# Class: Float

Inherits:
Numeric
show all
Defined in:
numeric.c,
numeric.c

## Overview

******************************************************************

``````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
``````

## Constant Summary

ROUNDS =

-1:: Indeterminable 0:: Rounding towards zero 1:: Rounding to the nearest number 2:: Rounding towards positive infinity 3:: Rounding towards negative infinity

```Represents the rounding mode for floating point addition.

Usually defaults to 1, rounding to the nearest number.

Other modes include```

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.``
`INT2FIX(FLT_RADIX)`
MANT_DIG =

The number of base digits for the double data type.

Usually defaults to 53.

`INT2FIX(DBL_MANT_DIG)`
DIG =

The number of decimal digits in a double-precision floating point.

Usually defaults to 15.

`INT2FIX(DBL_DIG)`
MIN_EXP =

The smallest posable exponent value in a double-precision floating point.

Usually defaults to -1021.

`INT2FIX(DBL_MIN_EXP)`
MAX_EXP =

The largest possible exponent value in a double-precision floating point.

Usually defaults to 1024.

`INT2FIX(DBL_MAX_EXP)`
MIN_10_EXP =

The smallest negative exponent in a double-precision floating point where 10 raised to this power minus 1.

Usually defaults to -307.

`INT2FIX(DBL_MIN_10_EXP)`
MAX_10_EXP =

The largest positive exponent in a double-precision floating point where 10 raised to this power minus 1.

Usually defaults to 308.

`INT2FIX(DBL_MAX_10_EXP)`
MIN =

The smallest positive integer in a double-precision floating point.

Usually defaults to 2.2250738585072014e-308.

`DBL2NUM(DBL_MIN)`
MAX =

The largest possible integer in a double-precision floating point number.

Usually defaults to 1.7976931348623157e+308.

`DBL2NUM(DBL_MAX)`
EPSILON =

The difference between 1 and the smallest double-precision floating point number.

Usually defaults to 2.2204460492503131e-16.

`DBL2NUM(DBL_EPSILON)`
INFINITY =

An expression representing positive infinity.

`DBL2NUM(INFINITY)`
NAN =

An expression representing a value which is “not a number”.

`DBL2NUM(NAN)`

## Instance Method Summary (collapse)

• Return the modulo after division of float by other.

• Returns a new float which is the product of float and other.

• Raises float to the power of other.

• Returns a new float which is the sum of float and other.

• Returns a new float which is the difference of float and other.

• Returns float, negated.

• Returns a new float which is the result of dividing float by other.

• Returns true if float is less than real.

• Returns true if float is less than or equal to real.

• Returns -1, 0, +1 or nil depending on whether float is less than, equal to, or greater than real.

• Returns true only if obj has the same value as float.

• Returns true only if obj has the same value as float.

• Returns true if float is greater than real.

• Returns true if float is greater than or equal to real.

• Returns the absolute value of float.

• Returns 0 if the value is positive, pi otherwise.

• Returns 0 if the value is positive, pi otherwise.

• Returns the smallest Integer greater than or equal to float.

• Returns an array with both a numeric and a float represented as Float objects.

• Returns the denominator (always positive).

• See Numeric#divmod.

• Returns true only if obj is a Float with the same value as float.

• Returns float / numeric, same as Float#/.

• Returns true if float is a valid IEEE floating point number (it is not infinite, and Float#nan? is false).

• Returns the largest integer less than or equal to float.

• Returns a hash code for this float.

• Return values corresponding to the value of float:.

• Returns the absolute value of float.

• Return the modulo after division of float by other.

• Returns true if float is an invalid IEEE floating point number.

• Returns the numerator.

• Returns 0 if the value is positive, pi otherwise.

• Returns float / numeric, same as Float#/.

• Returns a simpler approximation of the value (flt-|eps| (3/10) 1.333.rationalize #=> (1333/1000) 1.333.rationalize(0.01) #=> (4/3)

``See to_r..``
• Rounds float to a given precision in decimal digits (default 0 digits).

• Since float is already a float, returns self.

• Returns the float truncated to an Integer.

• Returns the float truncated to an Integer.

• Returns the value as a rational.

• - (String) to_s (also: #inspect)

Returns a string containing a representation of self.

• Returns the float truncated to an Integer.

• Returns true if float is 0.0.

#between?

## Instance Method Details

### - (Float) %(other) - (Float) modulo(other)

Return the modulo after division of float by other.

