diff options
Diffstat (limited to 'numeric.c')
| -rw-r--r-- | numeric.c | 6836 |
1 files changed, 4772 insertions, 2064 deletions
@@ -9,19 +9,13 @@ **********************************************************************/ -#include "ruby/ruby.h" -#include "ruby/encoding.h" -#include "ruby/util.h" -#include "internal.h" -#include "id.h" +#include "ruby/internal/config.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 @@ -30,21 +24,28 @@ #include <ieeefp.h> #endif -#if !defined HAVE_ISFINITE && !defined isfinite -#if defined HAVE_FINITE && !defined finite && !defined _WIN32 -extern int finite(double); -# define HAVE_ISFINITE 1 -# define isfinite(x) finite(x) -#endif -#endif +#include "id.h" +#include "internal.h" +#include "internal/array.h" +#include "internal/compilers.h" +#include "internal/complex.h" +#include "internal/enumerator.h" +#include "internal/gc.h" +#include "internal/hash.h" +#include "internal/numeric.h" +#include "internal/object.h" +#include "internal/rational.h" +#include "internal/string.h" +#include "internal/util.h" +#include "internal/variable.h" +#include "ruby/encoding.h" +#include "ruby/util.h" +#include "builtin.h" /* use IEEE 64bit values if not defined */ #ifndef FLT_RADIX #define FLT_RADIX 2 #endif -#ifndef FLT_ROUNDS -#define FLT_ROUNDS 1 -#endif #ifndef DBL_MIN #define DBL_MIN 2.2250738585072014e-308 #endif @@ -73,14 +74,14 @@ extern int finite(double); #define DBL_EPSILON 2.2204460492503131e-16 #endif -#ifdef HAVE_INFINITY +#ifndef USE_RB_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 +#ifndef USE_RB_NAN #elif !defined(WORDS_BIGENDIAN) /* BYTE_ORDER == LITTLE_ENDIAN */ const union bytesequence4_or_float rb_nan = {{0x00, 0x00, 0xc0, 0x7f}}; #else @@ -94,37 +95,163 @@ round(double x) double f; if (x > 0.0) { - f = floor(x); - x = f + (x - f >= 0.5); + f = floor(x); + x = f + (x - f >= 0.5); } else if (x < 0.0) { - f = ceil(x); - x = f - (f - x >= 0.5); + f = ceil(x); + x = f - (f - x >= 0.5); } return x; } #endif -static VALUE fix_uminus(VALUE num); -static VALUE fix_mul(VALUE x, VALUE y); -static VALUE int_pow(long x, unsigned long y); +static double +round_half_up(double x, double s) +{ + double f, xs = x * s; -static ID id_coerce, id_to_i, id_eq, id_div; + 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 u, v, us, vs, f, d, uf; + + v = modf(x, &u); + us = u * s; + vs = v * s; + + if (x > 0.0) { + f = floor(vs); + uf = us + f; + d = vs - f; + if (d > 0.5) + d = 1.0; + else if (d == 0.5 || ((double)((uf + 0.5) / s) <= x)) + d = fmod(uf, 2.0); + else + d = 0.0; + x = f + d; + } + else if (x < 0.0) { + f = ceil(vs); + uf = us + f; + d = f - vs; + if (d > 0.5) + d = 1.0; + else if (d == 0.5 || ((double)((uf - 0.5) / s) >= x)) + d = fmod(-uf, 2.0); + else + d = 0.0; + x = f - d; + } + return us + x; +} + +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 rb_int_floor(VALUE num, int ndigits); +static 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; +#define id_div idDiv +#define id_divmod idDivmod +#define id_to_i idTo_i +#define id_eq idEq +#define id_cmp idCmp VALUE rb_cNumeric; VALUE rb_cFloat; VALUE rb_cInteger; -VALUE rb_cFixnum; VALUE rb_eZeroDivError; VALUE rb_eFloatDomainError; +static ID id_to, id_by; + void 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; + } + rb_must_asciicompat(str); + 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) @@ -133,27 +260,25 @@ rb_num_to_uint(VALUE val, unsigned int *ret) #define NUMERR_NEGATIVE 2 #define NUMERR_TOOLARGE 3 if (FIXNUM_P(val)) { - long v = FIX2LONG(val); + long v = FIX2LONG(val); #if SIZEOF_INT < SIZEOF_LONG - if (v > (long)UINT_MAX) return NUMERR_TOOLARGE; + if (v > (long)UINT_MAX) return NUMERR_TOOLARGE; #endif - if (v < 0) return NUMERR_NEGATIVE; - *ret = (unsigned int)v; - return 0; + if (v < 0) return NUMERR_NEGATIVE; + *ret = (unsigned int)v; + return 0; } - switch (TYPE(val)) { - case T_BIGNUM: - if (RBIGNUM_NEGATIVE_P(val)) return NUMERR_NEGATIVE; + if (RB_BIGNUM_TYPE_P(val)) { + if (BIGNUM_NEGATIVE_P(val)) return NUMERR_NEGATIVE; #if SIZEOF_INT < SIZEOF_LONG - /* long is 64bit */ - return NUMERR_TOOLARGE; + /* long is 64bit */ + return NUMERR_TOOLARGE; #else - /* long is 32bit */ -#define DIGSPERLONG (SIZEOF_LONG/SIZEOF_BDIGITS) - if (RBIGNUM_LEN(val) > DIGSPERLONG) return NUMERR_TOOLARGE; - *ret = (unsigned int)rb_big2ulong((VALUE)val); - return 0; + /* 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; @@ -162,121 +287,189 @@ rb_num_to_uint(VALUE val, unsigned int *ret) #define method_basic_p(klass) rb_method_basic_definition_p(klass, mid) static inline int -positive_int_p(VALUE num) +int_pos_p(VALUE num) { - const ID mid = '>'; - if (FIXNUM_P(num)) { - if (method_basic_p(rb_cFixnum)) - return (SIGNED_VALUE)num > 0; + return FIXNUM_POSITIVE_P(num); } - else if (RB_TYPE_P(num, T_BIGNUM)) { - if (method_basic_p(rb_cBignum)) - return RBIGNUM_POSITIVE_P(num); + else if (RB_BIGNUM_TYPE_P(num)) { + return BIGNUM_POSITIVE_P(num); } - return RTEST(rb_funcall(num, mid, 1, INT2FIX(0))); + rb_raise(rb_eTypeError, "not an Integer"); } static inline int -negative_int_p(VALUE num) +int_neg_p(VALUE num) { - const ID mid = '<'; - if (FIXNUM_P(num)) { - if (method_basic_p(rb_cFixnum)) - return (SIGNED_VALUE)num < 0; + return FIXNUM_NEGATIVE_P(num); } - else if (RB_TYPE_P(num, T_BIGNUM)) { - if (method_basic_p(rb_cBignum)) - return RBIGNUM_NEGATIVE_P(num); + else if (RB_BIGNUM_TYPE_P(num)) { + return BIGNUM_NEGATIVE_P(num); } - return RTEST(rb_funcall(num, mid, 1, INT2FIX(0))); + rb_raise(rb_eTypeError, "not an Integer"); +} + +int +rb_int_positive_p(VALUE num) +{ + return int_pos_p(num); +} + +int +rb_int_negative_p(VALUE num) +{ + return int_neg_p(num); } int rb_num_negative_p(VALUE num) { - return negative_int_p(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); +} + +NORETURN(static void num_funcall_op_1_recursion(VALUE x, ID func, VALUE y)); + +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 + * coerce(other) -> array + * + * Returns a 2-element array containing two numeric elements, + * formed from the two operands +self+ and +other+, + * of a common compatible type. + * + * Of the Core and Standard Library classes, + * Integer, Rational, and Complex use this implementation. + * + * Examples: + * + * i = 2 # => 2 + * i.coerce(3) # => [3, 2] + * i.coerce(3.0) # => [3.0, 2.0] + * i.coerce(Rational(1, 2)) # => [0.5, 2.0] + * i.coerce(Complex(3, 4)) # Raises RangeError. + * + * r = Rational(5, 2) # => (5/2) + * r.coerce(2) # => [(2/1), (5/2)] + * r.coerce(2.0) # => [2.0, 2.5] + * r.coerce(Rational(2, 3)) # => [(2/3), (5/2)] + * r.coerce(Complex(3, 4)) # => [(3+4i), ((5/2)+0i)] * - * 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. + * c = Complex(2, 3) # => (2+3i) + * c.coerce(2) # => [(2+0i), (2+3i)] + * c.coerce(2.0) # => [(2.0+0i), (2+3i)] + * c.coerce(Rational(1, 2)) # => [((1/2)+0i), (2+3i)] + * c.coerce(Complex(3, 4)) # => [(3+4i), (2+3i)] + * + * Raises an exception if any type conversion fails. * - * 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(VALUE x, VALUE y) { if (CLASS_OF(x) == CLASS_OF(y)) - return rb_assoc_new(y, x); + return rb_assoc_new(y, x); x = rb_Float(x); y = rb_Float(y); return rb_assoc_new(y, x); } -static VALUE -coerce_body(VALUE *x) -{ - return rb_funcall(x[1], id_coerce, 1, x[0]); -} - NORETURN(static void coerce_failed(VALUE x, VALUE y)); static void coerce_failed(VALUE x, VALUE y) { - if (SPECIAL_CONST_P(y) || BUILTIN_TYPE(y) == T_FLOAT) { - y = rb_inspect(y); + if (SPECIAL_CONST_P(y) || SYMBOL_P(y) || RB_FLOAT_TYPE_P(y)) { + y = rb_inspect(y); } else { - y = rb_obj_class(y); + y = rb_obj_class(y); } rb_raise(rb_eTypeError, "%"PRIsVALUE" can't be coerced into %"PRIsVALUE, - y, rb_obj_class(x)); -} - -static VALUE -coerce_rescue(VALUE *x) -{ - coerce_failed(x[0], x[1]); - return Qnil; /* dummy */ + y, rb_obj_class(x)); } static int do_coerce(VALUE *x, VALUE *y, int err) { - VALUE ary; - VALUE a[2]; - - a[0] = *x; a[1] = *y; - - if (!rb_respond_to(*y, id_coerce)) { - if (err) { - coerce_rescue(a); - } - return FALSE; + VALUE ary = rb_check_funcall(*y, id_coerce, 1, x); + if (UNDEF_P(ary)) { + if (err) { + coerce_failed(*x, *y); + } + return FALSE; + } + if (!err && NIL_P(ary)) { + return FALSE; } - - ary = rb_rescue(coerce_body, (VALUE)a, err ? coerce_rescue : 0, (VALUE)a); if (!RB_TYPE_P(ary, T_ARRAY) || RARRAY_LEN(ary) != 2) { - if (err) { - rb_raise(rb_eTypeError, "coerce must return [x, y]"); - } - return FALSE; + rb_raise(rb_eTypeError, "coerce must return [x, y]"); } - *x = RARRAY_PTR(ary)[0]; - *y = RARRAY_PTR(ary)[1]; + *x = RARRAY_AREF(ary, 0); + *y = RARRAY_AREF(ary, 1); return TRUE; } @@ -291,26 +484,37 @@ VALUE rb_num_coerce_cmp(VALUE x, VALUE y, ID func) { if (do_coerce(&x, &y, FALSE)) - return rb_funcall(x, func, 1, y); + return rb_funcall(x, func, 1, y); return Qnil; } +static VALUE +ensure_cmp(VALUE c, VALUE x, VALUE y) +{ + if (NIL_P(c)) rb_cmperr(x, y); + return c; +} + VALUE rb_num_coerce_relop(VALUE x, VALUE y, ID func) { - VALUE c, x0 = x, y0 = y; + VALUE x0 = x, y0 = y; - if (!do_coerce(&x, &y, FALSE) || - NIL_P(c = rb_funcall(x, func, 1, y))) { - rb_cmperr(x0, y0); - return Qnil; /* not reached */ + if (!do_coerce(&x, &y, FALSE)) { + rb_cmperr(x0, y0); + UNREACHABLE_RETURN(Qnil); } - return c; + return ensure_cmp(rb_funcall(x, func, 1, y), x0, y0); } +NORETURN(static VALUE num_sadded(VALUE x, VALUE name)); + /* - * 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 @@ -318,45 +522,48 @@ num_sadded(VALUE x, VALUE name) { ID mid = rb_to_id(name); /* ruby_frame = ruby_frame->prev; */ /* pop frame for "singleton_method_added" */ - /* Numerics should be values; singleton_methods should not be added to them */ rb_remove_method_id(rb_singleton_class(x), mid); rb_raise(rb_eTypeError, - "can't define singleton method \"%"PRIsVALUE"\" for %"PRIsVALUE, - rb_id2str(mid), - rb_obj_class(x)); - - UNREACHABLE; -} - -/* :nodoc: */ -static VALUE -num_init_copy(VALUE x, VALUE y) -{ - /* Numerics are immutable values, which should not be copied */ - rb_raise(rb_eTypeError, "can't copy %"PRIsVALUE, rb_obj_class(x)); + "can't define singleton method \"%"PRIsVALUE"\" for %"PRIsVALUE, + rb_id2str(mid), + rb_obj_class(x)); - UNREACHABLE; + UNREACHABLE_RETURN(Qnil); } +#if 0 /* * call-seq: - * +num -> num + * clone(freeze: true) -> self + * + * Returns +self+. + * + * Raises an exception if the value for +freeze+ is neither +true+ nor +nil+. + * + * Related: Numeric#dup. * - * Unary Plus---Returns the receiver's value. */ - static VALUE -num_uplus(VALUE num) +num_clone(int argc, VALUE *argv, VALUE x) { - return num; + return rb_immutable_obj_clone(argc, argv, x); } +#else +# define num_clone rb_immutable_obj_clone +#endif /* * call-seq: - * num.i -> Complex(0,num) + * i -> complex + * + * Returns <tt>Complex(0, self)</tt>: + * + * 2.i # => (0+2i) + * -2.i # => (0-2i) + * 2.0.i # => (0+2.0i) + * Rational(1, 2).i # => (0+(1/2)*i) + * Complex(3, 4).i # Raises NoMethodError. * - * Returns the corresponding imaginary number. - * Not available for complex numbers. */ static VALUE @@ -365,12 +572,11 @@ num_imaginary(VALUE num) return rb_complex_new(INT2FIX(0), num); } - /* * call-seq: - * -num -> numeric + * -self -> numeric * - * Unary Minus---Returns the receiver's value, negated. + * Returns +self+, negated. */ static VALUE @@ -381,28 +587,20 @@ num_uminus(VALUE num) zero = INT2FIX(0); do_coerce(&zero, &num, TRUE); - return rb_funcall(zero, '-', 1, num); + return num_funcall1(zero, '-', num); } /* * call-seq: - * num.quo(numeric) -> real + * fdiv(other) -> float * - * Returns most exact division (rational for integers, float for floats). - */ - -static VALUE -num_quo(VALUE x, VALUE y) -{ - return rb_funcall(rb_rational_raw1(x), '/', 1, y); -} - - -/* - * call-seq: - * num.fdiv(numeric) -> float + * Returns the quotient <tt>self/other</tt> as a float, + * using method +/+ as defined in the subclass of \Numeric. + * (\Numeric itself does not define +/+.) + * + * Of the Core and Standard Library classes, + * only BigDecimal uses this implementation. * - * Returns float division. */ static VALUE @@ -411,112 +609,148 @@ num_fdiv(VALUE x, VALUE y) return rb_funcall(rb_Float(x), '/', 1, y); } - /* * call-seq: - * num.div(numeric) -> integer + * div(other) -> 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. + * Returns the quotient <tt>self/other</tt> as an integer (via +floor+), + * using method +/+ as defined in the subclass of \Numeric. + * (\Numeric itself does not define +/+.) * - * Equivalent to - * <i>num</i>.<code>divmod(</code><i>aNumeric</i><code>)[0]</code>. + * Of the Core and Standard Library classes, + * Only Float and Rational use this implementation. * - * See <code>Numeric#divmod</code>. */ static VALUE num_div(VALUE x, VALUE y) { if (rb_equal(INT2FIX(0), y)) rb_num_zerodiv(); - return rb_funcall(rb_funcall(x, '/', 1, y), rb_intern("floor"), 0); + return rb_funcall(num_funcall1(x, '/', y), rb_intern("floor"), 0); } - /* * call-seq: - * num.modulo(numeric) -> real + * self % other -> real_numeric + * + * Returns +self+ modulo +other+ as a real numeric (\Integer, \Float, or \Rational). + * + * Of the Core and Standard Library classes, + * only Rational uses this implementation. * - * x.modulo(y) means x-y*(x/y).floor + * For Rational +r+ and real number +n+, these expressions are equivalent: * - * Equivalent to - * <i>num</i>.<code>divmod(</code><i>aNumeric</i><code>)[1]</code>. + * r % n + * r-n*(r/n).floor + * r.divmod(n)[1] + * + * See Numeric#divmod. + * + * Examples: + * + * r = Rational(1, 2) # => (1/2) + * r2 = Rational(2, 3) # => (2/3) + * r % r2 # => (1/2) + * r % 2 # => (1/2) + * r % 2.0 # => 0.5 + * + * r = Rational(301,100) # => (301/100) + * r2 = Rational(7,5) # => (7/5) + * r % r2 # => (21/100) + * r % -r2 # => (-119/100) + * (-r) % r2 # => (119/100) + * (-r) %-r2 # => (-21/100) * - * See <code>Numeric#divmod</code>. */ static VALUE num_modulo(VALUE x, VALUE y) { + VALUE q = num_funcall1(x, id_div, y); return rb_funcall(x, '-', 1, - rb_funcall(y, '*', 1, - rb_funcall(x, rb_intern("div"), 1, y))); + rb_funcall(y, '*', 1, q)); } /* * call-seq: - * num.remainder(numeric) -> real + * remainder(other) -> real_number + * + * Returns the remainder after dividing +self+ by +other+. + * + * Of the Core and Standard Library classes, + * only Float and Rational use this implementation. * - * x.remainder(y) means x-y*(x/y).truncate + * Examples: + * + * 11.0.remainder(4) # => 3.0 + * 11.0.remainder(-4) # => 3.0 + * -11.0.remainder(4) # => -3.0 + * -11.0.remainder(-4) # => -3.0 + * + * 12.0.remainder(4) # => 0.0 + * 12.0.remainder(-4) # => 0.0 + * -12.0.remainder(4) # => -0.0 + * -12.0.remainder(-4) # => -0.0 + * + * 13.0.remainder(4.0) # => 1.0 + * 13.0.remainder(Rational(4, 1)) # => 1.0 + * + * Rational(13, 1).remainder(4) # => (1/1) + * Rational(13, 1).remainder(-4) # => (1/1) + * Rational(-13, 1).remainder(4) # => (-1/1) + * Rational(-13, 1).remainder(-4) # => (-1/1) * - * See <code>Numeric#divmod</code>. */ static VALUE num_remainder(VALUE x, VALUE y) { - VALUE z = rb_funcall(x, '%', 1, y); + if (!rb_obj_is_kind_of(y, rb_cNumeric)) { + do_coerce(&x, &y, TRUE); + } + VALUE z = num_funcall1(x, '%', y); if ((!rb_equal(z, INT2FIX(0))) && - ((negative_int_p(x) && - positive_int_p(y)) || - (positive_int_p(x) && - negative_int_p(y)))) { - return rb_funcall(z, '-', 1, y); + ((rb_num_negative_int_p(x) && + rb_num_positive_int_p(y)) || + (rb_num_positive_int_p(x) && + rb_num_negative_int_p(y)))) { + if (RB_FLOAT_TYPE_P(y)) { + if (isinf(RFLOAT_VALUE(y))) { + return x; + } + } + return rb_funcall(z, '-', 1, y); } return z; } /* * call-seq: - * num.divmod(numeric) -> array + * divmod(other) -> array * - * Returns an array containing the quotient and modulus obtained by - * dividing <i>num</i> by <i>numeric</i>. If <code>q, r = - * x.divmod(y)</code>, then + * Returns a 2-element array <tt>[q, r]</tt>, where * - * q = floor(x/y) - * x = q*y+r + * q = (self/other).floor # Quotient + * r = self % other # Remainder * - * The quotient is rounded toward -infinity, as shown in the following table: + * Of the Core and Standard Library classes, + * only Rational uses this implementation. * - * a | b | a.divmod(b) | a/b | a.modulo(b) | a.remainder(b) - * ------+-----+---------------+---------+-------------+--------------- - * 13 | 4 | 3, 1 | 3 | 1 | 1 - * ------+-----+---------------+---------+-------------+--------------- - * 13 | -4 | -4, -3 | -4 | -3 | 1 - * ------+-----+---------------+---------+-------------+--------------- - * -13 | 4 | -4, 3 | -4 | 3 | -1 - * ------+-----+---------------+---------+-------------+--------------- - * -13 | -4 | 3, -1 | 3 | -1 | -1 - * ------+-----+---------------+---------+-------------+--------------- - * 11.5 | 4 | 2, 3.5 | 2.875 | 3.5 | 3.5 - * ------+-----+---------------+---------+-------------+--------------- - * 11.5 | -4 | -3, -0.5 | -2.875 | -0.5 | 3.5 - * ------+-----+---------------+---------+-------------+--------------- - * -11.5 | 4 | -3, 0.5 | -2.875 | 0.5 | -3.5 - * ------+-----+---------------+---------+-------------+--------------- - * -11.5 | -4 | 2, -3.5 | 2.875 | -3.5 | -3.5 + * Examples: * + * Rational(11, 1).divmod(4) # => [2, (3/1)] + * Rational(11, 1).divmod(-4) # => [-3, (-1/1)] + * Rational(-11, 1).divmod(4) # => [-3, (1/1)] + * Rational(-11, 1).divmod(-4) # => [2, (-3/1)] * - * Examples + * Rational(12, 1).divmod(4) # => [3, (0/1)] + * Rational(12, 1).divmod(-4) # => [-3, (0/1)] + * Rational(-12, 1).divmod(4) # => [-3, (0/1)] + * Rational(-12, 1).divmod(-4) # => [3, (0/1)] * - * 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] + * Rational(13, 1).divmod(4.0) # => [3, 1.0] + * Rational(13, 1).divmod(Rational(4, 11)) # => [35, (3/11)] */ static VALUE @@ -527,227 +761,279 @@ num_divmod(VALUE x, VALUE y) /* * call-seq: - * num.real? -> true or false + * abs -> numeric + * + * Returns the absolute value of +self+. + * + * 12.abs #=> 12 + * (-34.56).abs #=> 34.56 + * -34.56.abs #=> 34.56 * - * Returns <code>true</code> if <i>num</i> is a <code>Real</code> - * (i.e. non <code>Complex</code>). */ static VALUE -num_real_p(VALUE num) +num_abs(VALUE num) { - return Qtrue; + if (rb_num_negative_int_p(num)) { + return num_funcall0(num, idUMinus); + } + return num; } /* * call-seq: - * num.integer? -> true or false + * zero? -> true or false + * + * Returns +true+ if +zero+ has a zero value, +false+ otherwise. * - * Returns +true+ if +num+ is an Integer (including Fixnum and Bignum). + * Of the Core and Standard Library classes, + * only Rational and Complex use this implementation. * - * (1.0).integer? #=> false - * (1).integer? #=> true */ static VALUE -num_int_p(VALUE num) +num_zero_p(VALUE num) { - return Qfalse; + return rb_equal(num, INT2FIX(0)); +} + +static bool +int_zero_p(VALUE num) +{ + if (FIXNUM_P(num)) { + return FIXNUM_ZERO_P(num); + } + RUBY_ASSERT(RB_BIGNUM_TYPE_P(num)); + return rb_bigzero_p(num); +} + +VALUE +rb_int_zero_p(VALUE num) +{ + return RBOOL(int_zero_p(num)); } /* * call-seq: - * num.abs -> numeric - * num.magnitude -> numeric + * nonzero? -> self or nil + * + * Returns +self+ if +self+ is not a zero value, +nil+ otherwise; + * uses method <tt>zero?