numeric.c

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/**********************************************************************

  numeric.c -

  $Author: matz $
  $Date: 2005/10/30 18:20:53 $
  created at: Fri Aug 13 18:33:09 JST 1993

  Copyright (C) 1993-2003 Yukihiro Matsumoto

**********************************************************************/

#include "ruby.h"
#include "env.h"
#include <ctype.h>
#include <math.h>
#include <stdio.h>

#if defined(__FreeBSD__) && __FreeBSD__ < 4
#include <floatingpoint.h>
#endif

#ifdef HAVE_FLOAT_H
#include <float.h>
#endif

#ifdef HAVE_IEEEFP_H
#include <ieeefp.h>
#endif

/* use IEEE 64bit values if not defined */
#ifndef FLT_RADIX
#define FLT_RADIX 2
#endif
#ifndef FLT_ROUNDS
#define FLT_ROUNDS 1
#endif
#ifndef DBL_MIN
#define DBL_MIN 2.2250738585072014e-308
#endif
#ifndef DBL_MAX
#define DBL_MAX 1.7976931348623157e+308
#endif
#ifndef DBL_MIN_EXP
#define DBL_MIN_EXP (-1021)
#endif
#ifndef DBL_MAX_EXP
#define DBL_MAX_EXP 1024
#endif
#ifndef DBL_MIN_10_EXP
#define DBL_MIN_10_EXP (-307)
#endif
#ifndef DBL_MAX_10_EXP
#define DBL_MAX_10_EXP 308
#endif
#ifndef DBL_DIG
#define DBL_DIG 15
#endif
#ifndef DBL_MANT_DIG
#define DBL_MANT_DIG 53
#endif
#ifndef DBL_EPSILON
#define DBL_EPSILON 2.2204460492503131e-16
#endif

static ID id_coerce, id_to_i, id_eq;

VALUE rb_cNumeric;
VALUE rb_cFloat;
VALUE rb_cInteger;
VALUE rb_cFixnum;

VALUE rb_eZeroDivError;
VALUE rb_eFloatDomainError;

void
rb_num_zerodiv()
{
    rb_raise(rb_eZeroDivError, "divided by 0");
}


/*
 *  call-seq:
 *     num.coerce(numeric)   => array
 *  
 *  If <i>aNumeric</i> is the same type as <i>num</i>, returns an array
 *  containing <i>aNumeric</i> and <i>num</i>. Otherwise, returns an
 *  array with both <i>aNumeric</i> and <i>num</i> represented as
 *  <code>Float</code> objects. This coercion mechanism is used by
 *  Ruby to handle mixed-type numeric operations: it is intended to
 *  find a compatible common type between the two operands of the operator.
 *     
 *     1.coerce(2.5)   #=> [2.5, 1.0]
 *     1.2.coerce(3)   #=> [3.0, 1.2]
 *     1.coerce(2)     #=> [2, 1]
 */

static VALUE
num_coerce(x, y)
    VALUE x, y;
{
    if (CLASS_OF(x) == CLASS_OF(y))
        return rb_assoc_new(y, x);
    return rb_assoc_new(rb_Float(y), rb_Float(x));
}

static VALUE
coerce_body(x)
    VALUE *x;
{
    return rb_funcall(x[1], id_coerce, 1, x[0]);
}

static VALUE
coerce_rescue(x)
    VALUE *x;
{
    volatile VALUE v = rb_inspect(x[1]);

    rb_raise(rb_eTypeError, "%s can't be coerced into %s",
             rb_special_const_p(x[1])?
             RSTRING(v)->ptr:
             rb_obj_classname(x[1]),
             rb_obj_classname(x[0]));
    return Qnil;                /* dummy */
}

static int
do_coerce(x, y, err)
    VALUE *x, *y;
    int err;
{
    VALUE ary;
    VALUE a[2];

    a[0] = *x; a[1] = *y;

    ary = rb_rescue(coerce_body, (VALUE)a, err?coerce_rescue:0, (VALUE)a);
    if (TYPE(ary) != T_ARRAY || RARRAY(ary)->len != 2) {
        if (err) {
            rb_raise(rb_eTypeError, "coerce must return [x, y]");
        }
        return Qfalse;
    }

    *x = RARRAY(ary)->ptr[0];
    *y = RARRAY(ary)->ptr[1];
    return Qtrue;
}

VALUE
rb_num_coerce_bin(x, y)
    VALUE x, y;
{
    do_coerce(&x, &y, Qtrue);
    return rb_funcall(x, ruby_frame->orig_func, 1, y);
}

VALUE
rb_num_coerce_cmp(x, y)
    VALUE x, y;
{
    if (do_coerce(&x, &y, Qfalse)) 
        return rb_funcall(x, ruby_frame->orig_func, 1, y);
    return Qnil;
}

VALUE
rb_num_coerce_relop(x, y)
    VALUE x, y;
{
    VALUE c, x0 = x, y0 = y;

    if (!do_coerce(&x, &y, Qfalse) ||
        NIL_P(c = rb_funcall(x, ruby_frame->orig_func, 1, y))) {
        rb_cmperr(x0, y0);
        return Qnil;            /* not reached */
    }
    return c;
}

/*
 * Trap attempts to add methods to <code>Numeric</code> objects. Always
 * raises a <code>TypeError</code>
 */

static VALUE
num_sadded(x, name)
    VALUE x, name;
{
    ruby_frame = ruby_frame->prev; /* pop frame for "singleton_method_added" */
    /* Numerics should be values; singleton_methods should not be added to them */
    rb_raise(rb_eTypeError,
             "can't define singleton method \"%s\" for %s",
             rb_id2name(rb_to_id(name)),
             rb_obj_classname(x)); 
    return Qnil;                /* not reached */
}

