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/internal/config.h"
  13
  14 #ifdef _MSC_VER
  15 # define _USE_MATH_DEFINES 1
  16 #endif
  17
  18 #include <errno.h>
  19 #include <float.h>
  20 #include <math.h>
  21
  22 #include "internal.h"
  23 #include "internal/bignum.h"
  24 #include "internal/complex.h"
  25 #include "internal/math.h"
  26 #include "internal/object.h"
  27 #include "internal/vm.h"
  28
  29 VALUE rb_mMath;
  30 VALUE rb_eMathDomainError;
  31
  32 #define Get_Double(x) rb_num_to_dbl(x)
  33
  34 #define domain_error(msg) \
  35     rb_raise(rb_eMathDomainError, "Numerical argument is out of domain - " msg)
  36 #define domain_check_min(val, min, msg) \
  37     ((val) < (min) ? domain_error(msg) : (void)0)
  38 #define domain_check_range(val, min, max, msg) \
  39     ((val) < (min) || (max) < (val) ? domain_error(msg) : (void)0)
  40
  41 /*
  42  *  call-seq:
  43  *     Math.atan2(y, x)  -> Float
  44  *
  45  *  Computes the arc tangent given +y+ and +x+.
  46  *  Returns a Float in the range -PI..PI. Return value is a angle
  47  *  in radians between the positive x-axis of cartesian plane
  48  *  and the point given by the coordinates (+x+, +y+) on it.
  49  *
  50  *  Domain: (-INFINITY, INFINITY)
  51  *
  52  *  Codomain: [-PI, PI]
  53  *
  54  *    Math.atan2(-0.0, -1.0) #=> -3.141592653589793
  55  *    Math.atan2(-1.0, -1.0) #=> -2.356194490192345
  56  *    Math.atan2(-1.0, 0.0)  #=> -1.5707963267948966
  57  *    Math.atan2(-1.0, 1.0)  #=> -0.7853981633974483
  58  *    Math.atan2(-0.0, 1.0)  #=> -0.0
  59  *    Math.atan2(0.0, 1.0)   #=> 0.0
  60  *    Math.atan2(1.0, 1.0)   #=> 0.7853981633974483
  61  *    Math.atan2(1.0, 0.0)   #=> 1.5707963267948966
  62  *    Math.atan2(1.0, -1.0)  #=> 2.356194490192345
  63  *    Math.atan2(0.0, -1.0)  #=> 3.141592653589793
  64  *    Math.atan2(INFINITY, INFINITY)   #=> 0.7853981633974483
  65  *    Math.atan2(INFINITY, -INFINITY)  #=> 2.356194490192345
  66  *    Math.atan2(-INFINITY, INFINITY)  #=> -0.7853981633974483
  67  *    Math.atan2(-INFINITY, -INFINITY) #=> -2.356194490192345
  68  *
  69  */
  70
  71 static VALUE
  72 math_atan2(VALUE unused_obj, VALUE y, VALUE x)
  73 {
  74     double dx, dy;
  75     dx = Get_Double(x);
  76     dy = Get_Double(y);
  77     if (dx == 0.0 && dy == 0.0) {
  78         if (!signbit(dx))
  79             return DBL2NUM(dy);
  80         if (!signbit(dy))
  81             return DBL2NUM(M_PI);
  82         return DBL2NUM(-M_PI);
  83     }
  84 #ifndef ATAN2_INF_C99
  85     if (isinf(dx) && isinf(dy)) {
  86         /* optimization for FLONUM */
  87         if (dx < 0.0) {
  88             const double dz = (3.0 * M_PI / 4.0);
  89             return (dy < 0.0) ? DBL2NUM(-dz) : DBL2NUM(dz);
  90         }
  91         else {
  92             const double dz = (M_PI / 4.0);
  93             return (dy < 0.0) ? DBL2NUM(-dz) : DBL2NUM(dz);
  94         }
  95     }
  96 #endif
  97     return DBL2NUM(atan2(dy, dx));
  98 }
  99
 100
 101 /*
 102  *  call-seq:
 103  *     Math.cos(x)    -> Float
 104  *
 105  *  Computes the cosine of +x+ (expressed in radians).
 106  *  Returns a Float in the range -1.0..1.0.
 107  *
 108  *  Domain: (-INFINITY, INFINITY)
 109  *
 110  *  Codomain: [-1, 1]
 111  *
 112  *    Math.cos(Math::PI) #=> -1.0
 113  *
 114  */
 115
 116 static VALUE
 117 math_cos(VALUE unused_obj, VALUE x)
 118 {
 119     return DBL2NUM(cos(Get_Double(x)));
 120 }
 121
 122 /*
 123  *  call-seq:
 124  *     Math.sin(x)    -> Float
 125  *
 126  *  Computes the sine of +x+ (expressed in radians).
