diff options
Diffstat (limited to 'numeric.c')
| -rw-r--r-- | numeric.c | 5547 |
1 files changed, 4071 insertions, 1476 deletions
@@ -2,24 +2,21 @@ numeric.c - - $Author: matz $ - $Date: 2006/05/01 03:46:46 $ + $Author$ created at: Fri Aug 13 18:33:09 JST 1993 - Copyright (C) 1993-2003 Yukihiro Matsumoto + Copyright (C) 1993-2007 Yukihiro Matsumoto **********************************************************************/ -#include "ruby.h" -#include "env.h" +#include "internal.h" +#include "ruby/util.h" +#include "id.h" +#include <assert.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 @@ -63,10 +60,23 @@ #define DBL_EPSILON 2.2204460492503131e-16 #endif +#ifdef HAVE_INFINITY +#elif !defined(WORDS_BIGENDIAN) /* BYTE_ORDER == LITTLE_ENDIAN */ +const union bytesequence4_or_float rb_infinity = {{0x00, 0x00, 0x80, 0x7f}}; +#else +const union bytesequence4_or_float rb_infinity = {{0x7f, 0x80, 0x00, 0x00}}; +#endif + +#ifdef HAVE_NAN +#elif !defined(WORDS_BIGENDIAN) /* BYTE_ORDER == LITTLE_ENDIAN */ +const union bytesequence4_or_float rb_nan = {{0x00, 0x00, 0xc0, 0x7f}}; +#else +const union bytesequence4_or_float rb_nan = {{0x7f, 0xc0, 0x00, 0x00}}; +#endif + #ifndef HAVE_ROUND double -round(x) - double x; +round(double x) { double f; @@ -82,117 +92,361 @@ round(x) } #endif -static ID id_coerce, id_to_i, id_eq; +static double +round_half_up(double x, double s) +{ + double f, xs = x * s; + + f = round(xs); + if (s == 1.0) return f; + if (x > 0) { + if ((double)((f + 0.5) / s) <= x) f += 1; + x = f; + } + else { + if ((double)((f - 0.5) / s) >= x) f -= 1; + x = f; + } + return x; +} + +static double +round_half_down(double x, double s) +{ + double f, xs = x * s; + + f = round(xs); + if (x > 0) { + if ((double)((f - 0.5) / s) >= x) f -= 1; + x = f; + } + else { + if ((double)((f + 0.5) / s) <= x) f += 1; + x = f; + } + return x; +} + +static double +round_half_even(double x, double s) +{ + double f, d, xs = x * s; + + if (x > 0.0) { + f = floor(xs); + d = xs - f; + if (d > 0.5) + d = 1.0; + else if (d == 0.5 || ((double)((f + 0.5) / s) <= x)) + d = fmod(f, 2.0); + else + d = 0.0; + x = f + d; + } + else if (x < 0.0) { + f = ceil(xs); + d = f - xs; + if (d > 0.5) + d = 1.0; + else if (d == 0.5 || ((double)((f - 0.5) / s) >= x)) + d = fmod(-f, 2.0); + else + d = 0.0; + x = f - d; + } + return x; +} + +static VALUE fix_uminus(VALUE num); +static VALUE fix_mul(VALUE x, VALUE y); +static VALUE fix_lshift(long, unsigned long); +static VALUE fix_rshift(long, unsigned long); +static VALUE int_pow(long x, unsigned long y); +static VALUE int_even_p(VALUE x); +static int int_round_zero_p(VALUE num, int ndigits); +VALUE rb_int_floor(VALUE num, int ndigits); +VALUE rb_int_ceil(VALUE num, int ndigits); +static VALUE flo_to_i(VALUE num); +static int float_round_overflow(int ndigits, int binexp); +static int float_round_underflow(int ndigits, int binexp); + +static ID id_coerce, id_div, id_divmod; +#define id_to_i idTo_i +#define id_eq idEq +#define id_cmp idCmp VALUE rb_cNumeric; VALUE rb_cFloat; VALUE rb_cInteger; +#ifndef RUBY_INTEGER_UNIFICATION VALUE rb_cFixnum; +#endif VALUE rb_eZeroDivError; VALUE rb_eFloatDomainError; +static ID id_to, id_by; + void -rb_num_zerodiv() +rb_num_zerodiv(void) { rb_raise(rb_eZeroDivError, "divided by 0"); } +enum ruby_num_rounding_mode +rb_num_get_rounding_option(VALUE opts) +{ + static ID round_kwds[1]; + VALUE rounding; + VALUE str; + const char *s; + + if (!NIL_P(opts)) { + if (!round_kwds[0]) { + round_kwds[0] = rb_intern_const("half"); + } + if (!rb_get_kwargs(opts, round_kwds, 0, 1, &rounding)) goto noopt; + if (SYMBOL_P(rounding)) { + str = rb_sym2str(rounding); + } + else if (NIL_P(rounding)) { + goto noopt; + } + else if (!RB_TYPE_P(str = rounding, T_STRING)) { + str = rb_check_string_type(rounding); + if (NIL_P(str)) goto invalid; + } + s = RSTRING_PTR(str); + switch (RSTRING_LEN(str)) { + case 2: + if (rb_memcicmp(s, "up", 2) == 0) + return RUBY_NUM_ROUND_HALF_UP; + break; + case 4: + if (rb_memcicmp(s, "even", 4) == 0) + return RUBY_NUM_ROUND_HALF_EVEN; + if (strncasecmp(s, "down", 4) == 0) + return RUBY_NUM_ROUND_HALF_DOWN; + break; + } + invalid: + rb_raise(rb_eArgError, "invalid rounding mode: % "PRIsVALUE, rounding); + } + noopt: + return RUBY_NUM_ROUND_DEFAULT; +} + +/* experimental API */ +int +rb_num_to_uint(VALUE val, unsigned int *ret) +{ +#define NUMERR_TYPE 1 +#define NUMERR_NEGATIVE 2 +#define NUMERR_TOOLARGE 3 + if (FIXNUM_P(val)) { + long v = FIX2LONG(val); +#if SIZEOF_INT < SIZEOF_LONG + if (v > (long)UINT_MAX) return NUMERR_TOOLARGE; +#endif + if (v < 0) return NUMERR_NEGATIVE; + *ret = (unsigned int)v; + return 0; + } + + if (RB_TYPE_P(val, T_BIGNUM)) { + if (BIGNUM_NEGATIVE_P(val)) return NUMERR_NEGATIVE; +#if SIZEOF_INT < SIZEOF_LONG + /* long is 64bit */ + return NUMERR_TOOLARGE; +#else + /* long is 32bit */ + if (rb_absint_size(val, NULL) > sizeof(int)) return NUMERR_TOOLARGE; + *ret = (unsigned int)rb_big2ulong((VALUE)val); + return 0; +#endif + } + return NUMERR_TYPE; +} + +#define method_basic_p(klass) rb_method_basic_definition_p(klass, mid) + +static inline int +int_pos_p(VALUE num) +{ + if (FIXNUM_P(num)) { + return FIXNUM_POSITIVE_P(num); + } + else if (RB_TYPE_P(num, T_BIGNUM)) { + return BIGNUM_POSITIVE_P(num); + } + rb_raise(rb_eTypeError, "not an Integer"); +} + +static inline int +int_neg_p(VALUE num) +{ + if (FIXNUM_P(num)) { + return FIXNUM_NEGATIVE_P(num); + } + else if (RB_TYPE_P(num, T_BIGNUM)) { + return BIGNUM_NEGATIVE_P(num); + } + rb_raise(rb_eTypeError, "not an Integer"); +} + +int +rb_num_negative_p(VALUE num) +{ + return rb_num_negative_int_p(num); +} + +static VALUE +num_funcall_op_0(VALUE x, VALUE arg, int recursive) +{ + ID func = (ID)arg; + if (recursive) { + const char *name = rb_id2name(func); + if (ISALNUM(name[0])) { + rb_name_error(func, "%"PRIsVALUE".%"PRIsVALUE, + x, ID2SYM(func)); + } + else if (name[0] && name[1] == '@' && !name[2]) { + rb_name_error(func, "%c%"PRIsVALUE, + name[0], x); + } + else { + rb_name_error(func, "%"PRIsVALUE"%"PRIsVALUE, + ID2SYM(func), x); + } + } + return rb_funcallv(x, func, 0, 0); +} + +static VALUE +num_funcall0(VALUE x, ID func) +{ + return rb_exec_recursive(num_funcall_op_0, x, (VALUE)func); +} + +static void +num_funcall_op_1_recursion(VALUE x, ID func, VALUE y) +{ + const char *name = rb_id2name(func); + if (ISALNUM(name[0])) { + rb_name_error(func, "%"PRIsVALUE".%"PRIsVALUE"(%"PRIsVALUE")", + x, ID2SYM(func), y); + } + else { + rb_name_error(func, "%"PRIsVALUE"%"PRIsVALUE"%"PRIsVALUE, + x, ID2SYM(func), y); + } +} + +static VALUE +num_funcall_op_1(VALUE y, VALUE arg, int recursive) +{ + ID func = (ID)((VALUE *)arg)[0]; + VALUE x = ((VALUE *)arg)[1]; + if (recursive) { + num_funcall_op_1_recursion(x, func, y); + } + return rb_funcall(x, func, 1, y); +} + +static VALUE +num_funcall1(VALUE x, ID func, VALUE y) +{ + VALUE args[2]; + args[0] = (VALUE)func; + args[1] = x; + return rb_exec_recursive_paired(num_funcall_op_1, y, x, (VALUE)args); +} /* * 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. - * + * num.coerce(numeric) -> array + * + * If +numeric+ is the same type as +num+, returns an array + * <code>[numeric, num]</code>. Otherwise, returns an array with both + * +numeric+ and +num+ represented as Float 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; +num_coerce(VALUE x, VALUE y) { if (CLASS_OF(x) == CLASS_OF(y)) return rb_assoc_new(y, x); - return rb_assoc_new(rb_Float(y), rb_Float(x)); + x = rb_Float(x); + y = rb_Float(y); + return rb_assoc_new(y, 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; +NORETURN(static void coerce_failed(VALUE x, VALUE y)); +static void +coerce_failed(VALUE x, VALUE y) { - 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 */ + if (SPECIAL_CONST_P(y) || BUILTIN_TYPE(y) == T_FLOAT) { + y = rb_inspect(y); + } + else { + y = rb_obj_class(y); + } + rb_raise(rb_eTypeError, "%"PRIsVALUE" can't be coerced into %"PRIsVALUE, + y, rb_obj_class(x)); } static int -do_coerce(x, y, err) - VALUE *x, *y; - int err; +do_coerce(VALUE *x, VALUE *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) { + VALUE ary = rb_check_funcall(*y, id_coerce, 1, x); + if (ary == Qundef) { if (err) { - rb_raise(rb_eTypeError, "coerce must return [x, y]"); + coerce_failed(*x, *y); } - return Qfalse; + return FALSE; + } + if (!err && NIL_P(ary)) { + return FALSE; + } + if (!RB_TYPE_P(ary, T_ARRAY) || RARRAY_LEN(ary) != 2) { + rb_raise(rb_eTypeError, "coerce must return [x, y]"); } - *x = RARRAY(ary)->ptr[0]; - *y = RARRAY(ary)->ptr[1]; - return Qtrue; + *x = RARRAY_AREF(ary, 0); + *y = RARRAY_AREF(ary, 1); + return TRUE; } VALUE -rb_num_coerce_bin(x, y) - VALUE x, y; +rb_num_coerce_bin(VALUE x, VALUE y, ID func) { - do_coerce(&x, &y, Qtrue); - return rb_funcall(x, ruby_frame->orig_func, 1, y); + do_coerce(&x, &y, TRUE); + return rb_funcall(x, func, 1, y); } VALUE -rb_num_coerce_cmp(x, y) - VALUE x, y; +rb_num_coerce_cmp(VALUE x, VALUE y, ID func) { - if (do_coerce(&x, &y, Qfalse)) - return rb_funcall(x, ruby_frame->orig_func, 1, y); + if (do_coerce(&x, &y, FALSE)) + return rb_funcall(x, func, 1, y); return Qnil; } VALUE -rb_num_coerce_relop(x, y) - VALUE x, y; +rb_num_coerce_relop(VALUE x, VALUE y, ID func) { VALUE c, x0 = x, y0 = y; - if (!do_coerce(&x, &y, Qfalse) || - NIL_P(c = rb_funcall(x, ruby_frame->orig_func, 1, y))) { + if (!do_coerce(&x, &y, FALSE) || + NIL_P(c = rb_funcall(x, func, 1, y))) { rb_cmperr(x0, y0); return Qnil; /* not reached */ } @@ -200,119 +454,202 @@ rb_num_coerce_relop(x, y) } /* - * Trap attempts to add methods to <code>Numeric</code> objects. Always - * raises a <code>TypeError</code> + * :nodoc: + * + * Trap attempts to add methods to Numeric objects. Always raises a TypeError. + * + * Numerics should be values; singleton_methods should not be added to them. */ static VALUE -num_sadded(x, name) - VALUE x, name; +num_sadded(VALUE x, VALUE name) { - ruby_frame = ruby_frame->prev; /* pop frame for "singleton_method_added" */ - /* Numerics should be values; singleton_methods should not be added to them */ + ID mid = rb_to_id(name); + /* ruby_frame = ruby_frame->prev; */ /* pop frame for "singleton_method_added" */ + rb_remove_method_id(rb_singleton_class(x), mid); 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 */ + "can't define singleton method \"%"PRIsVALUE"\" for %"PRIsVALUE, + rb_id2str(mid), + rb_obj_class(x)); + + UNREACHABLE; +} + +#if 0 +/* + * call-seq: + * num.clone(freeze: true) -> num + * + * Returns the receiver. +freeze+ cannot be +false+. + */ +static VALUE +num_clone(int argc, VALUE *argv, VALUE x) +{ + return rb_immutable_obj_clone(argc, argv, x); } +#else +# define num_clone rb_immutable_obj_clone +#endif -/* :nodoc: */ +#if 0 +/* + * call-seq: + * num.dup -> num + * + * Returns the receiver. + */ static VALUE -num_init_copy(x, y) - VALUE x, y; +num_dup(VALUE x) { - /* 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 */ + return x; } +#else +# define num_dup num_uplus +#endif /* * call-seq: - * +num => num - * - * Unary Plus---Returns the receiver's value. + * +num -> num + * + * Unary Plus---Returns the receiver. */ static VALUE -num_uplus(num) - VALUE num; +num_uplus(VALUE num) { return num; } /* * call-seq: - * -num => numeric - * - * Unary Minus---Returns the receiver's value, negated. + * num.i -> Complex(0, num) + * + * Returns the corresponding imaginary number. + * Not available for complex numbers. + * + * -42.i #=> (0-42i) + * 2.0.i #=> (0+2.0i) + */ + +static VALUE +num_imaginary(VALUE num) +{ + return rb_complex_new(INT2FIX(0), num); +} + +/* + * call-seq: + * -num -> numeric + * + * Unary Minus---Returns the receiver, negated. */ static VALUE -num_uminus(num) - VALUE num; +num_uminus(VALUE num) { VALUE zero; zero = INT2FIX(0); - do_coerce(&zero, &num, Qtrue); + do_coerce(&zero, &num, TRUE); - return rb_funcall(zero, '-', 1, num); + return num_funcall1(zero, '-', num); } /* * call-seq: - * num.quo(numeric) => result - * - * Equivalent to <code>Numeric#/</code>, but overridden in subclasses. + * num.fdiv(numeric) -> float + * + * Returns float division. */ static VALUE -num_quo(x, y) - VALUE x, y; +num_fdiv(VALUE x, VALUE y) { - return rb_funcall(x, '/', 1, y); + return rb_funcall(rb_Float(x), '/', 1, y); } +/* + * call-seq: + * num.div(numeric) -> integer + * + * Uses +/+ to perform division, then converts the result to an integer. + * Numeric does not define the +/+ operator; this is left to subclasses. + * + * Equivalent to <code>num.divmod(numeric)[0]</code>. + * + * See Numeric#divmod. + */ -static VALUE num_floor(VALUE num); +static VALUE +num_div(VALUE x, VALUE y) +{ + if (rb_equal(INT2FIX(0), y)) rb_num_zerodiv(); + return rb_funcall(num_funcall1(x, '/', y), rb_intern("floor"), 0); +} /* * 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. + * num.modulo(numeric) -> real + * + * <code>x.modulo(y)</code> means <code>x-y*(x/y).floor</code>. + * + * Equivalent to <code>num.divmod(numeric)[1]</code>. + * + * See Numeric#divmod. */ static VALUE -num_div(x, y) - VALUE x, y; +num_modulo(VALUE x, VALUE y) { - return num_floor(rb_funcall(x, '/', 1, y)); + VALUE q = num_funcall1(x, id_div, y); + return rb_funcall(x, '-', 1, + rb_funcall(y, '*', 1, q)); } +/* + * call-seq: + * num.remainder(numeric) -> real + * + * <code>x.remainder(y)</code> means <code>x-y*(x/y).truncate</code>. + * + * See Numeric#divmod. + */ + +static VALUE +num_remainder(VALUE x, VALUE y) +{ + VALUE z = num_funcall1(x, '%', y); + if ((!rb_equal(z, INT2FIX(0))) && + ((rb_num_negative_int_p(x) && + rb_num_positive_int_p(y)) || + (rb_num_positive_int_p(x) && + rb_num_negative_int_p(y)))) { + return rb_funcall(z, '-', 1, y); + } + return z; +} /* * 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 + * num.divmod(numeric) -> array * - * q = floor(float(x)/float(y)) + * Returns an array containing the quotient and modulus obtained by dividing + * +num+ by +numeric+. + * + * If <code>q, r = x.divmod(y)</code>, then + * + * q = floor(x/y) * x = q*y + r - * - * The quotient is rounded toward -infinity, as shown in the following table: - * + * + * The quotient is rounded toward negative 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 | -4, 3 | -4 | 3 | -1 * ------+-----+---------------+---------+-------------+--------------- @@ -324,139 +661,120 @@ num_div(x, y) * ------+-----+---------------+---------+-------------+--------------- * -11.5 | 4 | -3, 0.5 | -2.875 | 0.5 | -3.5 * ------+-----+---------------+---------+-------------+--------------- - * -11.5 | -4 | 2 -3.5 | 2.875 | -3.5 | -3.5 + * -11.5 | -4 | 2, -3.5 | 2.875 | -3.5 | -3.5 * * * Examples - * 11.divmod(3) #=> [3, 2] - * 11.divmod(-3) #=> [-4, -1] - * 11.divmod(3.5) #=> [3, 0.5] - * (-11).divmod(3.5) #=> [-4, 3.0] - * (11.5).divmod(3.5) #=> [3, 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>. + * + * 11.divmod(3) #=> [3, 2] + * 11.divmod(-3) #=> [-4, -1] + * 11.divmod(3.5) #=> [3, 0.5] + * (-11).divmod(3.5) #=> [-4, 3.0] + * 11.5.divmod(3.5) #=> [3, 1.0] */ static VALUE -num_modulo(x, y) - VALUE x, y; +num_divmod(VALUE x, VALUE y) { - return rb_funcall(x, '%', 1, y); + return rb_assoc_new(num_div(x, y), num_modulo(x, 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>. + * num.real? -> true or false + * + * Returns +true+ if +num+ is a real number (i.e. not Complex). */ static VALUE -num_remainder(x, y) - VALUE x, y; +num_real_p(VALUE num) { - 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; + return Qtrue; } /* * 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>). + * num.integer? -> true or false + * + * Returns +true+ if +num+ is an Integer. + * + * 1.0.integer? #=> false + * 1.integer? #=> true */ static VALUE -num_int_p(num) - VALUE num; +num_int_p(VALUE num) { return Qfalse; } /* * call-seq: - * num.abs => num or numeric - * - * Returns the absolute value of <i>num</i>. - * + * num.abs -> numeric + * num.magnitude -> numeric + * + * Returns the absolute value of +num+. + * * 12.abs #=> 12 * (-34.56).abs #=> 34.56 * -34.56.abs #=> 34.56 + * + * Numeric#magnitude is an alias for Numeric#abs. */ static VALUE -num_abs(num) - VALUE num; +num_abs(VALUE num) { - if (RTEST(rb_funcall(num, '<', 1, INT2FIX(0)))) { - return rb_funcall(num, rb_intern("-@"), 0); + if (rb_num_negative_int_p(num)) { + return num_funcall0(num, idUMinus); } return num; } - /* * call-seq: - * num.zero? => true or false - * - * Returns <code>true</code> if <i>num</i> has a zero value. + * num.zero? -> true or false + * + * Returns +true+ if +num+ has a zero value. */ static VALUE -num_zero_p(num) - VALUE num; +num_zero_p(VALUE num) { - if (rb_equal(num, INT2FIX(0))) { + if (FIXNUM_P(num)) { + if (FIXNUM_ZERO_P(num)) { + return Qtrue; + } + } + else if (RB_TYPE_P(num, T_BIGNUM)) { + if (rb_bigzero_p(num)) { + /* this should not happen usually */ + return Qtrue; + } + } + else 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: - * + * num.nonzero? -> self or nil + * + * Returns +self+ if +num+ is not zero, +nil+ 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; +num_nonzero_p(VALUE num) { - if (RTEST(rb_funcall(num, rb_intern("zero?"), 0, 0))) { + if (RTEST(num_funcall0(num, rb_intern("zero?")))) { return Qnil; } return num; @@ -464,227 +782,365 @@ num_nonzero_p(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. + * num.finite? -> true or false + * + * Returns +true+ if +num+ is a finite number, otherwise returns +false+. + */ +static VALUE +num_finite_p(VALUE num) +{ + return Qtrue; +} + +/* + * call-seq: + * num.infinite? -> -1, 1, or nil + * + * Returns +nil+, -1, or 1 depending on whether the value is + * finite, <code>-Infinity</code>, or <code>+Infinity</code>. + */ +static VALUE +num_infinite_p(VALUE num) +{ + return Qnil; +} + +/* + * call-seq: + * num.to_int -> integer + * + * Invokes the child class's +to_i+ method to convert +num+ to an integer. + * + * 1.0.class #=> Float + * 1.0.to_int.class #=> Integer + * 1.0.to_i.class #=> Integer + */ + +static VALUE +num_to_int(VALUE num) +{ + return num_funcall0(num, id_to_i); +} + +/* + * call-seq: + * num.positive? -> true or false + * + * Returns +true+ if +num+ is greater than 0. + */ + +static VALUE +num_positive_p(VALUE num) +{ + const ID mid = '>'; + + if (FIXNUM_P(num)) { + if (method_basic_p(rb_cInteger)) + return (SIGNED_VALUE)num > (SIGNED_VALUE)INT2FIX(0) ? Qtrue : Qfalse; + } + else if (RB_TYPE_P(num, T_BIGNUM)) { + if (method_basic_p(rb_cInteger)) + return BIGNUM_POSITIVE_P(num) && !rb_bigzero_p(num) ? Qtrue : Qfalse; + } + return rb_num_compare_with_zero(num, mid); +} + +/* + * call-seq: + * num.negative? -> true or false + * + * Returns +true+ if +num+ is less than 0. */ static VALUE -num_to_int(num) - VALUE num; +num_negative_p(VALUE num) { - return rb_funcall(num, id_to_i, 0, 0); + return rb_num_negative_int_p(num) ? Qtrue : Qfalse; } /******************************************************************** - * + * * Document-class: Float * - * <code>Float</code> objects represent real numbers using the native + * Float objects represent inexact real numbers using the native * architecture's double-precision floating point representation. + * + * Floating point has a different arithmetic and is an inexact number. + * So you should know its esoteric system. See following: + * + * - http://docs.sun.com/source/806-3568/ncg_goldberg.html + * - https://github.com/rdp/ruby_tutorials_core/wiki/Ruby-Talk-FAQ#floats_imprecise + * - http://en.wikipedia.org/wiki/Floating_point#Accuracy_problems */ VALUE -rb_float_new(d) - double d; +rb_float_new_in_heap(double d) { - NEWOBJ(flt, struct RFloat); - OBJSETUP(flt, rb_cFloat, T_FLOAT); + NEWOBJ_OF(flt, struct RFloat, rb_cFloat, T_FLOAT | (RGENGC_WB_PROTECTED_FLOAT ? FL_WB_PROTECTED : 0)); - flt->value = d; + flt->float_value = d; + OBJ_FREEZE(flt); 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>''. + * float.to_s -> string + * + * Returns a string containing a representation of +self+. + * As well as a fixed or exponential form of the +float+, + * the call may return +NaN+, +Infinity+, and +-Infinity+. */ static VALUE -flo_to_s(flt) - VALUE flt; +flo_to_s(VALUE flt) { - char buf[32]; - double value = RFLOAT(flt)->value; + enum {decimal_mant = DBL_MANT_DIG-DBL_DIG}; + enum {float_dig = DBL_DIG+1}; + char buf[float_dig + (decimal_mant + CHAR_BIT - 1) / CHAR_BIT + 10]; + double value = RFLOAT_VALUE(flt); + VALUE s; char *p, *e; + int sign, decpt, digs; - 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 (isinf(value)) { + static const char minf[] = "-Infinity"; + const int pos = (value > 0); /* skip "-" */ + return rb_usascii_str_new(minf+pos, strlen(minf)-pos); + } + else if (isnan(value)) + return rb_usascii_str_new2("NaN"); + + p = ruby_dtoa(value, 0, 0, &decpt, &sign, &e); + s = sign ? rb_usascii_str_new_cstr("-") : rb_usascii_str_new(0, 0); + if ((digs = (int)(e - p)) >= (int)sizeof(buf)) digs = (int)sizeof(buf) - 1; + memcpy(buf, p, digs); + xfree(p); + if (decpt > 0) { + if (decpt < digs) { + memmove(buf + decpt + 1, buf + decpt, digs - decpt); + buf[decpt] = '.'; + rb_str_cat(s, buf, digs + 1); + } + else if (decpt <= DBL_DIG) { + long len; + char *ptr; + rb_str_cat(s, buf, digs); + rb_str_resize(s, (len = RSTRING_LEN(s)) + decpt - digs + 2); + ptr = RSTRING_PTR(s) + len; + if (decpt > digs) { + memset(ptr, '0', decpt - digs); + ptr += decpt - digs; + } + memcpy(ptr, ".0", 2); + } + else { + goto exp; + } + } + else if (decpt > -4) { + long len; + char *ptr; + rb_str_cat(s, "0.", 2); + rb_str_resize(s, (len = RSTRING_LEN(s)) - decpt + digs); + ptr = RSTRING_PTR(s); + memset(ptr += len, '0', -decpt); + memcpy(ptr -= decpt, buf, digs); } - 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); + else { + exp: + if (digs > 1) { + memmove(buf + 2, buf + 1, digs - 1); } + else { + buf[2] = '0'; + digs++; + } + buf[1] = '.'; + rb_str_cat(s, buf, digs + 1); + rb_str_catf(s, "e%+03d", decpt - 1); } - p = e; - while (p[-1]=='0' && ISDIGIT(p[-2])) - p--; - memmove(p, e, strlen(e)+1); - return rb_str_new2(buf); + return s; } /* - * MISSING: documentation + * call-seq: + * float.coerce(numeric) -> array + * + * Returns an array with both +numeric+ and +float+ represented as Float + * objects. + * + * This is achieved by converting +numeric+ to a Float. + * + * 1.2.coerce(3) #=> [3.0, 1.2] + * 2.5.coerce(1.1) #=> [1.1, 2.5] */ static VALUE -flo_coerce(x, y) - VALUE x, y; +flo_coerce(VALUE x, VALUE y) { return rb_assoc_new(rb_Float(y), x); } /* * call-seq: - * -float => float + * -float -> float * - * Returns float, negated. + * Returns +float+, negated. */ -static VALUE -flo_uminus(flt) - VALUE flt; +VALUE +rb_float_uminus(VALUE flt) { - return rb_float_new(-RFLOAT(flt)->value); + return DBL2NUM(-RFLOAT_VALUE(flt)); } /* * call-seq: - * float + other => float + * float + other -> float * - * Returns a new float which is the sum of <code>float</code> - * and <code>other</code>. + * Returns a new Float which is the sum of +float+ and +other+. */ static VALUE -flo_plus(x, y) - VALUE x, y; +flo_plus(VALUE x, VALUE 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); + if (RB_TYPE_P(y, T_FIXNUM)) { + return DBL2NUM(RFLOAT_VALUE(x) + (double)FIX2LONG(y)); + } + else if (RB_TYPE_P(y, T_BIGNUM)) { + return DBL2NUM(RFLOAT_VALUE(x) + rb_big2dbl(y)); + } + else if (RB_TYPE_P(y, T_FLOAT)) { + return DBL2NUM(RFLOAT_VALUE(x) + RFLOAT_VALUE(y)); + } + else { + return rb_num_coerce_bin(x, y, '+'); } } /* * call-seq: - * float + other => float + * float - other -> float * - * Returns a new float which is the difference of <code>float</code> - * and <code>other</code>. + * Returns a new Float which is the difference of +float+ and +other+. */ static VALUE -flo_minus(x, y) - VALUE x, y; +flo_minus(VALUE x, VALUE 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); + if (RB_TYPE_P(y, T_FIXNUM)) { + return DBL2NUM(RFLOAT_VALUE(x) - (double)FIX2LONG(y)); + } + else if (RB_TYPE_P(y, T_BIGNUM)) { + return DBL2NUM(RFLOAT_VALUE(x) - rb_big2dbl(y)); + } + else if (RB_TYPE_P(y, T_FLOAT)) { + return DBL2NUM(RFLOAT_VALUE(x) - RFLOAT_VALUE(y)); + } + else { + return rb_num_coerce_bin(x, y, '-'); } } /* * call-seq: - * float * other => float + * float * other -> float * - * Returns a new float which is the product of <code>float</code> - * and <code>other</code>. + * Returns a new Float which is the product of +float+ and +other+. */ static VALUE -flo_mul(x, y) - VALUE x, y; +flo_mul(VALUE x, VALUE 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); + if (RB_TYPE_P(y, T_FIXNUM)) { + return DBL2NUM(RFLOAT_VALUE(x) * (double)FIX2LONG(y)); + } + else if (RB_TYPE_P(y, T_BIGNUM)) { + return DBL2NUM(RFLOAT_VALUE(x) * rb_big2dbl(y)); + } + else if (RB_TYPE_P(y, T_FLOAT)) { + return DBL2NUM(RFLOAT_VALUE(x) * RFLOAT_VALUE(y)); + } + else { + return rb_num_coerce_bin(x, y, '*'); } } /* * call-seq: - * float / other => float + * float / other -> float * - * Returns a new float which is the result of dividing - * <code>float</code> by <code>other</code>. + * Returns a new Float which is the result of dividing +float+ by +other+. */ static VALUE -flo_div(x, y) - VALUE x, y; +flo_div(VALUE x, VALUE y) { long f_y; double d; - switch (TYPE(y)) { - case T_FIXNUM: + if (RB_TYPE_P(y, T_FIXNUM)) { f_y = FIX2LONG(y); - return rb_float_new(RFLOAT(x)->value / (double)f_y); - case T_BIGNUM: + return DBL2NUM(RFLOAT_VALUE(x) / (double)f_y); + } + else if (RB_TYPE_P(y, 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); + return DBL2NUM(RFLOAT_VALUE(x) / d); + } + else if (RB_TYPE_P(y, T_FLOAT)) { + return DBL2NUM(RFLOAT_VALUE(x) / RFLOAT_VALUE(y)); + } + else { + return rb_num_coerce_bin(x, y, '/'); } } +/* + * call-seq: + * float.fdiv(numeric) -> float + * float.quo(numeric) -> float + * + * Returns <code>float / numeric</code>, same as Float#/. + */ + +static VALUE +flo_quo(VALUE x, VALUE y) +{ + return num_funcall1(x, '/', y); +} static void -flodivmod(x, y, divp, modp) - double x, y; - double *divp, *modp; +flodivmod(double x, double y, double *divp, double *modp) { double div, mod; + if (isnan(y)) { + /* y is NaN so all results are NaN */ + if (modp) *modp = y; + if (divp) *divp = y; + return; + } + if (y == 0.0) rb_num_zerodiv(); + if ((x == 0.0) || (isinf(y) && !isinf(x))) + mod = x; + else { #ifdef HAVE_FMOD - mod = fmod(x, y); + mod = fmod(x, y); #else - { double z; modf(x/y, &z); mod = x - z * y; - } #endif - if (isinf(x) && !isinf(y) && !isnan(y)) + } + if (isinf(x) && !isinf(y)) div = x; - else + else { div = (x - mod) / y; + if (modp && divp) div = round(div); + } if (y*mod < 0) { mod += y; div -= 1.0; @@ -693,214 +1149,236 @@ flodivmod(x, y, divp, modp) if (divp) *divp = div; } +/* + * Returns the modulo of division of x by y. + * An error will be raised if y == 0. + */ + +double +ruby_float_mod(double x, double y) +{ + double mod; + flodivmod(x, y, 0, &mod); + return mod; +} /* * 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 + * float % other -> float + * float.modulo(other) -> float + * + * Returns the modulo after division of +float+ by +other+. + * + * 6543.21.modulo(137) #=> 104.21000000000004 + * 6543.21.modulo(137.24) #=> 92.92999999999961 */ static VALUE -flo_mod(x, y) - VALUE x, y; +flo_mod(VALUE x, VALUE y) { - double fy, mod; + double fy; - switch (TYPE(y)) { - case T_FIXNUM: + if (RB_TYPE_P(y, T_FIXNUM)) { fy = (double)FIX2LONG(y); - break; - case T_BIGNUM: + } + else if (RB_TYPE_P(y, 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); + else if (RB_TYPE_P(y, T_FLOAT)) { + fy = RFLOAT_VALUE(y); + } + else { + return rb_num_coerce_bin(x, y, '%'); + } + return DBL2NUM(ruby_float_mod(RFLOAT_VALUE(x), fy)); +} + +static VALUE +dbl2ival(double d) +{ + if (FIXABLE(d)) { + return LONG2FIX((long)d); + } + return rb_dbl2big(d); } /* * call-seq: - * flt.divmod(numeric) => array - * - * See <code>Numeric#divmod</code>. + * float.divmod(numeric) -> array + * + * See Numeric#divmod. + * + * 42.0.divmod(6) #=> [7, 0.0] + * 42.0.divmod(5) #=> [8, 2.0] */ static VALUE -flo_divmod(x, y) - VALUE x, y; +flo_divmod(VALUE x, VALUE y) { - double fy, div, mod, val; + double fy, div, mod; volatile VALUE a, b; - switch (TYPE(y)) { - case T_FIXNUM: + if (RB_TYPE_P(y, T_FIXNUM)) { fy = (double)FIX2LONG(y); - break; - case T_BIGNUM: + } + else if (RB_TYPE_P(y, 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); - if (FIXABLE(div)) { - val = round(div); - a = LONG2FIX(val); + else if (RB_TYPE_P(y, T_FLOAT)) { + fy = RFLOAT_VALUE(y); } else { - a = rb_dbl2big(div); + return rb_num_coerce_bin(x, y, id_divmod); } - b = rb_float_new(mod); + flodivmod(RFLOAT_VALUE(x), fy, &div, &mod); + a = dbl2ival(div); + b = DBL2NUM(mod); return rb_assoc_new(a, b); } /* * call-seq: + * float ** other -> float * - * flt ** other => float + * Raises +float+ to the power of +other+. * - * Raises <code>float</code> the <code>other</code> power. + * 2.0**3 #=> 8.0 */ - -static VALUE -flo_pow(x, y) - VALUE x, y; + +VALUE +rb_float_pow(VALUE x, VALUE 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); + double dx, dy; + if (RB_TYPE_P(y, T_FIXNUM)) { + dx = RFLOAT_VALUE(x); + dy = (double)FIX2LONG(y); + } + else if (RB_TYPE_P(y, T_BIGNUM)) { + dx = RFLOAT_VALUE(x); + dy = rb_big2dbl(y); } + else if (RB_TYPE_P(y, T_FLOAT)) { + dx = RFLOAT_VALUE(x); + dy = RFLOAT_VALUE(y); + if (dx < 0 && dy != round(dy)) + return num_funcall1(rb_complex_raw1(x), idPow, y); + } + else { + return rb_num_coerce_bin(x, y, idPow); + } + return DBL2NUM(pow(dx, dy)); } /* * 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 + * num.eql?(numeric) -> true or false + * + * Returns +true+ if +num+ and +numeric+ are the same type and have equal + * values. Contrast this with Numeric#==, which performs type conversions. + * + * 1 == 1.0 #=> true + * 1.eql?(1.0) #=> false + * 1.0.eql?(1.0) #=> true */ static VALUE -num_eql(x, y) - VALUE x, y; +num_eql(VALUE x, VALUE y) { if (TYPE(x) != TYPE(y)) return Qfalse; + if (RB_TYPE_P(x, T_BIGNUM)) { + return rb_big_eql(x, y); + } + 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. + * number <=> other -> 0 or nil + * + * Returns zero if +number+ equals +other+, otherwise returns +nil+. */ static VALUE -num_cmp(x, y) - VALUE x, y; +num_cmp(VALUE x, VALUE y) { if (x == y) return INT2FIX(0); return Qnil; } static VALUE -num_equal(x, y) - VALUE x, y; +num_equal(VALUE x, VALUE y) { + VALUE result; if (x == y) return Qtrue; - return rb_funcall(y, id_eq, 1, x); + result = num_funcall1(y, id_eq, x); + if (RTEST(result)) return Qtrue; + return Qfalse; } /* * 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>. - * + * float == obj -> true or false + * + * Returns +true+ only if +obj+ has the same value as +float+. + * Contrast this with Float#eql?, which requires +obj+ to be a Float. + * * 1.0 == 1 #=> true - * + * + * The result of <code>NaN == NaN</code> is undefined, + * so an implementation-dependent value is returned. */ -static VALUE -flo_eq(x, y) - VALUE x, y; +VALUE +rb_float_equal(VALUE x, VALUE 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 (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) { + return rb_integer_float_eq(y, x); + } + else if (RB_TYPE_P(y, T_FLOAT)) { + b = RFLOAT_VALUE(y); +#if defined(_MSC_VER) && _MSC_VER < 1300 if (isnan(b)) return Qfalse; - break; - default: +#endif + } + else { return num_equal(x, y); } - a = RFLOAT(x)->value; + a = RFLOAT_VALUE(x); +#if defined(_MSC_VER) && _MSC_VER < 1300 if (isnan(a)) return Qfalse; +#endif return (a == b)?Qtrue:Qfalse; } +#define flo_eq rb_float_equal + /* * call-seq: - * flt.hash => integer + * float.hash -> integer * * Returns a hash code for this float. + * + * See also Object#hash. */ static VALUE -flo_hash(num) - VALUE num; +flo_hash(VALUE num) { - double d; - char *c; - int i, hash; + return rb_dbl_hash(RFLOAT_VALUE(num)); +} - 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_hash(double d) +{ + return LONG2FIX(rb_dbl_long_hash(d)); } VALUE -rb_dbl_cmp(a, b) - double a, b; +rb_dbl_cmp(double a, double b) { if (isnan(a) || isnan(b)) return Qnil; if (a == b) return INT2FIX(0); @@ -911,252 +1389,279 @@ rb_dbl_cmp(a, b) /* * 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>. + * float <=> real -> -1, 0, +1, or nil + * + * Returns -1, 0, or +1 depending on whether +float+ is + * less than, equal to, or greater than +real+. + * This is the basis for the tests in the Comparable module. + * + * The result of <code>NaN <=> NaN</code> is undefined, + * so an implementation-dependent value is returned. + * + * +nil+ is returned if the two values are incomparable. */ static VALUE -flo_cmp(x, y) - VALUE x, y; +flo_cmp(VALUE x, VALUE 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); + VALUE i; + + a = RFLOAT_VALUE(x); + if (isnan(a)) return Qnil; + if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) { + VALUE rel = rb_integer_float_cmp(y, x); + if (FIXNUM_P(rel)) + return INT2FIX(-FIX2INT(rel)); + return rel; + } + else if (RB_TYPE_P(y, T_FLOAT)) { + b = RFLOAT_VALUE(y); + } + else { + if (isinf(a) && (i = rb_check_funcall(y, rb_intern("infinite?"), 0, 0)) != Qundef) { + if (RTEST(i)) { + int j = rb_cmpint(i, x, y); + j = (a > 0.0) ? (j > 0 ? 0 : +1) : (j < 0 ? 0 : -1); + return INT2FIX(j); + } + if (a > 0.0) return INT2FIX(1); + return INT2FIX(-1); + } + return rb_num_coerce_cmp(x, y, id_cmp); } return rb_dbl_cmp(a, b); } +int +rb_float_cmp(VALUE x, VALUE y) +{ + return NUM2INT(flo_cmp(x, y)); +} + /* * call-seq: - * flt > other => true or false + * float > real -> true or false * - * <code>true</code> if <code>flt</code> is greater than <code>other</code>. + * Returns +true+ if +float+ is greater than +real+. + * + * The result of <code>NaN > NaN</code> is undefined, + * so an implementation-dependent value is returned. */ -static VALUE -flo_gt(x, y) - VALUE x, y; +VALUE +rb_float_gt(VALUE x, VALUE 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; + a = RFLOAT_VALUE(x); + if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) { + VALUE rel = rb_integer_float_cmp(y, x); + if (FIXNUM_P(rel)) + return -FIX2INT(rel) > 0 ? Qtrue : Qfalse; + return Qfalse; + } + else if (RB_TYPE_P(y, T_FLOAT)) { + b = RFLOAT_VALUE(y); +#if defined(_MSC_VER) && _MSC_VER < 1300 if (isnan(b)) return Qfalse; - break; - - default: - return rb_num_coerce_relop(x, y); +#endif + } + else { + return rb_num_coerce_relop(x, y, '>'); } +#if defined(_MSC_VER) && _MSC_VER < 1300 if (isnan(a)) return Qfalse; +#endif return (a > b)?Qtrue:Qfalse; } /* * call-seq: - * flt >= other => true or false + * float >= real -> true or false * - * <code>true</code> if <code>flt</code> is greater than - * or equal to <code>other</code>. + * Returns +true+ if +float+ is greater than or equal to +real+. + * + * The result of <code>NaN >= NaN</code> is undefined, + * so an implementation-dependent value is returned. */ static VALUE -flo_ge(x, y) - VALUE x, y; +flo_ge(VALUE x, VALUE 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; + a = RFLOAT_VALUE(x); + if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) { + VALUE rel = rb_integer_float_cmp(y, x); + if (FIXNUM_P(rel)) + return -FIX2INT(rel) >= 0 ? Qtrue : Qfalse; + return Qfalse; + } + else if (RB_TYPE_P(y, T_FLOAT)) { + b = RFLOAT_VALUE(y); +#if defined(_MSC_VER) && _MSC_VER < 1300 if (isnan(b)) return Qfalse; - break; - - default: - return rb_num_coerce_relop(x, y); +#endif } + else { + return rb_num_coerce_relop(x, y, idGE); + } +#if defined(_MSC_VER) && _MSC_VER < 1300 if (isnan(a)) return Qfalse; +#endif return (a >= b)?Qtrue:Qfalse; } /* * call-seq: - * flt < other => true or false + * float < real -> true or false * - * <code>true</code> if <code>flt</code> is less than <code>other</code>. + * Returns +true+ if +float+ is less than +real+. + * + * The result of <code>NaN < NaN</code> is undefined, + * so an implementation-dependent value is returned. */ static VALUE -flo_lt(x, y) - VALUE x, y; +flo_lt(VALUE x, VALUE 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; + a = RFLOAT_VALUE(x); + if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) { + VALUE rel = rb_integer_float_cmp(y, x); + if (FIXNUM_P(rel)) + return -FIX2INT(rel) < 0 ? Qtrue : Qfalse; + return Qfalse; + } + else if (RB_TYPE_P(y, T_FLOAT)) { + b = RFLOAT_VALUE(y); +#if defined(_MSC_VER) && _MSC_VER < 1300 if (isnan(b)) return Qfalse; - break; - - default: - return rb_num_coerce_relop(x, y); +#endif } + else { + return rb_num_coerce_relop(x, y, '<'); + } +#if defined(_MSC_VER) && _MSC_VER < 1300 if (isnan(a)) return Qfalse; +#endif return (a < b)?Qtrue:Qfalse; } /* * call-seq: - * flt <= other => true or false + * float <= real -> true or false + * + * Returns +true+ if +float+ is less than or equal to +real+. * - * <code>true</code> if <code>flt</code> is less than - * or equal to <code>other</code>. + * The result of <code>NaN <= NaN</code> is undefined, + * so an implementation-dependent value is returned. */ static VALUE -flo_le(x, y) - VALUE x, y; +flo_le(VALUE x, VALUE 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; + a = RFLOAT_VALUE(x); + if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) { + VALUE rel = rb_integer_float_cmp(y, x); + if (FIXNUM_P(rel)) + return -FIX2INT(rel) <= 0 ? Qtrue : Qfalse; + return Qfalse; + } + else if (RB_TYPE_P(y, T_FLOAT)) { + b = RFLOAT_VALUE(y); +#if defined(_MSC_VER) && _MSC_VER < 1300 if (isnan(b)) return Qfalse; - break; - - default: - return rb_num_coerce_relop(x, y); +#endif } + else { + return rb_num_coerce_relop(x, y, idLE); + } +#if defined(_MSC_VER) && _MSC_VER < 1300 if (isnan(a)) return Qfalse; +#endif 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. - * + * float.eql?(obj) -> true or false + * + * Returns +true+ only if +obj+ is a Float with the same value as +float+. + * Contrast this with Float#==, which performs type conversions. + * * 1.0.eql?