/* :nodoc: */
static VALUE
num_init_copy(x, y)
    VALUE x, y;
{
    /* Numerics are immutable values, which should not be copied */
    rb_raise(rb_eTypeError, "can't copy %s", rb_obj_classname(x));
    return Qnil;                /* not reached */
}

/*
 *  call-seq:
 *     +num    => num
 *  
 *  Unary Plus---Returns the receiver's value.
 */

static VALUE
num_uplus(num)
    VALUE num;
{
    return num;
}

/*
 *  call-seq:
 *     -num    => numeric
 *  
 *  Unary Minus---Returns the receiver's value, negated.
 */

static VALUE
num_uminus(num)
    VALUE num;
{
    VALUE zero;

    zero = INT2FIX(0);
    do_coerce(&zero, &num, Qtrue);

    return rb_funcall(zero, '-', 1, num);
}

/*
 *  call-seq:
 *     num.quo(numeric)    =>   result
 *  
 *  Equivalent to <code>Numeric#/</code>, but overridden in subclasses.
 */

static VALUE
num_quo(x, y)
    VALUE x, y;
{
    return rb_funcall(x, '/', 1, y);
}


/*
 *  call-seq:
 *     num.div(numeric)    => integer
 *  
 *  Uses <code>/</code> to perform division, then converts the result to
 *  an integer. <code>Numeric</code> does not define the <code>/</code>
 *  operator; this is left to subclasses.
 */

static VALUE
num_div(x, y)
    VALUE x, y;
{
    return rb_Integer(rb_funcall(x, '/', 1, y));
}



/*
 *  call-seq:
 *     num.divmod( aNumeric ) -> anArray
 *  
 *  Returns an array containing the quotient and modulus obtained by
 *  dividing <i>num</i> by <i>aNumeric</i>. If <code>q, r =
 *  x.divmod(y)</code>, then
 *
 *      q = floor(float(x)/float(y))
 *      x = q*y + r
 *     
 *  The quotient is rounded toward -infinity, as shown in the following table:
 *     
 *     a    |  b  |  a.divmod(b)  |   a/b   | a.modulo(b) | a.remainder(b)
 *    ------+-----+---------------+---------+-------------+---------------
 *     13   |  4  |   3,    1     |   3     |    1        |     1
 *    ------+-----+---------------+---------+-------------+---------------
 *     13   | -4  |  -4,   -3     |  -3     |   -3        |     1
 *    ------+-----+---------------+---------+-------------+---------------
 *    -13   |  4  |  -4,    3     |  -4     |    3        |    -1
 *    ------+-----+---------------+---------+-------------+---------------
 *    -13   | -4  |   3,   -1     |   3     |   -1        |    -1
 *    ------+-----+---------------+---------+-------------+---------------
 *     11.5 |  4  |   2.0,  3.5   |   2.875 |    3.5      |     3.5
 *    ------+-----+---------------+---------+-------------+---------------
 *     11.5 | -4  |  -3.0, -0.5   |  -2.875 |   -0.5      |     3.5
 *    ------+-----+---------------+---------+-------------+---------------
 *    -11.5 |  4  |  -3.0   0.5   |  -2.875 |    0.5      |    -3.5
 *    ------+-----+---------------+---------+-------------+---------------
 *    -11.5 | -4  |   2.0  -3.5   |   2.875 |   -3.5      |    -3.5
 *
 *
 *  Examples
 *     11.divmod(3)         #=> [3, 2]
 *     11.divmod(-3)        #=> [-4, -1]
 *     11.divmod(3.5)       #=> [3.0, 0.5]
 *     (-11).divmod(3.5)    #=> [-4.0, 3.0]
 *     (11.5).divmod(3.5)   #=> [3.0, 1.0]
 */

static VALUE
num_divmod(x, y)
    VALUE x, y;
{
    return rb_assoc_new(num_div(x, y), rb_funcall(x, '%', 1, y));
}

/*
 *  call-seq:
 *     num.modulo(numeric)    => result
 *  
 *  Equivalent to
 *  <i>num</i>.<code>divmod(</code><i>aNumeric</i><code>)[1]</code>.
 */

static VALUE
num_modulo(x, y)
    VALUE x, y;
{
    return rb_funcall(x, '%', 1, y);
}

/*
 *  call-seq:
 *     num.remainder(numeric)    => result
 *  
 *  If <i>num</i> and <i>numeric</i> have different signs, returns
 *  <em>mod</em>-<i>numeric</i>; otherwise, returns <em>mod</em>. In
 *  both cases <em>mod</em> is the value
 *  <i>num</i>.<code>modulo(</code><i>numeric</i><code>)</code>. The
 *  differences between <code>remainder</code> and modulo
 *  (<code>%</code>) are shown in the table under <code>Numeric#divmod</code>.
 */

static VALUE
num_remainder(x, y)
    VALUE x, y;
{
    VALUE z = rb_funcall(x, '%', 1, y);

    if ((!rb_equal(z, INT2FIX(0))) &&
        ((RTEST(rb_funcall(x, '<', 1, INT2FIX(0))) &&
          RTEST(rb_funcall(y, '>', 1, INT2FIX(0)))) ||
         (RTEST(rb_funcall(x, '>', 1, INT2FIX(0))) &&
          RTEST(rb_funcall(y, '<', 1, INT2FIX(0)))))) {
        return rb_funcall(z, '-', 1, y);
    }
    return z;
}

