/********************************************************************** numeric.c - $Author$ created at: Fri Aug 13 18:33:09 JST 1993 Copyright (C) 1993-2007 Yukihiro Matsumoto **********************************************************************/ #include "ruby/internal/config.h" #include #include #include #include #ifdef HAVE_FLOAT_H #include #endif #ifdef HAVE_IEEEFP_H #include #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 DBL_MIN #define DBL_MIN 2.2250738585072014e-308 #endif #ifndef DBL_MAX #define DBL_MAX 1.7976931348623157e+308 #endif #ifndef DBL_MIN_EXP #define DBL_MIN_EXP (-1021) #endif #ifndef DBL_MAX_EXP #define DBL_MAX_EXP 1024 #endif #ifndef DBL_MIN_10_EXP #define DBL_MIN_10_EXP (-307) #endif #ifndef DBL_MAX_10_EXP #define DBL_MAX_10_EXP 308 #endif #ifndef DBL_DIG #define DBL_DIG 15 #endif #ifndef DBL_MANT_DIG #define DBL_MANT_DIG 53 #endif #ifndef DBL_EPSILON #define DBL_EPSILON 2.2204460492503131e-16 #endif #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 #ifndef USE_RB_NAN #elif !defined(WORDS_BIGENDIAN) /* BYTE_ORDER == LITTLE_ENDIAN */ const union bytesequence4_or_float rb_nan = {{0x00, 0x00, 0xc0, 0x7f}}; #else const union bytesequence4_or_float rb_nan = {{0x7f, 0xc0, 0x00, 0x00}}; #endif #ifndef HAVE_ROUND double round(double x) { double f; if (x > 0.0) { f = floor(x); x = f + (x - f >= 0.5); } else if (x < 0.0) { f = ceil(x); x = f - (f - x >= 0.5); } return x; } #endif static double round_half_up(double x, double s) { double f, xs = x * s; f = round(xs); if (s == 1.0) return f; if (x > 0) { if ((double)((f + 0.5) / s) <= x) f += 1; x = f; } else { if ((double)((f - 0.5) / s) >= x) f -= 1; x = f; } return x; } static double round_half_down(double x, double s) { double f, xs = x * s; f = round(xs); if (x > 0) { if ((double)((f - 0.5) / s) >= x) f -= 1; x = f; } else { if ((double)((f + 0.5) / s) <= x) f += 1; x = f; } return x; } static double round_half_even(double x, double s) { double 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_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) { #define NUMERR_TYPE 1 #define NUMERR_NEGATIVE 2 #define NUMERR_TOOLARGE 3 if (FIXNUM_P(val)) { long v = FIX2LONG(val); #if SIZEOF_INT < SIZEOF_LONG if (v > (long)UINT_MAX) return NUMERR_TOOLARGE; #endif if (v < 0) return NUMERR_NEGATIVE; *ret = (unsigned int)v; return 0; } if (RB_BIGNUM_TYPE_P(val)) { if (BIGNUM_NEGATIVE_P(val)) return NUMERR_NEGATIVE; #if SIZEOF_INT < SIZEOF_LONG /* long is 64bit */ return NUMERR_TOOLARGE; #else /* long is 32bit */ if (rb_absint_size(val, NULL) > sizeof(int)) return NUMERR_TOOLARGE; *ret = (unsigned int)rb_big2ulong((VALUE)val); return 0; #endif } return NUMERR_TYPE; } #define method_basic_p(klass) rb_method_basic_definition_p(klass, mid) static inline int int_pos_p(VALUE num) { if (FIXNUM_P(num)) { return FIXNUM_POSITIVE_P(num); } else if (RB_BIGNUM_TYPE_P(num)) { return BIGNUM_POSITIVE_P(num); } rb_raise(rb_eTypeError, "not an Integer"); } static inline int int_neg_p(VALUE num) { if (FIXNUM_P(num)) { return FIXNUM_NEGATIVE_P(num); } else if (RB_BIGNUM_TYPE_P(num)) { return BIGNUM_NEGATIVE_P(num); } 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 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: * 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)] * * 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. * */ static VALUE num_coerce(VALUE x, VALUE y) { if (CLASS_OF(x) == CLASS_OF(y)) return rb_assoc_new(y, x); x = rb_Float(x); y = rb_Float(y); return rb_assoc_new(y, x); } NORETURN(static void coerce_failed(VALUE x, VALUE y)); static void coerce_failed(VALUE x, VALUE y) { if (SPECIAL_CONST_P(y) || SYMBOL_P(y) || RB_FLOAT_TYPE_P(y)) { y = rb_inspect(y); } else { y = rb_obj_class(y); } rb_raise(rb_eTypeError, "%"PRIsVALUE" can't be coerced into %"PRIsVALUE, y, rb_obj_class(x)); } static int do_coerce(VALUE *x, VALUE *y, int err) { 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; } if (!RB_TYPE_P(ary, T_ARRAY) || RARRAY_LEN(ary) != 2) { rb_raise(rb_eTypeError, "coerce must return [x, y]"); } *x = RARRAY_AREF(ary, 0); *y = RARRAY_AREF(ary, 1); return TRUE; } VALUE rb_num_coerce_bin(VALUE x, VALUE y, ID func) { do_coerce(&x, &y, TRUE); return rb_funcall(x, func, 1, y); } 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 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 x0 = x, y0 = y; if (!do_coerce(&x, &y, FALSE)) { rb_cmperr(x0, y0); UNREACHABLE_RETURN(Qnil); } return ensure_cmp(rb_funcall(x, func, 1, y), x0, y0); } NORETURN(static VALUE num_sadded(VALUE x, VALUE name)); /* * :nodoc: * * Trap attempts to add methods to Numeric objects. Always raises a TypeError. * * Numerics should be values; singleton_methods should not be added to them. */ static VALUE num_sadded(VALUE x, VALUE name) { ID mid = rb_to_id(name); /* ruby_frame = ruby_frame->prev; */ /* pop frame for "singleton_method_added" */ rb_remove_method_id(rb_singleton_class(x), mid); rb_raise(rb_eTypeError, "can't define singleton method \"%"PRIsVALUE"\" for %"PRIsVALUE, rb_id2str(mid), rb_obj_class(x)); UNREACHABLE_RETURN(Qnil); } #if 0 /* * call-seq: * clone(freeze: true) -> self * * Returns +self+. * * Raises an exception if the value for +freeze+ is neither +true+ nor +nil+. * * Related: Numeric#dup. * */ static VALUE num_clone(int argc, VALUE *argv, VALUE x) { return rb_immutable_obj_clone(argc, argv, x); } #else # define num_clone rb_immutable_obj_clone #endif /* * call-seq: * i -> complex * * Returns Complex(0, self): * * 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. * */ static VALUE num_imaginary(VALUE num) { return rb_complex_new(INT2FIX(0), num); } /* * call-seq: * -self -> numeric * * Unary Minus---Returns the receiver, negated. */ static VALUE num_uminus(VALUE num) { VALUE zero; zero = INT2FIX(0); do_coerce(&zero, &num, TRUE); return num_funcall1(zero, '-', num); } /* * call-seq: * fdiv(other) -> float * * Returns the quotient self/other as a float, * using method +/+ in the derived class of +self+. * (\Numeric itself does not define method +/+.) * * Of the Core and Standard Library classes, * only BigDecimal uses this implementation. * */ static VALUE num_fdiv(VALUE x, VALUE y) { return rb_funcall(rb_Float(x), '/', 1, y); } /* * call-seq: * div(other) -> integer * * Returns the quotient self/other as an integer (via +floor+), * using method +/+ in the derived class of +self+. * (\Numeric itself does not define method +/+.) * * Of the Core and Standard Library classes, * Only Float and Rational use this implementation. * */ static VALUE num_div(VALUE x, VALUE y) { if (rb_equal(INT2FIX(0), y)) rb_num_zerodiv(); return rb_funcall(num_funcall1(x, '/', y), rb_intern("floor"), 0); } /* * call-seq: * self % other -> real_numeric * * Returns +self+ modulo +other+ as a real number. * * Of the Core and Standard Library classes, * only Rational uses this implementation. * * For Rational +r+ and real number +n+, these expressions are equivalent: * * 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) * */ 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, q)); } /* * call-seq: * 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. * * 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) * */ static VALUE num_remainder(VALUE x, VALUE 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))) && ((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: * divmod(other) -> array * * Returns a 2-element array [q, r], where * * q = (self/other).floor # Quotient * r = self % other # Remainder * * Of the Core and Standard Library classes, * only Rational uses this implementation. * * 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)] * * 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)] * * Rational(13, 1).divmod(4.0) # => [3, 1.0] * Rational(13, 1).divmod(Rational(4, 11)) # => [35, (3/11)] */ static VALUE num_divmod(VALUE x, VALUE y) { return rb_assoc_new(num_div(x, y), num_modulo(x, y)); } /* * call-seq: * abs -> numeric * * Returns the absolute value of +self+. * * 12.abs #=> 12 * (-34.56).abs #=> 34.56 * -34.56.abs #=> 34.56 * */ static VALUE num_abs(VALUE num) { if (rb_num_negative_int_p(num)) { return num_funcall0(num, idUMinus); } return num; } /* * call-seq: * zero? -> true or false * * Returns +true+ if +zero+ has a zero value, +false+ otherwise. * * Of the Core and Standard Library classes, * only Rational and Complex use this implementation. * */ static VALUE num_zero_p(VALUE num) { 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: * nonzero? -> self or nil * * Returns +self+ if +self+ is not a zero value, +nil+ otherwise; * uses method zero? 