1 /*
2 complex.c: Coded by Tadayoshi Funaba 2008-2012
3
4 This implementation is based on Keiju Ishitsuka's Complex library
5 which is written in ruby.
6 */
7
8 #include "ruby/config.h"
9 #if defined _MSC_VER
10 /* Microsoft Visual C does not define M_PI and others by default */
11 # define _USE_MATH_DEFINES 1
12 #endif
13 #include <math.h>
14 #include "internal.h"
15 #include "id.h"
16
17 #define NDEBUG
18 #include "ruby_assert.h"
19
20 #define ZERO INT2FIX(0)
21 #define ONE INT2FIX(1)
22 #define TWO INT2FIX(2)
23 #if USE_FLONUM
24 #define RFLOAT_0 DBL2NUM(0)
25 #else
26 static VALUE RFLOAT_0;
27 #endif
28 #if defined(HAVE_SIGNBIT) && defined(__GNUC__) && defined(__sun) && \
29 !defined(signbit)
30 extern int signbit(double);
31 #endif
32
33 VALUE rb_cComplex;
34
35 static ID id_abs, id_arg,
36 id_denominator, id_fdiv, id_numerator, id_quo,
37 id_real_p, id_i_real, id_i_imag,
38 id_finite_p, id_infinite_p, id_rationalize,
39 id_PI;
40 #define id_to_i idTo_i
41 #define id_to_r idTo_r
42 #define id_negate idUMinus
43 #define id_expt idPow
44 #define id_to_f idTo_f
45
46 #define f_boolcast(x) ((x) ? Qtrue : Qfalse)
47
48 #define binop(n,op) \
49 inline static VALUE \
50 f_##n(VALUE x, VALUE y)\
51 {\
52 return rb_funcall(x, (op), 1, y);\
53 }
54
55 #define fun1(n) \
56 inline static VALUE \
57 f_##n(VALUE x)\
58 {\
59 return rb_funcall(x, id_##n, 0);\
60 }
61
62 #define fun2(n) \
63 inline static VALUE \
64 f_##n(VALUE x, VALUE y)\
65 {\
66 return rb_funcall(x, id_##n, 1, y);\
67 }
68
69 #define PRESERVE_SIGNEDZERO
70
71 inline static VALUE
f_add(VALUE x,VALUE y)72 f_add(VALUE x, VALUE y)
73 {
74 if (RB_INTEGER_TYPE_P(x) &&
75 LIKELY(rb_method_basic_definition_p(rb_cInteger, idPLUS))) {
76 if (FIXNUM_ZERO_P(x))
77 return y;
78 if (FIXNUM_ZERO_P(y))
79 return x;
80 return rb_int_plus(x, y);
81 }
82 else if (RB_FLOAT_TYPE_P(x) &&
83 LIKELY(rb_method_basic_definition_p(rb_cFloat, idPLUS))) {
84 if (FIXNUM_ZERO_P(y))
85 return x;
86 return rb_float_plus(x, y);
87 }
88 else if (RB_TYPE_P(x, T_RATIONAL) &&
89 LIKELY(rb_method_basic_definition_p(rb_cRational, idPLUS))) {
90 if (FIXNUM_ZERO_P(y))
91 return x;
92 return rb_rational_plus(x, y);
93 }
94
95 return rb_funcall(x, '+', 1, y);
96 }
97
98 inline static VALUE
f_div(VALUE x,VALUE y)99 f_div(VALUE x, VALUE y)
100 {
101 if (FIXNUM_P(y) && FIX2LONG(y) == 1)
102 return x;
103 return rb_funcall(x, '/', 1, y);
104 }
105
106 inline static int
f_gt_p(VALUE x,VALUE y)107 f_gt_p(VALUE x, VALUE y)
108 {
109 if (RB_INTEGER_TYPE_P(x)) {
110 if (FIXNUM_P(x) && FIXNUM_P(y))
111 return (SIGNED_VALUE)x > (SIGNED_VALUE)y;
112 return RTEST(rb_int_gt(x, y));
113 }
114 else if (RB_FLOAT_TYPE_P(x))
115 return RTEST(rb_float_gt(x, y));
116 else if (RB_TYPE_P(x, T_RATIONAL)) {
117 int const cmp = rb_cmpint(rb_rational_cmp(x, y), x, y);
118 return cmp > 0;
119 }
120 return RTEST(rb_funcall(x, '>', 1, y));
121 }
122
123 inline static VALUE
f_mul(VALUE x,VALUE y)124 f_mul(VALUE x, VALUE y)
125 {
126 if (RB_INTEGER_TYPE_P(x) &&
127 LIKELY(rb_method_basic_definition_p(rb_cInteger, idMULT))) {
128 if (FIXNUM_ZERO_P(y))
129 return ZERO;
130 if (FIXNUM_ZERO_P(x) && RB_INTEGER_TYPE_P(y))
131 return ZERO;
132 if (x == ONE) return y;
133 if (y == ONE) return x;
134 return rb_int_mul(x, y);
135 }
136 else if (RB_FLOAT_TYPE_P(x) &&
137 LIKELY(rb_method_basic_definition_p(rb_cFloat, idMULT))) {
138 if (y == ONE) return x;
139 return rb_float_mul(x, y);
140 }
141 else if (RB_TYPE_P(x, T_RATIONAL) &&
142 LIKELY(rb_method_basic_definition_p(rb_cRational, idMULT))) {
143 if (y == ONE) return x;
144 return rb_rational_mul(x, y);
145 }
146 else if (LIKELY(rb_method_basic_definition_p(CLASS_OF(x), idMULT))) {
147 if (y == ONE) return x;
148 }
149 return rb_funcall(x, '*', 1, y);
150 }
151
152 inline static VALUE
f_sub(VALUE x,VALUE y)153 f_sub(VALUE x, VALUE y)
154 {
155 if (FIXNUM_ZERO_P(y) &&
156 LIKELY(rb_method_basic_definition_p(CLASS_OF(x), idMINUS))) {
157 return x;
158 }
159 return rb_funcall(x, '-', 1, y);
160 }
161
162 fun1(abs)
fun1(arg)163 fun1(arg)
164 fun1(denominator)
165
166 inline static VALUE
167 f_negate(VALUE x)
168 {
169 if (RB_INTEGER_TYPE_P(x)) {
170 return rb_int_uminus(x);
171 }
172 else if (RB_FLOAT_TYPE_P(x)) {
173 return rb_float_uminus(x);
174 }
175 else if (RB_TYPE_P(x, T_RATIONAL)) {
176 return rb_rational_uminus(x);
177 }
178 else if (RB_TYPE_P(x, T_COMPLEX)) {
179 return rb_complex_uminus(x);
180 }
181 return rb_funcall(x, id_negate, 0);
182 }
183
184 fun1(numerator)
fun1(real_p)185 fun1(real_p)
186
187 inline static VALUE
188 f_to_i(VALUE x)
189 {
190 if (RB_TYPE_P(x, T_STRING))
191 return rb_str_to_inum(x, 10, 0);
192 return rb_funcall(x, id_to_i, 0);
193 }
194 inline static VALUE
f_to_f(VALUE x)195 f_to_f(VALUE x)
196 {
197 if (RB_TYPE_P(x, T_STRING))
198 return DBL2NUM(rb_str_to_dbl(x, 0));
199 return rb_funcall(x, id_to_f, 0);
200 }
201
fun1(to_r)202 fun1(to_r)
203
204 inline static int
205 f_eqeq_p(VALUE x, VALUE y)
206 {
207 if (FIXNUM_P(x) && FIXNUM_P(y))
208 return x == y;
209 else if (RB_FLOAT_TYPE_P(x) || RB_FLOAT_TYPE_P(y))
210 return NUM2DBL(x) == NUM2DBL(y);
211 return (int)rb_equal(x, y);
212 }
213
214 fun2(expt)
fun2(fdiv)215 fun2(fdiv)
216 fun2(quo)
217
218 inline static int
219 f_negative_p(VALUE x)
220 {
221 if (RB_INTEGER_TYPE_P(x))
222 return INT_NEGATIVE_P(x);
223 else if (RB_FLOAT_TYPE_P(x))
224 return RFLOAT_VALUE(x) < 0.0;
225 else if (RB_TYPE_P(x, T_RATIONAL))
226 return INT_NEGATIVE_P(RRATIONAL(x)->num);
227 return rb_num_negative_p(x);
228 }
229
230 #define f_positive_p(x) (!f_negative_p(x))
231
232 inline static int
f_zero_p(VALUE x)233 f_zero_p(VALUE x)
234 {
235 if (RB_INTEGER_TYPE_P(x)) {
236 return FIXNUM_ZERO_P(x);
237 }
238 else if (RB_TYPE_P(x, T_RATIONAL)) {
239 const VALUE num = RRATIONAL(x)->num;
240 return FIXNUM_ZERO_P(num);
241 }
242 return (int)rb_equal(x, ZERO);
243 }
244
245 #define f_nonzero_p(x) (!f_zero_p(x))
246
247 VALUE rb_flo_is_finite_p(VALUE num);
248 inline static int
f_finite_p(VALUE x)249 f_finite_p(VALUE x)
250 {
251 if (RB_INTEGER_TYPE_P(x)) {
252 return TRUE;
253 }
254 else if (RB_FLOAT_TYPE_P(x)) {
255 return (int)rb_flo_is_finite_p(x);
256 }
257 else if (RB_TYPE_P(x, T_RATIONAL)) {
258 return TRUE;
259 }
260 return RTEST(rb_funcallv(x, id_finite_p, 0, 0));
261 }
262
263 VALUE rb_flo_is_infinite_p(VALUE num);
264 inline static VALUE
f_infinite_p(VALUE x)265 f_infinite_p(VALUE x)
266 {
267 if (RB_INTEGER_TYPE_P(x)) {
268 return Qnil;
269 }
270 else if (RB_FLOAT_TYPE_P(x)) {
271 return rb_flo_is_infinite_p(x);
272 }
273 else if (RB_TYPE_P(x, T_RATIONAL)) {
274 return Qnil;
275 }
276 return rb_funcallv(x, id_infinite_p, 0, 0);
277 }
278
279 inline static int
f_kind_of_p(VALUE x,VALUE c)280 f_kind_of_p(VALUE x, VALUE c)
281 {
282 return (int)rb_obj_is_kind_of(x, c);
283 }
284
285 inline static int
k_numeric_p(VALUE x)286 k_numeric_p(VALUE x)
287 {
288 return f_kind_of_p(x, rb_cNumeric);
289 }
290
291 #define k_exact_p(x) (!RB_FLOAT_TYPE_P(x))
292
293 #define k_exact_zero_p(x) (k_exact_p(x) && f_zero_p(x))
294
295 #define get_dat1(x) \
296 struct RComplex *dat = RCOMPLEX(x)
297
298 #define get_dat2(x,y) \
299 struct RComplex *adat = RCOMPLEX(x), *bdat = RCOMPLEX(y)
300
301 inline static VALUE
nucomp_s_new_internal(VALUE klass,VALUE real,VALUE imag)302 nucomp_s_new_internal(VALUE klass, VALUE real, VALUE imag)
303 {
304 NEWOBJ_OF(obj, struct RComplex, klass, T_COMPLEX | (RGENGC_WB_PROTECTED_COMPLEX ? FL_WB_PROTECTED : 0));
305
306 RCOMPLEX_SET_REAL(obj, real);
307 RCOMPLEX_SET_IMAG(obj, imag);
308 OBJ_FREEZE_RAW(obj);
309
310 return (VALUE)obj;
311 }
312
313 static VALUE
nucomp_s_alloc(VALUE klass)314 nucomp_s_alloc(VALUE klass)
315 {
316 return nucomp_s_new_internal(klass, ZERO, ZERO);
317 }
318
319 inline static VALUE