/*
 *  call-seq:
 *     num.integer? -> true or false
 *  
 *  Returns <code>true</code> if <i>num</i> is an <code>Integer</code>
 *  (including <code>Fixnum</code> and <code>Bignum</code>).
 */

static VALUE
num_int_p(num)
    VALUE num;
{
    return Qfalse;
}

/*
 *  call-seq:
 *     num.abs   => num or numeric
 *  
 *  Returns the absolute value of <i>num</i>.
 *     
 *     12.abs         #=> 12
 *     (-34.56).abs   #=> 34.56
 *     -34.56.abs     #=> 34.56
 */

static VALUE
num_abs(num)
    VALUE num;
{
    if (RTEST(rb_funcall(num, '<', 1, INT2FIX(0)))) {
        return rb_funcall(num, rb_intern("-@"), 0);
    }
    return num;
}


/*
 *  call-seq:
 *     num.zero?    => true or false
 *  
 *  Returns <code>true</code> if <i>num</i> has a zero value.
 */

static VALUE
num_zero_p(num)
    VALUE num;
{
    if (rb_equal(num, INT2FIX(0))) {
        return Qtrue;
    }
    return Qfalse;
}


/*
 *  call-seq:
 *     num.nonzero?    => num or nil
 *  
 *  Returns <i>num</i> if <i>num</i> is not zero, <code>nil</code>
 *  otherwise. This behavior is useful when chaining comparisons:
 *     
 *     a = %w( z Bb bB bb BB a aA Aa AA A )
 *     b = a.sort {|a,b| (a.downcase <=> b.downcase).nonzero? || a <=> b }
 *     b   #=> ["A", "a", "AA", "Aa", "aA", "BB", "Bb", "bB", "bb", "z"]
 */

static VALUE
num_nonzero_p(num)
    VALUE num;
{
    if (RTEST(rb_funcall(num, rb_intern("zero?"), 0, 0))) {
        return Qnil;
    }
    return num;
}

/*
 *  call-seq:
 *     num.to_int    => integer
 *  
 *  Invokes the child class's <code>to_i</code> method to convert
 *  <i>num</i> to an integer.
 */

static VALUE
num_to_int(num)
    VALUE num;
{
    return rb_funcall(num, id_to_i, 0, 0);
}


/********************************************************************
 * 
 * Document-class: Float
 *
 *  <code>Float</code> objects represent real numbers using the native
 *  architecture's double-precision floating point representation.
 */

VALUE
rb_float_new(d)
    double d;
{
    NEWOBJ(flt, struct RFloat);
    OBJSETUP(flt, rb_cFloat, T_FLOAT);

    flt->value = d;
    return (VALUE)flt;
}

/*
 *  call-seq:
 *     flt.to_s    => string
 *  
 *  Returns a string containing a representation of self. As well as a
 *  fixed or exponential form of the number, the call may return
 *  ``<code>NaN</code>'', ``<code>Infinity</code>'', and
 *  ``<code>-Infinity</code>''.
 */

static VALUE
flo_to_s(flt)
    VALUE flt;
{
    char buf[32];
    double value = RFLOAT(flt)->value;
    char *p, *e;

    if (isinf(value))
        return rb_str_new2(value < 0 ? "-Infinity" : "Infinity");
    else if(isnan(value))
        return rb_str_new2("NaN");

    sprintf(buf, "%#.15g", value); /* ensure to print decimal point */
    if (!(e = strchr(buf, 'e'))) {
        e = buf + strlen(buf);
    }
    if (!ISDIGIT(e[-1])) { /* reformat if ended with decimal point (ex 111111111111111.) */
        sprintf(buf, "%#.14e", value);
        if (!(e = strchr(buf, 'e'))) {
            e = buf + strlen(buf);
        }
    }
    p = e;
    while (p[-1]=='0' && ISDIGIT(p[-2]))
        p--;
    memmove(p, e, strlen(e)+1);
    return rb_str_new2(buf);
}

/*
 * MISSING: documentation
 */

static VALUE
flo_coerce(x, y)
    VALUE x, y;
{
    return rb_assoc_new(rb_Float(y), x);
}

/*
 * call-seq:
 *    -float   => float
 *
 * Returns float, negated.
 */

static VALUE
flo_uminus(flt)
    VALUE flt;
{
    return rb_float_new(-RFLOAT(flt)->value);
}

/*
 * call-seq:
 *   float + other   => float
 *
 * Returns a new float which is the sum of <code>float</code>
 * and <code>other</code>.
 */

static VALUE
flo_plus(x, y)
    VALUE x, y;
{
    switch (TYPE(y)) {
      case T_FIXNUM:
        return rb_float_new(RFLOAT(x)->value + (double)FIX2LONG(y));
      case T_BIGNUM:
        return rb_float_new(RFLOAT(x)->value + rb_big2dbl(y));
      case T_FLOAT:
        return rb_float_new(RFLOAT(x)->value + RFLOAT(y)->value);
      default:
        return rb_num_coerce_bin(x, y);
    }
}

/*
 * call-seq:
 *   float + other   => float
 *
 * Returns a new float which is the difference of <code>float</code>
 * and <code>other</code>.
 */

static VALUE
flo_minus(x, y)
    VALUE x, y;
{
    switch (TYPE(y)) {
      case T_FIXNUM:
        return rb_float_new(RFLOAT(x)->value - (double)FIX2LONG(y));
      case T_BIGNUM:
        return rb_float_new(RFLOAT(x)->value - rb_big2dbl(y));
      case T_FLOAT:
        return rb_float_new(RFLOAT(x)->value - RFLOAT(y)->value);
      default:
        return rb_num_coerce_bin(x, y);
    }
}