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"] * * Of the Core and Standard Library classes, * Integer, Float, Rational, and Complex use this implementation. * * Related: #zero? * */ static VALUE num_nonzero_p(VALUE num) { if (RTEST(num_funcall0(num, rb_intern("zero?")))) { return Qnil; } return num; } /* * call-seq: * to_int -> integer * * Returns +self+ as an integer; * converts using method +to_i+ in the derived class. * * 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) # Raises RangeError (non-zero imaginary part) * */ static VALUE num_to_int(VALUE num) { return num_funcall0(num, id_to_i); } /* * call-seq: * positive? -> true or false * * Returns +true+ if +self+ is greater than 0, +false+ otherwise. * */ static VALUE num_positive_p(VALUE num) { const ID mid = '>'; if (FIXNUM_P(num)) { if (method_basic_p(rb_cInteger)) return RBOOL((SIGNED_VALUE)num > (SIGNED_VALUE)INT2FIX(0)); } 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: * negative? -> true or false * * Returns +true+ if +self+ is less than 0, +false+ otherwise. * */ static VALUE num_negative_p(VALUE num) { return RBOOL(rb_num_negative_int_p(num)); } /******************************************************************** * * Document-class: Float * * A \Float object represents a sometimes-inexact real number using the native * architecture's double-precision floating point representation. * * Floating point has a different arithmetic and is an inexact number. * So you should know its esoteric system. See following: * * - https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html * - https://github.com/rdp/ruby_tutorials_core/wiki/Ruby-Talk-FAQ#-why-are-rubys-floats-imprecise * - https://en.wikipedia.org/wiki/Floating_point#Accuracy_problems * * You can create a \Float object explicitly with: * * - A {floating-point literal}[rdoc-ref:syntax/literals.rdoc@Float+Literals]. * * You can convert certain objects to Floats with: * * - \Method #Float. * * == What's Here * * First, what's elsewhere. \Class \Float: * * - 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 \Float provides methods for: * * - {Querying}[rdoc-ref:Float@Querying] * - {Comparing}[rdoc-ref:Float@Comparing] * - {Converting}[rdoc-ref:Float@Converting] * * === Querying * * - #finite?: Returns whether +self+ is finite. * - #hash: Returns the integer hash code for +self+. * - #infinite?: Returns whether +self+ is infinite. * - #nan?: Returns whether +self+ is a NaN (not-a-number). * * === 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 #=== and #eql?): 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 * * - #% (aliased as #modulo): Returns +self+ modulo 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. * - #ceil: Returns the smallest number greater than or equal to +self+. * - #coerce: Returns a 2-element array containing the given value converted to a \Float * and +self+ * - #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+. * - #next_float: Returns the next-larger representable \Float. * - #prev_float: Returns the next-smaller representable \Float. * - #quo: Returns the quotient from dividing +self+ by the given value. * - #round: Returns +self+ rounded to the nearest value, to a given precision. * - #to_i (aliased as #to_int): Returns +self+ truncated to an Integer. * - #to_s (aliased as #inspect): Returns a string containing the place-value * representation of +self+ in the given radix. * - #truncate: Returns +self+ truncated to a given precision. * */ VALUE rb_float_new_in_heap(double d) { 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; #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: * 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" * */ static VALUE flo_to_s(VALUE flt) { enum {decimal_mant = DBL_MANT_DIG-DBL_DIG}; enum {float_dig = DBL_DIG+1}; 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)) { static const char minf[] = "-Infinity"; const int pos = (value > 0); /* skip "-" */ return rb_usascii_str_new(minf+pos, strlen(minf)-pos); } else if (isnan(value)) return rb_usascii_str_new2("NaN"); p = ruby_dtoa(value, 0, 0, &decpt, &sign, &e); s = sign ? rb_usascii_str_new_cstr("-") : rb_usascii_str_new(0, 0); if ((digs = (int)(e - p)) >= (int)sizeof(buf)) digs = (int)sizeof(buf) - 1; memcpy(buf, p, digs); 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; } } 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 { 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: * coerce(other) -> array * * 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. * */ static VALUE flo_coerce(VALUE x, VALUE y) { return rb_assoc_new(rb_Float(y), x); } VALUE rb_float_uminus(VALUE flt) { return DBL2NUM(-RFLOAT_VALUE(flt)); } /* * call-seq: * self + other -> numeric * * Returns a new \Float which is the sum of +self+ and +other+: * * f = 3.14 * f + 1 # => 4.140000000000001 * f + 1.0 # => 4.140000000000001 * f + Rational(1, 1) # => 4.140000000000001 * f + Complex(1, 0) # => (4.140000000000001+0i) * */ VALUE rb_float_plus(VALUE x, VALUE 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: * self - other -> numeric * * Returns a new \Float which is 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) * */ VALUE rb_float_minus(VALUE x, VALUE 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: * self * other -> numeric * * Returns a new \Float which is the 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) */ VALUE rb_float_mul(VALUE x, VALUE 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: * self / other -> numeric * * Returns a new \Float which is the result of dividing +self+ by +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) * */ VALUE rb_float_div(VALUE x, VALUE y) { double num = RFLOAT_VALUE(x); double den; double ret; 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: * 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) * */ static VALUE flo_quo(VALUE x, VALUE y) { return num_funcall1(x, '/', y); } static void 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); #else double z; modf(x/y, &z); mod = x - z * y; #endif } 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; } if (modp) *modp = mod; if (divp) *divp = div; } /* * Returns the modulo of division of x by y. * An error will be raised if y == 0. */ double ruby_float_mod(double x, double y) { double mod; flodivmod(x, y, 0, &mod); return mod; } /* * call-seq: * self % other -> float * * Returns +self+ modulo +other+ as a float. * * For float +f+ and real number +r+, these expressions are equivalent: * * 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 * */ static VALUE flo_mod(VALUE x, VALUE y) { double fy; 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)); } static VALUE dbl2ival(double d) { if (FIXABLE(d)) { return LONG2FIX((long)d); } return rb_dbl2big(d); } /* * call-seq: * divmod(other) -> array * * Returns a 2-element array [q, r], 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] * */ static VALUE flo_divmod(VALUE x, VALUE y) { double fy, div, mod; volatile VALUE a, b; 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); b = DBL2NUM(mod); return rb_assoc_new(a, b); } /* * call-seq: * self ** other -> numeric * * Raises +self+ to the power of +other+: * * 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) * */ VALUE rb_float_pow(VALUE x, VALUE y) { 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: * 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. * * 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 == in that +eql?