/********************************************************************** numeric.c - $Author$ created at: Fri Aug 13 18:33:09 JST 1993 Copyright (C) 1993-2007 Yukihiro Matsumoto **********************************************************************/ #include "ruby/ruby.h" #include "ruby/encoding.h" #include "ruby/util.h" #include "internal.h" #include "id.h" #include #include #include #if defined(__FreeBSD__) && __FreeBSD__ < 4 #include #endif #ifdef HAVE_FLOAT_H #include #endif #ifdef HAVE_IEEEFP_H #include #endif #if !defined HAVE_ISFINITE && !defined isfinite #if defined HAVE_FINITE && !defined finite && !defined _WIN32 extern int finite(double); # define HAVE_ISFINITE 1 # define isfinite(x) finite(x) #endif #endif /* use IEEE 64bit values if not defined */ #ifndef FLT_RADIX #define FLT_RADIX 2 #endif #ifndef FLT_ROUNDS #define FLT_ROUNDS 1 #endif #ifndef DBL_MIN #define DBL_MIN 2.2250738585072014e-308 #endif #ifndef DBL_MAX #define DBL_MAX 1.7976931348623157e+308 #endif #ifndef DBL_MIN_EXP #define DBL_MIN_EXP (-1021) #endif #ifndef DBL_MAX_EXP #define DBL_MAX_EXP 1024 #endif #ifndef DBL_MIN_10_EXP #define DBL_MIN_10_EXP (-307) #endif #ifndef DBL_MAX_10_EXP #define DBL_MAX_10_EXP 308 #endif #ifndef DBL_DIG #define DBL_DIG 15 #endif #ifndef DBL_MANT_DIG #define DBL_MANT_DIG 53 #endif #ifndef DBL_EPSILON #define DBL_EPSILON 2.2204460492503131e-16 #endif #ifdef HAVE_INFINITY #elif !defined(WORDS_BIGENDIAN) /* BYTE_ORDER == LITTLE_ENDIAN */ const union bytesequence4_or_float rb_infinity = {{0x00, 0x00, 0x80, 0x7f}}; #else const union bytesequence4_or_float rb_infinity = {{0x7f, 0x80, 0x00, 0x00}}; #endif #ifdef HAVE_NAN #elif !defined(WORDS_BIGENDIAN) /* BYTE_ORDER == LITTLE_ENDIAN */ const union bytesequence4_or_float rb_nan = {{0x00, 0x00, 0xc0, 0x7f}}; #else const union bytesequence4_or_float rb_nan = {{0x7f, 0xc0, 0x00, 0x00}}; #endif #ifndef HAVE_ROUND double round(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 VALUE fix_uminus(VALUE num); static VALUE fix_mul(VALUE x, VALUE y); static VALUE int_pow(long x, unsigned long y); static ID id_coerce, id_div; #define id_to_i idTo_i #define id_eq idEq #define id_cmp idCmp VALUE rb_cNumeric; VALUE rb_cFloat; VALUE rb_cInteger; VALUE rb_cFixnum; VALUE rb_eZeroDivError; VALUE rb_eFloatDomainError; static VALUE sym_to, sym_by; void rb_num_zerodiv(void) { rb_raise(rb_eZeroDivError, "divided by 0"); } /* 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 positive_int_p(VALUE num) { const ID mid = '>'; if (FIXNUM_P(num)) { if (method_basic_p(rb_cFixnum)) return (SIGNED_VALUE)num > 0; } else if (RB_TYPE_P(num, T_BIGNUM)) { if (method_basic_p(rb_cBignum)) return BIGNUM_POSITIVE_P(num); } return RTEST(rb_funcall(num, mid, 1, INT2FIX(0))); } static inline int negative_int_p(VALUE num) { const ID mid = '<'; if (FIXNUM_P(num)) { if (method_basic_p(rb_cFixnum)) return (SIGNED_VALUE)num < 0; } else if (RB_TYPE_P(num, T_BIGNUM)) { if (method_basic_p(rb_cBignum)) return BIGNUM_NEGATIVE_P(num); } return RTEST(rb_funcall(num, mid, 1, INT2FIX(0))); } int rb_num_negative_p(VALUE num) { return negative_int_p(num); } /* * call-seq: * num.coerce(numeric) -> array * * If a +numeric is the same type as +num+, returns an array containing * +numeric+ and +num+. Otherwise, returns an array with both a +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); } static VALUE coerce_body(VALUE *x) { return rb_funcall(x[1], id_coerce, 1, x[0]); } NORETURN(static void coerce_failed(VALUE x, VALUE y)); static void coerce_failed(VALUE x, VALUE y) { rb_raise(rb_eTypeError, "%"PRIsVALUE" can't be coerced into %"PRIsVALUE, (rb_special_const_p(y)? rb_inspect(y) : rb_obj_class(y)), rb_obj_class(x)); } static VALUE coerce_rescue(VALUE *x) { coerce_failed(x[0], x[1]); return Qnil; /* dummy */ } static int do_coerce(VALUE *x, VALUE *y, int err) { VALUE ary; VALUE a[2]; a[0] = *x; a[1] = *y; if (!rb_respond_to(*y, id_coerce)) { if (err) { coerce_rescue(a); } return FALSE; } ary = rb_rescue(coerce_body, (VALUE)a, err ? coerce_rescue : 0, (VALUE)a); if (!RB_TYPE_P(ary, T_ARRAY) || RARRAY_LEN(ary) != 2) { if (err) { rb_raise(rb_eTypeError, "coerce must return [x, y]"); } return FALSE; } *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; } /* * 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; } /* * Numerics are immutable values, which should not be copied. * * Any attempt to use this method on a Numeric will raise a TypeError. */ static VALUE num_init_copy(VALUE x, VALUE y) { rb_raise(rb_eTypeError, "can't copy %"PRIsVALUE, rb_obj_class(x)); UNREACHABLE; } /* * call-seq: * +num -> num * * Unary Plus---Returns the receiver's value. */ 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. */ static VALUE num_imaginary(VALUE num) { return rb_complex_new(INT2FIX(0), num); } /* * call-seq: * -num -> numeric * * Unary Minus---Returns the receiver's value, negated. */ static VALUE num_uminus(VALUE num) { VALUE zero; zero = INT2FIX(0); do_coerce(&zero, &num, TRUE); return rb_funcall(zero, '-', 1, 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(rb_funcall(x, '/', 1, 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) { return rb_funcall(x, '-', 1, rb_funcall(y, '*', 1, rb_funcall(x, rb_intern("div"), 1, y))); } /* * 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 = rb_funcall(x, '%', 1, y); if ((!rb_equal(z, INT2FIX(0))) && ((negative_int_p(x) && positive_int_p(y)) || (positive_int_p(x) && negative_int_p(y)))) { return rb_funcall(z, '-', 1, y); } 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 -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 (including Fixnum and Bignum). * * (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 of Numeric#abs. */ static VALUE num_abs(VALUE num) { if (negative_int_p(num)) { return rb_funcall(num, rb_intern("-@"), 0); } 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; } /* * 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(rb_funcall(num, rb_intern("zero?"), 0, 0))) { return Qnil; } return num; } /* * 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 => Fixnum * 1.0.to_i.class => Fixnum */ static VALUE num_to_int(VALUE num) { return rb_funcall(num, id_to_i, 0, 0); } /******************************************************************** * * 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: * * - http://docs.sun.com/source/806-3568/ncg_goldberg.html * - http://wiki.github.com/rdp/ruby_tutorials_core/ruby-talk-faq#wiki-floats_imprecise * - http://en.wikipedia.org/wiki/Floating_point#Accuracy_problems */ VALUE rb_float_new_in_heap(double d) { NEWOBJ_OF(flt, struct RFloat, rb_cFloat, T_FLOAT | (RGENGC_WB_PROTECTED_FLOAT ? FL_WB_PROTECTED : 0)); flt->float_value = d; OBJ_FREEZE(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) { char *ruby_dtoa(double d_, int