/*
 * call-seq:
 *   float * other   => float
 *
 * Returns a new float which is the product of <code>float</code>
 * and <code>other</code>.
 */

static VALUE
flo_mul(x, y)
    VALUE x, y;
{
    switch (TYPE(y)) {
      case T_FIXNUM:
        return rb_float_new(RFLOAT(x)->value * (double)FIX2LONG(y));
      case T_BIGNUM:
        return rb_float_new(RFLOAT(x)->value * rb_big2dbl(y));
      case T_FLOAT:
        return rb_float_new(RFLOAT(x)->value * RFLOAT(y)->value);
      default:
        return rb_num_coerce_bin(x, y);
    }
}

/*
 * call-seq:
 *   float / other   => float
 *
 * Returns a new float which is the result of dividing
 * <code>float</code> by <code>other</code>.
 */

static VALUE
flo_div(x, y)
    VALUE x, y;
{
    long f_y;
    double d;

    switch (TYPE(y)) {
      case T_FIXNUM:
        f_y = FIX2LONG(y);
        return rb_float_new(RFLOAT(x)->value / (double)f_y);
      case T_BIGNUM:
        d = rb_big2dbl(y);
        return rb_float_new(RFLOAT(x)->value / d);
      case T_FLOAT:
        return rb_float_new(RFLOAT(x)->value / RFLOAT(y)->value);
      default:
        return rb_num_coerce_bin(x, y);
    }
}


static void
flodivmod(x, y, divp, modp)
    double x, y;
    double *divp, *modp;
{
    double div, mod;

#ifdef HAVE_FMOD
    mod = fmod(x, y);
#else
    {
        double z;

        modf(x/y, &z);
        mod = x - z * y;
    }
#endif
    div = (x - mod) / y;
    if (y*mod < 0) {
        mod += y;
        div -= 1.0;
    }
    if (modp) *modp = mod;
    if (divp) *divp = div;
}


/*
 *  call-seq:
 *     flt % other         => float
 *     flt.modulo(other)   => float
 *  
 *  Return the modulo after division of <code>flt</code> by <code>other</code>.
 *     
 *     6543.21.modulo(137)      #=> 104.21
 *     6543.21.modulo(137.24)   #=> 92.9299999999996
 */

static VALUE
flo_mod(x, y)
    VALUE x, y;
{
    double fy, mod;

    switch (TYPE(y)) {
      case T_FIXNUM:
        fy = (double)FIX2LONG(y);
        break;
      case T_BIGNUM:
        fy = rb_big2dbl(y);
        break;
      case T_FLOAT:
        fy = RFLOAT(y)->value;
        break;
      default:
        return rb_num_coerce_bin(x, y);
    }
    flodivmod(RFLOAT(x)->value, fy, 0, &mod);
    return rb_float_new(mod);
}

/*
 *  call-seq:
 *     flt.divmod(numeric)    => array
 *  
 *  See <code>Numeric#divmod</code>.
 */

static VALUE
flo_divmod(x, y)
    VALUE x, y;
{
    double fy, div, mod;
    volatile VALUE a, b;

    switch (TYPE(y)) {
      case T_FIXNUM:
        fy = (double)FIX2LONG(y);
        break;
      case T_BIGNUM:
        fy = rb_big2dbl(y);
        break;
      case T_FLOAT:
        fy = RFLOAT(y)->value;
        break;
      default:
        return rb_num_coerce_bin(x, y);
    }
    flodivmod(RFLOAT(x)->value, fy, &div, &mod);
    a = rb_float_new(div);
    b = rb_float_new(mod);
    return rb_assoc_new(a, b);
}

/*
 * call-seq:
 *
 *  flt ** other   => float
 *
 * Raises <code>float</code> the <code>other</code> power.
 */
 
static VALUE
flo_pow(x, y)
    VALUE x, y;
{
    switch (TYPE(y)) {
      case T_FIXNUM:
        return rb_float_new(pow(RFLOAT(x)->value, (double)FIX2LONG(y)));
      case T_BIGNUM:
        return rb_float_new(pow(RFLOAT(x)->value, rb_big2dbl(y)));
      case T_FLOAT:
        return rb_float_new(pow(RFLOAT(x)->value, RFLOAT(y)->value));
      default:
        return rb_num_coerce_bin(x, y);
    }
}

/*
 *  call-seq:
 *     num.eql?(numeric)    => true or false
 *  
 *  Returns <code>true</code> if <i>num</i> and <i>numeric</i> are the
 *  same type and have equal values.
 *     
 *     1 == 1.0          #=> true
 *     1.eql?(1.0)       #=> false
 *     (1.0).eql?(1.0)   #=> true
 */

static VALUE
num_eql(x, y)
    VALUE x, y;
{
    if (TYPE(x) != TYPE(y)) return Qfalse;

    return rb_equal(x, y);
}

/*
 *  call-seq:
 *     num <=> other -> 0 or nil
 *  
 *  Returns zero if <i>num</i> equals <i>other</i>, <code>nil</code>
 *  otherwise.
 */

static VALUE
num_cmp(x, y)
    VALUE x, y;
{
    if (x == y) return INT2FIX(0);
    return Qnil;
}

static VALUE
num_equal(x, y)
    VALUE x, y;
{
    if (x == y) return Qtrue;
    return rb_funcall(y, id_eq, 1, x);
}