+ requires matching types, * while == does not. * */ static VALUE 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: * self <=> other -> zero or nil * * Returns zero if +self+ is the same as +other+, +nil+ otherwise. * * No subclass in the Ruby Core or Standard Library uses this implementation. * */ static VALUE num_cmp(VALUE x, VALUE y) { if (x == y) return INT2FIX(0); return Qnil; } static VALUE num_equal(VALUE x, VALUE y) { VALUE result; if (x == y) return Qtrue; result = num_funcall1(y, id_eq, x); return RBOOL(RTEST(result)); } /* * call-seq: * self == other -> true or false * * Returns +true+ if +other+ has the same value as +self+, +false+ otherwise: * * 2.0 == 2 # => true * 2.0 == 2.0 # => true * 2.0 == Rational(2, 1) # => true * 2.0 == Complex(2, 0) # => true * * Float::NAN == Float::NAN returns an implementation-dependent value. * * Related: Float#eql? (requires +other+ to be a \Float). * */ VALUE rb_float_equal(VALUE x, VALUE y) { volatile double a, b; if (RB_INTEGER_TYPE_P(y)) { return rb_integer_float_eq(y, x); } else if (RB_FLOAT_TYPE_P(y)) { b = RFLOAT_VALUE(y); #if MSC_VERSION_BEFORE(1300) if (isnan(b)) return Qfalse; #endif } else { return num_equal(x, y); } a = RFLOAT_VALUE(x); #if MSC_VERSION_BEFORE(1300) if (isnan(a)) return Qfalse; #endif return RBOOL(a == b); } #define flo_eq rb_float_equal static VALUE rb_dbl_hash(double d); /* * call-seq: * hash -> integer * * Returns the integer hash value for +self+. * * See also Object#hash. */ static VALUE flo_hash(VALUE num) { return rb_dbl_hash(RFLOAT_VALUE(num)); } static VALUE rb_dbl_hash(double d) { return ST2FIX(rb_dbl_long_hash(d)); } VALUE rb_dbl_cmp(double a, double b) { if (isnan(a) || isnan(b)) return Qnil; if (a == b) return INT2FIX(0); if (a > b) return INT2FIX(1); if (a < b) return INT2FIX(-1); return Qnil; } /* * call-seq: * self <=> other -> -1, 0, +1, or nil * * Returns a value that depends on the numeric relation * between +self+ and +other+: * * - -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 # => 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 <=> 2.1 # => -1 * 2.0 <=> 'foo' # => nil * * This is the basis for the tests in the Comparable module. * * Float::NAN <=> Float::NAN returns an implementation-dependent value. * */ static VALUE flo_cmp(VALUE x, VALUE y) { double a, b; VALUE i; a = RFLOAT_VALUE(x); if (isnan(a)) return Qnil; if (RB_INTEGER_TYPE_P(y)) { VALUE rel = rb_integer_float_cmp(y, x); if (FIXNUM_P(rel)) return LONG2FIX(-FIX2LONG(rel)); return rel; } 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: * self > other -> true or false * * Returns +true+ if +self+ is numerically greater than +other+: * * 2.0 > 1 # => true * 2.0 > 1.0 # => true * 2.0 > Rational(1, 2) # => true * 2.0 > 2.0 # => false * * Float::NAN > Float::NAN returns an implementation-dependent value. * */ VALUE rb_float_gt(VALUE x, VALUE y) { double a, b; a = RFLOAT_VALUE(x); if (RB_INTEGER_TYPE_P(y)) { VALUE rel = rb_integer_float_cmp(y, x); if (FIXNUM_P(rel)) return RBOOL(-FIX2LONG(rel) > 0); return Qfalse; } else if (RB_FLOAT_TYPE_P(y)) { b = RFLOAT_VALUE(y); #if MSC_VERSION_BEFORE(1300) if (isnan(b)) return Qfalse; #endif } else { return rb_num_coerce_relop(x, y, '>'); } #if MSC_VERSION_BEFORE(1300) if (isnan(a)) return Qfalse; #endif return RBOOL(a > b); } /* * call-seq: * self >= other -> true or false * * Returns +true+ if +self+ is numerically greater than or equal to +other+: * * 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 * * Float::NAN >= Float::NAN returns an implementation-dependent value. * */ static VALUE flo_ge(VALUE x, VALUE y) { double a, b; a = RFLOAT_VALUE(x); 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 RBOOL(-FIX2LONG(rel) >= 0); return Qfalse; } else if (RB_FLOAT_TYPE_P(y)) { b = RFLOAT_VALUE(y); #if MSC_VERSION_BEFORE(1300) if (isnan(b)) return Qfalse; #endif } else { return rb_num_coerce_relop(x, y, idGE); } #if MSC_VERSION_BEFORE(1300) if (isnan(a)) return Qfalse; #endif return RBOOL(a >= b); } /* * call-seq: * self < other -> true or false * * Returns +true+ if +self+ is numerically less than +other+: * * 2.0 < 3 # => true * 2.0 < 3.0 # => true * 2.0 < Rational(3, 1) # => true * 2.0 < 2.0 # => false * * Float::NAN < Float::NAN returns an implementation-dependent value. * */ static VALUE flo_lt(VALUE x, VALUE y) { double a, b; a = RFLOAT_VALUE(x); if (RB_INTEGER_TYPE_P(y)) { VALUE rel = rb_integer_float_cmp(y, x); if (FIXNUM_P(rel)) return RBOOL(-FIX2LONG(rel) < 0); return Qfalse; } else if (RB_FLOAT_TYPE_P(y)) { b = RFLOAT_VALUE(y); #if MSC_VERSION_BEFORE(1300) if (isnan(b)) return Qfalse; #endif } else { return rb_num_coerce_relop(x, y, '<'); } #if MSC_VERSION_BEFORE(1300) if (isnan(a)) return Qfalse; #endif return RBOOL(a < b); } /* * call-seq: * self <= other -> true or false * * Returns +true+ if +self+ is numerically less than or equal to +other+: * * 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 * * Float::NAN <= Float::NAN returns an implementation-dependent value. * */ static VALUE flo_le(VALUE x, VALUE y) { double a, b; a = RFLOAT_VALUE(x); if (RB_INTEGER_TYPE_P(y)) { VALUE rel = rb_integer_float_cmp(y, x); if (FIXNUM_P(rel)) return RBOOL(-FIX2LONG(rel) <= 0); return Qfalse; } else if (RB_FLOAT_TYPE_P(y)) { b = RFLOAT_VALUE(y); #if MSC_VERSION_BEFORE(1300) if (isnan(b)) return Qfalse; #endif } else { return rb_num_coerce_relop(x, y, idLE); } #if MSC_VERSION_BEFORE(1300) if (isnan(a)) return Qfalse; #endif return RBOOL(a <= b); } /* * call-seq: * 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 * * Float::NAN.eql?(Float::NAN) returns an implementation-dependent value. * * Related: Float#== (performs type conversions). */ VALUE rb_float_eql(VALUE x, VALUE y) { if (RB_FLOAT_TYPE_P(y)) { double a = RFLOAT_VALUE(x); double b = RFLOAT_VALUE(y); #if MSC_VERSION_BEFORE(1300) if (isnan(a) || isnan(b)) return Qfalse; #endif return RBOOL(a == b); } return Qfalse; } #define flo_eql rb_float_eql VALUE rb_float_abs(VALUE flt) { double val = fabs(RFLOAT_VALUE(flt)); return DBL2NUM(val); } /* * call-seq: * nan? -> true or false * * 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_is_nan_p(VALUE num) { double value = RFLOAT_VALUE(num); return RBOOL(isnan(value)); } /* * call-seq: * infinite? -> -1, 1, or nil * * Returns: * * - 1, if +self+ is Infinity. * - -1 if +self+ is -Infinity. * - +nil+, otherwise. * * 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 * */ VALUE rb_flo_is_infinite_p(VALUE num) { double value = RFLOAT_VALUE(num); if (isinf(value)) { return INT2FIX( value < 0 ? -1 : 1 ); } return Qnil; } /* * call-seq: * finite? -> true or false * * Returns +true+ if +self+ is not +Infinity+, +-Infinity+, or +NaN+, * +false+ otherwise: * * 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 * */ VALUE rb_flo_is_finite_p(VALUE num) { double value = RFLOAT_VALUE(num); 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: * 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 f.next_float: * * 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 * */ static VALUE flo_next_float(VALUE vx) { return flo_nextafter(vx, HUGE_VAL); } /* * call-seq: * 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 f.pev_float: * * 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+): * * 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_prev_float(VALUE vx) { return flo_nextafter(vx, -HUGE_VAL); } 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; } } static int flo_ndigits(int argc, VALUE *argv) { if (rb_check_arity(argc, 0, 1)) { return NUM2INT(argv[0]); } return 0; } /* * :markup: markdown * * 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. * */ static VALUE flo_floor(int argc, VALUE *argv, VALUE num) { int ndigits = flo_ndigits(argc, argv); return rb_float_floor(num, ndigits); } /* * :markup: markdown * * 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. * */ static VALUE 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 number, f; number = RFLOAT_VALUE(num); if (number == 0.0) { return ndigits > 0 ? DBL2NUM(number) : INT2FIX(0); } if (ndigits > 0) { int binexp; frexp(number, &binexp); if (float_round_overflow(ndigits, binexp)) return num; if (number < 0.0 && float_round_underflow(ndigits, binexp)) return DBL2NUM(0.0); f = pow(10, ndigits); f = ceil(number * f) / f; return DBL2NUM(f); } else { num = dbl2ival(ceil(number)); if (ndigits < 0) num = rb_int_ceil(num, ndigits); return num; } } static int int_round_zero_p(VALUE num, int ndigits) { long bytes; /* If 10**N / 2 > num, then return 0 */ /* We have log_256(10) > 0.415241 and log_256(1/2) = -0.125, so */ if (FIXNUM_P(num)) { bytes = sizeof(long); } else if (RB_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 */ static VALUE rb_int_round(VALUE num, int ndigits, enum ruby_num_rounding_mode mode) { VALUE n, f, h, r; if (int_round_zero_p(num, ndigits)) { return INT2FIX(0); } f = int_pow(10, -ndigits); if (FIXNUM_P(num) && FIXNUM_P(f)) { SIGNED_VALUE x = FIX2LONG(num), y = FIX2LONG(f); int neg = x < 0; if (neg) x = -x; x = ROUND_CALL(mode, int_round, (x, y)); if (neg) x = -x; return LONG2NUM(x); } if (RB_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 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: * 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 ndigits.abs 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 * * - +:down+: round toward zero: * * 2.5.round(half: :down) # => 2 * 3.5.round(half: :down) # => 3 * (-2.5).round(half: :down) # => -2 * * - +:even+: round toward the candidate whose last nonzero digit is even: * * 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) { double number, f, x; VALUE nd, opt; int ndigits = 0; enum ruby_num_rounding_mode mode; if (rb_scan_args(argc, argv, "01:", &nd, &opt)) { ndigits = NUM2INT(nd); } mode = rb_num_get_rounding_option(opt); number = RFLOAT_VALUE(num); if (number == 0.0) { return ndigits > 0 ? DBL2NUM(number) : INT2FIX(0); } if (ndigits < 0) { return rb_int_round(flo_to_i(num), ndigits, mode); } if (ndigits == 0) { x = ROUND_CALL(mode, round, (number, 1.0)); return dbl2ival(x); } if (isfinite(number)) { int binexp; frexp(number, &binexp); if (float_round_overflow(ndigits, binexp)) return num; if (float_round_underflow(ndigits, binexp)) return DBL2NUM(0); 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); } 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 Recall that up to float_dig digits can be needed to represent a double, so if ndigits + exp >= float_dig, the intermediate value (number * 10 ** ndigits) will be an integer and thus the result is the original number. If ndigits + exp <= 0, the result is 0 or "1e#{exp}", so if ndigits + exp < 0, the result is 0. We have: 2 ** (binexp-1) <= |number| < 2 ** binexp 10 ** ((binexp-1)/log_2(10)) <= |number| < 10 ** (binexp/log_2(10)) If binexp >= 0, and since log_2(10) = 3.322259: 10 ** (binexp/4 - 1) < |number| < 10 ** (binexp/3) floor(binexp/4) <= exp <= ceil(binexp/3) If binexp <= 0, swap the /4 and the /3 So if ndigits + floor(binexp/(4 or 3)) >= float_dig, the result is number If ndigits + ceil(binexp/(3 or 4)) < 0 the result is 0 */ if (ndigits >= float_dig - (binexp > 0 ? binexp / 4 : binexp / 3 - 1)) { return TRUE; } return FALSE; } static int float_round_underflow(int ndigits, int binexp) { if (ndigits < - (binexp > 0 ? binexp / 3 + 1 : binexp / 4)) { return TRUE; } return FALSE; } /* * call-seq: * 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 (!) * */ static VALUE flo_to_i(VALUE num) { double f = RFLOAT_VALUE(num); if (f > 0.0) f = floor(f); if (f < 0.0) f = ceil(f); return dbl2ival(f); } /* * call-seq: * 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): * * 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 ndigits.abs 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. * */ static VALUE flo_truncate(int argc, VALUE *argv, VALUE num) { if (signbit(RFLOAT_VALUE(num))) return flo_ceil(argc, argv, num); else return flo_floor(argc, argv, num); } /* * call-seq: * 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 self.to_f.floor(ndigits). * * Related: #ceil, Float#floor. */ static VALUE num_floor(int argc, VALUE *argv, VALUE num) { return flo_floor(argc, argv, rb_Float(num)); } /* * call-seq: * ceil(ndigits = 0) -> float or integer * * 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]. * * Equivalent to self.to_f.ceil(ndigits). * * Related: #floor, Float#ceil. */ static VALUE num_ceil(int argc, VALUE *argv, VALUE num) { return flo_ceil(argc, argv, rb_Float(num)); } /* * call-seq: * round(digits = 0) -> integer or float * * Returns +self+ rounded to the nearest value with * a precision of +digits+ decimal digits. * * \Numeric implements this by converting +self+ to a Float and * invoking Float#round. */ static VALUE num_round(int argc, VALUE* argv, VALUE num) { return flo_round(argc, argv, rb_Float(num)); } /* * call-seq: * truncate(digits = 0) -> integer or float * * Returns +self+ truncated (toward zero) to * a precision of +digits+ decimal digits. * * \Numeric implements this by converting +self+ to a Float and * invoking Float#truncate. */ static VALUE num_truncate(int argc, VALUE *argv, VALUE num) { return flo_truncate(argc, argv, rb_Float(num)); } double ruby_float_step_size(double beg, double end, double unit, int excl) { const double epsilon = DBL_EPSILON; double d, n, err; if (unit == 0) { return HUGE_VAL; } if (isinf(unit)) { 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); 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); 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, 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= 0 ? end < d : d < end) d = end; rb_yield(DBL2NUM(d)); } } return TRUE; } return FALSE; } VALUE ruby_num_interval_step_size(VALUE from, VALUE to, VALUE step, int excl) { if (FIXNUM_P(from) && FIXNUM_P(to) && FIXNUM_P(step)) { long 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); } r = rb_check_funcall(num, '>', 1, &zero); if (UNDEF_P(r)) { coerce_failed(num, INT2FIX(0)); } return !RTEST(r); } 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 { /* 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, VALUE eobj) { VALUE to, step; int argc = args ? RARRAY_LENINT(args) : 0; const VALUE *argv = args ? RARRAY_CONST_PTR(args) : 0; num_step_scan_args(argc, argv, &to, &step, TRUE, FALSE); return ruby_num_interval_step_size(from, to, step, FALSE); } /* * call-seq: * 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. * * Keyword Arguments * * 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 * * Positional Arguments * * 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] * * Implementation Notes * * 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 * floor(n + n*Float::EPSILON) + 1 times, * where n = (limit - self)/step. * */ static VALUE num_step(int argc, VALUE *argv, VALUE from) { VALUE to, step; int desc, inf; 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); } 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) && (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)) long rb_num2long(VALUE val) { again: if (NIL_P(val)) { rb_raise(rb_eTypeError, "no implicit conversion from nil to integer"); } if (FIXNUM_P(val)) return FIX2LONG(val); 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; } } static unsigned long rb_num2ulong_internal(VALUE val, int *wrap_p) { again: if (NIL_P(val)) { rb_raise(rb_eTypeError, "no implicit conversion of nil into Integer"); } 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); } 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"); } #if SIZEOF_INT < SIZEOF_LONG static void check_int(long num) { if ((long)(int)num != num) { rb_out_of_int(num); } } static void check_uint(unsigned long num, int sign) { if (sign) { /* minus */ if (num < (unsigned long)INT_MIN) rb_raise(rb_eRangeError, "integer %ld too small to convert to 'unsigned int'", (long)num); } else { /* plus */ if (UINT_MAX < num) rb_raise(rb_eRangeError, "integer %lu too big to convert to 'unsigned int'", num); } } long rb_num2int(VALUE val) { long num = rb_num2long(val); check_int(num); return num; } long rb_fix2int(VALUE val) { long num = FIXNUM_P(val)?FIX2LONG(val):rb_num2long(val); check_int(num); return num; } unsigned long rb_num2uint(VALUE val) { int wrap; unsigned long num = rb_num2ulong_internal(val, &wrap); check_uint(num, wrap); return num; } unsigned long rb_fix2uint(VALUE val) { unsigned long num; if (!FIXNUM_P(val)) { return rb_num2uint(val); } num = FIX2ULONG(val); check_uint(num, FIXNUM_NEGATIVE_P(val)); return num; } #else long rb_num2int(VALUE val) { return rb_num2long(val); } long 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 NORETURN(static void rb_out_of_short(SIGNED_VALUE num)); static void rb_out_of_short(SIGNED_VALUE num) { rb_raise(rb_eRangeError, "integer %"PRIdVALUE " too %s to convert to 'short'", num, num < 0 ? "small" : "big"); } static void check_short(long num) { if ((long)(short)num != num) { rb_out_of_short(num); } } static void check_ushort(unsigned long num, int sign) { if (sign) { /* minus */ if (num < (unsigned long)SHRT_MIN) rb_raise(rb_eRangeError, "integer %ld too small to convert to 'unsigned short'", (long)num); } else { /* plus */ if (USHRT_MAX < num) rb_raise(rb_eRangeError, "integer %lu too big to convert to 'unsigned short'", num); } } short rb_num2short(VALUE val) { long num = rb_num2long(val); check_short(num); return num; } short rb_fix2short(VALUE val) { long num = FIXNUM_P(val)?FIX2LONG(val):rb_num2long(val); check_short(num); return num; } unsigned short rb_num2ushort(VALUE val) { int wrap; unsigned long num = rb_num2ulong_internal(val, &wrap); check_ushort(num, wrap); return num; } unsigned short rb_fix2ushort(VALUE val) { unsigned long num; if (!FIXNUM_P(val)) { return rb_num2ushort(val); } num = FIX2ULONG(val); check_ushort(num, FIXNUM_NEGATIVE_P(val)); return num; } VALUE rb_num2fix(VALUE val) { long v; if (FIXNUM_P(val)) return val; v = rb_num2long(val); if (!FIXABLE(v)) rb_raise(rb_eRangeError, "integer %ld out of range of fixnum", v); return LONG2FIX(v); } #if HAVE_LONG_LONG #define LLONG_MIN_MINUS_ONE ((double)LLONG_MIN-1) #define LLONG_MAX_PLUS_ONE (2*(double)(LLONG_MAX/2+1)) #define ULLONG_MAX_PLUS_ONE (2*(double)(ULLONG_MAX/2+1)) #ifndef ULLONG_MAX #define ULLONG_MAX ((unsigned LONG_LONG)LLONG_MAX*2+1) #endif #define LLONG_MIN_MINUS_ONE_IS_LESS_THAN(n) \ (LLONG_MIN_MINUS_ONE == (double)LLONG_MIN ? \ LLONG_MIN <= (n): \ LLONG_MIN_MINUS_ONE < (n)) LONG_LONG rb_num2ll(VALUE val) { if (NIL_P(val)) { rb_raise(rb_eTypeError, "no implicit conversion from nil"); } if (FIXNUM_P(val)) return (LONG_LONG)FIX2LONG(val); 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); return NUM2LL(val); } unsigned LONG_LONG rb_num2ull(VALUE val) { 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); } } #endif /* HAVE_LONG_LONG */ /******************************************************************** * * Document-class: Integer * * 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. * - #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. * - #|: Returns the bitwise OR of +self+ and the given value. * * === 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 (0..self-1). * - #upto: Calls the given block with each integer value from +self+ * up to the given value. * */ 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_even_p(VALUE num) { if (FIXNUM_P(num)) { return RBOOL((num & 2) == 0); } else { RUBY_ASSERT(RB_BIGNUM_TYPE_P(num)); return rb_big_even_p(num); } } VALUE rb_int_even_p(VALUE num) { return int_even_p(num); } /* * call-seq: * 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?. * */ static VALUE int_allbits_p(VALUE num, VALUE mask) { mask = rb_to_int(mask); return rb_int_equal(rb_int_and(num, mask), mask); } /* * call-seq: * 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?. * */ static VALUE int_anybits_p(VALUE num, VALUE mask) { mask = rb_to_int(mask); return RBOOL(!int_zero_p(rb_int_and(num, mask))); } /* * call-seq: * 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) * * Related: Integer#allbits?, Integer#anybits?. * */ static VALUE int_nobits_p(VALUE num, VALUE mask) { mask = rb_to_int(mask); return RBOOL(int_zero_p(rb_int_and(num, mask))); } /* * call-seq: * succ -> next_integer * * Returns the successor integer of +self+ (equivalent to self + 1): * * 1.succ #=> 2 * -1.succ #=> 0 * * Related: Integer#pred (predecessor value). */ VALUE rb_int_succ(VALUE num) { if (FIXNUM_P(num)) { long i = FIX2LONG(num) + 1; return LONG2NUM(i); } 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: * pred -> next_integer * * Returns the predecessor of +self+ (equivalent to self - 1): * * 1.pred #=> 0 * -1.pred #=> -2 * * Related: Integer#succ (successor value). * */ static VALUE rb_int_pred(VALUE num) { if (FIXNUM_P(num)) { long i = FIX2LONG(num) - 1; return LONG2NUM(i); } 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 VALUE rb_enc_uint_chr(unsigned int code, rb_encoding *enc) { int n; VALUE str; switch (n = rb_enc_codelen(code, enc)) { case ONIGERR_INVALID_CODE_POINT_VALUE: rb_raise(rb_eRangeError, "invalid codepoint 0x%X in %s", code, rb_enc_name(enc)); break; case ONIGERR_TOO_BIG_WIDE_CHAR_VALUE: case 0: rb_raise(rb_eRangeError, "%u out of char range", code); break; } str = rb_enc_str_new(0, n, enc); rb_enc_mbcput(code, RSTRING_PTR(str), enc); if (rb_enc_precise_mbclen(RSTRING_PTR(str), RSTRING_END(str), enc) != n) { rb_raise(rb_eRangeError, "invalid codepoint 0x%X in %s", code, rb_enc_name(enc)); } return str; } /* 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. * * Related: Integer#ord. * */ static VALUE int_chr(int argc, VALUE *argv, VALUE num) { char c; unsigned int i; rb_encoding *enc; if (rb_num_to_uint(num, &i) == 0) { } else if (FIXNUM_P(num)) { rb_raise(rb_eRangeError, "%ld out of char range", FIX2LONG(num)); } else { rb_raise(rb_eRangeError, "bignum out of char range"); } switch (argc) { case 0: if (0xff < i) { enc = rb_default_internal_encoding(); if (!enc) { rb_raise(rb_eRangeError, "%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; default: rb_error_arity(argc, 0, 1); } enc = rb_to_encoding(argv[0]); if (!enc) enc = rb_ascii8bit_encoding(); decode: return rb_enc_uint_chr(i, enc); } /* * Fixnum */ static VALUE fix_uminus(VALUE num) { return LONG2NUM(-FIX2LONG(num)); } VALUE rb_int_uminus(VALUE 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) { 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); } #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"); } if (val < 0) { u = 1 + (unsigned long)(-(val + 1)); /* u = -val avoiding overflow */ neg = 1; } else { u = val; } do { *--b = ruby_digitmap[(int)(u % base)]; } while (u /= base); if (neg) { *--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: * to_s(base = 10) -> string * * 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" * 78546939656932.to_s(36) # => "rubyrules" * * Raises an exception if +base+ is out of range. */ VALUE rb_int_to_s(int argc, VALUE *argv, VALUE x) { int base; if (rb_check_arity(argc, 0, 1)) base = NUM2INT(argv[0]); else base = 10; return rb_int2str(x, base); } VALUE rb_int2str(VALUE x, int base) { if (FIXNUM_P(x)) { return rb_fix2str(x, base); } else if (RB_BIGNUM_TYPE_P(x)) { return rb_big2str(x, base); } return rb_any_to_s(x); } static VALUE fix_plus(VALUE x, VALUE y) { if (FIXNUM_P(y)) { return rb_fix_plus_fix(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: * self + numeric -> numeric_result * * Performs addition: * * 2 + 2 # => 4 * -2 + 2 # => 0 * -2 + -2 # => -4 * 2 + 2.0 # => 4.0 * 2 + Rational(2, 1) # => (4/1) * 2 + Complex(2, 0) # => (4+0i) * */ 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)) { 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, '-'); } } /* * call-seq: * self - numeric -> numeric_result * * Performs subtraction: * * 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) * */ 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)) static VALUE fix_mul(VALUE x, VALUE y) { if (FIXNUM_P(y)) { 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, '*'); } } /* * call-seq: * self * numeric -> numeric_result * * Performs multiplication: * * 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) */ VALUE rb_int_mul(VALUE x, VALUE y) { if (FIXNUM_P(x)) { return fix_mul(x, y); } else if (RB_BIGNUM_TYPE_P(x)) { return rb_big_mul(x, y); } return rb_num_coerce_bin(x, y, '*'); } static double fix_fdiv_double(VALUE x, VALUE 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 { 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); } } 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(""); } } /* * call-seq: * fdiv(numeric) -> float * * Returns the Float result of dividing +self+ by +numeric+: * * 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. * */ VALUE rb_int_fdiv(VALUE x, VALUE y) { 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)) { 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); } } static VALUE fix_div(VALUE x, VALUE y) { return fix_divide(x, y, '/'); } /* * call-seq: * self / numeric -> numeric_result * * Performs division; for integer +numeric+, truncates the result to an integer: * * 4 / 3 # => 1 * 4 / -3 # => -2 * -4 / 3 # => -2 * -4 / -3 # => 1 * * For other +numeric+, returns non-integer result: * * 4 / 3.0 # => 1.3333333333333333 * 4 / Rational(3, 1) # => (4/3) * 4 / Complex(3, 0) # => ((4/3)+0i) * */ 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, id_div); } /* * call-seq: * 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+. * */ 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)) { 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, '%'); } } /* * call-seq: * self % other -> real_number * * Returns +self+ modulo +other+ as a real number. * * 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); } else if (RB_BIGNUM_TYPE_P(x)) { return rb_big_modulo(x, y); } return num_modulo(x, y); } /* * call-seq: * 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) * */ 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)) { 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 [q, r], 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 ** numeric -> numeric_result * * Raises +self+ to the power of +numeric+: * * 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; else neg = 0; y &= ~1; do { 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; } } 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; } 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) { long a = FIX2LONG(x); if (FIXNUM_P(y)) { 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: * self ** numeric -> numeric_result * * Raises +self+ to the power of +numeric+: * * 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) * */ 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; 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); } else { return num_equal(x, y); } } /* * call-seq: * self == other -> true or false * * Returns +true+ if +self+ is numerically equal to +other+; +false+ otherwise. * * 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); } 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; } else if (RB_FLOAT_TYPE_P(y)) { return rb_integer_float_cmp(x, y); } else { return rb_num_coerce_cmp(x, y, id_cmp); } } /* * call-seq: * self <=> other -> -1, 0, +1, or nil * * Returns: * * - -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 <=> 0 # => 1 * 1 <=> 'foo' # => nil * * 1 <=> 1.0 # => 0 * 1 <=> Rational(1, 1) # => 0 * 1 <=> Complex(1, 0) # => 0 * * This method is the basis for comparisons in module Comparable. * */ 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)) { 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: * self > other -> true or false * * Returns +true+ if the value of +self+ is greater than that of +other+: * * 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. * */ 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)) { 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)) { 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: * self >= real -> true or false * * Returns +true+ if the value of +self+ is greater than or equal to * that of +other+: * * 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. * */ 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)) { 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: * self < other -> true or false * * Returns +true+ if the value of +self+ is less than that of +other+: * * 1 < 0 # => false * 1 < 1 # => false * 1 < 2 # => true * 1 < 0.5 # => false * 1 < Rational(1, 2) # => false * * Raises an exception if the comparison cannot be made. * */ 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)) { 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)) { 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: * self <= real -> true or false * * Returns +true+ if the value of +self+ is less than or equal to * that of +other+: * * 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. * */ static VALUE 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; } VALUE rb_int_comp(VALUE num) { if (FIXNUM_P(num)) { return fix_comp(num); } 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) { VALUE ret, args[3]; args[0] = (VALUE)func; args[1] = x; args[2] = y; do_coerce(&args[1], &args[2], TRUE); ret = rb_exec_recursive_paired(num_funcall_bit_1, args[2], args[1], (VALUE)args); if (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); } if (RB_BIGNUM_TYPE_P(y)) { return rb_big_and(y, x); } return rb_num_coerce_bit(x, y, '&'); } /* * 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). * */ 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); } if (RB_BIGNUM_TYPE_P(y)) { return rb_big_or(y, x); } return rb_num_coerce_bit(x, y, '|'); } /* * 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). * */ 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); } if (RB_BIGNUM_TYPE_P(y)) { return rb_big_xor(y, x); } return rb_num_coerce_bit(x, y, '^'); } /* * 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). * */ static VALUE 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); width = FIX2LONG(y); if (width < 0) return fix_rshift(val, (unsigned long)-width); return fix_lshift(val, width); } 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)); } val = val << width; return LONG2NUM(val); } /* * 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#>>. * */ 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); i = FIX2LONG(y); if (i == 0) return x; if (i < 0) return fix_lshift(val, (unsigned long)-i); return fix_rshift(val, i); } 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); } val = RSHIFT(val, i); return LONG2FIX(val); } /* * call-seq: * self >> count -> integer * * Returns +self+ with bits shifted +count+ positions to the right, * or to the left if +count+ is negative: * * n = 0b11110000 * "%08b" % (n >> 1) # => "01111000" * "%08b" % (n >> 3) # => "00011110" * "%08b" % (n >> -1) # => "111100000" * "%08b" % (n >> -3) # => "11110000000" * * Related: Integer#<<. * */ 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 (!