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Diffstat (limited to 'jni/ruby/numeric.c')
| -rw-r--r-- | jni/ruby/numeric.c | 4271 |
1 files changed, 4271 insertions, 0 deletions
diff --git a/jni/ruby/numeric.c b/jni/ruby/numeric.c new file mode 100644 index 0000000..bf03f3e --- /dev/null +++ b/jni/ruby/numeric.c @@ -0,0 +1,4271 @@ +/********************************************************************** + + numeric.c - + + $Author: nagachika $ + created at: Fri Aug 13 18:33:09 JST 1993 + + Copyright (C) 1993-2007 Yukihiro Matsumoto + +**********************************************************************/ + +#include "internal.h" +#include "ruby/util.h" +#include "id.h" +#include <ctype.h> +#include <math.h> +#include <stdio.h> + +#if defined(__FreeBSD__) && __FreeBSD__ < 4 +#include <floatingpoint.h> +#endif + +#ifdef HAVE_FLOAT_H +#include <float.h> +#endif + +#ifdef HAVE_IEEEFP_H +#include <ieeefp.h> +#endif + +#if !defined HAVE_ISFINITE && !defined isfinite +#if defined HAVE_FINITE && !defined finite && !defined _WIN32 +extern int finite(double); +# define HAVE_ISFINITE 1 +# define isfinite(x) finite(x) +#endif +#endif + +/* 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 ID id_to, id_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) +{ + if (SPECIAL_CONST_P(y) || BUILTIN_TYPE(y) == T_FLOAT) { + y = rb_inspect(y); + } + else { + y = rb_obj_class(y); + } + rb_raise(rb_eTypeError, "%"PRIsVALUE" can't be coerced into %"PRIsVALUE, + y, rb_obj_class(x)); +} + +static VALUE +coerce_rescue(VALUE *x) +{ + coerce_failed(x[0], x[1]); + return Qnil; /* dummy */ +} + +static VALUE +coerce_rescue_quiet(VALUE *x) +{ + return Qundef; +} + +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 : coerce_rescue_quiet, (VALUE)a); + if (ary == Qundef) { + rb_warn("Numerical comparison operators will no more rescue exceptions of #coerce"); + rb_warn("in the next release. Return nil in #coerce if the coercion is impossible."); + return FALSE; + } + if (!RB_TYPE_P(ary, T_ARRAY) || RARRAY_LEN(ary) != 2) { + if (err) { + rb_raise(rb_eTypeError, "coerce must return [x, y]"); + } else if (!NIL_P(ary)) { + rb_warn("Bad return value for #coerce, called by numerical comparison operators."); + rb_warn("#coerce must return [x, y]. The next release will raise an error for this."); + } + 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 <code>num.divmod(numeric)[0]</code>. + * + * 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 <code>num.divmod(numeric)[1]</code>. + * + * 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 <code>q, r = * x.divmod(y)</code>, then + * + * q = floor(x/y) + * x = q*y+r + * + * The quotient is rounded toward -infinity, as shown in the following table: + * + * 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) +{ + 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 <code>float / numeric</code>, 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 (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 (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 <code>NaN == NaN</code> 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) +{ + return rb_dbl_hash(RFLOAT_VALUE(num)); +} + +VALUE +rb_dbl_hash(double d) +{ + st_index_t hash; + + /* 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 <code>NaN <=> NaN</code> 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 <code>NaN > NaN</code> 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 <code>NaN >= NaN</code> 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 <code>NaN < NaN</code> 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 <code>NaN <= NaN</code> 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 <code>NaN.eql?