/*
 *  call-seq:
 *     flt == obj   => true or false
 *  
 *  Returns <code>true</code> only if <i>obj</i> has the same value
 *  as <i>flt</i>. Contrast this with <code>Float#eql?</code>, which
 *  requires <i>obj</i> to be a <code>Float</code>.
 *     
 *     1.0 == 1   #=> true
 *     
 */

static VALUE
flo_eq(x, y)
    VALUE x, y;
{
    volatile double a, b;

    switch (TYPE(y)) {
      case T_FIXNUM:
        b = FIX2LONG(y);
        break;
      case T_BIGNUM:
        b = rb_big2dbl(y);
        break;
      case T_FLOAT:
        b = RFLOAT(y)->value;
        if (isnan(b)) return Qfalse;
        break;
      default:
        return num_equal(x, y);
    }
    a = RFLOAT(x)->value;
    if (isnan(a)) return Qfalse;
    return (a == b)?Qtrue:Qfalse;
}

/*
 * call-seq:
 *   flt.hash   => integer
 *
 * Returns a hash code for this float.
 */

static VALUE
flo_hash(num)
    VALUE num;
{
    double d;
    char *c;
    int i, hash;

    d = RFLOAT(num)->value;
    if (d == 0) d = fabs(d);
    c = (char*)&d;
    for (hash=0, i=0; i<sizeof(double);i++) {
        hash += c[i] * 971;
    }
    if (hash < 0) hash = -hash;
    return INT2FIX(hash);
}

VALUE
rb_dbl_cmp(a, b)
    double a, b;
{
    if (isnan(a) || isnan(b)) return Qnil;
    if (a == b) return INT2FIX(0);
    if (a > b) return INT2FIX(1);
    if (a < b) return INT2FIX(-1);
    return Qnil;
}

/*
 *  call-seq:
 *     flt <=> numeric   => -1, 0, +1
 *  
 *  Returns -1, 0, or +1 depending on whether <i>flt</i> is less than,
 *  equal to, or greater than <i>numeric</i>. This is the basis for the
 *  tests in <code>Comparable</code>.
 */

static VALUE
flo_cmp(x, y)
    VALUE x, y;
{
    double a, b;

    a = RFLOAT(x)->value;
    switch (TYPE(y)) {
      case T_FIXNUM:
        b = (double)FIX2LONG(y);
        break;

      case T_BIGNUM:
        b = rb_big2dbl(y);
        break;

      case T_FLOAT:
        b = RFLOAT(y)->value;
        break;

      default:
        return rb_num_coerce_cmp(x, y);
    }
    return rb_dbl_cmp(a, b);
}

/*
 * call-seq:
 *   flt > other    =>  true or false
 *
 * <code>true</code> if <code>flt</code> is greater than <code>other</code>.
 */

static VALUE
flo_gt(x, y)
    VALUE x, y;
{
    double a, b;

    a = RFLOAT(x)->value;
    switch (TYPE(y)) {
      case T_FIXNUM:
        b = (double)FIX2LONG(y);
        break;

      case T_BIGNUM:
        b = rb_big2dbl(y);
        break;

      case T_FLOAT:
        b = RFLOAT(y)->value;
        if (isnan(b)) return Qfalse;
        break;

      default:
        return rb_num_coerce_relop(x, y);
    }
    if (isnan(a)) return Qfalse;
    return (a > b)?Qtrue:Qfalse;
}

/*
 * call-seq:
 *   flt >= other    =>  true or false
 *
 * <code>true</code> if <code>flt</code> is greater than 
 * or equal to <code>other</code>.
 */

static VALUE
flo_ge(x, y)
    VALUE x, y;
{
    double a, b;

    a = RFLOAT(x)->value;
    switch (TYPE(y)) {
      case T_FIXNUM:
        b = (double)FIX2LONG(y);
        break;

      case T_BIGNUM:
        b = rb_big2dbl(y);
        break;

      case T_FLOAT:
        b = RFLOAT(y)->value;
        if (isnan(b)) return Qfalse;
        break;

      default:
        return rb_num_coerce_relop(x, y);
    }
    if (isnan(a)) return Qfalse;
    return (a >= b)?Qtrue:Qfalse;
}

/*
 * call-seq:
 *   flt < other    =>  true or false
 *
 * <code>true</code> if <code>flt</code> is less than <code>other</code>.
 */

static VALUE
flo_lt(x, y)
    VALUE x, y;
{
    double a, b;

    a = RFLOAT(x)->value;
    switch (TYPE(y)) {
      case T_FIXNUM:
        b = (double)FIX2LONG(y);
        break;

      case T_BIGNUM:
        b = rb_big2dbl(y);
        break;

      case T_FLOAT:
        b = RFLOAT(y)->value;
        if (isnan(b)) return Qfalse;
        break;

      default:
        return rb_num_coerce_relop(x, y);
    }
    if (isnan(a)) return Qfalse;
    return (a < b)?Qtrue:Qfalse;
}

/*
 * call-seq:
 *   flt <= other    =>  true or false
 *
 * <code>true</code> if <code>flt</code> is less than
 * or equal to <code>other</code>.
 */

static VALUE
flo_le(x, y)
    VALUE x, y;
{
    double a, b;

    a = RFLOAT(x)->value;
    switch (TYPE(y)) {
      case T_FIXNUM:
        b = (double)FIX2LONG(y);
        break;

      case T_BIGNUM:
        b = rb_big2dbl(y);
        break;

      case T_FLOAT:
        b = RFLOAT(y)->value;
        if (isnan(b)) return Qfalse;
        break;

      default:
        return rb_num_coerce_relop(x, y);
    }
    if (isnan(a)) return Qfalse;
    return (a <= b)?Qtrue:Qfalse;
}

