In Files

  • bigdecimal/bigdecimal.c
  • bigdecimal/lib/bigdecimal/math.rb

Class/Module Index [+]

Quicksearch

BigMath

mathematical functions

Provides mathematical functions.

Example:

require "bigdecimal"
require "bigdecimal/math"

include BigMath

a = BigDecimal((PI(100)/2).to_s)
puts sin(a,100) # -> 0.10000000000000000000......E1

Public Class Methods

exp(x, prec) click to toggle source

Computes the value of e (the base of natural logarithms) raised to the power of x, to the specified number of digits of precision.

If x is infinity, returns Infinity.

If x is NaN, returns NaN.

 
               static VALUE
BigMath_s_exp(VALUE klass, VALUE x, VALUE vprec)
{
    ssize_t prec, n, i;
    Real* vx = NULL;
    VALUE one, d, x1, y, z;
    int negative = 0;
    int infinite = 0;
    int nan = 0;
    double flo;

    prec = NUM2SSIZET(vprec);
    if (prec <= 0) {
        rb_raise(rb_eArgError, "Zero or negative precision for exp");
    }

    /* TODO: the following switch statement is almostly the same as one in the
     *       BigDecimalCmp function. */
    switch (TYPE(x)) {
      case T_DATA:
          if (!is_kind_of_BigDecimal(x)) break;
          vx = DATA_PTR(x);
          negative = VpGetSign(vx) < 0;
          infinite = VpIsPosInf(vx) || VpIsNegInf(vx);
          nan = VpIsNaN(vx);
          break;

      case T_FIXNUM:
          /* fall through */
      case T_BIGNUM:
          vx = GetVpValue(x, 0);
          break;

      case T_FLOAT:
        flo = RFLOAT_VALUE(x);
        negative = flo < 0;
        infinite = isinf(flo);
        nan = isnan(flo);
        if (!infinite && !nan) {
            vx = GetVpValueWithPrec(x, DBL_DIG+1, 0);
        }
        break;

      case T_RATIONAL:
        vx = GetVpValueWithPrec(x, prec, 0);
        break;

      default:
        break;
    }
    if (infinite) {
        if (negative) {
            return ToValue(GetVpValueWithPrec(INT2NUM(0), prec, 1));
        }
        else {
            Real* vy;
            vy = VpCreateRbObject(prec, "#0");
            RB_GC_GUARD(vy->obj);
            VpSetInf(vy, VP_SIGN_POSITIVE_INFINITE);
            return ToValue(vy);
        }
    }
    else if (nan) {
        Real* vy;
        vy = VpCreateRbObject(prec, "#0");
        RB_GC_GUARD(vy->obj);
        VpSetNaN(vy);
        return ToValue(vy);
    }
    else if (vx == NULL) {
        cannot_be_coerced_into_BigDecimal(rb_eArgError, x);
    }
    x = RB_GC_GUARD(vx->obj);

    n = prec + rmpd_double_figures();
    negative = VpGetSign(vx) < 0;
    if (negative) {
        VpSetSign(vx, 1);
    }

    RB_GC_GUARD(one) = ToValue(VpCreateRbObject(1, "1"));
    RB_GC_GUARD(x1) = one;
    RB_GC_GUARD(y)  = one;
    RB_GC_GUARD(d)  = y;
    RB_GC_GUARD(z)  = one;
    i  = 0;

    while (!VpIsZero((Real*)DATA_PTR(d))) {
        VALUE argv[2];
        SIGNED_VALUE const ey = VpExponent10(DATA_PTR(y));
        SIGNED_VALUE const ed = VpExponent10(DATA_PTR(d));
        ssize_t m = n - vabs(ey - ed);
        if (m <= 0) {
            break;
        }
        else if ((size_t)m < rmpd_double_figures()) {
            m = rmpd_double_figures();
        }

        x1 = BigDecimal_mult2(x1, x, SSIZET2NUM(n));
        ++i;
        z = BigDecimal_mult(z, SSIZET2NUM(i));
        argv[0] = z;
        argv[1] = SSIZET2NUM(m);
        d = BigDecimal_div2(2, argv, x1);
        y = BigDecimal_add(y, d);
    }

    if (negative) {
        VALUE argv[2];
        argv[0] = y;
        argv[1] = vprec;
        return BigDecimal_div2(2, argv, one);
    }
    else {
        vprec = SSIZET2NUM(prec - VpExponent10(DATA_PTR(y)));
        return BigDecimal_round(1, &vprec, y);
    }
}
            
log(x, prec) click to toggle source

Computes the natural logarithm of x to the specified number of digits of precision.

