Module | Math |
In: |
math.c
lib/complex.rb lib/mathn.rb |
PI | = | rb_float_new(M_PI) |
PI | = | rb_float_new(atan(1.0)*4.0) |
E | = | rb_float_new(M_E) |
E | = | rb_float_new(exp(1.0)) |
sqrt | -> | sqrt! |
exp | -> | exp! |
log | -> | log! |
log10 | -> | log10! |
cos | -> | cos! |
sin | -> | sin! |
tan | -> | tan! |
cosh | -> | cosh! |
sinh | -> | sinh! |
tanh | -> | tanh! |
acos | -> | acos! |
asin | -> | asin! |
atan | -> | atan! |
atan2 | -> | atan2! |
acosh | -> | acosh! |
asinh | -> | asinh! |
atanh | -> | atanh! |
Computes the arc cosine of x. Returns 0..PI.
/* * call-seq: * Math.acos(x) => float * * Computes the arc cosine of <i>x</i>. Returns 0..PI. */ static VALUE math_acos(obj, x) VALUE obj, x; { double d; Need_Float(x); errno = 0; d = acos(RFLOAT(x)->value); domain_check(d, "acos"); return rb_float_new(d); }
Computes the inverse hyperbolic cosine of x.
/* * call-seq: * Math.acosh(x) => float * * Computes the inverse hyperbolic cosine of <i>x</i>. */ static VALUE math_acosh(obj, x) VALUE obj, x; { double d; Need_Float(x); errno = 0; d = acosh(RFLOAT(x)->value); domain_check(d, "acosh"); return rb_float_new(d); }
Computes the arc sine of x. Returns -{PI/2} .. {PI/2}.
/* * call-seq: * Math.asin(x) => float * * Computes the arc sine of <i>x</i>. Returns -{PI/2} .. {PI/2}. */ static VALUE math_asin(obj, x) VALUE obj, x; { double d; Need_Float(x); errno = 0; d = asin(RFLOAT(x)->value); domain_check(d, "asin"); return rb_float_new(d); }
Computes the inverse hyperbolic sine of x.
/* * call-seq: * Math.asinh(x) => float * * Computes the inverse hyperbolic sine of <i>x</i>. */ static VALUE math_asinh(obj, x) VALUE obj, x; { Need_Float(x); return rb_float_new(asinh(RFLOAT(x)->value)); }
Computes the arc tangent of x. Returns -{PI/2} .. {PI/2}.
/* * call-seq: * Math.atan(x) => float * * Computes the arc tangent of <i>x</i>. Returns -{PI/2} .. {PI/2}. */ static VALUE math_atan(obj, x) VALUE obj, x; { Need_Float(x); return rb_float_new(atan(RFLOAT(x)->value)); }
Computes the arc tangent given y and x. Returns -PI..PI.
/* * call-seq: * Math.atan2(y, x) => float * * Computes the arc tangent given <i>y</i> and <i>x</i>. Returns * -PI..PI. * */ static VALUE math_atan2(obj, y, x) VALUE obj, x, y; { Need_Float2(y, x); return rb_float_new(atan2(RFLOAT(y)->value, RFLOAT(x)->value)); }
Computes the inverse hyperbolic tangent of x.
/* * call-seq: * Math.atanh(x) => float * * Computes the inverse hyperbolic tangent of <i>x</i>. */ static VALUE math_atanh(obj, x) VALUE obj, x; { double d; Need_Float(x); errno = 0; d = atanh(RFLOAT(x)->value); domain_check(d, "atanh"); return rb_float_new(d); }
Computes the cosine of x (expressed in radians). Returns -1..1.
/* * call-seq: * Math.cos(x) => float * * Computes the cosine of <i>x</i> (expressed in radians). Returns * -1..1. */ static VALUE math_cos(obj, x) VALUE obj, x; { Need_Float(x); return rb_float_new(cos(RFLOAT(x)->value)); }
Computes the hyperbolic cosine of x (expressed in radians).
/* * call-seq: * Math.cosh(x) => float * * Computes the hyperbolic cosine of <i>x</i> (expressed in radians). */ static VALUE math_cosh(obj, x) VALUE obj, x; { Need_Float(x); return rb_float_new(cosh(RFLOAT(x)->value)); }
Calculates the error function of x.
/* * call-seq: * Math.erf(x) => float * * Calculates the error function of x. */ static VALUE math_erf(obj, x) VALUE obj, x; { Need_Float(x); return rb_float_new(erf(RFLOAT(x)->value)); }
Calculates the complementary error function of x.
/* * call-seq: * Math.erfc(x) => float * * Calculates the complementary error function of x. */ static VALUE math_erfc(obj, x) VALUE obj, x; { Need_Float(x); return rb_float_new(erfc(RFLOAT(x)->value)); }
Returns e**x.