(NaN)</code> 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); + +#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: + * + * 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<n; i++) { + double d = i*unit+beg; + if (unit >= 0 ? end < d : d < end) d = end; + rb_yield(DBL2NUM(d)); + } + } + return TRUE; + } + return FALSE; +} + +VALUE +ruby_num_interval_step_size(VALUE from, VALUE to, VALUE step, int excl) +{ + if (FIXNUM_P(from) && FIXNUM_P(to) && FIXNUM_P(step)) { + long 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] = id_to; + keys[1] = id_by; + rb_get_kwargs(hash, keys, 0, 2, values); + if (values[0] != Qundef) { + if (argc > 0) rb_raise(rb_eArgError, "to is given twice"); + *to = values[0]; + } + if (values[1] != Qundef) { + if (argc > 1) rb_raise(rb_eArgError, "step is given twice"); + *step = values[1]; + } + } + else { + /* 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 <i>limit</i> 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 <code>+</code> operator. + * + * If no block is given, an Enumerator is returned instead. + * + * For example: + * + * p 1.step.take(4) + * p 10.step(by: -1).take(4) + * 3.step(to: 5) { |i| print i, " " } + * 1.step(10, 2) { |i| print i, " " } + * Math::E.step(to: Math::PI, by: 0.2) { |f| print f, " " } + * + * Will produce: + * + * [1, 2, 3, 4] + * [10, 9, 8, 7] + * 3 4 5 + * 1 3 5 7 9 + * 2.71828182845905 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) +{ + 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)&&((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) +{ + if (!FIXNUM_P(*y) && !RB_TYPE_P(*y, T_BIGNUM)) { + VALUE orig = *x; + do_coerce(x, y, TRUE); + if (!FIXNUM_P(*x) && !RB_TYPE_P(*x, T_BIGNUM) + && !FIXNUM_P(*y) && !RB_TYPE_P(*y, T_BIGNUM)) { + coerce_failed(orig, *y); + } + } + return TRUE; +} + +VALUE +rb_num_coerce_bit(VALUE x, VALUE y, ID func) +{ + bit_coerce(&x, &y); + 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); + 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); + 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); + 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 <code>fix[0]</code> 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<<i)) + return INT2FIX(1); + return INT2FIX(0); +} + +/* + * call-seq: + * fix.to_f -> 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 <i>int</i>. + * + * "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 + * <code>int - 1</code>. + * + * 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<end; i++) { + rb_yield(LONG2FIX(i)); + } + } + else { + VALUE i = INT2FIX(0); + + for (;;) { + if (!RTEST(rb_funcall(i, '<', 1, num))) break; + rb_yield(i); + i = rb_funcall(i, '+', 1, INT2FIX(1)); + } + } + return num; +} + +/* + * call-seq: + * int.round([ndigits]) -> 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 normalized number in a double-precision floating point. + * + * Usually defaults to 2.2250738585072014e-308. + * + * If the platform supports denormalized numbers, + * there are numbers between zero and Float::MIN. + * 0.0.next_float returns the smallest positive floating point number + * including denormalized numbers. + */ + rb_define_const(rb_cFloat, "MIN", DBL2NUM(DBL_MIN)); + /* + * The largest possible integer in a double-precision floating point number. + * + * Usually defaults to 1.7976931348623157e+308. + */ + rb_define_const(rb_cFloat, "MAX", DBL2NUM(DBL_MAX)); + /* + * The difference between 1 and the smallest double-precision floating + * point number greater than 1. + * + * Usually defaults to 2.2204460492503131e-16. + */ + rb_define_const(rb_cFloat, "EPSILON", DBL2NUM(DBL_EPSILON)); + /* + * An expression representing positive infinity. + */ + rb_define_const(rb_cFloat, "INFINITY", DBL2NUM(INFINITY)); + /* + * An expression representing a value which is "not a number". + */ + rb_define_const(rb_cFloat, "NAN", DBL2NUM(NAN)); + + rb_define_method(rb_cFloat, "to_s", flo_to_s, 0); + rb_define_alias(rb_cFloat, "inspect", "to_s"); + rb_define_method(rb_cFloat, "coerce", flo_coerce, 1); + rb_define_method(rb_cFloat, "-@", flo_uminus, 0); + rb_define_method(rb_cFloat, "+", 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); + + id_to = rb_intern("to"); + id_by = rb_intern("by"); +} + +#undef rb_float_value +double +rb_float_value(VALUE v) +{ + return rb_float_value_inline(v); +} + +#undef rb_float_new +VALUE +rb_float_new(double d) +{ + return rb_float_new_inline(d); +} |