f_complex_new_bang1(VALUE klass,VALUE x)320 f_complex_new_bang1(VALUE klass, VALUE x)
321 {
322 assert(!RB_TYPE_P(x, T_COMPLEX));
323 return nucomp_s_new_internal(klass, x, ZERO);
324 }
325
326 inline static VALUE
f_complex_new_bang2(VALUE klass,VALUE x,VALUE y)327 f_complex_new_bang2(VALUE klass, VALUE x, VALUE y)
328 {
329 assert(!RB_TYPE_P(x, T_COMPLEX));
330 assert(!RB_TYPE_P(y, T_COMPLEX));
331 return nucomp_s_new_internal(klass, x, y);
332 }
333
334 #ifdef CANONICALIZATION_FOR_MATHN
335 static int canonicalization = 0;
336
337 RUBY_FUNC_EXPORTED void
nucomp_canonicalization(int f)338 nucomp_canonicalization(int f)
339 {
340 canonicalization = f;
341 }
342 #else
343 #define canonicalization 0
344 #endif
345
346 inline static void
nucomp_real_check(VALUE num)347 nucomp_real_check(VALUE num)
348 {
349 if (!RB_INTEGER_TYPE_P(num) &&
350 !RB_FLOAT_TYPE_P(num) &&
351 !RB_TYPE_P(num, T_RATIONAL)) {
352 if (!k_numeric_p(num) || !f_real_p(num))
353 rb_raise(rb_eTypeError, "not a real");
354 }
355 }
356
357 inline static VALUE
nucomp_s_canonicalize_internal(VALUE klass,VALUE real,VALUE imag)358 nucomp_s_canonicalize_internal(VALUE klass, VALUE real, VALUE imag)
359 {
360 int complex_r, complex_i;
361 #ifdef CANONICALIZATION_FOR_MATHN
362 if (k_exact_zero_p(imag) && canonicalization)
363 return real;
364 #endif
365 complex_r = RB_TYPE_P(real, T_COMPLEX);
366 complex_i = RB_TYPE_P(imag, T_COMPLEX);
367 if (!complex_r && !complex_i) {
368 return nucomp_s_new_internal(klass, real, imag);
369 }
370 else if (!complex_r) {
371 get_dat1(imag);
372
373 return nucomp_s_new_internal(klass,
374 f_sub(real, dat->imag),
375 f_add(ZERO, dat->real));
376 }
377 else if (!complex_i) {
378 get_dat1(real);
379
380 return nucomp_s_new_internal(klass,
381 dat->real,
382 f_add(dat->imag, imag));
383 }
384 else {
385 get_dat2(real, imag);
386
387 return nucomp_s_new_internal(klass,
388 f_sub(adat->real, bdat->imag),
389 f_add(adat->imag, bdat->real));
390 }
391 }
392
393 /*
394 * call-seq:
395 * Complex.rect(real[, imag]) -> complex
396 * Complex.rectangular(real[, imag]) -> complex
397 *
398 * Returns a complex object which denotes the given rectangular form.
399 *
400 * Complex.rectangular(1, 2) #=> (1+2i)
401 */
402 static VALUE
nucomp_s_new(int argc,VALUE * argv,VALUE klass)403 nucomp_s_new(int argc, VALUE *argv, VALUE klass)
404 {
405 VALUE real, imag;
406
407 switch (rb_scan_args(argc, argv, "11", &real, &imag)) {
408 case 1:
409 nucomp_real_check(real);
410 imag = ZERO;
411 break;
412 default:
413 nucomp_real_check(real);
414 nucomp_real_check(imag);
415 break;
416 }
417
418 return nucomp_s_canonicalize_internal(klass, real, imag);
419 }
420
421 inline static VALUE
f_complex_new2(VALUE klass,VALUE x,VALUE y)422 f_complex_new2(VALUE klass, VALUE x, VALUE y)
423 {
424 assert(!RB_TYPE_P(x, T_COMPLEX));
425 return nucomp_s_canonicalize_internal(klass, x, y);
426 }
427
428 static VALUE nucomp_convert(VALUE klass, VALUE a1, VALUE a2, int raise);
429 static VALUE nucomp_s_convert(int argc, VALUE *argv, VALUE klass);
430
431 /*
432 * call-seq:
433 * Complex(x[, y], exception: false) -> numeric
434 *
435 * Returns x+i*y;
436 *
437 * Complex(1, 2) #=> (1+2i)
438 * Complex('1+2i') #=> (1+2i)
439 * Complex(nil) #=> TypeError
440 * Complex(1, nil) #=> TypeError
441 *
442 * Complex(1, nil, exception: false) #=> nil
443 * Complex('1+2', exception: false) #=> nil
444 *
445 * Syntax of string form:
446 *
447 * string form = extra spaces , complex , extra spaces ;
448 * complex = real part | [ sign ] , imaginary part
449 * | real part , sign , imaginary part
450 * | rational , "@" , rational ;
451 * real part = rational ;
452 * imaginary part = imaginary unit | unsigned rational , imaginary unit ;
453 * rational = [ sign ] , unsigned rational ;
454 * unsigned rational = numerator | numerator , "/" , denominator ;
455 * numerator = integer part | fractional part | integer part , fractional part ;
456 * denominator = digits ;
457 * integer part = digits ;
458 * fractional part = "." , digits , [ ( "e" | "E" ) , [ sign ] , digits ] ;
459 * imaginary unit = "i" | "I" | "j" | "J" ;
460 * sign = "-" | "+" ;
461 * digits = digit , { digit | "_" , digit };
462 * digit = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9" ;
463 * extra spaces = ? \s* ? ;
464 *
465 * See String#to_c.
466 */
467 static VALUE
nucomp_f_complex(int argc,VALUE * argv,VALUE klass)468 nucomp_f_complex(int argc, VALUE *argv, VALUE klass)
469 {
470 VALUE a1, a2, opts = Qnil;
471 int raise = TRUE;
472
473 if (rb_scan_args(argc, argv, "11:", &a1, &a2, &opts) == 1) {
474 a2 = Qundef;
475 }
476 if (!NIL_P(opts)) {
477 static ID kwds[1];
478 VALUE exception;
479 if (!kwds[0]) {
480 kwds[0] = idException;
481 }
482 rb_get_kwargs(opts, kwds, 0, 1, &exception);
483 raise = (exception != Qfalse);
484 }
485 return nucomp_convert(rb_cComplex, a1, a2, raise);
486 }
487
488 #define imp1(n) \
489 inline static VALUE \
490 m_##n##_bang(VALUE x)\
491 {\
492 return rb_math_##n(x);\
493 }
494
495 imp1(cos)
imp1(cosh)496 imp1(cosh)
497 imp1(exp)
498
499 static VALUE
500 m_log_bang(VALUE x)
501 {
502 return rb_math_log(1, &x);
503 }
504
505 imp1(sin)
imp1(sinh)506 imp1(sinh)
507
508 static VALUE
509 m_cos(VALUE x)
510 {
511 if (!RB_TYPE_P(x, T_COMPLEX))
512 return m_cos_bang(x);
513 {
514 get_dat1(x);
515 return f_complex_new2(rb_cComplex,
516 f_mul(m_cos_bang(dat->real),
517 m_cosh_bang(dat->imag)),
518 f_mul(f_negate(m_sin_bang(dat->real)),
519 m_sinh_bang(dat->imag)));
520 }
521 }
522
523 static VALUE
m_sin(VALUE x)524 m_sin(VALUE x)
525 {
526 if (!RB_TYPE_P(x, T_COMPLEX))
527 return m_sin_bang(x);
528 {
529 get_dat1(x);
530 return f_complex_new2(rb_cComplex,
531 f_mul(m_sin_bang(dat->real),
532 m_cosh_bang(dat->imag)),
533 f_mul(m_cos_bang(dat->real),
534 m_sinh_bang(dat->imag)));
535 }
536 }
537
538 static VALUE
f_complex_polar(VALUE klass,VALUE x,VALUE y)539 f_complex_polar(VALUE klass, VALUE x, VALUE y)
540 {
541 assert(!RB_TYPE_P(x, T_COMPLEX));
542 assert(!RB_TYPE_P(y, T_COMPLEX));
543 if (f_zero_p(x) || f_zero_p(y)) {
544 if (canonicalization) return x;
545 return nucomp_s_new_internal(klass, x, RFLOAT_0);
546 }
547 if (RB_FLOAT_TYPE_P(y)) {
548 const double arg = RFLOAT_VALUE(y);
549 if (arg == M_PI) {
550 x = f_negate(x);
551 if (canonicalization) return x;
552 y = RFLOAT_0;
553 }
554 else if (arg == M_PI_2) {
555 y = x;
556 x = RFLOAT_0;
557 }
558 else if (arg == M_PI_2+M_PI) {
559 y = f_negate(x);
560 x = RFLOAT_0;
561 }
562 else if (RB_FLOAT_TYPE_P(x)) {
563 const double abs = RFLOAT_VALUE(x);
564 const double real = abs * cos(arg), imag = abs * sin(arg);
565 x = DBL2NUM(real);
566 if (canonicalization && imag == 0.0) return x;
567 y = DBL2NUM(imag);
568 }
569 else {
570 y = f_mul(x, DBL2NUM(sin(arg)));
571 x = f_mul(x, DBL2NUM(cos(arg)));
572 if (canonicalization && f_zero_p(y)) return x;
573 }
574 return nucomp_s_new_internal(klass, x, y);
575 }
576 return nucomp_s_canonicalize_internal(klass,
577 f_mul(x, m_cos(y)),
578 f_mul(x, m_sin(y)));
579 }
580
581 /* returns a Complex or Float of ang*PI-rotated abs */
582 VALUE
rb_dbl_complex_new_polar_pi(double abs,double ang)583 rb_dbl_complex_new_polar_pi(double abs, double ang)
584 {
585 double fi;
586 const double fr = modf(ang, &fi);
587 int pos = fr == +0.5;
588
589 if (pos || fr == -0.5) {
590 if ((modf(fi / 2.0, &fi) != fr) ^ pos) abs = -abs;
591 return rb_complex_new(RFLOAT_0, DBL2NUM(abs));
592 }
593 else if (fr == 0.0) {
594 if (modf(fi / 2.0, &fi) != 0.0) abs = -abs;
595 return DBL2NUM(abs);
596 }
597 else {
598 ang *= M_PI;
599 return rb_complex_new(DBL2NUM(abs * cos(ang)), DBL2NUM(abs * sin(ang)));
600 }
601 }
602
603 /*
604 * call-seq:
605 * Complex.polar(abs[, arg]) -> complex
606 *
607 * Returns a complex object which denotes the given polar form.
