math.c

   1 /**********************************************************************
   2
   3   math.c -
   4
   5   $Author$
   6   created at: Tue Jan 25 14:12:56 JST 1994
   7
   8   Copyright (C) 1993-2007 Yukihiro Matsumoto
   9
  10 **********************************************************************/
  11
  12 #include "ruby/ruby.h"
  13 #include <math.h>
  14 #include <errno.h>
  15
  16 VALUE rb_mMath;
  17
  18 static VALUE
  19 to_flo(VALUE x)
  20 {
  21     if (!rb_obj_is_kind_of(x, rb_cNumeric)) {
  22         rb_raise(rb_eTypeError, "can't convert %s into Float",
  23                  NIL_P(x) ? "nil" :
  24                  x == Qtrue ? "true" :
  25                  x == Qfalse ? "false" :
  26                  rb_obj_classname(x));
  27     }
  28     return rb_convert_type(x, T_FLOAT, "Float", "to_f");
  29 }
  30
  31 #define Need_Float(x) (x) = to_flo(x)
  32 #define Need_Float2(x,y) do {\
  33     Need_Float(x);\
  34     Need_Float(y);\
  35 } while (0)
  36
  37 static void
  38 domain_check(double x, const char *msg)
  39 {
  40     while(1) {
  41         if (errno) {
  42             rb_sys_fail(msg);
  43         }
  44         if (isnan(x)) {
  45 #if defined(EDOM)
  46             errno = EDOM;
  47 #elif defined(ERANGE)
  48             errno = ERANGE;
  49 #endif
  50             continue;
  51         }
  52         break;
  53     }
  54 }
  55
  56 static void
  57 infinity_check(VALUE arg, double res, const char *msg)
  58 {
  59     while(1) {
  60         if (errno) {
  61             rb_sys_fail(msg);
  62         }
  63         if (isinf(res) && !isinf(RFLOAT_VALUE(arg))) {
  64 #if defined(EDOM)
  65             errno = EDOM;
  66 #elif defined(ERANGE)
  67             errno = ERANGE;
  68 #endif
  69             continue;
  70         }
  71         break;
  72     }
  73 }
  74
  75 /*
  76  *  call-seq:
  77  *     Math.atan2(y, x)  => float
  78  *
  79  *  Computes the arc tangent given <i>y</i> and <i>x</i>. Returns
  80  *  -PI..PI.
  81  *
  82  */
  83
  84 VALUE
  85 math_atan2(VALUE obj, VALUE y, VALUE x)
  86 {
  87     Need_Float2(y, x);
  88     return DOUBLE2NUM(atan2(RFLOAT_VALUE(y), RFLOAT_VALUE(x)));
  89 }
  90
  91
  92 /*
  93  *  call-seq:
  94  *     Math.cos(x)    => float
  95  *
  96  *  Computes the cosine of <i>x</i> (expressed in radians). Returns
  97  *  -1..1.
  98  */
  99
 100 VALUE
 101 math_cos(VALUE obj, VALUE x)
 102 {
 103     Need_Float(x);
 104     return DOUBLE2NUM(cos(RFLOAT_VALUE(x)));
 105 }
 106
 107 /*
 108  *  call-seq:
 109  *     Math.sin(x)    => float
 110  *
 111  *  Computes the sine of <i>x</i> (expressed in radians). Returns
 112  *  -1..1.
 113  */
 114
 115 VALUE
 116 math_sin(VALUE obj, VALUE x)
 117 {
 118     Need_Float(x);
 119
 120     return DOUBLE2NUM(sin(RFLOAT_VALUE(x)));
 121 }
 122
 123
 124 /*
 125  *  call-seq:
 126  *     Math.tan(x)    => float
 127  *
 128  *  Returns the tangent of <i>x</i> (expressed in radians).
 129  */
 130
 131 static VALUE
 132 math_tan(VALUE obj, VALUE x)
 133 {
 134     Need_Float(x);
 135
 136     return DOUBLE2NUM(tan(RFLOAT_VALUE(x)));
 137 }
 138
 139 /*
 140  *  call-seq:
 141  *     Math.acos(x)    => float
 142  *
 143  *  Computes the arc cosine of <i>x</i>. Returns 0..PI.