/* * call-seq: * Math.exp(x) => float * * Returns e**x. */ static VALUE math_exp(obj, x) VALUE obj, x; { Need_Float(x); return rb_float_new(exp(RFLOAT(x)->value)); }
Returns a two-element array containing the normalized fraction (a Float) and exponent (a Fixnum) of numeric.
fraction, exponent = Math.frexp(1234) #=> [0.6025390625, 11] fraction * 2**exponent #=> 1234.0
/* * call-seq: * Math.frexp(numeric) => [ fraction, exponent ] * * Returns a two-element array containing the normalized fraction (a * <code>Float</code>) and exponent (a <code>Fixnum</code>) of * <i>numeric</i>. * * fraction, exponent = Math.frexp(1234) #=> [0.6025390625, 11] * fraction * 2**exponent #=> 1234.0 */ static VALUE math_frexp(obj, x) VALUE obj, x; { double d; int exp; Need_Float(x); d = frexp(RFLOAT(x)->value, &exp); return rb_assoc_new(rb_float_new(d), INT2NUM(exp)); }
Returns sqrt(x**2 + y**2), the hypotenuse of a right-angled triangle with sides x and y.
Math.hypot(3, 4) #=> 5.0
/* * call-seq: * Math.hypot(x, y) => float * * Returns sqrt(x**2 + y**2), the hypotenuse of a right-angled triangle * with sides <i>x</i> and <i>y</i>. * * Math.hypot(3, 4) #=> 5.0 */ static VALUE math_hypot(obj, x, y) VALUE obj, x, y; { Need_Float2(x, y); return rb_float_new(hypot(RFLOAT(x)->value, RFLOAT(y)->value)); }
Returns the value of flt*(2**int).
fraction, exponent = Math.frexp(1234) Math.ldexp(fraction, exponent) #=> 1234.0
/* * call-seq: * Math.ldexp(flt, int) -> float * * Returns the value of <i>flt</i>*(2**<i>int</i>). * * fraction, exponent = Math.frexp(1234) * Math.ldexp(fraction, exponent) #=> 1234.0 */ static VALUE math_ldexp(obj, x, n) VALUE obj, x, n; { Need_Float(x); return rb_float_new(ldexp(RFLOAT(x)->value, NUM2INT(n))); }
Returns the natural logarithm of numeric.
/* * call-seq: * Math.log(numeric) => float * * Returns the natural logarithm of <i>numeric</i>. */ static VALUE math_log(obj, x) VALUE obj, x; { double d; Need_Float(x); errno = 0; d = log(RFLOAT(x)->value); domain_check(d, "log"); return rb_float_new(d); }
Returns the base 10 logarithm of numeric.
/* * call-seq: * Math.log10(numeric) => float * * Returns the base 10 logarithm of <i>numeric</i>. */ static VALUE math_log10(obj, x) VALUE obj, x; { double d; Need_Float(x); errno = 0; d = log10(RFLOAT(x)->value); domain_check(d, "log10"); return rb_float_new(d); }
Computes the sine of x (expressed in radians). Returns -1..1.
/* * call-seq: * Math.sin(x) => float * * Computes the sine of <i>x</i> (expressed in radians). Returns * -1..1. */ static VALUE math_sin(obj, x) VALUE obj, x; { Need_Float(x); return rb_float_new(sin(RFLOAT(x)->value)); }
Computes the hyperbolic sine of x (expressed in radians).
/* * call-seq: * Math.sinh(x) => float * * Computes the hyperbolic sine of <i>x</i> (expressed in * radians). */ static VALUE math_sinh(obj, x) VALUE obj, x; { Need_Float(x); return rb_float_new(sinh(RFLOAT(x)->value)); }
Returns the non-negative square root of numeric.
/* * call-seq: * Math.sqrt(numeric) => float * * Returns the non-negative square root of <i>numeric</i>. */ static VALUE math_sqrt(obj, x) VALUE obj, x; { double d; Need_Float(x); errno = 0; d = sqrt(RFLOAT(x)->value); domain_check(d, "sqrt"); return rb_float_new(d); }
Returns the tangent of x (expressed in radians).
/* * call-seq: * Math.tan(x) => float * * Returns the tangent of <i>x</i> (expressed in radians). */ static VALUE math_tan(obj, x) VALUE obj, x; { Need_Float(x); return rb_float_new(tan(RFLOAT(x)->value)); }
Computes the hyperbolic tangent of x (expressed in radians).