/*
 *  call-seq:
 *     flt.eql?(obj)   => true or false
 *  
 *  Returns <code>true</code> only if <i>obj</i> is a
 *  <code>Float</code> with the same value as <i>flt</i>. Contrast this
 *  with <code>Float#==</code>, which performs type conversions.
 *     
 *     1.0.eql?(1)   #=> false
 */

static VALUE
flo_eql(x, y)
    VALUE x, y;
{
    if (TYPE(y) == T_FLOAT) {
        double a = RFLOAT(x)->value;
        double b = RFLOAT(y)->value;

        if (isnan(a) || isnan(b)) return Qfalse;
        if (a == b) return Qtrue;
    }
    return Qfalse;
}

/*
 * call-seq:
 *   flt.to_f   => flt
 *
 * As <code>flt</code> is already a float, returns <i>self</i>.
 */

static VALUE
flo_to_f(num)
    VALUE num;
{
    return num;
}

/*
 *  call-seq:
 *     flt.abs    => float
 *  
 *  Returns the absolute value of <i>flt</i>.
 *     
 *     (-34.56).abs   #=> 34.56
 *     -34.56.abs     #=> 34.56
 *     
 */

static VALUE
flo_abs(flt)
    VALUE flt;
{
    double val = fabs(RFLOAT(flt)->value);
    return rb_float_new(val);
}

/*
 *  call-seq:
 *     flt.zero? -> true or false
 *  
 *  Returns <code>true</code> if <i>flt</i> is 0.0.
 *     
 */

static VALUE
flo_zero_p(num)
    VALUE num;
{
    if (RFLOAT(num)->value == 0.0) {
        return Qtrue;
    }
    return Qfalse;
}

/*
 *  call-seq:
 *     flt.nan? -> true or false
 *  
 *  Returns <code>true</code> if <i>flt</i> is an invalid IEEE floating
 *  point number.
 *     
 *     a = -1.0      #=> -1.0
 *     a.nan?        #=> false
 *     a = 0.0/0.0   #=> NaN
 *     a.nan?        #=> true
 */

static VALUE
flo_is_nan_p(num)
     VALUE num;
{     
    double value = RFLOAT(num)->value;

    return isnan(value) ? Qtrue : Qfalse;
}

/*
 *  call-seq:
 *     flt.infinite? -> nil, -1, +1
 *  
 *  Returns <code>nil</code>, -1, or +1 depending on whether <i>flt</i>
 *  is finite, -infinity, or +infinity.
 *     
 *     (0.0).infinite?        #=> nil
 *     (-1.0/0.0).infinite?   #=> -1
 *     (+1.0/0.0).infinite?   #=> 1
 */

static VALUE
flo_is_infinite_p(num)
     VALUE num;
{     
    double value = RFLOAT(num)->value;

    if (isinf(value)) {
        return INT2FIX( value < 0 ? -1 : 1 );
    }

    return Qnil;
}

/*
 *  call-seq:
 *     flt.finite? -> true or false
 *  
 *  Returns <code>true</code> if <i>flt</i> is a valid IEEE floating
 *  point number (it is not infinite, and <code>nan?</code> is
 *  <code>false</code>).
 *     
 */

static VALUE
flo_is_finite_p(num)
     VALUE num;
{     
    double value = RFLOAT(num)->value;

#if HAVE_FINITE
    if (!finite(value))
        return Qfalse;
#else
    if (isinf(value) || isnan(value))
        return Qfalse;
#endif

    return Qtrue;
}

/*
 *  call-seq:
 *     flt.floor   => integer
 *  
 *  Returns the largest integer less than or equal to <i>flt</i>.
 *     
 *     1.2.floor      #=> 1
 *     2.0.floor      #=> 2
 *     (-1.2).floor   #=> -2
 *     (-2.0).floor   #=> -2
 */

static VALUE
flo_floor(num)
    VALUE num;
{
    double f = floor(RFLOAT(num)->value);
    long val;

    if (!FIXABLE(f)) {
        return rb_dbl2big(f);
    }
    val = f;
    return LONG2FIX(val);
}

/*
 *  call-seq:
 *     flt.ceil    => integer
 *  
 *  Returns the smallest <code>Integer</code> greater than or equal to
 *  <i>flt</i>.
 *     
 *     1.2.ceil      #=> 2
 *     2.0.ceil      #=> 2
 *     (-1.2).ceil   #=> -1
 *     (-2.0).ceil   #=> -2
 */

static VALUE
flo_ceil(num)
    VALUE num;
{
    double f = ceil(RFLOAT(num)->value);
    long val;

    if (!FIXABLE(f)) {
        return rb_dbl2big(f);
    }
    val = f;
    return LONG2FIX(val);
}

/*
 *  call-seq:
 *     flt.round   => integer
 *  
 *  Rounds <i>flt</i> to the nearest integer. Equivalent to:
 *     
 *     def round
 *       return floor(self+0.5) if self > 0.0
 *       return ceil(self-0.5)  if self < 0.0
 *       return 0.0
 *     end
 *     
 *     1.5.round      #=> 2
 *     (-1.5).round   #=> -2
 *     
 */

static VALUE
flo_round(num)
    VALUE num;
{
    double f = RFLOAT(num)->value;
    long val;

    if (f > 0.0) f = floor(f+0.5);
    if (f < 0.0) f = ceil(f-0.5);

    if (!FIXABLE(f)) {
        return rb_dbl2big(f);
    }
    val = f;
    return LONG2FIX(val);
}

/*
 *  call-seq:
 *     flt.to_i       => integer
 *     flt.to_int     => integer
 *     flt.truncate   => integer
 *  
 *  Returns <i>flt</i> truncated to an <code>Integer</code>.
 */

static VALUE
flo_truncate(num)
    VALUE num;
{
    double f = RFLOAT(num)->value;
    long val;

    if (f > 0.0) f = floor(f);
    if (f < 0.0) f = ceil(f);

    if (!FIXABLE(f)) {
        return rb_dbl2big(f);
    }
    val = f;
    return LONG2FIX(val);
}