(1) #=> false + * + * The result of <code>NaN.eql?(NaN)</code> is undefined, + * so an implementation-dependent value is returned. */ -static VALUE -flo_eql(x, y) - VALUE x, y; +VALUE +rb_float_eql(VALUE x, VALUE y) { - if (TYPE(y) == T_FLOAT) { - double a = RFLOAT(x)->value; - double b = RFLOAT(y)->value; - + if (RB_TYPE_P(y, T_FLOAT)) { + double a = RFLOAT_VALUE(x); + double b = RFLOAT_VALUE(y); +#if defined(_MSC_VER) && _MSC_VER < 1300 if (isnan(a) || isnan(b)) return Qfalse; - if (a == b) return Qtrue; +#endif + if (a == b) + return Qtrue; } return Qfalse; } +#define flo_eql rb_float_eql + /* * call-seq: - * flt.to_f => flt + * float.to_f -> self * - * As <code>flt</code> is already a float, returns <i>self</i>. + * Since +float+ is already a Float, returns +self+. */ static VALUE -flo_to_f(num) - VALUE num; +flo_to_f(VALUE num) { return num; } /* * call-seq: - * flt.abs => float - * - * Returns the absolute value of <i>flt</i>. - * + * float.abs -> float + * float.magnitude -> float + * + * Returns the absolute value of +float+. + * * (-34.56).abs #=> 34.56 * -34.56.abs #=> 34.56 - * + * 34.56.abs #=> 34.56 + * + * Float#magnitude is an alias for Float#abs. */ -static VALUE -flo_abs(flt) - VALUE flt; +VALUE +rb_float_abs(VALUE flt) { - double val = fabs(RFLOAT(flt)->value); - return rb_float_new(val); + double val = fabs(RFLOAT_VALUE(flt)); + return DBL2NUM(val); } /* * call-seq: - * flt.zero? -> true or false - * - * Returns <code>true</code> if <i>flt</i> is 0.0. - * + * float.zero? -> true or false + * + * Returns +true+ if +float+ is 0.0. */ static VALUE -flo_zero_p(num) - VALUE num; +flo_zero_p(VALUE num) { - if (RFLOAT(num)->value == 0.0) { + if (RFLOAT_VALUE(num) == 0.0) { return Qtrue; } return Qfalse; @@ -1164,11 +1669,10 @@ flo_zero_p(num) /* * call-seq: - * flt.nan? -> true or false - * - * Returns <code>true</code> if <i>flt</i> is an invalid IEEE floating - * point number. - * + * float.nan? -> true or false + * + * Returns +true+ if +float+ is an invalid IEEE floating point number. + * * a = -1.0 #=> -1.0 * a.nan? #=> false * a = 0.0/0.0 #=> NaN @@ -1176,31 +1680,29 @@ flo_zero_p(num) */ static VALUE -flo_is_nan_p(num) - VALUE num; -{ - double value = RFLOAT(num)->value; +flo_is_nan_p(VALUE num) +{ + double value = RFLOAT_VALUE(num); 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. - * + * float.infinite? -> -1, 1, or nil + * + * Returns +nil+, -1, or 1 depending on whether the value is + * finite, <code>-Infinity</code>, or <code>+Infinity</code>. + * * (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; +VALUE +rb_flo_is_infinite_p(VALUE num) +{ + double value = RFLOAT_VALUE(num); if (isinf(value)) { return INT2FIX( value < 0 ? -1 : 1 ); @@ -1211,22 +1713,19 @@ flo_is_infinite_p(num) /* * 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>). - * + * float.finite? -> true or false + * + * Returns +true+ if +float+ is a valid IEEE floating point number, + * i.e. it is not infinite and Float#nan? is +false+. */ -static VALUE -flo_is_finite_p(num) - VALUE num; -{ - double value = RFLOAT(num)->value; +VALUE +rb_flo_is_finite_p(VALUE num) +{ + double value = RFLOAT_VALUE(num); -#if HAVE_FINITE - if (!finite(value)) +#ifdef HAVE_ISFINITE + if (!isfinite(value)) return Qfalse; #else if (isinf(value) || isnan(value)) @@ -1238,301 +1737,1022 @@ flo_is_finite_p(num) /* * call-seq: - * flt.floor => integer - * - * Returns the largest integer less than or equal to <i>flt</i>. - * + * float.next_float -> float + * + * Returns the next representable floating point number. + * + * Float::MAX.next_float and Float::INFINITY.next_float is Float::INFINITY. + * + * Float::NAN.next_float is Float::NAN. + * + * For example: + * + * 0.01.next_float #=> 0.010000000000000002 + * 1.0.next_float #=> 1.0000000000000002 + * 100.0.next_float #=> 100.00000000000001 + * + * 0.01.next_float - 0.01 #=> 1.734723475976807e-18 + * 1.0.next_float - 1.0 #=> 2.220446049250313e-16 + * 100.0.next_float - 100.0 #=> 1.4210854715202004e-14 + * + * f = 0.01; 20.times { printf "%-20a %s\n", f, f.to_s; f = f.next_float } + * #=> 0x1.47ae147ae147bp-7 0.01 + * # 0x1.47ae147ae147cp-7 0.010000000000000002 + * # 0x1.47ae147ae147dp-7 0.010000000000000004 + * # 0x1.47ae147ae147ep-7 0.010000000000000005 + * # 0x1.47ae147ae147fp-7 0.010000000000000007 + * # 0x1.47ae147ae148p-7 0.010000000000000009 + * # 0x1.47ae147ae1481p-7 0.01000000000000001 + * # 0x1.47ae147ae1482p-7 0.010000000000000012 + * # 0x1.47ae147ae1483p-7 0.010000000000000014 + * # 0x1.47ae147ae1484p-7 0.010000000000000016 + * # 0x1.47ae147ae1485p-7 0.010000000000000018 + * # 0x1.47ae147ae1486p-7 0.01000000000000002 + * # 0x1.47ae147ae1487p-7 0.010000000000000021 + * # 0x1.47ae147ae1488p-7 0.010000000000000023 + * # 0x1.47ae147ae1489p-7 0.010000000000000024 + * # 0x1.47ae147ae148ap-7 0.010000000000000026 + * # 0x1.47ae147ae148bp-7 0.010000000000000028 + * # 0x1.47ae147ae148cp-7 0.01000000000000003 + * # 0x1.47ae147ae148dp-7 0.010000000000000031 + * # 0x1.47ae147ae148ep-7 0.010000000000000033 + * + * f = 0.0 + * 100.times { f += 0.1 } + * f #=> 9.99999999999998 # should be 10.0 in the ideal world. + * 10-f #=> 1.9539925233402755e-14 # the floating point error. + * 10.0.next_float-10 #=> 1.7763568394002505e-15 # 1 ulp (unit in the last place). + * (10-f)/(10.0.next_float-10) #=> 11.0 # the error is 11 ulp. + * (10-f)/(10*Float::EPSILON) #=> 8.8 # approximation of the above. + * "%a" % 10 #=> "0x1.4p+3" + * "%a" % f #=> "0x1.3fffffffffff5p+3" # the last hex digit is 5. 16 - 5 = 11 ulp. + */ +static VALUE +flo_next_float(VALUE vx) +{ + double x, y; + x = NUM2DBL(vx); + y = nextafter(x, INFINITY); + return DBL2NUM(y); +} + +/* + * call-seq: + * float.prev_float -> float + * + * Returns the previous representable floating point number. + * + * (-Float::MAX).prev_float and (-Float::INFINITY).prev_float is -Float::INFINITY. + * + * Float::NAN.prev_float is Float::NAN. + * + * For example: + * + * 0.01.prev_float #=> 0.009999999999999998 + * 1.0.prev_float #=> 0.9999999999999999 + * 100.0.prev_float #=> 99.99999999999999 + * + * 0.01 - 0.01.prev_float #=> 1.734723475976807e-18 + * 1.0 - 1.0.prev_float #=> 1.1102230246251565e-16 + * 100.0 - 100.0.prev_float #=> 1.4210854715202004e-14 + * + * f = 0.01; 20.times { printf "%-20a %s\n", f, f.to_s; f = f.prev_float } + * #=> 0x1.47ae147ae147bp-7 0.01 + * # 0x1.47ae147ae147ap-7 0.009999999999999998 + * # 0x1.47ae147ae1479p-7 0.009999999999999997 + * # 0x1.47ae147ae1478p-7 0.009999999999999995 + * # 0x1.47ae147ae1477p-7 0.009999999999999993 + * # 0x1.47ae147ae1476p-7 0.009999999999999992 + * # 0x1.47ae147ae1475p-7 0.00999999999999999 + * # 0x1.47ae147ae1474p-7 0.009999999999999988 + * # 0x1.47ae147ae1473p-7 0.009999999999999986 + * # 0x1.47ae147ae1472p-7 0.009999999999999985 + * # 0x1.47ae147ae1471p-7 0.009999999999999983 + * # 0x1.47ae147ae147p-7 0.009999999999999981 + * # 0x1.47ae147ae146fp-7 0.00999999999999998 + * # 0x1.47ae147ae146ep-7 0.009999999999999978 + * # 0x1.47ae147ae146dp-7 0.009999999999999976 + * # 0x1.47ae147ae146cp-7 0.009999999999999974 + * # 0x1.47ae147ae146bp-7 0.009999999999999972 + * # 0x1.47ae147ae146ap-7 0.00999999999999997 + * # 0x1.47ae147ae1469p-7 0.009999999999999969 + * # 0x1.47ae147ae1468p-7 0.009999999999999967 + */ +static VALUE +flo_prev_float(VALUE vx) +{ + double x, y; + x = NUM2DBL(vx); + y = nextafter(x, -INFINITY); + return DBL2NUM(y); +} + +/* + * call-seq: + * float.floor([ndigits]) -> integer or float + * + * Returns the largest number less than or equal to +float+ with + * a precision of +ndigits+ decimal digits (default: 0). + * + * When the precision is negative, the returned value is an integer + * with at least <code>ndigits.abs</code> trailing zeros. + * + * Returns a floating point number when +ndigits+ is positive, + * otherwise returns an integer. + * * 1.2.floor #=> 1 * 2.0.floor #=> 2 * (-1.2).floor #=> -2 * (-2.0).floor #=> -2 + * + * 1.234567.floor(2) #=> 1.23 + * 1.234567.floor(3) #=> 1.234 + * 1.234567.floor(4) #=> 1.2345 + * 1.234567.floor(5) #=> 1.23456 + * + * 34567.89.floor(-5) #=> 0 + * 34567.89.floor(-4) #=> 30000 + * 34567.89.floor(-3) #=> 34000 + * 34567.89.floor(-2) #=> 34500 + * 34567.89.floor(-1) #=> 34560 + * 34567.89.floor(0) #=> 34567 + * 34567.89.floor(1) #=> 34567.8 + * 34567.89.floor(2) #=> 34567.89 + * 34567.89.floor(3) #=> 34567.89 + * + * Note that the limited precision of floating point arithmetic + * might lead to surprising results: + * + * (0.3 / 0.1).floor #=> 2 (!) */ static VALUE -flo_floor(num) - VALUE num; +flo_floor(int argc, VALUE *argv, VALUE num) { - double f = floor(RFLOAT(num)->value); - long val; + double number, f; + int ndigits = 0; - if (!FIXABLE(f)) { - return rb_dbl2big(f); + if (rb_check_arity(argc, 0, 1)) { + ndigits = NUM2INT(argv[0]); + } + number = RFLOAT_VALUE(num); + if (number == 0.0) { + return ndigits > 0 ? DBL2NUM(number) : INT2FIX(0); + } + if (ndigits > 0) { + int binexp; + frexp(number, &binexp); + if (float_round_overflow(ndigits, binexp)) return num; + if (number > 0.0 && float_round_underflow(ndigits, binexp)) + return DBL2NUM(0.0); + f = pow(10, ndigits); + f = floor(number * f) / f; + return DBL2NUM(f); + } + else { + num = dbl2ival(floor(number)); + if (ndigits < 0) num = rb_int_floor(num, ndigits); + return num; } - val = f; - return LONG2FIX(val); } /* * call-seq: - * flt.ceil => integer - * - * Returns the smallest <code>Integer</code> greater than or equal to - * <i>flt</i>. - * + * float.ceil([ndigits]) -> integer or float + * + * Returns the smallest number greater than or equal to +float+ with + * a precision of +ndigits+ decimal digits (default: 0). + * + * When the precision is negative, the returned value is an integer + * with at least <code>ndigits.abs</code> trailing zeros. + * + * Returns a floating point number when +ndigits+ is positive, + * otherwise returns an integer. + * * 1.2.ceil #=> 2 * 2.0.ceil #=> 2 * (-1.2).ceil #=> -1 * (-2.0).ceil #=> -2 + * + * 1.234567.ceil(2) #=> 1.24 + * 1.234567.ceil(3) #=> 1.235 + * 1.234567.ceil(4) #=> 1.2346 + * 1.234567.ceil(5) #=> 1.23457 + * + * 34567.89.ceil(-5) #=> 100000 + * 34567.89.ceil(-4) #=> 40000 + * 34567.89.ceil(-3) #=> 35000 + * 34567.89.ceil(-2) #=> 34600 + * 34567.89.ceil(-1) #=> 34570 + * 34567.89.ceil(0) #=> 34568 + * 34567.89.ceil(1) #=> 34567.9 + * 34567.89.ceil(2) #=> 34567.89 + * 34567.89.ceil(3) #=> 34567.89 + * + * Note that the limited precision of floating point arithmetic + * might lead to surprising results: + * + * (2.1 / 0.7).ceil #=> 4 (!) */ static VALUE -flo_ceil(num) - VALUE num; +flo_ceil(int argc, VALUE *argv, VALUE num) { - double f = ceil(RFLOAT(num)->value); - long val; + double number, f; + int ndigits = 0; - if (!FIXABLE(f)) { - return rb_dbl2big(f); + if (rb_check_arity(argc, 0, 1)) { + ndigits = NUM2INT(argv[0]); + } + number = RFLOAT_VALUE(num); + if (number == 0.0) { + return ndigits > 0 ? DBL2NUM(number) : INT2FIX(0); + } + if (ndigits > 0) { + int binexp; + frexp(number, &binexp); + if (float_round_overflow(ndigits, binexp)) return num; + if (number < 0.0 && float_round_underflow(ndigits, binexp)) + return DBL2NUM(0.0); + f = pow(10, ndigits); + f = ceil(number * f) / f; + return DBL2NUM(f); + } + else { + num = dbl2ival(ceil(number)); + if (ndigits < 0) num = rb_int_ceil(num, ndigits); + return num; + } +} + +static int +int_round_zero_p(VALUE num, int ndigits) +{ + long bytes; + /* If 10**N / 2 > num, then return 0 */ + /* We have log_256(10) > 0.415241 and log_256(1/2) = -0.125, so */ + if (FIXNUM_P(num)) { + bytes = sizeof(long); + } + else if (RB_TYPE_P(num, T_BIGNUM)) { + bytes = rb_big_size(num); + } + else { + bytes = NUM2LONG(rb_funcall(num, idSize, 0)); + } + return (-0.415241 * ndigits - 0.125 > bytes); +} + +static SIGNED_VALUE +int_round_half_even(SIGNED_VALUE x, SIGNED_VALUE y) +{ + SIGNED_VALUE z = +(x + y / 2) / y; + if ((z * y - x) * 2 == y) { + z &= ~1; + } + return z * y; +} + +static SIGNED_VALUE +int_round_half_up(SIGNED_VALUE x, SIGNED_VALUE y) +{ + return (x + y / 2) / y * y; +} + +static SIGNED_VALUE +int_round_half_down(SIGNED_VALUE x, SIGNED_VALUE y) +{ + return (x + y / 2 - 1) / y * y; +} + +static int +int_half_p_half_even(VALUE num, VALUE n, VALUE f) +{ + return (int)rb_int_odd_p(rb_int_idiv(n, f)); +} + +static int +int_half_p_half_up(VALUE num, VALUE n, VALUE f) +{ + return int_pos_p(num); +} + +static int +int_half_p_half_down(VALUE num, VALUE n, VALUE f) +{ + return int_neg_p(num); +} + +/* + * Assumes num is an Integer, ndigits <= 0 + */ +VALUE +rb_int_round(VALUE num, int ndigits, enum ruby_num_rounding_mode mode) +{ + VALUE n, f, h, r; + + if (int_round_zero_p(num, ndigits)) { + return INT2FIX(0); + } + + f = int_pow(10, -ndigits); + if (FIXNUM_P(num) && FIXNUM_P(f)) { + SIGNED_VALUE x = FIX2LONG(num), y = FIX2LONG(f); + int neg = x < 0; + if (neg) x = -x; + x = ROUND_CALL(mode, int_round, (x, y)); + if (neg) x = -x; + return LONG2NUM(x); + } + if (RB_TYPE_P(f, T_FLOAT)) { + /* then int_pow overflow */ + return INT2FIX(0); + } + h = rb_int_idiv(f, INT2FIX(2)); + r = rb_int_modulo(num, f); + n = rb_int_minus(num, r); + r = rb_int_cmp(r, h); + if (FIXNUM_POSITIVE_P(r) || + (FIXNUM_ZERO_P(r) && ROUND_CALL(mode, int_half_p, (num, n, f)))) { + n = rb_int_plus(n, f); + } + return n; +} + +VALUE +rb_int_floor(VALUE num, int ndigits) +{ + VALUE f; + + if (int_round_zero_p(num, ndigits)) + return INT2FIX(0); + f = int_pow(10, -ndigits); + if (FIXNUM_P(num) && FIXNUM_P(f)) { + SIGNED_VALUE x = FIX2LONG(num), y = FIX2LONG(f); + int neg = x < 0; + if (neg) x = -x + y - 1; + x = x / y * y; + if (neg) x = -x; + return LONG2NUM(x); + } + if (RB_TYPE_P(f, T_FLOAT)) { + /* then int_pow overflow */ + return INT2FIX(0); + } + return rb_int_minus(num, rb_int_modulo(num, f)); +} + +VALUE +rb_int_ceil(VALUE num, int ndigits) +{ + VALUE f; + + if (int_round_zero_p(num, ndigits)) + return INT2FIX(0); + f = int_pow(10, -ndigits); + if (FIXNUM_P(num) && FIXNUM_P(f)) { + SIGNED_VALUE x = FIX2LONG(num), y = FIX2LONG(f); + int neg = x < 0; + if (neg) x = -x; + else x += y - 1; + x = (x / y) * y; + if (neg) x = -x; + return LONG2NUM(x); + } + if (RB_TYPE_P(f, T_FLOAT)) { + /* then int_pow overflow */ + return INT2FIX(0); + } + return rb_int_plus(num, rb_int_minus(f, rb_int_modulo(num, f))); +} + +VALUE +rb_int_truncate(VALUE num, int ndigits) +{ + VALUE f; + VALUE m; + + if (int_round_zero_p(num, ndigits)) + return INT2FIX(0); + f = int_pow(10, -ndigits); + if (FIXNUM_P(num) && FIXNUM_P(f)) { + SIGNED_VALUE x = FIX2LONG(num), y = FIX2LONG(f); + int neg = x < 0; + if (neg) x = -x; + x = x / y * y; + if (neg) x = -x; + return LONG2NUM(x); + } + if (RB_TYPE_P(f, T_FLOAT)) { + /* then int_pow overflow */ + return INT2FIX(0); + } + m = rb_int_modulo(num, f); + if (int_neg_p(num)) { + return rb_int_plus(num, rb_int_minus(f, m)); + } + else { + return rb_int_minus(num, m); } - 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 - * + * float.round([ndigits] [, half: mode]) -> integer or float + * + * Returns +float+ rounded to the nearest value with + * a precision of +ndigits+ decimal digits (default: 0). + * + * When the precision is negative, the returned value is an integer + * with at least <code>ndigits.abs</code> trailing zeros. + * + * Returns a floating point number when +ndigits+ is positive, + * otherwise returns an integer. + * + * 1.4.round #=> 1 * 1.5.round #=> 2 + * 1.6.round #=> 2 * (-1.5).round #=> -2 - * + * + * 1.234567.round(2) #=> 1.23 + * 1.234567.round(3) #=> 1.235 + * 1.234567.round(4) #=> 1.2346 + * 1.234567.round(5) #=> 1.23457 + * + * 34567.89.round(-5) #=> 0 + * 34567.89.round(-4) #=> 30000 + * 34567.89.round(-3) #=> 35000 + * 34567.89.round(-2) #=> 34600 + * 34567.89.round(-1) #=> 34570 + * 34567.89.round(0) #=> 34568 + * 34567.89.round(1) #=> 34567.9 + * 34567.89.round(2) #=> 34567.89 + * 34567.89.round(3) #=> 34567.89 + * + * If the optional +half+ keyword argument is given, + * numbers that are half-way between two possible rounded values + * will be rounded according to the specified tie-breaking +mode+: + * + * * <code>:up</code> or +nil+: round half away from zero (default) + * * <code>:down</code>: round half toward zero + * * <code>:even</code>: round half toward the nearest even number + * + * 2.5.round(half: :up) #=> 3 + * 2.5.round(half: :down) #=> 2 + * 2.5.round(half: :even) #=> 2 + * 3.5.round(half: :up) #=> 4 + * 3.5.round(half: :down) #=> 3 + * 3.5.round(half: :even) #=> 4 + * (-2.5).round(half: :up) #=> -3 + * (-2.5).round(half: :down) #=> -2 + * (-2.5).round(half: :even) #=> -2 */ static VALUE -flo_round(num) - VALUE num; +flo_round(int argc, VALUE *argv, VALUE num) { - double f = RFLOAT(num)->value; - long val; + double number, f, x; + VALUE nd, opt; + int ndigits = 0; + enum ruby_num_rounding_mode mode; + + if (rb_scan_args(argc, argv, "01:", &nd, &opt)) { + ndigits = NUM2INT(nd); + } + mode = rb_num_get_rounding_option(opt); + number = RFLOAT_VALUE(num); + if (number == 0.0) { + return ndigits > 0 ? DBL2NUM(number) : INT2FIX(0); + } + if (ndigits < 0) { + return rb_int_round(flo_to_i(num), ndigits, mode); + } + if (ndigits == 0) { + x = ROUND_CALL(mode, round, (number, 1.0)); + return dbl2ival(x); + } + if (isfinite(number)) { + int binexp; + frexp(number, &binexp); + if (float_round_overflow(ndigits, binexp)) return num; + if (float_round_underflow(ndigits, binexp)) return DBL2NUM(0); + f = pow(10, ndigits); + x = ROUND_CALL(mode, round, (number, f)); + return DBL2NUM(x / f); + } + return num; +} - f = round(f); +static int +float_round_overflow(int ndigits, int binexp) +{ + enum {float_dig = DBL_DIG+2}; + +/* Let `exp` be such that `number` is written as:"0.