 127  *  Returns a Float in the range -1.0..1.0.
 128  *
 129  *  Domain: (-INFINITY, INFINITY)
 130  *
 131  *  Codomain: [-1, 1]
 132  *
 133  *    Math.sin(Math::PI/2) #=> 1.0
 134  *
 135  */
 136
 137 static VALUE
 138 math_sin(VALUE unused_obj, VALUE x)
 139 {
 140     return DBL2NUM(sin(Get_Double(x)));
 141 }
 142
 143
 144 /*
 145  *  call-seq:
 146  *     Math.tan(x)    -> Float
 147  *
 148  *  Computes the tangent of +x+ (expressed in radians).
 149  *
 150  *  Domain: (-INFINITY, INFINITY)
 151  *
 152  *  Codomain: (-INFINITY, INFINITY)
 153  *
 154  *    Math.tan(0) #=> 0.0
 155  *
 156  */
 157
 158 static VALUE
 159 math_tan(VALUE unused_obj, VALUE x)
 160 {
 161     return DBL2NUM(tan(Get_Double(x)));
 162 }
 163
 164 /*
 165  *  call-seq:
 166  *     Math.acos(x)    -> Float
 167  *
 168  *  Computes the arc cosine of +x+. Returns 0..PI.
 169  *
 170  *  Domain: [-1, 1]
 171  *
 172  *  Codomain: [0, PI]
 173  *
 174  *    Math.acos(0) == Math::PI/2  #=> true
 175  *
 176  */
 177
 178 static VALUE
 179 math_acos(VALUE unused_obj, VALUE x)
 180 {
 181     double d;
 182
 183     d = Get_Double(x);
 184     domain_check_range(d, -1.0, 1.0, "acos");
 185     return DBL2NUM(acos(d));
 186 }
 187
 188 /*
 189  *  call-seq:
 190  *     Math.asin(x)    -> Float
 191  *
 192  *  Computes the arc sine of +x+. Returns -PI/2..PI/2.
 193  *
 194  *  Domain: [-1, -1]
 195  *
 196  *  Codomain: [-PI/2, PI/2]
 197  *
 198  *    Math.asin(1) == Math::PI/2  #=> true
 199  */
 200
 201 static VALUE
 202 math_asin(VALUE unused_obj, VALUE x)
 203 {
 204     double d;
 205
 206     d = Get_Double(x);
 207     domain_check_range(d, -1.0, 1.0, "asin");
 208     return DBL2NUM(asin(d));
 209 }
 210
 211 /*
 212  *  call-seq:
 213  *     Math.atan(x)    -> Float
 214  *
 215  *  Computes the arc tangent of +x+. Returns -PI/2..PI/2.
 216  *
 217  *  Domain: (-INFINITY, INFINITY)
 218  *
 219  *  Codomain: (-PI/2, PI/2)
 220  *
 221  *    Math.atan(0) #=> 0.0
 222  */
 223
 224 static VALUE
 225 math_atan(VALUE unused_obj, VALUE x)
 226 {
 227     return DBL2NUM(atan(Get_Double(x)));
 228 }
 229
 230 #ifndef HAVE_COSH
 231 double
 232 cosh(double x)
 233 {
 234     return (exp(x) + exp(-x)) / 2;
 235 }
 236 #endif
 237
 238 /*
 239  *  call-seq:
 240  *     Math.cosh(x)    -> Float
 241  *
 242  *  Computes the hyperbolic cosine of +x+ (expressed in radians).
 243  *
 244  *  Domain: (-INFINITY, INFINITY)
 245  *
 246  *  Codomain: [1, INFINITY)
 247  *
 248  *    Math.cosh(0) #=> 1.0
 249  *
 250  */
 251
 252 static VALUE
 253 math_cosh(VALUE unused_obj, VALUE x)
 254 {
 255     return DBL2NUM(cosh(Get_Double(x)));
 256 }
 257
 258 #ifndef HAVE_SINH
 259 double
 260 sinh(double x)
 261 {
 262     return (exp(x) - exp(-x)) / 2;
 263 }
 264 #endif
 265
 266 /*
 267  *  call-seq:
 268  *     Math.sinh(x)    -> Float
 269  *
 270  *  Computes the hyperbolic sine of +x+ (expressed in radians).