If x is zero or negative, raises Math::DomainError.

If x is positive infinity, returns Infinity.

If x is NaN, returns NaN.

 
               static VALUE
BigMath_s_log(VALUE klass, VALUE x, VALUE vprec)
{
    ssize_t prec, n, i;
    SIGNED_VALUE expo;
    Real* vx = NULL;
    VALUE argv[2], vn, one, two, w, x2, y, d;
    int zero = 0;
    int negative = 0;
    int infinite = 0;
    int nan = 0;
    double flo;
    long fix;

    if (!is_integer(vprec)) {
        rb_raise(rb_eArgError, "precision must be an Integer");
    }

    prec = NUM2SSIZET(vprec);
    if (prec <= 0) {
        rb_raise(rb_eArgError, "Zero or negative precision for exp");
    }

    /* TODO: the following switch statement is almostly the same as one in the
     *       BigDecimalCmp function. */
    switch (TYPE(x)) {
      case T_DATA:
          if (!is_kind_of_BigDecimal(x)) break;
          vx = DATA_PTR(x);
          zero = VpIsZero(vx);
          negative = VpGetSign(vx) < 0;
          infinite = VpIsPosInf(vx) || VpIsNegInf(vx);
          nan = VpIsNaN(vx);
          break;

      case T_FIXNUM:
        fix = FIX2LONG(x);
        zero = fix == 0;
        negative = fix < 0;
        goto get_vp_value;

      case T_BIGNUM:
        zero = RBIGNUM_ZERO_P(x);
        negative = RBIGNUM_NEGATIVE_P(x);
get_vp_value:
        if (zero || negative) break;
        vx = GetVpValue(x, 0);
        break;

      case T_FLOAT:
        flo = RFLOAT_VALUE(x);
        zero = flo == 0;
        negative = flo < 0;
        infinite = isinf(flo);
        nan = isnan(flo);
        if (!zero && !negative && !infinite && !nan) {
            vx = GetVpValueWithPrec(x, DBL_DIG+1, 1);
        }
        break;

      case T_RATIONAL:
        zero = RRATIONAL_ZERO_P(x);
        negative = RRATIONAL_NEGATIVE_P(x);
        if (zero || negative) break;
        vx = GetVpValueWithPrec(x, prec, 1);
        break;

      case T_COMPLEX:
        rb_raise(rb_eMathDomainError,
                 "Complex argument for BigMath.log");

      default:
        break;
    }
    if (infinite && !negative) {
        Real* vy;
        vy = VpCreateRbObject(prec, "#0");
        RB_GC_GUARD(vy->obj);
        VpSetInf(vy, VP_SIGN_POSITIVE_INFINITE);
        return ToValue(vy);
    }
    else if (nan) {
        Real* vy;
        vy = VpCreateRbObject(prec, "#0");
        RB_GC_GUARD(vy->obj);
        VpSetNaN(vy);
        return ToValue(vy);
    }
    else if (zero || negative) {
        rb_raise(rb_eMathDomainError,
                 "Zero or negative argument for log");
    }
    else if (vx == NULL) {
        cannot_be_coerced_into_BigDecimal(rb_eArgError, x);
    }
    x = ToValue(vx);