 144  */
 145
 146 static VALUE
 147 math_acos(VALUE obj, VALUE x)
 148 {
 149     double d;
 150
 151     Need_Float(x);
 152     errno = 0;
 153     d = acos(RFLOAT_VALUE(x));
 154     domain_check(d, "acos");
 155     return DOUBLE2NUM(d);
 156 }
 157
 158 /*
 159  *  call-seq:
 160  *     Math.asin(x)    => float
 161  *
 162  *  Computes the arc sine of <i>x</i>. Returns -{PI/2} .. {PI/2}.
 163  */
 164
 165 static VALUE
 166 math_asin(VALUE obj, VALUE x)
 167 {
 168     double d;
 169
 170     Need_Float(x);
 171     errno = 0;
 172     d = asin(RFLOAT_VALUE(x));
 173     domain_check(d, "asin");
 174     return DOUBLE2NUM(d);
 175 }
 176
 177 /*
 178  *  call-seq:
 179  *     Math.atan(x)    => float
 180  *
 181  *  Computes the arc tangent of <i>x</i>. Returns -{PI/2} .. {PI/2}.
 182  */
 183
 184 static VALUE
 185 math_atan(VALUE obj, VALUE x)
 186 {
 187     Need_Float(x);
 188     return DOUBLE2NUM(atan(RFLOAT_VALUE(x)));
 189 }
 190
 191 #ifndef HAVE_COSH
 192 double
 193 cosh(double x)
 194 {
 195     return (exp(x) + exp(-x)) / 2;
 196 }
 197 #endif
 198
 199 /*
 200  *  call-seq:
 201  *     Math.cosh(x)    => float
 202  *
 203  *  Computes the hyperbolic cosine of <i>x</i> (expressed in radians).
 204  */
 205
 206 VALUE
 207 math_cosh(VALUE obj, VALUE x)
 208 {
 209     Need_Float(x);
 210
 211     return DOUBLE2NUM(cosh(RFLOAT_VALUE(x)));
 212 }
 213
 214 #ifndef HAVE_SINH
 215 double
 216 sinh(double x)
 217 {
 218     return (exp(x) - exp(-x)) / 2;
 219 }
 220 #endif
 221
 222 /*
 223  *  call-seq:
 224  *     Math.sinh(x)    => float
 225  *
 226  *  Computes the hyperbolic sine of <i>x</i> (expressed in
 227  *  radians).
 228  */
 229
 230 VALUE
 231 math_sinh(VALUE obj, VALUE x)
 232 {
 233     Need_Float(x);
 234     return DOUBLE2NUM(sinh(RFLOAT_VALUE(x)));
 235 }
 236
 237 #ifndef HAVE_TANH
 238 double
 239 tanh(double x)
 240 {
 241     return sinh(x) / cosh(x);
 242 }
 243 #endif
 244
 245 /*
 246  *  call-seq:
 247  *     Math.tanh()    => float
 248  *
 249  *  Computes the hyperbolic tangent of <i>x</i> (expressed in
 250  *  radians).
 251  */
 252
 253 static VALUE
 254 math_tanh(VALUE obj, VALUE x)
 255 {
 256     Need_Float(x);
 257     return DOUBLE2NUM(tanh(RFLOAT_VALUE(x)));
 258 }
 259
 260 /*
 261  *  call-seq:
 262  *     Math.acosh(x)    => float
 263  *
 264  *  Computes the inverse hyperbolic cosine of <i>x</i>.
 265  */
 266
 267 static VALUE
 268 math_acosh(VALUE obj, VALUE x)
 269 {
 270     double d;
 271
 272     Need_Float(x);
 273     errno = 0;
 274     d = acosh(RFLOAT_VALUE(x));
 275     domain_check(d, "acosh");
 276     return DOUBLE2NUM(d);
 277 }
 278
 279 /*
 280  *  call-seq:
 281  *     Math.asinh(x)    => float
 282  *
 283  *  Computes the inverse hyperbolic sine of <i>x</i>.