 271  *
 272  *  Domain: (-INFINITY, INFINITY)
 273  *
 274  *  Codomain: (-INFINITY, INFINITY)
 275  *
 276  *    Math.sinh(0) #=> 0.0
 277  *
 278  */
 279
 280 static VALUE
 281 math_sinh(VALUE unused_obj, VALUE x)
 282 {
 283     return DBL2NUM(sinh(Get_Double(x)));
 284 }
 285
 286 #ifndef HAVE_TANH
 287 double
 288 tanh(double x)
 289 {
 290 # if defined(HAVE_SINH) && defined(HAVE_COSH)
 291     const double c = cosh(x);
 292     if (!isinf(c)) return sinh(x) / c;
 293 # else
 294     const double e = exp(x+x);
 295     if (!isinf(e)) return (e - 1) / (e + 1);
 296 # endif
 297     return x > 0 ? 1.0 : -1.0;
 298 }
 299 #endif
 300
 301 /*
 302  *  call-seq:
 303  *     Math.tanh(x)    -> Float
 304  *
 305  *  Computes the hyperbolic tangent of +x+ (expressed in radians).
 306  *
 307  *  Domain: (-INFINITY, INFINITY)
 308  *
 309  *  Codomain: (-1, 1)
 310  *
 311  *    Math.tanh(0) #=> 0.0
 312  *
 313  */
 314
 315 static VALUE
 316 math_tanh(VALUE unused_obj, VALUE x)
 317 {
 318     return DBL2NUM(tanh(Get_Double(x)));
 319 }
 320
 321 /*
 322  *  call-seq:
 323  *     Math.acosh(x)    -> Float
 324  *
 325  *  Computes the inverse hyperbolic cosine of +x+.
 326  *
 327  *  Domain: [1, INFINITY)
 328  *
 329  *  Codomain: [0, INFINITY)
 330  *
 331  *    Math.acosh(1) #=> 0.0
 332  *
 333  */
 334
 335 static VALUE
 336 math_acosh(VALUE unused_obj, VALUE x)
 337 {
 338     double d;
 339
 340     d = Get_Double(x);
 341     domain_check_min(d, 1.0, "acosh");
 342     return DBL2NUM(acosh(d));
 343 }
 344
 345 /*
 346  *  call-seq:
 347  *     Math.asinh(x)    -> Float
 348  *
 349  *  Computes the inverse hyperbolic sine of +x+.
 350  *
 351  *  Domain: (-INFINITY, INFINITY)
 352  *
 353  *  Codomain: (-INFINITY, INFINITY)
 354  *
 355  *    Math.asinh(1) #=> 0.881373587019543
 356  *
 357  */
 358
 359 static VALUE
 360 math_asinh(VALUE unused_obj, VALUE x)
 361 {
 362     return DBL2NUM(asinh(Get_Double(x)));
 363 }
 364
 365 /*
 366  *  call-seq:
 367  *     Math.atanh(x)    -> Float
 368  *
 369  *  Computes the inverse hyperbolic tangent of +x+.
 370  *
 371  *  Domain: (-1, 1)
 372  *
 373  *  Codomain: (-INFINITY, INFINITY)
 374  *
 375  *   Math.atanh(1) #=> Infinity
 376  *
 377  */
 378
 379 static VALUE
 380 math_atanh(VALUE unused_obj, VALUE x)
 381 {
 382     double d;
 383
 384     d = Get_Double(x);
 385     domain_check_range(d, -1.0, +1.0, "atanh");
 386     /* check for pole error */
 387     if (d == -1.0) return DBL2NUM(-HUGE_VAL);
 388     if (d == +1.0) return DBL2NUM(+HUGE_VAL);
 389     return DBL2NUM(atanh(d));
 390 }
 391
 392 /*
 393  *  call-seq:
 394  *     Math.exp(x)    -> Float
 395  *
 396  *  Returns e**x.
 397  *
 398  *  Domain: (-INFINITY, INFINITY)
 399  *
 400  *  Codomain: (0, INFINITY)
 401  *
 402  *    Math.exp(0)       #=> 1.0
 403  *    Math.exp(1)       #=> 2.718281828459045
 404  *    Math.exp(1.5)     #=> 4.4816890703380645
 405  *
 406  */
 407
 408 static VALUE
 409 math_exp(VALUE unused_obj, VALUE x)
 410 {
 411     return DBL2NUM(exp(Get_Double(x)));
 412 }
 413
 414 #if defined __CYGWIN__
 415 # include <cygwin/version.h>
 416 # if CYGWIN_VERSION_DLL_MAJOR < 1005
 417 #  define nan(x) nan()
 418 # endif
 419 # define log(x) ((x) < 0.0 ? nan("") : log(x))
 420 # define log10(x) ((x) < 0.0 ? nan("") : log10(x))
 421 #endif
 422
 423 #ifndef M_LN2
 424 # define M_LN2 0.693147180559945309417232121458176568
 425 #endif
 426 #ifndef M_LN10
 427 # define M_LN10 2.30258509299404568401799145468436421
 428 #endif
 429
 430 static double math_log1(VALUE x);
 431 FUNC_MINIMIZED(static VALUE math_log(int, const VALUE *, VALUE));
 432
 433 /*
 434  *  call-seq:
 435  *     Math.log(x)          -> Float
 436  *     Math.log(x, base)    -> Float
 437  *
 438  *  Returns the logarithm of +x+.