608 *
609 * Complex.polar(3, 0) #=> (3.0+0.0i)
610 * Complex.polar(3, Math::PI/2) #=> (1.836909530733566e-16+3.0i)
611 * Complex.polar(3, Math::PI) #=> (-3.0+3.673819061467132e-16i)
612 * Complex.polar(3, -Math::PI/2) #=> (1.836909530733566e-16-3.0i)
613 */
614 static VALUE
nucomp_s_polar(int argc,VALUE * argv,VALUE klass)615 nucomp_s_polar(int argc, VALUE *argv, VALUE klass)
616 {
617 VALUE abs, arg;
618
619 switch (rb_scan_args(argc, argv, "11", &abs, &arg)) {
620 case 1:
621 nucomp_real_check(abs);
622 if (canonicalization) return abs;
623 return nucomp_s_new_internal(klass, abs, ZERO);
624 default:
625 nucomp_real_check(abs);
626 nucomp_real_check(arg);
627 break;
628 }
629 return f_complex_polar(klass, abs, arg);
630 }
631
632 /*
633 * call-seq:
634 * cmp.real -> real
635 *
636 * Returns the real part.
637 *
638 * Complex(7).real #=> 7
639 * Complex(9, -4).real #=> 9
640 */
641 VALUE
rb_complex_real(VALUE self)642 rb_complex_real(VALUE self)
643 {
644 get_dat1(self);
645 return dat->real;
646 }
647
648 /*
649 * call-seq:
650 * cmp.imag -> real
651 * cmp.imaginary -> real
652 *
653 * Returns the imaginary part.
654 *
655 * Complex(7).imaginary #=> 0
656 * Complex(9, -4).imaginary #=> -4
657 */
658 VALUE
rb_complex_imag(VALUE self)659 rb_complex_imag(VALUE self)
660 {
661 get_dat1(self);
662 return dat->imag;
663 }
664
665 /*
666 * call-seq:
667 * -cmp -> complex
668 *
669 * Returns negation of the value.
670 *
671 * -Complex(1, 2) #=> (-1-2i)
672 */
673 VALUE
rb_complex_uminus(VALUE self)674 rb_complex_uminus(VALUE self)
675 {
676 get_dat1(self);
677 return f_complex_new2(CLASS_OF(self),
678 f_negate(dat->real), f_negate(dat->imag));
679 }
680
681 /*
682 * call-seq:
683 * cmp + numeric -> complex
684 *
685 * Performs addition.
686 *
687 * Complex(2, 3) + Complex(2, 3) #=> (4+6i)
688 * Complex(900) + Complex(1) #=> (901+0i)
689 * Complex(-2, 9) + Complex(-9, 2) #=> (-11+11i)
690 * Complex(9, 8) + 4 #=> (13+8i)
691 * Complex(20, 9) + 9.8 #=> (29.8+9i)
692 */
693 VALUE
rb_complex_plus(VALUE self,VALUE other)694 rb_complex_plus(VALUE self, VALUE other)
695 {
696 if (RB_TYPE_P(other, T_COMPLEX)) {
697 VALUE real, imag;
698
699 get_dat2(self, other);
700
701 real = f_add(adat->real, bdat->real);
702 imag = f_add(adat->imag, bdat->imag);
703
704 return f_complex_new2(CLASS_OF(self), real, imag);
705 }
706 if (k_numeric_p(other) && f_real_p(other)) {
707 get_dat1(self);
708
709 return f_complex_new2(CLASS_OF(self),
710 f_add(dat->real, other), dat->imag);
711 }
712 return rb_num_coerce_bin(self, other, '+');
713 }
714
715 /*
716 * call-seq:
717 * cmp - numeric -> complex
718 *
719 * Performs subtraction.
720 *
721 * Complex(2, 3) - Complex(2, 3) #=> (0+0i)
722 * Complex(900) - Complex(1) #=> (899+0i)
723 * Complex(-2, 9) - Complex(-9, 2) #=> (7+7i)
724 * Complex(9, 8) - 4 #=> (5+8i)
725 * Complex(20, 9) - 9.8 #=> (10.2+9i)
726 */
727 VALUE
rb_complex_minus(VALUE self,VALUE other)728 rb_complex_minus(VALUE self, VALUE other)
729 {
730 if (RB_TYPE_P(other, T_COMPLEX)) {
731 VALUE real, imag;
732
733 get_dat2(self, other);
734
735 real = f_sub(adat->real, bdat->real);
736 imag = f_sub(adat->imag, bdat->imag);
737
738 return f_complex_new2(CLASS_OF(self), real, imag);
739 }
740 if (k_numeric_p(other) && f_real_p(other)) {
741 get_dat1(self);
742
743 return f_complex_new2(CLASS_OF(self),
744 f_sub(dat->real, other), dat->imag);
745 }
746 return rb_num_coerce_bin(self, other, '-');
747 }
748
749 static VALUE
safe_mul(VALUE a,VALUE b,int az,int bz)750 safe_mul(VALUE a, VALUE b, int az, int bz)
751 {
752 double v;
753 if (!az && bz && RB_FLOAT_TYPE_P(a) && (v = RFLOAT_VALUE(a), !isnan(v))) {
754 a = signbit(v) ? DBL2NUM(-1.0) : DBL2NUM(1.0);
755 }
756 if (!bz && az && RB_FLOAT_TYPE_P(b) && (v = RFLOAT_VALUE(b), !isnan(v))) {
757 b = signbit(v) ? DBL2NUM(-1.0) : DBL2NUM(1.0);
758 }
759 return f_mul(a, b);
760 }
761
762 static void
comp_mul(VALUE areal,VALUE aimag,VALUE breal,VALUE bimag,VALUE * real,VALUE * imag)763 comp_mul(VALUE areal, VALUE aimag, VALUE breal, VALUE bimag, VALUE *real, VALUE *imag)
764 {
765 int arzero = f_zero_p(areal);
766 int aizero = f_zero_p(aimag);
767 int brzero = f_zero_p(breal);
768 int bizero = f_zero_p(bimag);
769 *real = f_sub(safe_mul(areal, breal, arzero, brzero),
770 safe_mul(aimag, bimag, aizero, bizero));
771 *imag = f_add(safe_mul(areal, bimag, arzero, bizero),
772 safe_mul(aimag, breal, aizero, brzero));
773 }
774
775 /*
776 * call-seq:
777 * cmp * numeric -> complex
778 *
779 * Performs multiplication.
780 *
781 * Complex(2, 3) * Complex(2, 3) #=> (-5+12i)
782 * Complex(900) * Complex(1) #=> (900+0i)
783 * Complex(-2, 9) * Complex(-9, 2) #=> (0-85i)
784 * Complex(9, 8) * 4 #=> (36+32i)
785 * Complex(20, 9) * 9.8 #=> (196.0+88.2i)
786 */
787 VALUE
rb_complex_mul(VALUE self,VALUE other)788 rb_complex_mul(VALUE self, VALUE other)
789 {
790 if (RB_TYPE_P(other, T_COMPLEX)) {
791 VALUE real, imag;
792 get_dat2(self, other);
793
794 comp_mul(adat->real, adat->imag, bdat->real, bdat->imag, &real, &imag);
795
796 return f_complex_new2(CLASS_OF(self), real, imag);
797 }
798 if (k_numeric_p(other) && f_real_p(other)) {
799 get_dat1(self);
800
801 return f_complex_new2(CLASS_OF(self),
802 f_mul(dat->real, other),
803 f_mul(dat->imag, other));
804 }
805 return rb_num_coerce_bin(self, other, '*');
806 }
807
808 inline static VALUE
f_divide(VALUE self,VALUE other,VALUE (* func)(VALUE,VALUE),ID id)809 f_divide(VALUE self, VALUE other,
810 VALUE (*func)(VALUE, VALUE), ID id)
811 {
812 if (RB_TYPE_P(other, T_COMPLEX)) {
813 VALUE r, n, x, y;
814 int flo;
815 get_dat2(self, other);
816
817 flo = (RB_FLOAT_TYPE_P(adat->real) || RB_FLOAT_TYPE_P(adat->imag) ||
818 RB_FLOAT_TYPE_P(bdat->real) || RB_FLOAT_TYPE_P(bdat->imag));
819
820 if (f_gt_p(f_abs(bdat->real), f_abs(bdat->imag))) {
821 r = (*func)(bdat->imag, bdat->real);
822 n = f_mul(bdat->real, f_add(ONE, f_mul(r, r)));
823 if (flo)
824 return f_complex_new2(CLASS_OF(self),
825 (*func)(self, n),
826 (*func)(f_negate(f_mul(self, r)), n));
827 x = (*func)(f_add(adat->real, f_mul(adat->imag, r)), n);
828 y = (*func)(f_sub(adat->imag, f_mul(adat->real, r)), n);
829 }
830 else {
831 r = (*func)(bdat->real, bdat->imag);
832 n = f_mul(bdat->imag, f_add(ONE, f_mul(r, r)));
833 if (flo)
834 return f_complex_new2(CLASS_OF(self),
835 (*func)(f_mul(self, r), n),
836 (*func)(f_negate(self), n));
837 x = (*func)(f_add(f_mul(adat->real, r), adat->imag), n);
838 y = (*func)(f_sub(f_mul(adat->imag, r), adat->real), n);
839 }
840 x = rb_rational_canonicalize(x);
841 y = rb_rational_canonicalize(y);
842 return f_complex_new2(CLASS_OF(self), x, y);
843 }
844 if (k_numeric_p(other) && f_real_p(other)) {
845 get_dat1(self);
846
847 return f_complex_new2(CLASS_OF(self),
848 (*func)(dat->real, other),
849 (*func)(dat->imag, other));
850 }
851 return rb_num_coerce_bin(self, other, id);
852 }
853
854 #define rb_raise_zerodiv() rb_raise(rb_eZeroDivError, "divided by 0")
855
856 /*
857 * call-seq:
858 * cmp / numeric -> complex
859 * cmp.quo(numeric) -> complex
860 *
861 * Performs division.
