should be exactly zero).
+ * 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)
*
- * Complex(1, 0).to_r #=> (1/1)
- * Complex(1, 0.0).to_r # RangeError
- * Complex(1, 2).to_r # RangeError
+ * 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.
*
- * See rationalize.
+ * Related: Complex#rationalize.
*/
static VALUE
nucomp_to_r(VALUE self)
{
get_dat1(self);
- if (!k_exact_zero_p(dat->imag)) {
- rb_raise(rb_eRangeError, "can't convert %"PRIsVALUE" into Rational",
- self);
+ 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);
+ }
}
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.
+ * 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.
*/
static VALUE
nucomp_rationalize(int argc, VALUE *argv, VALUE self)
@@ -1660,12 +1915,9 @@ nucomp_rationalize(int argc, VALUE *argv, VALUE self)
/*
* call-seq:
- * complex.to_c -> self
- *
- * Returns self.
+ * to_c -> self
*
- * Complex(2).to_c #=> (2+0i)
- * Complex(-8, 6).to_c #=> (-8+6i)
+ * Returns +self+.
*/
static VALUE
nucomp_to_c(VALUE self)
@@ -1675,9 +1927,12 @@ nucomp_to_c(VALUE self)
/*
* call-seq:
- * nil.to_c -> (0+0i)
+ * to_c -> (0+0i)
+ *
+ * Returns zero as a Complex:
+ *
+ * nil.to_c # => (0+0i)
*
- * Returns zero as a complex.
*/
static VALUE
nilclass_to_c(VALUE self)
@@ -1687,9 +1942,9 @@ nilclass_to_c(VALUE self)
/*
* call-seq:
- * num.to_c -> complex
+ * to_c -> complex
*
- * Returns the value as a complex.
+ * Returns +self+ as a Complex object.
*/
static VALUE
numeric_to_c(VALUE self)
@@ -1705,14 +1960,14 @@ 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;
}
@@ -1725,32 +1980,32 @@ 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 (strict) {
- if (us)
- return 0;
- }
- us = 1;
- }
- else {
- **b = **s;
- (*b)++;
- us = 0;
- }
- (*s)++;
+ if (**s == '_') {
+ if (us) {
+ if (strict) return 0;
+ break;
+ }
+ us = 1;
+ }
+ else {
+ **b = **s;
+ (*b)++;
+ us = 0;
+ }
+ (*s)++;
}
if (us)
- do {
- (*s)--;
- } while (**s == '_');
+ do {
+ (*s)--;
+ } while (**s == '_');
return 1;
}
@@ -1762,70 +2017,70 @@ 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;
}
@@ -1833,22 +2088,22 @@ 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;
@@ -1859,72 +2114,72 @@ 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_new_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" */
}
}
@@ -1932,7 +2187,7 @@ inline static void
skip_ws(const char **s)
{
while (isspace((unsigned char)**s))
- (*s)++;
+ (*s)++;
}
static int
@@ -1969,26 +2224,17 @@ string_to_c_strict(VALUE self, int raise)
rb_must_asciicompat(self);
- s = RSTRING_PTR(self);
-
- if (!s || memchr(s, '\0', RSTRING_LEN(self))) {
- if (!raise) return Qnil;
- rb_raise(rb_eArgError, "string contains null byte");
+ if (raise) {
+ s = StringValueCStr(self);
}
-
- if (s && s[RSTRING_LEN(self)]) {
- rb_str_modify(self);
- s = RSTRING_PTR(self);
- s[RSTRING_LEN(self)] = '\0';
+ else if (!(s = rb_str_to_cstr(self))) {
+ return Qnil;
}
- if (!s)
- s = (char *)"";
-
- if (!parse_comp(s, 1, &num)) {
+ if (!parse_comp(s, TRUE, &num)) {
if (!raise) return Qnil;
- rb_raise(rb_eArgError, "invalid value for convert(): %+"PRIsVALUE,
- self);
+ rb_raise(rb_eArgError, "invalid value for convert(): %+"PRIsVALUE,
+ self);
}
return num;
@@ -1996,47 +2242,39 @@ string_to_c_strict(VALUE self, int raise)
/*
* 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.
+ * 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.