 439  *  If additional second argument is given, it will be the base
 440  *  of logarithm. Otherwise it is +e+ (for the natural logarithm).
 441  *
 442  *  Domain: (0, INFINITY)
 443  *
 444  *  Codomain: (-INFINITY, INFINITY)
 445  *
 446  *    Math.log(0)          #=> -Infinity
 447  *    Math.log(1)          #=> 0.0
 448  *    Math.log(Math::E)    #=> 1.0
 449  *    Math.log(Math::E**3) #=> 3.0
 450  *    Math.log(12, 3)      #=> 2.2618595071429146
 451  *
 452  */
 453
 454 static VALUE
 455 math_log(int argc, const VALUE *argv, VALUE unused_obj)
 456 {
 457     return rb_math_log(argc, argv);
 458 }
 459
 460 VALUE
 461 rb_math_log(int argc, const VALUE *argv)
 462 {
 463     VALUE x, base;
 464     double d;
 465
 466     rb_scan_args(argc, argv, "11", &x, &base);
 467     d = math_log1(x);
 468     if (argc == 2) {
 469         d /= math_log1(base);
 470     }
 471     return DBL2NUM(d);
 472 }
 473
 474 static double
 475 get_double_rshift(VALUE x, size_t *pnumbits)
 476 {
 477     size_t numbits;
 478
 479     if (RB_BIGNUM_TYPE_P(x) && BIGNUM_POSITIVE_P(x) &&
 480             DBL_MAX_EXP <= (numbits = rb_absint_numwords(x, 1, NULL))) {
 481         numbits -= DBL_MANT_DIG;
 482         x = rb_big_rshift(x, SIZET2NUM(numbits));
 483     }
 484     else {
 485         numbits = 0;
 486     }
 487     *pnumbits = numbits;
 488     return Get_Double(x);
 489 }
 490
 491 static double
 492 math_log1(VALUE x)
 493 {
 494     size_t numbits;
 495     double d = get_double_rshift(x, &numbits);
 496
 497     domain_check_min(d, 0.0, "log");
 498     /* check for pole error */
 499     if (d == 0.0) return -HUGE_VAL;
 500
 501     return log(d) + numbits * M_LN2; /* log(d * 2 ** numbits) */
 502 }
 503
 504 #ifndef log2
 505 #ifndef HAVE_LOG2
 506 double
 507 log2(double x)
 508 {
 509     return log10(x)/log10(2.0);
 510 }
 511 #else
 512 extern double log2(double);
 513 #endif
 514 #endif
 515
 516 /*
 517  *  call-seq:
 518  *     Math.log2(x)    -> Float
 519  *
 520  *  Returns the base 2 logarithm of +x+.
 521  *
 522  *  Domain: (0, INFINITY)
 523  *
 524  *  Codomain: (-INFINITY, INFINITY)
 525  *
 526  *    Math.log2(1)      #=> 0.0
 527  *    Math.log2(2)      #=> 1.0
 528  *    Math.log2(32768)  #=> 15.0
 529  *    Math.log2(65536)  #=> 16.0
 530  *
 531  */
 532
 533 static VALUE
 534 math_log2(VALUE unused_obj, VALUE x)
 535 {
 536     size_t numbits;
 537     double d = get_double_rshift(x, &numbits);
 538
 539     domain_check_min(d, 0.0, "log2");
 540     /* check for pole error */
 541     if (d == 0.0) return DBL2NUM(-HUGE_VAL);
 542
 543     return DBL2NUM(log2(d) + numbits); /* log2(d * 2 ** numbits) */
 544 }
 545
 546 /*
 547  *  call-seq:
 548  *     Math.log10(x)    -> Float
 549  *
 550  *  Returns the base 10 logarithm of +x+.
 551  *
 552  *  Domain: (0, INFINITY)
 553  *
 554  *  Codomain: (-INFINITY, INFINITY)
 555  *
 556  *    Math.log10(1)       #=> 0.0
 557  *    Math.log10(10)      #=> 1.0
 558  *    Math.log10(10**100) #=> 100.0
 559  *
 560  */
 561
 562 static VALUE
 563 math_log10(VALUE unused_obj, VALUE x)
 564 {
 565     size_t numbits;
 566     double d = get_double_rshift(x, &numbits);
 567
 568     domain_check_min(d, 0.0, "log10");
 569     /* check for pole error */
 570     if (d == 0.0) return DBL2NUM(-HUGE_VAL);
 571
 572     return DBL2NUM(log10(d) + numbits * log10(2)); /* log10(d * 2 ** numbits) */
 573 }
 574
 575 static VALUE rb_math_sqrt(VALUE x);
 576
 577 /*
 578  *  call-seq:
 579  *     Math.sqrt(x)    -> Float
 580  *
 581  *  Returns the non-negative square root of +x+.