mode, int ndigits, int *decpt, int *sign, char **rve); enum {decimal_mant = DBL_MANT_DIG-DBL_DIG}; enum {float_dig = DBL_DIG+1}; char buf[float_dig + (decimal_mant + CHAR_BIT - 1) / CHAR_BIT + 10]; double value = RFLOAT_VALUE(flt); VALUE s; char *p, *e; int sign, decpt, digs; if (isinf(value)) return rb_usascii_str_new2(value < 0 ? "-Infinity" : "Infinity"); 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 { 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 a +numeric+ and a +float+ represented as Float * objects. * * This is achieved by converting a +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. */ static VALUE flo_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+. */ static VALUE flo_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+. */ static VALUE flo_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, '*'); } } /* * call-seq: * float / other -> float * * Returns a new float which is the result of dividing +float+ by +other+. */ static VALUE flo_div(VALUE x, VALUE y) { long f_y; double d; if (RB_TYPE_P(y, T_FIXNUM)) { f_y = FIX2LONG(y); return DBL2NUM(RFLOAT_VALUE(x) / (double)f_y); } else if (RB_TYPE_P(y, T_BIGNUM)) { d = rb_big2dbl(y); return DBL2NUM(RFLOAT_VALUE(x) / d); } else if (RB_TYPE_P(y, T_FLOAT)) { return DBL2NUM(RFLOAT_VALUE(x) / RFLOAT_VALUE(y)); } else { return rb_num_coerce_bin(x, y, '/'); } } /* * call-seq: * float.fdiv(numeric) -> float * float.quo(numeric) -> float * * Returns float / numeric, same as Float#/. */ static VALUE flo_quo(VALUE x, VALUE y) { return rb_funcall(x, '/', 1, y); } static void flodivmod(double x, double y, double *divp, double *modp) { double div, mod; 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) && !isnan(y)) div = x; else div = (x - mod) / y; if (y*mod < 0) { mod += y; div -= 1.0; } if (modp) *modp = mod; if (divp) *divp = div; } /* * Returns the modulo of division of x by y. * An error will be raised if y == 0. */ double ruby_float_mod(double x, double y) { double mod; flodivmod(x, y, 0, &mod); return mod; } /* * call-seq: * float % other -> float * float.modulo(other) -> float * * Return the modulo after division of +float+ by +other+. * * 6543.21.modulo(137) #=> 104.21 * 6543.21.modulo(137.24) #=> 92.9299999999996 */ 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) { d = round(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, rb_intern("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 */ static VALUE flo_pow(VALUE x, VALUE y) { if (RB_TYPE_P(y, T_FIXNUM)) { return DBL2NUM(pow(RFLOAT_VALUE(x), (double)FIX2LONG(y))); } else if (RB_TYPE_P(y, T_BIGNUM)) { return DBL2NUM(pow(RFLOAT_VALUE(x), rb_big2dbl(y))); } else if (RB_TYPE_P(y, T_FLOAT)) { { double dx = RFLOAT_VALUE(x); double dy = RFLOAT_VALUE(y); if (dx < 0 && dy != round(dy)) return rb_funcall(rb_complex_raw1(x), rb_intern("**"), 1, y); return DBL2NUM(pow(dx, dy)); } } else { return rb_num_coerce_bin(x, y, rb_intern("**")); } } /* * call-seq: * num.eql?(numeric) -> true or false * * Returns +true+ if +num+ and +numeric+ are the same type and have equal * values. * * 1 == 1.0 #=> true * 1.eql?(1.0) #=> false * (1.0).eql?(1.0) #=> true */ static VALUE num_eql(VALUE x, VALUE y) { if (TYPE(x) != TYPE(y)) return Qfalse; return rb_equal(x, y); } /* * call-seq: * number <=> other -> 0 or nil * * Returns zero if +number+ equals +other+, otherwise +nil+ is returned if the * two values are incomparable. */ static VALUE num_cmp(VALUE x, VALUE y) { if (x == y) return INT2FIX(0); return Qnil; } static VALUE num_equal(VALUE x, VALUE y) { if (x == y) return Qtrue; return rb_funcall(y, id_eq, 1, x); } /* * 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. * * The result of NaN == NaN is undefined, so the * implementation-dependent value is returned. * * 1.0 == 1 #=> true * */ static VALUE flo_eq(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 defined(_MSC_VER) && _MSC_VER < 1300 if (isnan(b)) return Qfalse; #endif } else { return num_equal(x, y); } a = RFLOAT_VALUE(x); #if defined(_MSC_VER) && _MSC_VER < 1300 if (isnan(a)) return Qfalse; #endif return (a == b)?Qtrue:Qfalse; } /* * call-seq: * float.hash -> integer * * Returns a hash code for this float. * * See also Object#hash. */ static VALUE flo_hash(VALUE num) { double d; st_index_t hash; d = RFLOAT_VALUE(num); /* normalize -0.0 to 0.0 */ if (d == 0.0) d = 0.0; hash = rb_memhash(&d, sizeof(d)); return LONG2FIX(hash); } 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, +1 or nil depending on whether +float+ is less than, equal * to, or greater than +real+. This is the basis for the tests in Comparable. * * The result of NaN <=> NaN is undefined, so the * 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 INT2FIX(-FIX2INT(rel)); return rel; } else if (RB_TYPE_P(y, T_FLOAT)) { b = RFLOAT_VALUE(y); } else { if (isinf(a) && (i = rb_check_funcall(y, rb_intern("infinite?"), 0, 0)) != Qundef) { if (RTEST(i)) { int j = rb_cmpint(i, x, y); j = (a > 0.0) ? (j > 0 ? 0 : +1) : (j < 0 ? 0 : -1); return INT2FIX(j); } if (a > 0.0) return INT2FIX(1); return INT2FIX(-1); } return rb_num_coerce_cmp(x, y, id_cmp); } return rb_dbl_cmp(a, b); } /* * call-seq: * float > real -> true or false * * Returns +true+ if +float+ is greater than +real+. * * The result of NaN > NaN is undefined, so the * implementation-dependent value is returned. */ static VALUE flo_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 -FIX2INT(rel) > 0 ? Qtrue : Qfalse; return Qfalse; } else if (RB_TYPE_P(y, T_FLOAT)) { b = RFLOAT_VALUE(y); #if defined(_MSC_VER) && _MSC_VER < 1300 if (isnan(b)) return Qfalse; #endif } else { return rb_num_coerce_relop(x, y, '>'); } #if defined(_MSC_VER) && _MSC_VER < 1300 if (isnan(a)) return Qfalse; #endif return (a > b)?Qtrue:Qfalse; } /* * call-seq: * float >= real -> true or false * * Returns +true+ if +float+ is greater than or equal to +real+. * * The result of NaN >= NaN is undefined, so the * 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 -FIX2INT(rel) >= 0 ? Qtrue : Qfalse; return Qfalse; } else if (RB_TYPE_P(y, T_FLOAT)) { b = RFLOAT_VALUE(y); #if defined(_MSC_VER) && _MSC_VER < 1300 if (isnan(b)) return Qfalse; #endif } else { return rb_num_coerce_relop(x, y, rb_intern(">=")); } #if defined(_MSC_VER) && _MSC_VER < 1300 if (isnan(a)) return Qfalse; #endif return (a >= b)?Qtrue:Qfalse; } /* * call-seq: * float < real -> true or false * * Returns +true+ if +float+ is less than +real+. * * The result of NaN < NaN is undefined, so the * 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 -FIX2INT(rel) < 0 ? Qtrue : Qfalse; return Qfalse; } else if (RB_TYPE_P(y, T_FLOAT)) { b = RFLOAT_VALUE(y); #if defined(_MSC_VER) && _MSC_VER < 1300 if (isnan(b)) return Qfalse; #endif } else { return rb_num_coerce_relop(x, y, '<'); } #if defined(_MSC_VER) && _MSC_VER < 1300 if (isnan(a)) return Qfalse; #endif return (a < b)?Qtrue:Qfalse; } /* * call-seq: * float <= real -> true or false * * Returns +true+ if +float+ is less than or equal to +real+. * * The result of NaN <= NaN is undefined, so the * 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 -FIX2INT(rel) <= 0 ? Qtrue : Qfalse; return Qfalse; } else if (RB_TYPE_P(y, T_FLOAT)) { b = RFLOAT_VALUE(y); #if defined(_MSC_VER) && _MSC_VER < 1300 if (isnan(b)) return Qfalse; #endif } else { return rb_num_coerce_relop(x, y, rb_intern("<=")); } #if defined(_MSC_VER) && _MSC_VER < 1300 if (isnan(a)) return Qfalse; #endif return (a <= b)?Qtrue:Qfalse; } /* * 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. * * The result of NaN.eql?