/*
 *  call-seq:
 *     num.floor    => integer
 *  
 *  Returns the largest integer less than or equal to <i>num</i>.
 *  <code>Numeric</code> implements this by converting <i>anInteger</i>
 *  to a <code>Float</code> and invoking <code>Float#floor</code>.
 *     
 *     1.floor      #=> 1
 *     (-1).floor   #=> -1
 */

static VALUE
num_floor(num)
    VALUE num;
{
    return flo_floor(rb_Float(num));
}


/*
 *  call-seq:
 *     num.ceil    => integer
 *  
 *  Returns the smallest <code>Integer</code> greater than or equal to
 *  <i>num</i>. Class <code>Numeric</code> achieves this by converting
 *  itself to a <code>Float</code> then invoking
 *  <code>Float#ceil</code>.
 *     
 *     1.ceil        #=> 1
 *     1.2.ceil      #=> 2
 *     (-1.2).ceil   #=> -1
 *     (-1.0).ceil   #=> -1
 */

static VALUE
num_ceil(num)
    VALUE num;
{
    return flo_ceil(rb_Float(num));
}

/*
 *  call-seq:
 *     num.round    => integer
 *  
 *  Rounds <i>num</i> to the nearest integer. <code>Numeric</code>
 *  implements this by converting itself to a
 *  <code>Float</code> and invoking <code>Float#round</code>.
 */

static VALUE
num_round(num)
    VALUE num;
{
    return flo_round(rb_Float(num));
}

/*
 *  call-seq:
 *     num.truncate    => integer
 *  
 *  Returns <i>num</i> truncated to an integer. <code>Numeric</code>
 *  implements this by converting its value to a float and invoking
 *  <code>Float#truncate</code>.
 */

static VALUE
num_truncate(num)
    VALUE num;
{
    return flo_truncate(rb_Float(num));
}


/*
 *  call-seq:
 *     num.step(limit, step ) {|i| block }     => num
 *  
 *  Invokes <em>block</em> with the sequence of numbers starting at
 *  <i>num</i>, incremented by <i>step</i> on each call. The loop
 *  finishes when the value to be passed to the block is greater than
 *  <i>limit</i> (if <i>step</i> is positive) or less than
 *  <i>limit</i> (if <i>step</i> is negative). If all the arguments are
 *  integers, the loop operates using an integer counter. If any of the
 *  arguments are floating point numbers, all are converted to floats,
 *  and the loop is executed <i>floor(n + n*epsilon)+ 1</i> times,
 *  where <i>n = (limit - num)/step</i>. Otherwise, the loop
 *  starts at <i>num</i>, uses either the <code><</code> or
 *  <code>></code> operator to compare the counter against
 *  <i>limit</i>, and increments itself using the <code>+</code>
 *  operator.
 *     
 *     1.step(10, 2) { |i| print i, " " }
 *     Math::E.step(Math::PI, 0.2) { |f| print f, " " }
 *     
 *  <em>produces:</em>
 *     
 *     1 3 5 7 9
 *     2.71828182845905 2.91828182845905 3.11828182845905
 */

static VALUE
num_step(argc, argv, from)
    int argc;
    VALUE *argv;
    VALUE from;
{
    VALUE to, step;

    if (argc == 1) {
        to = argv[0];
        step = INT2FIX(1);
    }
    else {
        if (argc == 2) {
            to = argv[0];
            step = argv[1];
        }
        else {
            rb_raise(rb_eArgError, "wrong number of arguments");
        }
        if (rb_equal(step, INT2FIX(0))) {
            rb_raise(rb_eArgError, "step can't be 0");
        }
    }

    if (FIXNUM_P(from) && FIXNUM_P(to) && FIXNUM_P(step)) {
        long i, end, diff;

        i = FIX2LONG(from);
        end = FIX2LONG(to);
        diff = FIX2LONG(step);

        if (diff > 0) {
            while (i <= end) {
                rb_yield(LONG2FIX(i));
                i += diff;
            }
        }
        else {
            while (i >= end) {
                rb_yield(LONG2FIX(i));
                i += diff;
            }
        }
    }
    else if (TYPE(from) == T_FLOAT || TYPE(to) == T_FLOAT || TYPE(step) == T_FLOAT) {
        const double epsilon = DBL_EPSILON;
        double beg = NUM2DBL(from);
        double end = NUM2DBL(to);
        double unit = NUM2DBL(step);
        double n = (end - beg)/unit;
        double err = (fabs(beg) + fabs(end) + fabs(end-beg)) / fabs(unit) * epsilon;
        long i;

        if (err>0.5) err=0.5;
        n = floor(n + err) + 1;
        for (i=0; i<n; i++) {
            rb_yield(rb_float_new(i*unit+beg));
        }
    }
    else {
        VALUE i = from;
        ID cmp;

        if (RTEST(rb_funcall(step, '>', 1, INT2FIX(0)))) {
            cmp = '>';
        }
        else {
            cmp = '<';
        }
        for (;;) {
            if (RTEST(rb_funcall(i, cmp, 1, to))) break;
            rb_yield(i);
            i = rb_funcall(i, '+', 1, step);
        }
    }
    return from;
}

long
rb_num2long(val)
    VALUE val;
{
    if (NIL_P(val)) {
        rb_raise(rb_eTypeError, "no implicit conversion from nil to integer");
    }

    if (FIXNUM_P(val)) return FIX2LONG(val);

    switch (TYPE(val)) {
      case T_FLOAT:
        if (RFLOAT(val)->value <= (double)LONG_MAX
            && RFLOAT(val)->value >= (double)LONG_MIN) {
            return (long)(RFLOAT(val)->value);
        }
        else {
            char buf[24];
            char *s;

            sprintf(buf, "%-.10g", RFLOAT(val)->value);
            if (s = strchr(buf, ' ')) *s = '\0';
            rb_raise(rb_eRangeError, "float %s out of range of integer", buf);
        }

      case T_BIGNUM:
        return rb_big2long(val);

      default:
        val = rb_to_int(val);
        return NUM2LONG(val);
    }
}

unsigned long
rb_num2ulong(val)
    VALUE val;
{
    if (TYPE(val) == T_BIGNUM) {
        return rb_big2ulong(val);
    }
    return (unsigned long)rb_num2long(val);
}