 582  *
 583  *  Domain: [0, INFINITY)
 584  *
 585  *  Codomain:[0, INFINITY)
 586  *
 587  *    0.upto(10) {|x|
 588  *      p [x, Math.sqrt(x), Math.sqrt(x)**2]
 589  *    }
 590  *    #=> [0, 0.0, 0.0]
 591  *    #   [1, 1.0, 1.0]
 592  *    #   [2, 1.4142135623731, 2.0]
 593  *    #   [3, 1.73205080756888, 3.0]
 594  *    #   [4, 2.0, 4.0]
 595  *    #   [5, 2.23606797749979, 5.0]
 596  *    #   [6, 2.44948974278318, 6.0]
 597  *    #   [7, 2.64575131106459, 7.0]
 598  *    #   [8, 2.82842712474619, 8.0]
 599  *    #   [9, 3.0, 9.0]
 600  *    #   [10, 3.16227766016838, 10.0]
 601  *
 602  *  Note that the limited precision of floating point arithmetic
 603  *  might lead to surprising results:
 604  *
 605  *    Math.sqrt(10**46).to_i  #=> 99999999999999991611392 (!)
 606  *
 607  *  See also BigDecimal#sqrt and Integer.sqrt.
 608  */
 609
 610 static VALUE
 611 math_sqrt(VALUE unused_obj, VALUE x)
 612 {
 613     return rb_math_sqrt(x);
 614 }
 615
 616 inline static VALUE
 617 f_negative_p(VALUE x)
 618 {
 619     if (FIXNUM_P(x))
 620         return RBOOL(FIX2LONG(x) < 0);
 621     return rb_funcall(x, '<', 1, INT2FIX(0));
 622 }
 623 inline static VALUE
 624 f_signbit(VALUE x)
 625 {
 626     if (RB_FLOAT_TYPE_P(x)) {
 627         double f = RFLOAT_VALUE(x);
 628         return RBOOL(!isnan(f) && signbit(f));
 629     }
 630     return f_negative_p(x);
 631 }
 632
 633 static VALUE
 634 rb_math_sqrt(VALUE x)
 635 {
 636     double d;
 637
 638     if (RB_TYPE_P(x, T_COMPLEX)) {
 639         VALUE neg = f_signbit(RCOMPLEX(x)->imag);
 640         double re = Get_Double(RCOMPLEX(x)->real), im;
 641         d = Get_Double(rb_complex_abs(x));
 642         im = sqrt((d - re) / 2.0);
 643         re = sqrt((d + re) / 2.0);
 644         if (neg) im = -im;
 645         return rb_complex_new(DBL2NUM(re), DBL2NUM(im));
 646     }
 647     d = Get_Double(x);
 648     domain_check_min(d, 0.0, "sqrt");
 649     if (d == 0.0) return DBL2NUM(0.0);
 650     return DBL2NUM(sqrt(d));
 651 }
 652
 653 /*
 654  *  call-seq:
 655  *     Math.cbrt(x)    -> Float
 656  *
 657  *  Returns the cube root of +x+.
 658  *
 659  *  Domain: (-INFINITY, INFINITY)
 660  *
 661  *  Codomain: (-INFINITY, INFINITY)
 662  *
 663  *    -9.upto(9) {|x|
 664  *      p [x, Math.cbrt(x), Math.cbrt(x)**3]
 665  *    }
 666  *    #=> [-9, -2.0800838230519, -9.0]
 667  *    #   [-8, -2.0, -8.0]
 668  *    #   [-7, -1.91293118277239, -7.0]
 669  *    #   [-6, -1.81712059283214, -6.0]
 670  *    #   [-5, -1.7099759466767, -5.0]
 671  *    #   [-4, -1.5874010519682, -4.0]
 672  *    #   [-3, -1.44224957030741, -3.0]
 673  *    #   [-2, -1.25992104989487, -2.0]
 674  *    #   [-1, -1.0, -1.0]
 675  *    #   [0, 0.0, 0.0]
 676  *    #   [1, 1.0, 1.0]
 677  *    #   [2, 1.25992104989487, 2.0]
 678  *    #   [3, 1.44224957030741, 3.0]
 679  *    #   [4, 1.5874010519682, 4.0]
 680  *    #   [5, 1.7099759466767, 5.0]
 681  *    #   [6, 1.81712059283214, 6.0]
 682  *    #   [7, 1.91293118277239, 7.0]
 683  *    #   [8, 2.0, 8.0]
 684  *    #   [9, 2.0800838230519, 9.0]
 685  *
 686  */
 687
 688 static VALUE
 689 math_cbrt(VALUE unused_obj, VALUE x)
 690 {
 691     double f = Get_Double(x);
 692     double r = cbrt(f);
 693 #if defined __GLIBC__
 694     if (isfinite(r) && !(f == 0.0 && r == 0.0)) {
 695         r = (2.0 * r + (f / r / r)) / 3.0;
 696     }
 697 #endif
 698     return DBL2NUM(r);
 699 }
 700
 701 /*
 702  *  call-seq:
 703  *     Math.frexp(x)    -> [fraction, exponent]
 704  *
 705  *  Returns a two-element array containing the normalized fraction (a Float)
 706  *  and exponent (an Integer) of +x+.
