/********************************************************************** 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/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 f, d, xs = x * s; if (x > 0.0) { f = floor(xs); d = xs - f; if (d > 0.5) d = 1.0; else if (d == 0.5 || ((double)((f + 0.5) / s) <= x)) d = fmod(f, 2.0); else d = 0.0; x = f + d; } else if (x < 0.0) { f = ceil(xs); d = f - xs; if (d > 0.5) d = 1.0; else if (d == 0.5 || ((double)((f - 0.5) / s) >= x)) d = fmod(-f, 2.0); else d = 0.0; x = f - d; } return x; } static VALUE fix_uminus(VALUE num); static VALUE fix_mul(VALUE x, VALUE y); static VALUE fix_lshift(long, unsigned long); static VALUE fix_rshift(long, unsigned long); static VALUE int_pow(long x, unsigned long y); static VALUE int_even_p(VALUE x); static int int_round_zero_p(VALUE num, int ndigits); 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_TYPE_P(val, T_BIGNUM)) { if (BIGNUM_NEGATIVE_P(val)) return NUMERR_NEGATIVE; #if SIZEOF_INT < SIZEOF_LONG /* long is 64bit */ return NUMERR_TOOLARGE; #else /* long is 32bit */ if (rb_absint_size(val, NULL) > sizeof(int)) return NUMERR_TOOLARGE; *ret = (unsigned int)rb_big2ulong((VALUE)val); return 0; #endif } return NUMERR_TYPE; } #define method_basic_p(klass) rb_method_basic_definition_p(klass, mid) static inline int int_pos_p(VALUE num) { if (FIXNUM_P(num)) { return FIXNUM_POSITIVE_P(num); } else if (RB_TYPE_P(num, T_BIGNUM)) { return BIGNUM_POSITIVE_P(num); } rb_raise(rb_eTypeError, "not an Integer"); } static inline int int_neg_p(VALUE num) { if (FIXNUM_P(num)) { return FIXNUM_NEGATIVE_P(num); } else if (RB_TYPE_P(num, T_BIGNUM)) { return BIGNUM_NEGATIVE_P(num); } rb_raise(rb_eTypeError, "not an Integer"); } int rb_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: * num.coerce(numeric) -> array * * If +numeric+ is the same type as +num+, returns an array * [numeric, num]. Otherwise, returns an array with both * +numeric+ and +num+ represented as Float objects. * * This coercion mechanism is used by Ruby to handle mixed-type numeric * operations: it is intended to find a compatible common type between the two * operands of the operator. * * 1.coerce(2.5) #=> [2.5, 1.0] * 1.2.coerce(3) #=> [3.0, 1.2] * 1.coerce(2) #=> [2, 1] */ static VALUE num_coerce(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 (ary == Qundef) { 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; } VALUE rb_num_coerce_relop(VALUE x, VALUE y, ID func) { VALUE c, x0 = x, y0 = y; if (!do_coerce(&x, &y, FALSE) || NIL_P(c = rb_funcall(x, func, 1, y))) { rb_cmperr(x0, y0); return Qnil; /* not reached */ } return c; } 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: * num.clone(freeze: true) -> num * * Returns the receiver. +freeze+ cannot be +false+. */ static VALUE num_clone(int argc, VALUE *argv, VALUE x) { return rb_immutable_obj_clone(argc, argv, x); } #else # define num_clone rb_immutable_obj_clone #endif #if 0 /* * call-seq: * num.dup -> num * * Returns the receiver. */ static VALUE num_dup(VALUE x) { return x; } #else # define num_dup num_uplus #endif /* * call-seq: * +num -> num * * Unary Plus---Returns the receiver. */ static VALUE num_uplus(VALUE num) { return num; } /* * call-seq: * num.i -> Complex(0, num) * * Returns the corresponding imaginary number. * Not available for complex numbers. * * -42.i #=> (0-42i) * 2.0.i #=> (0+2.0i) */ static VALUE num_imaginary(VALUE num) { return rb_complex_new(INT2FIX(0), num); } /* * call-seq: * -num -> numeric * * Unary Minus---Returns the receiver, negated. */ static VALUE num_uminus(VALUE num) { VALUE zero; zero = INT2FIX(0); do_coerce(&zero, &num, TRUE); return num_funcall1(zero, '-', num); } /* * call-seq: * num.fdiv(numeric) -> float * * Returns float division. */ static VALUE num_fdiv(VALUE x, VALUE y) { return rb_funcall(rb_Float(x), '/', 1, y); } /* * call-seq: * num.div(numeric) -> integer * * Uses +/+ to perform division, then converts the result to an integer. * Numeric does not define the +/+ operator; this is left to subclasses. * * Equivalent to num.divmod(numeric)[0]. * * See Numeric#divmod. */ static VALUE num_div(VALUE x, VALUE y) { if (rb_equal(INT2FIX(0), y)) rb_num_zerodiv(); return rb_funcall(num_funcall1(x, '/', y), rb_intern("floor"), 0); } /* * call-seq: * num.modulo(numeric) -> real * * x.modulo(y) means x-y*(x/y).floor. * * Equivalent to num.divmod(numeric)[1]. * * See Numeric#divmod. */ 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: * num.remainder(numeric) -> real * * x.remainder(y) means x-y*(x/y).truncate. * * See Numeric#divmod. */ static VALUE num_remainder(VALUE x, VALUE y) { VALUE z = num_funcall1(x, '%', y); if ((!rb_equal(z, INT2FIX(0))) && ((rb_num_negative_int_p(x) && rb_num_positive_int_p(y)) || (rb_num_positive_int_p(x) && rb_num_negative_int_p(y)))) { return rb_funcall(z, '-', 1, y); } return z; } /* * call-seq: * num.divmod(numeric) -> array * * Returns an array containing the quotient and modulus obtained by dividing * +num+ by +numeric+. * * If q, r = x.divmod(y), then * * q = floor(x/y) * x = q*y + r * * The quotient is rounded toward negative infinity, as shown in the * following table: * * a | b | a.divmod(b) | a/b | a.modulo(b) | a.remainder(b) * ------+-----+---------------+---------+-------------+--------------- * 13 | 4 | 3, 1 | 3 | 1 | 1 * ------+-----+---------------+---------+-------------+--------------- * 13 | -4 | -4, -3 | -4 | -3 | 1 * ------+-----+---------------+---------+-------------+--------------- * -13 | 4 | -4, 3 | -4 | 3 | -1 * ------+-----+---------------+---------+-------------+--------------- * -13 | -4 | 3, -1 | 3 | -1 | -1 * ------+-----+---------------+---------+-------------+--------------- * 11.5 | 4 | 2, 3.5 | 2.875 | 3.5 | 3.5 * ------+-----+---------------+---------+-------------+--------------- * 11.5 | -4 | -3, -0.5 | -2.875 | -0.5 | 3.5 * ------+-----+---------------+---------+-------------+--------------- * -11.5 | 4 | -3, 0.5 | -2.875 | 0.5 | -3.5 * ------+-----+---------------+---------+-------------+--------------- * -11.5 | -4 | 2, -3.5 | 2.875 | -3.5 | -3.5 * * * Examples * * 11.divmod(3) #=> [3, 2] * 11.divmod(-3) #=> [-4, -1] * 11.divmod(3.5) #=> [3, 0.5] * (-11).divmod(3.5) #=> [-4, 3.0] * 11.5.divmod(3.5) #=> [3, 1.0] */ static VALUE num_divmod(VALUE x, VALUE y) { return rb_assoc_new(num_div(x, y), num_modulo(x, y)); } /* * call-seq: * num.real? -> true or false * * Returns +true+ if +num+ is a real number (i.e. not Complex). */ static VALUE num_real_p(VALUE num) { return Qtrue; } /* * call-seq: * num.integer? -> true or false * * Returns +true+ if +num+ is an Integer. * * 1.0.integer? #=> false * 1.integer? #=> true */ static VALUE num_int_p(VALUE num) { return Qfalse; } /* * call-seq: * num.abs -> numeric * num.magnitude -> numeric * * Returns the absolute value of +num+. * * 12.abs #=> 12 * (-34.56).abs #=> 34.56 * -34.56.abs #=> 34.56 * * Numeric#magnitude is an alias for Numeric#abs. */ static VALUE num_abs(VALUE num) { if (rb_num_negative_int_p(num)) { return num_funcall0(num, idUMinus); } return num; } /* * call-seq: * num.zero? -> true or false * * Returns +true+ if +num+ has a zero value. */ static VALUE num_zero_p(VALUE num) { if (rb_equal(num, INT2FIX(0))) { return Qtrue; } return Qfalse; } static VALUE int_zero_p(VALUE num) { if (FIXNUM_P(num)) { if (FIXNUM_ZERO_P(num)) { return Qtrue; } } else { assert(RB_TYPE_P(num, T_BIGNUM)); if (rb_bigzero_p(num)) { /* this should not happen usually */ return Qtrue; } } return Qfalse; } VALUE rb_int_zero_p(VALUE num) { return int_zero_p(num); } /* * call-seq: * num.nonzero? -> self or nil * * Returns +self+ if +num+ is not zero, +nil+ otherwise. * * This behavior is useful when chaining comparisons: * * a = %w( z Bb bB bb BB a aA Aa AA A ) * b = a.sort {|a,b| (a.downcase <=> b.downcase).nonzero? || a <=> b } * b #=> ["A", "a", "AA", "Aa", "aA", "BB", "Bb", "bB", "bb", "z"] */ static VALUE num_nonzero_p(VALUE num) { if (RTEST(num_funcall0(num, rb_intern("zero?")))) { return Qnil; } return num; } /* * call-seq: * num.finite? -> true or false * * Returns +true+ if +num+ is a finite number, otherwise returns +false+. */ static VALUE num_finite_p(VALUE num) { return Qtrue; } /* * call-seq: * num.infinite? -> -1, 1, or nil * * Returns +nil+, -1, or 1 depending on whether the value is * finite, -Infinity, or +Infinity. */ static VALUE num_infinite_p(VALUE num) { return Qnil; } /* * call-seq: * num.to_int -> integer * * Invokes the child class's +to_i+ method to convert +num+ to an integer. * * 1.0.class #=> Float * 1.0.to_int.class #=> Integer * 1.0.to_i.class #=> Integer */ static VALUE num_to_int(VALUE num) { return num_funcall0(num, id_to_i); } /* * call-seq: * num.positive? -> true or false * * Returns +true+ if +num+ is greater than 0. */ static VALUE num_positive_p(VALUE num) { const ID mid = '>'; if (FIXNUM_P(num)) { if (method_basic_p(rb_cInteger)) return (SIGNED_VALUE)num > (SIGNED_VALUE)INT2FIX(0) ? Qtrue : Qfalse; } else if (RB_TYPE_P(num, T_BIGNUM)) { if (method_basic_p(rb_cInteger)) return BIGNUM_POSITIVE_P(num) && !rb_bigzero_p(num) ? Qtrue : Qfalse; } return rb_num_compare_with_zero(num, mid); } /* * call-seq: * num.negative? -> true or false * * Returns +true+ if +num+ is less than 0. */ static VALUE num_negative_p(VALUE num) { return rb_num_negative_int_p(num) ? Qtrue : Qfalse; } /******************************************************************** * * Document-class: Float * * Float objects represent inexact real numbers using the native * architecture's double-precision floating point representation. * * Floating point has a different arithmetic and is an inexact number. * So you should know its esoteric system. See following: * * - https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html * - https://github.com/rdp/ruby_tutorials_core/wiki/Ruby-Talk-FAQ#floats_imprecise * - https://en.wikipedia.org/wiki/Floating_point#Accuracy_problems */ VALUE rb_float_new_in_heap(double d) { NEWOBJ_OF(flt, struct RFloat, rb_cFloat, T_FLOAT | (RGENGC_WB_PROTECTED_FLOAT ? FL_WB_PROTECTED : 0)); flt->float_value = d; OBJ_FREEZE((VALUE)flt); return (VALUE)flt; } /* * call-seq: * float.to_s -> string * * Returns a string containing a representation of +self+. * As well