</tt> for the evaluation. + * + * The returned +self+ allows the method to be chained: + * + * a = %w[z Bb bB bb BB a aA Aa AA A] + * a.sort {|a, b| (a.downcase <=> b.downcase).nonzero? || a <=> b } + * # => ["A", "a", "AA", "Aa", "aA", "BB", "Bb", "bB", "bb", "z"] * - * Returns the absolute value of <i>num</i>. + * Of the Core and Standard Library classes, + * Integer, Float, Rational, and Complex use this implementation. + * + * Related: #zero? * - * 12.abs #=> 12 - * (-34.56).abs #=> 34.56 - * -34.56.abs #=> 34.56 */ static VALUE -num_abs(VALUE num) +num_nonzero_p(VALUE num) { - if (negative_int_p(num)) { - return rb_funcall(num, rb_intern("-@"), 0); + if (RTEST(num_funcall0(num, rb_intern("zero?")))) { + return Qnil; } return num; } - /* * call-seq: - * num.zero? -> true or false + * to_int -> integer + * + * Returns +self+ as an integer; + * converts using method +to_i+ in the subclass of \Numeric. + * (\Numeric itself does not define +to_i+.) + * + * Of the Core and Standard Library classes, + * only Rational and Complex use this implementation. + * + * Examples: + * + * Rational(1, 2).to_int # => 0 + * Rational(2, 1).to_int # => 2 + * Complex(2, 0).to_int # => 2 + * Complex(2, 1).to_int # Raises RangeError (non-zero imaginary part) * - * Returns <code>true</code> if <i>num</i> has a zero value. */ static VALUE -num_zero_p(VALUE num) +num_to_int(VALUE num) { - if (rb_equal(num, INT2FIX(0))) { - return Qtrue; - } - return Qfalse; + return num_funcall0(num, id_to_i); } - /* * call-seq: - * num.nonzero? -> self or nil + * positive? -> true or false * - * Returns +self+ if <i>num</i> is not zero, <code>nil</code> - * otherwise. This behavior is useful when chaining comparisons: + * Returns +true+ if +self+ is greater than 0, +false+ otherwise. * - * 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(VALUE num) +num_positive_p(VALUE num) { - if (RTEST(rb_funcall(num, rb_intern("zero?"), 0, 0))) { - return Qnil; + const ID mid = '>'; + + if (FIXNUM_P(num)) { + if (method_basic_p(rb_cInteger)) + return RBOOL((SIGNED_VALUE)num > (SIGNED_VALUE)INT2FIX(0)); } - return num; + else if (RB_BIGNUM_TYPE_P(num)) { + if (method_basic_p(rb_cInteger)) + return RBOOL(BIGNUM_POSITIVE_P(num) && !rb_bigzero_p(num)); + } + return rb_num_compare_with_zero(num, mid); } /* * call-seq: - * num.to_int -> integer + * negative? -> true or false * - * Invokes the child class's +to_i+ method to convert +num+ to an integer. + * Returns +true+ if +self+ is less than 0, +false+ otherwise. * - * 1.0.class => Float - * 1.0.to_int.class => Fixnum - * 1.0.to_i.class => Fixnum */ static VALUE -num_to_int(VALUE num) +num_negative_p(VALUE num) { - return rb_funcall(num, id_to_i, 0, 0); + return RBOOL(rb_num_negative_int_p(num)); } - -/******************************************************************** - * - * Document-class: Float - * - * <code>Float</code> objects represent inexact real numbers using - * the native architecture's double-precision floating point - * representation. - * - * Floating point has a different arithmetic and is a inexact number. - * So you should know its esoteric system. see following: - * - * - http://docs.sun.com/source/806-3568/ncg_goldberg.html - * - http://wiki.github.com/rdp/ruby_tutorials_core/ruby-talk-faq#wiki-floats_imprecise - * - http://en.wikipedia.org/wiki/Floating_point#Accuracy_problems - */ - VALUE rb_float_new_in_heap(double d) { - NEWOBJ_OF(flt, struct RFloat, rb_cFloat, T_FLOAT); + NEWOBJ_OF(flt, struct RFloat, rb_cFloat, T_FLOAT | (RGENGC_WB_PROTECTED_FLOAT ? FL_WB_PROTECTED : 0), sizeof(struct RFloat), 0); +#if SIZEOF_DOUBLE <= SIZEOF_VALUE flt->float_value = d; - OBJ_FREEZE(flt); +#else + union { + double d; + rb_float_value_type v; + } u = {d}; + flt->float_value = u.v; +#endif + OBJ_FREEZE((VALUE)flt); return (VALUE)flt; } /* * call-seq: - * flt.to_s -> string + * to_s -> string + * + * Returns a string containing a representation of +self+; + * depending of the value of +self+, the string representation + * may contain: + * + * - A fixed-point number. + * 3.14.to_s # => "3.14" + * - A number in "scientific notation" (containing an exponent). + * (10.1**50).to_s # => "1.644631821843879e+50" + * - 'Infinity'. + * (10.1**500).to_s # => "Infinity" + * - '-Infinity'. + * (-10.1**500).to_s # => "-Infinity" + * - 'NaN' (indicating not-a-number). + * (0.0/0.0).to_s # => "NaN" * - * Returns a string containing a representation of self. As well as a - * fixed or exponential form of the number, the call may return - * ``<code>NaN</code>'', ``<code>Infinity</code>'', and - * ``<code>-Infinity</code>''. */ static VALUE flo_to_s(VALUE flt) { - char *ruby_dtoa(double d_, int mode, int ndigits, int *decpt, int *sign, char **rve); 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]; + char buf[float_dig + roomof(decimal_mant, CHAR_BIT) + 10]; double value = RFLOAT_VALUE(flt); VALUE s; char *p, *e; int sign, decpt, digs; - if (isinf(value)) - return rb_usascii_str_new2(value < 0 ? "-Infinity" : "Infinity"); + 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"); + 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); + free(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; - } + 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); - } - 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); + 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); + } + else { + goto exp; } return s; + + 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); + return s; } /* * call-seq: - * flt.coerce(numeric) -> array + * coerce(other) -> array * - * Returns an array with both <i>aNumeric</i> and <i>flt</i> represented - * as <code>Float</code> objects. - * This is achieved by converting <i>aNumeric</i> to a <code>Float</code>. + * Returns a 2-element array containing +other+ converted to a \Float + * and +self+: + * + * f = 3.14 # => 3.14 + * f.coerce(2) # => [2.0, 3.14] + * f.coerce(2.0) # => [2.0, 3.14] + * f.coerce(Rational(1, 2)) # => [0.5, 3.14] + * f.coerce(Complex(1, 0)) # => [1.0, 3.14] + * + * Raises an exception if a type conversion fails. * - * 1.2.coerce(3) #=> [3.0, 1.2] - * 2.5.coerce(1.1) #=> [1.1, 2.5] */ static VALUE @@ -756,127 +1042,191 @@ flo_coerce(VALUE x, VALUE y) return rb_assoc_new(rb_Float(y), x); } -/* - * call-seq: - * -float -> float - * - * Returns float, negated. - */ - -static VALUE -flo_uminus(VALUE flt) +VALUE +rb_float_uminus(VALUE flt) { return DBL2NUM(-RFLOAT_VALUE(flt)); } /* - * call-seq: - * float + other -> float + * call-seq: + * self + other -> float or complex + * + * Returns the sum of +self+ and +other+; + * the result may be inexact (see Float): + * + * 3.14 + 0 # => 3.14 + * 3.14 + 1 # => 4.140000000000001 + * -3.14 + 0 # => -3.14 + * -3.14 + 1 # => -2.14 + + * 3.14 + -3.14 # => 0.0 + * -3.14 + -3.14 # => -6.28 + * + * 3.14 + Complex(1, 0) # => (4.140000000000001+0i) + * 3.14 + Rational(1, 1) # => 4.140000000000001 * - * Returns a new float which is the sum of <code>float</code> - * and <code>other</code>. */ -static VALUE -flo_plus(VALUE x, VALUE y) +VALUE +rb_float_plus(VALUE x, VALUE y) { - switch (TYPE(y)) { - case T_FIXNUM: - return DBL2NUM(RFLOAT_VALUE(x) + (double)FIX2LONG(y)); - case T_BIGNUM: - return DBL2NUM(RFLOAT_VALUE(x) + rb_big2dbl(y)); - case T_FLOAT: - return DBL2NUM(RFLOAT_VALUE(x) + RFLOAT_VALUE(y)); - default: - return rb_num_coerce_bin(x, y, '+'); + if (FIXNUM_P(y)) { + return DBL2NUM(RFLOAT_VALUE(x) + (double)FIX2LONG(y)); + } + else if (RB_BIGNUM_TYPE_P(y)) { + return DBL2NUM(RFLOAT_VALUE(x) + rb_big2dbl(y)); + } + else if (RB_FLOAT_TYPE_P(y)) { + return DBL2NUM(RFLOAT_VALUE(x) + RFLOAT_VALUE(y)); + } + else { + return rb_num_coerce_bin(x, y, '+'); } } /* - * call-seq: - * float - other -> float + * call-seq: + * self - other -> numeric + * + * Returns the difference of +self+ and +other+: + * + * f = 3.14 + * f - 1 # => 2.14 + * f - 1.0 # => 2.14 + * f - Rational(1, 1) # => 2.14 + * f - Complex(1, 0) # => (2.14+0i) * - * Returns a new float which is the difference of <code>float</code> - * and <code>other</code>. */ -static VALUE -flo_minus(VALUE x, VALUE y) +VALUE +rb_float_minus(VALUE x, VALUE y) { - switch (TYPE(y)) { - case T_FIXNUM: - return DBL2NUM(RFLOAT_VALUE(x) - (double)FIX2LONG(y)); - case T_BIGNUM: - return DBL2NUM(RFLOAT_VALUE(x) - rb_big2dbl(y)); - case T_FLOAT: - return DBL2NUM(RFLOAT_VALUE(x) - RFLOAT_VALUE(y)); - default: - return rb_num_coerce_bin(x, y, '-'); + if (FIXNUM_P(y)) { + return DBL2NUM(RFLOAT_VALUE(x) - (double)FIX2LONG(y)); + } + else if (RB_BIGNUM_TYPE_P(y)) { + return DBL2NUM(RFLOAT_VALUE(x) - rb_big2dbl(y)); + } + else if (RB_FLOAT_TYPE_P(y)) { + return DBL2NUM(RFLOAT_VALUE(x) - RFLOAT_VALUE(y)); + } + else { + return rb_num_coerce_bin(x, y, '-'); } } /* - * call-seq: - * float * other -> float + * call-seq: + * self * other -> numeric + * + * Returns the numeric product of +self+ and +other+: + * + * f = 3.14 + * f * 2 # => 6.28 + * f * 2.0 # => 6.28 + * f * Rational(1, 2) # => 1.57 + * f * Complex(2, 0) # => (6.28+0.0i) * - * Returns a new float which is the product of <code>float</code> - * and <code>other</code>. */ -static VALUE -flo_mul(VALUE x, VALUE y) +VALUE +rb_float_mul(VALUE x, VALUE y) { - switch (TYPE(y)) { - case T_FIXNUM: - return DBL2NUM(RFLOAT_VALUE(x) * (double)FIX2LONG(y)); - case T_BIGNUM: - return DBL2NUM(RFLOAT_VALUE(x) * rb_big2dbl(y)); - case T_FLOAT: - return DBL2NUM(RFLOAT_VALUE(x) * RFLOAT_VALUE(y)); - default: - return rb_num_coerce_bin(x, y, '*'); + if (FIXNUM_P(y)) { + return DBL2NUM(RFLOAT_VALUE(x) * (double)FIX2LONG(y)); + } + else if (RB_BIGNUM_TYPE_P(y)) { + return DBL2NUM(RFLOAT_VALUE(x) * rb_big2dbl(y)); + } + else if (RB_FLOAT_TYPE_P(y)) { + return DBL2NUM(RFLOAT_VALUE(x) * RFLOAT_VALUE(y)); + } + else { + return rb_num_coerce_bin(x, y, '*'); + } +} + +static double +double_div_double(double x, double y) +{ + if (LIKELY(y != 0.0)) { + return x / y; + } + else if (x == 0.0) { + return nan(""); + } + else { + double z = signbit(y) ? -1.0 : 1.0; + return x * z * HUGE_VAL; } } +VALUE +rb_flo_div_flo(VALUE x, VALUE y) +{ + double num = RFLOAT_VALUE(x); + double den = RFLOAT_VALUE(y); + double ret = double_div_double(num, den); + return DBL2NUM(ret); +} + /* - * call-seq: - * float / other -> float + * call-seq: + * self / other -> numeric + * + * Returns the quotient of +self+ and +other+: + * + * f = 3.14 + * f / 2 # => 1.57 + * f / 2.0 # => 1.57 + * f / Rational(2, 1) # => 1.57 + * f / Complex(2, 0) # => (1.57+0.0i) * - * Returns a new float which is the result of dividing - * <code>float</code> by <code>other</code>. */ -static VALUE -flo_div(VALUE x, VALUE y) +VALUE +rb_float_div(VALUE x, VALUE y) { - long f_y; - double d; + double num = RFLOAT_VALUE(x); + double den; + double ret; - switch (TYPE(y)) { - case T_FIXNUM: - f_y = FIX2LONG(y); - return DBL2NUM(RFLOAT_VALUE(x) / (double)f_y); - case T_BIGNUM: - d = rb_big2dbl(y); - return DBL2NUM(RFLOAT_VALUE(x) / d); - case T_FLOAT: - return DBL2NUM(RFLOAT_VALUE(x) / RFLOAT_VALUE(y)); - default: - return rb_num_coerce_bin(x, y, '/'); + if (FIXNUM_P(y)) { + den = FIX2LONG(y); + } + else if (RB_BIGNUM_TYPE_P(y)) { + den = rb_big2dbl(y); } + else if (RB_FLOAT_TYPE_P(y)) { + den = RFLOAT_VALUE(y); + } + else { + return rb_num_coerce_bin(x, y, '/'); + } + + ret = double_div_double(num, den); + return DBL2NUM(ret); } /* * call-seq: - * float.quo(numeric) -> float + * quo(other) -> numeric + * + * Returns the quotient from dividing +self+ by +other+: + * + * f = 3.14 + * f.quo(2) # => 1.57 + * f.quo(-2) # => -1.57 + * f.quo(Rational(2, 1)) # => 1.57 + * f.quo(Complex(2, 0)) # => (1.57+0.0i) * - * Returns float / numeric. */ static VALUE flo_quo(VALUE x, VALUE y) { - return rb_funcall(x, '/', 1, y); + return num_funcall1(x, '/', y); } static void @@ -884,26 +1234,34 @@ 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; + double z; - modf(x/y, &z); - mod = x - z * y; + modf(x/y, &z); + mod = x - z * y; #endif } - if (isinf(x) && !isinf(y) && !isnan(y)) - div = x; - else - div = (x - mod) / y; + if (isinf(x) && !isinf(y)) + div = x; + else { + div = (x - mod) / y; + if (modp && divp) div = round(div); + } if (y*mod < 0) { - mod += y; - div -= 1.0; + mod += y; + div -= 1.0; } if (modp) *modp = mod; if (divp) *divp = div; @@ -922,16 +1280,33 @@ ruby_float_mod(double x, double y) return mod; } - /* * call-seq: - * float % other -> float - * float.modulo(other) -> float + * self % other -> float + * + * Returns +self+ modulo +other+ as a \Float. + * + * For float +f+ and real number +r+, these expressions are equivalent: * - * Return the modulo after division of +float+ by +other+. + * f % r + * f-r*(f/r).floor + * f.divmod(r)[1] + * + * See Numeric#divmod. + * + * Examples: + * + * 10.0 % 2 # => 0.0 + * 10.0 % 3 # => 1.0 + * 10.0 % 4 # => 2.0 + * + * 10.0 % -2 # => 0.0 + * 10.0 % -3 # => -2.0 + * 10.0 % -4 # => -2.0 + * + * 10.0 % 4.0 # => 2.0 + * 10.0 % Rational(4, 1) # => 2.0 * - * 6543.21.modulo(137) #=> 104.21 - * 6543.21.modulo(137.24) #=> 92.9299999999996 */ static VALUE @@ -939,18 +1314,17 @@ flo_mod(VALUE x, VALUE y) { double fy; - switch (TYPE(y)) { - case T_FIXNUM: - fy = (double)FIX2LONG(y); - break; - case T_BIGNUM: - fy = rb_big2dbl(y); - break; - case T_FLOAT: - fy = RFLOAT_VALUE(y); - break; - default: - return rb_num_coerce_bin(x, y, '%'); + if (FIXNUM_P(y)) { + fy = (double)FIX2LONG(y); + } + else if (RB_BIGNUM_TYPE_P(y)) { + fy = rb_big2dbl(y); + } + else if (RB_FLOAT_TYPE_P(y)) { + fy = RFLOAT_VALUE(y); + } + else { + return rb_num_coerce_bin(x, y, '%'); } return DBL2NUM(ruby_float_mod(RFLOAT_VALUE(x), fy)); } @@ -958,21 +1332,36 @@ flo_mod(VALUE x, VALUE y) static VALUE dbl2ival(double d) { - d = round(d); if (FIXABLE(d)) { - return LONG2FIX((long)d); + return LONG2FIX((long)d); } return rb_dbl2big(d); } /* * call-seq: - * float.divmod(numeric) -> array + * divmod(other) -> array * - * See Numeric#divmod. + * Returns a 2-element array <tt>[q, r]</tt>, where + * + * q = (self/other).floor # Quotient + * r = self % other # Remainder + * + * Examples: + * + * 11.0.divmod(4) # => [2, 3.0] + * 11.0.divmod(-4) # => [-3, -1.0] + * -11.0.divmod(4) # => [-3, 1.0] + * -11.0.divmod(-4) # => [2, -3.0] + * + * 12.0.divmod(4) # => [3, 0.0] + * 12.0.divmod(-4) # => [-3, 0.0] + * -12.0.divmod(4) # => [-3, -0.0] + * -12.0.divmod(-4) # => [3, -0.0] + * + * 13.0.divmod(4.0) # => [3, 1.0] + * 13.0.divmod(Rational(4, 1)) # => [3, 1.0] * - * 42.0.divmod 6 #=> [7, 0.0] - * 42.0.divmod 5 #=> [8, 2.0] */ static VALUE @@ -981,18 +1370,17 @@ flo_divmod(VALUE x, VALUE y) double fy, div, mod; volatile VALUE a, b; - switch (TYPE(y)) { - case T_FIXNUM: - fy = (double)FIX2LONG(y); - break; - case T_BIGNUM: - fy = rb_big2dbl(y); - break; - case T_FLOAT: - fy = RFLOAT_VALUE(y); - break; - default: - return rb_num_coerce_bin(x, y, rb_intern("divmod")); + if (FIXNUM_P(y)) { + fy = (double)FIX2LONG(y); + } + else if (RB_BIGNUM_TYPE_P(y)) { + fy = rb_big2dbl(y); + } + else if (RB_FLOAT_TYPE_P(y)) { + fy = RFLOAT_VALUE(y); + } + else { + return rb_num_coerce_bin(x, y, id_divmod); } flodivmod(RFLOAT_VALUE(x), fy, &div, &mod); a = dbl2ival(div); @@ -1001,46 +1389,67 @@ flo_divmod(VALUE x, VALUE y) } /* - * call-seq: + * call-seq: + * self ** exponent -> numeric * - * flt ** other -> float + * Returns +self+ raised to the power +exponent+: * - * Raises <code>float</code> the <code>other</code> power. + * f = 3.14 + * f ** 2 # => 9.8596 + * f ** -2 # => 0.1014239928597509 + * f ** 2.1 # => 11.054834900588839 + * f ** Rational(2, 1) # => 9.8596 + * f ** Complex(2, 0) # => (9.8596+0i) * - * 2.0**3 #=> 8.0 */ -static VALUE -flo_pow(VALUE x, VALUE y) +VALUE +rb_float_pow(VALUE x, VALUE y) { - switch (TYPE(y)) { - case T_FIXNUM: - return DBL2NUM(pow(RFLOAT_VALUE(x), (double)FIX2LONG(y))); - case T_BIGNUM: - return DBL2NUM(pow(RFLOAT_VALUE(x), rb_big2dbl(y))); - case T_FLOAT: - { - double dx = RFLOAT_VALUE(x); - double dy = RFLOAT_VALUE(y); - if (dx < 0 && dy != round(dy)) - return rb_funcall(rb_complex_raw1(x), rb_intern("**"), 1, y); - return DBL2NUM(pow(dx, dy)); - } - default: - return rb_num_coerce_bin(x, y, rb_intern("**")); + double dx, dy; + if (y == INT2FIX(2)) { + dx = RFLOAT_VALUE(x); + return DBL2NUM(dx * dx); + } + else if (FIXNUM_P(y)) { + dx = RFLOAT_VALUE(x); + dy = (double)FIX2LONG(y); } + else if (RB_BIGNUM_TYPE_P(y)) { + dx = RFLOAT_VALUE(x); + dy = rb_big2dbl(y); + } + else if (RB_FLOAT_TYPE_P(y)) { + dx = RFLOAT_VALUE(x); + dy = RFLOAT_VALUE(y); + if (dx < 0 && dy != round(dy)) + return rb_dbl_complex_new_polar_pi(pow(-dx, dy), dy); + } + else { + return rb_num_coerce_bin(x, y, idPow); + } + return DBL2NUM(pow(dx, dy)); } /* * call-seq: - * num.eql?(numeric) -> true or false + * eql?(other) -> true or false + * + * Returns +true+ if +self+ and +other+ are the same type and have equal values. + * + * Of the Core and Standard Library classes, + * only Integer, Rational, and Complex use this implementation. * - * Returns <code>true</code> if <i>num</i> and <i>numeric</i> are the - * same type and have equal values. + * Examples: + * + * 1.eql?(1) # => true + * 1.eql?(1.0) # => false + * 1.eql?(Rational(1, 1)) # => false + * 1.eql?(Complex(1, 0)) # => false + * + * Method +eql?+ is different from <tt>==</tt> in that +eql?+ requires matching types, + * while <tt>==</tt> does not. * - * 1 == 1.0 #=> true - * 1.eql?(1.0) #=> false - * (1.0).eql?(1.0) #=> true */ static VALUE @@ -1048,15 +1457,28 @@ num_eql(VALUE x, VALUE y) { if (TYPE(x) != TYPE(y)) return Qfalse; + if (RB_BIGNUM_TYPE_P(x)) { + return rb_big_eql(x, y); + } + return rb_equal(x, y); } /* * call-seq: - * number <=> other -> 0 or nil + * self <=> other -> zero or nil + * + * Compares +self+ and +other+. + * + * Returns: + * + * - Zero, if +self+ is the same as +other+. + * - +nil+, otherwise. * - * Returns zero if +number+ equals +other+, otherwise +nil+ is returned if the - * two values are incomparable. + * \Class \Numeric includes module Comparable, + * each of whose methods uses Numeric#<=> for comparison. + * + * No subclass in the Ruby Core or Standard Library uses this implementation. */ static VALUE @@ -1069,67 +1491,69 @@ num_cmp(VALUE x, VALUE y) static VALUE 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); + return RBOOL(RTEST(result)); } /* * call-seq: - * flt == obj -> true or false + * self == other -> true or false + * + * Returns whether +other+ is numerically equal to +self+: + * + * 2.0 == 2 # => true + * 2.0 == 2.0 # => true + * 2.0 == Rational(2, 1) # => true + * 2.0 == Complex(2, 0) # => true * - * 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>. - * The result of <code>NaN == NaN</code> is undefined, so the - * implementation-dependent value is returned. + * <tt>Float::NAN == Float::NAN</tt> returns an implementation-dependent value. * - * 1.0 == 1 #=> true + * Related: Float#eql? (requires +other+ to be a \Float). * */ -static VALUE -flo_eq(VALUE x, VALUE y) +VALUE +rb_float_equal(VALUE x, VALUE y) { volatile double a, b; - switch (TYPE(y)) { - case T_FIXNUM: - case T_BIGNUM: + if (RB_INTEGER_TYPE_P(y)) { return rb_integer_float_eq(y, x); - case T_FLOAT: - b = RFLOAT_VALUE(y); -#if defined(_MSC_VER) && _MSC_VER < 1300 - if (isnan(b)) return Qfalse; -#endif - break; - default: - return num_equal(x, y); + } + else if (RB_FLOAT_TYPE_P(y)) { + b = RFLOAT_VALUE(y); + } + else { + return num_equal(x, y); } a = RFLOAT_VALUE(x); -#if defined(_MSC_VER) && _MSC_VER < 1300 - if (isnan(a)) return Qfalse; -#endif - return (a == b)?Qtrue:Qfalse; + return RBOOL(a == b); } +#define flo_eq rb_float_equal +static VALUE rb_dbl_hash(double d); + /* * call-seq: - * flt.hash -> integer + * hash -> integer + * + * Returns the integer hash value for +self+. * - * Returns a hash code for this float. + * See also Object#hash. */ static VALUE flo_hash(VALUE num) { - double d; - st_index_t hash; + return rb_dbl_hash(RFLOAT_VALUE(num)); +} - d = RFLOAT_VALUE(num); - /* normalize -0.0 to 0.0 */ - if (d == 0.0) d = 0.0; - hash = rb_memhash(&d, sizeof(d)); - return LONG2FIX(hash); +static VALUE +rb_dbl_hash(double d) +{ + return ST2FIX(rb_dbl_long_hash(d)); } VALUE @@ -1144,15 +1568,32 @@ rb_dbl_cmp(double a, double b) /* * call-seq: - * float <=> real -> -1, 0, +1 or nil + * self <=> other -> -1, 0, 1, or nil * - * Returns -1, 0, +1 or nil depending on whether +float+ is less than, equal - * to, or greater than +real+. This is the basis for the tests in Comparable. + * Compares +self+ and +other+. * - * The result of <code>NaN <=> NaN</code> is undefined, so the - * implementation-dependent value is returned. + * Returns: + * + * - +-1+, if +self+ is less than +other+. + * - +0+, if +self+ is equal to +other+. + * - +1+, if +self+ is greater than +other+. + * - +nil+, if the two values are incommensurate. + * + * Examples: + * + * 2.0 <=> 2.1 # => -1 + * 2.0 <=> 2 # => 0 + * 2.0 <=> 2.0 # => 0 + * 2.0 <=> Rational(2, 1) # => 0 + * 2.0 <=> Complex(2, 0) # => 0 + * 2.0 <=> 1.9 # => 1 + * 2.0 <=> 'foo' # => nil + * + * <tt>Float::NAN <=> Float::NAN</tt> returns an implementation-dependent value. + * + * \Class \Float includes module Comparable, + * each of whose methods uses Float#<=> for comparison. * - * +nil+ is returned if the two values are incomparable. */ static VALUE @@ -1163,84 +1604,88 @@ flo_cmp(VALUE x, VALUE y) a = RFLOAT_VALUE(x); if (isnan(a)) return Qnil; - switch (TYPE(y)) { - case T_FIXNUM: - case T_BIGNUM: - { + if (RB_INTEGER_TYPE_P(y)) { VALUE rel = rb_integer_float_cmp(y, x); if (FIXNUM_P(rel)) - return INT2FIX(-FIX2INT(rel)); + return LONG2FIX(-FIX2LONG(rel)); return rel; - } - - case T_FLOAT: - b = RFLOAT_VALUE(y); - break; - - default: - 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, rb_intern("<=>")); + } + else if (RB_FLOAT_TYPE_P(y)) { + b = RFLOAT_VALUE(y); + } + else { + if (isinf(a) && !UNDEF_P(i = rb_check_funcall(y, rb_intern("infinite?"), 0, 0))) { + 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(ensure_cmp(flo_cmp(x, y), x, y)); +} + /* - * call-seq: - * flt > real -> true or false + * call-seq: + * self > other -> true or false + * + * Returns whether the value of +self+ is greater than the value of +other+; + * +other+ must be numeric, but may not be Complex: + * + * 2.0 > 1 # => true + * 2.0 > 1.0 # => true + * 2.0 > Rational(1, 2) # => true + * 2.0 > 2.0 # => false + * + * <tt>Float::NAN > Float::NAN</tt> returns an implementation-dependent value. * - * <code>true</code> if <code>flt</code> is greater than <code>real</code>. - * The result of <code>NaN > NaN</code> is undefined, so the - * implementation-dependent value is returned. */ -static VALUE -flo_gt(VALUE x, VALUE y) +VALUE +rb_float_gt(VALUE x, VALUE y) { double a, b; a = RFLOAT_VALUE(x); - switch (TYPE(y)) { - case T_FIXNUM: - case T_BIGNUM: - { + if (RB_INTEGER_TYPE_P(y)) { VALUE rel = rb_integer_float_cmp(y, x); if (FIXNUM_P(rel)) - return -FIX2INT(rel) > 0 ? Qtrue : Qfalse; + return RBOOL(-FIX2LONG(rel) > 0); return Qfalse; - } - - case T_FLOAT: - b = RFLOAT_VALUE(y); -#if defined(_MSC_VER) && _MSC_VER < 1300 - if (isnan(b)) return Qfalse; -#endif - break; - - default: - 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; + else if (RB_FLOAT_TYPE_P(y)) { + b = RFLOAT_VALUE(y); + } + else { + return rb_num_coerce_relop(x, y, '>'); + } + return RBOOL(a > b); } /* - * call-seq: - * flt >= real -> true or false + * call-seq: + * self >= other -> true or false + * + * Returns whether the value of +self+ is greater than or equal to the value of +other+; + * +other+ must be numeric, but may not be Complex: + * + * 2.0 >= 1 # => true + * 2.0 >= 1.0 # => true + * 2.0 >= Rational(1, 2) # => true + * 2.0 >= 2.0 # => true + * 2.0 >= 2.1 # => false + * + * <tt>Float::NAN >= Float::NAN</tt> returns an implementation-dependent value. * - * <code>true</code> if <code>flt</code> is greater than - * or equal to <code>real</code>. - * The result of <code>NaN >= NaN</code> is undefined, so the - * implementation-dependent value is returned. */ static VALUE @@ -1249,39 +1694,34 @@ flo_ge(VALUE x, VALUE y) double a, b; a = RFLOAT_VALUE(x); - switch (TYPE(y)) { - case T_FIXNUM: - case T_BIGNUM: - { + if (RB_TYPE_P(y, T_FIXNUM) || RB_BIGNUM_TYPE_P(y)) { VALUE rel = rb_integer_float_cmp(y, x); if (FIXNUM_P(rel)) - return -FIX2INT(rel) >= 0 ? Qtrue : Qfalse; + return RBOOL(-FIX2LONG(rel) >= 0); return Qfalse; - } - - case T_FLOAT: - b = RFLOAT_VALUE(y); -#if defined(_MSC_VER) && _MSC_VER < 1300 - if (isnan(b)) return Qfalse; -#endif - break; - - default: - return rb_num_coerce_relop(x, y, rb_intern(">=")); } -#if defined(_MSC_VER) && _MSC_VER < 1300 - if (isnan(a)) return Qfalse; -#endif - return (a >= b)?Qtrue:Qfalse; + else if (RB_FLOAT_TYPE_P(y)) { + b = RFLOAT_VALUE(y); + } + else { + return rb_num_coerce_relop(x, y, idGE); + } + return RBOOL(a >= b); } /* - * call-seq: - * flt < real -> true or false + * call-seq: + * self < other -> true or false + * + * Returns whether the value of +self+ is less than the value of +other+; + * +other+ must be numeric, but may not be Complex: * - * <code>true</code> if <code>flt</code> is less than <code>real</code>. - * The result of <code>NaN < NaN</code> is undefined, so the - * implementation-dependent value is returned. + * 2.0 < 3 # => true + * 2.0 < 3.0 # => true + * 2.0 < Rational(3, 1) # => true + * 2.0 < 2.0 # => false + * + * <tt>Float::NAN < Float::NAN</tt> returns an implementation-dependent value. */ static VALUE @@ -1290,40 +1730,36 @@ flo_lt(VALUE x, VALUE y) double a, b; a = RFLOAT_VALUE(x); - switch (TYPE(y)) { - case T_FIXNUM: - case T_BIGNUM: - { + if (RB_INTEGER_TYPE_P(y)) { VALUE rel = rb_integer_float_cmp(y, x); if (FIXNUM_P(rel)) - return -FIX2INT(rel) < 0 ? Qtrue : Qfalse; + return RBOOL(-FIX2LONG(rel) < 0); return Qfalse; - } - - case T_FLOAT: - b = RFLOAT_VALUE(y); -#if defined(_MSC_VER) && _MSC_VER < 1300 - if (isnan(b)) return Qfalse; -#endif - break; - - default: - 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; + else if (RB_FLOAT_TYPE_P(y)) { + b = RFLOAT_VALUE(y); + } + else { + return rb_num_coerce_relop(x, y, '<'); + } + return RBOOL(a < b); } /* - * call-seq: - * flt <= real -> true or false + * call-seq: + * self <= other -> true or false + * + * Returns whether the value of +self+ is less than or equal to the value of +other+; + * +other+ must be numeric, but may not be Complex: + * + * 2.0 <= 3 # => true + * 2.0 <= 3.0 # => true + * 2.0 <= Rational(3, 1) # => true + * 2.0 <= 2.0 # => true + * 2.0 <= 1.0 # => false + * + * <tt>Float::NAN <= Float::NAN</tt> returns an implementation-dependent value. * - * <code>true</code> if <code>flt</code> is less than - * or equal to <code>real</code>. - * The result of <code>NaN <= NaN</code> is undefined, so the - * implementation-dependent value is returned. */ static VALUE @@ -1332,323 +1768,742 @@ flo_le(VALUE x, VALUE y) double a, b; a = RFLOAT_VALUE(x); - switch (TYPE(y)) { - case T_FIXNUM: - case T_BIGNUM: - { + if (RB_INTEGER_TYPE_P(y)) { VALUE rel = rb_integer_float_cmp(y, x); if (FIXNUM_P(rel)) - return -FIX2INT(rel) <= 0 ? Qtrue : Qfalse; + return RBOOL(-FIX2LONG(rel) <= 0); return Qfalse; - } - - case T_FLOAT: - b = RFLOAT_VALUE(y); -#if defined(_MSC_VER) && _MSC_VER < 1300 - if (isnan(b)) return Qfalse; -#endif - break; - - default: - return rb_num_coerce_relop(x, y, rb_intern("<=")); } -#if defined(_MSC_VER) && _MSC_VER < 1300 - if (isnan(a)) return Qfalse; -#endif - return (a <= b)?Qtrue:Qfalse; + else if (RB_FLOAT_TYPE_P(y)) { + b = RFLOAT_VALUE(y); + } + else { + return rb_num_coerce_relop(x, y, idLE); + } + return RBOOL(a <= b); } /* * call-seq: - * flt.eql?