 707  *
 708  *     fraction, exponent = Math.frexp(1234)   #=> [0.6025390625, 11]
 709  *     fraction * 2**exponent                  #=> 1234.0
 710  */
 711
 712 static VALUE
 713 math_frexp(VALUE unused_obj, VALUE x)
 714 {
 715     double d;
 716     int exp;
 717
 718     d = frexp(Get_Double(x), &exp);
 719     return rb_assoc_new(DBL2NUM(d), INT2NUM(exp));
 720 }
 721
 722 /*
 723  *  call-seq:
 724  *     Math.ldexp(fraction, exponent) -> float
 725  *
 726  *  Returns the value of +fraction+*(2**+exponent+).
 727  *
 728  *     fraction, exponent = Math.frexp(1234)
 729  *     Math.ldexp(fraction, exponent)   #=> 1234.0
 730  */
 731
 732 static VALUE
 733 math_ldexp(VALUE unused_obj, VALUE x, VALUE n)
 734 {
 735     return DBL2NUM(ldexp(Get_Double(x), NUM2INT(n)));
 736 }
 737
 738 /*
 739  *  call-seq:
 740  *     Math.hypot(x, y)    -> Float
 741  *
 742  *  Returns sqrt(x**2 + y**2), the hypotenuse of a right-angled triangle with
 743  *  sides +x+ and +y+.
 744  *
 745  *     Math.hypot(3, 4)   #=> 5.0
 746  */
 747
 748 static VALUE
 749 math_hypot(VALUE unused_obj, VALUE x, VALUE y)
 750 {
 751     return DBL2NUM(hypot(Get_Double(x), Get_Double(y)));
 752 }
 753
 754 /*
 755  * call-seq:
 756  *    Math.erf(x)  -> Float
 757  *
 758  *  Calculates the error function of +x+.
 759  *
 760  *  Domain: (-INFINITY, INFINITY)
 761  *
 762  *  Codomain: (-1, 1)
 763  *
 764  *    Math.erf(0) #=> 0.0
 765  *
 766  */
 767
 768 static VALUE
 769 math_erf(VALUE unused_obj, VALUE x)
 770 {
 771     return DBL2NUM(erf(Get_Double(x)));
 772 }
 773
 774 /*
 775  * call-seq:
 776  *    Math.erfc(x)  -> Float
 777  *
 778  *  Calculates the complementary error function of x.
 779  *
 780  *  Domain: (-INFINITY, INFINITY)
 781  *
 782  *  Codomain: (0, 2)
 783  *
 784  *    Math.erfc(0) #=> 1.0
 785  *
 786  */
 787
 788 static VALUE
 789 math_erfc(VALUE unused_obj, VALUE x)
 790 {
 791     return DBL2NUM(erfc(Get_Double(x)));
 792 }
 793
 794 /*
 795  * call-seq:
 796  *    Math.gamma(x)  -> Float
 797  *
 798  *  Calculates the gamma function of x.
 799  *
 800  *  Note that gamma(n) is the same as fact(n-1) for integer n > 0.
 801  *  However gamma(n) returns float and can be an approximation.