(NaN) is undefined, so the * implementation-dependent value is returned. * * 1.0.eql?(1) #=> false */ static VALUE flo_eql(VALUE x, VALUE y) { if (RB_TYPE_P(y, T_FLOAT)) { double a = RFLOAT_VALUE(x); double b = RFLOAT_VALUE(y); #if defined(_MSC_VER) && _MSC_VER < 1300 if (isnan(a) || isnan(b)) return Qfalse; #endif if (a == b) return Qtrue; } return Qfalse; } /* * 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 * */ static VALUE flo_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) { if (RFLOAT_VALUE(num) == 0.0) { return Qtrue; } return 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? -> nil, -1, +1 * * Return values corresponding to the value of +float+: * * +finite+:: +nil+ * +-Infinity+:: +-1+ * ++Infinity+:: +1+ * * For example: * * (0.0).infinite? #=> nil * (-1.0/0.0).infinite? #=> -1 * (+1.0/0.0).infinite? #=> 1 */ static VALUE 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 (it is not * infinite, and Float#nan? is +false+). * */ static VALUE flo_is_finite_p(VALUE num) { double value = RFLOAT_VALUE(num); #if 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: * * p 0.01.next_float #=> 0.010000000000000002 * p 1.0.next_float #=> 1.0000000000000002 * p 100.0.next_float #=> 100.00000000000001 * * p 0.01.next_float - 0.01 #=> 1.734723475976807e-18 * p 1.0.next_float - 1.0 #=> 2.220446049250313e-16 * p 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 } * p f #=> 9.99999999999998 # should be 10.0 in the ideal world. * p 10-f #=> 1.9539925233402755e-14 # the floating-point error. * p(10.0.next_float-10) #=> 1.7763568394002505e-15 # 1 ulp (units in the last place). * p((10-f)/(10.0.next_float-10)) #=> 11.0 # the error is 11 ulp. * p((10-f)/(10*Float::EPSILON)) #=> 8.8 # approximation of the above. * p "%a" % f #=> "0x1.3fffffffffff5p+3" # the last hex digit is 5. 16 - 5 = 11 ulp. * */ static VALUE flo_next_float(VALUE vx) { double x, y; x = NUM2DBL(vx); y = nextafter(x, INFINITY); return DBL2NUM(y); } /* * call-seq: * float.prev_float -> float * * Returns the previous representable floatint-point number. * * (-Float::MAX).prev_float and (-Float::INFINITY).prev_float is -Float::INFINITY. * * Float::NAN.prev_float is Float::NAN. * * For example: * * p 0.01.prev_float #=> 0.009999999999999998 * p 1.0.prev_float #=> 0.9999999999999999 * p 100.0.prev_float #=> 99.99999999999999 * * p 0.01 - 0.01.prev_float #=> 1.734723475976807e-18 * p 1.0 - 1.0.prev_float #=> 1.1102230246251565e-16 * p 100.0 - 100.0.prev_float #=> 1.4210854715202004e-14 * * f = 0.01; 20.times { printf "%-20a %s\n", f, f.to_s; f = f.prev_float } * #=> 0x1.47ae147ae147bp-7 0.01 * # 0x1.47ae147ae147ap-7 0.009999999999999998 * # 0x1.47ae147ae1479p-7 0.009999999999999997 * # 0x1.47ae147ae1478p-7 0.009999999999999995 * # 0x1.47ae147ae1477p-7 0.009999999999999993 * # 0x1.47ae147ae1476p-7 0.009999999999999992 * # 0x1.47ae147ae1475p-7 0.00999999999999999 * # 0x1.47ae147ae1474p-7 0.009999999999999988 * # 0x1.47ae147ae1473p-7 0.009999999999999986 * # 0x1.47ae147ae1472p-7 0.009999999999999985 * # 0x1.47ae147ae1471p-7 0.009999999999999983 * # 0x1.47ae147ae147p-7 0.009999999999999981 * # 0x1.47ae147ae146fp-7 0.00999999999999998 * # 0x1.47ae147ae146ep-7 0.009999999999999978 * # 0x1.47ae147ae146dp-7 0.009999999999999976 * # 0x1.47ae147ae146cp-7 0.009999999999999974 * # 0x1.47ae147ae146bp-7 0.009999999999999972 * # 0x1.47ae147ae146ap-7 0.00999999999999997 * # 0x1.47ae147ae1469p-7 0.009999999999999969 * # 0x1.47ae147ae1468p-7 0.009999999999999967 * */ static VALUE flo_prev_float(VALUE vx) { double x, y; x = NUM2DBL(vx); y = nextafter(x, -INFINITY); return DBL2NUM(y); } /* * call-seq: * float.floor -> integer * * Returns the largest integer less than or equal to +float+. * * 1.2.floor #=> 1 * 2.0.floor #=> 2 * (-1.2).floor #=> -2 * (-2.0).floor #=> -2 */ static VALUE flo_floor(VALUE num) { double f = floor(RFLOAT_VALUE(num)); long val; if (!FIXABLE(f)) { return rb_dbl2big(f); } val = (long)f; return LONG2FIX(val); } /* * call-seq: * float.ceil -> integer * * Returns the smallest Integer greater than or equal to +float+. * * 1.2.ceil #=> 2 * 2.0.ceil #=> 2 * (-1.2).ceil #=> -1 * (-2.0).ceil #=> -2 */ static VALUE flo_ceil(VALUE num) { double f = ceil(RFLOAT_VALUE(num)); long val; if (!FIXABLE(f)) { return rb_dbl2big(f); } val = (long)f; return LONG2FIX(val); } /* * Assumes num is an Integer, ndigits <= 0 */ static VALUE int_round_0(VALUE num, int ndigits) { VALUE n, f, h, r; long bytes; ID op; /* If 10**N / 2 > num, then return 0 */ /* We have log_256(10) > 0.415241 and log_256(1/2) = -0.125, so */ bytes = FIXNUM_P(num) ? sizeof(long) : rb_funcall(num, idSize, 0); if (-0.415241 * ndigits - 0.125 > bytes ) { return INT2FIX(0); } f = int_pow(10, -ndigits); if (FIXNUM_P(num) && FIXNUM_P(f)) { SIGNED_VALUE x = FIX2LONG(num), y = FIX2LONG(f); int neg = x < 0; if (neg) x = -x; x = (x + y / 2) / y * y; if (neg) x = -x; return LONG2NUM(x); } if (RB_TYPE_P(f, T_FLOAT)) { /* then int_pow overflow */ return INT2FIX(0); } h = rb_funcall(f, '/', 1, INT2FIX(2)); r = rb_funcall(num, '%', 1, f); n = rb_funcall(num, '-', 1, r); op = negative_int_p(num) ? rb_intern("<=") : '<'; if (!RTEST(rb_funcall(r, op, 1, h))) { n = rb_funcall(n, '+', 1, f); } return n; } static VALUE flo_truncate(VALUE num); /* * call-seq: * float.round([ndigits]) -> integer or float * * Rounds +float+ to a given precision in decimal digits (default 0 digits). * * Precision may be negative. Returns a floating point number when +ndigits+ * is more than zero. * * 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 * */ static VALUE flo_round(int argc, VALUE *argv, VALUE num) { VALUE nd; double number, f; int ndigits = 0; int binexp; enum {float_dig = DBL_DIG+2}; if (argc > 0 && rb_scan_args(argc, argv, "01", &nd) == 1) { ndigits = NUM2INT(nd); } if (ndigits < 0) { return int_round_0(flo_truncate(num), ndigits); } number = RFLOAT_VALUE(num); if (ndigits == 0) { return dbl2ival(number); } frexp(number, &binexp); /* 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 (isinf(number) || isnan(number) || (ndigits >= float_dig - (binexp > 0 ? binexp / 4 : binexp / 3 - 1))) { return num; } if (ndigits < - (binexp > 0 ? binexp / 3 + 1 : binexp / 4)) { return DBL2NUM(0); } f = pow(10, ndigits); return DBL2NUM(round(number * f) / f); } /* * call-seq: * float.to_i -> integer * float.to_int -> integer * float.truncate -> integer * * Returns the +float+ truncated to an Integer. * * Synonyms are #to_i, #to_int, and #truncate. */ static VALUE flo_truncate(VALUE num) { double f = RFLOAT_VALUE(num); long val; if (f > 0.0) f = floor(f); if (f < 0.0) f = ceil(f); if (!FIXABLE(f)) { return rb_dbl2big(f); } val = (long)f; return LONG2FIX(val); } /* * call-seq: * num.floor -> integer * * Returns the largest integer less than or equal to +num+. * * Numeric implements this by converting an Integer to a Float and invoking * Float#floor. * * 1.floor #=> 1 * (-1).floor #=> -1 */ static VALUE num_floor(VALUE num) { return flo_floor(rb_Float(num)); } /* * call-seq: * num.ceil -> integer * * Returns the smallest possible Integer that is greater than or equal to * +num+. * * Numeric achieves this by converting itself to a Float then invoking * Float#ceil. * * 1.ceil #=> 1 * 1.2.ceil #=> 2 * (-1.2).ceil #=> -1 * (-1.0).ceil #=> -1 */ static VALUE num_ceil(VALUE num) { return flo_ceil(rb_Float(num)); } /* * call-seq: * num.round([ndigits]) -> integer or float * * Rounds +num+ to a given precision in decimal digits (default 0 digits). * * Precision may be negative. Returns a floating point number when +ndigits+ * is more than zero. * * Numeric implements this by converting itself 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 -> integer * * Returns +num+ truncated to an Integer. * * Numeric implements this by converting its value to a Float and invoking * Float#truncate. */ static VALUE num_truncate(VALUE num) { return flo_truncate(rb_Float(num)); } static double ruby_float_step_size(double beg, double end, double unit, int excl) { const double epsilon = DBL_EPSILON; double n = (end - beg)/unit; double err = (fabs(beg) + fabs(end) + fabs(end-beg)) / fabs(unit) * epsilon; if (isinf(unit)) { return unit > 0 ? beg <= end : beg >= end; } if (unit == 0) { return INFINITY; } if (err>0.5) err=0.5; if (excl) { if (n<=0) return 0; if (n<1) n = 0; else n = floor(n - err); } else { if (n<0) return 0; n = floor(n + err); } return n+1; } int ruby_float_step(VALUE from, VALUE to, VALUE step, int excl) { if (RB_TYPE_P(from, T_FLOAT) || RB_TYPE_P(to, T_FLOAT) || RB_TYPE_P(step, T_FLOAT)) { double beg = NUM2DBL(from); double end = NUM2DBL(to); double unit = NUM2DBL(step); double n = ruby_float_step_size(beg, end, unit, excl); long i; if (isinf(unit)) { /* if unit is infinity, i*unit+beg is NaN */ if (n) rb_yield(DBL2NUM(beg)); } else 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(INFINITY); } delta = FIX2LONG(to) - FIX2LONG(from); if (diff < 0) { diff = -diff; delta = -delta; } if (excl) { delta--; } if (delta < 0) { return INT2FIX(0); } return ULONG2NUM(delta / diff + 1UL); } else if (RB_TYPE_P(from, T_FLOAT) || RB_TYPE_P(to, T_FLOAT) || RB_TYPE_P(step, T_FLOAT)) { double n = ruby_float_step_size(NUM2DBL(from), NUM2DBL(to), NUM2DBL(step), excl); if (isinf(n)) return DBL2NUM(n); if (POSFIXABLE(n)) return LONG2FIX(n); return rb_dbl2big(n); } else { VALUE result; ID cmp = '>'; switch (rb_cmpint(rb_num_coerce_cmp(step, INT2FIX(0), id_cmp), step, INT2FIX(0))) { case 0: return DBL2NUM(INFINITY); case -1: cmp = '<'; break; } 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_scan_args(int argc, const VALUE *argv, VALUE *to, VALUE *step) { VALUE hash; int desc; argc = rb_scan_args(argc, argv, "02:", to, step, &hash); if (!NIL_P(hash)) { ID keys[2]; VALUE values[2]; keys[0] = sym_to; keys[1] = sym_by; rb_get_kwargs(hash, keys, 0, 2, values); if (values[0] != Qundef) { if (argc > 0) rb_raise(rb_eArgError, "to is given twice"); *to = values[0]; } if (values[1] != Qundef) { if (argc > 1) rb_raise(rb_eArgError, "step is given twice"); *step = values[1]; } } else { /* compatibility */ if (argc > 1 && NIL_P(*step)) { rb_raise(rb_eTypeError, "step must be numeric"); } if (rb_equal(*step, INT2FIX(0))) { rb_raise(rb_eArgError, "step can't be 0"); } } if (NIL_P(*step)) { *step = INT2FIX(1); } desc = !positive_int_p(*step); if (NIL_P(*to)) { *to = desc ? DBL2NUM(-INFINITY) : DBL2NUM(INFINITY); } return desc; } static VALUE num_step_size(VALUE from, VALUE args, VALUE eobj) { VALUE to, step; int argc = args ? RARRAY_LENINT(args) : 0; const VALUE *argv = args ? RARRAY_CONST_PTR(args) : 0; num_step_scan_args(argc, argv, &to, &step); return ruby_num_interval_step_size(from, to, step, FALSE); } /* * call-seq: * num.step(by: step, to: limit) {|i| block } -> self * num.step(by: step, to: limit) -> an_enumerator * num.step(limit=nil, step=1) {|i| block } -> self * num.step(limit=nil, step=1) -> an_enumerator * * Invokes the given block with the sequence of numbers starting at +num+, * incremented by +step+ (defaulted to +1+) on each call. * * The loop finishes when the value to be passed to the block is greater than * +limit+ (if +step+ is positive) or less than +limit+ (if +step+ is * negative), where limit is defaulted to infinity. * * In the recommended keyword argument style, either or both of * +step+ and +limit+ (default infinity) can be omitted. In the * fixed position argument style, zero as a step * (i.e. 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 the following expression: * * floor(n + n*epsilon)+ 1 * * Where the +n+ is the following: * * 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. * * 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 * 2.71828182845905 2.91828182845905 3.11828182845905 */ static VALUE num_step(int argc, VALUE *argv, VALUE from) { VALUE to, step; int desc, inf; RETURN_SIZED_ENUMERATOR(from, argc, argv, num_step_size); desc = num_step_scan_args(argc, argv, &to, &step); if (RTEST(rb_num_coerce_cmp(step, INT2FIX(0), id_eq))) { 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)) { 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, inteneded */ if (wrap_p) *wrap_p = l < 0; return (unsigned long)l; } else if (RB_TYPE_P(val, T_FLOAT)) { if (RFLOAT_VALUE(val) < ULONG_MAX_PLUS_ONE && LONG_MIN_MINUS_ONE_IS_LESS_THAN(RFLOAT_VALUE(val))) { double d = RFLOAT_VALUE(val); if (wrap_p) *wrap_p = d <= -1.0; /* NUM2ULONG(v) uses v.to_int conceptually. */ if (0 <= d) return (unsigned long)d; return (unsigned long)(long)d; } else { FLOAT_OUT_OF_RANGE(val, "integer"); } } else if (RB_TYPE_P(val, T_BIGNUM)) { { unsigned long ul = rb_big2ulong(val); if (wrap_p) *wrap_p = BIGNUM_NEGATIVE_P(val); return ul; } } else { val = rb_to_int(val); goto again; } } unsigned long rb_num2ulong(VALUE val) { return rb_num2ulong_internal(val, NULL); } #if SIZEOF_INT < SIZEOF_LONG 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"); } 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, negative_int_p(val)); return num; } #else long rb_num2int(VALUE val) { return rb_num2long(val); } long rb_fix2int(VALUE val) { return FIX2INT(val); } #endif 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, 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)) { if (RFLOAT_VALUE(val) < LLONG_MAX_PLUS_ONE && (LLONG_MIN_MINUS_ONE_IS_LESS_THAN(RFLOAT_VALUE(val)))) { return (LONG_LONG)(RFLOAT_VALUE(val)); } 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, inteneded */ } else if (RB_TYPE_P(val, T_FLOAT)) { if (RFLOAT_VALUE(val) < ULLONG_MAX_PLUS_ONE && LLONG_MIN_MINUS_ONE_IS_LESS_THAN(RFLOAT_VALUE(val))) { if (0 <= RFLOAT_VALUE(val)) return (unsigned LONG_LONG)(RFLOAT_VALUE(val)); return (unsigned LONG_LONG)(LONG_LONG)(RFLOAT_VALUE(val)); } 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 * * This class is the basis for the two concrete classes that hold whole * numbers, Bignum and Fixnum. * */ /* * call-seq: * int.to_i -> integer * * As +int+ is already an Integer, all these methods simply return the receiver. * * Synonyms are #to_int, #floor, #ceil, #truncate. */ static VALUE int_to_i(VALUE num) { return num; } /* * call-seq: * int.integer? -> true * * Since +int+ is already an Integer, this always returns +true+. */ static VALUE int_int_p(VALUE num) { return Qtrue; } /* * call-seq: * int.odd? -> true or false * * Returns +true+ if +int+ is an odd number. */ static VALUE int_odd_p(VALUE num) { if (rb_funcall(num, '%', 1, INT2FIX(2)) != INT2FIX(0)) { return Qtrue; } return Qfalse; } /* * call-seq: * int.even? -> true or false * * Returns +true+ if +int+ is an even number. */ static VALUE int_even_p(VALUE num) { if (rb_funcall(num, '%', 1, INT2FIX(2)) == INT2FIX(0)) { return Qtrue; } return Qfalse; } /* * call-seq: * int.next -> integer * int.succ -> integer * * Returns the Integer equal to +int+ + 1. * * 1.next #=> 2 * (-1).next #=> 0 */ static VALUE fix_succ(VALUE num) { long i = FIX2LONG(num) + 1; return LONG2NUM(i); } /* * call-seq: * int.next -> integer * int.succ -> integer * * Returns the Integer equal to +int+ + 1, same as Fixnum#next. * * 1.next #=> 2 * (-1).next #=> 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 rb_funcall(num, '+', 1, INT2FIX(1)); } #define int_succ rb_int_succ /* * call-seq: * int.pred -> integer * * Returns the Integer equal to +int+ - 1. * * 1.pred #=> 0 * (-1).pred #=> -2 */ 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 rb_funcall(num, '-', 1, INT2FIX(1)); } #define int_pred rb_int_pred VALUE rb_enc_uint_chr(unsigned int code, rb_encoding *enc) { int n; VALUE str; switch (n = rb_enc_codelen(code, enc)) { case ONIGERR_INVALID_CODE_POINT_VALUE: rb_raise(rb_eRangeError, "invalid codepoint 0x%X in %s", code, rb_enc_name(enc)); break; case ONIGERR_TOO_BIG_WIDE_CHAR_VALUE: case 0: rb_raise(rb_eRangeError, "%u out of char range", code); break; } str = rb_enc_str_new(0, n, enc); rb_enc_mbcput(code, RSTRING_PTR(str), enc); if (rb_enc_precise_mbclen(RSTRING_PTR(str), RSTRING_END(str), enc) != n) { rb_raise(rb_eRangeError, "invalid codepoint 0x%X in %s", code, rb_enc_name(enc)); } return str; } /* * call-seq: * int.chr([encoding]) -> string * * Returns a string containing the character represented by the +int+'s value * according to +encoding+. * * 65.chr #=> "A" * 230.chr #=> "\346" * 255.chr(Encoding::UTF_8) #=> "\303\277" */ 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_check_arity(argc, 0, 1); break; } enc = rb_to_encoding(argv[0]); if (!enc) enc = rb_ascii8bit_encoding(); decode: return rb_enc_uint_chr(i, enc); } /* * call-seq: * int.ord -> self * * Returns the +int+ itself. * * ?a.ord #=> 97 * * This method is intended for compatibility to character constant in Ruby * 1.9. * * For example, ?a.ord returns 97 both in 1.8 and 1.9. */ static VALUE int_ord(VALUE num) { return num; } /******************************************************************** * * Document-class: Fixnum * * Holds Integer values that can be represented in a native machine word * (minus 1 bit). If any operation on a Fixnum exceeds this range, the value * is automatically converted to a Bignum. * * Fixnum objects have immediate value. This means that when they are assigned * or passed as parameters, the actual object is passed, rather than a * reference to that object. * * Assignment does not alias Fixnum objects. There is effectively only one * Fixnum object instance for any given integer value, so, for example, you * cannot add a singleton method to a Fixnum. Any attempt to add a singleton * method to a Fixnum object will raise a TypeError. */ /* * call-seq: * -fix -> integer * * Negates +fix+, which may return a Bignum. */ static VALUE fix_uminus(VALUE num) { return LONG2NUM(-FIX2LONG(num)); } VALUE rb_fix2str(VALUE x, int base) { extern const char ruby_digitmap[]; char buf[SIZEOF_VALUE*CHAR_BIT + 2], *b = buf + sizeof buf; long val = FIX2LONG(x); int neg = 0; if (base < 2 || 36 < base) { rb_raise(rb_eArgError, "invalid radix %d", base); } if (val == 0) { return rb_usascii_str_new2("0"); } if (val < 0) { val = -val; neg = 1; } *--b = '\0'; do { *--b = ruby_digitmap[(int)(val % base)]; } while (val /= base); if (neg) { *--b = '-'; } return rb_usascii_str_new2(b); } /* * call-seq: * fix.to_s(base=10) -> string * * Returns a string containing the representation of +fix+ 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" * */ static VALUE fix_to_s(int argc, VALUE *argv, VALUE x) { int base; if (argc == 0) base = 10; else { VALUE b; rb_scan_args(argc, argv, "01", &b); base = NUM2INT(b); } return rb_fix2str(x, base); } /* * call-seq: * fix + numeric -> numeric_result * * Performs addition: the class of the resulting object depends on the class of * +numeric+ and on the magnitude of the result. It may return a Bignum. */ static VALUE fix_plus(VALUE x, VALUE y) { if (FIXNUM_P(y)) { long a, b, c; VALUE r; a = FIX2LONG(x); b = FIX2LONG(y); c = a + b; r = LONG2NUM(c); return r; } 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 { return rb_num_coerce_bin(x, y, '+'); } } /* * call-seq: * fix - numeric -> numeric_result * * Performs subtraction: the class of the resulting object depends on the class * of +numeric+ and on the magnitude of the result. It may return a Bignum. */ static VALUE fix_minus(VALUE x, VALUE y) { if (FIXNUM_P(y)) { long a, b, c; VALUE r; a = FIX2LONG(x); b = FIX2LONG(y); c = a - b; r = LONG2NUM(c); return r; } 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, '-'); } } #define SQRT_LONG_MAX ((SIGNED_VALUE)1<<((SIZEOF_LONG*CHAR_BIT-1)/2)) /*tests if N*N would overflow*/ #define FIT_SQRT_LONG(n) (((n)=-SQRT_LONG_MAX)) /* * call-seq: * fix * numeric -> numeric_result * * Performs