``````6543.21.modulo(137)      #=> 104.21
6543.21.modulo(137.24)   #=> 92.9299999999996``````
 ``` 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938``` ```# File 'numeric.c', line 920 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)); }```

### - (Float) *(other)

Returns a new float which is the product of float and other.

 ``` 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820``` ```# File 'numeric.c', line 805 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, '*'); } }```

### - (Float) **(other)

Raises float to the power of other.

``2.0**3      #=> 8.0``
 ``` 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015``` ```# File 'numeric.c', line 994 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("**")); } }```

### - (Float) +(other)

Returns a new float which is the sum of float and other.

 ``` 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772``` ```# File 'numeric.c', line 757 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, '+'); } }```

### - (Float) -(other)

Returns a new float which is the difference of float and other.

 ``` 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796``` ```# File 'numeric.c', line 781 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, '-'); } }```

### - (Float) -

Returns float, negated.

 ``` 744 745 746 747 748``` ```# File 'numeric.c', line 744 static VALUE flo_uminus(VALUE flt) { return DBL2NUM(-RFLOAT_VALUE(flt)); }```

### - (Float) /(other)

Returns a new float which is the result of dividing float by other.

 ``` 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849``` ```# File 'numeric.c', line 829 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, '/'); } }```

### - (Boolean) <(real)

Returns true if float is less than real.

The result of NaN < NaN is undefined, so the implementation-dependent value is returned.

 ``` 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281``` ```# File 'numeric.c', line 1256 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; }```

### - (Boolean) <=(real)

Returns true if float is less than or equal to real.

The result of NaN <= NaN is undefined, so the implementation-dependent value is returned.

 ``` 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318``` ```# File 'numeric.c', line 1293 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; }```

### - (-1, ...) <=>(real)

Returns -1, 0, +1 or nil depending on whether float is less than, equal to, or greater than real. This is the basis for the tests in Comparable.

The result of NaN <=> NaN is undefined, so the implementation-dependent value is returned.

nil is returned if the two values are incomparable.

 ``` 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170``` ```# File 'numeric.c', line 1140 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, rb_intern("<=>")); } return rb_dbl_cmp(a, b); }```

### - (Boolean) ==(obj)

Returns true only if obj has the same value as float. Contrast this with Float#eql?, which requires obj to be a Float.

The result of NaN == NaN is undefined, so the implementation-dependent value is returned.

``1.0 == 1   #=> true``
 ``` 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095``` ```# File 'numeric.c', line 1073 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; }```

### - (Boolean) ==(obj)

Returns true only if obj has the same value as float. Contrast this with Float#eql?, which requires obj to be a Float.

The result of NaN == NaN is undefined, so the implementation-dependent value is returned.

``1.0 == 1   #=> true``
 ``` 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095``` ```# File 'numeric.c', line 1073 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; }```

### - (Boolean) >(real)

Returns true if float is greater than real.

The result of NaN > NaN is undefined, so the implementation-dependent value is returned.

 ``` 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207``` ```# File 'numeric.c', line 1182 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; }```

### - (Boolean) >=(real)

Returns true if float is greater than or equal to real.

The result of NaN >= NaN is undefined, so the implementation-dependent value is returned.