 802  *
 803  *   def fact(n) (1..n).inject(1) {|r,i| r*i } end
 804  *   1.upto(26) {|i| p [i, Math.gamma(i), fact(i-1)] }
 805  *   #=> [1, 1.0, 1]
 806  *   #   [2, 1.0, 1]
 807  *   #   [3, 2.0, 2]
 808  *   #   [4, 6.0, 6]
 809  *   #   [5, 24.0, 24]
 810  *   #   [6, 120.0, 120]
 811  *   #   [7, 720.0, 720]
 812  *   #   [8, 5040.0, 5040]
 813  *   #   [9, 40320.0, 40320]
 814  *   #   [10, 362880.0, 362880]
 815  *   #   [11, 3628800.0, 3628800]
 816  *   #   [12, 39916800.0, 39916800]
 817  *   #   [13, 479001600.0, 479001600]
 818  *   #   [14, 6227020800.0, 6227020800]
 819  *   #   [15, 87178291200.0, 87178291200]
 820  *   #   [16, 1307674368000.0, 1307674368000]
 821  *   #   [17, 20922789888000.0, 20922789888000]
 822  *   #   [18, 355687428096000.0, 355687428096000]
 823  *   #   [19, 6.402373705728e+15, 6402373705728000]
 824  *   #   [20, 1.21645100408832e+17, 121645100408832000]
 825  *   #   [21, 2.43290200817664e+18, 2432902008176640000]
 826  *   #   [22, 5.109094217170944e+19, 51090942171709440000]
 827  *   #   [23, 1.1240007277776077e+21, 1124000727777607680000]
 828  *   #   [24, 2.5852016738885062e+22, 25852016738884976640000]
 829  *   #   [25, 6.204484017332391e+23, 620448401733239439360000]
 830  *   #   [26, 1.5511210043330954e+25, 15511210043330985984000000]
 831  *
 832  */
 833
 834 static VALUE
 835 math_gamma(VALUE unused_obj, VALUE x)
 836 {
 837     static const double fact_table[] = {
 838         /* fact(0) */ 1.0,
 839         /* fact(1) */ 1.0,
 840         /* fact(2) */ 2.0,
 841         /* fact(3) */ 6.0,
 842         /* fact(4) */ 24.0,
 843         /* fact(5) */ 120.0,
 844         /* fact(6) */ 720.0,
 845         /* fact(7) */ 5040.0,
 846         /* fact(8) */ 40320.0,
 847         /* fact(9) */ 362880.0,
 848         /* fact(10) */ 3628800.0,
 849         /* fact(11) */ 39916800.0,
 850         /* fact(12) */ 479001600.0,
 851         /* fact(13) */ 6227020800.0,
 852         /* fact(14) */ 87178291200.0,
 853         /* fact(15) */ 1307674368000.0,
 854         /* fact(16) */ 20922789888000.0,
 855         /* fact(17) */ 355687428096000.0,
 856         /* fact(18) */ 6402373705728000.0,
 857         /* fact(19) */ 121645100408832000.0,
 858         /* fact(20) */ 2432902008176640000.0,
 859         /* fact(21) */ 51090942171709440000.0,
 860         /* fact(22) */ 1124000727777607680000.0,
 861         /* fact(23)=25852016738884976640000 needs 56bit mantissa which is
 862          * impossible to represent exactly in IEEE 754 double which have
 863          * 53bit mantissa. */
 864     };
 865     enum {NFACT_TABLE = numberof(fact_table)};
 866     double d;
 867     d = Get_Double(x);
 868     /* check for domain error */
 869     if (isinf(d)) {
 870         if (signbit(d)) domain_error("gamma");
 871         return DBL2NUM(HUGE_VAL);
 872     }
 873     if (d == 0.0) {
 874         return signbit(d) ? DBL2NUM(-HUGE_VAL) : DBL2NUM(HUGE_VAL);
 875     }
 876     if (d == floor(d)) {
 877         domain_check_min(d, 0.0, "gamma");
 878         if (1.0 <= d && d <= (double)NFACT_TABLE) {
 879             return DBL2NUM(fact_table[(int)d - 1]);
 880         }
 881     }
 882     return DBL2NUM(tgamma(d));
 883 }
 884
 885 /*
 886  * call-seq:
 887  *    Math.lgamma(x)  -> [float, -1 or 1]
 888  *
 889  *  Calculates the logarithmic gamma of +x+ and the sign of gamma of +x+.
 890  *
 891  *  Math.lgamma(x) is the same as
 892  *   [Math.log(Math.gamma(x).abs), Math.gamma(x) < 0 ? -1 : 1]
 893  *  but avoids overflow by Math.gamma(x) for large x.