 284  */
 285
 286 static VALUE
 287 math_asinh(VALUE obj, VALUE x)
 288 {
 289     Need_Float(x);
 290     return DOUBLE2NUM(asinh(RFLOAT_VALUE(x)));
 291 }
 292
 293 /*
 294  *  call-seq:
 295  *     Math.atanh(x)    => float
 296  *
 297  *  Computes the inverse hyperbolic tangent of <i>x</i>.
 298  */
 299
 300 static VALUE
 301 math_atanh(VALUE obj, VALUE x)
 302 {
 303     double d;
 304
 305     Need_Float(x);
 306     errno = 0;
 307     d = atanh(RFLOAT_VALUE(x));
 308     domain_check(d, "atanh");
 309     infinity_check(x, d, "atanh");
 310     return DOUBLE2NUM(d);
 311 }
 312
 313 /*
 314  *  call-seq:
 315  *     Math.exp(x)    => float
 316  *
 317  *  Returns e**x.
 318  */
 319
 320 VALUE
 321 math_exp(VALUE obj, VALUE x)
 322 {
 323     Need_Float(x);
 324     return DOUBLE2NUM(exp(RFLOAT_VALUE(x)));
 325 }
 326
 327 #if defined __CYGWIN__
 328 # include <cygwin/version.h>
 329 # if CYGWIN_VERSION_DLL_MAJOR < 1005
 330 #  define nan(x) nan()
 331 # endif
 332 # define log(x) ((x) < 0.0 ? nan("") : log(x))
 333 # define log10(x) ((x) < 0.0 ? nan("") : log10(x))
 334 #endif
 335
 336 /*
 337  *  call-seq:
 338  *     Math.log(numeric)    => float
 339  *     Math.log(num,base)   => float
 340  *
 341  *  Returns the natural logarithm of <i>numeric</i>.
 342  *  If additional second argument is given, it will be the base
 343  *  of logarithm.
 344  */
 345
 346 VALUE
 347 math_log(int argc, VALUE *argv)
 348 {
 349     VALUE x, base;
 350     double d;
 351
 352     rb_scan_args(argc, argv, "11", &x, &base);
 353     Need_Float(x);
 354     errno = 0;
 355     d = log(RFLOAT_VALUE(x));
 356     if (!NIL_P(base)) {
 357         Need_Float(base);
 358         d /= log(RFLOAT_VALUE(base));
 359     }
 360     domain_check(d, "log");
 361     infinity_check(x, d, "log");
 362     return DOUBLE2NUM(d);
 363 }
 364
 365 #ifndef log2
 366 #ifndef HAVE_LOG2
 367 double
 368 log2(double x)
 369 {
 370     return log10(x)/log10(2.0);
 371 }
 372 #else
 373 extern double log2(double);
 374 #endif
 375 #endif
 376
 377 /*
 378  *  call-seq:
 379  *     Math.log2(numeric)    => float
 380  *
 381  *  Returns the base 2 logarithm of <i>numeric</i>.
 382  */
 383
 384 static VALUE
 385 math_log2(VALUE obj, VALUE x)
 386 {
 387     double d;
 388
 389     Need_Float(x);
 390     errno = 0;
 391     d = log2(RFLOAT_VALUE(x));
 392     domain_check(d, "log2");
 393     infinity_check(x, d, "log2");
 394     return DOUBLE2NUM(d);
 395 }
 396
 397 /*
 398  *  call-seq:
 399  *     Math.log10(numeric)    => float
 400  *
 401  *  Returns the base 10 logarithm of <i>numeric</i>.
 402  */
 403
 404 static VALUE
 405 math_log10(VALUE obj, VALUE x)
 406 {
 407     double d;
 408
 409     Need_Float(x);
 410     errno = 0;
 411     d = log10(RFLOAT_VALUE(x));
 412     domain_check(d, "log10");
 413     infinity_check(x, d, "log10");
 414     return DOUBLE2NUM(d);
 415 }
 416
 417 /*
 418  *  call-seq:
 419  *     Math.sqrt(numeric)    => float
 420  *
 421  *  Returns the non-negative square root of <i>numeric</i>.