 ``` 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244``` ```# File 'numeric.c', line 1219 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; }```

### - (Float) abs - (Float) magnitude

Returns the absolute value of float.

``````(-34.56).abs   #=> 34.56
-34.56.abs     #=> 34.56``````
 ``` 1373 1374 1375 1376 1377 1378``` ```# File 'numeric.c', line 1373 static VALUE flo_abs(VALUE flt) { double val = fabs(RFLOAT_VALUE(flt)); return DBL2NUM(val); }```

### - (0, Float) arg - (0, Float) angle - (0, Float) phase

Returns 0 if the value is positive, pi otherwise.

 ``` 2042 2043 2044 2045 2046 2047 2048 2049 2050``` ```# File 'complex.c', line 2042 static VALUE float_arg(VALUE self) { if (isnan(RFLOAT_VALUE(self))) return self; if (f_tpositive_p(self)) return INT2FIX(0); return rb_const_get(rb_mMath, id_PI); }```

### - (0, Float) arg - (0, Float) angle - (0, Float) phase

Returns 0 if the value is positive, pi otherwise.

 ``` 2042 2043 2044 2045 2046 2047 2048 2049 2050``` ```# File 'complex.c', line 2042 static VALUE float_arg(VALUE self) { if (isnan(RFLOAT_VALUE(self))) return self; if (f_tpositive_p(self)) return INT2FIX(0); return rb_const_get(rb_mMath, id_PI); }```

### - (Integer) ceil

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``````
 ``` 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519``` ```# File 'numeric.c', line 1508 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); }```

### - (Array) coerce(numeric)

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]``````
 ``` 731 732 733 734 735``` ```# File 'numeric.c', line 731 static VALUE flo_coerce(VALUE x, VALUE y) { return rb_assoc_new(rb_Float(y), x); }```

### - (Integer) denominator

Returns the denominator (always positive). The result is machine dependent.

See numerator.

 ``` 1923 1924 1925 1926 1927 1928 1929 1930``` ```# File 'rational.c', line 1923 static VALUE float_denominator(VALUE self) { double d = RFLOAT_VALUE(self); if (isinf(d) || isnan(d)) return INT2FIX(1); return rb_call_super(0, 0); }```

### - (Array) divmod(numeric)

See Numeric#divmod.

``````42.0.divmod 6 #=> [7, 0.0]
42.0.divmod 5 #=> [8, 2.0]``````
 ``` 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982``` ```# File 'numeric.c', line 960 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); }```

### - (Boolean) eql?(obj)

Returns true only if obj is a Float with the same value as float. Contrast this with Float#==, which performs type conversions.

The result of NaN.eql?(NaN) is undefined, so the implementation-dependent value is returned.

``1.0.eql?(1)   #=> false``
 ``` 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346``` ```# File 'numeric.c', line 1333 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; }```

### - (Float) fdiv(numeric) - (Float) quo(numeric)

Returns float / numeric, same as Float#/.

 ``` 859 860 861 862 863``` ```# File 'numeric.c', line 859 static VALUE flo_quo(VALUE x, VALUE y) { return rb_funcall(x, '/', 1, y); }```

### - (Boolean) finite?

Returns true if float is a valid IEEE floating point number (it is not infinite, and Float#nan? is false).

 ``` 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469``` ```# File 'numeric.c', line 1455 static VALUE flo_is_finite_p(VALUE num) { double value = RFLOAT_VALUE(num); #if HAVE_FINITE if (!finite(value)) return Qfalse; #else if (isinf(value) || isnan(value)) return Qfalse; #endif return Qtrue; }```

### - (Integer) floor

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``````
 ``` 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494``` ```# File 'numeric.c', line 1483 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); }```

### - (Integer) hash

Returns a hash code for this float.

 ``` 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115``` ```# File 'numeric.c', line 1104 static VALUE flo_hash(VALUE num) { double d; st_index_t hash; d = RFLOAT_VALUE(num); /* normalize -0.0 to 0.0 */ if (d == 0.0) d = 0.0; hash = rb_memhash(&d, sizeof(d)); return LONG2FIX(hash); }```

### - (nil, ...) infinite?

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``````
 ``` 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444``` ```# File 'numeric.c', line 1434 static VALUE flo_is_infinite_p(VALUE num) { double value = RFLOAT_VALUE(num); if (isinf(value)) { return INT2FIX( value < 0 ? -1 : 1 ); } return Qnil; }```

### - (Float) abs - (Float) magnitude

Returns the absolute value of float.