#if SIZEOF_INT < SIZEOF_LONG
static void
check_int(num)
    long num;
{
    const char *s;

    if (num < INT_MIN) {
        s = "small";
    }
    else if (num > INT_MAX) {
        s = "big";
    }
    else {
        return;
    }
    rb_raise(rb_eRangeError, "integer %ld too %s to convert to `int'", num, s);
}

static void
check_uint(num)
    unsigned long num;
{
    if (num > UINT_MAX) {
        rb_raise(rb_eRangeError, "integer %lu too big to convert to `unsigned int'", num);
    }
}

long
rb_num2int(val)
    VALUE val;
{
    long num = rb_num2long(val);

    check_int(num);
    return num;
}

long
rb_fix2int(val)
    VALUE val;
{
    long num = FIXNUM_P(val)?FIX2LONG(val):rb_num2long(val);

    check_int(num);
    return num;
}

unsigned long
rb_num2uint(val)
    VALUE val;
{
    unsigned long num = rb_num2ulong(val);

    if (RTEST(rb_funcall(INT2FIX(0), '<', 1, val))) {
        check_uint(num);
    }
    return num;
}

unsigned long
rb_fix2uint(val)
    VALUE val;
{
    unsigned long num;

    if (!FIXNUM_P(val)) {
        return rb_num2uint(val);
    }
    num = FIX2ULONG(val);
    if (FIX2LONG(val) > 0) {
        check_uint(num);
    }
    return num;
}
#else
long
rb_num2int(val)
    VALUE val;
{
    return rb_num2long(val);
}

long
rb_fix2int(val)
    VALUE val;
{
    return FIX2INT(val);
}
#endif

VALUE
rb_num2fix(val)
    VALUE val;
{
    long v;

    if (FIXNUM_P(val)) return val;

    v = rb_num2long(val);
    if (!FIXABLE(v))
        rb_raise(rb_eRangeError, "integer %ld out of range of fixnum", v);
    return LONG2FIX(v);
}

#if HAVE_LONG_LONG

LONG_LONG
rb_num2ll(val)
    VALUE val;
{
    if (NIL_P(val)) {
        rb_raise(rb_eTypeError, "no implicit conversion from nil");
    }

    if (FIXNUM_P(val)) return (LONG_LONG)FIX2LONG(val);

    switch (TYPE(val)) {
    case T_FLOAT:
        if (RFLOAT(val)->value <= (double)LLONG_MAX
            && RFLOAT(val)->value >= (double)LLONG_MIN) {
            return (LONG_LONG)(RFLOAT(val)->value);
        }
        else {
            char buf[24];
            char *s;

            sprintf(buf, "%-.10g", RFLOAT(val)->value);
            if (s = strchr(buf, ' ')) *s = '\0';
            rb_raise(rb_eRangeError, "float %s out of range of long long", buf);
        }

    case T_BIGNUM:
        return rb_big2ll(val);

    case T_STRING:
        rb_raise(rb_eTypeError, "no implicit conversion from string");
        return Qnil;            /* not reached */

    case T_TRUE:
    case T_FALSE:
        rb_raise(rb_eTypeError, "no implicit conversion from boolean");
        return Qnil;            /* not reached */

      default:
          val = rb_to_int(val);
          return NUM2LL(val);
    }
}

unsigned LONG_LONG
rb_num2ull(val)
    VALUE val;
{
    if (TYPE(val) == T_BIGNUM) {
        return rb_big2ull(val);
    }
    return (unsigned LONG_LONG)rb_num2ll(val);
}

#endif  /* HAVE_LONG_LONG */


/*
 * Document-class: Integer
 *
 *  <code>Integer</code> is the basis for the two concrete classes that
 *  hold whole numbers, <code>Bignum</code> and <code>Fixnum</code>.
 *     
 */


/*
 *  call-seq:
 *     int.to_i      => int
 *     int.to_int    => int
 *     int.floor     => int
 *     int.ceil      => int
 *     int.round     => int
 *     int.truncate  => int
 *
 *  As <i>int</i> is already an <code>Integer</code>, all these
 *  methods simply return the receiver.
 */

static VALUE
int_to_i(num)
    VALUE num;
{
    return num;
}

/*
 *  call-seq:
 *     int.integer? -> true
 *  
 *  Always returns <code>true</code>.
 */

static VALUE
int_int_p(num)
    VALUE num;
{
    return Qtrue;
}

/*
 *  call-seq:
 *     int.next    => integer
 *     int.succ    => integer
 *  
 *  Returns the <code>Integer</code> equal to <i>int</i> + 1.
 *     
 *     1.next      #=> 2
 *     (-1).next   #=> 0
 */

static VALUE
int_succ(num)
    VALUE num;
{
    if (FIXNUM_P(num)) {
        long i = FIX2LONG(num) + 1;
        return LONG2NUM(i);
    }
    return rb_funcall(num,