(obj) -> true or false + * eql?(other) -> true or false + * + * Returns +true+ if +other+ is a \Float with the same value as +self+, + * +false+ otherwise: + * + * 2.0.eql?(2.0) # => true + * 2.0.eql?(1.0) # => false + * 2.0.eql?(1) # => false + * 2.0.eql?(Rational(2, 1)) # => false + * 2.0.eql?(Complex(2, 0)) # => 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. - * The result of <code>NaN.eql?(NaN)</code> is undefined, so the - * implementation-dependent value is returned. + * <tt>Float::NAN.eql?(Float::NAN)</tt> returns an implementation-dependent value. * - * 1.0.eql?(1) #=> false + * Related: Float#== (performs type conversions). */ -static VALUE -flo_eql(VALUE x, VALUE y) +VALUE +rb_float_eql(VALUE x, VALUE y) { - 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; -#endif - if (a == b) - return Qtrue; + if (RB_FLOAT_TYPE_P(y)) { + double a = RFLOAT_VALUE(x); + double b = RFLOAT_VALUE(y); + return RBOOL(a == b); } return Qfalse; } -/* - * call-seq: - * flt.to_f -> self - * - * As <code>flt</code> is already a float, returns +self+. - */ +#define flo_eql rb_float_eql -static VALUE -flo_to_f(VALUE num) +VALUE +rb_float_abs(VALUE flt) { - return num; + double val = fabs(RFLOAT_VALUE(flt)); + return DBL2NUM(val); } /* * call-seq: - * flt.abs -> float - * flt.magnitude -> float - * - * Returns the absolute value of <i>flt</i>. + * nan? -> true or false * - * (-34.56).abs #=> 34.56 - * -34.56.abs #=> 34.56 + * Returns +true+ if +self+ is a NaN, +false+ otherwise. * + * f = -1.0 #=> -1.0 + * f.nan? #=> false + * f = 0.0/0.0 #=> NaN + * f.nan? #=> true */ static VALUE -flo_abs(VALUE flt) +flo_is_nan_p(VALUE num) { - double val = fabs(RFLOAT_VALUE(flt)); - return DBL2NUM(val); + double value = RFLOAT_VALUE(num); + + return RBOOL(isnan(value)); } /* * call-seq: - * flt.zero? -> true or false + * infinite? -> -1, 1, or nil + * + * Returns: + * + * - 1, if +self+ is <tt>Infinity</tt>. + * - -1 if +self+ is <tt>-Infinity</tt>. + * - +nil+, otherwise. * - * Returns <code>true</code> if <i>flt</i> is 0.0. + * Examples: + * + * f = 1.0/0.0 # => Infinity + * f.infinite? # => 1 + * f = -1.0/0.0 # => -Infinity + * f.infinite? # => -1 + * f = 1.0 # => 1.0 + * f.infinite? # => nil + * f = 0.0/0.0 # => NaN + * f.infinite? # => nil * */ -static VALUE -flo_zero_p(VALUE num) +VALUE +rb_flo_is_infinite_p(VALUE num) { - if (RFLOAT_VALUE(num) == 0.0) { - return Qtrue; + double value = RFLOAT_VALUE(num); + + if (isinf(value)) { + return INT2FIX( value < 0 ? -1 : 1 ); } - return Qfalse; + + return Qnil; } /* * call-seq: - * flt.nan? -> true or false + * finite? -> true or false + * + * Returns +true+ if +self+ is not +Infinity+, +-Infinity+, or +NaN+, + * +false+ otherwise: * - * Returns <code>true</code> if <i>flt</i> is an invalid IEEE floating - * point number. + * f = 2.0 # => 2.0 + * f.finite? # => true + * f = 1.0/0.0 # => Infinity + * f.finite? # => false + * f = -1.0/0.0 # => -Infinity + * f.finite? # => false + * f = 0.0/0.0 # => NaN + * f.finite? # => false * - * a = -1.0 #=> -1.0 - * a.nan? #=> false - * a = 0.0/0.0 #=> NaN - * a.nan? #=> true */ -static VALUE -flo_is_nan_p(VALUE num) +VALUE +rb_flo_is_finite_p(VALUE num) { double value = RFLOAT_VALUE(num); - return isnan(value) ? Qtrue : Qfalse; + return RBOOL(isfinite(value)); +} + +static VALUE +flo_nextafter(VALUE flo, double value) +{ + double x, y; + x = NUM2DBL(flo); + y = nextafter(x, value); + return DBL2NUM(y); } /* * call-seq: - * flt.infinite? -> nil, -1, +1 + * next_float -> float + * + * Returns the next-larger representable \Float. + * + * These examples show the internally stored values (64-bit hexadecimal) + * for each \Float +f+ and for the corresponding <tt>f.next_float</tt>: * - * Returns <code>nil</code>, -1, or +1 depending on whether <i>flt</i> - * is finite, -infinity, or +infinity. + * f = 0.0 # 0x0000000000000000 + * f.next_float # 0x0000000000000001 + * + * f = 0.01 # 0x3f847ae147ae147b + * f.next_float # 0x3f847ae147ae147c + * + * In the remaining examples here, the output is shown in the usual way + * (result +to_s+): + * + * 0.01.next_float # => 0.010000000000000002 + * 1.0.next_float # => 1.0000000000000002 + * 100.0.next_float # => 100.00000000000001 + * + * f = 0.01 + * (0..3).each_with_index {|i| printf "%2d %-20a %s\n", i, f, f.to_s; f = f.next_float } + * + * Output: + * + * 0 0x1.47ae147ae147bp-7 0.01 + * 1 0x1.47ae147ae147cp-7 0.010000000000000002 + * 2 0x1.47ae147ae147dp-7 0.010000000000000004 + * 3 0x1.47ae147ae147ep-7 0.010000000000000005 + * + * 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. + * + * Related: Float#prev_float * - * (0.0).infinite? #=> nil - * (-1.0/0.0).infinite? #=> -1 - * (+1.0/0.0).infinite? #=> 1 */ - static VALUE -flo_is_infinite_p(VALUE num) +flo_next_float(VALUE vx) { - double value = RFLOAT_VALUE(num); - - if (isinf(value)) { - return INT2FIX( value < 0 ? -1 : 1 ); - } - - return Qnil; + return flo_nextafter(vx, HUGE_VAL); } /* * call-seq: - * flt.finite? -> true or false + * float.prev_float -> float + * + * Returns the next-smaller representable \Float. + * + * These examples show the internally stored values (64-bit hexadecimal) + * for each \Float +f+ and for the corresponding <tt>f.pev_float</tt>: + * + * f = 5e-324 # 0x0000000000000001 + * f.prev_float # 0x0000000000000000 + * + * f = 0.01 # 0x3f847ae147ae147b + * f.prev_float # 0x3f847ae147ae147a + * + * In the remaining examples here, the output is shown in the usual way + * (result +to_s+): * - * 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>). + * 0.01.prev_float # => 0.009999999999999998 + * 1.0.prev_float # => 0.9999999999999999 + * 100.0.prev_float # => 99.99999999999999 + * + * f = 0.01 + * (0..3).each_with_index {|i| printf "%2d %-20a %s\n", i, f, f.to_s; f = f.prev_float } + * + * Output: + * + * 0 0x1.47ae147ae147bp-7 0.01 + * 1 0x1.47ae147ae147ap-7 0.009999999999999998 + * 2 0x1.47ae147ae1479p-7 0.009999999999999997 + * 3 0x1.47ae147ae1478p-7 0.009999999999999995 + * + * Related: Float#next_float. * */ - static VALUE -flo_is_finite_p(VALUE num) +flo_prev_float(VALUE vx) { - double value = RFLOAT_VALUE(num); + return flo_nextafter(vx, -HUGE_VAL); +} -#if HAVE_ISFINITE - if (!isfinite(value)) - return Qfalse; -#else - if (isinf(value) || isnan(value)) - return Qfalse; -#endif +VALUE +rb_float_floor(VALUE num, int ndigits) +{ + double number; + number = RFLOAT_VALUE(num); + if (number == 0.0) { + return ndigits > 0 ? DBL2NUM(number) : INT2FIX(0); + } + if (ndigits > 0) { + int binexp; + double f, mul, res; + 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); + mul = floor(number * f); + res = (mul + 1) / f; + if (res > number) + res = mul / f; + return DBL2NUM(res); + } + else { + num = dbl2ival(floor(number)); + if (ndigits < 0) num = rb_int_floor(num, ndigits); + return num; + } +} - return Qtrue; +static int +flo_ndigits(int argc, VALUE *argv) +{ + if (rb_check_arity(argc, 0, 1)) { + return NUM2INT(argv[0]); + } + return 0; } /* - * call-seq: - * flt.floor -> integer + * :markup: markdown * - * Returns the largest integer less than or equal to <i>flt</i>. + * call-seq: + * floor(ndigits = 0) -> float or integer + * + * Returns a float or integer that is a "floor" value for `self`, + * as specified by `ndigits`, + * which must be an + * [integer-convertible object](rdoc-ref:implicit_conversion.rdoc@Integer-Convertible+Objects). + * + * When `self` is zero, + * returns a zero value: + * a float if `ndigits` is positive, + * an integer otherwise: + * + * ``` + * f = 0.0 # => 0.0 + * f.floor(20) # => 0.0 + * f.floor(0) # => 0 + * f.floor(-20) # => 0 + * ``` + * + * When `self` is non-zero and `ndigits` is positive, returns a float with `ndigits` + * digits after the decimal point (as available): + * + * ``` + * f = 12345.6789 + * f.floor(1) # => 12345.6 + * f.floor(3) # => 12345.678 + * f.floor(30) # => 12345.6789 + * f = -12345.6789 + * f.floor(1) # => -12345.7 + * f.floor(3) # => -12345.679 + * f.floor(30) # => -12345.6789 + * ``` + * + * When `self` is non-zero and `ndigits` is non-positive, + * returns an integer value based on a computed granularity: + * + * - The granularity is `10 ** ndigits.abs`. + * - The returned value is the largest multiple of the granularity + * that is less than or equal to `self`. + * + * Examples with positive `self`: + * + * | ndigits | Granularity | 12345.6789.floor(ndigits) | + * |--------:|------------:|--------------------------:| + * | 0 | 1 | 12345 | + * | -1 | 10 | 12340 | + * | -2 | 100 | 12300 | + * | -3 | 1000 | 12000 | + * | -4 | 10000 | 10000 | + * | -5 | 100000 | 0 | + * + * Examples with negative `self`: + * + * | ndigits | Granularity | -12345.6789.floor(ndigits) | + * |--------:|------------:|---------------------------:| + * | 0 | 1 | -12346 | + * | -1 | 10 | -12350 | + * | -2 | 100 | -12400 | + * | -3 | 1000 | -13000 | + * | -4 | 10000 | -20000 | + * | -5 | 100000 | -100000 | + * | -6 | 1000000 | -1000000 | + * + * Note that the limited precision of floating-point arithmetic + * may lead to surprising results: + * + * ``` + * (0.3 / 0.1).floor # => 2 # Not 3, (because (0.3 / 0.1) # => 2.9999999999999996, not 3.0) + * ``` + * + * Related: Float#ceil. * - * 1.2.floor #=> 1 - * 2.0.floor #=> 2 - * (-1.2).floor #=> -2 - * (-2.0).floor #=> -2 */ static VALUE -flo_floor(VALUE num) +flo_floor(int argc, VALUE *argv, VALUE num) { - double f = floor(RFLOAT_VALUE(num)); - long val; - - if (!FIXABLE(f)) { - return rb_dbl2big(f); - } - val = (long)f; - return LONG2FIX(val); + int ndigits = flo_ndigits(argc, argv); + return rb_float_floor(num, ndigits); } /* - * call-seq: - * flt.ceil -> integer + * :markup: markdown * - * Returns the smallest <code>Integer</code> greater than or equal to - * <i>flt</i>. + * call-seq: + * ceil(ndigits = 0) -> float or integer + * + * Returns a numeric that is a "ceiling" value for `self`, + * as specified by the given `ndigits`, + * which must be an + * [integer-convertible object](rdoc-ref:implicit_conversion.rdoc@Integer-Convertible+Objects). + * + * When `ndigits` is positive, returns a Float with `ndigits` + * decimal digits after the decimal point + * (as available, but no fewer than 1): + * + * ``` + * f = 12345.6789 + * f.ceil(1) # => 12345.7 + * f.ceil(3) # => 12345.679 + * f.ceil(30) # => 12345.6789 + * f = -12345.6789 + * f.ceil(1) # => -12345.6 + * f.ceil(3) # => -12345.678 + * f.ceil(30) # => -12345.6789 + * f = 0.0 + * f.ceil(1) # => 0.0 + * f.ceil(100) # => 0.0 + * ``` + * + * When `ndigits` is non-positive, + * returns an Integer based on a computed granularity: + * + * - The granularity is `10 ** ndigits.abs`. + * - The returned value is the largest multiple of the granularity + * that is less than or equal to `self`. + * + * Examples with positive `self`: + * + * | ndigits | Granularity | 12345.6789.ceil(ndigits) | + * |--------:|------------:|-------------------------:| + * | 0 | 1 | 12346 | + * | -1 | 10 | 12350 | + * | -2 | 100 | 12400 | + * | -3 | 1000 | 13000 | + * | -4 | 10000 | 20000 | + * | -5 | 100000 | 100000 | + * + * Examples with negative `self`: + * + * | ndigits | Granularity | -12345.6789.ceil(ndigits) | + * |--------:|------------:|--------------------------:| + * | 0 | 1 | -12345 | + * | -1 | 10 | -12340 | + * | -2 | 100 | -12300 | + * | -3 | 1000 | -12000 | + * | -4 | 10000 | -10000 | + * | -5 | 100000 | 0 | + * + * When `self` is zero and `ndigits` is non-positive, + * returns Integer zero: + * + * ``` + * 0.0.ceil(0) # => 0 + * 0.0.ceil(-1) # => 0 + * 0.0.ceil(-2) # => 0 + * ``` + * + * Note that the limited precision of floating-point arithmetic + * may lead to surprising results: + * + * ``` + * (2.1 / 0.7).ceil #=> 4 # Not 3 (because 2.1 / 0.7 # => 3.0000000000000004, not 3.0) + * ``` + * + * Related: Float#floor. * - * 1.2.ceil #=> 2 - * 2.0.ceil #=> 2 - * (-1.2).ceil #=> -1 - * (-2.0).ceil #=> -2 */ static VALUE -flo_ceil(VALUE num) +flo_ceil(int argc, VALUE *argv, VALUE num) +{ + int ndigits = flo_ndigits(argc, argv); + return rb_float_ceil(num, ndigits); +} + +VALUE +rb_float_ceil(VALUE num, int ndigits) { - double f = ceil(RFLOAT_VALUE(num)); - long val; + double number, f; - if (!FIXABLE(f)) { - return rb_dbl2big(f); + number = RFLOAT_VALUE(num); + if (number == 0.0) { + return ndigits > 0 ? DBL2NUM(number) : INT2FIX(0); } - val = (long)f; - return LONG2FIX(val); + 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_BIGNUM_TYPE_P(num)) { + 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 + * Assumes num is an \Integer, ndigits <= 0 */ static VALUE -int_round_0(VALUE num, int ndigits) +rb_int_round(VALUE num, int ndigits, enum ruby_num_rounding_mode mode) { VALUE n, f, h, r; - long bytes; - ID op; - /* If 10**N / 2 > num, then return 0 */ - /* We have log_256(10) > 0.415241 and log_256(1/2) = -0.125, so */ - bytes = FIXNUM_P(num) ? sizeof(long) : rb_funcall(num, idSize, 0); - if (-0.415241 * ndigits - 0.125 > bytes ) { - return INT2FIX(0); + + 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 / 2) / y * y; - if (neg) x = -x; - return LONG2NUM(x); - } - if (RB_TYPE_P(f, T_FLOAT)) { - /* then int_pow overflow */ - return INT2FIX(0); - } - h = rb_funcall(f, '/', 1, INT2FIX(2)); - r = rb_funcall(num, '%', 1, f); - n = rb_funcall(num, '-', 1, r); - op = negative_int_p(num) ? rb_intern("<=") : '<'; - if (!RTEST(rb_funcall(r, op, 1, h))) { - n = rb_funcall(n, '+', 1, 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_FLOAT_TYPE_P(f)) { + /* 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; } static VALUE -flo_truncate(VALUE num); +rb_int_floor(VALUE num, int ndigits) +{ + VALUE 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); + } + else { + bool neg = int_neg_p(num); + if (neg) num = rb_int_minus(rb_int_plus(rb_int_uminus(num), f), INT2FIX(1)); + num = rb_int_mul(rb_int_div(num, f), f); + if (neg) num = rb_int_uminus(num); + return num; + } +} + +static VALUE +rb_int_ceil(VALUE num, int ndigits) +{ + VALUE 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); + } + else { + bool neg = int_neg_p(num); + if (neg) + num = rb_int_uminus(num); + else + num = rb_int_plus(num, rb_int_minus(f, INT2FIX(1))); + num = rb_int_mul(rb_int_div(num, f), f); + if (neg) num = rb_int_uminus(num); + return num; + } +} + +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_FLOAT_TYPE_P(f)) { + /* 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); + } +} /* * call-seq: - * flt.round([ndigits]) -> integer or float + * round(ndigits = 0, half: :up) -> integer or float + * + * Returns +self+ rounded to the nearest value with + * a precision of +ndigits+ decimal digits. + * + * When +ndigits+ is non-negative, returns a float with +ndigits+ + * after the decimal point (as available): + * + * f = 12345.6789 + * f.round(1) # => 12345.7 + * f.round(3) # => 12345.679 + * f = -12345.6789 + * f.round(1) # => -12345.7 + * f.round(3) # => -12345.679 + * + * When +ndigits+ is negative, returns an integer + * with at least <tt>ndigits.abs</tt> trailing zeros: + * + * f = 12345.6789 + * f.round(0) # => 12346 + * f.round(-3) # => 12000 + * f = -12345.6789 + * f.round(0) # => -12346 + * f.round(-3) # => -12000 + * + * If keyword argument +half+ is given, + * and +self+ is equidistant from the two candidate values, + * the rounding is according to the given +half+ value: + * + * - +:up+ or +nil+: round away from zero: + * + * 2.5.round(half: :up) # => 3 + * 3.5.round(half: :up) # => 4 + * (-2.5).round(half: :up) # => -3 * - * Rounds <i>flt</i> to a given precision in decimal digits (default 0 digits). - * Precision may be negative. Returns a floating point number when ndigits - * is more than zero. + * - +:down+: round toward zero: * - * 1.4.round #=> 1 - * 1.5.round #=> 2 - * 1.6.round #=> 2 - * (-1.5).round #=> -2 + * 2.5.round(half: :down) # => 2 + * 3.5.round(half: :down) # => 3 + * (-2.5).round(half: :down) # => -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 + * - +:even+: round toward the candidate whose last nonzero digit is even: * - * 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 + * 2.5.round(half: :even) # => 2 + * 3.5.round(half: :even) # => 4 + * (-2.5).round(half: :even) # => -2 + * + * Raises and exception if the value for +half+ is invalid. + * + * Related: Float#truncate. * */ static VALUE flo_round(int argc, VALUE *argv, VALUE num) { - VALUE nd; - double number, f; + double number, f, x; + VALUE nd, opt; int ndigits = 0; - int binexp; - enum {float_dig = DBL_DIG+2}; + enum ruby_num_rounding_mode mode; - if (argc > 0 && rb_scan_args(argc, argv, "01", &nd) == 1) { - ndigits = NUM2INT(nd); + 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 int_round_0(flo_truncate(num), ndigits); + return rb_int_round(flo_to_i(num), ndigits, mode); } - number = RFLOAT_VALUE(num); if (ndigits == 0) { - return dbl2ival(number); + 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); + if (ndigits > 14) { + /* In this case, pow(10, ndigits) may not be accurate. */ + return rb_flo_round_by_rational(argc, argv, num); + } + f = pow(10, ndigits); + x = ROUND_CALL(mode, round, (number, f)); + return DBL2NUM(x / f); } - frexp(number, &binexp); + return num; +} + +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 @@ -1658,99 +2513,150 @@ flo_round(int argc, VALUE *argv, VALUE num) 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 + 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 (isinf(number) || isnan(number) || - (ndigits >= float_dig - (binexp > 0 ? binexp / 4 : binexp / 3 - 1))) { - return num; + if (ndigits >= float_dig - (binexp > 0 ? binexp / 4 : binexp / 3 - 1)) { + return TRUE; } + return FALSE; +} + +static int +float_round_underflow(int ndigits, int binexp) +{ if (ndigits < - (binexp > 0 ? binexp / 3 + 1 : binexp / 4)) { - return DBL2NUM(0); + return TRUE; } - f = pow(10, ndigits); - return DBL2NUM(round(number * f) / f); + return FALSE; } /* * call-seq: - * flt.to_i -> integer - * flt.to_int -> integer - * flt.truncate -> integer + * to_i -> integer + * + * Returns +self+ truncated to an Integer. + * + * 1.2.to_i # => 1 + * (-1.2).to_i # => -1 + * + * Note that the limited precision of floating-point arithmetic + * may lead to surprising results: + * + * (0.3 / 0.1).to_i # => 2 (!) * - * Returns <i>flt</i> truncated to an <code>Integer</code>. */ static VALUE -flo_truncate(VALUE num) +flo_to_i(VALUE num) { double f = RFLOAT_VALUE(num); - long val; if (f > 0.0) f = floor(f); if (f < 0.0) f = ceil(f); - if (!FIXABLE(f)) { - return rb_dbl2big(f); - } - val = (long)f; - return LONG2FIX(val); + return dbl2ival(f); } /* * call-seq: - * num.floor -> integer + * truncate(ndigits = 0) -> float or integer + * + * Returns +self+ truncated (toward zero) to + * a precision of +ndigits+ decimal digits. + * + * When +ndigits+ is positive, returns a float with +ndigits+ digits + * after the decimal point (as available): * - * 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>. + * f = 12345.6789 + * f.truncate(1) # => 12345.6 + * f.truncate(3) # => 12345.678 + * f = -12345.6789 + * f.truncate(1) # => -12345.6 + * f.truncate(3) # => -12345.678 + * + * When +ndigits+ is negative, returns an integer + * with at least <tt>ndigits.abs</tt> trailing zeros: + * + * f = 12345.6789 + * f.truncate(0) # => 12345 + * f.truncate(-3) # => 12000 + * f = -12345.6789 + * f.truncate(0) # => -12345 + * f.truncate(-3) # => -12000 + * + * Note that the limited precision of floating-point arithmetic + * may lead to surprising results: + * + * (0.3 / 0.1).truncate #=> 2 (!) + * + * Related: Float#round. * - * 1.floor #=> 1 - * (-1).floor #=> -1 */ - static VALUE -num_floor(VALUE num) +flo_truncate(int argc, VALUE *argv, VALUE num) { - return flo_floor(rb_Float(num)); + if (signbit(RFLOAT_VALUE(num))) + return flo_ceil(argc, argv, num); + else + return flo_floor(argc, argv, num); } +/* + * call-seq: + * floor(ndigits = 0) -> float or integer + * + * Returns the largest float or integer that is less than or equal to +self+, + * as specified by the given +ndigits+, + * which must be an + * {integer-convertible object}[rdoc-ref:implicit_conversion.rdoc@Integer-Convertible+Objects]. + * + * Equivalent to <tt>self.to_f.floor(ndigits)</tt>. + * + * Related: #ceil, Float#floor. + */ + +static VALUE +num_floor(int argc, VALUE *argv, VALUE num) +{ + return flo_floor(argc, argv, rb_Float(num)); +} /* * call-seq: - * num.ceil -> integer + * ceil(ndigits = 0) -> float or 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>. + * Returns the smallest float or integer that is greater than or equal to +self+, + * as specified by the given +ndigits+, + * which must be an + * {integer-convertible object}[rdoc-ref:implicit_conversion.rdoc@Integer-Convertible+Objects]. * - * 1.ceil #=> 1 - * 1.2.ceil #=> 2 - * (-1.2).ceil #=> -1 - * (-1.0).ceil #=> -1 + * Equivalent to <tt>self.to_f.ceil(ndigits)</tt>. + * + * Related: #floor, Float#ceil. */ static VALUE -num_ceil(VALUE num) +num_ceil(int argc, VALUE *argv, VALUE num) { - return flo_ceil(rb_Float(num)); + return flo_ceil(argc, argv, rb_Float(num)); } /* * call-seq: - * num.round([ndigits]) -> integer or float + * round(digits = 0) -> integer or float + * + * Returns +self+ rounded to the nearest value with + * a precision of +digits+ decimal digits. * - * Rounds <i>num</i> to a given precision in decimal digits (default 0 digits). - * Precision may be negative. Returns a floating point number when <i>ndigits</i> - * is more than zero. <code>Numeric</code> implements this by converting itself - * to a <code>Float</code> and invoking <code>Float#round</code>. + * \Numeric implements this by converting +self+ to a Float and + * invoking Float#round. */ static VALUE @@ -1761,308 +2667,539 @@ num_round(int argc, VALUE* argv, VALUE num) /* * call-seq: - * num.truncate -> integer + * truncate(digits = 0) -> integer or float + * + * Returns +self+ truncated (toward zero) to + * a precision of +digits+ decimal digits. * - * 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>. + * \Numeric implements this by converting +self+ to a Float and + * invoking Float#truncate. */ static VALUE -num_truncate(VALUE num) +num_truncate(int argc, VALUE *argv, VALUE num) { - return flo_truncate(rb_Float(num)); + return flo_truncate(argc, argv, rb_Float(num)); } -static double +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; + double d, n, err; + if (unit == 0) { + return HUGE_VAL; + } if (isinf(unit)) { - return unit > 0 ? beg <= end : beg >= end; + return unit > 0 ? beg <= end : beg >= end; } + n= (end - beg)/unit; + err = (fabs(beg) + fabs(end) + fabs(end-beg)) / fabs(unit) * epsilon; if (err>0.5) err=0.5; if (excl) { - if (n<=0) return 0; - if (n<1) - n = 0; - else - n = floor(n - err); + if (n<=0) return 0; + if (n<1) + n = 0; + else + n = floor(n - err); + d = +((n + 1) * unit) + beg; + if (beg < end) { + if (d < end) + n++; + } + else if (beg > end) { + if (d > end) + n++; + } } else { - if (n<0) return 0; - n = floor(n + err); + if (n<0) return 0; + n = floor(n + err); + d = +((n + 1) * unit) + beg; + if (beg < end) { + if (d <= end) + n++; + } + else if (beg > end) { + if (d >= end) + n++; + } } 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 { - 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; +ruby_float_step(VALUE from, VALUE to, VALUE step, int excl, int allow_endless) +{ + if (RB_FLOAT_TYPE_P(from) || RB_FLOAT_TYPE_P(to) || RB_FLOAT_TYPE_P(step)) { + double unit = NUM2DBL(step); + double beg = NUM2DBL(from); + double end = (allow_endless && NIL_P(to)) ? (unit < 0 ? -1 : 1)*HUGE_VAL : NUM2DBL(to); + 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 if (unit == 0) { + VALUE val = DBL2NUM(beg); + for (;;) + rb_yield(val); + } + 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 -num_interval_step_size(VALUE from, VALUE to, VALUE step, int excl) +ruby_num_interval_step_size(VALUE from, VALUE to, VALUE step, int excl) { if (FIXNUM_P(from) && FIXNUM_P(to) && FIXNUM_P(step)) { - long delta, diff; + long delta, diff; + + diff = FIX2LONG(step); + if (diff == 0) { + return DBL2NUM(HUGE_VAL); + } + 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_FLOAT_TYPE_P(from) || RB_FLOAT_TYPE_P(to) || RB_FLOAT_TYPE_P(step)) { + double n = ruby_float_step_size(NUM2DBL(from), NUM2DBL(to), NUM2DBL(step), excl); + + if (isinf(n)) return DBL2NUM(n); + if (POSFIXABLE(n)) return LONG2FIX((long)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(HUGE_VAL); + case -1: cmp = '<'; break; + } + 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(to, cmp, 1, rb_funcall(from, '+', 1, rb_funcall(result, '*', 1, step))))) { + 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_BIGNUM_TYPE_P(num)) { + if (method_basic_p(rb_cInteger)) + return BIGNUM_NEGATIVE_P(num); + } - diff = FIX2LONG(step); - if (!diff) rb_num_zerodiv(); - 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); + r = rb_check_funcall(num, '>', 1, &zero); + if (UNDEF_P(r)) { + coerce_failed(num, INT2FIX(0)); } - 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); + return !RTEST(r); +} - if (isinf(n)) return DBL2NUM(n); - if (POSFIXABLE(n)) return LONG2FIX(n); - return rb_dbl2big(n); +static int +num_step_extract_args(int argc, const VALUE *argv, VALUE *to, VALUE *step, VALUE *by) +{ + VALUE hash; + + 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 (!UNDEF_P(values[0])) { + if (argc > 0) rb_raise(rb_eArgError, "to is given twice"); + *to = values[0]; + } + if (!UNDEF_P(values[1])) { + if (argc > 1) rb_raise(rb_eArgError, "step is given twice"); + *by = values[1]; + } + } + + return argc; +} + +static int +num_step_check_fix_args(int argc, VALUE *to, VALUE *step, VALUE by, int fix_nil, int allow_zero_step) +{ + int desc; + if (!UNDEF_P(by)) { + *step = by; } else { - VALUE result; - ID cmp = RTEST(rb_funcall(step, '>', 1, INT2FIX(0))) ? '>' : '<'; - 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; + /* compatibility */ + if (argc > 1 && NIL_P(*step)) { + rb_raise(rb_eTypeError, "step must be numeric"); + } + } + if (!allow_zero_step && 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 (fix_nil && NIL_P(*to)) { + *to = desc ? DBL2NUM(-HUGE_VAL) : DBL2NUM(HUGE_VAL); + } + return desc; +} + +static int +num_step_scan_args(int argc, const VALUE *argv, VALUE *to, VALUE *step, int fix_nil, int allow_zero_step) +{ + VALUE by = Qundef; + argc = num_step_extract_args(argc, argv, to, step, &by); + return num_step_check_fix_args(argc, to, step, by, fix_nil, allow_zero_step); } static VALUE -num_step_size(VALUE from, VALUE args) +num_step_size(VALUE from, VALUE args, VALUE eobj) { - VALUE to = RARRAY_PTR(args)[0]; - VALUE step = (RARRAY_LEN(args) > 1) ? RARRAY_PTR(args)[1] : INT2FIX(1); - return num_interval_step_size(from, to, step, FALSE); + 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, TRUE, FALSE); + + return ruby_num_interval_step_size(from, to, step, FALSE); } + /* * call-seq: - * num.step(limit[, step]) {|i| block } -> self - * num.step(limit[, step]) -> an_enumerator - * - * Invokes <em>block</em> with the sequence of numbers starting at - * <i>num</i>, incremented by <i>step</i> (default 1) 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. - * - * If no block is given, an enumerator is returned instead. - * - * 1.step(10, 2) { |i| print i, " " } - * Math::E.step(Math::PI, 0.2) { |f| print f, " " } - * - * <em>produces:</em> + * step(to = nil, by = 1) {|n| ... } -> self + * step(to = nil, by = 1) -> enumerator + * step(to = nil, by: 1) {|n| ... } -> self + * step(to = nil, by: 1) -> enumerator + * step(by: 1, to: ) {|n| ... } -> self + * step(by: 1, to: ) -> enumerator + * step(by: , to: nil) {|n| ... } -> self + * step(by: , to: nil) -> enumerator + * + * Generates a sequence of numbers; with a block given, traverses the sequence. + * + * Of the Core and Standard Library classes, + * Integer, Float, and Rational use this implementation. + * + * A quick example: + * + * squares = [] + * 1.step(by: 2, to: 10) {|i| squares.push(i*i) } + * squares # => [1, 9, 25, 49, 81] + * + * The generated sequence: + * + * - Begins with +self+. + * - Continues at intervals of +by+ (which may not be zero). + * - Ends with the last number that is within or equal to +to+; + * that is, less than or equal to +to+ if +by+ is positive, + * greater than or equal to +to+ if +by+ is negative. + * If +to+ is +nil+, the sequence is of infinite length. + * + * If a block is given, calls the block with each number in the sequence; + * returns +self+. If no block is given, returns an Enumerator::ArithmeticSequence. + * + * <b>Keyword Arguments</b> + * + * With keyword arguments +by+ and +to+, + * their values (or defaults) determine the step and limit: + * + * # Both keywords given. + * squares = [] + * 4.step(by: 2, to: 10) {|i| squares.push(i*i) } # => 4 + * squares # => [16, 36, 64, 100] + * cubes = [] + * 3.step(by: -1.5, to: -3) {|i| cubes.push(i*i*i) } # => 3 + * cubes # => [27.0, 3.375, 0.0, -3.375, -27.0] + * squares = [] + * 1.2.step(by: 0.2, to: 2.0) {|f| squares.push(f*f) } + * squares # => [1.44, 1.9599999999999997, 2.5600000000000005, 3.24, 4.0] + * + * squares = [] + * Rational(6/5).step(by: 0.2, to: 2.0) {|r| squares.push(r*r) } + * squares # => [1.0, 1.44, 1.9599999999999997, 2.5600000000000005, 3.24, 4.0] + * + * # Only keyword to given. + * squares = [] + * 4.step(to: 10) {|i| squares.push(i*i) } # => 4 + * squares # => [16, 25, 36, 49, 64, 81, 100] + * # Only by given. + * + * # Only keyword by given + * squares = [] + * 4.step(by:2) {|i| squares.push(i*i); break if i > 10 } + * squares # => [16, 36, 64, 100, 144] + * + * # No block given. + * e = 3.step(by: -1.5, to: -3) # => (3.step(by: -1.5, to: -3)) + * e.class # => Enumerator::ArithmeticSequence + * + * <b>Positional Arguments</b> + * + * With optional positional arguments +to+ and +by+, + * their values (or defaults) determine the step and limit: + * + * squares = [] + * 4.step(10, 2) {|i| squares.push(i*i) } # => 4 + * squares # => [16, 36, 64, 100] + * squares = [] + * 4.step(10) {|i| squares.push(i*i) } + * squares # => [16, 25, 36, 49, 64, 81, 100] + * squares = [] + * 4.step {|i| squares.push(i*i); break if i > 10 } # => nil + * squares # => [16, 25, 36, 49, 64, 81, 100, 121] + * + * <b>Implementation Notes</b> + * + * 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 - self)/step</i>. * - * 1 3 5 7 9 - * 2.71828182845905 2.91828182845905 3.11828182845905 */ 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); - if (argc == 1) { - to = argv[0]; - step = INT2FIX(1); + if (!rb_block_given_p()) { + VALUE by = Qundef; + + num_step_extract_args(argc, argv, &to, &step, &by); + if (!UNDEF_P(by)) { + step = by; + } + if (NIL_P(step)) { + step = INT2FIX(1); + } + else if (rb_equal(step, INT2FIX(0))) { + rb_raise(rb_eArgError, "step can't be 0"); + } + if ((NIL_P(to) || rb_obj_is_kind_of(to, rb_cNumeric)) && + rb_obj_is_kind_of(step, rb_cNumeric)) { + return rb_arith_seq_new(from, ID2SYM(rb_frame_this_func()), argc, argv, + num_step_size, from, to, step, FALSE); + } + + return SIZED_ENUMERATOR_KW(from, 2, ((VALUE [2]){to, step}), num_step_size, FALSE); } - else { - rb_check_arity(argc, 1, 2); - to = argv[0]; - step = argv[1]; - if (rb_equal(step, INT2FIX(0))) { - rb_raise(rb_eArgError, "step can't be 0"); - } + + desc = num_step_scan_args(argc, argv, &to, &step, TRUE, FALSE); + if (rb_equal(step, INT2FIX(0))) { + inf = 1; + } + else if (RB_FLOAT_TYPE_P(to)) { + double f = RFLOAT_VALUE(to); + inf = isinf(f) && (signbit(f) ? desc : !desc); } + else inf = 0; - if (FIXNUM_P(from) && FIXNUM_P(to) && FIXNUM_P(step)) { - long i, end, diff; - - i = FIX2LONG(from); - end = FIX2LONG(to); - diff = FIX2LONG(step); - - if (diff > 0) { - while (i <= end) { - rb_yield(LONG2FIX(i)); - i += diff; - } - } - else { - while (i >= end) { - rb_yield(LONG2FIX(i)); - i += diff; - } - } - } - else if (!ruby_float_step(from, to, step, FALSE)) { - VALUE i = from; - ID cmp; - - if (positive_int_p(step)) { - cmp = '>'; - } - else { - cmp = '<'; - } - for (;;) { - if (RTEST(rb_funcall(i, cmp, 1, to))) break; - rb_yield(i); - i = rb_funcall(i, '+', 1, step); - } + 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 { + 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)); + } + } + } + else if (!ruby_float_step(from, to, step, FALSE, 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)) -SIGNED_VALUE +long rb_num2long(VALUE val) { again: if (NIL_P(val)) { - rb_raise(rb_eTypeError, "no implicit conversion from nil to integer"); + rb_raise(rb_eTypeError, "no implicit conversion from nil to integer"); } if (FIXNUM_P(val)) return FIX2LONG(val); - switch (TYPE(val)) { - case T_FLOAT: - if (RFLOAT_VALUE(val) < LONG_MAX_PLUS_ONE - && RFLOAT_VALUE(val) > LONG_MIN_MINUS_ONE) { - return (SIGNED_VALUE)(RFLOAT_VALUE(val)); - } - else { - char buf[24]; - char *s; - - snprintf(buf, sizeof(buf), "%-.10g", RFLOAT_VALUE(val)); - if ((s = strchr(buf, ' ')) != 0) *s = '\0'; - rb_raise(rb_eRangeError, "float %s out of range of integer", buf); - } - - case T_BIGNUM: - return rb_big2long(val); - - default: - val = rb_to_int(val); - goto again; + else if (RB_FLOAT_TYPE_P(val)) { + if (RFLOAT_VALUE(val) < LONG_MAX_PLUS_ONE + && LONG_MIN_MINUS_ONE_IS_LESS_THAN(RFLOAT_VALUE(val))) { + return (long)RFLOAT_VALUE(val); + } + else { + FLOAT_OUT_OF_RANGE(val, "integer"); + } + } + else if (RB_BIGNUM_TYPE_P(val)) { + return rb_big2long(val); + } + else { + val = rb_to_int(val); + goto again; } } -VALUE -rb_num2ulong(VALUE val) +static unsigned long +rb_num2ulong_internal(VALUE val, int *wrap_p) { again: if (NIL_P(val)) { - rb_raise(rb_eTypeError, "no implicit conversion from nil to integer"); + rb_raise(rb_eTypeError, "no implicit conversion of nil into Integer"); } - if (FIXNUM_P(val)) return FIX2LONG(val); /* this is FIX2LONG, inteneded */ - - switch (TYPE(val)) { - case T_FLOAT: - if (RFLOAT_VALUE(val) < ULONG_MAX_PLUS_ONE - && RFLOAT_VALUE(val) > LONG_MIN_MINUS_ONE) { - return (VALUE)RFLOAT_VALUE(val); - } - else { - char buf[24]; - char *s; - - snprintf(buf, sizeof(buf), "%-.10g", RFLOAT_VALUE(val)); - if ((s = strchr(buf, ' ')) != 0) *s = '\0'; - rb_raise(rb_eRangeError, "float %s out of range of integer", buf); - } - - case T_BIGNUM: - return rb_big2ulong(val); - - default: - val = rb_to_int(val); - goto again; + 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_FLOAT_TYPE_P(val)) { + 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_BIGNUM_TYPE_P(val)) { + { + 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_VALUE void rb_out_of_int(SIGNED_VALUE num) { - rb_raise(rb_eRangeError, "integer %"PRIdVALUE " too %s to convert to `int'", - num, num < 0 ? "small" : "big"); + rb_raise(rb_eRangeError, "integer %"PRIdVALUE " too %s to convert to 'int'", + num, num < 0 ? "small" : "big"); } +#if SIZEOF_INT < SIZEOF_LONG static void -check_int(SIGNED_VALUE num) +check_int(long num) { - if ((SIGNED_VALUE)(int)num != num) { - rb_out_of_int(num); + if ((long)(int)num != num) { + rb_out_of_int(num); } } static void -check_uint(VALUE num, int sign) +check_uint(unsigned long num, int sign) { - static const VALUE mask = ~(VALUE)UINT_MAX; - if (sign) { - /* minus */ - if ((num & mask) != mask || (num & ~mask) <= INT_MAX) -#define VALUE_MSBMASK ((VALUE)1 << ((sizeof(VALUE) * CHAR_BIT) - 1)) - rb_raise(rb_eRangeError, "integer %"PRIdVALUE " too small to convert to `unsigned int'", num|VALUE_MSBMASK); + /* 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 ((num & mask) != 0) - rb_raise(rb_eRangeError, "integer %"PRIuVALUE " too big to convert to `unsigned int'", num); + /* plus */ + if (UINT_MAX < num) + rb_raise(rb_eRangeError, "integer %lu too big to convert to 'unsigned int'", num); } } @@ -2087,10 +3224,11 @@ rb_fix2int(VALUE val) unsigned long rb_num2uint(VALUE val) { - VALUE num = rb_num2ulong(val); + int wrap; + unsigned long num = rb_num2ulong_internal(val, &wrap); - check_uint(num, negative_int_p(val)); - return (unsigned long)num; + check_uint(num, wrap); + return num; } unsigned long @@ -2099,11 +3237,11 @@ rb_fix2uint(VALUE val) unsigned long num; if (!FIXNUM_P(val)) { - return rb_num2uint(val); + return rb_num2uint(val); } num = FIX2ULONG(val); - check_uint(num, negative_int_p(val)); + check_uint(num, FIXNUM_NEGATIVE_P(val)); return num; } #else @@ -2118,38 +3256,48 @@ rb_fix2int(VALUE val) { return FIX2INT(val); } + +unsigned long +rb_num2uint(VALUE val) +{ + return rb_num2ulong(val); +} + +unsigned long +rb_fix2uint(VALUE val) +{ + return RB_FIX2ULONG(val); +} #endif -void +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"); + rb_raise(rb_eRangeError, "integer %"PRIdVALUE " too %s to convert to 'short'", + num, num < 0 ? "small" : "big"); } static void -check_short(SIGNED_VALUE num) +check_short(long num) { - if ((SIGNED_VALUE)(short)num != num) { - rb_out_of_short(num); + if ((long)(short)num != num) { + rb_out_of_short(num); } } static void -check_ushort(VALUE num, int sign) +check_ushort(unsigned long num, int sign) { - static const VALUE mask = ~(VALUE)USHRT_MAX; - if (sign) { - /* minus */ - if ((num & mask) != mask || (num & ~mask) <= SHRT_MAX) -#define VALUE_MSBMASK ((VALUE)1 << ((sizeof(VALUE) * CHAR_BIT) - 1)) - rb_raise(rb_eRangeError, "integer %"PRIdVALUE " too small to convert to `unsigned short'", num|VALUE_MSBMASK); + /* 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 ((num & mask) != 0) - rb_raise(rb_eRangeError, "integer %"PRIuVALUE " too big to convert to `unsigned short'", num); + /* plus */ + if (USHRT_MAX < num) + rb_raise(rb_eRangeError, "integer %lu too big to convert to 'unsigned short'", num); } } @@ -2174,10 +3322,11 @@ rb_fix2short(VALUE val) unsigned short rb_num2ushort(VALUE val) { - VALUE num = rb_num2ulong(val); + int wrap; + unsigned long num = rb_num2ulong_internal(val, &wrap); - check_ushort(num, negative_int_p(val)); - return (unsigned long)num; + check_ushort(num, wrap); + return num; } unsigned short @@ -2186,24 +3335,24 @@ rb_fix2ushort(VALUE val) unsigned long num; if (!FIXNUM_P(val)) { - return rb_num2ushort(val); + return rb_num2ushort(val); } num = FIX2ULONG(val); - check_ushort(num, negative_int_p(val)); + check_ushort(num, FIXNUM_NEGATIVE_P(val)); return num; } VALUE rb_num2fix(VALUE val) { - SIGNED_VALUE v; + long v; if (FIXNUM_P(val)) return val; v = rb_num2long(val); if (!FIXABLE(v)) - rb_raise(rb_eRangeError, "integer %"PRIdVALUE " out of range of fixnum", v); + rb_raise(rb_eRangeError, "integer %ld out of range of fixnum", v); return LONG2FIX(v); } @@ -2215,45 +3364,37 @@ rb_num2fix(VALUE val) #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(VALUE val) { if (NIL_P(val)) { - rb_raise(rb_eTypeError, "no implicit conversion from nil"); + rb_raise(rb_eTypeError, "no implicit conversion from nil"); } if (FIXNUM_P(val)) return (LONG_LONG)FIX2LONG(val); - switch (TYPE(val)) { - case T_FLOAT: - if (RFLOAT_VALUE(val) < LLONG_MAX_PLUS_ONE - && RFLOAT_VALUE(val) > LLONG_MIN_MINUS_ONE) { - return (LONG_LONG)(RFLOAT_VALUE(val)); - } - else { - char buf[24]; - char *s; - - snprintf(buf, sizeof(buf), "%-.10g", RFLOAT_VALUE(val)); - if ((s = strchr(buf, ' ')) != 0) *s = '\0'; - rb_raise(rb_eRangeError, "float %s out of range of long long", buf); - } - - case T_BIGNUM: - return rb_big2ll(val); - - case T_STRING: - rb_raise(rb_eTypeError, "no implicit conversion from string"); - break; - - case T_TRUE: - case T_FALSE: - rb_raise(rb_eTypeError, "no implicit conversion from boolean"); - break; - - default: - break; + else if (RB_FLOAT_TYPE_P(val)) { + double d = RFLOAT_VALUE(val); + if (d < LLONG_MAX_PLUS_ONE && (LLONG_MIN_MINUS_ONE_IS_LESS_THAN(d))) { + return (LONG_LONG)d; + } + else { + FLOAT_OUT_OF_RANGE(val, "long long"); + } + } + else if (RB_BIGNUM_TYPE_P(val)) { + return rb_big2ll(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); @@ -2263,179 +3404,528 @@ rb_num2ll(VALUE val) unsigned LONG_LONG rb_num2ull(VALUE val) { - switch (TYPE(val)) { - case T_NIL: - rb_raise(rb_eTypeError, "no implicit conversion from nil"); - - case T_FIXNUM: - return (LONG_LONG)FIX2LONG(val); /* this is FIX2LONG, inteneded */ + if (NIL_P(val)) { + rb_raise(rb_eTypeError, "no implicit conversion of nil into Integer"); + } + else if (FIXNUM_P(val)) { + return (LONG_LONG)FIX2LONG(val); /* this is FIX2LONG, intended */ + } + else if (RB_FLOAT_TYPE_P(val)) { + 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_BIGNUM_TYPE_P(val)) { + return rb_big2ull(val); + } + else { + val = rb_to_int(val); + return NUM2ULL(val); + } +} - case T_FLOAT: - if (RFLOAT_VALUE(val) < ULLONG_MAX_PLUS_ONE - && RFLOAT_VALUE(val) > 0) { - return (unsigned LONG_LONG)(RFLOAT_VALUE(val)); - } - else { - char buf[24]; - char *s; +#endif /* HAVE_LONG_LONG */ - snprintf(buf, sizeof(buf), "%-.10g", RFLOAT_VALUE(val)); - if ((s = strchr(buf, ' ')) != 0) *s = '\0'; - rb_raise(rb_eRangeError, "float %s out of range of unsgined long long", buf); - } +// Conversion functions for unified 128-bit integer structures, +// These work with or without native 128-bit integer support. - case T_BIGNUM: - return rb_big2ull(val); +#ifndef HAVE_UINT128_T +// Helper function to build 128-bit value from bignum digits (fallback path). +static inline void +rb_uint128_from_bignum_digits_fallback(rb_uint128_t *result, BDIGIT *digits, size_t length) +{ + // Build the 128-bit value from bignum digits: + for (long i = length - 1; i >= 0; i--) { + // Shift both low and high parts: + uint64_t carry = result->parts.low >> (64 - (SIZEOF_BDIGIT * CHAR_BIT)); + result->parts.low = (result->parts.low << (SIZEOF_BDIGIT * CHAR_BIT)) | digits[i]; + result->parts.high = (result->parts.high << (SIZEOF_BDIGIT * CHAR_BIT)) | carry; + } +} - case T_STRING: - rb_raise(rb_eTypeError, "no implicit conversion from string"); - break; +// Helper function to convert absolute value of negative bignum to two's complement. +// Ruby stores negative bignums as absolute values, so we need to convert to two's complement. +static inline void +rb_uint128_twos_complement_negate(rb_uint128_t *value) +{ + if (value->parts.low == 0) { + value->parts.high = ~value->parts.high + 1; + } + else { + value->parts.low = ~value->parts.low + 1; + value->parts.high = ~value->parts.high + (value->parts.low == 0 ? 