862 *
863 * Complex(2, 3) / Complex(2, 3) #=> ((1/1)+(0/1)*i)
864 * Complex(900) / Complex(1) #=> ((900/1)+(0/1)*i)
865 * Complex(-2, 9) / Complex(-9, 2) #=> ((36/85)-(77/85)*i)
866 * Complex(9, 8) / 4 #=> ((9/4)+(2/1)*i)
867 * Complex(20, 9) / 9.8 #=> (2.0408163265306123+0.9183673469387754i)
868 */
869 VALUE
rb_complex_div(VALUE self,VALUE other)870 rb_complex_div(VALUE self, VALUE other)
871 {
872 return f_divide(self, other, f_quo, id_quo);
873 }
874
875 #define nucomp_quo rb_complex_div
876
877 /*
878 * call-seq:
879 * cmp.fdiv(numeric) -> complex
880 *
881 * Performs division as each part is a float, never returns a float.
882 *
883 * Complex(11, 22).fdiv(3) #=> (3.6666666666666665+7.333333333333333i)
884 */
885 static VALUE
nucomp_fdiv(VALUE self,VALUE other)886 nucomp_fdiv(VALUE self, VALUE other)
887 {
888 return f_divide(self, other, f_fdiv, id_fdiv);
889 }
890
891 inline static VALUE
f_reciprocal(VALUE x)892 f_reciprocal(VALUE x)
893 {
894 return f_quo(ONE, x);
895 }
896
897 /*
898 * call-seq:
899 * cmp ** numeric -> complex
900 *
901 * Performs exponentiation.
902 *
903 * Complex('i') ** 2 #=> (-1+0i)
904 * Complex(-8) ** Rational(1, 3) #=> (1.0000000000000002+1.7320508075688772i)
905 */
906 VALUE
rb_complex_pow(VALUE self,VALUE other)907 rb_complex_pow(VALUE self, VALUE other)
908 {
909 if (k_numeric_p(other) && k_exact_zero_p(other))
910 return f_complex_new_bang1(CLASS_OF(self), ONE);
911
912 if (RB_TYPE_P(other, T_RATIONAL) && RRATIONAL(other)->den == LONG2FIX(1))
913 other = RRATIONAL(other)->num; /* c14n */
914
915 if (RB_TYPE_P(other, T_COMPLEX)) {
916 get_dat1(other);
917
918 if (k_exact_zero_p(dat->imag))
919 other = dat->real; /* c14n */
920 }
921
922 if (RB_TYPE_P(other, T_COMPLEX)) {
923 VALUE r, theta, nr, ntheta;
924
925 get_dat1(other);
926
927 r = f_abs(self);
928 theta = f_arg(self);
929
930 nr = m_exp_bang(f_sub(f_mul(dat->real, m_log_bang(r)),
931 f_mul(dat->imag, theta)));
932 ntheta = f_add(f_mul(theta, dat->real),
933 f_mul(dat->imag, m_log_bang(r)));
934 return f_complex_polar(CLASS_OF(self), nr, ntheta);
935 }
936 if (FIXNUM_P(other)) {
937 long n = FIX2LONG(other);
938 if (n == 0) {
939 return nucomp_s_new_internal(CLASS_OF(self), ONE, ZERO);
940 }
941 if (n < 0) {
942 self = f_reciprocal(self);
943 other = rb_int_uminus(other);
944 n = -n;
945 }
946 {
947 get_dat1(self);
948 VALUE xr = dat->real, xi = dat->imag, zr = xr, zi = xi;
949
950 if (f_zero_p(xi)) {
951 zr = rb_num_pow(zr, other);
952 }
953 else if (f_zero_p(xr)) {
954 zi = rb_num_pow(zi, other);
955 if (n & 2) zi = f_negate(zi);
956 if (!(n & 1)) {
957 VALUE tmp = zr;
958 zr = zi;
959 zi = tmp;
960 }
961 }
962 else {
963 while (--n) {
964 long q, r;
965
966 for (; q = n / 2, r = n % 2, r == 0; n = q) {
967 VALUE tmp = f_sub(f_mul(xr, xr), f_mul(xi, xi));
968 xi = f_mul(f_mul(TWO, xr), xi);
969 xr = tmp;
970 }
971 comp_mul(zr, zi, xr, xi, &zr, &zi);
972 }
973 }
974 return nucomp_s_new_internal(CLASS_OF(self), zr, zi);
975 }
976 }
977 if (k_numeric_p(other) && f_real_p(other)) {
978 VALUE r, theta;
979
980 if (RB_TYPE_P(other, T_BIGNUM))
981 rb_warn("in a**b, b may be too big");
982
983 r = f_abs(self);
984 theta = f_arg(self);
985
986 return f_complex_polar(CLASS_OF(self), f_expt(r, other),
987 f_mul(theta, other));
988 }
989 return rb_num_coerce_bin(self, other, id_expt);
990 }
991
992 /*
993 * call-seq:
994 * cmp == object -> true or false
995 *
996 * Returns true if cmp equals object numerically.
997 *
998 * Complex(2, 3) == Complex(2, 3) #=> true
999 * Complex(5) == 5 #=> true
1000 * Complex(0) == 0.0 #=> true
1001 * Complex('1/3') == 0.33 #=> false
1002 * Complex('1/2') == '1/2' #=> false
1003 */
1004 static VALUE
nucomp_eqeq_p(VALUE self,VALUE other)1005 nucomp_eqeq_p(VALUE self, VALUE other)
1006 {
1007 if (RB_TYPE_P(other, T_COMPLEX)) {
1008 get_dat2(self, other);
1009
1010 return f_boolcast(f_eqeq_p(adat->real, bdat->real) &&
1011 f_eqeq_p(adat->imag, bdat->imag));
1012 }
1013 if (k_numeric_p(other) && f_real_p(other)) {
1014 get_dat1(self);
1015
1016 return f_boolcast(f_eqeq_p(dat->real, other) && f_zero_p(dat->imag));
1017 }
1018 return f_boolcast(f_eqeq_p(other, self));
1019 }
1020
1021 /* :nodoc: */
1022 static VALUE
nucomp_coerce(VALUE self,VALUE other)1023 nucomp_coerce(VALUE self, VALUE other)
1024 {
1025 if (k_numeric_p(other) && f_real_p(other))
1026 return rb_assoc_new(f_complex_new_bang1(CLASS_OF(self), other), self);
1027 if (RB_TYPE_P(other, T_COMPLEX))
1028 return rb_assoc_new(other, self);
1029
1030 rb_raise(rb_eTypeError, "%"PRIsVALUE" can't be coerced into %"PRIsVALUE,
1031 rb_obj_class(other), rb_obj_class(self));
1032 return Qnil;
1033 }
1034
1035 /*
1036 * call-seq:
1037 * cmp.abs -> real
1038 * cmp.magnitude -> real
1039 *
1040 * Returns the absolute part of its polar form.
1041 *
1042 * Complex(-1).abs #=> 1
1043 * Complex(3.0, -4.0).abs #=> 5.0
1044 */
1045 VALUE
rb_complex_abs(VALUE self)1046 rb_complex_abs(VALUE self)
1047 {
1048 get_dat1(self);
1049
1050 if (f_zero_p(dat->real)) {
1051 VALUE a = f_abs(dat->imag);
1052 if (RB_FLOAT_TYPE_P(dat->real) && !RB_FLOAT_TYPE_P(dat->imag))
1053 a = f_to_f(a);
1054 return a;
1055 }
1056 if (f_zero_p(dat->imag)) {
1057 VALUE a = f_abs(dat->real);
1058 if (!RB_FLOAT_TYPE_P(dat->real) && RB_FLOAT_TYPE_P(dat->imag))
1059 a = f_to_f(a);
1060 return a;
1061 }
1062 return rb_math_hypot(dat->real, dat->imag);
1063 }
1064
1065 /*
1066 * call-seq:
1067 * cmp.abs2 -> real
1068 *
1069 * Returns square of the absolute value.
1070 *
1071 * Complex(-1).abs2 #=> 1
1072 * Complex(3.0, -4.0).abs2 #=> 25.0
1073 */
1074 static VALUE
nucomp_abs2(VALUE self)1075 nucomp_abs2(VALUE self)
1076 {
1077 get_dat1(self);
1078 return f_add(f_mul(dat->real, dat->real),
1079 f_mul(dat->imag, dat->imag));
1080 }
1081
1082 /*
1083 * call-seq:
1084 * cmp.arg -> float
1085 * cmp.angle -> float
1086 * cmp.phase -> float
1087 *
1088 * Returns the angle part of its polar form.
1089 *
1090 * Complex.polar(3, Math::PI/2).arg #=> 1.5707963267948966
1091 */
1092 VALUE
rb_complex_arg(VALUE self)1093 rb_complex_arg(VALUE self)
1094 {
1095 get_dat1(self);
1096 return rb_math_atan2(dat->imag, dat->real);
1097 }
1098
1099 /*
1100 * call-seq:
1101 * cmp.rect -> array
1102 * cmp.rectangular -> array
1103 *
1104 * Returns an array; [cmp.real, cmp.imag].
1105 *
1106 * Complex(1, 2).rectangular #=> [1, 2]
1107 */
1108 static VALUE
nucomp_rect(VALUE self)1109 nucomp_rect(VALUE self)
1110 {
1111 get_dat1(self);
1112 return rb_assoc_new(dat->real, dat->imag);
1113 }
1114
1115 /*
1116 * call-seq:
1117 * cmp.polar -> array
1118 *
1119 * Returns an array; [cmp.abs, cmp.arg].
1120 *
1121 * Complex(1, 2).polar #=> [2.23606797749979, 1.1071487177940904]
1122 */
1123 static VALUE
nucomp_polar(VALUE self)1124 nucomp_polar(VALUE self)
1125 {
1126 return rb_assoc_new(f_abs(self), f_arg(self));
1127 }
1128
1129 /*
1130 * call-seq:
1131 * cmp.conj -> complex
1132 * cmp.conjugate -> complex
1133 *
1134 * Returns the complex conjugate.
1135 *
1136 * Complex(1, 2).conjugate #=> (1-2i)
1137 */
1138 VALUE
rb_complex_conjugate(VALUE self)1139 rb_complex_conjugate(VALUE self)
1140 {
1141 get_dat1(self);
1142 return f_complex_new2(CLASS_OF(self), dat->real, f_negate(dat->imag));
1143 }
1144
1145 /*
1146 * call-seq:
1147 * cmp.real? -> false
1148 *
1149 * Returns false.