#{digits}e#{exp}", + i.e. such that 10 ** (exp - 1) <= |number| < 10 ** exp + Recall that up to float_dig digits can be needed to represent a double, + so if ndigits + exp >= float_dig, the intermediate value (number * 10 ** ndigits) + will be an integer and thus the result is the original number. + If ndigits + exp <= 0, the result is 0 or "1e#{exp}", so + if ndigits + exp < 0, the result is 0. + We have: + 2 ** (binexp-1) <= |number| < 2 ** binexp + 10 ** ((binexp-1)/log_2(10)) <= |number| < 10 ** (binexp/log_2(10)) + If binexp >= 0, and since log_2(10) = 3.322259: + 10 ** (binexp/4 - 1) < |number| < 10 ** (binexp/3) + floor(binexp/4) <= exp <= ceil(binexp/3) + If binexp <= 0, swap the /4 and the /3 + So if ndigits + floor(binexp/(4 or 3)) >= float_dig, the result is number + If ndigits + ceil(binexp/(3 or 4)) < 0 the result is 0 +*/ + if (ndigits >= float_dig - (binexp > 0 ? binexp / 4 : binexp / 3 - 1)) { + return TRUE; + } + return FALSE; +} - if (!FIXABLE(f)) { - return rb_dbl2big(f); +static int +float_round_underflow(int ndigits, int binexp) +{ + if (ndigits < - (binexp > 0 ? binexp / 3 + 1 : binexp / 4)) { + return TRUE; } - val = f; - return LONG2FIX(val); + return FALSE; } /* * call-seq: - * flt.to_i => integer - * flt.to_int => integer - * flt.truncate => integer - * - * Returns <i>flt</i> truncated to an <code>Integer</code>. + * float.to_i -> integer + * float.to_int -> integer + * + * Returns the +float+ truncated to an Integer. + * + * 1.2.to_i #=> 1 + * (-1.2).to_i #=> -1 + * + * Note that the limited precision of floating point arithmetic + * might lead to surprising results: + * + * (0.3 / 0.1).to_i #=> 2 (!) + * + * #to_int is an alias for #to_i. */ static VALUE -flo_truncate(num) - VALUE num; +flo_to_i(VALUE num) { - double f = RFLOAT(num)->value; - long val; + double f = RFLOAT_VALUE(num); 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); + return dbl2ival(f); } +/* + * call-seq: + * float.truncate([ndigits]) -> integer or float + * + * Returns +float+ truncated (toward zero) to + * a precision of +ndigits+ decimal digits (default: 0). + * + * When the precision is negative, the returned value is an integer + * with at least <code>ndigits.abs</code> trailing zeros. + * + * Returns a floating point number when +ndigits+ is positive, + * otherwise returns an integer. + * + * 2.8.truncate #=> 2 + * (-2.8).truncate #=> -2 + * 1.234567.truncate(2) #=> 1.23 + * 34567.89.truncate(-2) #=> 34500 + * + * Note that the limited precision of floating point arithmetic + * might lead to surprising results: + * + * (0.3 / 0.1).truncate #=> 2 (!) + */ +static VALUE +flo_truncate(int argc, VALUE *argv, VALUE num) +{ + if (signbit(RFLOAT_VALUE(num))) + return flo_ceil(argc, argv, num); + else + return flo_floor(argc, argv, num); +} /* * 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 + * float.positive? -> true or false + * + * Returns +true+ if +float+ is greater than 0. */ static VALUE -num_floor(num) - VALUE num; +flo_positive_p(VALUE num) { - return flo_floor(rb_Float(num)); + double f = RFLOAT_VALUE(num); + return f > 0.0 ? Qtrue : Qfalse; } - /* * 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 + * float.negative? -> true or false + * + * Returns +true+ if +float+ is less than 0. */ static VALUE -num_ceil(num) - VALUE num; +flo_negative_p(VALUE num) { - return flo_ceil(rb_Float(num)); + double f = RFLOAT_VALUE(num); + return f < 0.0 ? Qtrue : Qfalse; } /* * 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>. + * num.floor([ndigits]) -> integer or float + * + * Returns the largest number less than or equal to +num+ with + * a precision of +ndigits+ decimal digits (default: 0). + * + * Numeric implements this by converting its value to a Float and + * invoking Float#floor. */ static VALUE -num_round(num) - VALUE num; +num_floor(int argc, VALUE *argv, VALUE num) { - return flo_round(rb_Float(num)); + return flo_floor(argc, argv, 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>. + * num.ceil([ndigits]) -> integer or float + * + * Returns the smallest number greater than or equal to +num+ with + * a precision of +ndigits+ decimal digits (default: 0). + * + * Numeric implements this by converting its value to a Float and + * invoking Float#ceil. */ static VALUE -num_truncate(num) - VALUE num; +num_ceil(int argc, VALUE *argv, VALUE num) { - return flo_truncate(rb_Float(num)); + return flo_ceil(argc, argv, rb_Float(num)); } +/* + * call-seq: + * num.round([ndigits]) -> integer or float + * + * Returns +num+ rounded to the nearest value with + * a precision of +ndigits+ decimal digits (default: 0). + * + * Numeric implements this by converting its value to a Float and + * invoking Float#round. + */ + +static VALUE +num_round(int argc, VALUE* argv, VALUE num) +{ + return flo_round(argc, argv, 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 + * num.truncate([ndigits]) -> integer or float + * + * Returns +num+ truncated (toward zero) to + * a precision of +ndigits+ decimal digits (default: 0). + * + * Numeric implements this by converting its value to a Float and + * invoking Float#truncate. */ static VALUE -num_step(argc, argv, from) - int argc; - VALUE *argv; - VALUE from; +num_truncate(int argc, VALUE *argv, VALUE num) { - VALUE to, step; + return flo_truncate(argc, argv, rb_Float(num)); +} - if (argc == 1) { - to = argv[0]; - step = INT2FIX(1); +static double +ruby_float_step_size(double beg, double end, double unit, int excl) +{ + const double epsilon = DBL_EPSILON; + double n = (end - beg)/unit; + double err = (fabs(beg) + fabs(end) + fabs(end-beg)) / fabs(unit) * epsilon; + + if (isinf(unit)) { + return unit > 0 ? beg <= end : beg >= end; + } + if (unit == 0) { + return INFINITY; + } + if (err>0.5) err=0.5; + if (excl) { + if (n<=0) return 0; + if (n<1) + n = 0; + else + n = floor(n - err); } else { - if (argc == 2) { - to = argv[0]; - step = argv[1]; + if (n<0) return 0; + n = floor(n + err); + } + return n+1; +} + +int +ruby_float_step(VALUE from, VALUE to, VALUE step, int excl) +{ + if (RB_TYPE_P(from, T_FLOAT) || RB_TYPE_P(to, T_FLOAT) || RB_TYPE_P(step, T_FLOAT)) { + double beg = NUM2DBL(from); + double end = NUM2DBL(to); + double unit = NUM2DBL(step); + double n = ruby_float_step_size(beg, end, unit, excl); + long i; + + if (isinf(unit)) { + /* if unit is infinity, i*unit+beg is NaN */ + if (n) rb_yield(DBL2NUM(beg)); } - else { - rb_raise(rb_eArgError, "wrong number of arguments"); + else if (unit == 0) { + VALUE val = DBL2NUM(beg); + for (;;) + rb_yield(val); } - if (rb_equal(step, INT2FIX(0))) { - rb_raise(rb_eArgError, "step can't be 0"); + else { + for (i=0; i<n; i++) { + double d = i*unit+beg; + if (unit >= 0 ? end < d : d < end) d = end; + rb_yield(DBL2NUM(d)); + } } + return TRUE; } + return FALSE; +} +VALUE +ruby_num_interval_step_size(VALUE from, VALUE to, VALUE step, int excl) +{ if (FIXNUM_P(from) && FIXNUM_P(to) && FIXNUM_P(step)) { - long i, end, diff; + long delta, diff; - i = FIX2LONG(from); - end = FIX2LONG(to); diff = FIX2LONG(step); + if (diff == 0) { + return DBL2NUM(INFINITY); + } + delta = FIX2LONG(to) - FIX2LONG(from); + if (diff < 0) { + diff = -diff; + delta = -delta; + } + if (excl) { + delta--; + } + if (delta < 0) { + return INT2FIX(0); + } + return ULONG2NUM(delta / diff + 1UL); + } + else if (RB_TYPE_P(from, T_FLOAT) || RB_TYPE_P(to, T_FLOAT) || RB_TYPE_P(step, T_FLOAT)) { + double n = ruby_float_step_size(NUM2DBL(from), NUM2DBL(to), NUM2DBL(step), excl); - if (diff > 0) { - while (i <= end) { - rb_yield(LONG2FIX(i)); - i += diff; - } + if (isinf(n)) return DBL2NUM(n); + if (POSFIXABLE(n)) return LONG2FIX(n); + return rb_dbl2big(n); + } + else { + VALUE result; + ID cmp = '>'; + switch (rb_cmpint(rb_num_coerce_cmp(step, INT2FIX(0), id_cmp), step, INT2FIX(0))) { + case 0: return DBL2NUM(INFINITY); + case -1: cmp = '<'; break; } - else { - while (i >= end) { - rb_yield(LONG2FIX(i)); - i += diff; - } + if (RTEST(rb_funcall(from, cmp, 1, to))) return INT2FIX(0); + result = rb_funcall(rb_funcall(to, '-', 1, from), id_div, 1, step); + if (!excl || RTEST(rb_funcall(rb_funcall(from, '+', 1, rb_funcall(result, '*', 1, step)), cmp, 1, to))) { + result = rb_funcall(result, '+', 1, INT2FIX(1)); } + return result; + } +} + +static int +num_step_negative_p(VALUE num) +{ + const ID mid = '<'; + VALUE zero = INT2FIX(0); + VALUE r; + + if (FIXNUM_P(num)) { + if (method_basic_p(rb_cInteger)) + return (SIGNED_VALUE)num < 0; + } + else if (RB_TYPE_P(num, T_BIGNUM)) { + if (method_basic_p(rb_cInteger)) + return BIGNUM_NEGATIVE_P(num); } - 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)); + r = rb_check_funcall(num, '>', 1, &zero); + if (r == Qundef) { + coerce_failed(num, INT2FIX(0)); + } + return !RTEST(r); +} + +static int +num_step_scan_args(int argc, const VALUE *argv, VALUE *to, VALUE *step) +{ + VALUE hash; + int desc; + + argc = rb_scan_args(argc, argv, "02:", to, step, &hash); + if (!NIL_P(hash)) { + ID keys[2]; + VALUE values[2]; + keys[0] = id_to; + keys[1] = id_by; + rb_get_kwargs(hash, keys, 0, 2, values); + if (values[0] != Qundef) { + if (argc > 0) rb_raise(rb_eArgError, "to is given twice"); + *to = values[0]; + } + if (values[1] != Qundef) { + if (argc > 1) rb_raise(rb_eArgError, "step is given twice"); + *step = values[1]; } } else { - VALUE i = from; - ID cmp; + /* compatibility */ + if (argc > 1 && NIL_P(*step)) { + rb_raise(rb_eTypeError, "step must be numeric"); + } + if (rb_equal(*step, INT2FIX(0))) { + rb_raise(rb_eArgError, "step can't be 0"); + } + } + if (NIL_P(*step)) { + *step = INT2FIX(1); + } + desc = num_step_negative_p(*step); + if (NIL_P(*to)) { + *to = desc ? DBL2NUM(-INFINITY) : DBL2NUM(INFINITY); + } + return desc; +} + +static VALUE +num_step_size(VALUE from, VALUE args, VALUE eobj) +{ + VALUE to, step; + int argc = args ? RARRAY_LENINT(args) : 0; + const VALUE *argv = args ? RARRAY_CONST_PTR(args) : 0; + + num_step_scan_args(argc, argv, &to, &step); + + return ruby_num_interval_step_size(from, to, step, FALSE); +} + +/* + * call-seq: + * num.step(by: step, to: limit) {|i| block } -> self + * num.step(by: step, to: limit) -> an_enumerator + * num.step(limit=nil, step=1) {|i| block } -> self + * num.step(limit=nil, step=1) -> an_enumerator + * + * Invokes the given block with the sequence of numbers starting at +num+, + * incremented by +step+ (defaulted to +1+) on each call. + * + * The loop finishes when the value to be passed to the block is greater than + * +limit+ (if +step+ is positive) or less than +limit+ (if +step+ is + * negative), where +limit+ is defaulted to infinity. + * + * In the recommended keyword argument style, either or both of + * +step+ and +limit+ (default infinity) can be omitted. In the + * fixed position argument style, zero as a step + * (i.e. <code>num.step(limit, 0)</code>) is not allowed for historical + * compatibility reasons. + * + * 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*Float::EPSILON) + 1</i> times, + * where <i>n = (limit - num)/step</i>. + * + * Otherwise, the loop starts at +num+, uses either the + * less-than (<code><</code>) or greater-than (<code>></code>) operator + * to compare the counter against +limit+, + * and increments itself using the <code>+</code> operator. + * + * If no block is given, an Enumerator is returned instead. + * + * For example: + * + * p 1.step.take(4) + * p 10.step(by: -1).take(4) + * 3.step(to: 5) {|i| print i, " " } + * 1.step(10, 2) {|i| print i, " " } + * Math::E.step(to: Math::PI, by: 0.2) {|f| print f, " " } + * + * Will produce: + * + * [1, 2, 3, 4] + * [10, 9, 8, 7] + * 3 4 5 + * 1 3 5 7 9 + * 2.718281828459045 2.9182818284590453 3.118281828459045 + */ - if (RTEST(rb_funcall(step, '>', 1, INT2FIX(0)))) { - cmp = '>'; +static VALUE +num_step(int argc, VALUE *argv, VALUE from) +{ + VALUE to, step; + int desc, inf; + + RETURN_SIZED_ENUMERATOR(from, argc, argv, num_step_size); + + desc = num_step_scan_args(argc, argv, &to, &step); + if (rb_equal(step, INT2FIX(0))) { + inf = 1; + } + else if (RB_TYPE_P(to, T_FLOAT)) { + double f = RFLOAT_VALUE(to); + inf = isinf(f) && (signbit(f) ? desc : !desc); + } + else inf = 0; + + if (FIXNUM_P(from) && (inf || FIXNUM_P(to)) && FIXNUM_P(step)) { + long i = FIX2LONG(from); + long diff = FIX2LONG(step); + + if (inf) { + for (;; i += diff) + rb_yield(LONG2FIX(i)); } else { - cmp = '<'; + long end = FIX2LONG(to); + + if (desc) { + for (; i >= end; i += diff) + rb_yield(LONG2FIX(i)); + } + else { + for (; i <= end; i += diff) + rb_yield(LONG2FIX(i)); + } } - for (;;) { - if (RTEST(rb_funcall(i, cmp, 1, to))) break; - rb_yield(i); - i = rb_funcall(i, '+', 1, step); + } + else if (!ruby_float_step(from, to, step, FALSE)) { + VALUE i = from; + + if (inf) { + for (;; i = rb_funcall(i, '+', 1, step)) + rb_yield(i); + } + else { + ID cmp = desc ? '<' : '>'; + + for (; !RTEST(rb_funcall(i, cmp, 1, to)); i = rb_funcall(i, '+', 1, step)) + rb_yield(i); } } return from; } +static char * +out_of_range_float(char (*pbuf)[24], VALUE val) +{ + char *const buf = *pbuf; + char *s; + + snprintf(buf, sizeof(*pbuf), "%-.10g", RFLOAT_VALUE(val)); + if ((s = strchr(buf, ' ')) != 0) *s = '\0'; + return buf; +} + +#define FLOAT_OUT_OF_RANGE(val, type) do { \ + char buf[24]; \ + rb_raise(rb_eRangeError, "float %s out of range of "type, \ + out_of_range_float(&buf, (val))); \ +} while (0) + +#define LONG_MIN_MINUS_ONE ((double)LONG_MIN-1) +#define LONG_MAX_PLUS_ONE (2*(double)(LONG_MAX/2+1)) +#define ULONG_MAX_PLUS_ONE (2*(double)(ULONG_MAX/2+1)) +#define LONG_MIN_MINUS_ONE_IS_LESS_THAN(n) \ + (LONG_MIN_MINUS_ONE == (double)LONG_MIN ? \ + LONG_MIN <= (n): \ + LONG_MIN_MINUS_ONE < (n)) + long -rb_num2long(val) - VALUE val; +rb_num2long(VALUE val) { again: if (NIL_P(val)) { @@ -1541,71 +2761,104 @@ rb_num2long(val) 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 if (RB_TYPE_P(val, T_FLOAT)) { + if (RFLOAT_VALUE(val) < LONG_MAX_PLUS_ONE + && LONG_MIN_MINUS_ONE_IS_LESS_THAN(RFLOAT_VALUE(val))) { + return (long)RFLOAT_VALUE(val); } else { - char buf[24]; - char *s; - - sprintf(buf, "%-.10g", RFLOAT(val)->value); - if ((s = strchr(buf, ' ')) != 0) *s = '\0'; - rb_raise(rb_eRangeError, "float %s out of range of integer", buf); + FLOAT_OUT_OF_RANGE(val, "integer"); } - - case T_BIGNUM: + } + else if (RB_TYPE_P(val, T_BIGNUM)) { return rb_big2long(val); - - default: + } + else { val = rb_to_int(val); goto again; } } -unsigned long -rb_num2ulong(val) - VALUE val; +static unsigned long +rb_num2ulong_internal(VALUE val, int *wrap_p) { - if (TYPE(val) == T_BIGNUM) { - return rb_big2ulong(val); + again: + if (NIL_P(val)) { + rb_raise(rb_eTypeError, "no implicit conversion from nil to integer"); } - return (unsigned long)rb_num2long(val); + + if (FIXNUM_P(val)) { + long l = FIX2LONG(val); /* this is FIX2LONG, intended */ + if (wrap_p) + *wrap_p = l < 0; + return (unsigned long)l; + } + else if (RB_TYPE_P(val, T_FLOAT)) { + double d = RFLOAT_VALUE(val); + if (d < ULONG_MAX_PLUS_ONE && LONG_MIN_MINUS_ONE_IS_LESS_THAN(d)) { + if (wrap_p) + *wrap_p = d <= -1.0; /* NUM2ULONG(v) uses v.to_int conceptually. */ + if (0 <= d) + return (unsigned long)d; + return (unsigned long)(long)d; + } + else { + FLOAT_OUT_OF_RANGE(val, "integer"); + } + } + else if (RB_TYPE_P(val, T_BIGNUM)) { + { + unsigned long ul = rb_big2ulong(val); + if (wrap_p) + *wrap_p = BIGNUM_NEGATIVE_P(val); + return ul; + } + } + else { + val = rb_to_int(val); + goto again; + } +} + +unsigned long +rb_num2ulong(VALUE val) +{ + return rb_num2ulong_internal(val, NULL); } #if SIZEOF_INT < SIZEOF_LONG -static void -check_int(num) - long num; +void +rb_out_of_int(SIGNED_VALUE num) { - const char *s; + rb_raise(rb_eRangeError, "integer %"PRIdVALUE " too %s to convert to `int'", + num, num < 0 ? "small" : "big"); +} - if (num < INT_MIN) { - s = "small"; - } - else if (num > INT_MAX) { - s = "big"; - } - else { - return; +static void +check_int(long num) +{ + if ((long)(int)num != num) { + rb_out_of_int(num); } - rb_raise(rb_eRangeError, "integer %ld too %s to convert to `int'", num, s); } static void -check_uint(num) - unsigned long num; +check_uint(unsigned long num, int sign) { - if (num > UINT_MAX) { - rb_raise(rb_eRangeError, "integer %lu too big to convert to `unsigned int'", num); + if (sign) { + /* minus */ + if (num < (unsigned long)INT_MIN) + rb_raise(rb_eRangeError, "integer %ld too small to convert to `unsigned int'", (long)num); + } + else { + /* plus */ + if (UINT_MAX < num) + rb_raise(rb_eRangeError, "integer %lu too big to convert to `unsigned int'", num); } } long -rb_num2int(val) - VALUE val; +rb_num2int(VALUE val) { long num = rb_num2long(val); @@ -1614,8 +2867,7 @@ rb_num2int(val) } long -rb_fix2int(val) - VALUE val; +rb_fix2int(VALUE val) { long num = FIXNUM_P(val)?FIX2LONG(val):rb_num2long(val); @@ -1624,51 +2876,117 @@ rb_fix2int(val) } unsigned long -rb_num2uint(val) - VALUE val; +rb_num2uint(VALUE val) { - unsigned long num = rb_num2ulong(val); + int wrap; + unsigned long num = rb_num2ulong_internal(val, &wrap); - if (RTEST(rb_funcall(INT2FIX(0), '<', 1, val))) { - check_uint(num); - } + check_uint(num, wrap); return num; } unsigned long -rb_fix2uint(val) - VALUE val; +rb_fix2uint(VALUE val) { unsigned long num; if (!FIXNUM_P(val)) { - return rb_num2uint(val); + return rb_num2uint(val); } num = FIX2ULONG(val); - if (FIX2LONG(val) > 0) { - check_uint(num); - } + + check_uint(num, rb_num_negative_int_p(val)); return num; } #else long -rb_num2int(val) - VALUE val; +rb_num2int(VALUE val) { return rb_num2long(val); } long -rb_fix2int(val) - VALUE val; +rb_fix2int(VALUE val) { return FIX2INT(val); } #endif +NORETURN(static void rb_out_of_short(SIGNED_VALUE num)); +static void +rb_out_of_short(SIGNED_VALUE num) +{ + rb_raise(rb_eRangeError, "integer %"PRIdVALUE " too %s to convert to `short'", + num, num < 0 ? "small" : "big"); +} + +static void +check_short(long num) +{ + if ((long)(short)num != num) { + rb_out_of_short(num); + } +} + +static void +check_ushort(unsigned long num, int sign) +{ + if (sign) { + /* minus */ + if (num < (unsigned long)SHRT_MIN) + rb_raise(rb_eRangeError, "integer %ld too small to convert to `unsigned short'", (long)num); + } + else { + /* plus */ + if (USHRT_MAX < num) + rb_raise(rb_eRangeError, "integer %lu too big to convert to `unsigned short'", num); + } +} + +short +rb_num2short(VALUE val) +{ + long num = rb_num2long(val); + + check_short(num); + return num; +} + +short +rb_fix2short(VALUE val) +{ + long num = FIXNUM_P(val)?FIX2LONG(val):rb_num2long(val); + + check_short(num); + return num; +} + +unsigned short +rb_num2ushort(VALUE val) +{ + int wrap; + unsigned long num = rb_num2ulong_internal(val, &wrap); + + check_ushort(num, wrap); + return num; +} + +unsigned short +rb_fix2ushort(VALUE val) +{ + unsigned long num; + + if (!FIXNUM_P(val)) { + return rb_num2ushort(val); + } + num = FIX2ULONG(val); + + check_ushort(num, rb_num_negative_int_p(val)); + return num; +} + VALUE -rb_num2fix(val) - VALUE val; +rb_num2fix(VALUE val) { long v; @@ -1682,9 +3000,19 @@ rb_num2fix(val) #if HAVE_LONG_LONG +#define LLONG_MIN_MINUS_ONE ((double)LLONG_MIN-1) +#define LLONG_MAX_PLUS_ONE (2*(double)(LLONG_MAX/2+1)) +#define ULLONG_MAX_PLUS_ONE (2*(double)(ULLONG_MAX/2+1)) +#ifndef ULLONG_MAX +#define ULLONG_MAX ((unsigned LONG_LONG)LLONG_MAX*2+1) +#endif +#define LLONG_MIN_MINUS_ONE_IS_LESS_THAN(n) \ + (LLONG_MIN_MINUS_ONE == (double)LLONG_MIN ? \ + LLONG_MIN <= (n): \ + LLONG_MIN_MINUS_ONE < (n)) + LONG_LONG -rb_num2ll(val) - VALUE val; +rb_num2ll(VALUE val) { if (NIL_P(val)) { rb_raise(rb_eTypeError, "no implicit conversion from nil"); @@ -1692,827 +3020,1424 @@ rb_num2ll(val) 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 if (RB_TYPE_P(val, T_FLOAT)) { + double d = RFLOAT_VALUE(val); + if (d < LLONG_MAX_PLUS_ONE && (LLONG_MIN_MINUS_ONE_IS_LESS_THAN(d))) { + return (LONG_LONG)d; } else { - char buf[24]; - char *s; - - sprintf(buf, "%-.10g", RFLOAT(val)->value); - if ((s = strchr(buf, ' ')) != 0) *s = '\0'; - rb_raise(rb_eRangeError, "float %s out of range of long long", buf); + FLOAT_OUT_OF_RANGE(val, "long long"); } - - case T_BIGNUM: + } + else if (RB_TYPE_P(val, T_BIGNUM)) { return rb_big2ll(val); - - case T_STRING: + } + else if (RB_TYPE_P(val, T_STRING)) { rb_raise(rb_eTypeError, "no implicit conversion from string"); - return Qnil; /* not reached */ - - case T_TRUE: - case T_FALSE: + } + else if (RB_TYPE_P(val, T_TRUE) || RB_TYPE_P(val, T_FALSE)) { rb_raise(rb_eTypeError, "no implicit conversion from boolean"); - return Qnil; /* not reached */ - - default: - val = rb_to_int(val); - return NUM2LL(val); } + + val = rb_to_int(val); + return NUM2LL(val); } unsigned LONG_LONG -rb_num2ull(val) - VALUE val; +rb_num2ull(VALUE val) { - if (TYPE(val) == T_BIGNUM) { + if (RB_TYPE_P(val, T_NIL)) { + rb_raise(rb_eTypeError, "no implicit conversion from nil"); + } + else if (RB_TYPE_P(val, T_FIXNUM)) { + return (LONG_LONG)FIX2LONG(val); /* this is FIX2LONG, intended */ + } + else if (RB_TYPE_P(val, T_FLOAT)) { + double d = RFLOAT_VALUE(val); + if (d < ULLONG_MAX_PLUS_ONE && LLONG_MIN_MINUS_ONE_IS_LESS_THAN(d)) { + if (0 <= d) + return (unsigned LONG_LONG)d; + return (unsigned LONG_LONG)(LONG_LONG)d; + } + else { + FLOAT_OUT_OF_RANGE(val, "unsigned long long"); + } + } + else if (RB_TYPE_P(val, T_BIGNUM)) { return rb_big2ull(val); } - return (unsigned LONG_LONG)rb_num2ll(val); + else if (RB_TYPE_P(val, T_STRING)) { + rb_raise(rb_eTypeError, "no implicit conversion from string"); + } + else if (RB_TYPE_P(val, T_TRUE) || RB_TYPE_P(val, T_FALSE)) { + rb_raise(rb_eTypeError, "no implicit conversion from boolean"); + } + + val = rb_to_int(val); + return NUM2ULL(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>. - * + * Holds Integer values. You cannot add a singleton method to an + * Integer object, any attempt to do so will raise a TypeError. + * */ - /* * call-seq: - * int.to_i => int - * int.to_int => int - * int.floor => int - * int.ceil => int - * int.round => int - * int.truncate => int + * int.to_i -> integer + * int.to_int -> integer + * + * Since +int+ is already an Integer, returns +self+. * - * As <i>int</i> is already an <code>Integer</code>, all these - * methods simply return the receiver. + * #to_int is an alias for #to_i. */ static VALUE -int_to_i(num) - VALUE num; +int_to_i(VALUE num) { return num; } /* * call-seq: - * int.integer? -> true - * - * Always returns <code>true</code>. + * int.integer? -> true + * + * Since +int+ is already an Integer, this always returns +true+. */ static VALUE -int_int_p(num) - VALUE num; +int_int_p(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 + * int.odd? -> true or false + * + * Returns +true+ if +int+ is an odd number. */ -static VALUE -int_succ(num) - VALUE num; +VALUE +rb_int_odd_p(VALUE num) { if (FIXNUM_P(num)) { - long i = FIX2LONG(num) + 1; - return LONG2NUM(i); + if (num & 2) { + return Qtrue; + } + } + else if (RB_TYPE_P(num, T_BIGNUM)) { + return rb_big_odd_p(num); } - return rb_funcall(num, '+', 1, INT2FIX(1)); + else if (rb_funcall(num, '%', 1, INT2FIX(2)) != INT2FIX(0)) { + return Qtrue; + } + return Qfalse; } /* * call-seq: - * int.chr => string - * - * Returns a string containing the ASCII character represented by the - * receiver's value. - * - * 65.chr #=> "A" - * ?a.chr #=> "a" - * 230.chr #=> "\346" + * int.even? -> true or false + * + * Returns +true+ if +int+ is an even number. */ static VALUE -int_chr(num) - VALUE num; +int_even_p(VALUE num) { - char c; - long i = NUM2LONG(num); - - if (i < 0 || 0xff < i) - rb_raise(rb_eRangeError, "%ld out of char range", i); - c = i; - return rb_str_new(&c, 1); + if (FIXNUM_P(num)) { + if ((num & 2) == 0) { + return Qtrue; + } + } + else if (RB_TYPE_P(num, T_BIGNUM)) { + return rb_big_even_p(num); + } + else if (rb_funcall(num, '%', 1, INT2FIX(2)) == INT2FIX(0)) { + return Qtrue; + } + return Qfalse; } -/******************************************************************** - * - * Document-class: Fixnum +/* + * call-seq: + * int.allbits?(mask) -> true or false * - * A <code>Fixnum</code> holds <code>Integer</code> values that can be - * represented in a native machine word (minus 1 bit). If any operation - * on a <code>Fixnum</code> exceeds this range, the value is - * automatically converted to a <code>Bignum</code>. - * - * <code>Fixnum</code> objects have immediate value. This means that - * when they are assigned or passed as parameters, the actual object is - * passed, rather than a reference to that object. Assignment does not - * alias <code>Fixnum</code> objects. There is effectively only one - * <code>Fixnum</code> object instance for any given integer value, so, - * for example, you cannot add a singleton method to a - * <code>Fixnum</code>. + * Returns +true+ if all bits of <code>+int+ & +mask+</code> are 1. */ +static VALUE +int_allbits_p(VALUE num, VALUE mask) +{ + mask = rb_to_int(mask); + return rb_int_equal(rb_int_and(num, mask), mask); +} /* - * call-seq: - * Fixnum.induced_from(obj) => fixnum + * call-seq: + * int.anybits?(mask) -> true or false * - * Convert <code>obj</code> to a Fixnum. Works with numeric parameters. - * Also works with Symbols, but this is deprecated. + * Returns +true+ if any bits of <code>+int+ & +mask+</code> are 1. */ static VALUE -rb_fix_induced_from(klass, x) - VALUE klass, x; +int_anybits_p(VALUE num, VALUE mask) { - return rb_num2fix(x); + mask = rb_to_int(mask); + return num_zero_p(rb_int_and(num, mask)) ? Qfalse : Qtrue; } /* - * call-seq: - * Integer.induced_from(obj) => fixnum, bignum + * call-seq: + * int.nobits?(mask) -> true or false * - * Convert <code>obj</code> to an Integer. + * Returns +true+ if no bits of <code>+int+ & +mask+</code> are 1. */ static VALUE -rb_int_induced_from(klass, x) - VALUE klass, x; +int_nobits_p(VALUE num, VALUE mask) +{ + mask = rb_to_int(mask); + return num_zero_p(rb_int_and(num, mask)); +} + +/* + * Document-method: Integer#succ + * Document-method: Integer#next + * call-seq: + * int.next -> integer + * int.succ -> integer + * + * Returns the successor of +int+, + * i.e. the Integer equal to <code>int+1</code>. + * + * 1.next #=> 2 + * (-1).next #=> 0 + * 1.succ #=> 2 + * (-1).succ #=> 0 + */ + +VALUE +rb_int_succ(VALUE num) +{ + if (FIXNUM_P(num)) { + long i = FIX2LONG(num) + 1; + return LONG2NUM(i); + } + if (RB_TYPE_P(num, T_BIGNUM)) { + return rb_big_plus(num, INT2FIX(1)); + } + return num_funcall1(num, '+', INT2FIX(1)); +} + +#define int_succ rb_int_succ + +/* + * call-seq: + * int.pred -> integer + * + * Returns the predecessor of +int+, + * i.e. the Integer equal to <code>int-1</code>. + * + * 1.pred #=> 0 + * (-1).pred #=> -2 + */ + +VALUE +rb_int_pred(VALUE num) { - switch (TYPE(x)) { - case T_FIXNUM: - case T_BIGNUM: - return x; - case T_FLOAT: - return rb_funcall(x, id_to_i, 0); - default: - rb_raise(rb_eTypeError, "failed to convert %s into Integer", - rb_obj_classname(x)); + if (FIXNUM_P(num)) { + long i = FIX2LONG(num) - 1; + return LONG2NUM(i); + } + if (RB_TYPE_P(num, T_BIGNUM)) { + return rb_big_minus(num, INT2FIX(1)); } + return num_funcall1(num, '-', INT2FIX(1)); } +#define int_pred rb_int_pred + /* - * call-seq: - * Float.induced_from(obj) => float + * Document-method: Integer#chr + * call-seq: + * int.chr([encoding]) -> string + * + * Returns a string containing the character represented by the +int+'s value + * according to +encoding+. * - * Convert <code>obj</code> to a float. + * 65.chr #=> "A" + * 230.chr #=> "\xE6" + * 255.chr(Encoding::UTF_8) #=> "\u00FF" */ +VALUE +rb_enc_uint_chr(unsigned int code, rb_encoding *enc) +{ + int n; + VALUE str; + switch (n = rb_enc_codelen(code, enc)) { + case ONIGERR_INVALID_CODE_POINT_VALUE: + rb_raise(rb_eRangeError, "invalid codepoint 0x%X in %s", code, rb_enc_name(enc)); + break; + case ONIGERR_TOO_BIG_WIDE_CHAR_VALUE: + case 0: + rb_raise(rb_eRangeError, "%u out of char range", code); + break; + } + str = rb_enc_str_new(0, n, enc); + rb_enc_mbcput(code, RSTRING_PTR(str), enc); + if (rb_enc_precise_mbclen(RSTRING_PTR(str), RSTRING_END(str), enc) != n) { + rb_raise(rb_eRangeError, "invalid codepoint 0x%X in %s", code, rb_enc_name(enc)); + } + return str; +} + static VALUE -rb_flo_induced_from(klass, x) - VALUE klass, x; +int_chr(int argc, VALUE *argv, VALUE num) { - switch (TYPE(x)) { - case T_FIXNUM: - case T_BIGNUM: - return rb_funcall(x, rb_intern("to_f"), 0); - case T_FLOAT: - return x; - default: - rb_raise(rb_eTypeError, "failed to convert %s into Float", - rb_obj_classname(x)); + char c; + unsigned int i; + rb_encoding *enc; + + if (rb_num_to_uint(num, &i) == 0) { + } + else if (FIXNUM_P(num)) { + rb_raise(rb_eRangeError, "%ld out of char range", FIX2LONG(num)); + } + else { + rb_raise(rb_eRangeError, "bignum out of char range"); } + + switch (argc) { + case 0: + if (0xff < i) { + enc = rb_default_internal_encoding(); + if (!enc) { + rb_raise(rb_eRangeError, "%d out of char range", i); + } + goto decode; + } + c = (char)i; + if (i < 0x80) { + return rb_usascii_str_new(&c, 1); + } + else { + return rb_str_new(&c, 1); + } + case 1: + break; + default: + rb_check_arity(argc, 0, 1); + break; + } + enc = rb_to_encoding(argv[0]); + if (!enc) enc = rb_ascii8bit_encoding(); + decode: + return rb_enc_uint_chr(i, enc); } /* + * call-seq: + * int.ord -> self + * + * Returns the +int+ itself. + * + * 97.ord #=> 97 + * + * This method is intended for compatibility to character literals + * in Ruby 1.9. + * + * For example, <code>?a.ord</code> returns 97 both in 1.8 and 1.9. + */ + +static VALUE +int_ord(VALUE num) +{ + return num; +} + +/* + * Fixnum + */ + + +/* + * Document-method: Integer#-@ * call-seq: - * -fix => integer + * -int -> integer * - * Negates <code>fix</code> (which might return a Bignum). + * Returns +int+, negated. */ static VALUE -fix_uminus(num) - VALUE num; +fix_uminus(VALUE num) { return LONG2NUM(-FIX2LONG(num)); } VALUE -rb_fix2str(x, base) - VALUE x; - int base; +rb_int_uminus(VALUE num) +{ + if (FIXNUM_P(num)) { + return fix_uminus(num); + } + else if (RB_TYPE_P(num, T_BIGNUM)) { + return rb_big_uminus(num); + } + return num_funcall0(num, idUMinus); +} + +/* + * Document-method: Integer#to_s + * call-seq: + * int.to_s(base=10) -> string + * + * Returns a string containing the place-value representation of +int+ + * with radix +base+ (between 2 and 36). + * + * 12345.to_s #=> "12345" + * 12345.to_s(2) #=> "11000000111001" + * 12345.to_s(8) #=> "30071" + * 12345.to_s(10) #=> "12345" + * 12345.to_s(16) #=> "3039" + * 12345.to_s(36) #=> "9ix" + * 78546939656932.to_s(36) #=> "rubyrules" + */ + +VALUE +rb_fix2str(VALUE x, int base) { - extern const char ruby_digitmap[]; - char buf[SIZEOF_LONG*CHAR_BIT + 2], *b = buf + sizeof buf; + char buf[SIZEOF_VALUE*CHAR_BIT + 1], *const e = buf + sizeof buf, *b = e; long val = FIX2LONG(x); + unsigned long u; int neg = 0; if (base < 2 || 36 < base) { - rb_raise(rb_eArgError, "illegal radix %d", base); + rb_raise(rb_eArgError, "invalid radix %d", base); + } +#if SIZEOF_LONG < SIZEOF_VOIDP +# if SIZEOF_VOIDP == SIZEOF_LONG_LONG + if ((val >= 0 && (x & 0xFFFFFFFF00000000ull)) || + (val < 0 && (x & 0xFFFFFFFF00000000ull) != 0xFFFFFFFF00000000ull)) { + rb_bug("Unnormalized Fixnum value %p", (void *)x); } +# else + /* should do something like above code, but currently ruby does not know */ + /* such platforms */ +# endif +#endif if (val == 0) { - return rb_str_new2("0"); + return rb_usascii_str_new2("0"); } if (val < 0) { - val = -val; + u = 1 + (unsigned long)(-(val + 1)); /* u = -val avoiding overflow */ neg = 1; } - *--b = '\0'; + else { + u = val; + } do { - *--b = ruby_digitmap[(int)(val % base)]; - } while (val /= base); + *--b = ruby_digitmap[(int)(u % base)]; + } while (u /= base); if (neg) { *--b = '-'; } - return rb_str_new2(b); + return rb_usascii_str_new(b, e - b); } -/* - * call-seq: - * fix.to_s( base=10 ) -> aString - * - * Returns a string containing the representation of <i>fix</i> radix - * <i>base</i> (between 2 and 36). - * - * 12345.to_s #=> "12345" - * 12345.to_s(2) #=> "11000000111001" - * 12345.to_s(8) #=> "30071" - * 12345.to_s(10) #=> "12345" - * 12345.to_s(16) #=> "3039" - * 12345.to_s(36) #=> "9ix" - * - */ static VALUE -fix_to_s(argc, argv, x) - int argc; - VALUE *argv; - VALUE x; +int_to_s(int argc, VALUE *argv, VALUE x) { - VALUE b; int base; - rb_scan_args(argc, argv, "01", &b); - if (argc == 0) base = 10; - else base = NUM2INT(b); + if (rb_check_arity(argc, 0, 1)) + base = NUM2INT(argv[0]); + else + base = 10; + return rb_int2str(x, base); +} + +VALUE +rb_int2str(VALUE x, int base) +{ + if (FIXNUM_P(x)) { + return rb_fix2str(x, base); + } + else if (RB_TYPE_P(x, T_BIGNUM)) { + return rb_big2str(x, base); + } - return rb_fix2str(x, base); + return rb_any_to_s(x); } /* + * Document-method: Integer#+ * call-seq: - * fix + numeric => numeric_result + * int + numeric -> numeric_result * * Performs addition: the class of the resulting object depends on - * the class of <code>numeric</code> and on the magnitude of the - * result. + * the class of +numeric+. */ static VALUE -fix_plus(x, y) - VALUE x, y; +fix_plus(VALUE x, VALUE y) { if (FIXNUM_P(y)) { - long a, b, c; - VALUE r; + return rb_fix_plus_fix(x, y); + } + else if (RB_TYPE_P(y, T_BIGNUM)) { + return rb_big_plus(y, x); + } + else if (RB_TYPE_P(y, T_FLOAT)) { + return DBL2NUM((double)FIX2LONG(x) + RFLOAT_VALUE(y)); + } + else if (RB_TYPE_P(y, T_COMPLEX)) { + return rb_complex_plus(y, x); + } + else { + return rb_num_coerce_bin(x, y, '+'); + } +} - a = FIX2LONG(x); - b = FIX2LONG(y); - c = a + b; - r = LONG2FIX(c); +VALUE +rb_fix_plus(VALUE x, VALUE y) +{ + return fix_plus(x, y); +} - if (FIX2LONG(r) != c) { - r = rb_big_plus(rb_int2big(a), rb_int2big(b)); - } - return r; +VALUE +rb_int_plus(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return fix_plus(x, y); } - if (TYPE(y) == T_FLOAT) { - return rb_float_new((double)FIX2LONG(x) + RFLOAT(y)->value); + else if (RB_TYPE_P(x, T_BIGNUM)) { + return rb_big_plus(x, y); } - return rb_num_coerce_bin(x, y); + return rb_num_coerce_bin(x, y, '+'); } /* + * Document-method: Integer#- * call-seq: - * fix - numeric => numeric_result + * int - numeric -> numeric_result * * Performs subtraction: the class of the resulting object depends on - * the class of <code>numeric</code> and on the magnitude of the - * result. + * the class of +numeric+. */ static VALUE -fix_minus(x, y) - VALUE x, y; +fix_minus(VALUE x, VALUE y) { if (FIXNUM_P(y)) { - long a, b, c; - VALUE r; - - a = FIX2LONG(x); - b = FIX2LONG(y); - c = a - b; - r = LONG2FIX(c); + return rb_fix_minus_fix(x, y); + } + else if (RB_TYPE_P(y, T_BIGNUM)) { + x = rb_int2big(FIX2LONG(x)); + return rb_big_minus(x, y); + } + else if (RB_TYPE_P(y, T_FLOAT)) { + return DBL2NUM((double)FIX2LONG(x) - RFLOAT_VALUE(y)); + } + else { + return rb_num_coerce_bin(x, y, '-'); + } +} - if (FIX2LONG(r) != c) { - r = rb_big_minus(rb_int2big(a), rb_int2big(b)); - } - return r; +VALUE +rb_int_minus(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return fix_minus(x, y); } - if (TYPE(y) == T_FLOAT) { - return rb_float_new((double)FIX2LONG(x) - RFLOAT(y)->value); + else if (RB_TYPE_P(x, T_BIGNUM)) { + return rb_big_minus(x, y); } - return rb_num_coerce_bin(x, y); + return rb_num_coerce_bin(x, y, '-'); } + +#define SQRT_LONG_MAX HALF_LONG_MSB +/*tests if N*N would overflow*/ +#define FIT_SQRT_LONG(n) (((n)<SQRT_LONG_MAX)&&((n)>=-SQRT_LONG_MAX)) + /* + * Document-method: Integer#* * call-seq: - * fix * numeric => numeric_result + * int * numeric -> numeric_result * * Performs multiplication: the class of the resulting object depends on - * the class of <code>numeric</code> and on the magnitude of the - * result. + * the class of +numeric+. */ static VALUE -fix_mul(x, y) - VALUE x, y; +fix_mul(VALUE x, VALUE y) { if (FIXNUM_P(y)) { - long a, b, c; - VALUE r; - - a = FIX2LONG(x); - if (a == 0) return x; - - b = FIX2LONG(y); - c = a * b; - r = LONG2FIX(c); - - if (FIX2LONG(r) != c || c/a != b) { - r = rb_big_mul(rb_int2big(a), rb_int2big(b)); + return rb_fix_mul_fix(x, y); + } + else if (RB_TYPE_P(y, T_BIGNUM)) { + switch (x) { + case INT2FIX(0): return x; + case INT2FIX(1): return y; } - return r; + return rb_big_mul(y, x); + } + else if (RB_TYPE_P(y, T_FLOAT)) { + return DBL2NUM((double)FIX2LONG(x) * RFLOAT_VALUE(y)); } - if (TYPE(y) == T_FLOAT) { - return rb_float_new((double)FIX2LONG(x) * RFLOAT(y)->value); + else if (RB_TYPE_P(y, T_COMPLEX)) { + return rb_complex_mul(y, x); + } + else { + return rb_num_coerce_bin(x, y, '*'); } - return rb_num_coerce_bin(x, y); } -static void -fixdivmod(x, y, divp, modp) - long x, y; - long *divp, *modp; +VALUE +rb_int_mul(VALUE x, VALUE y) { - long div, mod; + if (FIXNUM_P(x)) { + return fix_mul(x, y); + } + else if (RB_TYPE_P(x, T_BIGNUM)) { + return rb_big_mul(x, y); + } + return rb_num_coerce_bin(x, y, '*'); +} - if (y == 0) rb_num_zerodiv(); - if (y < 0) { - if (x < 0) - div = -x / -y; - else - div = - (x / -y); +static double +fix_fdiv_double(VALUE x, VALUE y) +{ + if (FIXNUM_P(y)) { + return (double)FIX2LONG(x) / (double)FIX2LONG(y); + } + else if (RB_TYPE_P(y, T_BIGNUM)) { + return rb_big_fdiv_double(rb_int2big(FIX2LONG(x)), y); + } + else if (RB_TYPE_P(y, T_FLOAT)) { + return (double)FIX2LONG(x) / RFLOAT_VALUE(y); } else { - if (x < 0) - div = - (-x / y); - else - div = x / y; + return NUM2DBL(rb_num_coerce_bin(x, y, rb_intern("fdiv"))); } - mod = x - div*y; - if ((mod < 0 && y > 0) || (mod > 0 && y < 0)) { - mod += y; - div -= 1; +} + +double +rb_int_fdiv_double(VALUE x, VALUE y) +{ + if (RB_INTEGER_TYPE_P(y) && !FIXNUM_ZERO_P(y)) { + VALUE gcd = rb_gcd(x, y); + if (!FIXNUM_ZERO_P(gcd)) { + x = rb_int_idiv(x, gcd); + y = rb_int_idiv(y, gcd); + } } - if (divp) *divp = div; - if (modp) *modp = mod; + if (FIXNUM_P(x)) { + return fix_fdiv_double(x, y); + } + else if (RB_TYPE_P(x, T_BIGNUM)) { + return rb_big_fdiv_double(x, y); + } + return NAN; } /* + * Document-method: Integer#fdiv * call-seq: - * fix.quo(numeric) => float - * - * Returns the floating point result of dividing <i>fix</i> by - * <i>numeric</i>. - * - * 654321.quo(13731) #=> 47.6528293642124 - * 654321.quo(13731.24) #=> 47.6519964693647 - * + * int.fdiv(numeric) -> float + * + * Returns the floating point result of dividing +int+ by +numeric+. + * + * 654321.fdiv(13731) #=> 47.652829364212366 + * 654321.fdiv(13731.24) #=> 47.65199646936475 + * -654321.fdiv(13731) #=> -47.652829364212366 */ -static VALUE -fix_quo(x, y) - VALUE x, y; +VALUE +rb_int_fdiv(VALUE x, VALUE y) { - if (FIXNUM_P(y)) { - return rb_float_new((double)FIX2LONG(x) / (double)FIX2LONG(y)); + if (RB_INTEGER_TYPE_P(x)) { + return DBL2NUM(rb_int_fdiv_double(x, y)); } - return rb_num_coerce_bin(x, y); + return Qnil; } /* + * Document-method: Integer#/ * call-seq: - * fix / numeric => numeric_result - * fix.div(numeric) => numeric_result + * int / numeric -> numeric_result * * Performs division: the class of the resulting object depends on - * the class of <code>numeric</code> and on the magnitude of the - * result. + * the class of +numeric+. */ static VALUE -fix_div(x, y) - VALUE x, y; +fix_divide(VALUE x, VALUE y, ID op) { if (FIXNUM_P(y)) { - long div; + if (FIXNUM_ZERO_P(y)) rb_num_zerodiv(); + return rb_fix_div_fix(x, y); + } + else if (RB_TYPE_P(y, T_BIGNUM)) { + x = rb_int2big(FIX2LONG(x)); + return rb_big_div(x, y); + } + else if (RB_TYPE_P(y, T_FLOAT)) { + { + double div; + + if (op == '/') { + div = (double)FIX2LONG(x) / RFLOAT_VALUE(y); + return DBL2NUM(div); + } + else { + if (RFLOAT_VALUE(y) == 0) rb_num_zerodiv(); + div = (double)FIX2LONG(x) / RFLOAT_VALUE(y); + return rb_dbl2big(floor(div)); + } + } + } + else { + if (RB_TYPE_P(y, T_RATIONAL) && + op == '/' && FIX2LONG(x) == 1) + return rb_rational_reciprocal(y); + return rb_num_coerce_bin(x, y, op); + } +} - fixdivmod(FIX2LONG(x), FIX2LONG(y), &div, 0); - return LONG2NUM(div); +static VALUE +fix_div(VALUE x, VALUE y) +{ + return fix_divide(x, y, '/'); +} + +VALUE +rb_int_div(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return fix_div(x, y); + } + else if (RB_TYPE_P(x, T_BIGNUM)) { + return rb_big_div(x, y); } - return rb_num_coerce_bin(x, y); + return Qnil; } /* - * call-seq: - * fix % other => Numeric - * fix.modulo(other) => Numeric + * Document-method: Integer#div + * call-seq: + * int.div(numeric) -> integer * - * Returns <code>fix</code> modulo <code>other</code>. - * See <code>Numeric.divmod</code> for more information. + * Performs integer division: returns the integer result of dividing +int+ + * by +numeric+. */ static VALUE -fix_mod(x, y) - VALUE x, y; +fix_idiv(VALUE x, VALUE y) { - if (FIXNUM_P(y)) { - long mod; + return fix_divide(x, y, id_div); +} - fixdivmod(FIX2LONG(x), FIX2LONG(y), 0, &mod); - return LONG2NUM(mod); +VALUE +rb_int_idiv(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return fix_idiv(x, y); + } + else if (RB_TYPE_P(x, T_BIGNUM)) { + return rb_big_idiv(x, y); } - return rb_num_coerce_bin(x, y); + return num_div(x, y); } /* + * Document-method: Integer#% + * Document-method: Integer#modulo * call-seq: - * fix.divmod(numeric) => array - * - * See <code>Numeric#divmod</code>. + * int % other -> real + * int.modulo(other) -> real + * + * Returns +int+ modulo +other+. + * + * See Numeric#divmod for more information. */ + static VALUE -fix_divmod(x, y) - VALUE x, y; +fix_mod(VALUE x, VALUE y) { if (FIXNUM_P(y)) { - long div, mod; + if (FIXNUM_ZERO_P(y)) rb_num_zerodiv(); + return rb_fix_mod_fix(x, y); + } + else if (RB_TYPE_P(y, T_BIGNUM)) { + x = rb_int2big(FIX2LONG(x)); + return rb_big_modulo(x, y); + } + else if (RB_TYPE_P(y, T_FLOAT)) { + return DBL2NUM(ruby_float_mod((double)FIX2LONG(x), RFLOAT_VALUE(y))); + } + else { + return rb_num_coerce_bin(x, y, '%'); + } +} - fixdivmod(FIX2LONG(x), FIX2LONG(y), &div, &mod); +VALUE +rb_int_modulo(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return fix_mod(x, y); + } + else if (RB_TYPE_P(x, T_BIGNUM)) { + return rb_big_modulo(x, y); + } + return num_modulo(x, y); +} + +/* + * call-seq: + * int.remainder(numeric) -> real + * + * Returns the remainder after dividing +int+ by +numeric+. + * + * <code>x.remainder(y)</code> means <code>x-y*(x/y).truncate</code>. + * + * 5.remainder(3) #=> 2 + * -5.remainder(3) #=> -2 + * 5.remainder(-3) #=> 2 + * -5.remainder(-3) #=> -2 + * 5.remainder(1.5) #=> 0.5 + * + * See Numeric#divmod. + */ - return rb_assoc_new(LONG2NUM(div), LONG2NUM(mod)); +VALUE +int_remainder(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return num_remainder(x, y); + } + else if (RB_TYPE_P(x, T_BIGNUM)) { + return rb_big_remainder(x, y); } - return rb_num_coerce_bin(x, y); + return Qnil; } +/* + * Document-method: Integer#divmod + * call-seq: + * int.divmod(numeric) -> array + * + * See Numeric#divmod. + */ static VALUE -int_even_p(VALUE num) +fix_divmod(VALUE x, VALUE y) { - if (rb_funcall(num, '%', 1, INT2FIX(2)) == INT2FIX(0)) { - return Qtrue; + if (FIXNUM_P(y)) { + VALUE div, mod; + if (FIXNUM_ZERO_P(y)) rb_num_zerodiv(); + rb_fix_divmod_fix(x, y, &div, &mod); + return rb_assoc_new(div, mod); } - return Qfalse; + else if (RB_TYPE_P(y, T_BIGNUM)) { + x = rb_int2big(FIX2LONG(x)); + return rb_big_divmod(x, y); + } + else if (RB_TYPE_P(y, T_FLOAT)) { + { + double div, mod; + volatile VALUE a, b; + + flodivmod((double)FIX2LONG(x), RFLOAT_VALUE(y), &div, &mod); + a = dbl2ival(div); + b = DBL2NUM(mod); + return rb_assoc_new(a, b); + } + } + else { + return rb_num_coerce_bin(x, y, id_divmod); + } +} + +VALUE +rb_int_divmod(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return fix_divmod(x, y); + } + else if (RB_TYPE_P(x, T_BIGNUM)) { + return rb_big_divmod(x, y); + } + return Qnil; } /* + * Document-method: Integer#** * call-seq: - * fix ** other => Numeric + * int ** numeric -> numeric_result * - * Raises <code>fix</code> to the <code>other</code> power, which may - * be negative or fractional. + * Raises +int+ to the power of +numeric+, which may be negative or + * fractional. + * The result may be an Integer, a Float, a Rational, or a complex number. * - * 2 ** 3 #=> 8 - * 2 ** -1 #=> 0.5 - * 2 ** 0.5 #=> 1.4142135623731 + * 2 ** 3 #=> 8 + * 2 ** -1 #=> (1/2) + * 2 ** 0.5 #=> 1.4142135623730951 + * (-1) ** 0.5 #=> (0.0+1.0i) + * + * 123456789 ** 2 #=> 15241578750190521 + * 123456789 ** 1.2 #=> 5126464716.0993185 + * 123456789 ** -2 #=> (1/15241578750190521) */ static VALUE -fix_pow(x, y) - VALUE x, y; +int_pow(long x, unsigned long y) +{ + int neg = x < 0; + long z = 1; + + if (y == 0) return INT2FIX(1); + if (y == 1) return LONG2NUM(x); + if (neg) x = -x; + if (y & 1) + z = x; + else + neg = 0; + y &= ~1; + do { + while (y % 2 == 0) { + if (!FIT_SQRT_LONG(x)) { + VALUE v; + bignum: + v = rb_big_pow(rb_int2big(x), LONG2NUM(y)); + if (RB_FLOAT_TYPE_P(v)) /* infinity due to overflow */ + return v; + if (z != 1) v = rb_big_mul(rb_int2big(neg ? -z : z), v); + return v; + } + x = x * x; + y >>= 1; + } + { + if (MUL_OVERFLOW_FIXNUM_P(x, z)) { + goto bignum; + } + z = x * z; + } + } while (--y); + if (neg) z = -z; + return LONG2NUM(z); +} + +VALUE +rb_int_positive_pow(long x, unsigned long y) +{ + return int_pow(x, y); +} + +static VALUE +fix_pow(VALUE x, VALUE y) { - static const double zero = 0.0; long a = FIX2LONG(x); if (FIXNUM_P(y)) { - long b; + long b = FIX2LONG(y); - b = FIX2LONG(y); - if (b == 0) return INT2FIX(1); - if (b == 1) return x; - a = FIX2LONG(x); - if (a == 0) { - if (b > 0) return INT2FIX(0); - return rb_float_new(1.0 / zero); - } if (a == 1) return INT2FIX(1); if (a == -1) { if (b % 2 == 0) return INT2FIX(1); - else + else return INT2FIX(-1); } - if (b > 0) { - return rb_big_pow(rb_int2big(a), y); + if (b < 0) + return num_funcall1(rb_rational_raw1(x), idPow, y); + + if (b == 0) return INT2FIX(1); + if (b == 1) return x; + if (a == 0) { + if (b > 0) return INT2FIX(0); + return DBL2NUM(INFINITY); } - return rb_float_new(pow((double)a, (double)b)); + return int_pow(a, b); } - switch (TYPE(y)) { - case T_BIGNUM: - if (a == 0) return INT2FIX(0); + else if (RB_TYPE_P(y, T_BIGNUM)) { if (a == 1) return INT2FIX(1); if (a == -1) { if (int_even_p(y)) return INT2FIX(1); else return INT2FIX(-1); } + if (rb_num_negative_int_p(y)) + return num_funcall1(rb_rational_raw1(x), idPow, y); + if (a == 0) return INT2FIX(0); x = rb_int2big(FIX2LONG(x)); return rb_big_pow(x, y); - case T_FLOAT: + } + else if (RB_TYPE_P(y, T_FLOAT)) { + double dy = RFLOAT_VALUE(y); + if (dy == 0.0) return DBL2NUM(1.0); if (a == 0) { - return rb_float_new(RFLOAT(y)->value < 0 ? (1.0 / zero) : 0.0); + return DBL2NUM(dy < 0 ? INFINITY : 0.0); } - if (a == 1) return rb_float_new(1.0); - return rb_float_new(pow((double)a, RFLOAT(y)->value)); - default: - return rb_num_coerce_bin(x, y); + if (a == 1) return DBL2NUM(1.0); + { + if (a < 0 && dy != round(dy)) + return num_funcall1(rb_complex_raw1(x), idPow, y); + return DBL2NUM(pow((double)a, dy)); + } + } + else { + return rb_num_coerce_bin(x, y, idPow); + } +} + +VALUE +rb_int_pow(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return fix_pow(x, y); } + else if (RB_TYPE_P(x, T_BIGNUM)) { + return rb_big_pow(x, y); + } + return Qnil; } /* + * Document-method: Integer#== + * Document-method: Integer#=== * call-seq: - * fix == other + * int == other -> true or false * - * Return <code>true</code> if <code>fix</code> equals <code>other</code> - * numerically. + * Returns +true+ if +int+ equals +other+ numerically. + * Contrast this with Integer#eql?, which requires +other+ to be an Integer. * - * 1 == 2 #=> false - * 1 == 1.0 #=> true + * 1 == 2 #=> false + * 1 == 1.0 #=> true */ static VALUE -fix_equal(x, y) - VALUE x, y; +fix_equal(VALUE x, VALUE y) { - if (FIXNUM_P(y)) { - return (FIX2LONG(x) == FIX2LONG(y))?Qtrue:Qfalse; + if (x == y) return Qtrue; + if (FIXNUM_P(y)) return Qfalse; + else if (RB_TYPE_P(y, T_BIGNUM)) { + return rb_big_eq(y, x); + } + else if (RB_TYPE_P(y, T_FLOAT)) { + return rb_integer_float_eq(x, y); } else { return num_equal(x, y); } } +VALUE +rb_int_equal(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return fix_equal(x, y); + } + else if (RB_TYPE_P(x, T_BIGNUM)) { + return rb_big_eq(x, y); + } + return Qnil; +} + /* + * Document-method: Integer#<=> * call-seq: - * fix <=> numeric => -1, 0, +1 - * - * Comparison---Returns -1, 0, or +1 depending on whether <i>fix</i> is - * less than, equal to, or greater than <i>numeric</i>. This is the - * basis for the tests in <code>Comparable</code>. + * int <=> numeric -> -1, 0, +1, or nil + * + * Comparison---Returns -1, 0, or +1 depending on whether +int+ is + * less than, equal to, or greater than +numeric+. + * + * This is the basis for the tests in the Comparable module. + * + * +nil+ is returned if the two values are incomparable. */ static VALUE -fix_cmp(x, y) - VALUE x, y; +fix_cmp(VALUE x, VALUE y) { + if (x == y) return INT2FIX(0); if (FIXNUM_P(y)) { - long a = FIX2LONG(x), b = FIX2LONG(y); - - if (a == b) return INT2FIX(0); - if (a > b) return INT2FIX(1); + if (FIX2LONG(x) > FIX2LONG(y)) return INT2FIX(1); return INT2FIX(-1); } + else if (RB_TYPE_P(y, T_BIGNUM)) { + VALUE cmp = rb_big_cmp(y, x); + switch (cmp) { + case INT2FIX(+1): return INT2FIX(-1); + case INT2FIX(-1): return INT2FIX(+1); + } + return cmp; + } + else if (RB_TYPE_P(y, T_FLOAT)) { + return rb_integer_float_cmp(x, y); + } + else { + return rb_num_coerce_cmp(x, y, id_cmp); + } + return rb_num_coerce_cmp(x, y, id_cmp); +} + +VALUE +rb_int_cmp(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return fix_cmp(x, y); + } + else if (RB_TYPE_P(x, T_BIGNUM)) { + return rb_big_cmp(x, y); + } else { - return rb_num_coerce_cmp(x, y); + rb_raise(rb_eNotImpError, "need to define `<=>' in %s", rb_obj_classname(x)); } } /* + * Document-method: Integer#> * call-seq: - * fix > other => true or false + * int > real -> true or false * - * Returns <code>true</code> if the value of <code>fix</code> is - * greater than that of <code>other</code>. + * Returns +true+ if the value of +int+ is greater than that of +real+. */ static VALUE -fix_gt(x, y) - VALUE x, y; +fix_gt(VALUE x, VALUE y) { if (FIXNUM_P(y)) { - long a = FIX2LONG(x), b = FIX2LONG(y); - - if (a > b) return Qtrue; + if (FIX2LONG(x) > FIX2LONG(y)) return Qtrue; return Qfalse; } + else if (RB_TYPE_P(y, T_BIGNUM)) { + return rb_big_cmp(y, x) == INT2FIX(-1) ? Qtrue : Qfalse; + } + else if (RB_TYPE_P(y, T_FLOAT)) { + return rb_integer_float_cmp(x, y) == INT2FIX(1) ? Qtrue : Qfalse; + } else { - return rb_num_coerce_relop(x, y); + return rb_num_coerce_relop(x, y, '>'); } } +VALUE +rb_int_gt(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return fix_gt(x, y); + } + else if (RB_TYPE_P(x, T_BIGNUM)) { + return rb_big_gt(x, y); + } + return Qnil; +} + /* + * Document-method: Integer#>= * call-seq: - * fix >= other => true or false + * int >= real -> true or false * - * Returns <code>true</code> if the value of <code>fix</code> is - * greater than or equal to that of <code>other</code>. + * Returns +true+ if the value of +int+ is greater than or equal to that of + * +real+. */ static VALUE -fix_ge(x, y) - VALUE x, y; +fix_ge(VALUE x, VALUE y) { if (FIXNUM_P(y)) { - long a = FIX2LONG(x), b = FIX2LONG(y); - - if (a >= b) return Qtrue; + if (FIX2LONG(x) >= FIX2LONG(y)) return Qtrue; return Qfalse; } + else if (RB_TYPE_P(y, T_BIGNUM)) { + return rb_big_cmp(y, x) != INT2FIX(+1) ? Qtrue : Qfalse; + } + else if (RB_TYPE_P(y, T_FLOAT)) { + VALUE rel = rb_integer_float_cmp(x, y); + return rel == INT2FIX(1) || rel == INT2FIX(0) ? Qtrue : Qfalse; + } else { - return rb_num_coerce_relop(x, y); + return rb_num_coerce_relop(x, y, idGE); + } +} + +VALUE +rb_int_ge(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return fix_ge(x, y); } + else if (RB_TYPE_P(x, T_BIGNUM)) { + return rb_big_ge(x, y); + } + return Qnil; } /* + * Document-method: Integer#< * call-seq: - * fix < other => true or false + * int < real -> true or false * - * Returns <code>true</code> if the value of <code>fix</code> is - * less than that of <code>other</code>. + * Returns +true+ if the value of +int+ is less than that of +real+. */ static VALUE -fix_lt(x, y) - VALUE x, y; +fix_lt(VALUE x, VALUE y) { if (FIXNUM_P(y)) { - long a = FIX2LONG(x), b = FIX2LONG(y); - - if (a < b) return Qtrue; + if (FIX2LONG(x) < FIX2LONG(y)) return Qtrue; return Qfalse; } + else if (RB_TYPE_P(y, T_BIGNUM)) { + return rb_big_cmp(y, x) == INT2FIX(+1) ? Qtrue : Qfalse; + } + else if (RB_TYPE_P(y, T_FLOAT)) { + return rb_integer_float_cmp(x, y) == INT2FIX(-1) ? Qtrue : Qfalse; + } else { - return rb_num_coerce_relop(x, y); + return rb_num_coerce_relop(x, y, '<'); } } +static VALUE +int_lt(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return fix_lt(x, y); + } + else if (RB_TYPE_P(x, T_BIGNUM)) { + return rb_big_lt(x, y); + } + return Qnil; +} + /* + * Document-method: Integer#<= * call-seq: - * fix <= other => true or false + * int <= real -> true or false * - * Returns <code>true</code> if the value of <code>fix</code> is - * less thanor equal to that of <code>other</code>. + * Returns +true+ if the value of +int+ is less than or equal to that of + * +real+. */ static VALUE -fix_le(x, y) - VALUE x, y; +fix_le(VALUE x, VALUE y) { if (FIXNUM_P(y)) { - long a = FIX2LONG(x), b = FIX2LONG(y); - - if (a <= b) return Qtrue; + if (FIX2LONG(x) <= FIX2LONG(y)) return Qtrue; return Qfalse; } + else if (RB_TYPE_P(y, T_BIGNUM)) { + return rb_big_cmp(y, x) != INT2FIX(-1) ? Qtrue : Qfalse; + } + else if (RB_TYPE_P(y, T_FLOAT)) { + VALUE rel = rb_integer_float_cmp(x, y); + return rel == INT2FIX(-1) || rel == INT2FIX(0) ? Qtrue : Qfalse; + } else { - return rb_num_coerce_relop(x, y); + return rb_num_coerce_relop(x, y, idLE); } } +static VALUE +int_le(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return fix_le(x, y); + } + else if (RB_TYPE_P(x, T_BIGNUM)) { + return rb_big_le(x, y); + } + return Qnil; +} + /* + * Document-method: Integer#~ * call-seq: - * ~fix => integer + * ~int -> integer * * One's complement: returns a number where each bit is flipped. + * + * Inverts the bits in an Integer. As integers are conceptually of + * infinite length, the result acts as if it had an infinite number of + * one bits to the left. In hex representations, this is displayed + * as two periods to the left of the digits. + * + * sprintf("%X", ~0x1122334455) #=> "..FEEDDCCBBAA" */ static VALUE -fix_rev(num) - VALUE num; +fix_comp(VALUE num) { - long val = FIX2LONG(num); + return ~num | FIXNUM_FLAG; +} - val = ~val; - return LONG2NUM(val); +static VALUE +int_comp(VALUE num) +{ + if (FIXNUM_P(num)) { + return fix_comp(num); + } + else if (RB_TYPE_P(num, T_BIGNUM)) { + return rb_big_comp(num); + } + return Qnil; } static VALUE -fix_coerce(x) - VALUE x; +num_funcall_bit_1(VALUE y, VALUE arg, int recursive) { - while (!FIXNUM_P(x) && TYPE(x) != T_BIGNUM) { - x = rb_to_int(x); + ID func = (ID)((VALUE *)arg)[0]; + VALUE x = ((VALUE *)arg)[1]; + if (recursive) { + num_funcall_op_1_recursion(x, func, y); } - return x; + return rb_check_funcall(x, func, 1, &y); +} + +VALUE +rb_num_coerce_bit(VALUE x, VALUE y, ID func) +{ + VALUE ret, args[3]; + + args[0] = (VALUE)func; + args[1] = x; + args[2] = y; + do_coerce(&args[1], &args[2], TRUE); + ret = rb_exec_recursive_paired(num_funcall_bit_1, + args[2], args[1], (VALUE)args); + if (ret == Qundef) { + /* show the original object, not coerced object */ + coerce_failed(x, y); + } + return ret; } /* + * Document-method: Integer#& * call-seq: - * fix & other => integer + * int & other_int -> integer * * Bitwise AND. */ static VALUE -fix_and(x, y) - VALUE x, y; +fix_and(VALUE x, VALUE y) { - long val; + if (FIXNUM_P(y)) { + long val = FIX2LONG(x) & FIX2LONG(y); + return LONG2NUM(val); + } - if (!FIXNUM_P(y = fix_coerce(y))) { + if (RB_TYPE_P(y, T_BIGNUM)) { return rb_big_and(y, x); } - val = FIX2LONG(x) & FIX2LONG(y); - return LONG2NUM(val); + + return rb_num_coerce_bit(x, y, '&'); +} + +VALUE +rb_int_and(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return fix_and(x, y); + } + else if (RB_TYPE_P(x, T_BIGNUM)) { + return rb_big_and(x, y); + } + return Qnil; } /* + * Document-method: Integer#| * call-seq: - * fix | other => integer + * int | other_int -> integer * * Bitwise OR. */ static VALUE -fix_or(x, y) - VALUE x, y; +fix_or(VALUE x, VALUE y) { - long val; + if (FIXNUM_P(y)) { + long val = FIX2LONG(x) | FIX2LONG(y); + return LONG2NUM(val); + } - if (!FIXNUM_P(y = fix_coerce(y))) { + if (RB_TYPE_P(y, T_BIGNUM)) { return rb_big_or(y, x); } - val = FIX2LONG(x) | FIX2LONG(y); - return LONG2NUM(val); + + return rb_num_coerce_bit(x, y, '|'); +} + +static VALUE +int_or(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return fix_or(x, y); + } + else if (RB_TYPE_P(x, T_BIGNUM)) { + return rb_big_or(x, y); + } + return Qnil; } /* + * Document-method: Integer#^ * call-seq: - * fix ^ other => integer + * int ^ other_int -> integer * * Bitwise EXCLUSIVE OR. */ static VALUE -fix_xor(x, y) - VALUE x, y; +fix_xor(VALUE x, VALUE y) { - long val; + if (FIXNUM_P(y)) { + long val = FIX2LONG(x) ^ FIX2LONG(y); + return LONG2NUM(val); + } - if (!FIXNUM_P(y = fix_coerce(y))) { + if (RB_TYPE_P(y, T_BIGNUM)) { return rb_big_xor(y, x); } - val = FIX2LONG(x) ^ FIX2LONG(y); - return LONG2NUM(val); + + return rb_num_coerce_bit(x, y, '^'); } -static VALUE fix_lshift _((long, unsigned long)); -static VALUE fix_rshift _((long, unsigned long)); +static VALUE +int_xor(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return fix_xor(x, y); + } + else if (RB_TYPE_P(x, T_BIGNUM)) { + return rb_big_xor(x, y); + } + return Qnil; +} /* + * Document-method: Integer#<< * call-seq: - * fix << count => integer + * int << count -> integer * - * Shifts _fix_ left _count_ positions (right if _count_ is negative). + * Returns +int+ shifted left +count+ positions, or right if +count+ + * is negative. */ static VALUE -rb_fix_lshift(x, y) - VALUE x, y; +rb_fix_lshift(VALUE x, VALUE y) { long val, width; @@ -2526,28 +4451,39 @@ rb_fix_lshift(x, y) } static VALUE -fix_lshift(val, width) - long val; - unsigned long width; +fix_lshift(long val, unsigned long width) { - if (width > (sizeof(VALUE)*CHAR_BIT-1) - || ((unsigned long)val)>>(sizeof(VALUE)*CHAR_BIT-1-width) > 0) { + if (width > (SIZEOF_LONG*CHAR_BIT-1) + || ((unsigned long)val)>>(SIZEOF_LONG*CHAR_BIT-1-width) > 0) { return rb_big_lshift(rb_int2big(val), ULONG2NUM(width)); } val = val << width; return LONG2NUM(val); } +VALUE +rb_int_lshift(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return rb_fix_lshift(x, y); + } + else if (RB_TYPE_P(x, T_BIGNUM)) { + return rb_big_lshift(x, y); + } + return Qnil; +} + /* + * Document-method: Integer#>> * call-seq: - * fix >> count => integer + * int >> count -> integer * - * Shifts _fix_ right _count_ positions (left if _count_ is negative). + * Returns +int+ shifted right +count+ positions, or left if +count+ + * is negative. */ static VALUE -rb_fix_rshift(x, y) - VALUE x, y; +rb_fix_rshift(VALUE x, VALUE y) { long i, val; @@ -2572,33 +4508,47 @@ fix_rshift(long val, unsigned long i) return LONG2FIX(val); } +static VALUE +rb_int_rshift(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return rb_fix_rshift(x, y); + } + else if (RB_TYPE_P(x, T_BIGNUM)) { + return rb_big_rshift(x, y); + } + return Qnil; +} + /* + * Document-method: Integer#[] * call-seq: - * fix[n] => 0, 1 - * - * Bit Reference---Returns the <em>n</em>th bit in the binary - * representation of <i>fix</i>, where <i>fix</i>[0] is the least - * significant bit. - * + * int[n] -> 0, 1 + * + * Bit Reference---Returns the <code>n</code>th bit in the + * binary representation of +int+, where <code>int[0]</code> + * is the least significant bit. + * * a = 0b11001100101010 - * 30.downto(0) do |n| print a[n] end - * - * <em>produces:</em> - * - * 0000000000000000011001100101010 + * 30.downto(0) {|n| print a[n] } + * #=> 0000000000000000011001100101010 + * + * a = 9**15 + * 50.downto(0) {|n| print a[n] } + * #=> 000101110110100000111000011110010100111100010111001 */ static VALUE -fix_aref(fix, idx) - VALUE fix, idx; +fix_aref(VALUE fix, VALUE idx) { long val = FIX2LONG(fix); long i; - if (!FIXNUM_P(idx = fix_coerce(idx))) { + idx = rb_to_int(idx); + if (!FIXNUM_P(idx)) { idx = rb_big_norm(idx); if (!FIXNUM_P(idx)) { - if (!RBIGNUM(idx)->sign || val >= 0) + if (!BIGNUM_SIGN(idx) || val >= 0) return INT2FIX(0); return INT2FIX(1); } @@ -2606,7 +4556,7 @@ fix_aref(fix, idx) i = FIX2LONG(idx); if (i < 0) return INT2FIX(0); - if (sizeof(VALUE)*CHAR_BIT-1 < i) { + if (SIZEOF_LONG*CHAR_BIT-1 <= i) { if (val < 0) return INT2FIX(1); return INT2FIX(0); } @@ -2615,39 +4565,63 @@ fix_aref(fix, idx) return INT2FIX(0); } +static VALUE +int_aref(VALUE num, VALUE idx) +{ + if (FIXNUM_P(num)) { + return fix_aref(num, idx); + } + else if (RB_TYPE_P(num, T_BIGNUM)) { + return rb_big_aref(num, idx); + } + return Qnil; +} + /* + * Document-method: Integer#to_f * call-seq: - * fix.to_f -> float - * - * Converts <i>fix</i> to a <code>Float</code>. - * + * int.to_f -> float + * + * Converts +int+ to a Float. If +int+ doesn't fit in a Float, + * the result is infinity. */ static VALUE -fix_to_f(num) - VALUE num; +int_to_f(VALUE num) { double val; - val = (double)FIX2LONG(num); + if (FIXNUM_P(num)) { + val = (double)FIX2LONG(num); + } + else if (RB_TYPE_P(num, T_BIGNUM)) { + val = rb_big2dbl(num); + } + else { + rb_raise(rb_eNotImpError, "Unknown subclass for to_f: %s", rb_obj_classname(num)); + } - return rb_float_new(val); + return DBL2NUM(val); } /* + * Document-method: Integer#abs + * Document-method: Integer#magnitude * call-seq: - * fix.abs -> aFixnum - * - * Returns the absolute value of <i>fix</i>. - * - * -12345.abs #=> 12345 - * 12345.abs #=> 12345 - * + * int.abs -> integer + * int.magnitude -> integer + * + * Returns the absolute value of +int+. + * + * (-12345).abs #=> 12345 + * -12345.abs #=> 12345 + * 12345.abs #=> 12345 + * + * Integer#magnitude is an alias for Integer#abs. */ static VALUE -fix_abs(fix) - VALUE fix; +fix_abs(VALUE fix) { long i = FIX2LONG(fix); @@ -2656,93 +4630,251 @@ fix_abs(fix) return LONG2NUM(i); } +VALUE +rb_int_abs(VALUE num) +{ + if (FIXNUM_P(num)) { + return fix_abs(num); + } + else if (RB_TYPE_P(num, T_BIGNUM)) { + return rb_big_abs(num); + } + return Qnil; +} + /* + * Document-method: Integer#size * call-seq: - * fix.id2name -> string or nil - * - * Returns the name of the object whose symbol id is <i>fix</i>. If - * there is no symbol in the symbol table with this value, returns - * <code>nil</code>. <code>id2name</code> has nothing to do with the - * <code>Object.id</code> method. See also <code>Fixnum#to_sym</code>, - * <code>String#intern</code>, and class <code>Symbol</code>. - * - * symbol = :@inst_var #=> :@inst_var - * id = symbol.to_i #=> 9818 - * id.id2name #=> "@inst_var" + * int.size -> int + * + * Returns the number of bytes in the machine representation of +int+ + * (machine dependent). + * + * 1.size #=> 8 + * -1.size #=> 8 + * 2147483647.size #=> 8 + * (256**10 - 1).size #=> 10 + * (256**20 - 1).size #=> 20 + * (256**40 - 1).size #=> 40 */ static VALUE -fix_id2name(fix) - VALUE fix; +fix_size(VALUE fix) { - char *name = rb_id2name(FIX2UINT(fix)); - if (name) return rb_str_new2(name); - return Qnil; + return INT2FIX(sizeof(long)); } +static VALUE +int_size(VALUE num) +{ + if (FIXNUM_P(num)) { + return fix_size(num); + } + else if (RB_TYPE_P(num, T_BIGNUM)) { + return rb_big_size_m(num); + } + return Qnil; +} /* + * Document-method: Integer#bit_length * call-seq: - * fix.to_sym -> aSymbol - * - * Returns the symbol whose integer value is <i>fix</i>. See also - * <code>Fixnum#id2name</code>. - * - * fred = :fred.to_i - * fred.id2name #=> "fred" - * fred.to_sym #=> :fred + * int.bit_length -> integer + * + * Returns the number of bits of the value of +int+. + * + * "Number of bits" means the bit position of the highest bit + * which is different from the sign bit + * (where the least significant bit has bit position 1). + * If there is no such bit (zero or minus one), zero is returned. + * + * I.e. this method returns <i>ceil(log2(int < 0 ? -int : int+1))</i>. + * + * (-2**1000-1).bit_length #=> 1001 + * (-2**1000).bit_length #=> 1000 + * (-2**1000+1).bit_length #=> 1000 + * (-2**12-1).bit_length #=> 13 + * (-2**12).bit_length #=> 12 + * (-2**12+1).bit_length #=> 12 + * -0x101.bit_length #=> 9 + * -0x100.bit_length #=> 8 + * -0xff.bit_length #=> 8 + * -2.bit_length #=> 1 + * -1.bit_length #=> 0 + * 0.bit_length #=> 0 + * 1.bit_length #=> 1 + * 0xff.bit_length #=> 8 + * 0x100.bit_length #=> 9 + * (2**12-1).bit_length #=> 12 + * (2**12).bit_length #=> 13 + * (2**12+1).bit_length #=> 13 + * (2**1000-1).bit_length #=> 1000 + * (2**1000).bit_length #=> 1001 + * (2**1000+1).bit_length #=> 1001 + * + * This method can be used to detect overflow in Array#pack as follows: + * + * if n.bit_length < 32 + * [n].pack("l") # no overflow + * else + * raise "overflow" + * end */ static VALUE -fix_to_sym(fix) - VALUE fix; +rb_fix_bit_length(VALUE fix) { - ID id = FIX2UINT(fix); + long v = FIX2LONG(fix); + if (v < 0) + v = ~v; + return LONG2FIX(bit_length(v)); +} - if (rb_id2name(id)) { - return ID2SYM(id); +static VALUE +rb_int_bit_length(VALUE num) +{ + if (FIXNUM_P(num)) { + return rb_fix_bit_length(num); + } + else if (RB_TYPE_P(num, T_BIGNUM)) { + return rb_big_bit_length(num); } return Qnil; } - /* + * Document-method: Integer#digits * call-seq: - * fix.size -> fixnum - * - * Returns the number of <em>bytes</em> in the machine representation - * of a <code>Fixnum</code>. - * - * 1.size #=> 4 - * -1.size #=> 4 - * 2147483647.size #=> 4 + * int.digits -> array + * int.digits(base) -> array + * + * Returns the digits of +int+'s place-value representation + * with radix +base+ (default: 10). + * The digits are returned as an array with the least significant digit + * as the first array element. + * + * +base+ must be greater than or equal to 2. + * + * 12345.digits #=> [5, 4, 3, 2, 1] + * 12345.digits(7) #=> [4, 6, 6, 0, 5] + * 12345.digits(100) #=> [45, 23, 1] + * + * -12345.digits(7) #=> Math::DomainError */ static VALUE -fix_size(fix) - VALUE fix; +rb_fix_digits(VALUE fix, long base) { - return INT2FIX(sizeof(long)); + VALUE digits; + long x = FIX2LONG(fix); + + assert(x >= 0); + + if (base < 2) + rb_raise(rb_eArgError, "invalid radix %ld", base); + + if (x == 0) + return rb_ary_new_from_args(1, INT2FIX(0)); + + digits = rb_ary_new(); + while (x > 0) { + long q = x % base; + rb_ary_push(digits, LONG2NUM(q)); + x /= base; + } + + return digits; +} + +static VALUE +rb_int_digits_bigbase(VALUE num, VALUE base) +{ + VALUE digits; + + assert(!rb_num_negative_p(num)); + + if (RB_TYPE_P(base, T_BIGNUM)) + base = rb_big_norm(base); + + if (FIXNUM_P(base) && FIX2LONG(base) < 2) + rb_raise(rb_eArgError, "invalid radix %ld", FIX2LONG(base)); + else if (RB_TYPE_P(base, T_BIGNUM) && BIGNUM_NEGATIVE_P(base)) + rb_raise(rb_eArgError, "negative radix"); + + if (FIXNUM_P(base) && FIXNUM_P(num)) + return rb_fix_digits(num, FIX2LONG(base)); + + if (FIXNUM_P(num)) + return rb_ary_new_from_args(1, num); + + digits = rb_ary_new(); + while (!FIXNUM_P(num) || FIX2LONG(num) > 0) { + VALUE qr = rb_int_divmod(num, base); + rb_ary_push(digits, RARRAY_AREF(qr, 1)); + num = RARRAY_AREF(qr, 0); + } + + return digits; +} + +static VALUE +rb_int_digits(int argc, VALUE *argv, VALUE num) +{ + VALUE base_value; + long base; + + if (rb_num_negative_p(num)) + rb_raise(rb_eMathDomainError, "out of domain"); + + if (rb_check_arity(argc, 0, 1)) { + base_value = rb_to_int(argv[0]); + if (!RB_INTEGER_TYPE_P(base_value)) + rb_raise(rb_eTypeError, "wrong argument type %s (expected Integer)", + rb_obj_classname(argv[0])); + if (RB_TYPE_P(base_value, T_BIGNUM)) + return rb_int_digits_bigbase(num, base_value); + + base = FIX2LONG(base_value); + if (base < 0) + rb_raise(rb_eArgError, "negative radix"); + else if (base < 2) + rb_raise(rb_eArgError, "invalid radix %ld", base); + } + else + base = 10; + + if (FIXNUM_P(num)) + return rb_fix_digits(num, base); + else if (RB_TYPE_P(num, T_BIGNUM)) + return rb_int_digits_bigbase(num, LONG2FIX(base)); + + return Qnil; } /* + * Document-method: Integer#upto * call-seq: - * int.upto(limit) {|i| block } => int - * - * Iterates <em>block</em>, passing in integer values from <i>int</i> - * up to and including <i>limit</i>. - * - * 5.upto(10) { |i| print i, " " } - * - * <em>produces:</em> - * - * 5 6 7 8 9 10 + * int.upto(limit) {|i| block } -> self + * int.upto(limit) -> an_enumerator + * + * Iterates the given block, passing in integer values from +int+ up to and + * including +limit+. + * + * If no block is given, an Enumerator is returned instead. + * + * 5.upto(10) {|i| print i, " " } #=> 5 6 7 8 9 10 */ static VALUE -int_upto(from, to) - VALUE from, to; +int_upto_size(VALUE from, VALUE args, VALUE eobj) +{ + return ruby_num_interval_step_size(from, RARRAY_AREF(args, 0), INT2FIX(1), FALSE); +} + +static VALUE +int_upto(VALUE from, VALUE to) { + RETURN_SIZED_ENUMERATOR(from, 1, &to, int_upto_size); if (FIXNUM_P(from) && FIXNUM_P(to)) { long i, end; @@ -2764,24 +4896,31 @@ int_upto(from, to) } /* + * Document-method: Integer#downto * call-seq: - * int.downto(limit) {|i| block } => int - * - * Iterates <em>block</em>, passing decreasing values from <i>int</i> - * down to and including <i>limit</i>. - * + * int.downto(limit) {|i| block } -> self + * int.downto(limit) -> an_enumerator + * + * Iterates the given block, passing in decreasing values from +int+ down to + * and including +limit+. + * + * If no block is given, an Enumerator is returned instead. + * * 5.downto(1) { |n| print n, ".. " } - * print " Liftoff!\n" - * - * <em>produces:</em> - * - * 5.. 4.. 3.. 2.. 1.. Liftoff! + * puts "Liftoff!" + * #=> "5.. 4.. 3.. 2.. 1.. Liftoff!" */ static VALUE -int_downto(from, to) - VALUE from, to; +int_downto_size(VALUE from, VALUE args, VALUE eobj) { + return ruby_num_interval_step_size(from, RARRAY_AREF(args, 0), INT2FIX(-1), FALSE); +} + +static VALUE +int_downto(VALUE from, VALUE to) +{ + RETURN_SIZED_ENUMERATOR(from, 1, &to, int_downto_size); if (FIXNUM_P(from) && FIXNUM_P(to)) { long i, end; @@ -2803,31 +4942,42 @@ int_downto(from, to) } /* + * Document-method: Integer#times * call-seq: - * int.times {|i| block } => int - * - * Iterates block <i>int</i> times, passing in values from zero to - * <i>int</i> - 1. - * - * 5.times do |i| - * print i, " " - * end - * - * <em>produces:</em> - * - * 0 1 2 3 4 + * int.times {|i| block } -> self + * int.times -> an_enumerator + * + * Iterates the given block +int+ times, passing in values from zero to + * <code>int - 1</code>. + * + * If no block is given, an Enumerator is returned instead. + * + * 5.times {|i| print i, " " } #=> 0 1 2 3 4 */ static VALUE -int_dotimes(num) - VALUE num; +int_dotimes_size(VALUE num, VALUE args, VALUE eobj) { if (FIXNUM_P(num)) { + if (NUM2LONG(num) <= 0) return INT2FIX(0); + } + else { + if (RTEST(rb_funcall(num, '<', 1, INT2FIX(0)))) return INT2FIX(0); + } + return num; +} + +static VALUE +int_dotimes(VALUE num) +{ + RETURN_SIZED_ENUMERATOR(num, 0, 0, int_dotimes_size); + + if (FIXNUM_P(num)) { long i, end; end = FIX2LONG(num); for (i=0; i<end; i++) { - rb_yield(LONG2FIX(i)); + rb_yield_1(LONG2FIX(i)); } } else { @@ -2843,39 +4993,358 @@ int_dotimes(num) } /* + * Document-method: Integer#round + * call-seq: + * int.round([ndigits] [, half: mode]) -> integer or float + * + * Returns +int+ rounded to the nearest value with + * a precision of +ndigits+ decimal digits (default: 0). + * + * When the precision is negative, the returned value is an integer + * with at least <code>ndigits.abs</code> trailing zeros. + * + * Returns +self+ when +ndigits+ is zero or positive. + * + * 1.round #=> 1 + * 1.round(2) #=> 1 + * 15.round(-1) #=> 20 + * (-15).round(-1) #=> -20 + * + * The optional +half+ keyword argument is available + * similar to Float#round. + * + * 25.round(-1, half: :up) #=> 30 + * 25.round(-1, half: :down) #=> 20 + * 25.round(-1, half: :even) #=> 20 + * 35.round(-1, half: :up) #=> 40 + * 35.round(-1, half: :down) #=> 30 + * 35.round(-1, half: :even) #=> 40 + * (-25).round(-1, half: :up) #=> -30 + * (-25).round(-1, half: :down) #=> -20 + * (-25).round(-1, half: :even) #=> -20 + */ + +static VALUE +int_round(int argc, VALUE* argv, VALUE num) +{ + int ndigits; + int mode; + VALUE nd, opt; + + if (!rb_scan_args(argc, argv, "01:", &nd, &opt)) return num; + ndigits = NUM2INT(nd); + mode = rb_num_get_rounding_option(opt); + if (ndigits >= 0) { + return num; + } + return rb_int_round(num, ndigits, mode); +} + +/* + * Document-method: Integer#floor * call-seq: - * fix.zero? => true or false - * - * Returns <code>true</code> if <i>fix</i> is zero. - * + * int.floor([ndigits]) -> integer or float + * + * Returns the largest number less than or equal to +int+ with + * a precision of +ndigits+ decimal digits (default: 0). + * + * When the precision is negative, the returned value is an integer + * with at least <code>ndigits.abs</code> trailing zeros. + * + * Returns +self+ when +ndigits+ is zero or positive. + * + * 1.floor #=> 1 + * 1.floor(2) #=> 1 + * 18.floor(-1) #=> 10 + * (-18).floor(-1) #=> -20 */ static VALUE -fix_zero_p(num) - VALUE num; +int_floor(int argc, VALUE* argv, VALUE num) { - if (FIX2LONG(num) == 0) { - return Qtrue; + int ndigits; + + if (!rb_check_arity(argc, 0, 1)) return num; + ndigits = NUM2INT(argv[0]); + if (ndigits >= 0) { + return num; + } + return rb_int_floor(num, ndigits); +} + +/* + * Document-method: Integer#ceil + * call-seq: + * int.ceil([ndigits]) -> integer or float + * + * Returns the smallest number greater than or equal to +int+ with + * a precision of +ndigits+ decimal digits (default: 0). + * + * When the precision is negative, the returned value is an integer + * with at least <code>ndigits.abs</code> trailing zeros. + * + * Returns +self+ when +ndigits+ is zero or positive. + * + * 1.ceil #=> 1 + * 1.ceil(2) #=> 1 + * 18.ceil(-1) #=> 20 + * (-18).ceil(-1) #=> -10 + */ + +static VALUE +int_ceil(int argc, VALUE* argv, VALUE num) +{ + int ndigits; + + if (!rb_check_arity(argc, 0, 1)) return num; + ndigits = NUM2INT(argv[0]); + if (ndigits >= 0) { + return num; + } + return rb_int_ceil(num, ndigits); +} + +/* + * Document-method: Integer#truncate + * call-seq: + * int.truncate([ndigits]) -> integer or float + * + * Returns +int+ truncated (toward zero) to + * a precision of +ndigits+ decimal digits (default: 0). + * + * When the precision is negative, the returned value is an integer + * with at least <code>ndigits.abs</code> trailing zeros. + * + * Returns +self+ when +ndigits+ is zero or positive. + * + * 1.truncate #=> 1 + * 1.truncate(2) #=> 1 + * 18.truncate(-1) #=> 10 + * (-18).truncate(-1) #=> -10 + */ + +static VALUE +int_truncate(int argc, VALUE* argv, VALUE num) +{ + int ndigits; + + if (!rb_check_arity(argc, 0, 1)) return num; + ndigits = NUM2INT(argv[0]); + if (ndigits >= 0) { + return num; + } + return rb_int_truncate(num, ndigits); +} + +#define DEFINE_INT_SQRT(rettype, prefix, argtype) \ +rettype \ +prefix##_isqrt(argtype n) \ +{ \ + if (!argtype##_IN_DOUBLE_P(n)) { \ + unsigned int b = bit_length(n); \ + argtype t; \ + rettype x = (rettype)(n >> (b/2+1)); \ + x |= ((rettype)1LU << (b-1)/2); \ + while ((t = n/x) < (argtype)x) x = (rettype)((x + t) >> 1); \ + return x; \ + } \ + return (rettype)sqrt(argtype##_TO_DOUBLE(n)); \ +} + +#if SIZEOF_LONG*CHAR_BIT > DBL_MANT_DIG +# define RB_ULONG_IN_DOUBLE_P(n) ((n) < (1UL << DBL_MANT_DIG)) +#else +# define RB_ULONG_IN_DOUBLE_P(n) 1 +#endif +#define RB_ULONG_TO_DOUBLE(n) (double)(n) +#define RB_ULONG unsigned long +DEFINE_INT_SQRT(unsigned long, rb_ulong, RB_ULONG) + +#if 2*SIZEOF_BDIGIT > SIZEOF_LONG +# if 2*SIZEOF_BDIGIT*CHAR_BIT > DBL_MANT_DIG +# define BDIGIT_DBL_IN_DOUBLE_P(n) ((n) < ((BDIGIT_DBL)1UL << DBL_MANT_DIG)) +# else +# define BDIGIT_DBL_IN_DOUBLE_P(n) 1 +# endif +# ifdef ULL_TO_DOUBLE +# define BDIGIT_DBL_TO_DOUBLE(n) ULL_TO_DOUBLE(n) +# else +# define BDIGIT_DBL_TO_DOUBLE(n) (double)(n) +# endif +DEFINE_INT_SQRT(BDIGIT, rb_bdigit_dbl, BDIGIT_DBL) +#endif + +#define domain_error(msg) \ + rb_raise(rb_eMathDomainError, "Numerical argument is out of domain - " #msg) + +VALUE rb_big_isqrt(VALUE); + +/* + * Document-method: Integer::sqrt + * call-seq: + * Integer.sqrt(n) -> integer + * + * Returns the integer square root of the non-negative integer +n+, + * i.e. the largest non-negative integer less than or equal to the + * square root of +n+. + * + * Integer.sqrt(0) #=> 0 + * Integer.sqrt(1) #=> 1 + * Integer.sqrt(24) #=> 4 + * Integer.sqrt(25) #=> 5 + * Integer.sqrt(10**400) #=> 