as a fixed or exponential form of the +float+, * the call may return +NaN+, +Infinity+, and +-Infinity+. */ static VALUE flo_to_s(VALUE flt) { enum {decimal_mant = DBL_MANT_DIG-DBL_DIG}; enum {float_dig = DBL_DIG+1}; char buf[float_dig + (decimal_mant + CHAR_BIT - 1) / CHAR_BIT + 10]; double value = RFLOAT_VALUE(flt); VALUE s; char *p, *e; int sign, decpt, digs; if (isinf(value)) { static const char minf[] = "-Infinity"; const int pos = (value > 0); /* skip "-" */ return rb_usascii_str_new(minf+pos, strlen(minf)-pos); } else if (isnan(value)) return rb_usascii_str_new2("NaN"); p = ruby_dtoa(value, 0, 0, &decpt, &sign, &e); s = sign ? rb_usascii_str_new_cstr("-") : rb_usascii_str_new(0, 0); if ((digs = (int)(e - p)) >= (int)sizeof(buf)) digs = (int)sizeof(buf) - 1; memcpy(buf, p, digs); xfree(p); if (decpt > 0) { if (decpt < digs) { memmove(buf + decpt + 1, buf + decpt, digs - decpt); buf[decpt] = '.'; rb_str_cat(s, buf, digs + 1); } else if (decpt <= DBL_DIG) { long len; char *ptr; rb_str_cat(s, buf, digs); rb_str_resize(s, (len = RSTRING_LEN(s)) + decpt - digs + 2); ptr = RSTRING_PTR(s) + len; if (decpt > digs) { memset(ptr, '0', decpt - digs); ptr += decpt - digs; } memcpy(ptr, ".0", 2); } else { goto exp; } } else if (decpt > -4) { long len; char *ptr; rb_str_cat(s, "0.", 2); rb_str_resize(s, (len = RSTRING_LEN(s)) - decpt + digs); ptr = RSTRING_PTR(s); memset(ptr += len, '0', -decpt); memcpy(ptr -= decpt, buf, digs); } 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: * float.coerce(numeric) -> array * * Returns an array with both +numeric+ and +float+ represented as Float * objects. * * This is achieved by converting +numeric+ to a Float. * * 1.2.coerce(3) #=> [3.0, 1.2] * 2.5.coerce(1.1) #=> [1.1, 2.5] */ static VALUE flo_coerce(VALUE x, VALUE y) { return rb_assoc_new(rb_Float(y), x); } /* * call-seq: * -float -> float * * Returns +float+, negated. */ VALUE rb_float_uminus(VALUE flt) { return DBL2NUM(-RFLOAT_VALUE(flt)); } /* * call-seq: * float + other -> float * * Returns a new Float which is the sum of +float+ and +other+. */ VALUE rb_float_plus(VALUE x, VALUE y) { if (RB_TYPE_P(y, T_FIXNUM)) { return DBL2NUM(RFLOAT_VALUE(x) + (double)FIX2LONG(y)); } else if (RB_TYPE_P(y, T_BIGNUM)) { return DBL2NUM(RFLOAT_VALUE(x) + rb_big2dbl(y)); } else if (RB_TYPE_P(y, T_FLOAT)) { return DBL2NUM(RFLOAT_VALUE(x) + RFLOAT_VALUE(y)); } else { return rb_num_coerce_bin(x, y, '+'); } } /* * call-seq: * float - other -> float * * Returns a new Float which is the difference of +float+ and +other+. */ static VALUE flo_minus(VALUE x, VALUE y) { if (RB_TYPE_P(y, T_FIXNUM)) { return DBL2NUM(RFLOAT_VALUE(x) - (double)FIX2LONG(y)); } else if (RB_TYPE_P(y, T_BIGNUM)) { return DBL2NUM(RFLOAT_VALUE(x) - rb_big2dbl(y)); } else if (RB_TYPE_P(y, T_FLOAT)) { return DBL2NUM(RFLOAT_VALUE(x) - RFLOAT_VALUE(y)); } else { return rb_num_coerce_bin(x, y, '-'); } } /* * call-seq: * float * other -> float * * Returns a new Float which is the product of +float+ and +other+. */ VALUE rb_float_mul(VALUE x, VALUE y) { if (RB_TYPE_P(y, T_FIXNUM)) { return DBL2NUM(RFLOAT_VALUE(x) * (double)FIX2LONG(y)); } else if (RB_TYPE_P(y, T_BIGNUM)) { return DBL2NUM(RFLOAT_VALUE(x) * rb_big2dbl(y)); } else if (RB_TYPE_P(y, T_FLOAT)) { return DBL2NUM(RFLOAT_VALUE(x) * RFLOAT_VALUE(y)); } else { return rb_num_coerce_bin(x, y, '*'); } } static bool flo_iszero(VALUE f) { return FLOAT_ZERO_P(f); } 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; } } MJIT_FUNC_EXPORTED VALUE rb_flo_div_flo(VALUE x, VALUE y) { double num = RFLOAT_VALUE(x); double den = RFLOAT_VALUE(y); double ret = double_div_double(num, den); return DBL2NUM(ret); } /* * call-seq: * float / other -> float * * Returns a new Float which is the result of dividing +float+ by +other+. */ VALUE rb_float_div(VALUE x, VALUE y) { double num = RFLOAT_VALUE(x); double den; double ret; if (RB_TYPE_P(y, T_FIXNUM)) { den = FIX2LONG(y); } else if (RB_TYPE_P(y, T_BIGNUM)) { den = rb_big2dbl(y); } else if (RB_TYPE_P(y, T_FLOAT)) { den = RFLOAT_VALUE(y); } else { return rb_num_coerce_bin(x, y, '/'); } ret = double_div_double(num, den); return DBL2NUM(ret); } /* * call-seq: * float.fdiv(numeric) -> float * float.quo(numeric) -> float * * Returns float / numeric, same as Float#/. */ 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. */ MJIT_FUNC_EXPORTED double ruby_float_mod(double x, double y) { double mod; flodivmod(x, y, 0, &mod); return mod; } /* * call-seq: * float % other -> float * float.modulo(other) -> float * * Returns the modulo after division of +float+ by +other+. * * 6543.21.modulo(137) #=> 104.21000000000004 * 6543.21.modulo(137.24) #=> 92.92999999999961 */ static VALUE flo_mod(VALUE x, VALUE y) { double fy; if (RB_TYPE_P(y, T_FIXNUM)) { fy = (double)FIX2LONG(y); } else if (RB_TYPE_P(y, T_BIGNUM)) { fy = rb_big2dbl(y); } else if (RB_TYPE_P(y, T_FLOAT)) { fy = RFLOAT_VALUE(y); } else { return rb_num_coerce_bin(x, y, '%'); } return DBL2NUM(ruby_float_mod(RFLOAT_VALUE(x), fy)); } static VALUE dbl2ival(double d) { if (FIXABLE(d)) { return LONG2FIX((long)d); } return rb_dbl2big(d); } /* * call-seq: * float.divmod(numeric) -> array * * See Numeric#divmod. * * 42.0.divmod(6) #=> [7, 0.0] * 42.0.divmod(5) #=> [8, 2.0] */ static VALUE flo_divmod(VALUE x, VALUE y) { double fy, div, mod; volatile VALUE a, b; if (RB_TYPE_P(y, T_FIXNUM)) { fy = (double)FIX2LONG(y); } else if (RB_TYPE_P(y, T_BIGNUM)) { fy = rb_big2dbl(y); } else if (RB_TYPE_P(y, T_FLOAT)) { 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: * float ** other -> float * * Raises +float+ to the power of +other+. * * 2.0**3 #=> 8.0 */ 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 (RB_TYPE_P(y, T_FIXNUM)) { dx = RFLOAT_VALUE(x); dy = (double)FIX2LONG(y); } else if (RB_TYPE_P(y, T_BIGNUM)) { dx = RFLOAT_VALUE(x); dy = rb_big2dbl(y); } else if (RB_TYPE_P(y, T_FLOAT)) { dx = RFLOAT_VALUE(x); dy = RFLOAT_VALUE(y); if (dx < 0 && dy != round(dy)) return rb_dbl_complex_new_polar_pi(pow(-dx, dy), dy); } else { return rb_num_coerce_bin(x, y, idPow); } return DBL2NUM(pow(dx, dy)); } /* * call-seq: * num.eql?(numeric) -> true or false * * Returns +true+ if +num+ and +numeric+ are the same type and have equal * values. Contrast this with Numeric#==, which performs type conversions. * * 1 == 1.0 #=> true * 1.eql?(1.0) #=> false * 1.0.eql?(1.0) #=> true */ static VALUE num_eql(VALUE x, VALUE y) { if (TYPE(x) != TYPE(y)) return Qfalse; if (RB_TYPE_P(x, T_BIGNUM)) { return rb_big_eql(x, y); } return rb_equal(x, y); } /* * call-seq: * number <=> other -> 0 or nil * * Returns zero if +number+ equals +other+, otherwise returns +nil+. */ 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); if (RTEST(result)) return Qtrue; return Qfalse; } /* * call-seq: * float == obj -> true or false * * Returns +true+ only if +obj+ has the same value as +float+. * Contrast this with Float#eql?, which requires +obj+ to be a Float. * * 1.0 == 1 #=> true * * The result of NaN == NaN is undefined, * so an implementation-dependent value is returned. */ MJIT_FUNC_EXPORTED VALUE rb_float_equal(VALUE x, VALUE y) { volatile double a, b; if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) { return rb_integer_float_eq(y, x); } else if (RB_TYPE_P(y, T_FLOAT)) { b = RFLOAT_VALUE(y); #if 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 (a == b)?Qtrue:Qfalse; } #define flo_eq rb_float_equal static VALUE rb_dbl_hash(double d); /* * call-seq: * float.hash -> integer * * Returns a hash code for this float. * * 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: * float <=> real -> -1, 0, +1, or nil * * Returns -1, 0, or +1 depending on whether +float+ is * less than, equal to, or greater than +real+. * This is the basis for the tests in the Comparable module. * * The result of NaN <=> NaN is undefined, * so an implementation-dependent value is returned. * * +nil+ is returned if the two values are incomparable. */ static VALUE flo_cmp(VALUE x, VALUE y) { double a, b; VALUE i; a = RFLOAT_VALUE(x); if (isnan(a)) return Qnil; if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) { VALUE rel = rb_integer_float_cmp(y, x); if (FIXNUM_P(rel)) return LONG2FIX(-FIX2LONG(rel)); return rel; } else if (RB_TYPE_P(y, T_FLOAT)) { b = RFLOAT_VALUE(y); } else { if (isinf(a) && (i = rb_check_funcall(y, rb_intern("infinite?"), 0, 0)) != Qundef) { if (RTEST(i)) { int j = rb_cmpint(i, x, y); j = (a > 0.0) ? (j > 0 ? 0 : +1) : (j < 0 ? 0 : -1); return INT2FIX(j); } if (a > 0.0) return INT2FIX(1); return INT2FIX(-1); } return rb_num_coerce_cmp(x, y, id_cmp); } return rb_dbl_cmp(a, b); } MJIT_FUNC_EXPORTED int rb_float_cmp(VALUE x, VALUE y) { return NUM2INT(flo_cmp(x, y)); } /* * call-seq: * float > real -> true or false * * Returns +true+ if +float+ is greater than +real+. * * The result of NaN > NaN is undefined, * so an implementation-dependent value is returned. */ VALUE rb_float_gt(VALUE x, VALUE y) { double a, b; a = RFLOAT_VALUE(x); if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) { VALUE rel = rb_integer_float_cmp(y, x); if (FIXNUM_P(rel)) return -FIX2LONG(rel) > 0 ? Qtrue : Qfalse; return Qfalse; } else if (RB_TYPE_P(y, T_FLOAT)) { 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 (a > b)?Qtrue:Qfalse; } /* * call-seq: * float >= real -> true or false * * Returns +true+ if +float+ is greater than or equal to +real+. * * The result of NaN >= NaN is undefined, * so an implementation-dependent value is returned. */ static VALUE flo_ge(VALUE x, VALUE y) { double a, b; a = RFLOAT_VALUE(x); if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) { VALUE rel = rb_integer_float_cmp(y, x); if (FIXNUM_P(rel)) return -FIX2LONG(rel) >= 0 ? Qtrue : Qfalse; return Qfalse; } else if (RB_TYPE_P(y, T_FLOAT)) { 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 (a >= b)?Qtrue:Qfalse; } /* * call-seq: * float < real -> true or false * * Returns +true+ if +float+ is less than +real+. * * The result of NaN < NaN is undefined, * so an implementation-dependent value is returned. */ static VALUE flo_lt(VALUE x, VALUE y) { double a, b; a = RFLOAT_VALUE(x); if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) { VALUE rel = rb_integer_float_cmp(y, x); if (FIXNUM_P(rel)) return -FIX2LONG(rel) < 0 ? Qtrue : Qfalse; return Qfalse; } else if (RB_TYPE_P(y, T_FLOAT)) { 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 (a < b)?Qtrue:Qfalse; } /* * call-seq: * float <= real -> true or false * * Returns +true+ if +float+ is less than or equal to +real+. * * The result of NaN <= NaN is undefined, * so an implementation-dependent value is returned. */ static VALUE flo_le(VALUE x, VALUE y) { double a, b; a = RFLOAT_VALUE(x); if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) { VALUE rel = rb_integer_float_cmp(y, x); if (FIXNUM_P(rel)) return -FIX2LONG(rel) <= 0 ? Qtrue : Qfalse; return Qfalse; } else if (RB_TYPE_P(y, T_FLOAT)) { 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 (a <= b)?Qtrue:Qfalse; } /* * call-seq: * float.eql?