1150 */
1151 static VALUE
nucomp_false(VALUE self)1152 nucomp_false(VALUE self)
1153 {
1154 return Qfalse;
1155 }
1156
1157 /*
1158 * call-seq:
1159 * cmp.denominator -> integer
1160 *
1161 * Returns the denominator (lcm of both denominator - real and imag).
1162 *
1163 * See numerator.
1164 */
1165 static VALUE
nucomp_denominator(VALUE self)1166 nucomp_denominator(VALUE self)
1167 {
1168 get_dat1(self);
1169 return rb_lcm(f_denominator(dat->real), f_denominator(dat->imag));
1170 }
1171
1172 /*
1173 * call-seq:
1174 * cmp.numerator -> numeric
1175 *
1176 * Returns the numerator.
1177 *
1178 * 1 2 3+4i <- numerator
1179 * - + -i -> ----
1180 * 2 3 6 <- denominator
1181 *
1182 * c = Complex('1/2+2/3i') #=> ((1/2)+(2/3)*i)
1183 * n = c.numerator #=> (3+4i)
1184 * d = c.denominator #=> 6
1185 * n / d #=> ((1/2)+(2/3)*i)
1186 * Complex(Rational(n.real, d), Rational(n.imag, d))
1187 * #=> ((1/2)+(2/3)*i)
1188 * See denominator.
1189 */
1190 static VALUE
nucomp_numerator(VALUE self)1191 nucomp_numerator(VALUE self)
1192 {
1193 VALUE cd;
1194
1195 get_dat1(self);
1196
1197 cd = f_denominator(self);
1198 return f_complex_new2(CLASS_OF(self),
1199 f_mul(f_numerator(dat->real),
1200 f_div(cd, f_denominator(dat->real))),
1201 f_mul(f_numerator(dat->imag),
1202 f_div(cd, f_denominator(dat->imag))));
1203 }
1204
1205 /* :nodoc: */
1206 static VALUE
nucomp_hash(VALUE self)1207 nucomp_hash(VALUE self)
1208 {
1209 st_index_t v, h[2];
1210 VALUE n;
1211
1212 get_dat1(self);
1213 n = rb_hash(dat->real);
1214 h[0] = NUM2LONG(n);
1215 n = rb_hash(dat->imag);
1216 h[1] = NUM2LONG(n);
1217 v = rb_memhash(h, sizeof(h));
1218 return ST2FIX(v);
1219 }
1220
1221 /* :nodoc: */
1222 static VALUE
nucomp_eql_p(VALUE self,VALUE other)1223 nucomp_eql_p(VALUE self, VALUE other)
1224 {
1225 if (RB_TYPE_P(other, T_COMPLEX)) {
1226 get_dat2(self, other);
1227
1228 return f_boolcast((CLASS_OF(adat->real) == CLASS_OF(bdat->real)) &&
1229 (CLASS_OF(adat->imag) == CLASS_OF(bdat->imag)) &&
1230 f_eqeq_p(self, other));
1231
1232 }
1233 return Qfalse;
1234 }
1235
1236 inline static int
f_signbit(VALUE x)1237 f_signbit(VALUE x)
1238 {
1239 if (RB_FLOAT_TYPE_P(x)) {
1240 double f = RFLOAT_VALUE(x);
1241 return !isnan(f) && signbit(f);
1242 }
1243 return f_negative_p(x);
1244 }
1245
1246 inline static int
f_tpositive_p(VALUE x)1247 f_tpositive_p(VALUE x)
1248 {
1249 return !f_signbit(x);
1250 }
1251
1252 static VALUE
f_format(VALUE self,VALUE (* func)(VALUE))1253 f_format(VALUE self, VALUE (*func)(VALUE))
1254 {
1255 VALUE s;
1256 int impos;
1257
1258 get_dat1(self);
1259
1260 impos = f_tpositive_p(dat->imag);
1261
1262 s = (*func)(dat->real);
1263 rb_str_cat2(s, !impos ? "-" : "+");
1264
1265 rb_str_concat(s, (*func)(f_abs(dat->imag)));
1266 if (!rb_isdigit(RSTRING_PTR(s)[RSTRING_LEN(s) - 1]))
1267 rb_str_cat2(s, "*");
1268 rb_str_cat2(s, "i");
1269
1270 return s;
1271 }
1272
1273 /*
1274 * call-seq:
1275 * cmp.to_s -> string
1276 *
1277 * Returns the value as a string.
1278 *
1279 * Complex(2).to_s #=> "2+0i"
1280 * Complex('-8/6').to_s #=> "-4/3+0i"
1281 * Complex('1/2i').to_s #=> "0+1/2i"
1282 * Complex(0, Float::INFINITY).to_s #=> "0+Infinity*i"
1283 * Complex(Float::NAN, Float::NAN).to_s #=> "NaN+NaN*i"
1284 */
1285 static VALUE
nucomp_to_s(VALUE self)1286 nucomp_to_s(VALUE self)
1287 {
1288 return f_format(self, rb_String);
1289 }
1290
1291 /*
1292 * call-seq:
1293 * cmp.inspect -> string
1294 *
1295 * Returns the value as a string for inspection.
1296 *
1297 * Complex(2).inspect #=> "(2+0i)"
1298 * Complex('-8/6').inspect #=> "((-4/3)+0i)"
1299 * Complex('1/2i').inspect #=> "(0+(1/2)*i)"
1300 * Complex(0, Float::INFINITY).inspect #=> "(0+Infinity*i)"
1301 * Complex(Float::NAN, Float::NAN).inspect #=> "(NaN+NaN*i)"
1302 */
1303 static VALUE
nucomp_inspect(VALUE self)1304 nucomp_inspect(VALUE self)
1305 {
1306 VALUE s;
1307
1308 s = rb_usascii_str_new2("(");
1309 rb_str_concat(s, f_format(self, rb_inspect));
1310 rb_str_cat2(s, ")");
1311
1312 return s;
1313 }
1314
1315 #define FINITE_TYPE_P(v) (RB_INTEGER_TYPE_P(v) || RB_TYPE_P(v, T_RATIONAL))
1316
1317 /*
1318 * call-seq:
1319 * cmp.finite? -> true or false
1320 *
1321 * Returns +true+ if +cmp+'s real and imaginary parts are both finite numbers,
1322 * otherwise returns +false+.
1323 */
1324 static VALUE
rb_complex_finite_p(VALUE self)1325 rb_complex_finite_p(VALUE self)
1326 {
1327 get_dat1(self);
1328
1329 if (f_finite_p(dat->real) && f_finite_p(dat->imag)) {
1330 return Qtrue;
1331 }
1332 return Qfalse;
1333 }
1334
1335 /*
1336 * call-seq:
1337 * cmp.infinite? -> nil or 1
1338 *
1339 * Returns +1+ if +cmp+'s real or imaginary part is an infinite number,
1340 * otherwise returns +nil+.
1341 *
1342 * For example:
1343 *
1344 * (1+1i).infinite? #=> nil
1345 * (Float::INFINITY + 1i).infinite? #=> 1
1346 */
1347 static VALUE
rb_complex_infinite_p(VALUE self)1348 rb_complex_infinite_p(VALUE self)
1349 {
1350 get_dat1(self);
1351
1352 if (NIL_P(f_infinite_p(dat->real)) && NIL_P(f_infinite_p(dat->imag))) {
1353 return Qnil;
1354 }
1355 return ONE;
1356 }
1357
1358 /* :nodoc: */
1359 static VALUE
nucomp_dumper(VALUE self)1360 nucomp_dumper(VALUE self)
1361 {
1362 return self;
1363 }
1364
1365 /* :nodoc: */
1366 static VALUE
nucomp_loader(VALUE self,VALUE a)1367 nucomp_loader(VALUE self, VALUE a)
1368 {
1369 get_dat1(self);
1370
1371 RCOMPLEX_SET_REAL(dat, rb_ivar_get(a, id_i_real));
1372 RCOMPLEX_SET_IMAG(dat, rb_ivar_get(a, id_i_imag));
1373 OBJ_FREEZE_RAW(self);
1374
1375 return self;
1376 }
1377
1378 /* :nodoc: */
1379 static VALUE
nucomp_marshal_dump(VALUE self)1380 nucomp_marshal_dump(VALUE self)
1381 {
1382 VALUE a;
1383 get_dat1(self);
1384
1385 a = rb_assoc_new(dat->real, dat->imag);
1386 rb_copy_generic_ivar(a, self);
1387 return a;
1388 }
1389
1390 /* :nodoc: */
1391 static VALUE
nucomp_marshal_load(VALUE self,VALUE a)1392 nucomp_marshal_load(VALUE self, VALUE a)
1393 {
1394 Check_Type(a, T_ARRAY);
1395 if (RARRAY_LEN(a) != 2)
1396 rb_raise(rb_eArgError, "marshaled complex must have an array whose length is 2 but %ld", RARRAY_LEN(a));
1397 rb_ivar_set(self, id_i_real, RARRAY_AREF(a, 0));
1398 rb_ivar_set(self, id_i_imag, RARRAY_AREF(a, 1));
1399 return self;
1400 }
1401
1402 /* --- */
1403
1404 VALUE
rb_complex_raw(VALUE x,VALUE y)1405 rb_complex_raw(VALUE x, VALUE y)
1406 {
1407 return nucomp_s_new_internal(rb_cComplex, x, y);
1408 }
1409
1410 VALUE
rb_complex_new(VALUE x,VALUE y)1411 rb_complex_new(VALUE x, VALUE y)
1412 {
1413 return nucomp_s_canonicalize_internal(rb_cComplex, x, y);
1414 }
1415
1416 VALUE
rb_complex_new_polar(VALUE x,VALUE y)1417 rb_complex_new_polar(VALUE x, VALUE y)
1418 {
1419 return f_complex_polar(rb_cComplex, x, y);
1420 }
1421
1422 VALUE
rb_complex_polar(VALUE x,VALUE y)1423 rb_complex_polar(VALUE x, VALUE y)
1424 {
1425 return rb_complex_new_polar(x, y);
1426 }
1427
1428 VALUE
rb_Complex(VALUE x,VALUE y)1429 rb_Complex(VALUE x, VALUE y)
1430 {
1431 VALUE a[2];
1432 a[0] = x;
1433 a[1] = y;
1434 return nucomp_s_convert(2, a, rb_cComplex);
1435 }
1436
1437 /*!
1438 * Creates a Complex object.
1439 *
1440 * \param real real part value
1441 * \param imag imaginary part value
1442 * \return a new Complex object
1443 */
1444 VALUE
rb_dbl_complex_new(double real,double imag)1445 rb_dbl_complex_new(double real, double imag)
1446 {
1447 return rb_complex_raw(DBL2NUM(real), DBL2NUM(imag));
1448 }
1449
1450 /*
1451 * call-seq:
1452 * cmp.to_i -> integer
1453 *
1454 * Returns the value as an integer if possible (the imaginary part
1455 * should be exactly zero).