 422  *
 423  *    0.upto(10) {|x|
 424  *      p [x, Math.sqrt(x), Math.sqrt(x)**2]
 425  *    }
 426  *    #=>
 427  *    [0, 0.0, 0.0]
 428  *    [1, 1.0, 1.0]
 429  *    [2, 1.4142135623731, 2.0]
 430  *    [3, 1.73205080756888, 3.0]
 431  *    [4, 2.0, 4.0]
 432  *    [5, 2.23606797749979, 5.0]
 433  *    [6, 2.44948974278318, 6.0]
 434  *    [7, 2.64575131106459, 7.0]
 435  *    [8, 2.82842712474619, 8.0]
 436  *    [9, 3.0, 9.0]
 437  *    [10, 3.16227766016838, 10.0]
 438  *
 439  */
 440
 441 VALUE
 442 math_sqrt(VALUE obj, VALUE x)
 443 {
 444     double d;
 445
 446     Need_Float(x);
 447     errno = 0;
 448     d = sqrt(RFLOAT_VALUE(x));
 449     domain_check(d, "sqrt");
 450     return DOUBLE2NUM(d);
 451 }
 452
 453 /*
 454  *  call-seq:
 455  *     Math.cbrt(numeric)    => float
 456  *
 457  *  Returns the cube root of <i>numeric</i>.
 458  *
 459  *    -9.upto(9) {|x|
 460  *      p [x, Math.cbrt(x), Math.cbrt(x)**3]
 461  *    }
 462  *    #=>
 463  *    [-9, -2.0800838230519, -9.0]
 464  *    [-8, -2.0, -8.0]
 465  *    [-7, -1.91293118277239, -7.0]
 466  *    [-6, -1.81712059283214, -6.0]
 467  *    [-5, -1.7099759466767, -5.0]
 468  *    [-4, -1.5874010519682, -4.0]
 469  *    [-3, -1.44224957030741, -3.0]
 470  *    [-2, -1.25992104989487, -2.0]
 471  *    [-1, -1.0, -1.0]
 472  *    [0, 0.0, 0.0]
 473  *    [1, 1.0, 1.0]
 474  *    [2, 1.25992104989487, 2.0]
 475  *    [3, 1.44224957030741, 3.0]
 476  *    [4, 1.5874010519682, 4.0]
 477  *    [5, 1.7099759466767, 5.0]
 478  *    [6, 1.81712059283214, 6.0]
 479  *    [7, 1.91293118277239, 7.0]
 480  *    [8, 2.0, 8.0]
 481  *    [9, 2.0800838230519, 9.0]
 482  *
 483  */
 484
 485 static VALUE
 486 math_cbrt(VALUE obj, VALUE x)
 487 {
 488     Need_Float(x);
 489     return DOUBLE2NUM(cbrt(RFLOAT_VALUE(x)));
 490 }
 491
 492 /*
 493  *  call-seq:
 494  *     Math.frexp(numeric)    => [ fraction, exponent ]
 495  *
 496  *  Returns a two-element array containing the normalized fraction (a
 497  *  <code>Float</code>) and exponent (a <code>Fixnum</code>) of
 498  *  <i>numeric</i>.
 499  *
 500  *     fraction, exponent = Math.frexp(1234)   #=> [0.6025390625, 11]
 501  *     fraction * 2**exponent                  #=> 1234.0
 502  */
 503
 504 static VALUE
 505 math_frexp(VALUE obj, VALUE x)
 506 {
 507     double d;
 508     int exp;
 509
 510     Need_Float(x);
 511
 512     d = frexp(RFLOAT_VALUE(x), &exp);
 513     return rb_assoc_new(DOUBLE2NUM(d), INT2NUM(exp));
 514 }
 515
 516 /*
 517  *  call-seq:
 518  *     Math.ldexp(flt, int) -> float
 519  *
 520  *  Returns the value of <i>flt</i>*(2**<i>int</i>).