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 (val & (1L< 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_aref1(VALUE num, VALUE arg) { VALUE orig_num = num, 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); } } num = rb_int_rshift(num, beg); 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)); VALUE mask = generate_mask(len); num = rb_int_and(num, mask); } else if (cmp == 0) { if (excl) return INT2FIX(0); num = orig_num; arg = beg; goto one_bit; } return num; } 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; } static VALUE int_aref2(VALUE num, VALUE beg, VALUE len) { num = rb_int_rshift(num, beg); VALUE mask = generate_mask(len); num = rb_int_and(num, mask); return num; } /* * call-seq: * 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, n[i] is equivalent to (n >> i) & 1. * Thus, negative index always returns zero: * * 255[-1] # => 0 * * 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 range.size bits from +self+, * beginning at range.begin 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 int_aref(int const argc, VALUE * const argv, VALUE const 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 Qnil; } /* * call-seq: * to_f -> float * * Converts +self+ to a Float: * * 1.to_f # => 1.0 * -1.to_f # => -1.0 * * If the value of +self+ does not fit in a Float, * the result is infinity: * * (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); if (i < 0) i = -i; 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_lt(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: * 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] * * Raises an exception if +self+ is negative or +base+ is less than 2. * */ static VALUE rb_int_digits(int argc, VALUE *argv, VALUE num) { VALUE base_value; long base; if (rb_num_negative_p(num)) rb_raise(rb_eMathDomainError, "out of domain"); if (rb_check_arity(argc, 0, 1)) { base_value = rb_to_int(argv[0]); if (!RB_INTEGER_TYPE_P(base_value)) rb_raise(rb_eTypeError, "wrong argument type %s (expected Integer)", rb_obj_classname(argv[0])); if (RB_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, VALUE eobj) { return ruby_num_interval_step_size(from, RARRAY_AREF(args, 0), INT2FIX(1), FALSE); } /* * call-seq: * upto(limit) {|i| ... } -> self * upto(limit) -> enumerator * * Calls the given block with each integer value from +self+ up to +limit+; * returns +self+: * * 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 * * With no block given, returns an Enumerator. * */ static VALUE int_upto(VALUE from, VALUE to) { RETURN_SIZED_ENUMERATOR(from, 1, &to, int_upto_size); if (FIXNUM_P(from) && FIXNUM_P(to)) { long i, end; end = FIX2LONG(to); for (i = FIX2LONG(from); i <= end; i++) { rb_yield(LONG2FIX(i)); } } else { VALUE i = from, c; 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, VALUE eobj) { return ruby_num_interval_step_size(from, RARRAY_AREF(args, 0), INT2FIX(-1), FALSE); } /* * call-seq: * downto(limit) {|i| ... } -> self * downto(limit) -> enumerator * * Calls the given block with each integer value from +self+ down to +limit+; * returns +self+: * * 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 * * With no block given, returns an Enumerator. * */ static VALUE int_downto(VALUE from, VALUE to) { RETURN_SIZED_ENUMERATOR(from, 1, &to, int_downto_size); if (FIXNUM_P(from) && FIXNUM_P(to)) { long i, end; end = FIX2LONG(to); for (i=FIX2LONG(from); i >= end; i--) { rb_yield(LONG2FIX(i)); } } else { 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); } return from; } static VALUE int_dotimes_size(VALUE num, VALUE args, VALUE eobj) { return int_neg_p(num) ? INT2FIX(0) : num; } /* * call-seq: * round(ndigits= 0, half: :up) -> integer * * Returns +self+ rounded to the nearest value with * a precision of +ndigits+ decimal digits. * * When +ndigits+ is negative, the returned value * has at least ndigits.abs trailing zeros: * * 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 * * * - +: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_round(int argc, VALUE* argv, VALUE num) { int ndigits; int mode; VALUE nd, opt; if (!rb_scan_args(argc, argv, "01:", &nd, &opt)) return num; ndigits = NUM2INT(nd); mode = rb_num_get_rounding_option(opt); if (ndigits >= 0) { return num; } return rb_int_round(num, ndigits, mode); } /* * :markup: markdown * * call-seq: * floor(ndigits = 0) -> integer * * 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. * */ static VALUE int_floor(int argc, VALUE* argv, VALUE num) { int ndigits; if (!rb_check_arity(argc, 0, 1)) return num; ndigits = NUM2INT(argv[0]); if (ndigits >= 0) { return num; } return rb_int_floor(num, ndigits); } /* * :markup: markdown * * call-seq: * 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`: * * | 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 int_ceil(int argc, VALUE* argv, VALUE num) { int ndigits; if (!rb_check_arity(argc, 0, 1)) return num; ndigits = NUM2INT(argv[0]); if (ndigits >= 0) { return num; } return rb_int_ceil(num, ndigits); } /* * call-seq: * 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 ndigits.abs 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. * */ static VALUE int_truncate(int argc, VALUE* argv, VALUE num) { int ndigits; if (!rb_check_arity(argc, 0, 1)) return num; ndigits = NUM2INT(argv[0]); if (ndigits >= 0) { return num; } return rb_int_truncate(num, ndigits); } #define DEFINE_INT_SQRT(rettype, prefix, argtype) \ rettype \ prefix##_isqrt(argtype n) \ { \ if (!argtype##_IN_DOUBLE_P(n)) { \ unsigned int b = bit_length(n); \ argtype t; \ rettype x = (rettype)(n >> (b/2+1)); \ x |= ((rettype)1LU << (b-1)/2); \ while ((t = n/x) < (argtype)x) x = (rettype)((x + t) >> 1); \ return x; \ } \ return (rettype)sqrt(argtype##_TO_DOUBLE(n)); \ } #if SIZEOF_LONG*CHAR_BIT > DBL_MANT_DIG # define RB_ULONG_IN_DOUBLE_P(n) ((n) < (1UL << DBL_MANT_DIG)) #else # define RB_ULONG_IN_DOUBLE_P(n) 1 #endif #define RB_ULONG_TO_DOUBLE(n) (double)(n) #define RB_ULONG unsigned long DEFINE_INT_SQRT(unsigned long, rb_ulong, RB_ULONG) #if 2*SIZEOF_BDIGIT > SIZEOF_LONG # if 2*SIZEOF_BDIGIT*CHAR_BIT > DBL_MANT_DIG # define BDIGIT_DBL_IN_DOUBLE_P(n) ((n) < ((BDIGIT_DBL)1UL << DBL_MANT_DIG)) # else # define BDIGIT_DBL_IN_DOUBLE_P(n) 1 # endif # ifdef ULL_TO_DOUBLE # define BDIGIT_DBL_TO_DOUBLE(n) ULL_TO_DOUBLE(n) # else # define BDIGIT_DBL_TO_DOUBLE(n) (double)(n) # endif DEFINE_INT_SQRT(BDIGIT, rb_bdigit_dbl, BDIGIT_DBL) #endif #define domain_error(msg) \ rb_raise(rb_eMathDomainError, "Numerical argument is out of domain - " #msg) /* * call-seq: * 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 Math.sqrt(numeric).floor, * 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. * */ static VALUE rb_int_s_isqrt(VALUE self, VALUE num) { unsigned long n, sq; num = rb_to_int(num); if (FIXNUM_P(num)) { if (FIXNUM_NEGATIVE_P(num)) { domain_error("isqrt"); } n = FIX2ULONG(num); sq = rb_ulong_isqrt(n); return LONG2FIX(sq); } else { size_t biglen; if (RBIGNUM_NEGATIVE_P(num)) { domain_error("isqrt"); } biglen = BIGNUM_LEN(num); if (biglen == 0) return INT2FIX(0); #if SIZEOF_BDIGIT <= SIZEOF_LONG /* short-circuit */ if (biglen == 1) { n = BIGNUM_DIGITS(num)[0]; sq = rb_ulong_isqrt(n); return ULONG2NUM(sq); } #endif return rb_big_isqrt(num); } } /* * 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 :to_int, * calls object.to_int and returns the result. * Integer.try_convert(1.25) # => 1 * * Returns +nil+ if +object+ does not respond to :to_int * Integer.try_convert([]) # => nil * * Raises an exception unless object.to_int returns an \Integer object. */ static VALUE int_s_try_convert(VALUE self, VALUE num) { return rb_check_integer_type(num); } /* * Document-class: ZeroDivisionError * * Raised when attempting to divide an integer by 0. * * 42 / 0 #=> ZeroDivisionError: divided by 0 * * Note that only division by an exact 0 will raise the exception: * * 42 / 0.0 #=> Float::INFINITY * 42 / -0.0 #=> -Float::INFINITY * 0 / 0.0 #=> NaN */ /* * Document-class: FloatDomainError * * Raised when attempting to convert special float values (in particular * +Infinity+ or +NaN+) to numerical classes which don't support them. * * Float::INFINITY.to_r #=> FloatDomainError: Infinity */ /* * Document-class: Numeric * * \Numeric is the class from which all higher-level numeric classes should