multiplication: the class of the resulting object depends on the * class of +numeric+ and on the magnitude of the result. It may return a * Bignum. */ static VALUE fix_mul(VALUE x, VALUE y) { if (FIXNUM_P(y)) { #ifdef __HP_cc /* avoids an optimization bug of HP aC++/ANSI C B3910B A.06.05 [Jul 25 2005] */ volatile #endif long a, b; #if SIZEOF_LONG * 2 <= SIZEOF_LONG_LONG LONG_LONG d; #else VALUE r; #endif a = FIX2LONG(x); b = FIX2LONG(y); #if SIZEOF_LONG * 2 <= SIZEOF_LONG_LONG d = (LONG_LONG)a * b; if (FIXABLE(d)) return LONG2FIX(d); return rb_ll2inum(d); #else if (a == 0) return x; if (MUL_OVERFLOW_FIXNUM_P(a, b)) r = rb_big_mul(rb_int2big(a), rb_int2big(b)); else r = LONG2FIX(a * b); return r; #endif } else if (RB_TYPE_P(y, T_BIGNUM)) { return rb_big_mul(y, x); } else if (RB_TYPE_P(y, T_FLOAT)) { return DBL2NUM((double)FIX2LONG(x) * RFLOAT_VALUE(y)); } else { return rb_num_coerce_bin(x, y, '*'); } } static void fixdivmod(long x, long y, long *divp, long *modp) { long div, mod; if (y == 0) rb_num_zerodiv(); if (y < 0) { if (x < 0) div = -x / -y; else div = - (x / -y); } else { if (x < 0) div = - (-x / y); else div = x / y; } mod = x - div*y; if ((mod < 0 && y > 0) || (mod > 0 && y < 0)) { mod += y; div -= 1; } if (divp) *divp = div; if (modp) *modp = mod; } /* * call-seq: * fix.fdiv(numeric) -> float * * Returns the floating point result of dividing +fix+ by +numeric+. * * 654321.fdiv(13731) #=> 47.6528293642124 * 654321.fdiv(13731.24) #=> 47.6519964693647 * */ static VALUE fix_fdiv(VALUE x, VALUE y) { if (FIXNUM_P(y)) { return DBL2NUM((double)FIX2LONG(x) / (double)FIX2LONG(y)); } else if (RB_TYPE_P(y, T_BIGNUM)) { return rb_big_fdiv(rb_int2big(FIX2LONG(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, rb_intern("fdiv")); } } static VALUE fix_divide(VALUE x, VALUE y, ID op) { if (FIXNUM_P(y)) { long div; fixdivmod(FIX2LONG(x), FIX2LONG(y), &div, 0); return LONG2NUM(div); } else if (RB_TYPE_P(y, T_BIGNUM)) { x = rb_int2big(FIX2LONG(x)); return rb_big_div(x, y); } else if (RB_TYPE_P(y, T_FLOAT)) { { double div; if (op == '/') { div = (double)FIX2LONG(x) / RFLOAT_VALUE(y); return DBL2NUM(div); } else { if (RFLOAT_VALUE(y) == 0) rb_num_zerodiv(); div = (double)FIX2LONG(x) / RFLOAT_VALUE(y); return rb_dbl2big(floor(div)); } } } else { if (RB_TYPE_P(y, T_RATIONAL) && op == '/' && FIX2LONG(x) == 1) return rb_rational_reciprocal(y); return rb_num_coerce_bin(x, y, op); } } /* * call-seq: * fix / numeric -> numeric_result * * Performs division: the class of the resulting object depends on the class of * +numeric+ and on the magnitude of the result. It may return a Bignum. */ static VALUE fix_div(VALUE x, VALUE y) { return fix_divide(x, y, '/'); } /* * call-seq: * fix.div(numeric) -> integer * * Performs integer division: returns integer result of dividing +fix+ by * +numeric+. */ static VALUE fix_idiv(VALUE x, VALUE y) { return fix_divide(x, y, rb_intern("div")); } /* * call-seq: * fix % other -> real * fix.modulo(other) -> real * * Returns +fix+ modulo +other+. * * See Numeric#divmod for more information. */ static VALUE fix_mod(VALUE x, VALUE y) { if (FIXNUM_P(y)) { long mod; fixdivmod(FIX2LONG(x), FIX2LONG(y), 0, &mod); return LONG2NUM(mod); } 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, '%'); } } /* * call-seq: * fix.divmod(numeric) -> array * * See Numeric#divmod. */ static VALUE fix_divmod(VALUE x, VALUE y) { if (FIXNUM_P(y)) { long div, mod; fixdivmod(FIX2LONG(x), FIX2LONG(y), &div, &mod); return rb_assoc_new(LONG2NUM(div), LONG2NUM(mod)); } 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, rb_intern("divmod")); } } static VALUE int_pow(long x, unsigned long y) { int neg = x < 0; long z = 1; if (neg) x = -x; if (y & 1) z = x; else neg = 0; y &= ~1; do { while (y % 2 == 0) { if (!FIT_SQRT_LONG(x)) { VALUE v; bignum: v = rb_big_pow(rb_int2big(x), LONG2NUM(y)); if (z != 1) v = rb_big_mul(rb_int2big(neg ? -z : z), v); return v; } x = x * x; y >>= 1; } { if (MUL_OVERFLOW_FIXNUM_P(x, z)) { goto bignum; } z = x * z; } } while (--y); if (neg) z = -z; return LONG2NUM(z); } VALUE rb_int_positive_pow(long x, unsigned long y) { return int_pow(x, y); } /* * call-seq: * fix ** numeric -> numeric_result * * Raises +fix+ to the power of +numeric+, which may be negative or * fractional. * * 2 ** 3 #=> 8 * 2 ** -1 #=> (1/2) * 2 ** 0.5 #=> 1.4142135623731 */ 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) { if (b % 2 == 0) return INT2FIX(1); else return INT2FIX(-1); } if (b < 0) return rb_funcall(rb_rational_raw1(x), rb_intern("**"), 1, y); if (b == 0) return INT2FIX(1); if (b == 1) return x; if (a == 0) { if (b > 0) return INT2FIX(0); return DBL2NUM(INFINITY); } return int_pow(a, b); } else if (RB_TYPE_P(y, T_BIGNUM)) { if (a == 1) return INT2FIX(1); if (a == -1) { if (int_even_p(y)) return INT2FIX(1); else return INT2FIX(-1); } if (negative_int_p(y)) return rb_funcall(rb_rational_raw1(x), rb_intern("**"), 1, y); if (a == 0) return INT2FIX(0); x = rb_int2big(FIX2LONG(x)); return rb_big_pow(x, y); } else if (RB_TYPE_P(y, T_FLOAT)) { if (RFLOAT_VALUE(y) == 0.0) return DBL2NUM(1.0); if (a == 0) { return DBL2NUM(RFLOAT_VALUE(y) < 0 ? INFINITY : 0.0); } if (a == 1) return DBL2NUM(1.0); { double dy = RFLOAT_VALUE(y); if (a < 0 && dy != round(dy)) return rb_funcall(rb_complex_raw1(x), rb_intern("**"), 1, y); return DBL2NUM(pow((double)a, dy)); } } else { return rb_num_coerce_bin(x, y, rb_intern("**")); } } /* * call-seq: * fix == other -> true or false * * Return +true+ if +fix+ equals +other+ numerically. * * 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); } } /* * call-seq: * fix <=> numeric -> -1, 0, +1 or nil * * Comparison---Returns +-1+, +0+, ++1+ or +nil+ depending on whether +fix+ is * less than, equal to, or greater than +numeric+. * * This is the basis for the tests in 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)) { return rb_big_cmp(rb_int2big(FIX2LONG(x)), y); } 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); } } /* * call-seq: * fix > real -> true or false * * Returns +true+ if the value of +fix+ 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 FIX2INT(rb_big_cmp(rb_int2big(FIX2LONG(x)), y)) > 0 ? 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, '>'); } } /* * call-seq: * fix >= real -> true or false * * Returns +true+ if the value of +fix+ 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 FIX2INT(rb_big_cmp(rb_int2big(FIX2LONG(x)), y)) >= 0 ? 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, rb_intern(">=")); } } /* * call-seq: * fix < real -> true or false * * Returns +true+ if the value of +fix+ 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 FIX2INT(rb_big_cmp(rb_int2big(FIX2LONG(x)), y)) < 0 ? 