 521  *
 522  *     fraction, exponent = Math.frexp(1234)
 523  *     Math.ldexp(fraction, exponent)   #=> 1234.0
 524  */
 525
 526 static VALUE
 527 math_ldexp(VALUE obj, VALUE x, VALUE n)
 528 {
 529     Need_Float(x);
 530     return DOUBLE2NUM(ldexp(RFLOAT_VALUE(x), NUM2INT(n)));
 531 }
 532
 533 /*
 534  *  call-seq:
 535  *     Math.hypot(x, y)    => float
 536  *
 537  *  Returns sqrt(x**2 + y**2), the hypotenuse of a right-angled triangle
 538  *  with sides <i>x</i> and <i>y</i>.
 539  *
 540  *     Math.hypot(3, 4)   #=> 5.0
 541  */
 542
 543 VALUE
 544 math_hypot(VALUE obj, VALUE x, VALUE y)
 545 {
 546     Need_Float2(x, y);
 547     return DOUBLE2NUM(hypot(RFLOAT_VALUE(x), RFLOAT_VALUE(y)));
 548 }
 549
 550 /*
 551  * call-seq:
 552  *    Math.erf(x)  => float
 553  *
 554  *  Calculates the error function of x.
 555  */
 556
 557 static VALUE
 558 math_erf(VALUE obj, VALUE x)
 559 {
 560     Need_Float(x);
 561     return DOUBLE2NUM(erf(RFLOAT_VALUE(x)));
 562 }
 563
 564 /*
 565  * call-seq:
 566  *    Math.erfc(x)  => float
 567  *
 568  *  Calculates the complementary error function of x.
 569  */
 570
 571 static VALUE
 572 math_erfc(VALUE obj, VALUE x)
 573 {
 574     Need_Float(x);
 575     return DOUBLE2NUM(erfc(RFLOAT_VALUE(x)));
 576 }
 577
 578 /*
 579  * call-seq:
 580  *    Math.gamma(x)  => float
 581  *
 582  *  Calculates the gamma function of x.
 583  *
 584  *  Note that gamma(n) is same as fact(n-1) for integer n >= 0.
 585  *  However gamma(n) returns float and possibly has error in calculation.
 586  *
 587  *   def fact(n) (1..n).inject(1) {|r,i| r*i } end
 588  *   0.upto(25) {|i| p [i, Math.gamma(i+1), fact(i)] }
 589  *   #=>
 590  *   [0, 1.0, 1]
 591  *   [1, 1.0, 1]
 592  *   [2, 2.0, 2]
 593  *   [3, 6.0, 6]
 594  *   [4, 24.0, 24]
 595  *   [5, 120.0, 120]
 596  *   [6, 720.0, 720]
 597  *   [7, 5040.0, 5040]
 598  *   [8, 40320.0, 40320]
 599  *   [9, 362880.0, 362880]
 600  *   [10, 3628800.0, 3628800]
 601  *   [11, 39916800.0, 39916800]
 602  *   [12, 479001599.999999, 479001600]
 603  *   [13, 6227020800.00001, 6227020800]
 604  *   [14, 87178291199.9998, 87178291200]
 605  *   [15, 1307674368000.0, 1307674368000]
 606  *   [16, 20922789888000.0, 20922789888000]
 607  *   [17, 3.55687428096001e+14, 355687428096000]
 608  *   [18, 6.40237370572799e+15, 6402373705728000]
 609  *   [19, 1.21645100408832e+17, 121645100408832000]
 610  *   [20, 2.43290200817664e+18, 2432902008176640000]
 611  *   [21, 5.10909421717094e+19, 51090942171709440000]
 612  *   [22, 1.12400072777761e+21, 1124000727777607680000]
 613  *   [23, 2.58520167388851e+22, 25852016738884976640000]
 614  *   [24, 6.20448401733239e+23, 620448401733239439360000]
 615  *   [25, 1.5511210043331e+25, 15511210043330985984000000]
 616  *
 617  */
 618
 619 static VALUE
 620 math_gamma(VALUE obj, VALUE x)
 621 {
 622     double d;
 623     Need_Float(x);
 624     errno = 0;
 625     d = tgamma(RFLOAT_VALUE(x));
 626     domain_check(d, "gamma");
 627     return DOUBLE2NUM(d);
 628 }
 629
 630 /*
 631  * call-seq:
 632  *    Math.lgamma(x)  => [float, -1 or 1]
 633  *
 634  *  Calculates the logarithmic gamma of x and
 635  *  the sign of gamma of x.