    RB_GC_GUARD(one) = ToValue(VpCreateRbObject(1, "1"));
    RB_GC_GUARD(two) = ToValue(VpCreateRbObject(1, "2"));

    n = prec + rmpd_double_figures();
    RB_GC_GUARD(vn) = SSIZET2NUM(n);
    expo = VpExponent10(vx);
    if (expo < 0 || expo >= 3) {
        char buf[16];
        snprintf(buf, 16, "1E%"PRIdVALUE, -expo);
        x = BigDecimal_mult2(x, ToValue(VpCreateRbObject(1, buf)), vn);
    }
    else {
        expo = 0;
    }
    w = BigDecimal_sub(x, one);
    argv[0] = BigDecimal_add(x, one);
    argv[1] = vn;
    x = BigDecimal_div2(2, argv, w);
    RB_GC_GUARD(x2) = BigDecimal_mult2(x, x, vn);
    RB_GC_GUARD(y)  = x;
    RB_GC_GUARD(d)  = y;
    i = 1;
    while (!VpIsZero((Real*)DATA_PTR(d))) {
        SIGNED_VALUE const ey = VpExponent10(DATA_PTR(y));
        SIGNED_VALUE const ed = VpExponent10(DATA_PTR(d));
        ssize_t m = n - vabs(ey - ed);
        if (m <= 0) {
            break;
        }
        else if ((size_t)m < rmpd_double_figures()) {
            m = rmpd_double_figures();
        }

        x = BigDecimal_mult2(x2, x, vn);
        i += 2;
        argv[0] = SSIZET2NUM(i);
        argv[1] = SSIZET2NUM(m);
        d = BigDecimal_div2(2, argv, x);
        y = BigDecimal_add(y, d);
    }

    y = BigDecimal_mult(y, two);
    if (expo != 0) {
        VALUE log10, vexpo, dy;
        log10 = BigMath_s_log(klass, INT2FIX(10), vprec);
        vexpo = ToValue(GetVpValue(SSIZET2NUM(expo), 1));
        dy = BigDecimal_mult(log10, vexpo);
        y = BigDecimal_add(y, dy);
    }

    return y;
}
            

Public Instance Methods

E(prec) click to toggle source

Computes e (the base of natural logarithms) to the specified number of digits of precision.

 
               # File bigdecimal/lib/bigdecimal/math.rb, line 188
def E(prec)
  raise ArgumentError, "Zero or negative precision for E" if prec <= 0
  n    = prec + BigDecimal.double_fig
  one  = BigDecimal("1")
  y  = one
  d  = y
  z  = one
  i  = 0
  while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0)
    m = BigDecimal.double_fig if m < BigDecimal.double_fig
    i += 1
    z *= i
    d  = one.div(z,m)
    y += d
  end
  y
end
            
PI(prec) click to toggle source

Computes the value of pi to the specified number of digits of precision.

 
               # File bigdecimal/lib/bigdecimal/math.rb, line 148
def PI(prec)
  raise ArgumentError, "Zero or negative argument for PI" if prec <= 0
  n      = prec + BigDecimal.double_fig
  zero   = BigDecimal("0")
  one    = BigDecimal("1")
  two    = BigDecimal("2")

  m25    = BigDecimal("-0.04")
  m57121 = BigDecimal("-57121")

  pi     = zero

  d = one
  k = one
  w = one
  t = BigDecimal("-80")
  while d.nonzero? && ((m = n - (pi.exponent - d.exponent).abs) > 0)
    m = BigDecimal.double_fig if m < BigDecimal.double_fig
    t   = t*m25
    d   = t.div(k,m)
    k   = k+two
    pi  = pi + d
  end

  d = one
  k = one
  w = one
  t = BigDecimal("956")
  while d.nonzero? && ((m = n - (pi.exponent - d.exponent).abs) > 0)
    m = BigDecimal.double_fig if m < BigDecimal.double_fig
    t   = t.div(m57121,n)
    d   = t.div(k,m)
    pi  = pi + d
    k   = k+two
  end
  pi
end
            
atan(x, prec) click to toggle source

Computes the arctangent of x to the specified number of digits of precision.

If x is NaN, returns NaN.