(obj) -> true or false * * Returns +true+ only if +obj+ is a Float with the same value as +float+. * Contrast this with Float#==, which performs type conversions. * * 1.0.eql?(1) #=> false * * The result of NaN.eql?(NaN) is undefined, * so an implementation-dependent value is returned. */ MJIT_FUNC_EXPORTED VALUE rb_float_eql(VALUE x, VALUE y) { if (RB_TYPE_P(y, T_FLOAT)) { double a = RFLOAT_VALUE(x); double b = RFLOAT_VALUE(y); #if MSC_VERSION_BEFORE(1300) if (isnan(a) || isnan(b)) return Qfalse; #endif if (a == b) return Qtrue; } return Qfalse; } #define flo_eql rb_float_eql /* * call-seq: * float.to_f -> self * * Since +float+ is already a Float, returns +self+. */ static VALUE flo_to_f(VALUE num) { return num; } /* * call-seq: * float.abs -> float * float.magnitude -> float * * Returns the absolute value of +float+. * * (-34.56).abs #=> 34.56 * -34.56.abs #=> 34.56 * 34.56.abs #=> 34.56 * * Float#magnitude is an alias for Float#abs. */ VALUE rb_float_abs(VALUE flt) { double val = fabs(RFLOAT_VALUE(flt)); return DBL2NUM(val); } /* * call-seq: * float.zero? -> true or false * * Returns +true+ if +float+ is 0.0. */ static VALUE flo_zero_p(VALUE num) { return flo_iszero(num) ? Qtrue : Qfalse; } /* * call-seq: * float.nan? -> true or false * * Returns +true+ if +float+ is an invalid IEEE floating point number. * * a = -1.0 #=> -1.0 * a.nan? #=> false * a = 0.0/0.0 #=> NaN * a.nan? #=> true */ static VALUE flo_is_nan_p(VALUE num) { double value = RFLOAT_VALUE(num); return isnan(value) ? Qtrue : Qfalse; } /* * call-seq: * float.infinite? -> -1, 1, or nil * * Returns +nil+, -1, or 1 depending on whether the value is * finite, -Infinity, or +Infinity. * * (0.0).infinite? #=> nil * (-1.0/0.0).infinite? #=> -1 * (+1.0/0.0).infinite? #=> 1 */ 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: * float.finite? -> true or false * * Returns +true+ if +float+ is a valid IEEE floating point number, * i.e. it is not infinite and Float#nan? is +false+. */ VALUE rb_flo_is_finite_p(VALUE num) { double value = RFLOAT_VALUE(num); #ifdef HAVE_ISFINITE if (!isfinite(value)) return Qfalse; #else if (isinf(value) || isnan(value)) return Qfalse; #endif return Qtrue; } /* * call-seq: * float.next_float -> float * * Returns the next representable floating point number. * * Float::MAX.next_float and Float::INFINITY.next_float is Float::INFINITY. * * Float::NAN.next_float is Float::NAN. * * For example: * * 0.01.next_float #=> 0.010000000000000002 * 1.0.next_float #=> 1.0000000000000002 * 100.0.next_float #=> 100.00000000000001 * * 0.01.next_float - 0.01 #=> 1.734723475976807e-18 * 1.0.next_float - 1.0 #=> 2.220446049250313e-16 * 100.0.next_float - 100.0 #=> 1.4210854715202004e-14 * * f = 0.01; 20.times { printf "%-20a %s\n", f, f.to_s; f = f.next_float } * #=> 0x1.47ae147ae147bp-7 0.01 * # 0x1.47ae147ae147cp-7 0.010000000000000002 * # 0x1.47ae147ae147dp-7 0.010000000000000004 * # 0x1.47ae147ae147ep-7 0.010000000000000005 * # 0x1.47ae147ae147fp-7 0.010000000000000007 * # 0x1.47ae147ae148p-7 0.010000000000000009 * # 0x1.47ae147ae1481p-7 0.01000000000000001 * # 0x1.47ae147ae1482p-7 0.010000000000000012 * # 0x1.47ae147ae1483p-7 0.010000000000000014 * # 0x1.47ae147ae1484p-7 0.010000000000000016 * # 0x1.47ae147ae1485p-7 0.010000000000000018 * # 0x1.47ae147ae1486p-7 0.01000000000000002 * # 0x1.47ae147ae1487p-7 0.010000000000000021 * # 0x1.47ae147ae1488p-7 0.010000000000000023 * # 0x1.47ae147ae1489p-7 0.010000000000000024 * # 0x1.47ae147ae148ap-7 0.010000000000000026 * # 0x1.47ae147ae148bp-7 0.010000000000000028 * # 0x1.47ae147ae148cp-7 0.01000000000000003 * # 0x1.47ae147ae148dp-7 0.010000000000000031 * # 0x1.47ae147ae148ep-7 0.010000000000000033 * * f = 0.0 * 100.times { f += 0.1 } * f #=> 9.99999999999998 # should be 10.0 in the ideal world. * 10-f #=> 1.9539925233402755e-14 # the floating point error. * 10.0.next_float-10 #=> 1.7763568394002505e-15 # 1 ulp (unit in the last place). * (10-f)/(10.0.next_float-10) #=> 11.0 # the error is 11 ulp. * (10-f)/(10*Float::EPSILON) #=> 8.8 # approximation of the above. * "%a" % 10 #=> "0x1.4p+3" * "%a" % f #=> "0x1.3fffffffffff5p+3" # the last hex digit is 5. 16 - 5 = 11 ulp. */ static VALUE flo_next_float(VALUE vx) { double x, y; x = NUM2DBL(vx); y = nextafter(x, HUGE_VAL); return DBL2NUM(y); } /* * call-seq: * float.prev_float -> float * * Returns the previous representable floating point number. * * (-Float::MAX).prev_float and (-Float::INFINITY).prev_float is -Float::INFINITY. * * Float::NAN.prev_float is Float::NAN. * * For example: * * 0.01.prev_float #=> 0.009999999999999998 * 1.0.prev_float #=> 0.9999999999999999 * 100.0.prev_float #=> 99.99999999999999 * * 0.01 - 0.01.prev_float #=> 1.734723475976807e-18 * 1.0 - 1.0.prev_float #=> 1.1102230246251565e-16 * 100.0 - 100.0.prev_float #=> 1.4210854715202004e-14 * * f = 0.01; 20.times { printf "%-20a %s\n", f, f.to_s; f = f.prev_float } * #=> 0x1.47ae147ae147bp-7 0.01 * # 0x1.47ae147ae147ap-7 0.009999999999999998 * # 0x1.47ae147ae1479p-7 0.009999999999999997 * # 0x1.47ae147ae1478p-7 0.009999999999999995 * # 0x1.47ae147ae1477p-7 0.009999999999999993 * # 0x1.47ae147ae1476p-7 0.009999999999999992 * # 0x1.47ae147ae1475p-7 0.00999999999999999 * # 0x1.47ae147ae1474p-7 0.009999999999999988 * # 0x1.47ae147ae1473p-7 0.009999999999999986 * # 0x1.47ae147ae1472p-7 0.009999999999999985 * # 0x1.47ae147ae1471p-7 0.009999999999999983 * # 0x1.47ae147ae147p-7 0.009999999999999981 * # 0x1.47ae147ae146fp-7 0.00999999999999998 * # 0x1.47ae147ae146ep-7 0.009999999999999978 * # 0x1.47ae147ae146dp-7 0.009999999999999976 * # 0x1.47ae147ae146cp-7 0.009999999999999974 * # 0x1.47ae147ae146bp-7 0.009999999999999972 * # 0x1.47ae147ae146ap-7 0.00999999999999997 * # 0x1.47ae147ae1469p-7 0.009999999999999969 * # 0x1.47ae147ae1468p-7 0.009999999999999967 */ static VALUE flo_prev_float(VALUE vx) { double x, y; x = NUM2DBL(vx); y = nextafter(x, -HUGE_VAL); return DBL2NUM(y); } /* * call-seq: * float.floor([ndigits]) -> integer or float * * Returns the largest number less than or equal to +float+ with * a precision of +ndigits+ decimal digits (default: 0). * * When the precision is negative, the returned value is an integer * with at least ndigits.abs trailing zeros. * * Returns a floating point number when +ndigits+ is positive, * otherwise returns an integer. * * 1.2.floor #=> 1 * 2.0.floor #=> 2 * (-1.2).floor #=> -2 * (-2.0).floor #=> -2 * * 1.234567.floor(2) #=> 1.23 * 1.234567.floor(3) #=> 1.234 * 1.234567.floor(4) #=> 1.2345 * 1.234567.floor(5) #=> 1.23456 * * 34567.89.floor(-5) #=> 0 * 34567.89.floor(-4) #=> 30000 * 34567.89.floor(-3) #=> 34000 * 34567.89.floor(-2) #=> 34500 * 34567.89.floor(-1) #=> 34560 * 34567.89.floor(0) #=> 34567 * 34567.89.floor(1) #=> 34567.8 * 34567.89.floor(2) #=> 34567.89 * 34567.89.floor(3) #=> 34567.89 * * Note that the limited precision of floating point arithmetic * might lead to surprising results: * * (0.3 / 0.1).floor #=> 2 (!) */ static VALUE flo_floor(int argc, VALUE *argv, VALUE num) { double number, f; int ndigits = 0; if (rb_check_arity(argc, 0, 1)) { ndigits = NUM2INT(argv[0]); } number = RFLOAT_VALUE(num); if (number == 0.0) { return ndigits > 0 ? DBL2NUM(number) : INT2FIX(0); } if (ndigits > 0) { int binexp; frexp(number, &binexp); if (float_round_overflow(ndigits, binexp)) return num; if (number > 0.0 && float_round_underflow(ndigits, binexp)) return DBL2NUM(0.0); f = pow(10, ndigits); f = floor(number * f) / f; return DBL2NUM(f); } else { num = dbl2ival(floor(number)); if (ndigits < 0) num = rb_int_floor(num, ndigits); return num; } } /* * call-seq: * float.ceil([ndigits]) -> integer or float * * Returns the smallest number greater than or equal to +float+ with * a precision of +ndigits+ decimal digits (default: 0). * * When the precision is negative, the returned value is an integer * with at least ndigits.abs trailing zeros. * * Returns a floating point number when +ndigits+ is positive, * otherwise returns an integer. * * 1.2.ceil #=> 2 * 2.0.ceil #=> 2 * (-1.2).ceil #=> -1 * (-2.0).ceil #=> -2 * * 1.234567.ceil(2) #=> 1.24 * 1.234567.ceil(3) #=> 1.235 * 1.234567.ceil(4) #=> 1.2346 * 1.234567.ceil(5) #=> 1.23457 * * 34567.89.ceil(-5) #=> 100000 * 34567.89.ceil(-4) #=> 40000 * 34567.89.ceil(-3) #=> 35000 * 34567.89.ceil(-2) #=> 34600 * 34567.89.ceil(-1) #=> 34570 * 34567.89.ceil(0) #=> 34568 * 34567.89.ceil(1) #=> 34567.9 * 34567.89.ceil(2) #=> 34567.89 * 34567.89.ceil(3) #=> 34567.89 * * Note that the limited precision of floating point arithmetic * might lead to surprising results: * * (2.1 / 0.7).ceil #=> 4 (!) */ static VALUE flo_ceil(int argc, VALUE *argv, VALUE num) { int ndigits = 0; if (rb_check_arity(argc, 0, 1)) { ndigits = NUM2INT(argv[0]); } 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_TYPE_P(num, T_BIGNUM)) { bytes = rb_big_size(num); } else { bytes = NUM2LONG(rb_funcall(num, idSize, 0)); } return (-0.415241 * ndigits - 0.125 > bytes); } static SIGNED_VALUE int_round_half_even(SIGNED_VALUE x, SIGNED_VALUE y) { SIGNED_VALUE z = +(x + y / 2) / y; if ((z * y - x) * 2 == y) { z &= ~1; } return z * y; } static SIGNED_VALUE int_round_half_up(SIGNED_VALUE x, SIGNED_VALUE y) { return (x + y / 2) / y * y; } static SIGNED_VALUE int_round_half_down(SIGNED_VALUE x, SIGNED_VALUE y) { return (x + y / 2 - 1) / y * y; } static int int_half_p_half_even(VALUE num, VALUE n, VALUE f) { return (int)rb_int_odd_p(rb_int_idiv(n, f)); } static int int_half_p_half_up(VALUE num, VALUE n, VALUE f) { return int_pos_p(num); } static