1 : 0); + } +} +#endif - case T_TRUE: - case T_FALSE: - rb_raise(rb_eTypeError, "no implicit conversion from boolean"); - break; +rb_uint128_t +rb_numeric_to_uint128(VALUE x) +{ + rb_uint128_t result = {0}; + if (RB_FIXNUM_P(x)) { + long value = RB_FIX2LONG(x); + if (value < 0) { + rb_raise(rb_eRangeError, "negative integer cannot be converted to unsigned 128-bit integer"); + } +#ifdef HAVE_UINT128_T + result.value = (uint128_t)value; +#else + result.parts.low = (uint64_t)value; + result.parts.high = 0; +#endif + return result; + } + else if (RB_BIGNUM_TYPE_P(x)) { + if (BIGNUM_NEGATIVE_P(x)) { + rb_raise(rb_eRangeError, "negative integer cannot be converted to unsigned 128-bit integer"); + } + size_t length = BIGNUM_LEN(x); +#ifdef HAVE_UINT128_T + if (length > roomof(SIZEOF_INT128_T, SIZEOF_BDIGIT)) { + rb_raise(rb_eRangeError, "bignum too big to convert into 'unsigned 128-bit integer'"); + } + BDIGIT *digits = BIGNUM_DIGITS(x); + result.value = 0; + for (long i = length - 1; i >= 0; i--) { + result.value = (result.value << (SIZEOF_BDIGIT * CHAR_BIT)) | digits[i]; + } +#else + // Check if bignum fits in 128 bits (16 bytes) + if (length > roomof(16, SIZEOF_BDIGIT)) { + rb_raise(rb_eRangeError, "bignum too big to convert into 'unsigned 128-bit integer'"); + } + BDIGIT *digits = BIGNUM_DIGITS(x); + rb_uint128_from_bignum_digits_fallback(&result, digits, length); +#endif + return result; + } + else { + rb_raise(rb_eTypeError, "not an integer"); + } +} - default: - break; +rb_int128_t +rb_numeric_to_int128(VALUE x) +{ + rb_int128_t result = {0}; + if (RB_FIXNUM_P(x)) { + long value = RB_FIX2LONG(x); +#ifdef HAVE_UINT128_T + result.value = (int128_t)value; +#else + if (value < 0) { + // Two's complement representation: for negative values, sign extend + // Convert to unsigned: for -1, we want all bits set + result.parts.low = (uint64_t)value; // This will be the two's complement representation + result.parts.high = UINT64_MAX; // Sign extend: all bits set for negative + } + else { + result.parts.low = (uint64_t)value; + result.parts.high = 0; + } +#endif + return result; + } + else if (RB_BIGNUM_TYPE_P(x)) { + size_t length = BIGNUM_LEN(x); +#ifdef HAVE_UINT128_T + if (length > roomof(SIZEOF_INT128_T, SIZEOF_BDIGIT)) { + rb_raise(rb_eRangeError, "bignum too big to convert into 'signed 128-bit integer'"); + } + BDIGIT *digits = BIGNUM_DIGITS(x); + uint128_t unsigned_result = 0; + for (long i = length - 1; i >= 0; i--) { + unsigned_result = (unsigned_result << (SIZEOF_BDIGIT * CHAR_BIT)) | digits[i]; + } + if (BIGNUM_NEGATIVE_P(x)) { + // Convert from two's complement + // Maximum negative value is 2^127 + if (unsigned_result > ((uint128_t)1 << 127)) { + rb_raise(rb_eRangeError, "bignum too big to convert into 'signed 128-bit integer'"); + } + result.value = -(int128_t)(unsigned_result - 1) - 1; + } + else { + // Maximum positive value is 2^127 - 1 + if (unsigned_result > (((uint128_t)1 << 127) - 1)) { + rb_raise(rb_eRangeError, "bignum too big to convert into 'signed 128-bit integer'"); + } + result.value = (int128_t)unsigned_result; + } +#else + if (length > roomof(16, SIZEOF_BDIGIT)) { + rb_raise(rb_eRangeError, "bignum too big to convert into 'signed 128-bit integer'"); + } + BDIGIT *digits = BIGNUM_DIGITS(x); + rb_uint128_t unsigned_result = {0}; + rb_uint128_from_bignum_digits_fallback(&unsigned_result, digits, length); + if (BIGNUM_NEGATIVE_P(x)) { + // Check if value fits in signed 128-bit (max negative is 2^127) + uint64_t max_neg_high = (uint64_t)1 << 63; + if (unsigned_result.parts.high > max_neg_high || (unsigned_result.parts.high == max_neg_high && unsigned_result.parts.low > 0)) { + rb_raise(rb_eRangeError, "bignum too big to convert into 'signed 128-bit integer'"); + } + // Convert from absolute value to two's complement (Ruby stores negative as absolute value) + rb_uint128_twos_complement_negate(&unsigned_result); + result.parts.low = unsigned_result.parts.low; + result.parts.high = (int64_t)unsigned_result.parts.high; // Sign extend + } + else { + // Check if value fits in signed 128-bit (max positive is 2^127 - 1) + // Max positive: high = 0x7FFFFFFFFFFFFFFF, low = 0xFFFFFFFFFFFFFFFF + uint64_t max_pos_high = ((uint64_t)1 << 63) - 1; + if (unsigned_result.parts.high > max_pos_high) { + rb_raise(rb_eRangeError, "bignum too big to convert into 'signed 128-bit integer'"); + } + result.parts.low = unsigned_result.parts.low; + result.parts.high = unsigned_result.parts.high; + } +#endif + return result; + } + else { + rb_raise(rb_eTypeError, "not an integer"); } +} - val = rb_to_int(val); - return NUM2ULL(val); +VALUE +rb_uint128_to_numeric(rb_uint128_t n) +{ +#ifdef HAVE_UINT128_T + if (n.value <= (uint128_t)RUBY_FIXNUM_MAX) { + return LONG2FIX((long)n.value); + } + return rb_uint128t2big(n.value); +#else + // If high part is zero and low part fits in fixnum + if (n.parts.high == 0 && n.parts.low <= (uint64_t)RUBY_FIXNUM_MAX) { + return LONG2FIX((long)n.parts.low); + } + // Convert to bignum by building it from the two 64-bit parts + VALUE bignum = rb_ull2big(n.parts.low); + if (n.parts.high > 0) { + VALUE high_bignum = rb_ull2big(n.parts.high); + // Multiply high part by 2^64 and add to low part + VALUE shifted_value = rb_int_lshift(high_bignum, INT2FIX(64)); + bignum = rb_int_plus(bignum, shifted_value); + } + return bignum; +#endif } -#endif /* HAVE_LONG_LONG */ +VALUE +rb_int128_to_numeric(rb_int128_t n) +{ +#ifdef HAVE_UINT128_T + if (FIXABLE(n.value)) { + return LONG2FIX((long)n.value); + } + return rb_int128t2big(n.value); +#else + int64_t high = (int64_t)n.parts.high; + // If it's a small positive value that fits in fixnum + if (high == 0 && n.parts.low <= (uint64_t)RUBY_FIXNUM_MAX) { + return LONG2FIX((long)n.parts.low); + } + // Check if it's negative (high bit of high part is set) + if (high < 0) { + // Negative value - convert from two's complement to absolute value + rb_uint128_t unsigned_value = {0}; + if (n.parts.low == 0) { + unsigned_value.parts.low = 0; + unsigned_value.parts.high = ~n.parts.high + 1; + } + else { + unsigned_value.parts.low = ~n.parts.low + 1; + unsigned_value.parts.high = ~n.parts.high + (unsigned_value.parts.low == 0 ? 1 : 0); + } + VALUE bignum = rb_uint128_to_numeric(unsigned_value); + return rb_int_uminus(bignum); + } + else { + // Positive value + union uint128_int128_conversion conversion = { + .int128 = n + }; + return rb_uint128_to_numeric(conversion.uint128); + } +#endif +} -/* +/******************************************************************** + * * 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>. + * An \Integer object represents an integer value. + * + * You can create an \Integer object explicitly with: + * + * - An {integer literal}[rdoc-ref:syntax/literals.rdoc@Integer+Literals]. + * + * You can convert certain objects to Integers with: + * + * - Method #Integer. + * + * An attempt to add a singleton method to an instance of this class + * causes an exception to be raised. + * + * == What's Here + * + * First, what's elsewhere. Class \Integer: + * + * - Inherits from + * {class Numeric}[rdoc-ref:Numeric@What-27s+Here] + * and {class Object}[rdoc-ref:Object@What-27s+Here]. + * - Includes {module Comparable}[rdoc-ref:Comparable@What-27s+Here]. + * + * Here, class \Integer provides methods for: + * + * - {Querying}[rdoc-ref:Integer@Querying] + * - {Comparing}[rdoc-ref:Integer@Comparing] + * - {Converting}[rdoc-ref:Integer@Converting] + * - {Other}[rdoc-ref:Integer@Other] + * + * === Querying + * + * - #allbits?: Returns whether all bits in +self+ are set. + * - #anybits?: Returns whether any bits in +self+ are set. + * - #nobits?: Returns whether no bits in +self+ are set. + * + * === Comparing + * + * - #<: Returns whether +self+ is less than the given value. + * - #<=: Returns whether +self+ is less than or equal to the given value. + * - #<=>: Returns a number indicating whether +self+ is less than, equal + * to, or greater than the given value. + * - #== (aliased as #===): Returns whether +self+ is equal to the given + * value. + * - #>: Returns whether +self+ is greater than the given value. + * - #>=: Returns whether +self+ is greater than or equal to the given value. + * + * === Converting + * + * - ::sqrt: Returns the integer square root of the given value. + * - ::try_convert: Returns the given value converted to an \Integer. + * - #% (aliased as #modulo): Returns +self+ modulo the given value. + * - #&: Returns the bitwise AND of +self+ and the given value. + * - #*: Returns the product of +self+ and the given value. + * - #**: Returns the value of +self+ raised to the power of the given value. + * - #+: Returns the sum of +self+ and the given value. + * - #-: Returns the difference of +self+ and the given value. + * - #/: Returns the quotient of +self+ and the given value. + * - #<<: Returns the value of +self+ after a leftward bit-shift. + * - #>>: Returns the value of +self+ after a rightward bit-shift. + * - #[]: Returns a slice of bits from +self+. + * - #^: Returns the bitwise EXCLUSIVE OR of +self+ and the given value. + * - #|: Returns the bitwise OR of +self+ and the given value. + * - #ceil: Returns the smallest number greater than or equal to +self+. + * - #chr: Returns a 1-character string containing the character + * represented by the value of +self+. + * - #digits: Returns an array of integers representing the base-radix digits + * of +self+. + * - #div: Returns the integer result of dividing +self+ by the given value. + * - #divmod: Returns a 2-element array containing the quotient and remainder + * results of dividing +self+ by the given value. + * - #fdiv: Returns the Float result of dividing +self+ by the given value. + * - #floor: Returns the greatest number smaller than or equal to +self+. + * - #pow: Returns the modular exponentiation of +self+. + * - #pred: Returns the integer predecessor of +self+. + * - #remainder: Returns the remainder after dividing +self+ by the given value. + * - #round: Returns +self+ rounded to the nearest value with the given precision. + * - #succ (aliased as #next): Returns the integer successor of +self+. + * - #to_f: Returns +self+ converted to a Float. + * - #to_s (aliased as #inspect): Returns a string containing the place-value + * representation of +self+ in the given radix. + * - #truncate: Returns +self+ truncated to the given precision. + * + * === Other + * + * - #downto: Calls the given block with each integer value from +self+ + * down to the given value. + * - #times: Calls the given block +self+ times with each integer + * in <tt>(0..self-1)</tt>. + * - #upto: Calls the given block with each integer value from +self+ + * up to the given value. * */ -/* - * call-seq: - * int.to_i -> integer - * int.to_int -> integer - * int.floor -> integer - * int.ceil -> integer - * int.truncate -> integer - * - * As <i>int</i> is already an <code>Integer</code>, all these - * methods simply return the receiver. - */ +VALUE +rb_int_odd_p(VALUE num) +{ + if (FIXNUM_P(num)) { + return RBOOL(num & 2); + } + else { + RUBY_ASSERT(RB_BIGNUM_TYPE_P(num)); + return rb_big_odd_p(num); + } +} static VALUE -int_to_i(VALUE num) +int_even_p(VALUE num) { - return num; + if (FIXNUM_P(num)) { + return RBOOL((num & 2) == 0); + } + else { + RUBY_ASSERT(RB_BIGNUM_TYPE_P(num)); + return rb_big_even_p(num); + } } -/* - * call-seq: - * int.integer? -> true - * - * Always returns <code>true</code>. - */ - -static VALUE -int_int_p(VALUE num) +VALUE +rb_int_even_p(VALUE num) { - return Qtrue; + return int_even_p(num); } /* * call-seq: - * int.odd? -> true or false + * allbits?(mask) -> true or false + * + * Returns +true+ if all bits that are set (=1) in +mask+ + * are also set in +self+; returns +false+ otherwise. + * + * Example values: + * + * 0b1010101 self + * 0b1010100 mask + * 0b1010100 self & mask + * true self.allbits?(mask) + * + * 0b1010100 self + * 0b1010101 mask + * 0b1010100 self & mask + * false self.allbits?(mask) + * + * Related: Integer#anybits?, Integer#nobits?. * - * Returns <code>true</code> if <i>int</i> is an odd number. */ static VALUE -int_odd_p(VALUE num) +int_allbits_p(VALUE num, VALUE mask) { - if (rb_funcall(num, '%', 1, INT2FIX(2)) != INT2FIX(0)) { - return Qtrue; - } - return Qfalse; + mask = rb_to_int(mask); + return rb_int_equal(rb_int_and(num, mask), mask); } /* * call-seq: - * int.even? -> true or false + * anybits?(mask) -> true or false + * + * Returns +true+ if any bit that is set (=1) in +mask+ + * is also set in +self+; returns +false+ otherwise. + * + * Example values: + * + * 0b10000010 self + * 0b11111111 mask + * 0b10000010 self & mask + * true self.anybits?(mask) + * + * 0b00000000 self + * 0b11111111 mask + * 0b00000000 self & mask + * false self.anybits?(mask) + * + * Related: Integer#allbits?, Integer#nobits?. * - * Returns <code>true</code> if <i>int</i> is an even number. */ static VALUE -int_even_p(VALUE num) +int_anybits_p(VALUE num, VALUE mask) { - if (rb_funcall(num, '%', 1, INT2FIX(2)) == INT2FIX(0)) { - return Qtrue; - } - return Qfalse; + mask = rb_to_int(mask); + return RBOOL(!int_zero_p(rb_int_and(num, mask))); } /* * call-seq: - * fixnum.next -> integer - * fixnum.succ -> integer + * nobits?(mask) -> true or false + * + * Returns +true+ if no bit that is set (=1) in +mask+ + * is also set in +self+; returns +false+ otherwise. + * + * Example values: + * + * 0b11110000 self + * 0b00001111 mask + * 0b00000000 self & mask + * true self.nobits?(mask) + * + * 0b00000001 self + * 0b11111111 mask + * 0b00000001 self & mask + * false self.nobits?(mask) * - * Returns the <code>Integer</code> equal to <i>int</i> + 1. + * Related: Integer#allbits?, Integer#anybits?. * - * 1.next #=> 2 - * (-1).next #=> 0 */ static VALUE -fix_succ(VALUE num) +int_nobits_p(VALUE num, VALUE mask) { - long i = FIX2LONG(num) + 1; - return LONG2NUM(i); + mask = rb_to_int(mask); + return RBOOL(int_zero_p(rb_int_and(num, mask))); } /* * call-seq: - * int.next -> integer - * int.succ -> integer + * succ -> next_integer + * + * Returns the successor integer of +self+ (equivalent to <tt>self + 1</tt>): * - * Returns the <code>Integer</code> equal to <i>int</i> + 1. + * 1.succ #=> 2 + * -1.succ #=> 0 * - * 1.next #=> 2 - * (-1).next #=> 0 + * Related: Integer#pred (predecessor value). */ VALUE rb_int_succ(VALUE num) { if (FIXNUM_P(num)) { - long i = FIX2LONG(num) + 1; - return LONG2NUM(i); + long i = FIX2LONG(num) + 1; + return LONG2NUM(i); } - return rb_funcall(num, '+', 1, INT2FIX(1)); + if (RB_BIGNUM_TYPE_P(num)) { + return rb_big_plus(num, INT2FIX(1)); + } + return num_funcall1(num, '+', INT2FIX(1)); } #define int_succ rb_int_succ /* * call-seq: - * int.pred -> integer + * pred -> next_integer + * + * Returns the predecessor of +self+ (equivalent to <tt>self - 1</tt>): * - * Returns the <code>Integer</code> equal to <i>int</i> - 1. + * 1.pred #=> 0 + * -1.pred #=> -2 + * + * Related: Integer#succ (successor value). * - * 1.pred #=> 0 - * (-1).pred #=> -2 */ -VALUE +static VALUE rb_int_pred(VALUE num) { if (FIXNUM_P(num)) { - long i = FIX2LONG(num) - 1; - return LONG2NUM(i); + long i = FIX2LONG(num) - 1; + return LONG2NUM(i); } - return rb_funcall(num, '-', 1, INT2FIX(1)); + if (RB_BIGNUM_TYPE_P(num)) { + return rb_big_minus(num, INT2FIX(1)); + } + return num_funcall1(num, '-', INT2FIX(1)); } #define int_pred rb_int_pred @@ -2447,31 +3937,38 @@ rb_enc_uint_chr(unsigned int code, rb_encoding *enc) 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; + 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; + 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)); + rb_raise(rb_eRangeError, "invalid codepoint 0x%X in %s", code, rb_enc_name(enc)); } return str; } -/* - * call-seq: - * int.chr([encoding]) -> string +/* call-seq: + * chr -> string + * chr(encoding) -> string + * + * Returns a 1-character string containing the character + * represented by the value of +self+, according to the given +encoding+. + * + * 65.chr # => "A" + * 0.chr # => "\x00" + * 255.chr # => "\xFF" + * string = 255.chr(Encoding::UTF_8) + * string.encoding # => Encoding::UTF_8 + * + * Raises an exception if +self+ is negative. * - * Returns a string containing the character represented by the - * receiver's value according to +encoding+. + * Related: Integer#ord. * - * 65.chr #=> "A" - * 230.chr #=> "\346" - * 255.chr(Encoding::UTF_8) #=> "\303\277" */ static VALUE @@ -2484,33 +3981,32 @@ int_chr(int argc, VALUE *argv, VALUE num) if (rb_num_to_uint(num, &i) == 0) { } else if (FIXNUM_P(num)) { - rb_raise(rb_eRangeError, "%ld out of char range", FIX2LONG(num)); + rb_raise(rb_eRangeError, "%ld out of char range", FIX2LONG(num)); } else { - rb_raise(rb_eRangeError, "bignum out of char range"); + 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); - } + if (0xff < i) { + enc = rb_default_internal_encoding(); + if (!enc) { + rb_raise(rb_eRangeError, "%u 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; + break; default: - rb_check_arity(argc, 0, 1); - break; + rb_error_arity(argc, 0, 1); } enc = rb_to_encoding(argv[0]); if (!enc) enc = rb_ascii8bit_encoding(); @@ -2519,339 +4015,381 @@ int_chr(int argc, VALUE *argv, VALUE num) } /* - * call-seq: - * int.ord -> self - * - * Returns the int itself. - * - * ?a.ord #=> 97 - * - * This method is intended for compatibility to - * character constant in Ruby 1.9. - * For example, ?a.ord returns 97 both in 1.8 and 1.9. + * Fixnum */ static VALUE -int_ord(VALUE num) +fix_uminus(VALUE num) { - return num; + return LONG2NUM(-FIX2LONG(num)); } -/******************************************************************** - * - * Document-class: Fixnum - * - * 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>. - */ - - -/* - * call-seq: - * -fix -> integer - * - * Negates <code>fix</code> (which might return a Bignum). - */ - -static VALUE -fix_uminus(VALUE num) +VALUE +rb_int_uminus(VALUE num) { - return LONG2NUM(-FIX2LONG(num)); + if (FIXNUM_P(num)) { + return fix_uminus(num); + } + else { + RUBY_ASSERT(RB_BIGNUM_TYPE_P(num)); + return rb_big_uminus(num); + } } VALUE rb_fix2str(VALUE x, int base) { - extern const char ruby_digitmap[]; - char buf[SIZEOF_VALUE*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, "invalid 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_usascii_str_new2("0"); + return rb_usascii_str_new2("0"); } if (val < 0) { - val = -val; - neg = 1; + u = 1 + (unsigned long)(-(val + 1)); /* u = -val avoiding overflow */ + neg = 1; + } + else { + u = val; } - *--b = '\0'; do { - *--b = ruby_digitmap[(int)(val % base)]; - } while (val /= base); + *--b = ruby_digitmap[(int)(u % base)]; + } while (u /= base); if (neg) { - *--b = '-'; + *--b = '-'; } - return rb_usascii_str_new2(b); + return rb_usascii_str_new(b, e - b); +} + +static VALUE rb_fix_to_s_static[10]; + +VALUE +rb_fix_to_s(VALUE x) +{ + long i = FIX2LONG(x); + if (i >= 0 && i < 10) { + return rb_fix_to_s_static[i]; + } + return rb_fix2str(x, 10); } /* * call-seq: - * fix.to_s(base=10) -> string + * to_s(base = 10) -> string * - * Returns a string containing the representation of <i>fix</i> radix - * <i>base</i> (between 2 and 36). + * Returns a string containing the place-value representation of +self+ + * in radix +base+ (in 2..