``````(-34.56).abs   #=> 34.56
-34.56.abs     #=> 34.56``````
 ``` 1373 1374 1375 1376 1377 1378``` ```# File 'numeric.c', line 1373 static VALUE flo_abs(VALUE flt) { double val = fabs(RFLOAT_VALUE(flt)); return DBL2NUM(val); }```

### - (Float) %(other) - (Float) modulo(other)

Return the modulo after division of float by other.

``````6543.21.modulo(137)      #=> 104.21
6543.21.modulo(137.24)   #=> 92.9299999999996``````
 ``` 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938``` ```# File 'numeric.c', line 920 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)); }```

### - (Boolean) nan?

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``````
 ``` 1409 1410 1411 1412 1413 1414 1415``` ```# File 'numeric.c', line 1409 static VALUE flo_is_nan_p(VALUE num) { double value = RFLOAT_VALUE(num); return isnan(value) ? Qtrue : Qfalse; }```

### - (Integer) numerator

Returns the numerator. The result is machine dependent.

``````n = 0.3.numerator    #=> 5404319552844595
d = 0.3.denominator  #=> 18014398509481984
n.fdiv(d)            #=> 0.3``````
 ``` 1905 1906 1907 1908 1909 1910 1911 1912``` ```# File 'rational.c', line 1905 static VALUE float_numerator(VALUE self) { double d = RFLOAT_VALUE(self); if (isinf(d) || isnan(d)) return self; return rb_call_super(0, 0); }```

### - (0, Float) arg - (0, Float) angle - (0, Float) phase

Returns 0 if the value is positive, pi otherwise.

 ``` 2042 2043 2044 2045 2046 2047 2048 2049 2050``` ```# File 'complex.c', line 2042 static VALUE float_arg(VALUE self) { if (isnan(RFLOAT_VALUE(self))) return self; if (f_tpositive_p(self)) return INT2FIX(0); return rb_const_get(rb_mMath, id_PI); }```

### - (Float) fdiv(numeric) - (Float) quo(numeric)

Returns float / numeric, same as Float#/.

 ``` 859 860 861 862 863``` ```# File 'numeric.c', line 859 static VALUE flo_quo(VALUE x, VALUE y) { return rb_funcall(x, '/', 1, y); }```

### - (Object) rationalize([eps])

Returns a simpler approximation of the value (flt-|eps| <= result <= flt+|eps|). if the optional eps is not given, it will be chosen automatically.

``````0.3.rationalize          #=> (3/10)
1.333.rationalize        #=> (1333/1000)
1.333.rationalize(0.01)  #=> (4/3)``````

See to_r.

 ``` 2120 2121 2122 2123 2124 2125 2126 2127 2128 2129 2130 2131 2132 2133 2134 2135 2136``` ```# File 'rational.c', line 2120 static VALUE float_rationalize(int argc, VALUE *argv, VALUE self) { VALUE e; if (f_negative_p(self)) return f_negate(float_rationalize(argc, argv, f_abs(self))); rb_scan_args(argc, argv, "01", &e); if (argc != 0) { return rb_flt_rationalize_with_prec(self, e); } else { return rb_flt_rationalize(self); } }```

### - (Integer, Float) round([ndigits])

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``````
 ``` 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641``` ```# File 'numeric.c', line 1594 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); }```

### - (self) to_f

Since float is already a float, returns self.

 ``` 1355 1356 1357 1358 1359``` ```# File 'numeric.c', line 1355 static VALUE flo_to_f(VALUE num) { return num; }```

### - (Integer) to_i - (Integer) to_int - (Integer) truncate

Returns the float truncated to an Integer.

Synonyms are #to_i, #to_int, and #truncate.

 ``` 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668``` ```# File 'numeric.c', line 1654 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); }```

### - (Integer) to_i - (Integer) to_int - (Integer) truncate

Returns the float truncated to an Integer.

Synonyms are #to_i, #to_int, and #truncate.

 ``` 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668``` ```# File 'numeric.c', line 1654 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); }```

### - (Object) to_r

Returns the value as a rational.