1456 *
1457 * Complex(1, 0).to_i #=> 1
1458 * Complex(1, 0.0).to_i # RangeError
1459 * Complex(1, 2).to_i # RangeError
1460 */
1461 static VALUE
nucomp_to_i(VALUE self)1462 nucomp_to_i(VALUE self)
1463 {
1464 get_dat1(self);
1465
1466 if (!k_exact_zero_p(dat->imag)) {
1467 rb_raise(rb_eRangeError, "can't convert %"PRIsVALUE" into Integer",
1468 self);
1469 }
1470 return f_to_i(dat->real);
1471 }
1472
1473 /*
1474 * call-seq:
1475 * cmp.to_f -> float
1476 *
1477 * Returns the value as a float if possible (the imaginary part should
1478 * be exactly zero).
1479 *
1480 * Complex(1, 0).to_f #=> 1.0
1481 * Complex(1, 0.0).to_f # RangeError
1482 * Complex(1, 2).to_f # RangeError
1483 */
1484 static VALUE
nucomp_to_f(VALUE self)1485 nucomp_to_f(VALUE self)
1486 {
1487 get_dat1(self);
1488
1489 if (!k_exact_zero_p(dat->imag)) {
1490 rb_raise(rb_eRangeError, "can't convert %"PRIsVALUE" into Float",
1491 self);
1492 }
1493 return f_to_f(dat->real);
1494 }
1495
1496 /*
1497 * call-seq:
1498 * cmp.to_r -> rational
1499 *
1500 * Returns the value as a rational if possible (the imaginary part
1501 * should be exactly zero).
1502 *
1503 * Complex(1, 0).to_r #=> (1/1)
1504 * Complex(1, 0.0).to_r # RangeError
1505 * Complex(1, 2).to_r # RangeError
1506 *
1507 * See rationalize.
1508 */
1509 static VALUE
nucomp_to_r(VALUE self)1510 nucomp_to_r(VALUE self)
1511 {
1512 get_dat1(self);
1513
1514 if (!k_exact_zero_p(dat->imag)) {
1515 rb_raise(rb_eRangeError, "can't convert %"PRIsVALUE" into Rational",
1516 self);
1517 }
1518 return f_to_r(dat->real);
1519 }
1520
1521 /*
1522 * call-seq:
1523 * cmp.rationalize([eps]) -> rational
1524 *
1525 * Returns the value as a rational if possible (the imaginary part
1526 * should be exactly zero).
1527 *
1528 * Complex(1.0/3, 0).rationalize #=> (1/3)
1529 * Complex(1, 0.0).rationalize # RangeError
1530 * Complex(1, 2).rationalize # RangeError
1531 *
1532 * See to_r.
1533 */
1534 static VALUE
nucomp_rationalize(int argc,VALUE * argv,VALUE self)1535 nucomp_rationalize(int argc, VALUE *argv, VALUE self)
1536 {
1537 get_dat1(self);
1538
1539 rb_check_arity(argc, 0, 1);
1540
1541 if (!k_exact_zero_p(dat->imag)) {
1542 rb_raise(rb_eRangeError, "can't convert %"PRIsVALUE" into Rational",
1543 self);
1544 }
1545 return rb_funcallv(dat->real, id_rationalize, argc, argv);
1546 }
1547
1548 /*
1549 * call-seq:
1550 * complex.to_c -> self
1551 *
1552 * Returns self.
1553 *
1554 * Complex(2).to_c #=> (2+0i)
1555 * Complex(-8, 6).to_c #=> (-8+6i)
1556 */
1557 static VALUE
nucomp_to_c(VALUE self)1558 nucomp_to_c(VALUE self)
1559 {
1560 return self;
1561 }
1562
1563 /*
1564 * call-seq:
1565 * nil.to_c -> (0+0i)
1566 *
1567 * Returns zero as a complex.
1568 */
1569 static VALUE
nilclass_to_c(VALUE self)1570 nilclass_to_c(VALUE self)
1571 {
1572 return rb_complex_new1(INT2FIX(0));
1573 }
1574
1575 /*
1576 * call-seq:
1577 * num.to_c -> complex
1578 *
1579 * Returns the value as a complex.
1580 */
1581 static VALUE
numeric_to_c(VALUE self)1582 numeric_to_c(VALUE self)
1583 {
1584 return rb_complex_new1(self);
1585 }
1586
1587 #include <ctype.h>
1588
1589 inline static int
issign(int c)1590 issign(int c)
1591 {
1592 return (c == '-' || c == '+');
1593 }
1594
1595 static int
read_sign(const char ** s,char ** b)1596 read_sign(const char **s,
1597 char **b)
1598 {
1599 int sign = '?';
1600
1601 if (issign(**s)) {
1602 sign = **b = **s;
1603 (*s)++;
1604 (*b)++;
1605 }
1606 return sign;
1607 }
1608
1609 inline static int
isdecimal(int c)1610 isdecimal(int c)
1611 {
1612 return isdigit((unsigned char)c);
1613 }
1614
1615 static int
read_digits(const char ** s,int strict,char ** b)1616 read_digits(const char **s, int strict,
1617 char **b)
1618 {
1619 int us = 1;
1620
1621 if (!isdecimal(**s))
1622 return 0;
1623
1624 while (isdecimal(**s) || **s == '_') {
1625 if (**s == '_') {
1626 if (strict) {
1627 if (us)
1628 return 0;
1629 }
1630 us = 1;
1631 }
1632 else {
1633 **b = **s;
1634 (*b)++;
1635 us = 0;
1636 }
1637 (*s)++;
1638 }
1639 if (us)
1640 do {
1641 (*s)--;
1642 } while (**s == '_');
1643 return 1;
1644 }
1645
1646 inline static int
islettere(int c)1647 islettere(int c)
1648 {
1649 return (c == 'e' || c == 'E');
1650 }
1651
1652 static int
read_num(const char ** s,int strict,char ** b)1653 read_num(const char **s, int strict,
1654 char **b)
1655 {
1656 if (**s != '.') {
1657 if (!read_digits(s, strict, b))
1658 return 0;
1659 }
1660
1661 if (**s == '.') {
1662 **b = **s;
1663 (*s)++;
1664 (*b)++;
1665 if (!read_digits(s, strict, b)) {
1666 (*b)--;
1667 return 0;
1668 }
1669 }
1670
1671 if (islettere(**s)) {
1672 **b = **s;
1673 (*s)++;
1674 (*b)++;
1675 read_sign(s, b);
1676 if (!read_digits(s, strict, b)) {
1677 (*b)--;
1678 return 0;
1679 }
1680 }
1681 return 1;
1682 }
1683
1684 inline static int
read_den(const char ** s,int strict,char ** b)1685 read_den(const char **s, int strict,
1686 char **b)
1687 {
1688 if (!read_digits(s, strict, b))
1689 return 0;
1690 return 1;
1691 }
1692
1693 static int
read_rat_nos(const char ** s,int strict,char ** b)1694 read_rat_nos(const char **s, int strict,
1695 char **b)
1696 {
1697 if (!read_num(s, strict, b))
1698 return 0;
1699 if (**s == '/') {
1700 **b = **s;
1701 (*s)++;
1702 (*b)++;
1703 if (!read_den(s, strict, b)) {
1704 (*b)--;
1705 return 0;
1706 }
1707 }
1708 return 1;
1709 }
1710
1711 static int
read_rat(const char ** s,int strict,char ** b)1712 read_rat(const char **s, int strict,
1713 char **b)
1714 {
1715 read_sign(s, b);
1716 if (!read_rat_nos(s, strict, b))
1717 return 0;
1718 return 1;
1719 }
1720
1721 inline static int
isimagunit(int c)1722 isimagunit(int c)
1723 {
1724 return (c == 'i' || c == 'I' ||
1725 c == 'j' || c == 'J');
1726 }
1727
1728 static VALUE
str2num(char * s)1729 str2num(char *s)
1730 {
1731 if (strchr(s, '/'))
1732 return rb_cstr_to_rat(s, 0);
1733 if (strpbrk(s, ".eE"))
1734 return DBL2NUM(rb_cstr_to_dbl(s, 0));
1735 return rb_cstr_to_inum(s, 10, 0);
1736 }
1737
1738 static int
read_comp(const char ** s,int strict,VALUE * ret,char ** b)1739 read_comp(const char **s, int strict,
1740 VALUE *ret, char **b)
1741 {
1742 char *bb;
1743 int sign;
1744 VALUE num, num2;
1745
1746 bb = *b;
1747
1748 sign = read_sign(s, b);
1749
1750 if (isimagunit(**s)) {
1751 (*s)++;
1752 num = INT2FIX((sign == '-') ? -1 : + 1);
1753 *ret = rb_complex_new2(ZERO, num);
1754 return 1; /* e.g. "i" */
1755 }
1756
1757 if (!read_rat_nos(s, strict, b)) {
1758 **b = '\0';
1759 num = str2num(bb);
1760 *ret = rb_complex_new2(num, ZERO);
1761 return 0; /* e.g. "-" */
1762 }
1763 **b = '\0';
1764 num = str2num(bb);
1765
1766 if (isimagunit(**s)) {
1767 (*s)++;
1768 *ret = rb_complex_new2(ZERO, num);
1769 return 1; /* e.g. "3i" */
1770 }
1771
1772 if (**s == '@') {
1773 int st;
1774
1775 (*s)++;
1776 bb = *b;
1777 st = read_rat(s, strict, b);
1778 **b = '\0';
1779 if (strlen(bb) < 1 ||
1780 !isdecimal(*(bb + strlen(bb) - 1))) {
1781 *ret = rb_complex_new2(num, ZERO);
1782 return 0; /* e.g. "1@-" */
1783 }
1784 num2 = str2num(bb);
1785 *ret = rb_complex_new_polar(num, num2);
1786 if (!st)
1787 return 0; /* e.g. "1@2." */
1788 else
1789 return 1; /* e.g. "1@2" */
1790 }
1791
1792 if (issign(**s)) {
1793 bb = *b;
1794 sign = read_sign(s, b);
1795 if (isimagunit(**s))
1796 num2 = INT2FIX((sign == '-') ? -1 : + 1);
1797 else {
1798 if (!read_rat_nos(s, strict, b)) {
1799 *ret = rb_complex_new2(num, ZERO);
1800 return 0; /* e.g. "1+xi" */
1801 }
1802 **b = '\0';
1803 num2 = str2num(bb);
1804 }
1805 if (!isimagunit(**s)) {
1806 *ret = rb_complex_new2(num, ZERO);
1807 return 0; /* e.g. "1+3x" */
1808 }
1809 (*s)++;
1810 *ret = rb_complex_new2(num, num2);
1811 return 1; /* e.g. "1+2i" */
1812 }
1813 /* !(@, - or +) */
1814 {
1815 *ret = rb_complex_new2(num, ZERO);
1816 return 1; /* e.g. "3" */
1817 }
1818 }
1819
1820 inline static void
skip_ws(const char ** s)1821 skip_ws(const char **s)
1822 {
1823 while (isspace((unsigned char)**s))
1824 (*s)++;
1825 }
1826
1827 static int
parse_comp(const char * s,int strict,VALUE * num)1828 parse_comp(const char *s, int strict, VALUE *num)
1829 {
1830 char *buf, *b;
1831 VALUE tmp;
1832 int ret = 1;
1833
1834 buf = ALLOCV_N(char, tmp, strlen(s) + 1);
1835 b = buf;
1836
1837 skip_ws(&s);
1838 if (!read_comp(&s, strict, num, &b)) {
1839 ret = 0;
1840 }
1841 else {
1842 skip_ws(&s);
1843
1844 if (strict)
1845 if (*s != '\0')
1846 ret = 0;
1847 }
1848 ALLOCV_END(tmp);
1849
1850 return ret;
1851 }
1852
1853 static VALUE
string_to_c_strict(VALUE self,int raise)1854 string_to_c_strict(VALUE self, int raise)
1855 {
1856 char *s;
1857 VALUE num;
1858
1859 rb_must_asciicompat(self);
1860
1861 s = RSTRING_PTR(self);
1862
1863 if (!s || memchr(s, '\0', RSTRING_LEN(self))) {
1864 if (!raise) return Qnil;
1865 rb_raise(rb_eArgError, "string contains null byte");
1866 }
1867
1868 if (s && s[RSTRING_LEN(self)]) {
1869 rb_str_modify(self);
1870 s = RSTRING_PTR(self);
1871 s[RSTRING_LEN(self)] = '\0';
1872 }
1873
1874 if (!s)
1875 s = (char *)"";
1876
1877 if (!parse_comp(s, 1, &num)) {
1878 if (!raise) return Qnil;
1879 rb_raise(rb_eArgError, "invalid value for convert(): %+"PRIsVALUE,
1880 self);
1881 }
1882
1883 return num;
1884 }
1885
1886 /*
1887 * call-seq:
1888 * str.to_c -> complex
1889 *
1890 * Returns a complex which denotes the string form. The parser
1891 * ignores leading whitespaces and trailing garbage. Any digit
1892 * sequences can be separated by an underscore. Returns zero for null
1893 * or garbage string.