 
               # File bigdecimal/lib/bigdecimal/math.rb, line 119
def atan(x, prec)
  raise ArgumentError, "Zero or negative precision for atan" if prec <= 0
  return BigDecimal("NaN") if x.nan?
  pi = PI(prec)
  x = -x if neg = x < 0
  return pi.div(neg ? -2 : 2, prec) if x.infinite?
  return pi / (neg ? -4 : 4) if x.round(prec) == 1
  x = BigDecimal("1").div(x, prec) if inv = x > 1
  x = (-1 + sqrt(1 + x**2, prec))/x if dbl = x > 0.5
  n    = prec + BigDecimal.double_fig
  y = x
  d = y
  t = x
  r = BigDecimal("3")
  x2 = x.mult(x,n)
  while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0)
    m = BigDecimal.double_fig if m < BigDecimal.double_fig
    t = -t.mult(x2,n)
    d = t.div(r,m)
    y += d
    r += 2
  end
  y *= 2 if dbl
  y = pi / 2 - y if inv
  y = -y if neg
  y
end
            
cos(x, prec) click to toggle source

Computes the cosine of x to the specified number of digits of precision.

If x is infinite or NaN, returns NaN.

 
               # File bigdecimal/lib/bigdecimal/math.rb, line 83
def cos(x, prec)
  raise ArgumentError, "Zero or negative precision for cos" if prec <= 0
  return BigDecimal("NaN") if x.infinite? || x.nan?
  n    = prec + BigDecimal.double_fig
  one  = BigDecimal("1")
  two  = BigDecimal("2")
  x = -x if x < 0
  if x > (twopi = two * BigMath.PI(prec))
    if x > 30
      x = twopi
    else
      x -= twopi while x > twopi
    end
  end
  x1 = one
  x2 = x.mult(x,n)
  sign = 1
  y = one
  d = y
  i = BigDecimal("0")
  z = one
  while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0)
    m = BigDecimal.double_fig if m < BigDecimal.double_fig
    sign = -sign
    x1  = x2.mult(x1,n)
    i  += two
    z  *= (i-one) * i
    d   = sign * x1.div(z,m)
    y  += d
  end
  y
end
            
sin(x, prec) click to toggle source

Computes the sine of x to the specified number of digits of precision.

If x is infinite or NaN, returns NaN.

 
               # File bigdecimal/lib/bigdecimal/math.rb, line 47
def sin(x, prec)
  raise ArgumentError, "Zero or negative precision for sin" if prec <= 0
  return BigDecimal("NaN") if x.infinite? || x.nan?
  n    = prec + BigDecimal.double_fig
  one  = BigDecimal("1")
  two  = BigDecimal("2")
  x = -x if neg = x < 0
  if x > (twopi = two * BigMath.PI(prec))
    if x > 30
      x = twopi
    else
      x -= twopi while x > twopi
    end
  end
  x1   = x
  x2   = x.mult(x,n)
  sign = 1
  y    = x
  d    = y
  i    = one
  z    = one
  while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0)
    m = BigDecimal.double_fig if m < BigDecimal.double_fig
    sign = -sign
    x1  = x2.mult(x1,n)
    i  += two
    z  *= (i-one) * i
    d   = sign * x1.div(z,m)
    y  += d
  end
  neg ? -y : y
end
            
sqrt(x,prec) click to toggle source

Computes the square root of x to the specified number of digits of precision.

BigDecimal.new('2').sqrt(16).to_s

-> "0.14142135623730950488016887242096975E1"
 
               # File bigdecimal/lib/bigdecimal/math.rb, line 40
def sqrt(x,prec)
  x.sqrt(prec)
end
            

Commenting is here to help enhance the documentation. For example, code samples, or clarification of the documentation.

If you have questions about Ruby or the documentation, please post to one of the Ruby mailing lists. You will get better, faster, help that way.

If you wish to post a correction of the docs, please do so, but also file bug report so that it can be corrected for the next release. Thank you.

If you want to help improve the Ruby documentation, please visit Documenting-ruby.org.

blog comments powered by Disqus