*/
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);
+ (void)parse_comp(rb_str_fill_terminator(self, 1), FALSE, &num);
return num;
}
@@ -2052,65 +2290,68 @@ 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_raise(rb_eTypeError, "can't convert nil into Complex");
}
if (RB_TYPE_P(a1, T_STRING)) {
- a1 = string_to_c_strict(a1, raise);
+ a1 = string_to_c_strict(a1, raise);
if (NIL_P(a1)) return Qnil;
}
if (RB_TYPE_P(a2, T_STRING)) {
- a2 = string_to_c_strict(a2, raise);
+ a2 = string_to_c_strict(a2, raise);
if (NIL_P(a2)) return Qnil;
}
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 (a2 == Qundef || (k_exact_zero_p(a2)))
- return a1;
- }
-
- if (a2 == Qundef) {
- if (k_numeric_p(a1) && !f_real_p(a1))
- return a1;
- /* should raise exception for consistency */
- if (!k_numeric_p(a1)) {
- if (!raise)
- return rb_protect(to_complex, a1, NULL);
- return to_complex(a1);
+ 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);
}
}
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 (a2 == Qundef) {
+ VALUE argv2[2];
+ argv2[0] = a1;
+ if (UNDEF_P(a2)) {
argv2[1] = Qnil;
argc = 1;
}
@@ -2120,7 +2361,7 @@ nucomp_convert(VALUE klass, VALUE a1, VALUE a2, int raise)
argv2[1] = a2;
argc = 2;
}
- return nucomp_s_new(argc, argv2, klass);
+ return nucomp_s_new(argc, argv2, klass);
}
}
@@ -2138,34 +2379,9 @@ nucomp_s_convert(int argc, VALUE *argv, VALUE klass)
/*
* call-seq:
- * num.real -> self
+ * abs2 -> real
*
- * 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.
+ * Returns the square of +self+.
*/
static VALUE
numeric_abs2(VALUE self)
@@ -2175,11 +2391,9 @@ numeric_abs2(VALUE self)
/*
* call-seq:
- * num.arg -> 0 or float
- * num.angle -> 0 or float
- * num.phase -> 0 or float
+ * arg -> 0 or Math::PI
*
- * Returns 0 if the value is positive, pi otherwise.
+ * Returns zero if +self+ is positive, Math::PI otherwise.
*/
static VALUE
numeric_arg(VALUE self)
@@ -2191,10 +2405,9 @@ numeric_arg(VALUE self)
/*
* call-seq:
- * num.rect -> array
- * num.rectangular -> array
+ * rect -> array
*
- * Returns an array; [num, 0].
+ * Returns array <tt>[self, 0]</tt>.
*/
static VALUE
numeric_rect(VALUE self)
@@ -2204,9 +2417,9 @@ numeric_rect(VALUE self)
/*
* call-seq:
- * num.polar -> array
+ * polar -> array
*
- * Returns an array; [num.abs, num.arg].
+ * Returns array <tt>[self.abs, self.arg]</tt>.
*/
static VALUE
numeric_polar(VALUE self)
@@ -2234,67 +2447,152 @@ numeric_polar(VALUE 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
+ * arg -> 0 or Math::PI
*
- * Returns 0 if the value is positive, pi otherwise.
+ * Returns 0 if +self+ is positive, Math::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 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.
+ * 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].
+ *
+ * You can create a \Complex object from rectangular coordinates with:
+ *
+ * - A {complex literal}[rdoc-ref:doc/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_complex_plane].
+ *
+ * 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:
+ *
+ * - \Method Complex.polar.
+ * - \Method Kernel#Complex, 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#abs and Complex#arg.
+ * - Together, with method Complex#polar.
+ *
+ * The corresponding (computed) rectangular values may be retrieved:
+ *
+ * - Separately, with methods Complex#real and Complex#imag.
+ * - Together, with method Complex#rect.
+ *
+ * == 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+.
*
- * Complex object can be created as literal, and also by using
- * Kernel#Complex, Complex::rect, Complex::polar or to_c method.
+ * === Performing Complex Arithmetic
*
- * 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)
+ * - #*: 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>.
*
- * You can also create complex object from floating-point numbers or
- * strings.
+ * === Working with JSON
*
- * 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)
+ * - ::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+.
*
- * 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)
+ * These methods are provided by the {JSON gem}[https://github.com/flori/json]. To make these methods available:
*
- * A complex object is either an exact or an inexact number.
+ * require 'json/add/complex'
*
- * Complex(1, 1) / 2 #=> ((1/2)+(1/2)*i)
- * Complex(1, 1) / 2.0 #=> (0.5+0.5i)
*/
void
Init_Complex(void)
@@ -2402,9 +2700,6 @@ 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);
@@ -2412,21 +2707,23 @@ 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);
/*
- * The imaginary unit.
+ * Equivalent
+ * to <tt>Complex.rect(0, 1)</tt>:
+ *
+ * Complex::I # => (0+1i)
+ *
*/
rb_define_const(rb_cComplex, "I",
- f_complex_new_bang2(rb_cComplex, ZERO, ONE));
+ f_complex_new_bang2(rb_cComplex, ZERO, ONE));
#if !USE_FLONUM
- rb_gc_register_mark_object(RFLOAT_0 = DBL2NUM(0.0));
+ rb_vm_register_global_object(RFLOAT_0 = DBL2NUM(0.0));
#endif
rb_provide("complex.so"); /* for backward compatibility */