NOTE: 0.3.to_r isn't the same as '0.3'.to_r. The latter is equivalent to '3/10'.to_r, but the former isn't so.

``````2.0.to_r    #=> (2/1)
2.5.to_r    #=> (5/2)
-0.75.to_r  #=> (-3/4)
0.0.to_r    #=> (0/1)``````

See rationalize.

 ``` 2030 2031 2032 2033 2034 2035 2036 2037 2038 2039 2040 2041 2042 2043 2044 2045 2046 2047 2048 2049 2050``` ```# File 'rational.c', line 2030 static VALUE float_to_r(VALUE self) { VALUE f, n; float_decode_internal(self, &f, &n); #if FLT_RADIX == 2 { long ln = FIX2LONG(n); if (ln == 0) return f_to_r(f); if (ln > 0) return f_to_r(f_lshift(f, n)); ln = -ln; return rb_rational_new2(f, f_lshift(ONE, INT2FIX(ln))); } #else return f_to_r(f_mul(f, f_expt(INT2FIX(FLT_RADIX), n))); #endif }```

### - (String) to_sAlso known as: inspect

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.

 ``` 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716``` ```# File 'numeric.c', line 649 static VALUE flo_to_s(VALUE flt) { char *ruby_dtoa(double d_, int mode, int ndigits, int *decpt, int *sign, char **rve); enum {decimal_mant = DBL_MANT_DIG-DBL_DIG}; enum {float_dig = DBL_DIG+1}; char buf[float_dig + (decimal_mant + CHAR_BIT - 1) / CHAR_BIT + 10]; double value = RFLOAT_VALUE(flt); VALUE s; char *p, *e; int sign, decpt, digs; if (isinf(value)) return rb_usascii_str_new2(value < 0 ? "-Infinity" : "Infinity"); else if (isnan(value)) return rb_usascii_str_new2("NaN"); p = ruby_dtoa(value, 0, 0, &decpt, &sign, &e); s = sign ? rb_usascii_str_new_cstr("-") : rb_usascii_str_new(0, 0); if ((digs = (int)(e - p)) >= (int)sizeof(buf)) digs = (int)sizeof(buf) - 1; memcpy(buf, p, digs); xfree(p); if (decpt > 0) { if (decpt < digs) { memmove(buf + decpt + 1, buf + decpt, digs - decpt); buf[decpt] = '.'; rb_str_cat(s, buf, digs + 1); } else if (decpt <= DBL_DIG) { long len; char *ptr; rb_str_cat(s, buf, digs); rb_str_resize(s, (len = RSTRING_LEN(s)) + decpt - digs + 2); ptr = RSTRING_PTR(s) + len; if (decpt > digs) { memset(ptr, '0', decpt - digs); ptr += decpt - digs; } memcpy(ptr, ".0", 2); } else { goto exp; } } else if (decpt > -4) { long len; char *ptr; rb_str_cat(s, "0.", 2); rb_str_resize(s, (len = RSTRING_LEN(s)) - decpt + digs); ptr = RSTRING_PTR(s); memset(ptr += len, '0', -decpt); memcpy(ptr -= decpt, buf, digs); } else { exp: if (digs > 1) { memmove(buf + 2, buf + 1, digs - 1); } else { buf[2] = '0'; digs++; } buf[1] = '.'; rb_str_cat(s, buf, digs + 1); rb_str_catf(s, "e%+03d", decpt - 1); } return s; }```

### - (Integer) to_i - (Integer) to_int - (Integer) truncate

Returns the float truncated to an Integer.

Synonyms are #to_i, #to_int, and #truncate.

 ``` 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668``` ```# File 'numeric.c', line 1654 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); }```

### - (Boolean) zero?

Returns true if float is 0.0.

 ``` 1388 1389 1390 1391 1392 1393 1394 1395``` ```# File 'numeric.c', line 1388 static VALUE flo_zero_p(VALUE num) { if (RFLOAT_VALUE(num) == 0.0) { return Qtrue; } return Qfalse; }```