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" + * 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" * + * Raises an exception if +base+ is out of range. */ -static VALUE -fix_to_s(int argc, VALUE *argv, VALUE x) + +VALUE +rb_int_to_s(int argc, VALUE *argv, VALUE x) { int base; - if (argc == 0) base = 10; - else { - VALUE b; + if (rb_check_arity(argc, 0, 1)) + base = NUM2INT(argv[0]); + else + base = 10; + return rb_int2str(x, base); +} - rb_scan_args(argc, argv, "01", &b); - base = NUM2INT(b); +VALUE +rb_int2str(VALUE x, int base) +{ + if (FIXNUM_P(x)) { + return rb_fix2str(x, base); + } + else if (RB_BIGNUM_TYPE_P(x)) { + return rb_big2str(x, base); } - return rb_fix2str(x, base); + return rb_any_to_s(x); } -/* - * call-seq: - * fix + 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. - */ - static VALUE fix_plus(VALUE x, VALUE y) { if (FIXNUM_P(y)) { - long a, b, c; - VALUE r; - - a = FIX2LONG(x); - b = FIX2LONG(y); - c = a + b; - r = LONG2NUM(c); - - return r; + return rb_fix_plus_fix(x, y); } - switch (TYPE(y)) { - case T_BIGNUM: - return rb_big_plus(y, x); - case T_FLOAT: - return DBL2NUM((double)FIX2LONG(x) + RFLOAT_VALUE(y)); - default: - return rb_num_coerce_bin(x, y, '+'); + else if (RB_BIGNUM_TYPE_P(y)) { + return rb_big_plus(y, x); + } + else if (RB_FLOAT_TYPE_P(y)) { + 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, '+'); + } +} + +VALUE +rb_fix_plus(VALUE x, VALUE y) +{ + return fix_plus(x, y); } /* - * call-seq: - * fix - numeric -> numeric_result + * call-seq: + * self + other -> numeric + * + * Returns the sum of +self+ and +other+: + * + * 1 + 1 # => 2 + * 1 + -1 # => 0 + * 1 + 0 # => 1 + * 1 + -2 # => -1 + * 1 + Complex(1, 0) # => (2+0i) + * 1 + Rational(1, 1) # => (2/1) * - * Performs subtraction: the class of the resulting object depends on - * the class of <code>numeric</code> and on the magnitude of the - * result. + * For a computation involving Floats, the result may be inexact (see Float#+): + * + * 1 + 3.14 # => 4.140000000000001 */ +VALUE +rb_int_plus(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return fix_plus(x, y); + } + else if (RB_BIGNUM_TYPE_P(x)) { + return rb_big_plus(x, y); + } + return rb_num_coerce_bin(x, y, '+'); +} + static VALUE 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 = LONG2NUM(c); - - return r; - } - switch (TYPE(y)) { - case T_BIGNUM: - x = rb_int2big(FIX2LONG(x)); - return rb_big_minus(x, y); - case T_FLOAT: - return DBL2NUM((double)FIX2LONG(x) - RFLOAT_VALUE(y)); - default: - return rb_num_coerce_bin(x, y, '-'); + return rb_fix_minus_fix(x, y); + } + else if (RB_BIGNUM_TYPE_P(y)) { + x = rb_int2big(FIX2LONG(x)); + return rb_big_minus(x, y); + } + else if (RB_FLOAT_TYPE_P(y)) { + return DBL2NUM((double)FIX2LONG(x) - RFLOAT_VALUE(y)); + } + else { + return rb_num_coerce_bin(x, y, '-'); } } -#define SQRT_LONG_MAX ((SIGNED_VALUE)1<<((SIZEOF_LONG*CHAR_BIT-1)/2)) -/*tests if N*N would overflow*/ -#define FIT_SQRT_LONG(n) (((n)<SQRT_LONG_MAX)&&((n)>=-SQRT_LONG_MAX)) - /* - * call-seq: - * fix * numeric -> numeric_result + * call-seq: + * self - other -> numeric + * + * Returns the difference of +self+ and +other+: + * + * 4 - 2 # => 2 + * -4 - 2 # => -6 + * -4 - -2 # => -2 + * 4 - 2.0 # => 2.0 + * 4 - Rational(2, 1) # => (2/1) + * 4 - Complex(2, 0) # => (2+0i) * - * Performs multiplication: the class of the resulting object depends on - * the class of <code>numeric</code> and on the magnitude of the - * result. */ +VALUE +rb_int_minus(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return fix_minus(x, y); + } + else if (RB_BIGNUM_TYPE_P(x)) { + return rb_big_minus(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)) + static VALUE fix_mul(VALUE x, VALUE y) { if (FIXNUM_P(y)) { -#ifdef __HP_cc -/* avoids an optimization bug of HP aC++/ANSI C B3910B A.06.05 [Jul 25 2005] */ - volatile -#endif - long a, b; -#if SIZEOF_LONG * 2 <= SIZEOF_LONG_LONG - LONG_LONG d; -#else - VALUE r; -#endif + return rb_fix_mul_fix(x, y); + } + else if (RB_BIGNUM_TYPE_P(y)) { + switch (x) { + case INT2FIX(0): return x; + case INT2FIX(1): return y; + } + return rb_big_mul(y, x); + } + else if (RB_FLOAT_TYPE_P(y)) { + return DBL2NUM((double)FIX2LONG(x) * RFLOAT_VALUE(y)); + } + else if (RB_TYPE_P(y, T_COMPLEX)) { + return rb_complex_mul(y, x); + } + else { + return rb_num_coerce_bin(x, y, '*'); + } +} - a = FIX2LONG(x); - b = FIX2LONG(y); +/* + * call-seq: + * self * other -> numeric + * + * Returns the numeric product of +self+ and +other+: + * + * 4 * 2 # => 8 + * -4 * 2 # => -8 + * 4 * -2 # => -8 + * 4 * 2.0 # => 8.0 + * 4 * Rational(1, 3) # => (4/3) + * 4 * Complex(2, 0) # => (8+0i) + * + */ -#if SIZEOF_LONG * 2 <= SIZEOF_LONG_LONG - d = (LONG_LONG)a * b; - if (FIXABLE(d)) return LONG2FIX(d); - return rb_ll2inum(d); -#else - if (FIT_SQRT_LONG(a) && FIT_SQRT_LONG(b)) - return LONG2FIX(a*b); - if (a == 0) return x; - if (MUL_OVERFLOW_FIXNUM_P(a, b)) - r = rb_big_mul(rb_int2big(a), rb_int2big(b)); - else - r = LONG2FIX(a * b); - return r; -#endif +VALUE +rb_int_mul(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return fix_mul(x, y); } - switch (TYPE(y)) { - case T_BIGNUM: - return rb_big_mul(y, x); - case T_FLOAT: - return DBL2NUM((double)FIX2LONG(x) * RFLOAT_VALUE(y)); - default: - return rb_num_coerce_bin(x, y, '*'); + else if (RB_BIGNUM_TYPE_P(x)) { + return rb_big_mul(x, y); } + return rb_num_coerce_bin(x, y, '*'); } -static void -fixdivmod(long x, long y, long *divp, long *modp) +static double +fix_fdiv_double(VALUE x, VALUE y) { - long div, mod; - - if (y == 0) rb_num_zerodiv(); - if (y < 0) { - if (x < 0) - div = -x / -y; - else - div = - (x / -y); + if (FIXNUM_P(y)) { + long iy = FIX2LONG(y); +#if SIZEOF_LONG * CHAR_BIT > DBL_MANT_DIG + if ((iy < 0 ? -iy : iy) >= (1L << DBL_MANT_DIG)) { + return rb_big_fdiv_double(rb_int2big(FIX2LONG(x)), rb_int2big(iy)); + } +#endif + return double_div_double(FIX2LONG(x), iy); + } + else if (RB_BIGNUM_TYPE_P(y)) { + return rb_big_fdiv_double(rb_int2big(FIX2LONG(x)), y); + } + else if (RB_FLOAT_TYPE_P(y)) { + return double_div_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, idFdiv)); + } +} + +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) && gcd != INT2FIX(1)) { + x = rb_int_idiv(x, gcd); + y = rb_int_idiv(y, gcd); + } } - mod = x - div*y; - if ((mod < 0 && y > 0) || (mod > 0 && y < 0)) { - mod += y; - div -= 1; + if (FIXNUM_P(x)) { + return fix_fdiv_double(x, y); + } + else if (RB_BIGNUM_TYPE_P(x)) { + return rb_big_fdiv_double(x, y); + } + else { + return nan(""); } - if (divp) *divp = div; - if (modp) *modp = mod; } /* * call-seq: - * fix.fdiv(numeric) -> float + * fdiv(numeric) -> float * - * Returns the floating point result of dividing <i>fix</i> by - * <i>numeric</i>. + * Returns the Float result of dividing +self+ by +numeric+: * - * 654321.fdiv(13731) #=> 47.6528293642124 - * 654321.fdiv(13731.24) #=> 47.6519964693647 + * 4.fdiv(2) # => 2.0 + * 4.fdiv(-2) # => -2.0 + * -4.fdiv(2) # => -2.0 + * 4.fdiv(2.0) # => 2.0 + * 4.fdiv(Rational(3, 4)) # => 5.333333333333333 + * + * Raises an exception if +numeric+ cannot be converted to a Float. * */ -static VALUE -fix_fdiv(VALUE x, VALUE y) +VALUE +rb_int_fdiv(VALUE x, VALUE y) { - if (FIXNUM_P(y)) { - return DBL2NUM((double)FIX2LONG(x) / (double)FIX2LONG(y)); - } - switch (TYPE(y)) { - case T_BIGNUM: - return rb_big_fdiv(rb_int2big(FIX2LONG(x)), y); - case T_FLOAT: - return DBL2NUM((double)FIX2LONG(x) / RFLOAT_VALUE(y)); - default: - return rb_num_coerce_bin(x, y, rb_intern("fdiv")); + if (RB_INTEGER_TYPE_P(x)) { + return DBL2NUM(rb_int_fdiv_double(x, y)); } + return Qnil; } static VALUE fix_divide(VALUE x, VALUE y, ID op) { if (FIXNUM_P(y)) { - long div; - - fixdivmod(FIX2LONG(x), FIX2LONG(y), &div, 0); - return LONG2NUM(div); - } - switch (TYPE(y)) { - case T_BIGNUM: - x = rb_int2big(FIX2LONG(x)); - return rb_big_div(x, y); - case 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)); - } - } - case T_RATIONAL: - if (op == '/' && FIX2LONG(x) == 1) - return rb_rational_reciprocal(y); - /* fall through */ - default: - return rb_num_coerce_bin(x, y, op); + if (FIXNUM_ZERO_P(y)) rb_num_zerodiv(); + return rb_fix_div_fix(x, y); + } + else if (RB_BIGNUM_TYPE_P(y)) { + x = rb_int2big(FIX2LONG(x)); + return rb_big_div(x, y); + } + else if (RB_FLOAT_TYPE_P(y)) { + if (op == '/') { + double d = FIX2LONG(x); + return rb_flo_div_flo(DBL2NUM(d), y); + } + else { + VALUE v; + if (RFLOAT_VALUE(y) == 0) rb_num_zerodiv(); + v = fix_divide(x, y, '/'); + return flo_floor(0, 0, v); + } + } + 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); } } -/* - * call-seq: - * fix / 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. - */ - static VALUE fix_div(VALUE x, VALUE y) { @@ -2860,127 +4398,325 @@ fix_div(VALUE x, VALUE y) /* * call-seq: - * fix.div(numeric) -> integer + * self / other -> numeric + * + * Returns the quotient of +self+ and +other+. + * + * For integer +other+, truncates the result to an integer: + * + * 4 / 3 # => 1 + * 4 / -3 # => -2 + * -4 / 3 # => -2 + * -4 / -3 # => 1 + * + * For non-integer +other+, returns a non-integer result: + * + * 4 / 3.0 # => 1.3333333333333333 + * 4 / Rational(3, 1) # => (4/3) + * 4 / Complex(3, 0) # => ((4/3)+0i) * - * Performs integer division: returns integer value. */ +VALUE +rb_int_div(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return fix_div(x, y); + } + else if (RB_BIGNUM_TYPE_P(x)) { + return rb_big_div(x, y); + } + return Qnil; +} + static VALUE fix_idiv(VALUE x, VALUE y) { - return fix_divide(x, y, rb_intern("div")); + return fix_divide(x, y, id_div); } /* * call-seq: - * fix % other -> real - * fix.modulo(other) -> real + * div(numeric) -> integer + * + * Performs integer division; returns the integer result of dividing +self+ + * by +numeric+: + * + * 4.div(3) # => 1 + * 4.div(-3) # => -2 + * -4.div(3) # => -2 + * -4.div(-3) # => 1 + * 4.div(3.0) # => 1 + * 4.div(Rational(3, 1)) # => 1 + * + * Raises an exception if +numeric+ does not have method +div+. * - * Returns <code>fix</code> modulo <code>other</code>. - * See <code>numeric.divmod</code> for more information. */ +VALUE +rb_int_idiv(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return fix_idiv(x, y); + } + else if (RB_BIGNUM_TYPE_P(x)) { + return rb_big_idiv(x, y); + } + return num_div(x, y); +} + static VALUE fix_mod(VALUE x, VALUE y) { if (FIXNUM_P(y)) { - long mod; + if (FIXNUM_ZERO_P(y)) rb_num_zerodiv(); + return rb_fix_mod_fix(x, y); + } + else if (RB_BIGNUM_TYPE_P(y)) { + x = rb_int2big(FIX2LONG(x)); + return rb_big_modulo(x, y); + } + else if (RB_FLOAT_TYPE_P(y)) { + return DBL2NUM(ruby_float_mod((double)FIX2LONG(x), RFLOAT_VALUE(y))); + } + else { + return rb_num_coerce_bin(x, y, '%'); + } +} - fixdivmod(FIX2LONG(x), FIX2LONG(y), 0, &mod); - return LONG2NUM(mod); +/* + * call-seq: + * self % other -> real_numeric + * + * Returns +self+ modulo +other+ as a real numeric (\Integer, \Float, or \Rational). + * + * For integer +n+ and real number +r+, these expressions are equivalent: + * + * n % r + * n-r*(n/r).floor + * n.divmod(r)[1] + * + * See Numeric#divmod. + * + * Examples: + * + * 10 % 2 # => 0 + * 10 % 3 # => 1 + * 10 % 4 # => 2 + * + * 10 % -2 # => 0 + * 10 % -3 # => -2 + * 10 % -4 # => -2 + * + * 10 % 3.0 # => 1.0 + * 10 % Rational(3, 1) # => (1/1) + * + */ +VALUE +rb_int_modulo(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return fix_mod(x, y); } - switch (TYPE(y)) { - case T_BIGNUM: - x = rb_int2big(FIX2LONG(x)); - return rb_big_modulo(x, y); - case T_FLOAT: - return DBL2NUM(ruby_float_mod((double)FIX2LONG(x), RFLOAT_VALUE(y))); - default: - return rb_num_coerce_bin(x, y, '%'); + else if (RB_BIGNUM_TYPE_P(x)) { + return rb_big_modulo(x, y); } + return num_modulo(x, y); } /* * call-seq: - * fix.divmod(numeric) -> array + * remainder(other) -> real_number + * + * Returns the remainder after dividing +self+ by +other+. + * + * Examples: + * + * 11.remainder(4) # => 3 + * 11.remainder(-4) # => 3 + * -11.remainder(4) # => -3 + * -11.remainder(-4) # => -3 + * + * 12.remainder(4) # => 0 + * 12.remainder(-4) # => 0 + * -12.remainder(4) # => 0 + * -12.remainder(-4) # => 0 + * + * 13.remainder(4.0) # => 1.0 + * 13.remainder(Rational(4, 1)) # => (1/1) * - * See <code>Numeric#divmod</code>. */ + +static VALUE +int_remainder(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + if (FIXNUM_P(y)) { + VALUE z = fix_mod(x, y); + RUBY_ASSERT(FIXNUM_P(z)); + if (z != INT2FIX(0) && (SIGNED_VALUE)(x ^ y) < 0) + z = fix_minus(z, y); + return z; + } + else if (!RB_BIGNUM_TYPE_P(y)) { + return num_remainder(x, y); + } + x = rb_int2big(FIX2LONG(x)); + } + else if (!RB_BIGNUM_TYPE_P(x)) { + return Qnil; + } + return rb_big_remainder(x, y); +} + static VALUE fix_divmod(VALUE x, VALUE y) { if (FIXNUM_P(y)) { - long div, mod; - - fixdivmod(FIX2LONG(x), FIX2LONG(y), &div, &mod); - - return rb_assoc_new(LONG2NUM(div), LONG2NUM(mod)); - } - switch (TYPE(y)) { - case T_BIGNUM: - x = rb_int2big(FIX2LONG(x)); - return rb_big_divmod(x, y); - case 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); - } - default: - return rb_num_coerce_bin(x, y, rb_intern("divmod")); + 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); + } + else if (RB_BIGNUM_TYPE_P(y)) { + x = rb_int2big(FIX2LONG(x)); + return rb_big_divmod(x, y); + } + else if (RB_FLOAT_TYPE_P(y)) { + { + 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); + } +} + +/* + * call-seq: + * divmod(other) -> array + * + * Returns a 2-element array <tt>[q, r]</tt>, where + * + * q = (self/other).floor # Quotient + * r = self % other # Remainder + * + * Examples: + * + * 11.divmod(4) # => [2, 3] + * 11.divmod(-4) # => [-3, -1] + * -11.divmod(4) # => [-3, 1] + * -11.divmod(-4) # => [2, -3] + * + * 12.divmod(4) # => [3, 0] + * 12.divmod(-4) # => [-3, 0] + * -12.divmod(4) # => [-3, 0] + * -12.divmod(-4) # => [3, 0] + * + * 13.divmod(4.0) # => [3, 1.0] + * 13.divmod(Rational(4, 1)) # => [3, (1/1)] + * + */ +VALUE +rb_int_divmod(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return fix_divmod(x, y); + } + else if (RB_BIGNUM_TYPE_P(x)) { + return rb_big_divmod(x, y); } + return Qnil; } +/* + * call-seq: + * self ** exponent -> numeric + * + * Returns +self+ raised to the power +exponent+: + * + * 2 ** 3 # => 8 + * 2 ** -3 # => (1/8) + * -2 ** 3 # => -8 + * -2 ** -3 # => (-1/8) + * 2 ** 3.3 # => 9.849155306759329 + * 2 ** Rational(3, 1) # => (8/1) + * 2 ** Complex(3, 0) # => (8+0i) + * + */ + static VALUE 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; + z = x; else - neg = 0; + 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 (z != 1) v = rb_big_mul(rb_int2big(neg ? -z : z), v); - return v; - } - x = x * x; - y >>= 1; - } - { + while (y % 2 == 0) { + if (!FIT_SQRT_LONG(x)) { + goto bignum; + } + x = x * x; + y >>= 1; + } + { if (MUL_OVERFLOW_FIXNUM_P(x, z)) { - goto bignum; - } - z = x * z; - } + goto bignum; + } + z = x * z; + } } while (--y); if (neg) z = -z; return LONG2NUM(z); + + 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; } -/* - * call-seq: - * fix ** numeric -> numeric_result - * - * Raises <code>fix</code> to the <code>numeric</code> power, which may - * be negative or fractional. - * - * 2 ** 3 #=> 8 - * 2 ** -1 #=> (1/2) - * 2 ** 0.5 #=> 1.4142135623731 - */ +VALUE +rb_int_positive_pow(long x, unsigned long y) +{ + return int_pow(x, y); +} + +static VALUE +fix_pow_inverted(VALUE x, VALUE minusb) +{ + if (x == INT2FIX(0)) { + rb_num_zerodiv(); + UNREACHABLE_RETURN(Qundef); + } + else { + VALUE y = rb_int_pow(x, minusb); + + if (RB_FLOAT_TYPE_P(y)) { + double d = pow((double)FIX2LONG(x), RFLOAT_VALUE(y)); + return DBL2NUM(1.0 / d); + } + else { + return rb_rational_raw(INT2FIX(1), y); + } + } +} static VALUE fix_pow(VALUE x, VALUE y) @@ -2988,341 +4724,589 @@ fix_pow(VALUE x, VALUE y) long a = FIX2LONG(x); if (FIXNUM_P(y)) { - long b = FIX2LONG(y); - - if (a == 1) return INT2FIX(1); - if (a == -1) { - if (b % 2 == 0) - return INT2FIX(1); - else - return INT2FIX(-1); - } - if (b < 0) - return rb_funcall(rb_rational_raw1(x), rb_intern("**"), 1, 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 int_pow(a, b); - } - switch (TYPE(y)) { - case T_BIGNUM: - if (a == 1) return INT2FIX(1); - if (a == -1) { - if (int_even_p(y)) return INT2FIX(1); - else return INT2FIX(-1); - } - if (negative_int_p(y)) - return rb_funcall(rb_rational_raw1(x), rb_intern("**"), 1, y); - if (a == 0) return INT2FIX(0); - x = rb_int2big(FIX2LONG(x)); - return rb_big_pow(x, y); - case T_FLOAT: - if (RFLOAT_VALUE(y) == 0.0) return DBL2NUM(1.0); - if (a == 0) { - return DBL2NUM(RFLOAT_VALUE(y) < 0 ? INFINITY : 0.0); - } - if (a == 1) return DBL2NUM(1.0); - { - double dy = RFLOAT_VALUE(y); - if (a < 0 && dy != round(dy)) - return rb_funcall(rb_complex_raw1(x), rb_intern("**"), 1, y); - return DBL2NUM(pow((double)a, dy)); - } - default: - return rb_num_coerce_bin(x, y, rb_intern("**")); + long b = FIX2LONG(y); + + if (a == 1) return INT2FIX(1); + if (a == -1) return INT2FIX(b % 2 ? -1 : 1); + if (b < 0) return fix_pow_inverted(x, fix_uminus(y)); + if (b == 0) return INT2FIX(1); + if (b == 1) return x; + if (a == 0) return INT2FIX(0); + return int_pow(a, b); + } + else if (RB_BIGNUM_TYPE_P(y)) { + if (a == 1) return INT2FIX(1); + if (a == -1) return INT2FIX(int_even_p(y) ? 1 : -1); + if (BIGNUM_NEGATIVE_P(y)) return fix_pow_inverted(x, rb_big_uminus(y)); + if (a == 0) return INT2FIX(0); + x = rb_int2big(FIX2LONG(x)); + return rb_big_pow(x, y); + } + else if (RB_FLOAT_TYPE_P(y)) { + double dy = RFLOAT_VALUE(y); + if (dy == 0.0) return DBL2NUM(1.0); + if (a == 0) { + return DBL2NUM(dy < 0 ? HUGE_VAL : 0.0); + } + if (a == 1) return DBL2NUM(1.0); + if (a < 0 && dy != round(dy)) + return rb_dbl_complex_new_polar_pi(pow(-(double)a, dy), dy); + return DBL2NUM(pow((double)a, dy)); + } + else { + return rb_num_coerce_bin(x, y, idPow); } } /* - * call-seq: - * fix == other -> true or false - * - * Return <code>true</code> if <code>fix</code> equals <code>other</code> - * numerically. + * call-seq: + * self ** exponent -> numeric + * + * Returns +self+ raised to the power +exponent+: + * + * # Result for non-negative Integer exponent is Integer. + * 2 ** 0 # => 1 + * 2 ** 1 # => 2 + * 2 ** 2 # => 4 + * 2 ** 3 # => 8 + * -2 ** 3 # => -8 + * # Result for negative Integer exponent is Rational, not Float. + * 2 ** -3 # => (1/8) + * -2 ** -3 # => (-1/8) + * + * # Result for Float exponent is Float. + * 2 ** 0.0 # => 1.0 + * 2 ** 1.0 # => 2.0 + * 2 ** 2.0 # => 4.0 + * 2 ** 3.0 # => 8.0 + * -2 ** 3.0 # => -8.0 + * 2 ** -3.0 # => 0.125 + * -2 ** -3.0 # => -0.125 + * + * # Result for non-negative Complex exponent is Complex with Integer parts. + * 2 ** Complex(0, 0) # => (1+0i) + * 2 ** Complex(1, 0) # => (2+0i) + * 2 ** Complex(2, 0) # => (4+0i) + * 2 ** Complex(3, 0) # => (8+0i) + * -2 ** Complex(3, 0) # => (-8+0i) + * # Result for negative Complex exponent is Complex with Rational parts. + * 2 ** Complex(-3, 0) # => ((1/8)+(0/1)*i) + * -2 ** Complex(-3, 0) # => ((-1/8)+(0/1)*i) + * + * # Result for Rational exponent is Rational. + * 2 ** Rational(0, 1) # => (1/1) + * 2 ** Rational(1, 1) # => (2/1) + * 2 ** Rational(2, 1) # => (4/1) + * 2 ** Rational(3, 1) # => (8/1) + * -2 ** Rational(3, 1) # => (-8/1) + * 2 ** Rational(-3, 1) # => (1/8) + * -2 ** Rational(-3, 1) # => (-1/8) * - * 1 == 2 #=> false - * 1 == 1.0 #=> true */ +VALUE +rb_int_pow(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return fix_pow(x, y); + } + else if (RB_BIGNUM_TYPE_P(x)) { + return rb_big_pow(x, y); + } + return Qnil; +} + +VALUE +rb_num_pow(VALUE x, VALUE y) +{ + VALUE z = rb_int_pow(x, y); + if (!NIL_P(z)) return z; + if (RB_FLOAT_TYPE_P(x)) return rb_float_pow(x, y); + if (SPECIAL_CONST_P(x)) return Qnil; + switch (BUILTIN_TYPE(x)) { + case T_COMPLEX: + return rb_complex_pow(x, y); + case T_RATIONAL: + return rb_rational_pow(x, y); + default: + break; + } + return Qnil; +} static VALUE fix_equal(VALUE x, VALUE y) { if (x == y) return Qtrue; if (FIXNUM_P(y)) return Qfalse; - switch (TYPE(y)) { - case T_BIGNUM: - return rb_big_eq(y, x); - case T_FLOAT: + else if (RB_BIGNUM_TYPE_P(y)) { + return rb_big_eq(y, x); + } + else if (RB_FLOAT_TYPE_P(y)) { return rb_integer_float_eq(x, y); - default: - return num_equal(x, y); + } + else { + return num_equal(x, y); } } /* * call-seq: - * fix <=> numeric -> -1, 0, +1 or nil + * self == other -> true or false * - * Comparison---Returns -1, 0, +1 or nil depending on whether +fix+ is less - * than, equal to, or greater than +numeric+. This is the basis for the tests - * in Comparable. + * Returns whether +self+ is numerically equal to +other+: * - * +nil+ is returned if the two values are incomparable. + * 1 == 2 #=> false + * 1 == 1.0 #=> true + * + * Related: Integer#eql? (requires +other+ to be an \Integer). */ +VALUE +rb_int_equal(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return fix_equal(x, y); + } + else if (RB_BIGNUM_TYPE_P(x)) { + return rb_big_eq(x, y); + } + return Qnil; +} + static VALUE fix_cmp(VALUE x, VALUE y) { if (x == y) return INT2FIX(0); if (FIXNUM_P(y)) { - if (FIX2LONG(x) > FIX2LONG(y)) return INT2FIX(1); - return INT2FIX(-1); + if (FIX2LONG(x) > FIX2LONG(y)) return INT2FIX(1); + return INT2FIX(-1); + } + else if (RB_BIGNUM_TYPE_P(y)) { + VALUE cmp = rb_big_cmp(y, x); + switch (cmp) { + case INT2FIX(+1): return INT2FIX(-1); + case INT2FIX(-1): return INT2FIX(+1); + } + return cmp; } - switch (TYPE(y)) { - case T_BIGNUM: - return rb_big_cmp(rb_int2big(FIX2LONG(x)), y); - case T_FLOAT: + else if (RB_FLOAT_TYPE_P(y)) { return rb_integer_float_cmp(x, y); - default: - return rb_num_coerce_cmp(x, y, rb_intern("<=>")); + } + else { + return rb_num_coerce_cmp(x, y, id_cmp); } } /* - * call-seq: - * fix > real -> true or false + * call-seq: + * self <=> other -> -1, 0, 1, or nil + * + * Compares +self+ and +other+. + * + * Returns: * - * Returns <code>true</code> if the value of <code>fix</code> is - * greater than that of <code>real</code>. + * - +-1+, if +self+ is less than +other+. + * - +0+, if +self+ is equal to +other+. + * - +1+, if +self+ is greater then +other+. + * - +nil+, if +self+ and +other+ are incomparable. + * + * Examples: + * + * 1 <=> 2 # => -1 + * 1 <=> 1 # => 0 + * 1 <=> 1.0 # => 0 + * 1 <=> Rational(1, 1) # => 0 + * 1 <=> Complex(1, 0) # => 0 + * 1 <=> 0 # => 1 + * 1 <=> 'foo' # => nil + * + * \Class \Integer includes module Comparable, + * each of whose methods uses Integer#<=> for comparison. */ +VALUE +rb_int_cmp(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return fix_cmp(x, y); + } + else if (RB_BIGNUM_TYPE_P(x)) { + return rb_big_cmp(x, y); + } + else { + rb_raise(rb_eNotImpError, "need to define '<=>' in %s", rb_obj_classname(x)); + } +} + static VALUE fix_gt(VALUE x, VALUE y) { if (FIXNUM_P(y)) { - if (FIX2LONG(x) > FIX2LONG(y)) return Qtrue; - return Qfalse; - } - switch (TYPE(y)) { - case T_BIGNUM: - return FIX2INT(rb_big_cmp(rb_int2big(FIX2LONG(x)), y)) > 0 ? Qtrue : Qfalse; - case T_FLOAT: - return rb_integer_float_cmp(x, y) == INT2FIX(1) ? Qtrue : Qfalse; - default: - return rb_num_coerce_relop(x, y, '>'); + return RBOOL(FIX2LONG(x) > FIX2LONG(y)); + } + else if (RB_BIGNUM_TYPE_P(y)) { + return RBOOL(rb_big_cmp(y, x) == INT2FIX(-1)); + } + else if (RB_FLOAT_TYPE_P(y)) { + return RBOOL(rb_integer_float_cmp(x, y) == INT2FIX(1)); + } + else { + return rb_num_coerce_relop(x, y, '>'); } } /* - * call-seq: - * fix >= real -> true or false + * call-seq: + * self > other -> true or false + * + * Returns whether the value of +self+ is greater than the value of +other+; + * +other+ must be numeric, but may not be Complex: + * + * 1 > 0 # => true + * 1 > 1 # => false + * 1 > 2 # => false + * 1 > 0.5 # => true + * 1 > Rational(1, 2) # => true + * + * Raises an exception if the comparison cannot be made. * - * Returns <code>true</code> if the value of <code>fix</code> is - * greater than or equal to that of <code>real</code>. */ +VALUE +rb_int_gt(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return fix_gt(x, y); + } + else if (RB_BIGNUM_TYPE_P(x)) { + return rb_big_gt(x, y); + } + return Qnil; +} + static VALUE fix_ge(VALUE x, VALUE y) { if (FIXNUM_P(y)) { - if (FIX2LONG(x) >= FIX2LONG(y)) return Qtrue; - return Qfalse; + return RBOOL(FIX2LONG(x) >= FIX2LONG(y)); } - switch (TYPE(y)) { - case T_BIGNUM: - return FIX2INT(rb_big_cmp(rb_int2big(FIX2LONG(x)), y)) >= 0 ? Qtrue : Qfalse; - case T_FLOAT: - { - VALUE rel = rb_integer_float_cmp(x, y); - return rel == INT2FIX(1) || rel == INT2FIX(0) ? Qtrue : Qfalse; - } - default: - return rb_num_coerce_relop(x, y, rb_intern(">=")); + else if (RB_BIGNUM_TYPE_P(y)) { + return RBOOL(rb_big_cmp(y, x) != INT2FIX(+1)); + } + else if (RB_FLOAT_TYPE_P(y)) { + VALUE rel = rb_integer_float_cmp(x, y); + return RBOOL(rel == INT2FIX(1) || rel == INT2FIX(0)); + } + else { + return rb_num_coerce_relop(x, y, idGE); } } /* - * call-seq: - * fix < real -> true or false + * call-seq: + * self >= other -> true or false + * + * Returns whether the value of +self+ is greater than or equal to the value of +other+; + * +other+ must be numeric, but may not be Complex: + * + * 1 >= 0 # => true + * 1 >= 1 # => true + * 1 >= 2 # => false + * 1 >= 0.5 # => true + * 1 >= Rational(1, 2) # => true + * + * Raises an exception if the comparison cannot be made. * - * Returns <code>true</code> if the value of <code>fix</code> is - * less than that of <code>real</code>. */ +VALUE +rb_int_ge(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return fix_ge(x, y); + } + else if (RB_BIGNUM_TYPE_P(x)) { + return rb_big_ge(x, y); + } + return Qnil; +} + static VALUE fix_lt(VALUE x, VALUE y) { if (FIXNUM_P(y)) { - if (FIX2LONG(x) < FIX2LONG(y)) return Qtrue; - return Qfalse; - } - switch (TYPE(y)) { - case T_BIGNUM: - return FIX2INT(rb_big_cmp(rb_int2big(FIX2LONG(x)), y)) < 0 ? Qtrue : Qfalse; - case T_FLOAT: - return rb_integer_float_cmp(x, y) == INT2FIX(-1) ? Qtrue : Qfalse; - default: - return rb_num_coerce_relop(x, y, '<'); + return RBOOL(FIX2LONG(x) < FIX2LONG(y)); + } + else if (RB_BIGNUM_TYPE_P(y)) { + return RBOOL(rb_big_cmp(y, x) == INT2FIX(+1)); + } + else if (RB_FLOAT_TYPE_P(y)) { + return RBOOL(rb_integer_float_cmp(x, y) == INT2FIX(-1)); + } + else { + return rb_num_coerce_relop(x, y, '<'); } } /* * call-seq: - * fix <= real -> true or false + * self < other -> true or false + * + * Returns whether the value of +self+ is less than the value of +other+; + * +other+ must be numeric, but may not be Complex: + * + * 1 < 0 # => false + * 1 < 1 # => false + * 1 < 2 # => true + * 1 < 0.5 # => false + * 1 < Rational(1, 2) # => false * - * Returns <code>true</code> if the value of <code>fix</code> is - * less than or equal to that of <code>real</code>. */ static VALUE +int_lt(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return fix_lt(x, y); + } + else if (RB_BIGNUM_TYPE_P(x)) { + return rb_big_lt(x, y); + } + return Qnil; +} + +static VALUE fix_le(VALUE x, VALUE y) { if (FIXNUM_P(y)) { - if (FIX2LONG(x) <= FIX2LONG(y)) return Qtrue; - return Qfalse; + return RBOOL(FIX2LONG(x) <= FIX2LONG(y)); } - switch (TYPE(y)) { - case T_BIGNUM: - return FIX2INT(rb_big_cmp(rb_int2big(FIX2LONG(x)), y)) <= 0 ? Qtrue : Qfalse; - case T_FLOAT: - { - VALUE rel = rb_integer_float_cmp(x, y); - return rel == INT2FIX(-1) || rel == INT2FIX(0) ? Qtrue : Qfalse; - } - default: - return rb_num_coerce_relop(x, y, rb_intern("<=")); + else if (RB_BIGNUM_TYPE_P(y)) { + return RBOOL(rb_big_cmp(y, x) != INT2FIX(-1)); + } + else if (RB_FLOAT_TYPE_P(y)) { + VALUE rel = rb_integer_float_cmp(x, y); + return RBOOL(rel == INT2FIX(-1) || rel == INT2FIX(0)); + } + else { + return rb_num_coerce_relop(x, y, idLE); } } /* * call-seq: - * ~fix -> integer + * self <= other -> true or false + * + * Returns whether the value of +self+ is less than or equal to the value of +other+; + * +other+ must be numeric, but may not be Complex: + * + * 1 <= 0 # => false + * 1 <= 1 # => true + * 1 <= 2 # => true + * 1 <= 0.5 # => false + * 1 <= Rational(1, 2) # => false + * + * Raises an exception if the comparison cannot be made. * - * One's complement: returns a number where each bit is flipped. */ static VALUE -fix_rev(VALUE num) +int_le(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return fix_le(x, y); + } + else if (RB_BIGNUM_TYPE_P(x)) { + return rb_big_le(x, y); + } + return Qnil; +} + +static VALUE +fix_comp(VALUE num) { return ~num | FIXNUM_FLAG; } -static int -bit_coerce(VALUE *x, VALUE *y, int err) +VALUE +rb_int_comp(VALUE num) { - if (!FIXNUM_P(*y) && !RB_TYPE_P(*y, T_BIGNUM)) { - VALUE orig = *x; - do_coerce(x, y, err); - if (!FIXNUM_P(*x) && !RB_TYPE_P(*x, T_BIGNUM) - && !FIXNUM_P(*y) && !RB_TYPE_P(*y, T_BIGNUM)) { - if (!err) return FALSE; - coerce_failed(orig, *y); - } + if (FIXNUM_P(num)) { + return fix_comp(num); } - return TRUE; + else if (RB_BIGNUM_TYPE_P(num)) { + return rb_big_comp(num); + } + return Qnil; +} + +static VALUE +num_funcall_bit_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_check_funcall(x, func, 1, &y); } VALUE rb_num_coerce_bit(VALUE x, VALUE y, ID func) { - bit_coerce(&x, &y, TRUE); - return rb_funcall(x, func, 1, y); -} + VALUE ret, args[3]; -/* - * call-seq: - * fix & integer -> integer_result - * - * Bitwise AND. - */ + 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 (UNDEF_P(ret)) { + /* show the original object, not coerced object */ + coerce_failed(x, y); + } + return ret; +} static VALUE fix_and(VALUE x, VALUE y) { if (FIXNUM_P(y)) { - long val = FIX2LONG(x) & FIX2LONG(y); - return LONG2NUM(val); + long val = FIX2LONG(x) & FIX2LONG(y); + return LONG2NUM(val); } - if (RB_TYPE_P(y, T_BIGNUM)) { - return rb_big_and(y, x); + if (RB_BIGNUM_TYPE_P(y)) { + return rb_big_and(y, x); } - bit_coerce(&x, &y, TRUE); - return rb_funcall(x, rb_intern("&"), 1, y); + return rb_num_coerce_bit(x, y, '&'); } /* - * call-seq: - * fix | integer -> integer_result + * call-seq: + * self & other -> integer + * + * Bitwise AND; each bit in the result is 1 if both corresponding bits + * in +self+ and +other+ are 1, 0 otherwise: + * + * "%04b" % (0b0101 & 0b0110) # => "0100" + * + * Raises an exception if +other+ is not an \Integer. + * + * Related: Integer#| (bitwise OR), Integer#^ (bitwise EXCLUSIVE OR). * - * Bitwise OR. */ +VALUE +rb_int_and(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return fix_and(x, y); + } + else if (RB_BIGNUM_TYPE_P(x)) { + return rb_big_and(x, y); + } + return Qnil; +} + static VALUE fix_or(VALUE x, VALUE y) { if (FIXNUM_P(y)) { - long val = FIX2LONG(x) | FIX2LONG(y); - return LONG2NUM(val); + long val = FIX2LONG(x) | FIX2LONG(y); + return LONG2NUM(val); } - if (RB_TYPE_P(y, T_BIGNUM)) { - return rb_big_or(y, x); + if (RB_BIGNUM_TYPE_P(y)) { + return rb_big_or(y, x); } - bit_coerce(&x, &y, TRUE); - return rb_funcall(x, rb_intern("|"), 1, y); + return rb_num_coerce_bit(x, y, '|'); } /* - * call-seq: - * fix ^ integer -> integer_result + * call-seq: + * self | other -> integer + * + * Bitwise OR; each bit in the result is 1 if either corresponding bit + * in +self+ or +other+ is 1, 0 otherwise: + * + * "%04b" % (0b0101 | 0b0110) # => "0111" + * + * Raises an exception if +other+ is not an \Integer. + * + * Related: Integer#& (bitwise AND), Integer#^ (bitwise EXCLUSIVE OR). * - * Bitwise EXCLUSIVE OR. */ static VALUE +int_or(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return fix_or(x, y); + } + else if (RB_BIGNUM_TYPE_P(x)) { + return rb_big_or(x, y); + } + return Qnil; +} + +static VALUE fix_xor(VALUE x, VALUE y) { if (FIXNUM_P(y)) { - long val = FIX2LONG(x) ^ FIX2LONG(y); - return LONG2NUM(val); + long val = FIX2LONG(x) ^ FIX2LONG(y); + return LONG2NUM(val); } - if (RB_TYPE_P(y, T_BIGNUM)) { - return rb_big_xor(y, x); + if (RB_BIGNUM_TYPE_P(y)) { + return rb_big_xor(y, x); } - bit_coerce(&x, &y, TRUE); - return rb_funcall(x, rb_intern("^"), 1, y); + return rb_num_coerce_bit(x, y, '^'); } -static VALUE fix_lshift(long, unsigned long); -static VALUE fix_rshift(long, unsigned long); - /* - * call-seq: - * fix << count -> integer + * call-seq: + * self ^ other -> integer + * + * Bitwise EXCLUSIVE OR; each bit in the result is 1 if the corresponding bits + * in +self+ and +other+ are different, 0 otherwise: + * + * "%04b" % (0b0101 ^ 0b0110) # => "0011" + * + * Raises an exception if +other+ is not an \Integer. + * + * Related: Integer#& (bitwise AND), Integer#| (bitwise OR). * - * Shifts _fix_ left _count_ positions (right if _count_ is negative). */ +VALUE +rb_int_xor(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return fix_xor(x, y); + } + else if (RB_BIGNUM_TYPE_P(x)) { + return rb_big_xor(x, y); + } + return Qnil; +} + static VALUE rb_fix_lshift(VALUE x, VALUE y) { long val, width; val = NUM2LONG(x); + if (!val) return (rb_to_int(y), INT2FIX(0)); if (!FIXNUM_P(y)) - return rb_big_lshift(rb_int2big(val), y); + return rb_big_lshift(rb_int2big(val), y); width = FIX2LONG(y); if (width < 0) - return fix_rshift(val, (unsigned long)-width); + return fix_rshift(val, (unsigned long)-width); return fix_lshift(val, width); } @@ -3330,32 +5314,55 @@ static VALUE fix_lshift(long val, unsigned long width) { 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)); + || ((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); } /* - * call-seq: - * fix >> count -> integer + * call-seq: + * self << count -> integer + * + * Returns +self+ with bits shifted +count+ positions to the left, + * or to the right if +count+ is negative: + * + * n = 0b11110000 + * "%08b" % (n << 1) # => "111100000" + * "%08b" % (n << 3) # => "11110000000" + * "%08b" % (n << -1) # => "01111000" + * "%08b" % (n << -3) # => "00011110" + * + * Related: Integer#>>. * - * Shifts _fix_ right _count_ positions (left if _count_ is negative). */ +VALUE +rb_int_lshift(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return rb_fix_lshift(x, y); + } + else if (RB_BIGNUM_TYPE_P(x)) { + return rb_big_lshift(x, y); + } + return Qnil; +} + static VALUE rb_fix_rshift(VALUE x, VALUE y) { long i, val; val = FIX2LONG(x); + if (!val) return (rb_to_int(y), INT2FIX(0)); if (!FIXNUM_P(y)) - return rb_big_rshift(rb_int2big(val), y); + return rb_big_rshift(rb_int2big(val), y); i = FIX2LONG(y); if (i == 0) return x; if (i < 0) - return fix_lshift(val, (unsigned long)-i); + return fix_lshift(val, (unsigned long)-i); return fix_rshift(val, i); } @@ -3363,8 +5370,8 @@ static VALUE fix_rshift(long val, unsigned long i) { if (i >= sizeof(long)*CHAR_BIT-1) { - if (val < 0) return INT2FIX(-1); - return INT2FIX(0); + if (val < 0) return INT2FIX(-1); + return INT2FIX(0); } val = RSHIFT(val, i); return LONG2FIX(val); @@ -3372,78 +5379,231 @@ fix_rshift(long val, unsigned long i) /* * call-seq: - * fix[n] -> 0, 1 + * self >> count -> integer * - * 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. + * Returns +self+ with bits shifted +count+ positions to the right, + * or to the left if +count+ is negative: * - * a = 0b11001100101010 - * 30.downto(0) do |n| print a[n] end + * n = 0b11110000 + * "%08b" % (n >> 1) # => "01111000" + * "%08b" % (n >> 3) # => "00011110" + * "%08b" % (n >> -1) # => "111100000" + * "%08b" % (n >> -3) # => "11110000000" * - * <em>produces:</em> + * Related: Integer#<<. * - * 0000000000000000011001100101010 */ -static VALUE -fix_aref(VALUE fix, VALUE idx) +VALUE +rb_int_rshift(VALUE x, VALUE y) +{ + if (FIXNUM_P(x)) { + return rb_fix_rshift(x, y); + } + else if (RB_BIGNUM_TYPE_P(x)) { + return rb_big_rshift(x, y); + } + return Qnil; +} + +VALUE +rb_fix_aref(VALUE fix, VALUE idx) { long val = FIX2LONG(fix); long i; idx = rb_to_int(idx); if (!FIXNUM_P(idx)) { - idx = rb_big_norm(idx); - if (!FIXNUM_P(idx)) { - if (!RBIGNUM_SIGN(idx) || val >= 0) - return INT2FIX(0); - return INT2FIX(1); - } + idx = rb_big_norm(idx); + if (!FIXNUM_P(idx)) { + if (!BIGNUM_SIGN(idx) || val >= 0) + return INT2FIX(0); + return INT2FIX(1); + } } i = FIX2LONG(idx); if (i < 0) return INT2FIX(0); - if (SIZEOF_LONG*CHAR_BIT-1 < i) { - if (val < 0) return INT2FIX(1); - return INT2FIX(0); + if (SIZEOF_LONG*CHAR_BIT-1 <= i) { + if (val < 0) return INT2FIX(1); + return INT2FIX(0); } if (val & (1L<<i)) - return INT2FIX(1); + return INT2FIX(1); return INT2FIX(0); } + +/* copied from "r_less" in range.c */ +/* compares _a_ and _b_ and returns: + * < 0: a < b + * = 0: a = b + * > 0: a > b or non-comparable + */ +static int +compare_indexes(VALUE a, VALUE b) +{ + VALUE r = rb_funcall(a, id_cmp, 1, b); + + if (NIL_P(r)) + return INT_MAX; + return rb_cmpint(r, a, b); +} + +static VALUE +generate_mask(VALUE len) +{ + return rb_int_minus(rb_int_lshift(INT2FIX(1), len), INT2FIX(1)); +} + +static VALUE +int_aref2(VALUE num, VALUE beg, VALUE len) +{ + if (RB_TYPE_P(num, T_BIGNUM)) { + return rb_big_aref2(num, beg, len); + } + else { + num = rb_int_rshift(num, beg); + VALUE mask = generate_mask(len); + return rb_int_and(num, mask); + } +} + +static VALUE +int_aref1(VALUE num, VALUE arg) +{ + VALUE beg, end; + int excl; + + if (rb_range_values(arg, &beg, &end, &excl)) { + if (NIL_P(beg)) { + /* beginless range */ + if (!RTEST(num_negative_p(end))) { + if (!excl) end = rb_int_plus(end, INT2FIX(1)); + VALUE mask = generate_mask(end); + if (int_zero_p(rb_int_and(num, mask))) { + return INT2FIX(0); + } + else { + rb_raise(rb_eArgError, "The beginless range for Integer#[] results in infinity"); + } + } + else { + return INT2FIX(0); + } + } + + int cmp = compare_indexes(beg, end); + if (!NIL_P(end) && cmp < 0) { + VALUE len = rb_int_minus(end, beg); + if (!excl) len = rb_int_plus(len, INT2FIX(1)); + return int_aref2(num, beg, len); + } + else if (cmp == 0) { + if (excl) return INT2FIX(0); + arg = beg; + goto one_bit; + } + return rb_int_rshift(num, beg); + } + +one_bit: + if (FIXNUM_P(num)) { + return rb_fix_aref(num, arg); + } + else if (RB_BIGNUM_TYPE_P(num)) { + return rb_big_aref(num, arg); + } + return Qnil; +} + /* * call-seq: - * fix.to_f -> float + * self[offset] -> 0 or 1 + * self[offset, size] -> integer + * self[range] -> integer + * + * Returns a slice of bits from +self+. + * + * With argument +offset+, returns the bit at the given offset, + * where offset 0 refers to the least significant bit: + * + * n = 0b10 # => 2 + * n[0] # => 0 + * n[1] # => 1 + * n[2] # => 0 + * n[3] # => 0 + * + * In principle, <code>n[i]</code> is equivalent to <code>(n >> i) & 1</code>. + * Thus, negative index always returns zero: + * + * 255[-1] # => 0 * - * Converts <i>fix</i> to a <code>Float</code>. + * With arguments +offset+ and +size+, returns +size+ bits from +self+, + * beginning at +offset+ and including bits of greater significance: * + * n = 0b111000 # => 56 + * "%010b" % n[0, 10] # => "0000111000" + * "%010b" % n[4, 10] # => "0000000011" + * + * With argument +range+, returns <tt>range.size</tt> bits from +self+, + * beginning at <tt>range.begin</tt> and including bits of greater significance: + * + * n = 0b111000 # => 56 + * "%010b" % n[0..9] # => "0000111000" + * "%010b" % n[4..9] # => "0000000011" + * + * Raises an exception if the slice cannot be constructed. */ static VALUE -fix_to_f(VALUE num) +int_aref(int const argc, VALUE * const argv, VALUE const num) { - double val; - - val = (double)FIX2LONG(num); + rb_check_arity(argc, 1, 2); + if (argc == 2) { + return int_aref2(num, argv[0], argv[1]); + } + return int_aref1(num, argv[0]); - return DBL2NUM(val); + return Qnil; } /* * call-seq: - * fix.abs -> integer - * fix.magnitude -> integer + * to_f -> float + * + * Converts +self+ to a Float: + * + * 1.to_f # => 1.0 + * -1.to_f # => -1.0 * - * Returns the absolute value of <i>fix</i>. + * If the value of +self+ does not fit in a Float, + * the result is infinity: * - * -12345.abs #=> 12345 - * 12345.abs #=> 12345 + * (10**400).to_f # => Infinity + * (-10**400).to_f # => -Infinity * */ static VALUE +int_to_f(VALUE num) +{ + double val; + + if (FIXNUM_P(num)) { + val = (double)FIX2LONG(num); + } + else if (RB_BIGNUM_TYPE_P(num)) { + val = rb_big2dbl(num); + } + else { + rb_raise(rb_eNotImpError, "Unknown subclass for to_f: %s", rb_obj_classname(num)); + } + + return DBL2NUM(val); +} + +static VALUE fix_abs(VALUE fix) { long i = FIX2LONG(fix); @@ -3453,47 +5613,208 @@ fix_abs(VALUE fix) return LONG2NUM(i); } +VALUE +rb_int_abs(VALUE num) +{ + if (FIXNUM_P(num)) { + return fix_abs(num); + } + else if (RB_BIGNUM_TYPE_P(num)) { + return rb_big_abs(num); + } + return Qnil; +} + +static VALUE +fix_size(VALUE fix) +{ + return INT2FIX(sizeof(long)); +} + +VALUE +rb_int_size(VALUE num) +{ + if (FIXNUM_P(num)) { + return fix_size(num); + } + else if (RB_BIGNUM_TYPE_P(num)) { + return rb_big_size_m(num); + } + return Qnil; +} + +static VALUE +rb_fix_bit_length(VALUE fix) +{ + long v = FIX2LONG(fix); + if (v < 0) + v = ~v; + return LONG2FIX(bit_length(v)); +} + +VALUE +rb_int_bit_length(VALUE num) +{ + if (FIXNUM_P(num)) { + return rb_fix_bit_length(num); + } + else if (RB_BIGNUM_TYPE_P(num)) { + return rb_big_bit_length(num); + } + return Qnil; +} + +static VALUE +rb_fix_digits(VALUE fix, long base) +{ + VALUE digits; + long x = FIX2LONG(fix); + + RUBY_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 >= base) { + long q = x % base; + rb_ary_push(digits, LONG2NUM(q)); + x /= base; + } + rb_ary_push(digits, LONG2NUM(x)); + + return digits; +} + +static VALUE +rb_int_digits_bigbase(VALUE num, VALUE base) +{ + VALUE digits, bases; + + RUBY_ASSERT(!rb_num_negative_p(num)); + + if (RB_BIGNUM_TYPE_P(base)) + base = rb_big_norm(base); + if (FIXNUM_P(base) && FIX2LONG(base) < 2) + rb_raise(rb_eArgError, "invalid radix %ld", FIX2LONG(base)); + else if (RB_BIGNUM_TYPE_P(base) && 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); + + if (int_lt(rb_int_div(rb_int_bit_length(num), rb_int_bit_length(base)), INT2FIX(50))) { + 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; + } + + bases = rb_ary_new(); + for (VALUE b = base; int_le(b, num) == Qtrue; b = rb_int_mul(b, b)) { + rb_ary_push(bases, b); + } + digits = rb_ary_new_from_args(1, num); + while (RARRAY_LEN(bases)) { + VALUE b = rb_ary_pop(bases); + long i, last_idx = RARRAY_LEN(digits) - 1; + for(i = last_idx; i >= 0; i--) { + VALUE n = RARRAY_AREF(digits, i); + VALUE divmod = rb_int_divmod(n, b); + VALUE div = RARRAY_AREF(divmod, 0); + VALUE mod = RARRAY_AREF(divmod, 1); + if (i != last_idx || div != INT2FIX(0)) rb_ary_store(digits, 2 * i + 1, div); + rb_ary_store(digits, 2 * i, mod); + } + } + + return digits; +} /* * call-seq: - * fix.size -> fixnum + * digits(base = 10) -> array_of_integers + * + * Returns an array of integers representing the +base+-radix + * digits of +self+; + * the first element of the array represents the least significant digit: + * + * 12345.digits # => [5, 4, 3, 2, 1] + * 12345.digits(7) # => [4, 6, 6, 0, 5] + * 12345.digits(100) # => [45, 23, 1] * - * Returns the number of <em>bytes</em> in the machine representation - * of a <code>Fixnum</code>. + * Raises an exception if +self+ is negative or +base+ is less than 2. * - * 1.size #=> 4 - * -1.size #=> 4 - * 2147483647.size #=> 4 */ static VALUE -fix_size(VALUE fix) +rb_int_digits(int argc, VALUE *argv, VALUE num) { - return INT2FIX(sizeof(long)); + 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_BIGNUM_TYPE_P(base_value)) + 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_BIGNUM_TYPE_P(num)) + return rb_int_digits_bigbase(num, LONG2FIX(base)); + + return Qnil; } static VALUE -int_upto_size(VALUE from, VALUE args) +int_upto_size(VALUE from, VALUE args, VALUE eobj) { - return num_interval_step_size(from, RARRAY_PTR(args)[0], INT2FIX(1), FALSE); + return ruby_num_interval_step_size(from, RARRAY_AREF(args, 0), INT2FIX(1), FALSE); } /* * call-seq: - * int.upto(limit) {|i| block } -> self - * int.upto(limit) -> an_enumerator + * upto(limit) {|i| ... } -> self + * upto(limit) -> enumerator * - * Iterates <em>block</em>, passing in integer values from <i>int</i> - * up to and including <i>limit</i>. + * Calls the given block with each integer value from +self+ up to +limit+; + * returns +self+: * - * If no block is given, an enumerator is returned instead. + * a = [] + * 5.upto(10) {|i| a << i } # => 5 + * a # => [5, 6, 7, 8, 9, 10] + * a = [] + * -5.upto(0) {|i| a << i } # => -5 + * a # => [-5, -4, -3, -2, -1, 0] + * 5.upto(4) {|i| fail 'Cannot happen' } # => 5 * - * 5.upto(10) { |i| print i, " " } + * With no block given, returns an Enumerator. * - * <em>produces:</em> - * - * 5 6 7 8 9 10 */ static VALUE @@ -3501,47 +5822,49 @@ 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; + long i, end; - end = FIX2LONG(to); - for (i = FIX2LONG(from); i <= end; i++) { - rb_yield(LONG2FIX(i)); - } + end = FIX2LONG(to); + for (i = FIX2LONG(from); i <= end; i++) { + rb_yield(LONG2FIX(i)); + } } else { - VALUE i = from, c; + VALUE i = from, c; - while (!