inherit. * * \Numeric allows instantiation of heap-allocated objects. Other core numeric classes such as * Integer are implemented as immediates, which means that each Integer is a single immutable * object which is always passed by value. * * a = 1 * 1.object_id == a.object_id #=> true * * There can only ever be one instance of the integer +1+, for example. Ruby ensures this * by preventing instantiation. If duplication is attempted, the same instance is returned. * * Integer.new(1) #=> NoMethodError: undefined method `new' for Integer:Class * 1.dup #=> 1 * 1.object_id == 1.dup.object_id #=> true * * For this reason, \Numeric should be used when defining other numeric classes. * * Classes which inherit from \Numeric must implement +coerce+, which returns a two-member * Array containing an object that has been coerced into an instance of the new class * and +self+ (see #coerce). * * Inheriting classes should also implement arithmetic operator methods (+, * -, * and /) and the <=> operator (see * Comparable). These methods may rely on +coerce+ to ensure interoperability with * instances of other numeric classes. * * class Tally < Numeric * def initialize(string) * @string = string * end * * def to_s * @string * end * * def to_i * @string.size * end * * def coerce(other) * [self.class.new('|' * other.to_i), self] * end * * def <=>(other) * to_i <=> other.to_i * end * * def +(other) * self.class.new('|' * (to_i + other.to_i)) * end * * def -(other) * self.class.new('|' * (to_i - other.to_i)) * end * * def *(other) * self.class.new('|' * (to_i * other.to_i)) * end * * def /(other) * self.class.new('|' * (to_i / other.to_i)) * end * end * * tally = Tally.new('||') * puts tally * 2 #=> "||||" * puts tally > 1 #=> true * * == 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 -Infinity, finite, or +Infinity. * - #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 [coerced_self, coerced_other] * 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 [quotient, modulus] 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 Complex(0, self). * 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 [self.abs, self.arg]. * - #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 [self, 0]. * - #remainder: Returns self-arg*(self/arg).truncate 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. * */ void Init_Numeric(void) { #ifdef _UNICOSMP /* Turn off floating point exceptions for divide by zero, etc. */ _set_Creg(0, 0); #endif 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); rb_cNumeric = rb_define_class("Numeric", rb_cObject); rb_define_method(rb_cNumeric, "singleton_method_added", num_sadded, 1); rb_include_module(rb_cNumeric, rb_mComparable); 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_uminus, 0); rb_define_method(rb_cNumeric, "<=>", num_cmp, 1); rb_define_method(rb_cNumeric, "eql?", num_eql, 1); rb_define_method(rb_cNumeric, "fdiv", num_fdiv, 1); rb_define_method(rb_cNumeric, "div", num_div, 1); rb_define_method(rb_cNumeric, "divmod", num_divmod, 1); rb_define_method(rb_cNumeric, "%", num_modulo, 1); rb_define_method(rb_cNumeric, "modulo", num_modulo, 1); rb_define_method(rb_cNumeric, "remainder", num_remainder, 1); rb_define_method(rb_cNumeric, "abs", num_abs, 0); rb_define_method(rb_cNumeric, "magnitude", num_abs, 0); rb_define_method(rb_cNumeric, "to_int", num_to_int, 0); rb_define_method(rb_cNumeric, "zero?", num_zero_p, 0); rb_define_method(rb_cNumeric, "nonzero?", num_nonzero_p, 0); rb_define_method(rb_cNumeric, "floor", num_floor, -1); rb_define_method(rb_cNumeric, "ceil", num_ceil, -1); rb_define_method(rb_cNumeric, "round", num_round, -1); rb_define_method(rb_cNumeric, "truncate", num_truncate, -1); rb_define_method(rb_cNumeric, "step", num_step, -1); rb_define_method(rb_cNumeric, "positive?", num_positive_p, 0); rb_define_method(rb_cNumeric, "negative?", num_negative_p, 0); rb_cInteger = rb_define_class("Integer", rb_cNumeric); rb_undef_alloc_func(rb_cInteger); rb_undef_method(CLASS_OF(rb_cInteger), "new"); rb_define_singleton_method(rb_cInteger, "sqrt", rb_int_s_isqrt, 1); rb_define_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, "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, "to_f", int_to_f, 0); rb_define_method(rb_cInteger, "floor", int_floor, -1); rb_define_method(rb_cInteger, "ceil", int_ceil, -1); rb_define_method(rb_cInteger, "truncate", int_truncate, -1); rb_define_method(rb_cInteger, "round", int_round, -1); rb_define_method(rb_cInteger, "<=>", rb_int_cmp, 1); rb_define_method(rb_cInteger, "+", rb_int_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, "^", 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); rb_undef_alloc_func(rb_cFloat); rb_undef_method(CLASS_OF(rb_cFloat), "new"); /* * The base of the floating point, or number of unique digits used to * represent the number. * * Usually defaults to 2 on most systems, which would represent a base-10 decimal. */ rb_define_const(rb_cFloat, "RADIX", INT2FIX(FLT_RADIX)); /* * The number of base digits for the +double+ data type. * * Usually defaults to 53. */ rb_define_const(rb_cFloat, "MANT_DIG", INT2FIX(DBL_MANT_DIG)); /* * The minimum number of significant decimal digits in a double-precision * floating point. * * Usually defaults to 15. */ rb_define_const(rb_cFloat, "DIG", INT2FIX(DBL_DIG)); /* * The smallest possible exponent value in a double-precision floating * point. * * Usually defaults to -1021. */ rb_define_const(rb_cFloat, "MIN_EXP", INT2FIX(DBL_MIN_EXP)); /* * The largest possible exponent value in a double-precision floating * point. * * Usually defaults to 1024. */ rb_define_const(rb_cFloat, "MAX_EXP", INT2FIX(DBL_MAX_EXP)); /* * The smallest negative exponent in a double-precision floating point * where 10 raised to this power minus 1. * * Usually defaults to -307. */ rb_define_const(rb_cFloat, "MIN_10_EXP", INT2FIX(DBL_MIN_10_EXP)); /* * The largest positive exponent in a double-precision floating point where * 10 raised to this power minus 1. * * Usually defaults to 308. */ rb_define_const(rb_cFloat, "MAX_10_EXP", INT2FIX(DBL_MAX_10_EXP)); /* * The smallest positive normalized number in a double-precision floating point. * * Usually defaults to 2.2250738585072014e-308. * * If the platform supports denormalized numbers, * there are numbers between zero and Float::MIN. * 0.0.next_float returns the smallest positive floating point number * including denormalized numbers. */ rb_define_const(rb_cFloat, "MIN", DBL2NUM(DBL_MIN)); /* * The largest possible integer in a double-precision floating point number. * * Usually defaults to 1.7976931348623157e+308. */ rb_define_const(rb_cFloat, "MAX", DBL2NUM(DBL_MAX)); /* * The difference between 1 and the smallest double-precision floating * point number greater than 1. * * Usually defaults to 2.2204460492503131e-16. */ rb_define_const(rb_cFloat, "EPSILON", DBL2NUM(DBL_EPSILON)); /* * An expression representing positive infinity. */ rb_define_const(rb_cFloat, "INFINITY", DBL2NUM(HUGE_VAL)); /* * An expression representing a value which is "not a number". */ rb_define_const(rb_cFloat, "NAN", DBL2NUM(nan(""))); rb_define_method(rb_cFloat, "to_s", flo_to_s, 0); rb_define_alias(rb_cFloat, "inspect", "to_s"); rb_define_method(rb_cFloat, "coerce", flo_coerce, 1); rb_define_method(rb_cFloat, "+", 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, "**", 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, ">", 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_i", flo_to_i, 0); rb_define_method(rb_cFloat, "to_int", flo_to_i, 0); rb_define_method(rb_cFloat, "floor", flo_floor, -1); rb_define_method(rb_cFloat, "ceil", flo_ceil, -1); rb_define_method(rb_cFloat, "round", flo_round, -1); rb_define_method(rb_cFloat, "truncate", flo_truncate, -1); rb_define_method(rb_cFloat, "nan?", flo_is_nan_p, 0); rb_define_method(rb_cFloat, "infinite?", 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"