 894  *
 895  *    Math.lgamma(0) #=> [Infinity, 1]
 896  *
 897  */
 898
 899 static VALUE
 900 math_lgamma(VALUE unused_obj, VALUE x)
 901 {
 902     double d;
 903     int sign=1;
 904     VALUE v;
 905     d = Get_Double(x);
 906     /* check for domain error */
 907     if (isinf(d)) {
 908         if (signbit(d)) domain_error("lgamma");
 909         return rb_assoc_new(DBL2NUM(HUGE_VAL), INT2FIX(1));
 910     }
 911     if (d == 0.0) {
 912         VALUE vsign = signbit(d) ? INT2FIX(-1) : INT2FIX(+1);
 913         return rb_assoc_new(DBL2NUM(HUGE_VAL), vsign);
 914     }
 915     v = DBL2NUM(lgamma_r(d, &sign));
 916     return rb_assoc_new(v, INT2FIX(sign));
 917 }
 918
 919
 920 #define exp1(n) \
 921 VALUE \
 922 rb_math_##n(VALUE x)\
 923 {\
 924     return math_##n(0, x);\
 925 }
 926
 927 #define exp2(n) \
 928 VALUE \
 929 rb_math_##n(VALUE x, VALUE y)\
 930 {\
 931     return math_##n(0, x, y);\
 932 }
 933
 934 exp2(atan2)
 935 exp1(cos)
 936 exp1(cosh)
 937 exp1(exp)
 938 exp2(hypot)
 939 exp1(sin)
 940 exp1(sinh)
 941 #if 0
 942 exp1(sqrt)
 943 #endif
 944
 945
 946 /*
 947  *  Document-class: Math::DomainError
 948  *
 949  *  Raised when a mathematical function is evaluated outside of its
 950  *  domain of definition.
 951  *
 952  *  For example, since +cos+ returns values in the range -1..1,
 953  *  its inverse function +acos+ is only defined on that interval:
 954  *
 955  *     Math.acos(42)
 956  *
 957  *  <em>produces:</em>
 958  *
 959  *     Math::DomainError: Numerical argument is out of domain - "acos"
 960  */
 961
 962 /*
 963  *  Document-class: Math
 964  *
 965  *  The Math module contains module functions for basic
 966  *  trigonometric and transcendental functions. See class
 967  *  Float for a list of constants that
 968  *  define Ruby's floating point accuracy.
 969  *
 970  *  Domains and codomains are given only for real (not complex) numbers.
 971  */
 972
 973
 974 void
 975 InitVM_Math(void)
 976 {
 977     rb_mMath = rb_define_module("Math");
 978     rb_eMathDomainError = rb_define_class_under(rb_mMath, "DomainError", rb_eStandardError);
 979
 980     /*  Definition of the mathematical constant PI as a Float number. */
 981     rb_define_const(rb_mMath, "PI", DBL2NUM(M_PI));
 982
 983 #ifdef M_E
 984     /*  Definition of the mathematical constant E for Euler's number (e) as a Float number. */
 985     rb_define_const(rb_mMath, "E", DBL2NUM(M_E));
 986 #else
 987     rb_define_const(rb_mMath, "E", DBL2NUM(exp(1.0)));
 988 #endif
 989
 990     rb_define_module_function(rb_mMath, "atan2", math_atan2, 2);
 991     rb_define_module_function(rb_mMath, "cos", math_cos, 1);
 992     rb_define_module_function(rb_mMath, "sin", math_sin, 1);
 993     rb_define_module_function(rb_mMath, "tan", math_tan, 1);
 994
 995     rb_define_module_function(rb_mMath, "acos", math_acos, 1);
 996     rb_define_module_function(rb_mMath, "asin", math_asin, 1);
 997     rb_define_module_function(rb_mMath, "atan", math_atan, 1);
 998
 999     rb_define_module_function(rb_mMath, "cosh", math_cosh, 1);
1000     rb_define_module_function(rb_mMath, "sinh", math_sinh, 1);
1001     rb_define_module_function(rb_mMath, "tanh", math_tanh, 1);
1002
1003     rb_define_module_function(rb_mMath, "acosh", math_acosh, 1);
1004     rb_define_module_function(rb_mMath, "asinh", math_asinh, 1);
1005     rb_define_module_function(rb_mMath, "atanh", math_atanh, 1);
1006
1007     rb_define_module_function(rb_mMath, "exp", math_exp, 1);
1008     rb_define_module_function(rb_mMath, "log", math_log, -1);
1009     rb_define_module_function(rb_mMath, "log2", math_log2, 1);
1010     rb_define_module_function(rb_mMath, "log10", math_log10, 1);
1011     rb_define_module_function(rb_mMath, "sqrt", math_sqrt, 1);
1012     rb_define_module_function(rb_mMath, "cbrt", math_cbrt, 1);
1013
1014     rb_define_module_function(rb_mMath, "frexp", math_frexp, 1);
1015     rb_define_module_function(rb_mMath, "ldexp", math_ldexp, 2);
1016
1017     rb_define_module_function(rb_mMath, "hypot", math_hypot, 2);
1018
1019     rb_define_module_function(rb_mMath, "erf",  math_erf,  1);
1020     rb_define_module_function(rb_mMath, "erfc", math_erfc, 1);
1021
1022     rb_define_module_function(rb_mMath, "gamma", math_gamma, 1);
1023     rb_define_module_function(rb_mMath, "lgamma", math_lgamma, 1);
1024 }
1025
1026 void
1027 Init_Math(void)
1028 {
1029     InitVM(Math);
1030 }