1894 *
1895 * '9'.to_c #=> (9+0i)
1896 * '2.5'.to_c #=> (2.5+0i)
1897 * '2.5/1'.to_c #=> ((5/2)+0i)
1898 * '-3/2'.to_c #=> ((-3/2)+0i)
1899 * '-i'.to_c #=> (0-1i)
1900 * '45i'.to_c #=> (0+45i)
1901 * '3-4i'.to_c #=> (3-4i)
1902 * '-4e2-4e-2i'.to_c #=> (-400.0-0.04i)
1903 * '-0.0-0.0i'.to_c #=> (-0.0-0.0i)
1904 * '1/2+3/4i'.to_c #=> ((1/2)+(3/4)*i)
1905 * 'ruby'.to_c #=> (0+0i)
1906 *
1907 * See Kernel.Complex.
1908 */
1909 static VALUE
string_to_c(VALUE self)1910 string_to_c(VALUE self)
1911 {
1912 char *s;
1913 VALUE num;
1914
1915 rb_must_asciicompat(self);
1916
1917 s = RSTRING_PTR(self);
1918
1919 if (s && s[RSTRING_LEN(self)]) {
1920 rb_str_modify(self);
1921 s = RSTRING_PTR(self);
1922 s[RSTRING_LEN(self)] = '\0';
1923 }
1924
1925 if (!s)
1926 s = (char *)"";
1927
1928 (void)parse_comp(s, 0, &num);
1929
1930 return num;
1931 }
1932
1933 static VALUE
to_complex(VALUE val)1934 to_complex(VALUE val)
1935 {
1936 return rb_convert_type(val, T_COMPLEX, "Complex", "to_c");
1937 }
1938
1939 static VALUE
nucomp_convert(VALUE klass,VALUE a1,VALUE a2,int raise)1940 nucomp_convert(VALUE klass, VALUE a1, VALUE a2, int raise)
1941 {
1942 if (NIL_P(a1) || NIL_P(a2)) {
1943 if (!raise) return Qnil;
1944 rb_raise(rb_eTypeError, "can't convert nil into Complex");
1945 }
1946
1947 if (RB_TYPE_P(a1, T_STRING)) {
1948 a1 = string_to_c_strict(a1, raise);
1949 if (NIL_P(a1)) return Qnil;
1950 }
1951
1952 if (RB_TYPE_P(a2, T_STRING)) {
1953 a2 = string_to_c_strict(a2, raise);
1954 if (NIL_P(a2)) return Qnil;
1955 }
1956
1957 if (RB_TYPE_P(a1, T_COMPLEX)) {
1958 {
1959 get_dat1(a1);
1960
1961 if (k_exact_zero_p(dat->imag))
1962 a1 = dat->real;
1963 }
1964 }
1965
1966 if (RB_TYPE_P(a2, T_COMPLEX)) {
1967 {
1968 get_dat1(a2);
1969
1970 if (k_exact_zero_p(dat->imag))
1971 a2 = dat->real;
1972 }
1973 }
1974
1975 if (RB_TYPE_P(a1, T_COMPLEX)) {
1976 if (a2 == Qundef || (k_exact_zero_p(a2)))
1977 return a1;
1978 }
1979
1980 if (a2 == Qundef) {
1981 if (k_numeric_p(a1) && !f_real_p(a1))
1982 return a1;
1983 /* should raise exception for consistency */
1984 if (!k_numeric_p(a1)) {
1985 if (!raise)
1986 return rb_protect(to_complex, a1, NULL);
1987 return to_complex(a1);
1988 }
1989 }
1990 else {
1991 if ((k_numeric_p(a1) && k_numeric_p(a2)) &&
1992 (!f_real_p(a1) || !f_real_p(a2)))
1993 return f_add(a1,
1994 f_mul(a2,
1995 f_complex_new_bang2(rb_cComplex, ZERO, ONE)));
1996 }
1997
1998 {
1999 int argc;
2000 VALUE argv2[2];
2001 argv2[0] = a1;
2002 if (a2 == Qundef) {
2003 argv2[1] = Qnil;
2004 argc = 1;
2005 }
2006 else {
2007 if (!raise && !RB_INTEGER_TYPE_P(a2) && !RB_FLOAT_TYPE_P(a2) && !RB_TYPE_P(a2, T_RATIONAL))
2008 return Qnil;
2009 argv2[1] = a2;
2010 argc = 2;
2011 }
2012 return nucomp_s_new(argc, argv2, klass);
2013 }
2014 }
2015
2016 static VALUE
nucomp_s_convert(int argc,VALUE * argv,VALUE klass)2017 nucomp_s_convert(int argc, VALUE *argv, VALUE klass)
2018 {
2019 VALUE a1, a2;
2020
2021 if (rb_scan_args(argc, argv, "11", &a1, &a2) == 1) {
2022 a2 = Qundef;
2023 }
2024
2025 return nucomp_convert(klass, a1, a2, TRUE);
2026 }
2027
2028 /* --- */
2029
2030 /*
2031 * call-seq:
2032 * num.real -> self
2033 *
2034 * Returns self.
2035 */
2036 static VALUE
numeric_real(VALUE self)2037 numeric_real(VALUE self)
2038 {
2039 return self;
2040 }
2041
2042 /*
2043 * call-seq:
2044 * num.imag -> 0
2045 * num.imaginary -> 0
2046 *
2047 * Returns zero.
2048 */
2049 static VALUE
numeric_imag(VALUE self)2050 numeric_imag(VALUE self)
2051 {
2052 return INT2FIX(0);
2053 }
2054
2055 /*
2056 * call-seq:
2057 * num.abs2 -> real
2058 *
2059 * Returns square of self.
2060 */
2061 static VALUE
numeric_abs2(VALUE self)2062 numeric_abs2(VALUE self)
2063 {
2064 return f_mul(self, self);
2065 }
2066
2067 /*
2068 * call-seq:
2069 * num.arg -> 0 or float
2070 * num.angle -> 0 or float
2071 * num.phase -> 0 or float
2072 *
2073 * Returns 0 if the value is positive, pi otherwise.
2074 */
2075 static VALUE
numeric_arg(VALUE self)2076 numeric_arg(VALUE self)
2077 {
2078 if (f_positive_p(self))
2079 return INT2FIX(0);
2080 return DBL2NUM(M_PI);
2081 }
2082
2083 /*
2084 * call-seq:
2085 * num.rect -> array
2086 * num.rectangular -> array
2087 *
2088 * Returns an array; [num, 0].
2089 */
2090 static VALUE
numeric_rect(VALUE self)2091 numeric_rect(VALUE self)
2092 {
2093 return rb_assoc_new(self, INT2FIX(0));
2094 }
2095
2096 static VALUE float_arg(VALUE self);
2097
2098 /*
2099 * call-seq:
2100 * num.polar -> array
2101 *
2102 * Returns an array; [num.abs, num.arg].
2103 */
2104 static VALUE
numeric_polar(VALUE self)2105 numeric_polar(VALUE self)
2106 {
2107 VALUE abs, arg;
2108
2109 if (RB_INTEGER_TYPE_P(self)) {
2110 abs = rb_int_abs(self);
2111 arg = numeric_arg(self);
2112 }
2113 else if (RB_FLOAT_TYPE_P(self)) {
2114 abs = rb_float_abs(self);
2115 arg = float_arg(self);
2116 }
2117 else if (RB_TYPE_P(self, T_RATIONAL)) {
2118 abs = rb_rational_abs(self);
2119 arg = numeric_arg(self);
2120 }
2121 else {
2122 abs = f_abs(self);
2123 arg = f_arg(self);
2124 }
2125 return rb_assoc_new(abs, arg);
2126 }
2127
2128 /*
2129 * call-seq:
2130 * num.conj -> self
2131 * num.conjugate -> self
2132 *
2133 * Returns self.
2134 */
2135 static VALUE
numeric_conj(VALUE self)2136 numeric_conj(VALUE self)
2137 {
2138 return self;
2139 }
2140
2141 /*
2142 * call-seq:
2143 * flo.arg -> 0 or float
2144 * flo.angle -> 0 or float
2145 * flo.phase -> 0 or float
2146 *
2147 * Returns 0 if the value is positive, pi otherwise.