int int_half_p_half_down(VALUE num, VALUE n, VALUE f) { return int_neg_p(num); } /* * Assumes num is an Integer, ndigits <= 0 */ 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_TYPE_P(f, T_FLOAT)) { /* then int_pow overflow */ return INT2FIX(0); } h = rb_int_idiv(f, INT2FIX(2)); r = rb_int_modulo(num, f); n = rb_int_minus(num, r); r = rb_int_cmp(r, h); if (FIXNUM_POSITIVE_P(r) || (FIXNUM_ZERO_P(r) && ROUND_CALL(mode, int_half_p, (num, n, f)))) { n = rb_int_plus(n, f); } return n; } static VALUE rb_int_floor(VALUE num, int ndigits) { VALUE f; if (int_round_zero_p(num, ndigits)) return INT2FIX(0); f = int_pow(10, -ndigits); if (FIXNUM_P(num) && FIXNUM_P(f)) { SIGNED_VALUE x = FIX2LONG(num), y = FIX2LONG(f); int neg = x < 0; if (neg) x = -x + y - 1; x = x / y * y; if (neg) x = -x; return LONG2NUM(x); } if (RB_TYPE_P(f, T_FLOAT)) { /* then int_pow overflow */ return INT2FIX(0); } return rb_int_minus(num, rb_int_modulo(num, f)); } static VALUE rb_int_ceil(VALUE num, int ndigits) { VALUE f; if (int_round_zero_p(num, ndigits)) return INT2FIX(0); f = int_pow(10, -ndigits); if (FIXNUM_P(num) && FIXNUM_P(f)) { SIGNED_VALUE x = FIX2LONG(num), y = FIX2LONG(f); int neg = x < 0; if (neg) x = -x; else x += y - 1; x = (x / y) * y; if (neg) x = -x; return LONG2NUM(x); } if (RB_TYPE_P(f, T_FLOAT)) { /* then int_pow overflow */ return INT2FIX(0); } return rb_int_plus(num, rb_int_minus(f, rb_int_modulo(num, f))); } VALUE rb_int_truncate(VALUE num, int ndigits) { VALUE f; VALUE m; if (int_round_zero_p(num, ndigits)) return INT2FIX(0); f = int_pow(10, -ndigits); if (FIXNUM_P(num) && FIXNUM_P(f)) { SIGNED_VALUE x = FIX2LONG(num), y = FIX2LONG(f); int neg = x < 0; if (neg) x = -x; x = x / y * y; if (neg) x = -x; return LONG2NUM(x); } if (RB_TYPE_P(f, T_FLOAT)) { /* then int_pow overflow */ return INT2FIX(0); } m = rb_int_modulo(num, f); if (int_neg_p(num)) { return rb_int_plus(num, rb_int_minus(f, m)); } else { return rb_int_minus(num, m); } } /* * call-seq: * float.round([ndigits] [, half: mode]) -> integer or float * * Returns +float+ rounded to the nearest value with * a precision of +ndigits+ decimal digits (default: 0). * * When the precision is negative, the returned value is an integer * with at least ndigits.abs trailing zeros. * * Returns a floating point number when +ndigits+ is positive, * otherwise returns an integer. * * 1.4.round #=> 1 * 1.5.round #=> 2 * 1.6.round #=> 2 * (-1.5).round #=> -2 * * 1.234567.round(2) #=> 1.23 * 1.234567.round(3) #=> 1.235 * 1.234567.round(4) #=> 1.2346 * 1.234567.round(5) #=> 1.23457 * * 34567.89.round(-5) #=> 0 * 34567.89.round(-4) #=> 30000 * 34567.89.round(-3) #=> 35000 * 34567.89.round(-2) #=> 34600 * 34567.89.round(-1) #=> 34570 * 34567.89.round(0) #=> 34568 * 34567.89.round(1) #=> 34567.9 * 34567.89.round(2) #=> 34567.89 * 34567.89.round(3) #=> 34567.89 * * If the optional +half+ keyword argument is given, * numbers that are half-way between two possible rounded values * will be rounded according to the specified tie-breaking +mode+: * * * :up or +nil+: round half away from zero (default) * * :down: round half toward zero * * :even: round half toward the nearest even number * * 2.5.round(half: :up) #=> 3 * 2.5.round(half: :down) #=> 2 * 2.5.round(half: :even) #=> 2 * 3.5.round(half: :up) #=> 4 * 3.5.round(half: :down) #=> 3 * 3.5.round(half: :even) #=> 4 * (-2.5).round(half: :up) #=> -3 * (-2.5).round(half: :down) #=> -2 * (-2.5).round(half: :even) #=> -2 */ static VALUE flo_round(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); 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: * float.to_i -> integer * float.to_int -> integer * * Returns the +float+ truncated to an Integer. * * 1.2.to_i #=> 1 * (-1.2).to_i #=> -1 * * Note that the limited precision of floating point arithmetic * might lead to surprising results: * * (0.3 / 0.1).to_i #=> 2 (!) * * #to_int is an alias for #to_i. */ static VALUE flo_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: * float.truncate([ndigits]) -> integer or float * * Returns +float+ truncated (toward zero) to * a precision of +ndigits+ decimal digits (default: 0). * * When the precision is negative, the returned value is an integer * with at least ndigits.abs trailing zeros. * * Returns a floating point number when +ndigits+ is positive, * otherwise returns an integer. * * 2.8.truncate #=> 2 * (-2.8).truncate #=> -2 * 1.234567.truncate(2) #=> 1.23 * 34567.89.truncate(-2) #=> 34500 * * Note that the limited precision of floating point arithmetic * might lead to surprising results: * * (0.3 / 0.1).truncate #=> 2 (!) */ static VALUE flo_truncate(int argc, VALUE *argv, VALUE num) { if (signbit(RFLOAT_VALUE(num))) return flo_ceil(argc, argv, num); else return flo_floor(argc, argv, num); } /* * call-seq: * float.positive? -> true or false * * Returns +true+ if +float+ is greater than 0. */ static VALUE flo_positive_p(VALUE num) { double f = RFLOAT_VALUE(num); return f > 0.0 ? Qtrue : Qfalse; } /* * call-seq: * float.negative? -> true or false * * Returns +true+ if +float+ is less than 0. */ static VALUE flo_negative_p(VALUE num) { double f = RFLOAT_VALUE(num); return f < 0.0 ? Qtrue : Qfalse; } /* * call-seq: * num.floor([ndigits]) -> integer or float * * Returns the largest number less than or equal to +num+ with * a precision of +ndigits+ decimal digits (default: 0). * * Numeric implements this by converting its value to a Float and * invoking Float#floor. */ static VALUE num_floor(int argc, VALUE *argv, VALUE num) { return flo_floor(argc, argv, rb_Float(num)); } /* * call-seq: * num.ceil([ndigits]) -> integer or float * * Returns the smallest number greater than or equal to +num+ with * a precision of +ndigits+ decimal digits (default: 0). * * Numeric implements this by converting its value to a Float and * invoking Float#ceil. */ static VALUE num_ceil(int argc, VALUE *argv, VALUE num) { return flo_ceil(argc, argv, rb_Float(num)); } /* * call-seq: * num.round([ndigits]) -> integer or float * * Returns +num+ rounded to the nearest value with * a precision of +ndigits+ decimal digits (default: 0). * * Numeric implements this by converting its value to a Float and * invoking Float#round. */ static VALUE num_round(int argc, VALUE* argv, VALUE num) { return flo_round(argc, argv, rb_Float(num)); } /* * call-seq: * num.truncate([ndigits]) -> integer or float * * Returns +num+ truncated (toward zero) to * a precision of +ndigits+ decimal digits (default: 0). * * Numeric implements this by converting its value to a Float and * invoking Float#truncate. */ static VALUE num_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 n, err; if (unit == 0) { return HUGE_VAL; } n= (end - beg)/unit; err = (fabs(beg) + fabs(end) + fabs(end-beg)) / fabs(unit) * epsilon; if (isinf(unit)) { return unit > 0 ? beg <= end : beg >= end; } if (err>0.5) err=0.5; if (excl) { if (n<=0) return 0; if (n<1) n = 0; else n = floor(n - err); } else { if (n<0) return 0; n = floor(n + err); } return n+1; } int ruby_float_step(VALUE from, VALUE to, VALUE step, int excl, int allow_endless) { if (RB_TYPE_P(from, T_FLOAT) || RB_TYPE_P(to, T_FLOAT) || RB_TYPE_P(step, T_FLOAT)) { 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_TYPE_P(from, T_FLOAT) || RB_TYPE_P(to, T_FLOAT) || RB_TYPE_P(step, T_FLOAT)) { double n = ruby_float_step_size(NUM2DBL(from), NUM2DBL(to), NUM2DBL(step), excl); if (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(rb_funcall(from, '+', 1, rb_funcall(result, '*', 1, step)), cmp, 1, to))) { result = rb_funcall(result, '+', 1, INT2FIX(1)); } return result; } } static int num_step_negative_p(VALUE num) { const ID mid = '<'; VALUE zero = INT2FIX(0); VALUE r; if (FIXNUM_P(num)) { if (method_basic_p(rb_cInteger)) return (SIGNED_VALUE)num < 0; } else if (RB_TYPE_P(num, T_BIGNUM)) { if (method_basic_p(rb_cInteger)) return BIGNUM_NEGATIVE_P(num); } r = rb_check_funcall(num, '>', 1, &zero); if (r == Qundef) { 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 (values[0] != Qundef) { if (argc > 0) rb_raise(rb_eArgError, "to is given twice"); *to = values[0]; } if (values[1] != Qundef) { if (argc > 1) rb_raise(rb_eArgError, "step is given twice"); *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 (by != Qundef) { *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: * num.step(by: step, to: limit) {|i| block } -> self * num.step(by: step, to: limit) -> an_enumerator * num.step(by: step, to: limit) -> an_arithmetic_sequence * num.step(limit=nil, step=1) {|i| block } -> self * num.step(limit=nil, step=1) -> an_enumerator * num.step(limit=nil, step=1) -> an_arithmetic_sequence * * Invokes the given block with the sequence of numbers starting at +num+, * incremented by +step+ (defaulted to +1+) on each call. * * The loop finishes when the value to be passed to the block is greater than * +limit+ (if +step+ is positive) or less than +limit+ (if +step+ is * negative), where +limit+ is defaulted to infinity. * * In the recommended keyword argument style, either or both of * +step+ and +limit+ (default infinity) can be omitted. In the * fixed position argument style, zero as a step * (i.e. num.step(limit, 0)) is not allowed for historical * compatibility reasons. * * If all the arguments are integers, the loop operates using an integer * counter. * * If any of the arguments are floating point numbers, all are converted * to floats, and the loop is executed * floor(n + n*Float::EPSILON) + 1 times, * where n = (limit - num)/step. * * Otherwise, the loop starts at +num+, uses either the * less-than (<) or greater-than (>) operator * to compare the counter against +limit+, * and increments itself using the + operator. * * If no block is given, an Enumerator is returned instead. * Especially, the enumerator is an Enumerator::ArithmeticSequence * if both +limit+ and +step+ are kind of Numeric or nil. * * For example: * * p 1.step.take(4) * p 10.step(by: -1).take(4) * 3.step(to: 5) {|i| print i, " " } * 1.step(10, 2) {|i| print i, " " } * Math::E.step(to: Math::PI, by: 0.2) {|f| print f, " " } * * Will produce: * * [1, 2, 3, 4] * [10, 9, 8, 7] * 3 4 5 * 1 3 5 7 9 * 2.718281828459045 2.9182818284590453 3.118281828459045 */ 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 (by != Qundef) { step = by; } if (NIL_P(step)) { step = INT2FIX(1); } 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(from, 2, ((VALUE [2]){to, step}), num_step_size); } desc = num_step_scan_args(argc, argv, &to, &step, TRUE, FALSE); if (rb_equal(step, INT2FIX(0))) { inf = 1; } else if (RB_TYPE_P(to, T_FLOAT)) { double f = RFLOAT_VALUE(to); inf = isinf(f) && (signbit(f) ? desc : !desc); } else inf = 0; if (FIXNUM_P(from) && (inf || FIXNUM_P(to)) && FIXNUM_P(step)) { long i = FIX2LONG(from); long diff = FIX2LONG(step); if (inf) { for (;; i += diff) rb_yield(LONG2FIX(i)); } else { 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_TYPE_P(val, T_FLOAT)) { if (RFLOAT_VALUE(val) < LONG_MAX_PLUS_ONE && LONG_MIN_MINUS_ONE_IS_LESS_THAN(RFLOAT_VALUE(val))) { return (long)RFLOAT_VALUE(val); } else { FLOAT_OUT_OF_RANGE(val, "integer"); } } else if (RB_TYPE_P(val, T_BIGNUM)) { 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 from nil to 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_TYPE_P(val, T_FLOAT)) { double d = RFLOAT_VALUE(val); if (d < ULONG_MAX_PLUS_ONE && LONG_MIN_MINUS_ONE_IS_LESS_THAN(d)) { if (wrap_p) *wrap_p = d <= -1.0; /* NUM2ULONG(v) uses v.to_int conceptually. */ if (0 <= d) return (unsigned long)d; return (unsigned long)(long)d; } else { FLOAT_OUT_OF_RANGE(val, "integer"); } } else if (RB_TYPE_P(val, T_BIGNUM)) { { unsigned long ul = rb_big2ulong(val); if (wrap_p) *wrap_p = BIGNUM_NEGATIVE_P(val); return ul; } } else { val = rb_to_int(val); goto again; } } unsigned long rb_num2ulong(VALUE val) { return rb_num2ulong_internal(val, NULL); } 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, rb_num_negative_int_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, rb_num_negative_int_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_TYPE_P(val, T_FLOAT)) { double d = RFLOAT_VALUE(val); if (d < LLONG_MAX_PLUS_ONE && (LLONG_MIN_MINUS_ONE_IS_LESS_THAN(d))) { return (LONG_LONG)d; } else { FLOAT_OUT_OF_RANGE(val, "long long"); } } else if (RB_TYPE_P(val, T_BIGNUM)) { 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 (RB_TYPE_P(val, T_NIL)) { rb_raise(rb_eTypeError, "no implicit conversion from nil"); } else if (RB_TYPE_P(val, T_FIXNUM)) { return (LONG_LONG)FIX2LONG(val); /* this is FIX2LONG, intended */ } else if (RB_TYPE_P(val, T_FLOAT)) { double d = RFLOAT_VALUE(val); if (d < ULLONG_MAX_PLUS_ONE && LLONG_MIN_MINUS_ONE_IS_LESS_THAN(d)) { if (0 <= d) return (unsigned LONG_LONG)d; return (unsigned LONG_LONG)(LONG_LONG)d; } else { FLOAT_OUT_OF_RANGE(val, "unsigned long long"); } } else if (RB_TYPE_P(val, T_BIGNUM)) { return rb_big2ull(val); } else if (RB_TYPE_P(val, T_STRING)) { rb_raise(rb_eTypeError, "no implicit conversion from string"); } else if (RB_TYPE_P(val, T_TRUE) || RB_TYPE_P(val, T_FALSE)) { rb_raise(rb_eTypeError, "no implicit conversion from boolean"); } val = rb_to_int(val); return NUM2ULL(val); } #endif /* HAVE_LONG_LONG */ /******************************************************************** * * Document-class: Integer * * Holds Integer values. You cannot add a singleton method to an * Integer object, any attempt to do so will raise a TypeError. * */ VALUE rb_int_odd_p(VALUE num) { if (FIXNUM_P(num)) { if (num & 2) { return Qtrue; } return Qfalse; } else { assert(RB_TYPE_P(num, T_BIGNUM)); return rb_big_odd_p(num); } } static VALUE int_even_p(VALUE num) { if (FIXNUM_P(num)) { if ((num & 2) == 0) { return Qtrue; } return Qfalse; } else { assert(RB_TYPE_P(num, T_BIGNUM)); return rb_big_even_p(num); } } VALUE rb_int_even_p(VALUE num) { return int_even_p(num); } /* * call-seq: * int.allbits?(mask) -> true or false * * Returns +true+ if all bits of +int+ & +mask+ are 1. */ static VALUE int_allbits_p(VALUE num, VALUE mask) { mask = rb_to_int(mask); return rb_int_equal(rb_int_and(num, mask), mask); } /* * call-seq: * int.anybits?(mask) -> true or false * * Returns +true+ if any bits of +int+ & +mask+ are 1. */ static VALUE int_anybits_p(VALUE num, VALUE mask) { mask = rb_to_int(mask); return int_zero_p(rb_int_and(num, mask)) ? Qfalse : Qtrue; } /* * call-seq: * int.nobits?(mask) -> true or false * * Returns +true+ if no bits of +int+ & +mask+ are 1. */ static VALUE int_nobits_p(VALUE num, VALUE mask) { mask = rb_to_int(mask); return int_zero_p(rb_int_and(num, mask)); } /* * Document-method: Integer#succ * Document-method: Integer#next * call-seq: * int.next -> integer * int.succ -> integer * * Returns the successor of +int+, * i.e. the Integer equal to int+1. * * 1.next #=> 2 * (-1).next #=> 0 * 1.succ #=> 2 * (-1).succ #=> 0 */ VALUE rb_int_succ(VALUE num) { if (FIXNUM_P(num)) { long i = FIX2LONG(num) + 1; return LONG2NUM(i); } if (RB_TYPE_P(num, T_BIGNUM)) { return rb_big_plus(num, INT2FIX(1)); } return num_funcall1(num, '+', INT2FIX(1)); } #define int_succ rb_int_succ /* * call-seq: * int.pred -> integer * * Returns the predecessor of +int+, * i.e. the Integer equal to int-1. * * 1.pred #=> 0 * (-1).pred #=> -2 */ static VALUE rb_int_pred(VALUE num) { if (FIXNUM_P(num)) { long i = FIX2LONG(num) - 1; return LONG2NUM(i); } if (RB_TYPE_P(num, T_BIGNUM)) { return rb_big_minus(num, INT2FIX(1)); } return num_funcall1(num, '-', INT2FIX(1)); } #define int_pred rb_int_pred /* * Document-method: Integer#chr * call-seq: * int.chr([encoding]) -> string * * Returns a string containing the character represented by the +int+'s value * according to +encoding+. * * 65.chr #=> "A" * 230.chr #=> "\xE6" * 255.chr(Encoding::UTF_8) #=> "\u00FF" */ VALUE rb_enc_uint_chr(unsigned int code, rb_encoding *enc) { int n; VALUE str; switch (n = rb_enc_codelen(code, enc)) { case ONIGERR_INVALID_CODE_POINT_VALUE: rb_raise(rb_eRangeError, "invalid codepoint 0x%X in %s", code, rb_enc_name(enc)); break; case ONIGERR_TOO_BIG_WIDE_CHAR_VALUE: case 0: rb_raise(rb_eRangeError, "%u out of char range", code); break; } str = rb_enc_str_new(0, n, enc); rb_enc_mbcput(code, RSTRING_PTR(str), enc); if (rb_enc_precise_mbclen(RSTRING_PTR(str), RSTRING_END(str), enc) != n) { rb_raise(rb_eRangeError, "invalid codepoint 0x%X in %s", code, rb_enc_name(enc)); } return str; } static VALUE 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, "%d out of char range", i); } goto decode; } c = (char)i; if (i < 0x80) { return rb_usascii_str_new(&c, 1); } else { return rb_str_new(&c, 1); } case 1: break; default: rb_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 */ /* * Document-method: Integer#-@ * call-seq: * -int -> integer * * Returns +int+, negated. */ 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 if (RB_TYPE_P(num, T_BIGNUM)) { return rb_big_uminus(num); } return num_funcall0(num, idUMinus); } /* * Document-method: Integer#to_s * call-seq: * int.to_s(base=10) -> string * * Returns a string containing the place-value representation of +int+ * with radix +base+ (between 2 and 36). * * 12345.to_s #=> "12345" * 12345.to_s(2) #=> "11000000111001" * 12345.to_s(8) #=> "30071" * 12345.to_s(10) #=> "12345" * 12345.to_s(16) #=> "3039" * 12345.to_s(36) #=> "9ix" * 78546939656932.to_s(36) #=> "rubyrules" */ VALUE rb_fix2str(VALUE x, int base) { 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 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_TYPE_P(x, T_BIGNUM)) { return rb_big2str(x, base); } return rb_any_to_s(x); } /* * Document-method: Integer#+ * call-seq: * int + numeric -> numeric_result * * Performs addition: the class of the resulting object depends on * the class of +numeric+. */ static VALUE fix_plus(VALUE x, VALUE y) { if (FIXNUM_P(y)) { return rb_fix_plus_fix(x, y); } else if (RB_TYPE_P(y, T_BIGNUM)) { return rb_big_plus(y, x); } else if (RB_TYPE_P(y, T_FLOAT)) { return DBL2NUM((double)FIX2LONG(x) + RFLOAT_VALUE(y)); } else if (RB_TYPE_P(y, T_COMPLEX)) { return rb_complex_plus(y, x); } else { return rb_num_coerce_bin(x, y, '+'); } } VALUE rb_fix_plus(VALUE x, VALUE y) { return fix_plus(x, y); } VALUE rb_int_plus(VALUE x, VALUE y) { if (FIXNUM_P(x)) { return fix_plus(x, y); } else if (RB_TYPE_P(x, T_BIGNUM)) { return rb_big_plus(x, y); } return rb_num_coerce_bin(x, y, '+'); } /* * Document-method: Integer#- * call-seq: * int - numeric -> numeric_result * * Performs subtraction: the class of the resulting object depends on * the class of +numeric+. */ static VALUE fix_minus(VALUE x, VALUE y) { if (FIXNUM_P(y)) { return rb_fix_minus_fix(x, y); } else if (RB_TYPE_P(y, T_BIGNUM)) { x = rb_int2big(FIX2LONG(x)); return rb_big_minus(x, y); } else if (RB_TYPE_P(y, T_FLOAT)) { return DBL2NUM((double)FIX2LONG(x) - RFLOAT_VALUE(y)); } else { return rb_num_coerce_bin(x, y, '-'); } } VALUE rb_int_minus(VALUE x, VALUE y) { if (FIXNUM_P(x)) { return fix_minus(x, y); } else if (RB_TYPE_P(x, T_BIGNUM)) { 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)) /* * Document-method: Integer#* * call-seq: * int * numeric -> numeric_result * * Performs multiplication: the class of the resulting object depends on * the class of +numeric+. */ static VALUE fix_mul(VALUE x, VALUE y) { if (FIXNUM_P(y)) { return rb_fix_mul_fix(x, y); } else if (RB_TYPE_P(y, T_BIGNUM)) { switch (x) { case INT2FIX(0): return x; case INT2FIX(1): return y; } return rb_big_mul(y, x); } else if (RB_TYPE_P(y, T_FLOAT)) { return DBL2NUM((double)FIX2LONG(x) * RFLOAT_VALUE(y)); } else if (RB_TYPE_P(y, T_COMPLEX)) { return rb_complex_mul(y, x); } else { return rb_num_coerce_bin(x, y, '*'); } } VALUE rb_int_mul(VALUE x, VALUE y) { if (FIXNUM_P(x)) { return fix_mul(x, y); } else if (RB_TYPE_P(x, T_BIGNUM)) { return rb_big_mul(x, y); } return rb_num_coerce_bin(x, y, '*'); } static double fix_fdiv_double(VALUE x, VALUE y) { if (FIXNUM_P(y)) { return double_div_double(FIX2LONG(x), FIX2LONG(y)); } else if (RB_TYPE_P(y, T_BIGNUM)) { return rb_big_fdiv_double(rb_int2big(FIX2LONG(x)), y); } else if (RB_TYPE_P(y, T_FLOAT)) { return double_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)) { 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_TYPE_P(x, T_BIGNUM)) { return rb_big_fdiv_double(x, y); } else { return nan(""); } } /* * Document-method: Integer#fdiv * call-seq: * int.fdiv(numeric) -> float * * Returns the floating point result of dividing +int+ by +numeric+. * * 654321.fdiv(13731) #=> 47.652829364212366 * 654321.fdiv(13731.24) #=> 47.65199646936475 * -654321.fdiv(13731) #=> -47.652829364212366 */ VALUE rb_int_fdiv(VALUE x, VALUE y) { if (RB_INTEGER_TYPE_P(x)) { return DBL2NUM(rb_int_fdiv_double(x, y)); } return Qnil; } /* * Document-method: Integer#/ * call-seq: * int / numeric -> numeric_result * * Performs division: the class of the resulting object depends on * the class of +numeric+. */ 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_TYPE_P(y, T_BIGNUM)) { x = rb_int2big(FIX2LONG(x)); return rb_big_div(x, y); } else if (RB_TYPE_P(y, T_FLOAT)) { 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, '/'); } VALUE rb_int_div(VALUE x, VALUE y) { if (FIXNUM_P(x)) { return fix_div(x, y); } else if (RB_TYPE_P(x, T_BIGNUM)) { return rb_big_div(x, y); } return Qnil; } /* * Document-method: Integer#div * call-seq: * int.div(numeric) -> integer * * Performs integer division: returns the integer result of dividing +int+ * by +numeric+. */ static VALUE fix_idiv(VALUE x, VALUE y) { return fix_divide(x, y, id_div); } VALUE rb_int_idiv(VALUE x, VALUE y) { if (FIXNUM_P(x)) { return fix_idiv(x, y); } else if (RB_TYPE_P(x, T_BIGNUM)) { return rb_big_idiv(x, y); } return num_div(x, y); } /* * Document-method: Integer#% * Document-method: Integer#modulo * call-seq: * int % other -> real * int.modulo(other) -> real * * Returns +int+ modulo +other+. * * See Numeric#divmod for more information. */ 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_TYPE_P(y, T_BIGNUM)) { x = rb_int2big(FIX2LONG(x)); return rb_big_modulo(x, y); } else if (RB_TYPE_P(y, T_FLOAT)) { return DBL2NUM(ruby_float_mod((double)FIX2LONG(x), RFLOAT_VALUE(y))); } else { return rb_num_coerce_bin(x, y, '%'); } } VALUE rb_int_modulo(VALUE x, VALUE y) { if (FIXNUM_P(x)) { return fix_mod(x, y); } else if (RB_TYPE_P(x, T_BIGNUM)) { return rb_big_modulo(x, y); } return num_modulo(x, y); } /* * call-seq: * int.remainder(numeric) -> real * * Returns the remainder after dividing +int+ by +numeric+. * * x.remainder(y) means x-y*(x/y).truncate. * * 5.remainder(3) #=> 2 * -5.remainder(3) #=> -2 * 5.remainder(-3) #=> 2 * -5.remainder(-3) #=> -2 * 5.remainder(1.5) #=> 0.5 * * See Numeric#divmod. */ static VALUE int_remainder(VALUE x, VALUE y) { if (FIXNUM_P(x)) { return num_remainder(x, y); } else if (RB_TYPE_P(x, T_BIGNUM)) { return rb_big_remainder(x, y); } return Qnil; } /* * Document-method: Integer#divmod * call-seq: * int.divmod(numeric) -> array * * See Numeric#divmod. */ 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_TYPE_P(y, T_BIGNUM)) { x = rb_int2big(FIX2LONG(x)); return rb_big_divmod(x, y); } else if (RB_TYPE_P(y, T_FLOAT)) { { double div, mod; volatile VALUE a, b; flodivmod((double)FIX2LONG(x), RFLOAT_VALUE(y), &div, &mod); a = dbl2ival(div); b = DBL2NUM(mod); return rb_assoc_new(a, b); } } else { return rb_num_coerce_bin(x, y, id_divmod); } } VALUE rb_int_divmod(VALUE x, VALUE y) { if (FIXNUM_P(x)) { return fix_divmod(x, y); } else if (RB_TYPE_P(x, T_BIGNUM)) { return rb_big_divmod(x, y); } return Qnil; } /* * Document-method: Integer#** * call-seq: * int ** numeric -> numeric_result * * Raises +int+ to the power of +numeric+, which may be negative or * fractional. * The result may be an Integer, a Float, a Rational, or a complex number. * * 2 ** 3 #=> 8 * 2 ** -1 #=> (1/2) * 2 ** 0.5 #=> 1.4142135623730951 * (-1) ** 0.5 #=> (0.0+1.0i) * * 123456789 ** 2 #=> 15241578750190521 * 123456789 ** 1.2 #=> 5126464716.0993185 * 123456789 ** -2 #=> (1/15241578750190521) */ static VALUE 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_TYPE_P(y, T_BIGNUM)) { 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_TYPE_P(y, T_FLOAT)) { 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); } } VALUE rb_int_pow(VALUE x, VALUE y) { if (FIXNUM_P(x)) { return fix_pow(x, y); } else if (RB_TYPE_P(x, T_BIGNUM)) { return rb_big_pow(x, y); } return Qnil; } 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; } /* * Document-method: Integer#== * Document-method: Integer#=== * call-seq: * int == other -> true or false * * Returns +true+ if +int+ equals +other+ numerically. * Contrast this with Integer#eql?, which requires +other+ to be an Integer. * * 1 == 2 #=> false * 1 == 1.0 #=> true */ static VALUE fix_equal(VALUE x, VALUE y) { if (x == y) return Qtrue; if (FIXNUM_P(y)) return Qfalse; else if (RB_TYPE_P(y, T_BIGNUM)) { return rb_big_eq(y, x); } else if (RB_TYPE_P(y, T_FLOAT)) { return rb_integer_float_eq(x, y); } else { return num_equal(x, y); } } VALUE rb_int_equal(VALUE x, VALUE y) { if (FIXNUM_P(x)) { return fix_equal(x, y); } else if (RB_TYPE_P(x, T_BIGNUM)) { return rb_big_eq(x, y); } return Qnil; } /* * Document-method: Integer#<=> * call-seq: * int <=> numeric -> -1, 0, +1, or nil * * Comparison---Returns -1, 0, or +1 depending on whether +int+ is * less than, equal to, or greater than +numeric+. * * This is the basis for the tests in the Comparable module. * * +nil+ is returned if the two values are incomparable. */ static VALUE fix_cmp(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_TYPE_P(y, T_BIGNUM)) { VALUE cmp = rb_big_cmp(y, x); switch (cmp) { case INT2FIX(+1): return INT2FIX(-1); case INT2FIX(-1): return INT2FIX(+1); } return cmp; } else if (RB_TYPE_P(y, T_FLOAT)) { return rb_integer_float_cmp(x, y); } else { return rb_num_coerce_cmp(x, y, id_cmp); } } VALUE rb_int_cmp(VALUE x, VALUE y) { if (FIXNUM_P(x)) { return fix_cmp(x, y); } else if (RB_TYPE_P(x, T_BIGNUM)) { return rb_big_cmp(x, y); } else { rb_raise(rb_eNotImpError, "need to define `<=>' in %s", rb_obj_classname(x)); } } /* * Document-method: Integer#> * call-seq: * int > real -> true or false * * Returns +true+ if the value of +int+ is greater than that of +real+. */ static VALUE fix_gt(VALUE x, VALUE y) { if (FIXNUM_P(y)) { if (FIX2LONG(x) > FIX2LONG(y)) return Qtrue; return Qfalse; } else if (RB_TYPE_P(y, T_BIGNUM)) { return rb_big_cmp(y, x) == INT2FIX(-1) ? Qtrue : Qfalse; } else if (RB_TYPE_P(y, T_FLOAT)) { return rb_integer_float_cmp(x, y) == INT2FIX(1) ? Qtrue : Qfalse; } else { return rb_num_coerce_relop(x, y, '>'); } } VALUE rb_int_gt(VALUE x, VALUE y) { if (FIXNUM_P(x)) { return fix_gt(x, y); } else if (RB_TYPE_P(x, T_BIGNUM)) { return rb_big_gt(x, y); } return Qnil; } /* * Document-method: Integer#>= * call-seq: * int >= real -> true or false * * Returns +true+ if the value of +int+ is greater than or equal to that of * +real+. */ static VALUE fix_ge(VALUE x, VALUE y) { if (FIXNUM_P(y)) { if (FIX2LONG(x) >= FIX2LONG(y)) return Qtrue; return Qfalse; } else if (RB_TYPE_P(y, T_BIGNUM)) { return rb_big_cmp(y, x) != INT2FIX(+1) ? Qtrue : Qfalse; } else if (RB_TYPE_P(y, T_FLOAT)) { VALUE rel = rb_integer_float_cmp(x, y); return rel == INT2FIX(1) || rel == INT2FIX(0) ? Qtrue : Qfalse; } else { return rb_num_coerce_relop(x, y, idGE); } } VALUE rb_int_ge(VALUE x, VALUE y) { if (FIXNUM_P(x)) { return fix_ge(x, y); } else if (RB_TYPE_P(x, T_BIGNUM)) { return rb_big_ge(x, y); } return Qnil; } /* * Document-method: Integer#< * call-seq: * int < real -> true or false * * Returns +true+ if the value of +int+ is less than that of +real+. */ static VALUE fix_lt(VALUE x, VALUE y) { if (FIXNUM_P(y)) { if (FIX2LONG(x) < FIX2LONG(y)) return Qtrue; return Qfalse; } else if (RB_TYPE_P(y, T_BIGNUM)) { return rb_big_cmp(y, x) == INT2FIX(+1) ? Qtrue : Qfalse; } else if (RB_TYPE_P(y, T_FLOAT)) { return rb_integer_float_cmp(x, y) == INT2FIX(-1) ? Qtrue : Qfalse; } else { return rb_num_coerce_relop(x, y, '<'); } } static VALUE int_lt(VALUE x, VALUE y) { if (FIXNUM_P(x)) { return fix_lt(x, y); } else if (RB_TYPE_P(x, T_BIGNUM)) { return rb_big_lt(x, y); } return Qnil; } /* * Document-method: Integer#<= * call-seq: * int <= real -> true or false * * Returns +true+ if the value of +int+ is less than or equal to that of * +real+. */ static VALUE fix_le(VALUE x, VALUE y) { if (FIXNUM_P(y)) { if (FIX2LONG(x) <= FIX2LONG(y)) return Qtrue; return Qfalse; } else if (RB_TYPE_P(y, T_BIGNUM)) { return rb_big_cmp(y, x) != INT2FIX(-1) ? Qtrue : Qfalse; } else if (RB_TYPE_P(y, T_FLOAT)) { VALUE rel = rb_integer_float_cmp(x, y); return rel == INT2FIX(-1) || rel == INT2FIX(0) ? Qtrue : Qfalse; } else { return rb_num_coerce_relop(x, y, idLE); } } static VALUE int_le(VALUE x, VALUE y) { if (FIXNUM_P(x)) { return fix_le(x, y); } else if (RB_TYPE_P(x, T_BIGNUM)) { return rb_big_le(x, y); } return Qnil; } /* * Document-method: Integer#~ * call-seq: * ~int -> integer * * One's complement: returns a number where each bit is flipped. * * Inverts the bits in an Integer. As integers are conceptually of * infinite length, the result acts as if it had an infinite number of * one bits to the left. In hex representations, this is displayed * as two periods to the left of the digits. * * sprintf("%X", ~0x1122334455) #=> "..FEEDDCCBBAA" */ static VALUE fix_comp(VALUE num) { return ~num | FIXNUM_FLAG; } static VALUE int_comp(VALUE num) { if (FIXNUM_P(num)) { return fix_comp(num); } else if (RB_TYPE_P(num, T_BIGNUM)) { return rb_big_comp(num); } return Qnil; } static VALUE 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 (ret == Qundef) { /* show the original object, not coerced object */ coerce_failed(x, y); } return ret; } /* * Document-method: Integer#& * call-seq: * int & other_int -> integer * * Bitwise AND. */ static VALUE fix_and(VALUE x, VALUE y) { if (FIXNUM_P(y)) { long val = FIX2LONG(x) & FIX2LONG(y); return LONG2NUM(val); } if (RB_TYPE_P(y, T_BIGNUM)) { return rb_big_and(y, x); } return rb_num_coerce_bit(x, y, '&'); } VALUE rb_int_and(VALUE x, VALUE y) { if (FIXNUM_P(x)) { return fix_and(x, y); } else if (RB_TYPE_P(x, T_BIGNUM)) { return rb_big_and(x, y); } return Qnil; } /* * Document-method: Integer#| * call-seq: * int | other_int -> integer * * Bitwise OR. */ static VALUE fix_or(VALUE x, VALUE y) { if (FIXNUM_P(y)) { long val = FIX2LONG(x) | FIX2LONG(y); return LONG2NUM(val); } if (RB_TYPE_P(y, T_BIGNUM)) { return rb_big_or(y, x); } return rb_num_coerce_bit(x, y, '|'); } static VALUE int_or(VALUE x, VALUE y) { if (FIXNUM_P(x)) { return fix_or(x, y); } else if (RB_TYPE_P(x, T_BIGNUM)) { return rb_big_or(x, y); } return Qnil; } /* * Document-method: Integer#^ * call-seq: * int ^ other_int -> integer * * Bitwise EXCLUSIVE OR. */ static VALUE fix_xor(VALUE x, VALUE y) { if (FIXNUM_P(y)) { long val = FIX2LONG(x) ^ FIX2LONG(y); return LONG2NUM(val); } if (RB_TYPE_P(y, T_BIGNUM)) { return rb_big_xor(y, x); } return rb_num_coerce_bit(x, y, '^'); } static VALUE int_xor(VALUE x, VALUE y) { if (FIXNUM_P(x)) { return fix_xor(x, y); } else if (RB_TYPE_P(x, T_BIGNUM)) { return rb_big_xor(x, y); } return Qnil; } /* * Document-method: Integer#<< * call-seq: * int << count -> integer * * Returns +int+ shifted left +count+ positions, or right if +count+ * is negative. */ static VALUE rb_fix_lshift(VALUE x, VALUE y) { long val, width; val = NUM2LONG(x); 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); } VALUE rb_int_lshift(VALUE x, VALUE y) { if (FIXNUM_P(x)) { return rb_fix_lshift(x, y); } else if (RB_TYPE_P(x, T_BIGNUM)) { return rb_big_lshift(x, y); } return Qnil; } /* * Document-method: Integer#>> * call-seq: * int >> count -> integer * * Returns +int+ shifted right +count+ positions, or left if +count+ * is negative. */ static VALUE rb_fix_rshift(VALUE x, VALUE y) { long i, val; val = FIX2LONG(x); 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); } static VALUE rb_int_rshift(VALUE x, VALUE y) { if (FIXNUM_P(x)) { return rb_fix_rshift(x, y); } else if (RB_TYPE_P(x, T_BIGNUM)) { return rb_big_rshift(x, y); } return Qnil; } MJIT_FUNC_EXPORTED 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 (RTEST(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_TYPE_P(num, T_BIGNUM)) { 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; } /* * Document-method: Integer#[] * call-seq: * int[n] -> 0, 1 * int[n, m] -> num * int[range] -> num * * Bit Reference---Returns the nth bit in the * binary representation of +int+, where int[0] * is the least significant bit. * * a = 0b11001100101010 * 30.downto(0) {|n| print a[n] } * #=> 0000000000000000011001100101010 * * a = 9**15 * 50.downto(0) {|n| print a[n] } * #=> 000101110110100000111000011110010100111100010111001 * * In principle, n[i] is equivalent to (n >> i) & 1. * Thus, any negative index always returns zero: * * p 255[-1] #=> 0 * * Range operations n[i, len] and n[i..j] * are naturally extended. * * * n[i, len] equals to (n >> i) & ((1 << len) - 1). * * n[i..j] equals to (n >> i) & ((1 << (j - i + 1)) - 1). * * n[i...j] equals to (n >> i) & ((1 << (j - i)) - 1). * * n[i..] equals to (n >> i). * * n[..j] is zero if n & ((1 << (j + 1)) - 1) is zero. Otherwise, raises an ArgumentError. * * n[...j] is zero if n & ((1 << j) - 1) is zero. Otherwise, raises an ArgumentError. * * Note that range operation may exhaust memory. * For example, -1[0, 1000000000000] will raise NoMemoryError. */ 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; } /* * Document-method: Integer#to_f * call-seq: * int.to_f -> float * * Converts +int+ to a Float. If +int+ doesn't fit in a Float, * the result is infinity. */ static VALUE int_to_f(VALUE num) { double val; if (FIXNUM_P(num)) { val = (double)FIX2LONG(num); } else if (RB_TYPE_P(num, T_BIGNUM)) { val = rb_big2dbl(num); } else { rb_raise(rb_eNotImpError, "Unknown subclass for to_f: %s", rb_obj_classname(num)); } return DBL2NUM(val); } /* * Document-method: Integer#abs * Document-method: Integer#magnitude * call-seq: * int.abs -> integer * int.magnitude -> integer * * Returns the absolute value of +int+. * * (-12345).abs #=> 12345 * -12345.abs #=> 12345 * 12345.abs #=> 12345 * * Integer#magnitude is an alias for Integer#abs. */ static VALUE fix_abs(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_TYPE_P(num, T_BIGNUM)) { return rb_big_abs(num); } return Qnil; } /* * Document-method: Integer#size * call-seq: * int.size -> int * * Returns the number of bytes in the machine representation of +int+ * (machine dependent). * * 1.size #=> 8 * -1.size #=> 8 * 2147483647.size #=> 8 * (256**10 - 1).size #=> 10 * (256**20 - 1).size #=> 20 * (256**40 - 1).size #=> 40 */ static VALUE fix_size(VALUE fix) { return INT2FIX(sizeof(long)); } static VALUE int_size(VALUE num) { if (FIXNUM_P(num)) { return fix_size(num); } else if (RB_TYPE_P(num, T_BIGNUM)) { return rb_big_size_m(num); } return Qnil; } /* * Document-method: Integer#bit_length * call-seq: * int.bit_length -> integer * * Returns the number of bits of the value of +int+. * * "Number of bits" means the bit position of the highest bit * which is different from the sign bit * (where the least significant bit has bit position 1). * If there is no such bit (zero or minus one), zero is returned. * * I.e. this method returns ceil(log2(int < 0 ? -int : int+1)). * * (-2**1000-1).bit_length #=> 1001 * (-2**1000).bit_length #=> 1000 * (-2**1000+1).bit_length #=> 1000 * (-2**12-1).bit_length #=> 13 * (-2**12).bit_length #=> 12 * (-2**12+1).bit_length #=> 12 * -0x101.bit_length #=> 9 * -0x100.bit_length #=> 8 * -0xff.bit_length #=> 8 * -2.bit_length #=> 1 * -1.bit_length #=> 0 * 0.bit_length #=> 0 * 1.bit_length #=> 1 * 0xff.bit_length #=> 8 * 0x100.bit_length #=> 9 * (2**12-1).bit_length #=> 12 * (2**12).bit_length #=> 13 * (2**12+1).bit_length #=> 13 * (2**1000-1).bit_length #=> 1000 * (2**1000).bit_length #=> 1001 * (2**1000+1).bit_length #=> 1001 * * This method can be used to detect overflow in Array#pack as follows: * * if n.bit_length < 32 * [n].pack("l") # no overflow * else * raise "overflow" * end */ static VALUE 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_TYPE_P(num, T_BIGNUM)) { return rb_big_bit_length(num); } return Qnil; } /* * Document-method: Integer#digits * call-seq: * int.digits -> array * int.digits(base) -> array * * Returns the digits of +int+'s place-value representation * with radix +base+ (default: 10). * The digits are returned as an array with the least significant digit * as the first array element. * * +base+ must be greater than or equal to 2. * * 12345.digits #=> [5, 4, 3, 2, 1] * 12345.digits(7) #=> [4, 6, 6, 0, 5] * 12345.digits(100) #=> [45, 23, 1] * * -12345.digits(7) #=> Math::DomainError */ static VALUE rb_fix_digits(VALUE fix, long base) { VALUE digits; long x = FIX2LONG(fix); assert(x >= 0); if (base < 2) rb_raise(rb_eArgError, "invalid radix %ld", base); if (x == 0) return rb_ary_new_from_args(1, INT2FIX(0)); digits = rb_ary_new(); while (x > 0) { long q = x % base; rb_ary_push(digits, LONG2NUM(q)); x /= base; } return digits; } static VALUE rb_int_digits_bigbase(VALUE num, VALUE base) { VALUE digits; assert(!rb_num_negative_p(num)); if (RB_TYPE_P(base, T_BIGNUM)) base = rb_big_norm(base); if (FIXNUM_P(base) && FIX2LONG(base) < 2) rb_raise(rb_eArgError, "invalid radix %ld", FIX2LONG(base)); else if (RB_TYPE_P(base, T_BIGNUM) && BIGNUM_NEGATIVE_P(base)) rb_raise(rb_eArgError, "negative radix"); if (FIXNUM_P(base) && FIXNUM_P(num)) return rb_fix_digits(num, FIX2LONG(base)); if (FIXNUM_P(num)) return rb_ary_new_from_args(1, num); digits = rb_ary_new(); while (!FIXNUM_P(num) || FIX2LONG(num) > 0) { VALUE qr = rb_int_divmod(num, base); rb_ary_push(digits, RARRAY_AREF(qr, 1)); num = RARRAY_AREF(qr, 0); } return digits; } static VALUE rb_int_digits(int argc, VALUE *argv, VALUE num) { VALUE base_value; long base; if (rb_num_negative_p(num)) rb_raise(rb_eMathDomainError, "out of domain"); if (rb_check_arity(argc, 0, 1)) { base_value = rb_to_int(argv[0]); if (!RB_INTEGER_TYPE_P(base_value)) rb_raise(rb_eTypeError, "wrong argument type %s (expected Integer)", rb_obj_classname(argv[0])); if (RB_TYPE_P(base_value, T_BIGNUM)) return rb_int_digits_bigbase(num, base_value); base = FIX2LONG(base_value); if (base < 0) rb_raise(rb_eArgError, "negative radix"); else if (base < 2) rb_raise(rb_eArgError, "invalid radix %ld", base); } else base = 10; if (FIXNUM_P(num)) return rb_fix_digits(num, base); else if (RB_TYPE_P(num, T_BIGNUM)) return rb_int_digits_bigbase(num, LONG2FIX(base)); return Qnil; } /* * Document-method: Integer#upto * call-seq: * int.upto(limit) {|i| block } -> self * int.upto(limit) -> an_enumerator * * Iterates the given block, passing in integer values from +int+ up to and * including +limit+. * * If no block is given, an Enumerator is returned instead. * * 5.upto(10) {|i| print i, " " } #=> 5 6 7 8 9 10 */ static VALUE int_upto_size(VALUE from, VALUE args, VALUE eobj) { return ruby_num_interval_step_size(from, RARRAY_AREF(args, 0), INT2FIX(1), FALSE); } static VALUE int_upto(VALUE from, VALUE to) { RETURN_SIZED_ENUMERATOR(from, 1, &to, int_upto_size); if (FIXNUM_P(from) && FIXNUM_P(to)) { long i, end; 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; } /* * Document-method: Integer#downto * call-seq: * int.downto(limit) {|i| block } -> self * int.downto(limit) -> an_enumerator * * Iterates the given block, passing in decreasing values from +int+ down to * and including +limit+. * * If no block is given, an Enumerator is returned instead. * * 5.downto(1) { |n| print n, ".. " } * puts "Liftoff!" * #=> "5.. 4.. 3.. 2.. 