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, '<'); } } /* * call-seq: * fix <= real -> true or false * * Returns +true+ if the value of +fix+ 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 FIX2INT(rb_big_cmp(rb_int2big(FIX2LONG(x)), y)) <= 0 ? 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, rb_intern("<=")); } } /* * call-seq: * ~fix -> integer * * One's complement: returns a number where each bit is flipped. */ static VALUE fix_rev(VALUE num) { return ~num | FIXNUM_FLAG; } static int bit_coerce(VALUE *x, VALUE *y, int err) { if (!FIXNUM_P(*y) && !RB_TYPE_P(*y, T_BIGNUM)) { do_coerce(x, y, err); if (!FIXNUM_P(*x) && !RB_TYPE_P(*x, T_BIGNUM) && !FIXNUM_P(*y) && !RB_TYPE_P(*y, T_BIGNUM)) { if (!err) return FALSE; coerce_failed(*x, *y); } } return TRUE; } VALUE rb_num_coerce_bit(VALUE x, VALUE y, ID func) { bit_coerce(&x, &y, TRUE); return rb_funcall(x, func, 1, y); } /* * call-seq: * fix & integer -> integer_result * * 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); } bit_coerce(&x, &y, TRUE); return rb_funcall(x, rb_intern("&"), 1, y); } /* * call-seq: * fix | integer -> integer_result * * 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); } bit_coerce(&x, &y, TRUE); return rb_funcall(x, rb_intern("|"), 1, y); } /* * call-seq: * fix ^ integer -> integer_result * * 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); } bit_coerce(&x, &y, TRUE); return rb_funcall(x, rb_intern("^"), 1, y); } static VALUE fix_lshift(long, unsigned long); static VALUE fix_rshift(long, unsigned long); /* * call-seq: * fix << count -> integer * * Shifts +fix+ 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); } /* * call-seq: * fix >> count -> integer * * Shifts +fix+ 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); } /* * call-seq: * fix[n] -> 0, 1 * * Bit Reference---Returns the +n+th bit in the binary representation of * +fix+, where fix[0] is the least significant bit. * * For example: * * a = 0b11001100101010 * 30.downto(0) do |n| print a[n] end * #=> 0000000000000000011001100101010 */ static VALUE 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< float * * Converts +fix+ to a Float. * */ static VALUE fix_to_f(VALUE num) { double val; val = (double)FIX2LONG(num); return DBL2NUM(val); } /* * call-seq: * fix.abs -> integer * fix.magnitude -> integer * * Returns the absolute value of +fix+. * * -12345.abs #=> 12345 * 12345.abs #=> 12345 * */ static VALUE fix_abs(VALUE fix) { long i = FIX2LONG(fix); if (i < 0) i = -i; return LONG2NUM(i); } /* * call-seq: * fix.size -> fixnum * * Returns the number of bytes in the machine representation of +fix+. * * 1.size #=> 4 * -1.size #=> 4 * 2147483647.size #=> 4 */ static VALUE fix_size(VALUE fix) { return INT2FIX(sizeof(long)); } /* * call-seq: * int.bit_length -> integer * * Returns the number of bits of the value of int. * * "the number of bits" means that * the bit position of the highest bit which is different to the sign bit. * (The bit position of the bit 2**n is n+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**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 * * 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)); } static VALUE int_upto_size(VALUE from, VALUE args, VALUE eobj) { return ruby_num_interval_step_size(from, RARRAY_AREF(args, 0), INT2FIX(1), FALSE); } /* * call-seq: * 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. * * For example: * * 5.upto(10) { |i| print i, " " } * #=> 5 6 7 8 9 10 */ 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; } static VALUE int_downto_size(VALUE from, VALUE args, VALUE eobj) { return ruby_num_interval_step_size(from, RARRAY_AREF(args, 0), INT2FIX(-1), FALSE); } /* * call-seq: * int.downto(limit) {|i| block } -> self * int.downto(limit) -> an_enumerator * * Iterates the given block, passing decreasing values from +int+ down to and * including +limit+. * * If no block is given, an Enumerator is returned instead. * * 5.downto(1) { |n| print n, ".. " } * print " Liftoff!\n" * #=> "5.. 4.. 3.. 2.. 1.. Liftoff!" */ static VALUE int_downto(VALUE from, VALUE to) { RETURN_SIZED_ENUMERATOR(from, 1, &to, int_downto_size); if (FIXNUM_P(from) && FIXNUM_P(to)) { long i, end; end = FIX2LONG(to); for (i=FIX2LONG(from); i >= end; i--) { rb_yield(LONG2FIX(i)); } } else { VALUE i = from, c; while (!(c = rb_funcall(i, '<', 1, to))) { rb_yield(i); i = rb_funcall(i, '-', 1, INT2FIX(1)); } if (NIL_P(c)) rb_cmperr(i, to); } return from; } static VALUE int_dotimes_size(VALUE num, VALUE args, VALUE eobj) { 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; } /* * 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 do |i| * print i, " " * end * #=> 0 1 2 3 4 */ 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 * * Rounds +int+ to a given precision in decimal digits (default 0 digits). * * Precision may be negative. Returns a floating point number when +ndigits+ * is positive, +self+ for zero, and round down for negative. * * 1.round #=> 1 * 1.round(2) #=> 1.0 * 15.round(-1) #=> 20 */ static VALUE int_round(int argc, VALUE* argv, VALUE num) { VALUE n; int ndigits; if (argc == 0) return num; rb_scan_args(argc, argv, "1", &n); ndigits = NUM2INT(n); if (ndigits > 0) { return rb_Float(num); } if (ndigits == 0) { return num; } return int_round_0(num, ndigits); } /* * call-seq: * fix.zero? -> true or false * * Returns +true+ if +fix+ is zero. * */ static VALUE fix_zero_p(VALUE num) { if (FIX2LONG(num) == 0) { return Qtrue; } return Qfalse; } /* * call-seq: * fix.odd? -> true or false * * Returns +true+ if +fix+ is an odd number. */ static VALUE fix_odd_p(VALUE num) { if (num & 2) { return Qtrue; } return Qfalse; } /* * call-seq: * fix.even? -> true or false * * Returns +true+ if +fix+ is an even number. */ static VALUE fix_even_p(VALUE num) { if (num & 2) { return Qfalse; } return Qtrue; } /* * 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 * +infinite+ or +NaN+) to numerical classes which don't support them. * * Float::INFINITY.to_r * #=> FloatDomainError: Infinity */ /* * The top-level number class. */ void Init_Numeric(void) { #undef rb_intern #define rb_intern(str) rb_intern_const(str) #if defined(__FreeBSD__) && __FreeBSD__ < 4 /* allow divide by zero -- Inf */ fpsetmask(fpgetmask() & ~(FP_X_DZ|FP_X_INV|FP_X_OFL)); #elif defined(_UNICOSMP) /* Turn off floating point exceptions for divide by zero, etc. */ _set_Creg(0, 0); #elif defined(__BORLANDC__) /* Turn off floating point exceptions for overflow, etc. */ _control87(MCW_EM, MCW_EM); _control87(_control87(0,0),0x1FFF); #endif id_coerce = rb_intern("coerce"); id_div = rb_intern("div"); 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, "initialize_copy", num_init_copy, 1); rb_define_method(rb_cNumeric, "coerce", num_coerce, 1); rb_define_method(rb_cNumeric, "i", num_imaginary, 0); rb_define_method(rb_cNumeric, "+@", num_uplus, 