/* * call-seq: * Math.tanh() => float * * Computes the hyperbolic tangent of <i>x</i> (expressed in * radians). */ static VALUE math_tanh(obj, x) VALUE obj, x; { Need_Float(x); return rb_float_new(tanh(RFLOAT(x)->value)); }
# File lib/complex.rb, line 562 562: def acos(z) 563: if Complex.generic?(z) and z >= -1 and z <= 1 564: acos!(z) 565: else 566: -1.0.im * log( z + 1.0.im * sqrt(1.0-z*z) ) 567: end 568: end
# File lib/complex.rb, line 594 594: def acosh(z) 595: if Complex.generic?(z) and z >= 1 596: acosh!(z) 597: else 598: log( z + sqrt(z*z-1.0) ) 599: end 600: end
# File lib/complex.rb, line 570 570: def asin(z) 571: if Complex.generic?(z) and z >= -1 and z <= 1 572: asin!(z) 573: else 574: -1.0.im * log( 1.0.im * z + sqrt(1.0-z*z) ) 575: end 576: end
# File lib/complex.rb, line 602 602: def asinh(z) 603: if Complex.generic?(z) 604: asinh!(z) 605: else 606: log( z + sqrt(1.0+z*z) ) 607: end 608: end
# File lib/complex.rb, line 578 578: def atan(z) 579: if Complex.generic?(z) 580: atan!(z) 581: else 582: 1.0.im * log( (1.0.im+z) / (1.0.im-z) ) / 2.0 583: end 584: end
# File lib/complex.rb, line 586 586: def atan2(y,x) 587: if Complex.generic?(y) and Complex.generic?(x) 588: atan2!(y,x) 589: else 590: -1.0.im * log( (x+1.0.im*y) / sqrt(x*x+y*y) ) 591: end 592: end
# File lib/complex.rb, line 610 610: def atanh(z) 611: if Complex.generic?(z) and z >= -1 and z <= 1 612: atanh!(z) 613: else 614: log( (1.0+z) / (1.0-z) ) / 2.0 615: end 616: end
# File lib/complex.rb, line 527 527: def cosh(z) 528: if Complex.generic?(z) 529: cosh!(z) 530: else 531: Complex( cosh!(z.real)*cos!(z.image), sinh!(z.real)*sin!(z.image) ) 532: end 533: end
# File lib/mathn.rb, line 256 256: def rsqrt(a) 257: if a.kind_of?(Float) 258: sqrt!(a) 259: elsif a.kind_of?(Rational) 260: rsqrt(a.numerator)/rsqrt(a.denominator) 261: else 262: src = a 263: max = 2 ** 32 264: byte_a = [src & 0xffffffff] 265: # ruby's bug 266: while (src >= max) and (src >>= 32) 267: byte_a.unshift src & 0xffffffff 268: end 269: 270: answer = 0 271: main = 0 272: side = 0 273: for elm in byte_a 274: main = (main << 32) + elm 275: side <<= 16 276: if answer != 0 277: if main * 4 < side * side 278: applo = main.div(side) 279: else 280: applo = ((sqrt!(side * side + 4 * main) - side)/2.0).to_i + 1 281: end 282: else 283: applo = sqrt!(main).to_i + 1 284: end 285: 286: while (x = (side + applo) * applo) > main 287: applo -= 1 288: end 289: main -= x 290: answer = (answer << 16) + applo 291: side += applo * 2 292: end 293: if main == 0 294: answer 295: else 296: sqrt!(a) 297: end 298: end 299: end
# File lib/complex.rb, line 519 519: def sinh(z) 520: if Complex.generic?(z) 521: sinh!(z) 522: else 523: Complex( sinh!(z.real)*cos!(z.image), cosh!(z.real)*sin!(z.image) ) 524: end 525: end
Redefined to handle a Complex argument.
# File lib/complex.rb, line 463 463: def sqrt(z) 464: if Complex.generic?(z) 465: if z >= 0 466: sqrt!(z) 467: else 468: Complex(0,sqrt!(-z)) 469: end 470: else 471: if z.image < 0 472: sqrt(z.conjugate).conjugate 473: else 474: r = z.abs 475: x = z.real 476: Complex( sqrt!((r+x)/2), sqrt!((r-x)/2) ) 477: end 478: end 479: end
# File lib/mathn.rb, line 233 233: def sqrt(a) 234: if a.kind_of?(Complex) 235: abs = sqrt(a.real*a.real + a.image*a.image) 236: # if not abs.kind_of?(Rational) 237: # return a**Rational(1,2) 238: # end 239: x = sqrt((a.real + abs)/Rational(2)) 240: y = sqrt((-a.real + abs)/Rational(2)) 241: # if !(x.kind_of?(Rational) and y.kind_of?(Rational)) 242: # return a**Rational(1,2) 243: # end 244: if a.image >= 0 245: Complex(x, y) 246: else 247: Complex(x, -y) 248: end 249: elsif a >= 0 250: rsqrt(a) 251: else 252: Complex(0,rsqrt(-a)) 253: end 254: end