 636  *
 637  *  Math.lgamma(x) is same as
 638  *   [Math.log(Math.gamma(x).abs), Math.gamma(x) < 0 ? -1 : 1]
 639  *  but avoid overflow by Math.gamma(x) for large x.
 640  */
 641
 642 static VALUE
 643 math_lgamma(VALUE obj, VALUE x)
 644 {
 645     double d;
 646     int sign;
 647     VALUE v;
 648     Need_Float(x);
 649     errno = 0;
 650     d = lgamma_r(RFLOAT_VALUE(x), &sign);
 651     domain_check(d, "lgamma");
 652     v = DOUBLE2NUM(d);
 653     return rb_assoc_new(v, INT2FIX(sign));
 654 }
 655
 656 /*
 657  *  The <code>Math</code> module contains module functions for basic
 658  *  trigonometric and transcendental functions. See class
 659  *  <code>Float</code> for a list of constants that
 660  *  define Ruby's floating point accuracy.
 661  */
 662
 663
 664 void
 665 Init_Math(void)
 666 {
 667     rb_mMath = rb_define_module("Math");
 668
 669 #ifdef M_PI
 670     rb_define_const(rb_mMath, "PI", DOUBLE2NUM(M_PI));
 671 #else
 672     rb_define_const(rb_mMath, "PI", DOUBLE2NUM(atan(1.0)*4.0));
 673 #endif
 674
 675 #ifdef M_E
 676     rb_define_const(rb_mMath, "E", DOUBLE2NUM(M_E));
 677 #else
 678     rb_define_const(rb_mMath, "E", DOUBLE2NUM(exp(1.0)));
 679 #endif
 680
 681     rb_define_module_function(rb_mMath, "atan2", math_atan2, 2);
 682     rb_define_module_function(rb_mMath, "cos", math_cos, 1);
 683     rb_define_module_function(rb_mMath, "sin", math_sin, 1);
 684     rb_define_module_function(rb_mMath, "tan", math_tan, 1);
 685
 686     rb_define_module_function(rb_mMath, "acos", math_acos, 1);
 687     rb_define_module_function(rb_mMath, "asin", math_asin, 1);
 688     rb_define_module_function(rb_mMath, "atan", math_atan, 1);
 689
 690     rb_define_module_function(rb_mMath, "cosh", math_cosh, 1);
 691     rb_define_module_function(rb_mMath, "sinh", math_sinh, 1);
 692     rb_define_module_function(rb_mMath, "tanh", math_tanh, 1);
 693
 694     rb_define_module_function(rb_mMath, "acosh", math_acosh, 1);
 695     rb_define_module_function(rb_mMath, "asinh", math_asinh, 1);
 696     rb_define_module_function(rb_mMath, "atanh", math_atanh, 1);
 697
 698     rb_define_module_function(rb_mMath, "exp", math_exp, 1);
 699     rb_define_module_function(rb_mMath, "log", math_log, -1);
 700     rb_define_module_function(rb_mMath, "log2", math_log2, 1);
 701     rb_define_module_function(rb_mMath, "log10", math_log10, 1);
 702     rb_define_module_function(rb_mMath, "sqrt", math_sqrt, 1);
 703     rb_define_module_function(rb_mMath, "cbrt", math_cbrt, 1);
 704
 705     rb_define_module_function(rb_mMath, "frexp", math_frexp, 1);
 706     rb_define_module_function(rb_mMath, "ldexp", math_ldexp, 2);
 707
 708     rb_define_module_function(rb_mMath, "hypot", math_hypot, 2);
 709
 710     rb_define_module_function(rb_mMath, "erf",  math_erf,  1);
 711     rb_define_module_function(rb_mMath, "erfc", math_erfc, 1);
 712
 713     rb_define_module_function(rb_mMath, "gamma", math_gamma, 1);
 714     rb_define_module_function(rb_mMath, "lgamma", math_lgamma, 1);
 715 }