2148 */
2149 static VALUE
float_arg(VALUE self)2150 float_arg(VALUE self)
2151 {
2152 if (isnan(RFLOAT_VALUE(self)))
2153 return self;
2154 if (f_tpositive_p(self))
2155 return INT2FIX(0);
2156 return rb_const_get(rb_mMath, id_PI);
2157 }
2158
2159 /*
2160 * A complex number can be represented as a paired real number with
2161 * imaginary unit; a+bi. Where a is real part, b is imaginary part
2162 * and i is imaginary unit. Real a equals complex a+0i
2163 * mathematically.
2164 *
2165 * Complex object can be created as literal, and also by using
2166 * Kernel#Complex, Complex::rect, Complex::polar or to_c method.
2167 *
2168 * 2+1i #=> (2+1i)
2169 * Complex(1) #=> (1+0i)
2170 * Complex(2, 3) #=> (2+3i)
2171 * Complex.polar(2, 3) #=> (-1.9799849932008908+0.2822400161197344i)
2172 * 3.to_c #=> (3+0i)
2173 *
2174 * You can also create complex object from floating-point numbers or
2175 * strings.
2176 *
2177 * Complex(0.3) #=> (0.3+0i)
2178 * Complex('0.3-0.5i') #=> (0.3-0.5i)
2179 * Complex('2/3+3/4i') #=> ((2/3)+(3/4)*i)
2180 * Complex('1@2') #=> (-0.4161468365471424+0.9092974268256817i)
2181 *
2182 * 0.3.to_c #=> (0.3+0i)
2183 * '0.3-0.5i'.to_c #=> (0.3-0.5i)
2184 * '2/3+3/4i'.to_c #=> ((2/3)+(3/4)*i)
2185 * '1@2'.to_c #=> (-0.4161468365471424+0.9092974268256817i)
2186 *
2187 * A complex object is either an exact or an inexact number.
2188 *
2189 * Complex(1, 1) / 2 #=> ((1/2)+(1/2)*i)
2190 * Complex(1, 1) / 2.0 #=> (0.5+0.5i)
2191 */
2192 void
Init_Complex(void)2193 Init_Complex(void)
2194 {
2195 VALUE compat;
2196 #undef rb_intern
2197 #define rb_intern(str) rb_intern_const(str)
2198
2199 id_abs = rb_intern("abs");
2200 id_arg = rb_intern("arg");
2201 id_denominator = rb_intern("denominator");
2202 id_fdiv = rb_intern("fdiv");
2203 id_numerator = rb_intern("numerator");
2204 id_quo = rb_intern("quo");
2205 id_real_p = rb_intern("real?");
2206 id_i_real = rb_intern("@real");
2207 id_i_imag = rb_intern("@image"); /* @image, not @imag */
2208 id_finite_p = rb_intern("finite?");
2209 id_infinite_p = rb_intern("infinite?");
2210 id_rationalize = rb_intern("rationalize");
2211 id_PI = rb_intern("PI");
2212
2213 rb_cComplex = rb_define_class("Complex", rb_cNumeric);
2214
2215 rb_define_alloc_func(rb_cComplex, nucomp_s_alloc);
2216 rb_undef_method(CLASS_OF(rb_cComplex), "allocate");
2217
2218 rb_undef_method(CLASS_OF(rb_cComplex), "new");
2219
2220 rb_define_singleton_method(rb_cComplex, "rectangular", nucomp_s_new, -1);
2221 rb_define_singleton_method(rb_cComplex, "rect", nucomp_s_new, -1);
2222 rb_define_singleton_method(rb_cComplex, "polar", nucomp_s_polar, -1);
2223
2224 rb_define_global_function("Complex", nucomp_f_complex, -1);
2225
2226 rb_undef_methods_from(rb_cComplex, rb_mComparable);
2227 rb_undef_method(rb_cComplex, "%");
2228 rb_undef_method(rb_cComplex, "<=>");
2229 rb_undef_method(rb_cComplex, "div");
2230 rb_undef_method(rb_cComplex, "divmod");
2231 rb_undef_method(rb_cComplex, "floor");
2232 rb_undef_method(rb_cComplex, "ceil");
2233 rb_undef_method(rb_cComplex, "modulo");
2234 rb_undef_method(rb_cComplex, "remainder");
2235 rb_undef_method(rb_cComplex, "round");
2236 rb_undef_method(rb_cComplex, "step");
2237 rb_undef_method(rb_cComplex, "truncate");
2238 rb_undef_method(rb_cComplex, "i");
2239
2240 rb_define_method(rb_cComplex, "real", rb_complex_real, 0);
2241 rb_define_method(rb_cComplex, "imaginary", rb_complex_imag, 0);
2242 rb_define_method(rb_cComplex, "imag", rb_complex_imag, 0);
2243
2244 rb_define_method(rb_cComplex, "-@", rb_complex_uminus, 0);
2245 rb_define_method(rb_cComplex, "+", rb_complex_plus, 1);
2246 rb_define_method(rb_cComplex, "-", rb_complex_minus, 1);
2247 rb_define_method(rb_cComplex, "*", rb_complex_mul, 1);
2248 rb_define_method(rb_cComplex, "/", rb_complex_div, 1);
2249 rb_define_method(rb_cComplex, "quo", nucomp_quo, 1);
2250 rb_define_method(rb_cComplex, "fdiv", nucomp_fdiv, 1);
2251 rb_define_method(rb_cComplex, "**", rb_complex_pow, 1);
2252
2253 rb_define_method(rb_cComplex, "==", nucomp_eqeq_p, 1);
2254 rb_define_method(rb_cComplex, "coerce", nucomp_coerce, 1);
2255
2256 rb_define_method(rb_cComplex, "abs", rb_complex_abs, 0);
2257 rb_define_method(rb_cComplex, "magnitude", rb_complex_abs, 0);
2258 rb_define_method(rb_cComplex, "abs2", nucomp_abs2, 0);
2259 rb_define_method(rb_cComplex, "arg", rb_complex_arg, 0);
2260 rb_define_method(rb_cComplex, "angle", rb_complex_arg, 0);
2261 rb_define_method(rb_cComplex, "phase", rb_complex_arg, 0);
2262 rb_define_method(rb_cComplex, "rectangular", nucomp_rect, 0);
2263 rb_define_method(rb_cComplex, "rect", nucomp_rect, 0);
2264 rb_define_method(rb_cComplex, "polar", nucomp_polar, 0);
2265 rb_define_method(rb_cComplex, "conjugate", rb_complex_conjugate, 0);
2266 rb_define_method(rb_cComplex, "conj", rb_complex_conjugate, 0);
2267
2268 rb_define_method(rb_cComplex, "real?", nucomp_false, 0);
2269
2270 rb_define_method(rb_cComplex, "numerator", nucomp_numerator, 0);
2271 rb_define_method(rb_cComplex, "denominator", nucomp_denominator, 0);
2272
2273 rb_define_method(rb_cComplex, "hash", nucomp_hash, 0);
2274 rb_define_method(rb_cComplex, "eql?", nucomp_eql_p, 1);
2275
2276 rb_define_method(rb_cComplex, "to_s", nucomp_to_s, 0);
2277 rb_define_method(rb_cComplex, "inspect", nucomp_inspect, 0);
2278
2279 rb_undef_method(rb_cComplex, "positive?");
2280 rb_undef_method(rb_cComplex, "negative?");
2281
2282 rb_define_method(rb_cComplex, "finite?", rb_complex_finite_p, 0);
2283 rb_define_method(rb_cComplex, "infinite?", rb_complex_infinite_p, 0);
2284
2285 rb_define_private_method(rb_cComplex, "marshal_dump", nucomp_marshal_dump, 0);
2286 /* :nodoc: */
2287 compat = rb_define_class_under(rb_cComplex, "compatible", rb_cObject);
2288 rb_define_private_method(compat, "marshal_load", nucomp_marshal_load, 1);
2289 rb_marshal_define_compat(rb_cComplex, compat, nucomp_dumper, nucomp_loader);
2290
2291 /* --- */
2292
2293 rb_define_method(rb_cComplex, "to_i", nucomp_to_i, 0);
2294 rb_define_method(rb_cComplex, "to_f", nucomp_to_f, 0);
2295 rb_define_method(rb_cComplex, "to_r", nucomp_to_r, 0);
2296 rb_define_method(rb_cComplex, "rationalize", nucomp_rationalize, -1);
2297 rb_define_method(rb_cComplex, "to_c", nucomp_to_c, 0);
2298 rb_define_method(rb_cNilClass, "to_c", nilclass_to_c, 0);
2299 rb_define_method(rb_cNumeric, "to_c", numeric_to_c, 0);
2300
2301 rb_define_method(rb_cString, "to_c", string_to_c, 0);
2302
2303 rb_define_private_method(CLASS_OF(rb_cComplex), "convert", nucomp_s_convert, -1);
2304
2305 /* --- */
2306
2307 rb_define_method(rb_cNumeric, "real", numeric_real, 0);
2308 rb_define_method(rb_cNumeric, "imaginary", numeric_imag, 0);
2309 rb_define_method(rb_cNumeric, "imag", numeric_imag, 0);
2310 rb_define_method(rb_cNumeric, "abs2", numeric_abs2, 0);
2311 rb_define_method(rb_cNumeric, "arg", numeric_arg, 0);
2312 rb_define_method(rb_cNumeric, "angle", numeric_arg, 0);
2313 rb_define_method(rb_cNumeric, "phase", numeric_arg, 0);
2314 rb_define_method(rb_cNumeric, "rectangular", numeric_rect, 0);
2315 rb_define_method(rb_cNumeric, "rect", numeric_rect, 0);
2316 rb_define_method(rb_cNumeric, "polar", numeric_polar, 0);
2317 rb_define_method(rb_cNumeric, "conjugate", numeric_conj, 0);
2318 rb_define_method(rb_cNumeric, "conj", numeric_conj, 0);
2319
2320 rb_define_method(rb_cFloat, "arg", float_arg, 0);
2321 rb_define_method(rb_cFloat, "angle", float_arg, 0);
2322 rb_define_method(rb_cFloat, "phase", float_arg, 0);
2323
2324 /*
2325 * The imaginary unit.
2326 */
2327 rb_define_const(rb_cComplex, "I",
2328 f_complex_new_bang2(rb_cComplex, ZERO, ONE));
2329
2330 #if !USE_FLONUM
2331 rb_gc_register_mark_object(RFLOAT_0 = DBL2NUM(0.0));
2332 #endif
2333
2334 rb_provide("complex.so"); /* for backward compatibility */
2335 }
2336
2337 /*
2338 Local variables:
2339 c-file-style: "ruby"
2340 End:
2341 */
2342