1.. Liftoff!" */ 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); } 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; } /* * Document-method: Integer#times * call-seq: * int.times {|i| block } -> self * int.times -> an_enumerator * * Iterates the given block +int+ times, passing in values from zero to * int - 1. * * If no block is given, an Enumerator is returned instead. * * 5.times {|i| print i, " " } #=> 0 1 2 3 4 */ static VALUE int_dotimes_size(VALUE num, VALUE args, VALUE eobj) { if (FIXNUM_P(num)) { if (NUM2LONG(num) <= 0) return INT2FIX(0); } else { if (RTEST(rb_funcall(num, '<', 1, INT2FIX(0)))) return INT2FIX(0); } return num; } static VALUE int_dotimes(VALUE num) { RETURN_SIZED_ENUMERATOR(num, 0, 0, int_dotimes_size); if (FIXNUM_P(num)) { long i, end; end = FIX2LONG(num); for (i=0; i integer or float * * Returns +int+ rounded to the nearest value with * a precision of +ndigits+ decimal digits (default: 0). * * When the precision is negative, the returned value is an integer * with at least ndigits.abs trailing zeros. * * Returns +self+ when +ndigits+ is zero or positive. * * 1.round #=> 1 * 1.round(2) #=> 1 * 15.round(-1) #=> 20 * (-15).round(-1) #=> -20 * * The optional +half+ keyword argument is available * similar to Float#round. * * 25.round(-1, half: :up) #=> 30 * 25.round(-1, half: :down) #=> 20 * 25.round(-1, half: :even) #=> 20 * 35.round(-1, half: :up) #=> 40 * 35.round(-1, half: :down) #=> 30 * 35.round(-1, half: :even) #=> 40 * (-25).round(-1, half: :up) #=> -30 * (-25).round(-1, half: :down) #=> -20 * (-25).round(-1, half: :even) #=> -20 */ static VALUE int_round(int argc, VALUE* argv, VALUE num) { int ndigits; int mode; VALUE nd, opt; if (!rb_scan_args(argc, argv, "01:", &nd, &opt)) return num; ndigits = NUM2INT(nd); mode = rb_num_get_rounding_option(opt); if (ndigits >= 0) { return num; } return rb_int_round(num, ndigits, mode); } /* * Document-method: Integer#floor * call-seq: * int.floor([ndigits]) -> integer or float * * Returns the largest number less than or equal to +int+ with * a precision of +ndigits+ decimal digits (default: 0). * * When the precision is negative, the returned value is an integer * with at least ndigits.abs trailing zeros. * * Returns +self+ when +ndigits+ is zero or positive. * * 1.floor #=> 1 * 1.floor(2) #=> 1 * 18.floor(-1) #=> 10 * (-18).floor(-1) #=> -20 */ static VALUE 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); } /* * Document-method: Integer#ceil * call-seq: * int.ceil([ndigits]) -> integer or float * * Returns the smallest number greater than or equal to +int+ with * a precision of +ndigits+ decimal digits (default: 0). * * When the precision is negative, the returned value is an integer * with at least ndigits.abs trailing zeros. * * Returns +self+ when +ndigits+ is zero or positive. * * 1.ceil #=> 1 * 1.ceil(2) #=> 1 * 18.ceil(-1) #=> 20 * (-18).ceil(-1) #=> -10 */ static VALUE int_ceil(int argc, VALUE* argv, VALUE num) { int ndigits; if (!rb_check_arity(argc, 0, 1)) return num; ndigits = NUM2INT(argv[0]); if (ndigits >= 0) { return num; } return rb_int_ceil(num, ndigits); } /* * Document-method: Integer#truncate * call-seq: * int.truncate([ndigits]) -> integer or float * * Returns +int+ truncated (toward zero) to * a precision of +ndigits+ decimal digits (default: 0). * * When the precision is negative, the returned value is an integer * with at least ndigits.abs trailing zeros. * * Returns +self+ when +ndigits+ is zero or positive. * * 1.truncate #=> 1 * 1.truncate(2) #=> 1 * 18.truncate(-1) #=> 10 * (-18).truncate(-1) #=> -10 */ static VALUE int_truncate(int argc, VALUE* argv, VALUE num) { int ndigits; if (!rb_check_arity(argc, 0, 1)) return num; ndigits = NUM2INT(argv[0]); if (ndigits >= 0) { return num; } return rb_int_truncate(num, ndigits); } #define DEFINE_INT_SQRT(rettype, prefix, argtype) \ rettype \ prefix##_isqrt(argtype n) \ { \ if (!argtype##_IN_DOUBLE_P(n)) { \ unsigned int b = bit_length(n); \ argtype t; \ rettype x = (rettype)(n >> (b/2+1)); \ x |= ((rettype)1LU << (b-1)/2); \ while ((t = n/x) < (argtype)x) x = (rettype)((x + t) >> 1); \ return x; \ } \ return (rettype)sqrt(argtype##_TO_DOUBLE(n)); \ } #if SIZEOF_LONG*CHAR_BIT > DBL_MANT_DIG # define RB_ULONG_IN_DOUBLE_P(n) ((n) < (1UL << DBL_MANT_DIG)) #else # define RB_ULONG_IN_DOUBLE_P(n) 1 #endif #define RB_ULONG_TO_DOUBLE(n) (double)(n) #define RB_ULONG unsigned long DEFINE_INT_SQRT(unsigned long, rb_ulong, RB_ULONG) #if 2*SIZEOF_BDIGIT > SIZEOF_LONG # if 2*SIZEOF_BDIGIT*CHAR_BIT > DBL_MANT_DIG # define BDIGIT_DBL_IN_DOUBLE_P(n) ((n) < ((BDIGIT_DBL)1UL << DBL_MANT_DIG)) # else # define BDIGIT_DBL_IN_DOUBLE_P(n) 1 # endif # ifdef ULL_TO_DOUBLE # define BDIGIT_DBL_TO_DOUBLE(n) ULL_TO_DOUBLE(n) # else # define BDIGIT_DBL_TO_DOUBLE(n) (double)(n) # endif DEFINE_INT_SQRT(BDIGIT, rb_bdigit_dbl, BDIGIT_DBL) #endif #define domain_error(msg) \ rb_raise(rb_eMathDomainError, "Numerical argument is out of domain - " #msg) VALUE rb_big_isqrt(VALUE); /* * Document-method: Integer::sqrt * call-seq: * Integer.sqrt(n) -> integer * * Returns the integer square root of the non-negative integer +n+, * i.e. the largest non-negative integer less than or equal to the * square root of +n+. * * Integer.sqrt(0) #=> 0 * Integer.sqrt(1) #=> 1 * Integer.sqrt(24) #=> 4 * Integer.sqrt(25) #=> 5 * Integer.sqrt(10**400) #=> 10**200 * * Equivalent to Math.sqrt(n).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 (!) * * If +n+ is not an Integer, it is converted to an Integer first. * If +n+ is negative, a Math::DomainError is raised. */ static VALUE rb_int_s_isqrt(VALUE self, VALUE num) { unsigned long n, sq; num = rb_to_int(num); if (FIXNUM_P(num)) { if (FIXNUM_NEGATIVE_P(num)) { domain_error("isqrt"); } n = FIX2ULONG(num); sq = rb_ulong_isqrt(n); return LONG2FIX(sq); } else { size_t biglen; if (RBIGNUM_NEGATIVE_P(num)) { domain_error("isqrt"); } biglen = BIGNUM_LEN(num); if (biglen == 0) return INT2FIX(0); #if SIZEOF_BDIGIT <= SIZEOF_LONG /* short-circuit */ if (biglen == 1) { n = BIGNUM_DIGITS(num)[0]; sq = rb_ulong_isqrt(n); return ULONG2NUM(sq); } #endif return rb_big_isqrt(num); } } /* * 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 */ void Init_Numeric(void) { #undef rb_intern #define rb_intern(str) rb_intern_const(str) #ifdef _UNICOSMP /* Turn off floating point exceptions for divide by zero, etc. */ _set_Creg(0, 0); #endif id_coerce = rb_intern("coerce"); id_to = rb_intern("to"); id_by = rb_intern("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, "dup", num_dup, 0); rb_define_method(rb_cNumeric, "i", num_imaginary, 0); rb_define_method(rb_cNumeric, "+@", num_uplus, 0); rb_define_method(rb_cNumeric, "-@", num_uminus, 0); rb_define_method(rb_cNumeric, "<=>", num_cmp, 1); rb_define_method(rb_cNumeric, "eql?", num_eql, 1); rb_define_method(rb_cNumeric, "fdiv", num_fdiv, 1); rb_define_method(rb_cNumeric, "div", num_div, 1); rb_define_method(rb_cNumeric, "divmod", num_divmod, 1); rb_define_method(rb_cNumeric, "%", num_modulo, 1); rb_define_method(rb_cNumeric, "modulo", num_modulo, 1); rb_define_method(rb_cNumeric, "remainder", num_remainder, 1); rb_define_method(rb_cNumeric, "abs", num_abs, 0); rb_define_method(rb_cNumeric, "magnitude", num_abs, 0); rb_define_method(rb_cNumeric, "to_int", num_to_int, 0); rb_define_method(rb_cNumeric, "real?", num_real_p, 0); rb_define_method(rb_cNumeric, "integer?", num_int_p, 0); rb_define_method(rb_cNumeric, "zero?", num_zero_p, 0); rb_define_method(rb_cNumeric, "nonzero?", num_nonzero_p, 0); rb_define_method(rb_cNumeric, "finite?", num_finite_p, 0); rb_define_method(rb_cNumeric, "infinite?", num_infinite_p, 0); rb_define_method(rb_cNumeric, "floor", num_floor, -1); rb_define_method(rb_cNumeric, "ceil", num_ceil, -1); rb_define_method(rb_cNumeric, "round", num_round, -1); rb_define_method(rb_cNumeric, "truncate", num_truncate, -1); rb_define_method(rb_cNumeric, "step", num_step, -1); rb_define_method(rb_cNumeric, "positive?", num_positive_p, 0); rb_define_method(rb_cNumeric, "negative?", num_negative_p, 0); rb_cInteger = rb_define_class("Integer", rb_cNumeric); rb_undef_alloc_func(rb_cInteger); rb_undef_method(CLASS_OF(rb_cInteger), "new"); rb_define_singleton_method(rb_cInteger, "sqrt", rb_int_s_isqrt, 1); rb_define_method(rb_cInteger, "to_s", int_to_s, -1); rb_define_alias(rb_cInteger, "inspect", "to_s"); rb_define_method(rb_cInteger, "allbits?", int_allbits_p, 1); rb_define_method(rb_cInteger, "anybits?", int_anybits_p, 1); rb_define_method(rb_cInteger, "nobits?", int_nobits_p, 1); rb_define_method(rb_cInteger, "upto", int_upto, 1); rb_define_method(rb_cInteger, "downto", int_downto, 1); rb_define_method(rb_cInteger, "times", int_dotimes, 0); rb_define_method(rb_cInteger, "succ", int_succ, 0); rb_define_method(rb_cInteger, "next", int_succ, 0); rb_define_method(rb_cInteger, "pred", int_pred, 0); rb_define_method(rb_cInteger, "chr", int_chr, -1); rb_define_method(rb_cInteger, "to_f", int_to_f, 0); rb_define_method(rb_cInteger, "floor", int_floor, -1); rb_define_method(rb_cInteger, "ceil", int_ceil, -1); rb_define_method(rb_cInteger, "truncate", int_truncate, -1); rb_define_method(rb_cInteger, "round", int_round, -1); rb_define_method(rb_cInteger, "<=>", rb_int_cmp, 1); rb_define_method(rb_cInteger, "-@", rb_int_uminus, 0); rb_define_method(rb_cInteger, "+", rb_int_plus, 1); rb_define_method(rb_cInteger, "-", rb_int_minus, 1); rb_define_method(rb_cInteger, "*", rb_int_mul, 1); rb_define_method(rb_cInteger, "/", rb_int_div, 1); rb_define_method(rb_cInteger, "div", rb_int_idiv, 1); rb_define_method(rb_cInteger, "%", rb_int_modulo, 1); rb_define_method(rb_cInteger, "modulo", rb_int_modulo, 1); rb_define_method(rb_cInteger, "remainder", int_remainder, 1); rb_define_method(rb_cInteger, "divmod", rb_int_divmod, 1); rb_define_method(rb_cInteger, "fdiv", rb_int_fdiv, 1); rb_define_method(rb_cInteger, "**", rb_int_pow, 1); rb_define_method(rb_cInteger, "pow", rb_int_powm, -1); /* in bignum.c */ rb_define_method(rb_cInteger, "===", rb_int_equal, 1); rb_define_method(rb_cInteger, "==", rb_int_equal, 1); rb_define_method(rb_cInteger, ">", rb_int_gt, 1); rb_define_method(rb_cInteger, ">=", rb_int_ge, 1); rb_define_method(rb_cInteger, "<", int_lt, 1); rb_define_method(rb_cInteger, "<=", int_le, 1); rb_define_method(rb_cInteger, "~", int_comp, 0); rb_define_method(rb_cInteger, "&", rb_int_and, 1); rb_define_method(rb_cInteger, "|", int_or, 1); rb_define_method(rb_cInteger, "^", int_xor, 1); rb_define_method(rb_cInteger, "[]", int_aref, -1); rb_define_method(rb_cInteger, "<<", rb_int_lshift, 1); rb_define_method(rb_cInteger, ">>", rb_int_rshift, 1); rb_define_method(rb_cInteger, "size", int_size, 0); rb_define_method(rb_cInteger, "digits", rb_int_digits, -1); /* An obsolete class, use Integer */ rb_define_const(rb_cObject, "Fixnum", rb_cInteger); rb_deprecate_constant(rb_cObject, "Fixnum"); rb_cFloat = rb_define_class("Float", rb_cNumeric); rb_undef_alloc_func(rb_cFloat); rb_undef_method(CLASS_OF(rb_cFloat), "new"); /* * 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_uminus, 0); rb_define_method(rb_cFloat, "+", rb_float_plus, 1); rb_define_method(rb_cFloat, "-", flo_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_f", flo_to_f, 0); rb_define_method(rb_cFloat, "abs", rb_float_abs, 0); rb_define_method(rb_cFloat, "magnitude", rb_float_abs, 0); rb_define_method(rb_cFloat, "zero?", flo_zero_p, 0); rb_define_method(rb_cFloat, "to_i", flo_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); rb_define_method(rb_cFloat, "positive?", flo_positive_p, 0); rb_define_method(rb_cFloat, "negative?", flo_negative_p, 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 "integer.rbinc"