10**200 + * + * Equivalent to <code>Math.sqrt(n).floor</code>, except that + * the result of the latter code may differ from the true value + * due to the limited precision of floating point arithmetic. + * + * Integer.sqrt(10**46) #=> 100000000000000000000000 + * Math.sqrt(10**46).floor #=> 99999999999999991611392 (!) + * + * If +n+ is not an Integer, it is converted to an Integer first. + * If +n+ is negative, a Math::DomainError is raised. + */ + +static VALUE +rb_int_s_isqrt(VALUE self, VALUE num) +{ + unsigned long n, sq; + num = rb_to_int(num); + if (FIXNUM_P(num)) { + if (FIXNUM_NEGATIVE_P(num)) { + domain_error("isqrt"); + } + n = FIX2ULONG(num); + sq = rb_ulong_isqrt(n); + return LONG2FIX(sq); + } + else { + size_t biglen; + if (RBIGNUM_NEGATIVE_P(num)) { + domain_error("isqrt"); + } + biglen = BIGNUM_LEN(num); + if (biglen == 0) return INT2FIX(0); +#if SIZEOF_BDIGIT <= SIZEOF_LONG + /* short-circuit */ + if (biglen == 1) { + n = BIGNUM_DIGITS(num)[0]; + sq = rb_ulong_isqrt(n); + return ULONG2NUM(sq); + } +#endif + return rb_big_isqrt(num); } - return Qfalse; } +/* + * Document-class: ZeroDivisionError + * + * Raised when attempting to divide an integer by 0. + * + * 42 / 0 #=> ZeroDivisionError: divided by 0 + * + * Note that only division by an exact 0 will raise the exception: + * + * 42 / 0.0 #=> Float::INFINITY + * 42 / -0.0 #=> -Float::INFINITY + * 0 / 0.0 #=> NaN + */ + +/* + * Document-class: FloatDomainError + * + * Raised when attempting to convert special float values (in particular + * +Infinity+ or +NaN+) to numerical classes which don't support them. + * + * Float::INFINITY.to_r #=> FloatDomainError: Infinity + */ + +/* + * Document-class: Numeric + * + * Numeric is the class from which all higher-level numeric classes should inherit. + * + * Numeric allows instantiation of heap-allocated objects. Other core numeric classes such as + * Integer are implemented as immediates, which means that each Integer is a single immutable + * object which is always passed by value. + * + * a = 1 + * 1.object_id == a.object_id #=> true + * + * There can only ever be one instance of the integer +1+, for example. Ruby ensures this + * by preventing instantiation. If duplication is attempted, the same instance is returned. + * + * Integer.new(1) #=> NoMethodError: undefined method `new' for Integer:Class + * 1.dup #=> 1 + * 1.object_id == 1.dup.object_id #=> true + * + * For this reason, Numeric should be used when defining other numeric classes. + * + * Classes which inherit from Numeric must implement +coerce+, which returns a two-member + * Array containing an object that has been coerced into an instance of the new class + * and +self+ (see #coerce). + * + * Inheriting classes should also implement arithmetic operator methods (<code>+</code>, + * <code>-</code>, <code>*</code> and <code>/</code>) and the <code><=></code> operator (see + * Comparable). These methods may rely on +coerce+ to ensure interoperability with + * instances of other numeric classes. + * + * class Tally < Numeric + * def initialize(string) + * @string = string + * end + * + * def to_s + * @string + * end + * + * def to_i + * @string.size + * end + * + * def coerce(other) + * [self.class.new('|' * other.to_i), self] + * end + * + * def <=>(other) + * to_i <=> other.to_i + * end + * + * def +(other) + * self.class.new('|' * (to_i + other.to_i)) + * end + * + * def -(other) + * self.class.new('|' * (to_i - other.to_i)) + * end + * + * def *(other) + * self.class.new('|' * (to_i * other.to_i)) + * end + * + * def /(other) + * self.class.new('|' * (to_i / other.to_i)) + * end + * end + * + * tally = Tally.new('||') + * puts tally * 2 #=> "||||" + * puts tally > 1 #=> true + */ void -Init_Numeric() +Init_Numeric(void) { -#if defined(__FreeBSD__) && __FreeBSD__ < 4 - /* allow divide by zero -- Inf */ - fpsetmask(fpgetmask() & ~(FP_X_DZ|FP_X_INV|FP_X_OFL)); -#elif defined(_UNICOSMP) +#undef rb_intern +#define rb_intern(str) rb_intern_const(str) + +#ifdef _UNICOSMP /* Turn off floating point exceptions for divide by zero, etc. */ _set_Creg(0, 0); -#elif defined(__BORLANDC__) - /* Turn off floating point exceptions for overflow, etc. */ - _control87(MCW_EM, MCW_EM); #endif id_coerce = rb_intern("coerce"); - id_to_i = rb_intern("to_i"); - id_eq = rb_intern("=="); + id_div = rb_intern("div"); + id_divmod = rb_intern("divmod"); rb_eZeroDivError = rb_define_class("ZeroDivisionError", rb_eStandardError); rb_eFloatDomainError = rb_define_class("FloatDomainError", rb_eRangeError); @@ -2883,145 +5352,271 @@ Init_Numeric() rb_define_method(rb_cNumeric, "singleton_method_added", num_sadded, 1); rb_include_module(rb_cNumeric, rb_mComparable); - rb_define_method(rb_cNumeric, "initialize_copy", num_init_copy, 1); rb_define_method(rb_cNumeric, "coerce", num_coerce, 1); + rb_define_method(rb_cNumeric, "clone", num_clone, -1); + rb_define_method(rb_cNumeric, "dup", num_dup, 0); + rb_define_method(rb_cNumeric, "i", num_imaginary, 0); rb_define_method(rb_cNumeric, "+@", num_uplus, 0); rb_define_method(rb_cNumeric, "-@", num_uminus, 0); rb_define_method(rb_cNumeric, "<=>", num_cmp, 1); rb_define_method(rb_cNumeric, "eql?", num_eql, 1); - rb_define_method(rb_cNumeric, "quo", num_quo, 1); + rb_define_method(rb_cNumeric, "fdiv", num_fdiv, 1); rb_define_method(rb_cNumeric, "div", num_div, 1); rb_define_method(rb_cNumeric, "divmod", num_divmod, 1); + rb_define_method(rb_cNumeric, "%", num_modulo, 1); rb_define_method(rb_cNumeric, "modulo", num_modulo, 1); rb_define_method(rb_cNumeric, "remainder", num_remainder, 1); rb_define_method(rb_cNumeric, "abs", num_abs, 0); + rb_define_method(rb_cNumeric, "magnitude", num_abs, 0); rb_define_method(rb_cNumeric, "to_int", num_to_int, 0); + rb_define_method(rb_cNumeric, "real?", num_real_p, 0); rb_define_method(rb_cNumeric, "integer?", num_int_p, 0); rb_define_method(rb_cNumeric, "zero?", num_zero_p, 0); rb_define_method(rb_cNumeric, "nonzero?", num_nonzero_p, 0); + rb_define_method(rb_cNumeric, "finite?", num_finite_p, 0); + rb_define_method(rb_cNumeric, "infinite?", num_infinite_p, 0); - rb_define_method(rb_cNumeric, "floor", num_floor, 0); - rb_define_method(rb_cNumeric, "ceil", num_ceil, 0); - rb_define_method(rb_cNumeric, "round", num_round, 0); - rb_define_method(rb_cNumeric, "truncate", num_truncate, 0); + rb_define_method(rb_cNumeric, "floor", num_floor, -1); + rb_define_method(rb_cNumeric, "ceil", num_ceil, -1); + rb_define_method(rb_cNumeric, "round", num_round, -1); + rb_define_method(rb_cNumeric, "truncate", num_truncate, -1); rb_define_method(rb_cNumeric, "step", num_step, -1); + rb_define_method(rb_cNumeric, "positive?", num_positive_p, 0); + rb_define_method(rb_cNumeric, "negative?", num_negative_p, 0); rb_cInteger = rb_define_class("Integer", rb_cNumeric); rb_undef_alloc_func(rb_cInteger); rb_undef_method(CLASS_OF(rb_cInteger), "new"); + rb_define_singleton_method(rb_cInteger, "sqrt", rb_int_s_isqrt, 1); + rb_define_method(rb_cInteger, "to_s", int_to_s, -1); + rb_define_alias(rb_cInteger, "inspect", "to_s"); rb_define_method(rb_cInteger, "integer?", int_int_p, 0); + rb_define_method(rb_cInteger, "odd?", rb_int_odd_p, 0); + rb_define_method(rb_cInteger, "even?", int_even_p, 0); + rb_define_method(rb_cInteger, "allbits?", int_allbits_p, 1); + rb_define_method(rb_cInteger, "anybits?", int_anybits_p, 1); + rb_define_method(rb_cInteger, "nobits?", int_nobits_p, 1); rb_define_method(rb_cInteger, "upto", int_upto, 1); rb_define_method(rb_cInteger, "downto", int_downto, 1); rb_define_method(rb_cInteger, "times", int_dotimes, 0); - rb_include_module(rb_cInteger, rb_mPrecision); rb_define_method(rb_cInteger, "succ", int_succ, 0); rb_define_method(rb_cInteger, "next", int_succ, 0); - rb_define_method(rb_cInteger, "chr", int_chr, 0); + rb_define_method(rb_cInteger, "pred", int_pred, 0); + rb_define_method(rb_cInteger, "chr", int_chr, -1); + rb_define_method(rb_cInteger, "ord", int_ord, 0); rb_define_method(rb_cInteger, "to_i", int_to_i, 0); rb_define_method(rb_cInteger, "to_int", int_to_i, 0); - rb_define_method(rb_cInteger, "floor", int_to_i, 0); - rb_define_method(rb_cInteger, "ceil", int_to_i, 0); - rb_define_method(rb_cInteger, "round", int_to_i, 0); - rb_define_method(rb_cInteger, "truncate", int_to_i, 0); - - rb_cFixnum = rb_define_class("Fixnum", rb_cInteger); - rb_include_module(rb_cFixnum, rb_mPrecision); - rb_define_singleton_method(rb_cFixnum, "induced_from", rb_fix_induced_from, 1); - rb_define_singleton_method(rb_cInteger, "induced_from", rb_int_induced_from, 1); - - rb_define_method(rb_cFixnum, "to_s", fix_to_s, -1); - - rb_define_method(rb_cFixnum, "id2name", fix_id2name, 0); - rb_define_method(rb_cFixnum, "to_sym", fix_to_sym, 0); - - rb_define_method(rb_cFixnum, "-@", fix_uminus, 0); - rb_define_method(rb_cFixnum, "+", fix_plus, 1); - rb_define_method(rb_cFixnum, "-", fix_minus, 1); - rb_define_method(rb_cFixnum, "*", fix_mul, 1); - rb_define_method(rb_cFixnum, "/", fix_div, 1); - rb_define_method(rb_cFixnum, "div", fix_div, 1); - rb_define_method(rb_cFixnum, "%", fix_mod, 1); - rb_define_method(rb_cFixnum, "modulo", fix_mod, 1); - rb_define_method(rb_cFixnum, "divmod", fix_divmod, 1); - rb_define_method(rb_cFixnum, "quo", fix_quo, 1); - rb_define_method(rb_cFixnum, "**", fix_pow, 1); - - rb_define_method(rb_cFixnum, "abs", fix_abs, 0); - - rb_define_method(rb_cFixnum, "==", fix_equal, 1); - rb_define_method(rb_cFixnum, "<=>", fix_cmp, 1); - rb_define_method(rb_cFixnum, ">", fix_gt, 1); - rb_define_method(rb_cFixnum, ">=", fix_ge, 1); - rb_define_method(rb_cFixnum, "<", fix_lt, 1); - rb_define_method(rb_cFixnum, "<=", fix_le, 1); - - rb_define_method(rb_cFixnum, "~", fix_rev, 0); - rb_define_method(rb_cFixnum, "&", fix_and, 1); - rb_define_method(rb_cFixnum, "|", fix_or, 1); - rb_define_method(rb_cFixnum, "^", fix_xor, 1); - rb_define_method(rb_cFixnum, "[]", fix_aref, 1); - - rb_define_method(rb_cFixnum, "<<", rb_fix_lshift, 1); - rb_define_method(rb_cFixnum, ">>", rb_fix_rshift, 1); - - rb_define_method(rb_cFixnum, "to_f", fix_to_f, 0); - rb_define_method(rb_cFixnum, "size", fix_size, 0); - rb_define_method(rb_cFixnum, "zero?", fix_zero_p, 0); + rb_define_method(rb_cInteger, "to_f", int_to_f, 0); + rb_define_method(rb_cInteger, "floor", int_floor, -1); + rb_define_method(rb_cInteger, "ceil", int_ceil, -1); + rb_define_method(rb_cInteger, "truncate", int_truncate, -1); + rb_define_method(rb_cInteger, "round", int_round, -1); + rb_define_method(rb_cInteger, "<=>", rb_int_cmp, 1); + + rb_define_method(rb_cInteger, "-@", rb_int_uminus, 0); + rb_define_method(rb_cInteger, "+", rb_int_plus, 1); + rb_define_method(rb_cInteger, "-", rb_int_minus, 1); + rb_define_method(rb_cInteger, "*", rb_int_mul, 1); + rb_define_method(rb_cInteger, "/", rb_int_div, 1); + rb_define_method(rb_cInteger, "div", rb_int_idiv, 1); + rb_define_method(rb_cInteger, "%", rb_int_modulo, 1); + rb_define_method(rb_cInteger, "modulo", rb_int_modulo, 1); + rb_define_method(rb_cInteger, "remainder", int_remainder, 1); + rb_define_method(rb_cInteger, "divmod", rb_int_divmod, 1); + rb_define_method(rb_cInteger, "fdiv", rb_int_fdiv, 1); + rb_define_method(rb_cInteger, "**", rb_int_pow, 1); + + rb_define_method(rb_cInteger, "pow", rb_int_powm, -1); /* in bignum.c */ + + rb_define_method(rb_cInteger, "abs", rb_int_abs, 0); + rb_define_method(rb_cInteger, "magnitude", rb_int_abs, 0); + + rb_define_method(rb_cInteger, "===", rb_int_equal, 1); + rb_define_method(rb_cInteger, "==", rb_int_equal, 1); + rb_define_method(rb_cInteger, ">", rb_int_gt, 1); + rb_define_method(rb_cInteger, ">=", rb_int_ge, 1); + rb_define_method(rb_cInteger, "<", int_lt, 1); + rb_define_method(rb_cInteger, "<=", int_le, 1); + + rb_define_method(rb_cInteger, "~", int_comp, 0); + rb_define_method(rb_cInteger, "&", rb_int_and, 1); + rb_define_method(rb_cInteger, "|", int_or, 1); + rb_define_method(rb_cInteger, "^", int_xor, 1); + rb_define_method(rb_cInteger, "[]", int_aref, 1); + + rb_define_method(rb_cInteger, "<<", rb_int_lshift, 1); + rb_define_method(rb_cInteger, ">>", rb_int_rshift, 1); + + rb_define_method(rb_cInteger, "size", int_size, 0); + rb_define_method(rb_cInteger, "bit_length", rb_int_bit_length, 0); + rb_define_method(rb_cInteger, "digits", rb_int_digits, -1); + +#ifndef RUBY_INTEGER_UNIFICATION + rb_cFixnum = rb_cInteger; +#endif + rb_define_const(rb_cObject, "Fixnum", rb_cInteger); + rb_deprecate_constant(rb_cObject, "Fixnum"); rb_cFloat = rb_define_class("Float", rb_cNumeric); rb_undef_alloc_func(rb_cFloat); rb_undef_method(CLASS_OF(rb_cFloat), "new"); - rb_define_singleton_method(rb_cFloat, "induced_from", rb_flo_induced_from, 1); - rb_include_module(rb_cFloat, rb_mPrecision); - + /* + * Represents the rounding mode for floating point addition. + * + * Usually defaults to 1, rounding to the nearest number. + * + * Other modes include: + * + * -1:: Indeterminable + * 0:: Rounding towards zero + * 1:: Rounding to the nearest number + * 2:: Rounding towards positive infinity + * 3:: Rounding towards negative infinity + */ rb_define_const(rb_cFloat, "ROUNDS", INT2FIX(FLT_ROUNDS)); + /* + * The base of the floating point, or number of unique digits used to + * represent the number. + * + * Usually defaults to 2 on most systems, which would represent a base-10 decimal. + */ rb_define_const(rb_cFloat, "RADIX", INT2FIX(FLT_RADIX)); + /* + * The number of base digits for the +double+ data type. + * + * Usually defaults to 53. + */ rb_define_const(rb_cFloat, "MANT_DIG", INT2FIX(DBL_MANT_DIG)); + /* + * The minimum number of significant decimal digits in a double-precision + * floating point. + * + * Usually defaults to 15. + */ rb_define_const(rb_cFloat, "DIG", INT2FIX(DBL_DIG)); + /* + * The smallest possible exponent value in a double-precision floating + * point. + * + * Usually defaults to -1021. + */ rb_define_const(rb_cFloat, "MIN_EXP", INT2FIX(DBL_MIN_EXP)); + /* + * The largest possible exponent value in a double-precision floating + * point. + * + * Usually defaults to 1024. + */ rb_define_const(rb_cFloat, "MAX_EXP", INT2FIX(DBL_MAX_EXP)); + /* + * The smallest negative exponent in a double-precision floating point + * where 10 raised to this power minus 1. + * + * Usually defaults to -307. + */ rb_define_const(rb_cFloat, "MIN_10_EXP", INT2FIX(DBL_MIN_10_EXP)); + /* + * The largest positive exponent in a double-precision floating point where + * 10 raised to this power minus 1. + * + * Usually defaults to 308. + */ rb_define_const(rb_cFloat, "MAX_10_EXP", INT2FIX(DBL_MAX_10_EXP)); - rb_define_const(rb_cFloat, "MIN", rb_float_new(DBL_MIN)); - rb_define_const(rb_cFloat, "MAX", rb_float_new(DBL_MAX)); - rb_define_const(rb_cFloat, "EPSILON", rb_float_new(DBL_EPSILON)); + /* + * The smallest positive normalized number in a double-precision floating point. + * + * Usually defaults to 2.2250738585072014e-308. + * + * If the platform supports denormalized numbers, + * there are numbers between zero and Float::MIN. + * 0.0.next_float returns the smallest positive floating point number + * including denormalized numbers. + */ + rb_define_const(rb_cFloat, "MIN", DBL2NUM(DBL_MIN)); + /* + * The largest possible integer in a double-precision floating point number. + * + * Usually defaults to 1.7976931348623157e+308. + */ + rb_define_const(rb_cFloat, "MAX", DBL2NUM(DBL_MAX)); + /* + * The difference between 1 and the smallest double-precision floating + * point number greater than 1. + * + * Usually defaults to 2.2204460492503131e-16. + */ + rb_define_const(rb_cFloat, "EPSILON", DBL2NUM(DBL_EPSILON)); + /* + * An expression representing positive infinity. + */ + rb_define_const(rb_cFloat, "INFINITY", DBL2NUM(INFINITY)); + /* + * An expression representing a value which is "not a number". + */ + rb_define_const(rb_cFloat, "NAN", DBL2NUM(NAN)); rb_define_method(rb_cFloat, "to_s", flo_to_s, 0); + rb_define_alias(rb_cFloat, "inspect", "to_s"); rb_define_method(rb_cFloat, "coerce", flo_coerce, 1); - rb_define_method(rb_cFloat, "-@", flo_uminus, 0); + rb_define_method(rb_cFloat, "-@", rb_float_uminus, 0); rb_define_method(rb_cFloat, "+", flo_plus, 1); rb_define_method(rb_cFloat, "-", flo_minus, 1); rb_define_method(rb_cFloat, "*", flo_mul, 1); rb_define_method(rb_cFloat, "/", flo_div, 1); + rb_define_method(rb_cFloat, "quo", flo_quo, 1); + rb_define_method(rb_cFloat, "fdiv", flo_quo, 1); rb_define_method(rb_cFloat, "%", flo_mod, 1); rb_define_method(rb_cFloat, "modulo", flo_mod, 1); rb_define_method(rb_cFloat, "divmod", flo_divmod, 1); - rb_define_method(rb_cFloat, "**", flo_pow, 1); + rb_define_method(rb_cFloat, "**", rb_float_pow, 1); rb_define_method(rb_cFloat, "==", flo_eq, 1); + rb_define_method(rb_cFloat, "===", flo_eq, 1); rb_define_method(rb_cFloat, "<=>", flo_cmp, 1); - rb_define_method(rb_cFloat, ">", flo_gt, 1); + rb_define_method(rb_cFloat, ">", rb_float_gt, 1); rb_define_method(rb_cFloat, ">=", flo_ge, 1); rb_define_method(rb_cFloat, "<", flo_lt, 1); rb_define_method(rb_cFloat, "<=", flo_le, 1); rb_define_method(rb_cFloat, "eql?", flo_eql, 1); rb_define_method(rb_cFloat, "hash", flo_hash, 0); rb_define_method(rb_cFloat, "to_f", flo_to_f, 0); - rb_define_method(rb_cFloat, "abs", flo_abs, 0); + rb_define_method(rb_cFloat, "abs", rb_float_abs, 0); + rb_define_method(rb_cFloat, "magnitude", rb_float_abs, 0); rb_define_method(rb_cFloat, "zero?", flo_zero_p, 0); - rb_define_method(rb_cFloat, "to_i", flo_truncate, 0); - rb_define_method(rb_cFloat, "to_int", flo_truncate, 0); - rb_define_method(rb_cFloat, "floor", flo_floor, 0); - rb_define_method(rb_cFloat, "ceil", flo_ceil, 0); - rb_define_method(rb_cFloat, "round", flo_round, 0); - rb_define_method(rb_cFloat, "truncate", flo_truncate, 0); + rb_define_method(rb_cFloat, "to_i", flo_to_i, 0); + rb_define_method(rb_cFloat, "to_int", flo_to_i, 0); + rb_define_method(rb_cFloat, "floor", flo_floor, -1); + rb_define_method(rb_cFloat, "ceil", flo_ceil, -1); + rb_define_method(rb_cFloat, "round", flo_round, -1); + rb_define_method(rb_cFloat, "truncate", flo_truncate, -1); rb_define_method(rb_cFloat, "nan?", flo_is_nan_p, 0); - rb_define_method(rb_cFloat, "infinite?", flo_is_infinite_p, 0); - rb_define_method(rb_cFloat, "finite?", flo_is_finite_p, 0); + rb_define_method(rb_cFloat, "infinite?", rb_flo_is_infinite_p, 0); + rb_define_method(rb_cFloat, "finite?", rb_flo_is_finite_p, 0); + rb_define_method(rb_cFloat, "next_float", flo_next_float, 0); + rb_define_method(rb_cFloat, "prev_float", flo_prev_float, 0); + rb_define_method(rb_cFloat, "positive?", flo_positive_p, 0); + rb_define_method(rb_cFloat, "negative?", flo_negative_p, 0); + + id_to = rb_intern("to"); + id_by = rb_intern("by"); +} + +#undef rb_float_value +double +rb_float_value(VALUE v) +{ + return rb_float_value_inline(v); +} + +#undef rb_float_new +VALUE +rb_float_new(double d) +{ + return rb_float_new_inline(d); } |