(c = rb_funcall(i, '>', 1, to))) { - rb_yield(i); - i = rb_funcall(i, '+', 1, INT2FIX(1)); - } - if (NIL_P(c)) rb_cmperr(i, to); + while (!(c = rb_funcall(i, '>', 1, to))) { + rb_yield(i); + i = rb_funcall(i, '+', 1, INT2FIX(1)); + } + ensure_cmp(c, i, to); } return from; } static VALUE -int_downto_size(VALUE from, VALUE args) +int_downto_size(VALUE from, VALUE args, VALUE eobj) { - return num_interval_step_size(from, RARRAY_PTR(args)[0], INT2FIX(-1), FALSE); + return ruby_num_interval_step_size(from, RARRAY_AREF(args, 0), INT2FIX(-1), FALSE); } /* * call-seq: - * int.downto(limit) {|i| block } -> self - * int.downto(limit) -> an_enumerator + * downto(limit) {|i| ... } -> self + * downto(limit) -> enumerator * - * Iterates <em>block</em>, passing decreasing values from <i>int</i> - * down to and including <i>limit</i>. + * Calls the given block with each integer value from +self+ down to +limit+; + * returns +self+: * - * If no block is given, an enumerator is returned instead. + * a = [] + * 10.downto(5) {|i| a << i } # => 10 + * a # => [10, 9, 8, 7, 6, 5] + * a = [] + * 0.downto(-5) {|i| a << i } # => 0 + * a # => [0, -1, -2, -3, -4, -5] + * 4.downto(5) {|i| fail 'Cannot happen' } # => 4 * - * 5.downto(1) { |n| print n, ".. " } - * print " Liftoff!\n" + * With no block given, returns an Enumerator. * - * <em>produces:</em> - * - * 5.. 4.. 3.. 2.. 1.. Liftoff! */ static VALUE @@ -3549,159 +5872,398 @@ 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; + long i, end; - end = FIX2LONG(to); - for (i=FIX2LONG(from); i >= end; i--) { - rb_yield(LONG2FIX(i)); - } + end = FIX2LONG(to); + for (i=FIX2LONG(from); i >= end; i--) { + rb_yield(LONG2FIX(i)); + } } else { - VALUE i = from, c; + VALUE i = from, c; - while (!(c = rb_funcall(i, '<', 1, to))) { - rb_yield(i); - i = rb_funcall(i, '-', 1, INT2FIX(1)); - } - if (NIL_P(c)) rb_cmperr(i, to); + while (!(c = rb_funcall(i, '<', 1, to))) { + rb_yield(i); + i = rb_funcall(i, '-', 1, INT2FIX(1)); + } + if (NIL_P(c)) rb_cmperr(i, to); } return from; } static VALUE -int_dotimes_size(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; + return int_neg_p(num) ? INT2FIX(0) : num; } /* * call-seq: - * int.times {|i| block } -> self - * int.times -> an_enumerator + * round(ndigits= 0, half: :up) -> integer * - * Iterates block <i>int</i> times, passing in values from zero to - * <i>int</i> - 1. + * Returns +self+ rounded to the nearest value with + * a precision of +ndigits+ decimal digits. * - * If no block is given, an enumerator is returned instead. + * When +ndigits+ is negative, the returned value + * has at least <tt>ndigits.abs</tt> trailing zeros: * - * 5.times do |i| - * print i, " " - * end + * 555.round(-1) # => 560 + * 555.round(-2) # => 600 + * 555.round(-3) # => 1000 + * -555.round(-2) # => -600 + * 555.round(-4) # => 0 + * + * Returns +self+ when +ndigits+ is zero or positive. + * + * 555.round # => 555 + * 555.round(1) # => 555 + * 555.round(50) # => 555 + * + * If keyword argument +half+ is given, + * and +self+ is equidistant from the two candidate values, + * the rounding is according to the given +half+ value: + * + * - +:up+ or +nil+: round away from zero: + * + * 25.round(-1, half: :up) # => 30 + * (-25).round(-1, half: :up) # => -30 + * + * - +:down+: round toward zero: + * + * 25.round(-1, half: :down) # => 20 + * (-25).round(-1, half: :down) # => -20 * - * <em>produces:</em> * - * 0 1 2 3 4 + * - +:even+: round toward the candidate whose last nonzero digit is even: + * + * 25.round(-1, half: :even) # => 20 + * 15.round(-1, half: :even) # => 20 + * (-25).round(-1, half: :even) # => -20 + * + * Raises and exception if the value for +half+ is invalid. + * + * Related: Integer#truncate. + * */ static VALUE -int_dotimes(VALUE num) +int_round(int argc, VALUE* argv, 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)); - } - } - else { - VALUE i = INT2FIX(0); + int ndigits; + int mode; + VALUE nd, opt; - for (;;) { - if (!RTEST(rb_funcall(i, '<', 1, num))) break; - rb_yield(i); - i = rb_funcall(i, '+', 1, INT2FIX(1)); - } + 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 num; + return rb_int_round(num, ndigits, mode); } /* + * :markup: markdown + * * call-seq: - * int.round([ndigits]) -> integer or float + * floor(ndigits = 0) -> integer * - * Rounds <i>flt</i> to a given precision in decimal digits (default 0 digits). - * Precision may be negative. Returns a floating point number when +ndigits+ - * is positive, +self+ for zero, and round down for negative. + * Returns an integer that is a "floor" value for `self`, + * as specified by the given `ndigits`, + * which must be an + * [integer-convertible object](rdoc-ref:implicit_conversion.rdoc@Integer-Convertible+Objects). + * + * - When `self` is zero, returns zero (regardless of the value of `ndigits`): + * + * ``` + * 0.floor(2) # => 0 + * 0.floor(-2) # => 0 + * ``` + * + * - When `self` is non-zero and `ndigits` is non-negative, returns `self`: + * + * ``` + * 555.floor # => 555 + * 555.floor(50) # => 555 + * ``` + * + * - When `self` is non-zero and `ndigits` is negative, + * returns a value based on a computed granularity: + * + * - The granularity is `10 ** ndigits.abs`. + * - The returned value is the largest multiple of the granularity + * that is less than or equal to `self`. + * + * Examples with positive `self`: + * + * | ndigits | Granularity | 1234.floor(ndigits) | + * |--------:|------------:|--------------------:| + * | -1 | 10 | 1230 | + * | -2 | 100 | 1200 | + * | -3 | 1000 | 1000 | + * | -4 | 10000 | 0 | + * | -5 | 100000 | 0 | + * + * Examples with negative `self`: + * + * | ndigits | Granularity | -1234.floor(ndigits) | + * |--------:|------------:|---------------------:| + * | -1 | 10 | -1240 | + * | -2 | 100 | -1300 | + * | -3 | 1000 | -2000 | + * | -4 | 10000 | -10000 | + * | -5 | 100000 | -100000 | + * + * Related: Integer#ceil. * - * 1.round #=> 1 - * 1.round(2) #=> 1.0 - * 15.round(-1) #=> 20 */ static VALUE -int_round(int argc, VALUE* argv, VALUE num) +int_floor(int argc, VALUE* argv, VALUE num) { - VALUE n; int ndigits; - if (argc == 0) return num; - rb_scan_args(argc, argv, "1", &n); - ndigits = NUM2INT(n); - if (ndigits > 0) { - return rb_Float(num); + if (!rb_check_arity(argc, 0, 1)) return num; + ndigits = NUM2INT(argv[0]); + if (ndigits >= 0) { + return num; } - if (ndigits == 0) { - return num; - } - return int_round_0(num, ndigits); + return rb_int_floor(num, ndigits); } /* + * :markup: markdown + * * call-seq: - * fix.zero? -> true or false + * ceil(ndigits = 0) -> integer + * + * Returns an integer that is a "ceiling" value for `self`, + * as specified by the given `ndigits`, + * which must be an + * [integer-convertible object](rdoc-ref:implicit_conversion.rdoc@Integer-Convertible+Objects). + * + * - When `self` is zero, returns zero (regardless of the value of `ndigits`): + * + * ``` + * 0.ceil(2) # => 0 + * 0.ceil(-2) # => 0 + * ``` + * + * - When `self` is non-zero and `ndigits` is non-negative, returns `self`: + * + * ``` + * 555.ceil # => 555 + * 555.ceil(50) # => 555 + * ``` + * + * - When `self` is non-zero and `ndigits` is negative, + * returns a value based on a computed granularity: + * + * - The granularity is `10 ** ndigits.abs`. + * - The returned value is the smallest multiple of the granularity + * that is greater than or equal to `self`. + * + * Examples with positive `self`: + * + * | ndigits | Granularity | 1234.ceil(ndigits) | + * |--------:|------------:|-------------------:| + * | -1 | 10 | 1240 | + * | -2 | 100 | 1300 | + * | -3 | 1000 | 2000 | + * | -4 | 10000 | 10000 | + * | -5 | 100000 | 100000 | + * + * Examples with negative `self`: * - * Returns <code>true</code> if <i>fix</i> is zero. + * | ndigits | Granularity | -1234.ceil(ndigits) | + * |--------:|------------:|--------------------:| + * | -1 | 10 | -1230 | + * | -2 | 100 | -1200 | + * | -3 | 1000 | -1000 | + * | -4 | 10000 | 0 | + * | -5 | 100000 | 0 | * + * Related: Integer#floor. */ static VALUE -fix_zero_p(VALUE num) +int_ceil(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 Qfalse; + return rb_int_ceil(num, ndigits); } /* * call-seq: - * fix.odd? -> true or false + * truncate(ndigits = 0) -> integer + * + * Returns +self+ truncated (toward zero) to + * a precision of +ndigits+ decimal digits. + * + * When +ndigits+ is negative, the returned value + * has at least <tt>ndigits.abs</tt> trailing zeros: + * + * 555.truncate(-1) # => 550 + * 555.truncate(-2) # => 500 + * -555.truncate(-2) # => -500 + * + * Returns +self+ when +ndigits+ is zero or positive. + * + * 555.truncate # => 555 + * 555.truncate(50) # => 555 + * + * Related: Integer#round. * - * Returns <code>true</code> if <i>fix</i> is an odd number. */ static VALUE -fix_odd_p(VALUE num) +int_truncate(int argc, VALUE* argv, VALUE num) { - if (num & 2) { - return Qtrue; - } - return Qfalse; -} + 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; \ + } \ + rettype x = (rettype)sqrt(argtype##_TO_DOUBLE(n)); \ + /* libm sqrt may returns a larger approximation than actual. */ \ + /* Our isqrt always returns a smaller approximation. */ \ + if (x * x > n) x--; \ + return x; \ +} + +#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) /* * call-seq: - * fix.even? -> true or false + * Integer.sqrt(numeric) -> integer + * + * Returns the integer square root of the non-negative integer +n+, + * which is the largest non-negative integer less than or equal to the + * square root of +numeric+. + * + * Integer.sqrt(0) # => 0 + * Integer.sqrt(1) # => 1 + * Integer.sqrt(24) # => 4 + * Integer.sqrt(25) # => 5 + * Integer.sqrt(10**400) # => 10**200 + * + * If +numeric+ is not an \Integer, it is converted to an \Integer: + * + * Integer.sqrt(Complex(4, 0)) # => 2 + * Integer.sqrt(Rational(4, 1)) # => 2 + * Integer.sqrt(4.0) # => 2 + * Integer.sqrt(3.14159) # => 1 + * + * This method is equivalent to <tt>Math.sqrt(numeric).floor</tt>, + * 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 + * + * Raises an exception if +numeric+ is negative. * - * Returns <code>true</code> if <i>fix</i> is an even number. */ static VALUE -fix_even_p(VALUE num) +rb_int_s_isqrt(VALUE self, VALUE num) { - if (num & 2) { - return Qfalse; + 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); } - return Qtrue; + 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); + } +} + +/* + * call-seq: + * Integer.try_convert(object) -> object, integer, or nil + * + * If +object+ is an \Integer object, returns +object+. + * Integer.try_convert(1) # => 1 + * + * Otherwise if +object+ responds to <tt>:to_int</tt>, + * calls <tt>object.to_int</tt> and returns the result. + * Integer.try_convert(1.25) # => 1 + * + * Returns +nil+ if +object+ does not respond to <tt>:to_int</tt> + * Integer.try_convert([]) # => nil + * + * Raises an exception unless <tt>object.to_int</tt> returns an \Integer object. + */ +static VALUE +int_s_try_convert(VALUE self, VALUE num) +{ + return rb_check_integer_type(num); } /* @@ -3709,54 +6271,188 @@ fix_even_p(VALUE num) * * Raised when attempting to divide an integer by 0. * - * 42 / 0 + * 42 / 0 #=> ZeroDivisionError: divided by 0 * - * <em>raises the exception:</em> + * Note that only division by an exact 0 will raise the exception: * - * ZeroDivisionError: divided by 0 + * 42 / 0.0 #=> Float::INFINITY + * 42 / -0.0 #=> -Float::INFINITY + * 0 / 0.0 #=> NaN + */ + +/* + * Document-class: FloatDomainError * - * Note that only division by an exact 0 will raise that exception: + * Raised when attempting to convert special float values (in particular + * +Infinity+ or +NaN+) to numerical classes which don't support them. * - * 42 / 0.0 #=> Float::INFINITY - * 42 / -0.0 #=> -Float::INFINITY - * 0 / 0.0 #=> NaN + * Float::INFINITY.to_r #=> FloatDomainError: Infinity */ /* - * Document-class: FloatDomainError + * 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 * - * Raised when attempting to convert special float values - * (in particular infinite or NaN) - * to numerical classes which don't support them. + * def +(other) + * self.class.new('|' * (to_i + other.to_i)) + * end * - * Float::INFINITY.to_r + * def -(other) + * self.class.new('|' * (to_i - other.to_i)) + * end * - * <em>raises the exception:</em> + * 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 + * + * == What's Here + * + * First, what's elsewhere. Class \Numeric: + * + * - Inherits from {class Object}[rdoc-ref:Object@What-27s+Here]. + * - Includes {module Comparable}[rdoc-ref:Comparable@What-27s+Here]. + * + * Here, class \Numeric provides methods for: + * + * - {Querying}[rdoc-ref:Numeric@Querying] + * - {Comparing}[rdoc-ref:Numeric@Comparing] + * - {Converting}[rdoc-ref:Numeric@Converting] + * - {Other}[rdoc-ref:Numeric@Other] + * + * === Querying + * + * - #finite?: Returns true unless +self+ is infinite or not a number. + * - #infinite?: Returns -1, +nil+ or +1, depending on whether +self+ + * is <tt>-Infinity<tt>, finite, or <tt>+Infinity</tt>. + * - #integer?: Returns whether +self+ is an integer. + * - #negative?: Returns whether +self+ is negative. + * - #nonzero?: Returns whether +self+ is not zero. + * - #positive?: Returns whether +self+ is positive. + * - #real?: Returns whether +self+ is a real value. + * - #zero?: Returns whether +self+ is zero. + * + * === Comparing + * + * - #<=>: Returns: + * + * - -1 if +self+ is less than the given value. + * - 0 if +self+ is equal to the given value. + * - 1 if +self+ is greater than the given value. + * - +nil+ if +self+ and the given value are not comparable. + * + * - #eql?: Returns whether +self+ and the given value have the same value and type. + * + * === Converting + * + * - #% (aliased as #modulo): Returns the remainder of +self+ divided by the given value. + * - #-@: Returns the value of +self+, negated. + * - #abs (aliased as #magnitude): Returns the absolute value of +self+. + * - #abs2: Returns the square of +self+. + * - #angle (aliased as #arg and #phase): Returns 0 if +self+ is positive, + * Math::PI otherwise. + * - #ceil: Returns the smallest number greater than or equal to +self+, + * to a given precision. + * - #coerce: Returns array <tt>[coerced_self, coerced_other]</tt> + * for the given other value. + * - #conj (aliased as #conjugate): Returns the complex conjugate of +self+. + * - #denominator: Returns the denominator (always positive) + * of the Rational representation of +self+. + * - #div: Returns the value of +self+ divided by the given value + * and converted to an integer. + * - #divmod: Returns array <tt>[quotient, modulus]</tt> resulting + * from dividing +self+ the given divisor. + * - #fdiv: Returns the Float result of dividing +self+ by the given divisor. + * - #floor: Returns the largest number less than or equal to +self+, + * to a given precision. + * - #i: Returns the Complex object <tt>Complex(0, self)</tt>. + * the given value. + * - #imaginary (aliased as #imag): Returns the imaginary part of the +self+. + * - #numerator: Returns the numerator of the Rational representation of +self+; + * has the same sign as +self+. + * - #polar: Returns the array <tt>[self.abs, self.arg]</tt>. + * - #quo: Returns the value of +self+ divided by the given value. + * - #real: Returns the real part of +self+. + * - #rect (aliased as #rectangular): Returns the array <tt>[self, 0]</tt>. + * - #remainder: Returns <tt>self-arg*(self/arg).truncate</tt> for the given +arg+. + * - #round: Returns the value of +self+ rounded to the nearest value + * for the given a precision. + * - #to_c: Returns the Complex representation of +self+. + * - #to_int: Returns the Integer representation of +self+, truncating if necessary. + * - #truncate: Returns +self+ truncated (toward zero) to a given precision. + * + * === Other + * + * - #clone: Returns +self+; does not allow freezing. + * - #dup (aliased as #+@): Returns +self+. + * - #step: Invokes the given block with the sequence of specified numbers. * - * FloatDomainError: Infinity */ - void Init_Numeric(void) { -#undef rb_intern -#define rb_intern(str) rb_intern_const(str) - -#if defined(__FreeBSD__) && __FreeBSD__ < 4 - /* allow divide by zero -- Inf */ - fpsetmask(fpgetmask() & ~(FP_X_DZ|FP_X_INV|FP_X_OFL)); -#elif defined(_UNICOSMP) +#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); - _control87(_control87(0,0),0x1FFF); #endif - id_coerce = rb_intern("coerce"); - id_to_i = rb_intern("to_i"); - id_eq = rb_intern("=="); - id_div = rb_intern("div"); + id_coerce = rb_intern_const("coerce"); + id_to = rb_intern_const("to"); + id_by = rb_intern_const("by"); rb_eZeroDivError = rb_define_class("ZeroDivisionError", rb_eStandardError); rb_eFloatDomainError = rb_define_class("FloatDomainError", rb_eRangeError); @@ -3764,15 +6460,13 @@ Init_Numeric(void) 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, "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); @@ -3783,82 +6477,91 @@ Init_Numeric(void) 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, "floor", num_floor, 0); - rb_define_method(rb_cNumeric, "ceil", num_ceil, 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, 0); + 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_method(rb_cInteger, "integer?", int_int_p, 0); - rb_define_method(rb_cInteger, "odd?", int_odd_p, 0); - rb_define_method(rb_cInteger, "even?", int_even_p, 0); + rb_define_singleton_method(rb_cInteger, "sqrt", rb_int_s_isqrt, 1); + rb_define_singleton_method(rb_cInteger, "try_convert", int_s_try_convert, 1); + + rb_define_method(rb_cInteger, "to_s", rb_int_to_s, -1); + rb_define_alias(rb_cInteger, "inspect", "to_s"); + 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_define_method(rb_cInteger, "succ", int_succ, 0); rb_define_method(rb_cInteger, "next", int_succ, 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, "truncate", int_to_i, 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_cFixnum = rb_define_class("Fixnum", rb_cInteger); - - rb_define_method(rb_cFixnum, "to_s", fix_to_s, -1); - rb_define_alias(rb_cFixnum, "inspect", "to_s"); - - 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_idiv, 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, "fdiv", fix_fdiv, 1); - rb_define_method(rb_cFixnum, "**", fix_pow, 1); - - rb_define_method(rb_cFixnum, "abs", fix_abs, 0); - rb_define_method(rb_cFixnum, "magnitude", fix_abs, 0); - - rb_define_method(rb_cFixnum, "==", fix_equal, 1); - 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_cFixnum, "odd?", fix_odd_p, 0); - rb_define_method(rb_cFixnum, "even?", fix_even_p, 0); - rb_define_method(rb_cFixnum, "succ", fix_succ, 0); + rb_define_method(rb_cInteger, "<=>", rb_int_cmp, 1); + + 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, "===", 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, "&", rb_int_and, 1); + rb_define_method(rb_cInteger, "|", int_or, 1); + rb_define_method(rb_cInteger, "^", rb_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, "digits", rb_int_digits, -1); + +#define fix_to_s_static(n) do { \ + VALUE lit = rb_fstring_literal(#n); \ + rb_fix_to_s_static[n] = lit; \ + rb_vm_register_global_object(lit); \ + RB_GC_GUARD(lit); \ + } while (0) + + fix_to_s_static(0); + fix_to_s_static(1); + fix_to_s_static(2); + fix_to_s_static(3); + fix_to_s_static(4); + fix_to_s_static(5); + fix_to_s_static(6); + fix_to_s_static(7); + fix_to_s_static(8); + fix_to_s_static(9); + +#undef fix_to_s_static rb_cFloat = rb_define_class("Float", rb_cNumeric); @@ -3866,20 +6569,6 @@ Init_Numeric(void) rb_undef_method(CLASS_OF(rb_cFloat), "new"); /* - * 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. * @@ -3893,13 +6582,14 @@ Init_Numeric(void) */ rb_define_const(rb_cFloat, "MANT_DIG", INT2FIX(DBL_MANT_DIG)); /* - * The number of decimal digits in a double-precision floating point. + * 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 posable exponent value in a double-precision floating + * The smallest possible exponent value in a double-precision floating * point. * * Usually defaults to -1021. @@ -3927,9 +6617,14 @@ Init_Numeric(void) */ rb_define_const(rb_cFloat, "MAX_10_EXP", INT2FIX(DBL_MAX_10_EXP)); /* - * The smallest positive integer in a double-precision floating point. + * 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)); /* @@ -3940,7 +6635,7 @@ Init_Numeric(void) rb_define_const(rb_cFloat, "MAX", DBL2NUM(DBL_MAX)); /* * The difference between 1 and the smallest double-precision floating - * point number. + * point number greater than 1. * * Usually defaults to 2.2204460492503131e-16. */ @@ -3948,48 +6643,61 @@ Init_Numeric(void) /* * An expression representing positive infinity. */ - rb_define_const(rb_cFloat, "INFINITY", DBL2NUM(INFINITY)); + rb_define_const(rb_cFloat, "INFINITY", DBL2NUM(HUGE_VAL)); /* * An expression representing a value which is "not a number". */ - rb_define_const(rb_cFloat, "NAN", DBL2NUM(NAN)); + 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, "+", 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, "+", rb_float_plus, 1); + rb_define_method(rb_cFloat, "-", rb_float_minus, 1); + rb_define_method(rb_cFloat, "*", rb_float_mul, 1); + rb_define_method(rb_cFloat, "/", rb_float_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, "magnitude", flo_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, "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, 0); + 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); } + +#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); +} + +#include "numeric.rbinc" |