0); rb_define_method(rb_cNumeric, "-@", num_uminus, 0); rb_define_method(rb_cNumeric, "<=>", num_cmp, 1); rb_define_method(rb_cNumeric, "eql?", num_eql, 1); rb_define_method(rb_cNumeric, "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, "floor", num_floor, 0); rb_define_method(rb_cNumeric, "ceil", num_ceil, 0); rb_define_method(rb_cNumeric, "round", num_round, -1); rb_define_method(rb_cNumeric, "truncate", num_truncate, 0); rb_define_method(rb_cNumeric, "step", num_step, -1); rb_cInteger = rb_define_class("Integer", rb_cNumeric); rb_undef_alloc_func(rb_cInteger); rb_undef_method(CLASS_OF(rb_cInteger), "new"); rb_define_method(rb_cInteger, "integer?", int_int_p, 0); rb_define_method(rb_cInteger, "odd?", int_odd_p, 0); rb_define_method(rb_cInteger, "even?", int_even_p, 0); rb_define_method(rb_cInteger, "upto", int_upto, 1); rb_define_method(rb_cInteger, "downto", int_downto, 1); rb_define_method(rb_cInteger, "times", int_dotimes, 0); rb_define_method(rb_cInteger, "succ", int_succ, 0); rb_define_method(rb_cInteger, "next", int_succ, 0); rb_define_method(rb_cInteger, "pred", int_pred, 0); rb_define_method(rb_cInteger, "chr", int_chr, -1); rb_define_method(rb_cInteger, "ord", int_ord, 0); rb_define_method(rb_cInteger, "to_i", int_to_i, 0); rb_define_method(rb_cInteger, "to_int", int_to_i, 0); rb_define_method(rb_cInteger, "floor", int_to_i, 0); rb_define_method(rb_cInteger, "ceil", int_to_i, 0); rb_define_method(rb_cInteger, "truncate", int_to_i, 0); rb_define_method(rb_cInteger, "round", int_round, -1); rb_cFixnum = rb_define_class("Fixnum", rb_cInteger); rb_define_method(rb_cFixnum, "to_s", fix_to_s, -1); rb_define_alias(rb_cFixnum, "inspect", "to_s"); rb_define_method(rb_cFixnum, "-@", fix_uminus, 0); rb_define_method(rb_cFixnum, "+", fix_plus, 1); rb_define_method(rb_cFixnum, "-", fix_minus, 1); rb_define_method(rb_cFixnum, "*", fix_mul, 1); rb_define_method(rb_cFixnum, "/", fix_div, 1); rb_define_method(rb_cFixnum, "div", fix_idiv, 1); rb_define_method(rb_cFixnum, "%", fix_mod, 1); rb_define_method(rb_cFixnum, "modulo", fix_mod, 1); rb_define_method(rb_cFixnum, "divmod", fix_divmod, 1); rb_define_method(rb_cFixnum, "fdiv", fix_fdiv, 1); rb_define_method(rb_cFixnum, "**", fix_pow, 1); rb_define_method(rb_cFixnum, "abs", fix_abs, 0); rb_define_method(rb_cFixnum, "magnitude", fix_abs, 0); rb_define_method(rb_cFixnum, "==", fix_equal, 1); rb_define_method(rb_cFixnum, "===", fix_equal, 1); rb_define_method(rb_cFixnum, "<=>", fix_cmp, 1); rb_define_method(rb_cFixnum, ">", fix_gt, 1); rb_define_method(rb_cFixnum, ">=", fix_ge, 1); rb_define_method(rb_cFixnum, "<", fix_lt, 1); rb_define_method(rb_cFixnum, "<=", fix_le, 1); rb_define_method(rb_cFixnum, "~", fix_rev, 0); rb_define_method(rb_cFixnum, "&", fix_and, 1); rb_define_method(rb_cFixnum, "|", fix_or, 1); rb_define_method(rb_cFixnum, "^", fix_xor, 1); rb_define_method(rb_cFixnum, "[]", fix_aref, 1); rb_define_method(rb_cFixnum, "<<", rb_fix_lshift, 1); rb_define_method(rb_cFixnum, ">>", rb_fix_rshift, 1); rb_define_method(rb_cFixnum, "to_f", fix_to_f, 0); rb_define_method(rb_cFixnum, "size", fix_size, 0); rb_define_method(rb_cFixnum, "bit_length", rb_fix_bit_length, 0); rb_define_method(rb_cFixnum, "zero?", fix_zero_p, 0); rb_define_method(rb_cFixnum, "odd?", fix_odd_p, 0); rb_define_method(rb_cFixnum, "even?", fix_even_p, 0); rb_define_method(rb_cFixnum, "succ", fix_succ, 0); rb_cFloat = rb_define_class("Float", rb_cNumeric); rb_undef_alloc_func(rb_cFloat); rb_undef_method(CLASS_OF(rb_cFloat), "new"); /* * Represents the rounding mode for floating point addition. * * Usually defaults to 1, rounding to the nearest number. * * Other modes include: * * -1:: Indeterminable * 0:: Rounding towards zero * 1:: Rounding to the nearest number * 2:: Rounding towards positive infinity * 3:: Rounding towards negative infinity */ rb_define_const(rb_cFloat, "ROUNDS", INT2FIX(FLT_ROUNDS)); /* * The base of the floating point, or number of unique digits used to * represent the number. * * 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 posable 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 integer in a double-precision floating point. * * Usually defaults to 2.2250738585072014e-308. */ 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. * * Usually defaults to 2.2204460492503131e-16. */ rb_define_const(rb_cFloat, "EPSILON", DBL2NUM(DBL_EPSILON)); /* * An expression representing positive infinity. */ rb_define_const(rb_cFloat, "INFINITY", DBL2NUM(INFINITY)); /* * An expression representing a value which is "not a number". */ rb_define_const(rb_cFloat, "NAN", DBL2NUM(NAN)); rb_define_method(rb_cFloat, "to_s", flo_to_s, 0); rb_define_alias(rb_cFloat, "inspect", "to_s"); rb_define_method(rb_cFloat, "coerce", flo_coerce, 1); rb_define_method(rb_cFloat, "-@", flo_uminus, 0); rb_define_method(rb_cFloat, "+", flo_plus, 1); rb_define_method(rb_cFloat, "-", flo_minus, 1); rb_define_method(rb_cFloat, "*", flo_mul, 1); rb_define_method(rb_cFloat, "/", flo_div, 1); rb_define_method(rb_cFloat, "quo", flo_quo, 1); rb_define_method(rb_cFloat, "fdiv", flo_quo, 1); rb_define_method(rb_cFloat, "%", flo_mod, 1); rb_define_method(rb_cFloat, "modulo", flo_mod, 1); rb_define_method(rb_cFloat, "divmod", flo_divmod, 1); rb_define_method(rb_cFloat, "**", flo_pow, 1); rb_define_method(rb_cFloat, "==", flo_eq, 1); rb_define_method(rb_cFloat, "===", flo_eq, 1); rb_define_method(rb_cFloat, "<=>", flo_cmp, 1); rb_define_method(rb_cFloat, ">", flo_gt, 1); rb_define_method(rb_cFloat, ">=", flo_ge, 1); rb_define_method(rb_cFloat, "<", flo_lt, 1); rb_define_method(rb_cFloat, "<=", flo_le, 1); rb_define_method(rb_cFloat, "eql?", flo_eql, 1); rb_define_method(rb_cFloat, "hash", flo_hash, 0); rb_define_method(rb_cFloat, "to_f", flo_to_f, 0); rb_define_method(rb_cFloat, "abs", flo_abs, 0); rb_define_method(rb_cFloat, "magnitude", flo_abs, 0); rb_define_method(rb_cFloat, "zero?", flo_zero_p, 0); rb_define_method(rb_cFloat, "to_i", flo_truncate, 0); rb_define_method(rb_cFloat, "to_int", flo_truncate, 0); rb_define_method(rb_cFloat, "floor", flo_floor, 0); rb_define_method(rb_cFloat, "ceil", flo_ceil, 0); rb_define_method(rb_cFloat, "round", flo_round, -1); rb_define_method(rb_cFloat, "truncate", flo_truncate, 0); rb_define_method(rb_cFloat, "nan?", flo_is_nan_p, 0); rb_define_method(rb_cFloat, "infinite?", flo_is_infinite_p, 0); rb_define_method(rb_cFloat, "finite?", flo_is_finite_p, 0); rb_define_method(rb_cFloat, "next_float", flo_next_float, 0); rb_define_method(rb_cFloat, "prev_float", flo_prev_float, 0); sym_to = ID2SYM(rb_intern("to")); sym_by = ID2SYM(rb_intern("by")); } #undef rb_float_value double rb_float_value(VALUE v) { return rb_float_value_inline(v); } #undef rb_float_new VALUE rb_float_new(double d) { return rb_float_new_inline(d); }