# 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
- http://en.wikipedia.org/wiki/Floating_point#Accuracy_problems
``````

## 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 minimum number of significant 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 next representable floating-point number.

• Returns the numerator.

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

• Returns the previous representable floatint-point number.

• 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).

• 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.

• #to_s ⇒ String (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

### #%(other) ⇒ 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
``````

 ``` 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969``` ```# File 'numeric.c', line 951 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)); } ```

### #*(other) ⇒ Float

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

Returns:

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

### #**(other) ⇒ Float

Raises float to the power of other.

``````2.0**3      #=> 8.0
``````

Returns:

 ``` 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046``` ```# File 'numeric.c', line 1025 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("**")); } } ```

### #+(other) ⇒ Float

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

Returns:

 ``` 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797``` ```# File 'numeric.c', line 782 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, '+'); } } ```

### #-(other) ⇒ Float

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

Returns:

 ``` 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821``` ```# File 'numeric.c', line 806 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.

Returns:

 ``` 769 770 771 772 773``` ```# File 'numeric.c', line 769 static VALUE flo_uminus(VALUE flt) { return DBL2NUM(-RFLOAT_VALUE(flt)); } ```

### #/(other) ⇒ Float

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

Returns:

 ``` 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874``` ```# File 'numeric.c', line 854 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, '/'); } } ```

### #<(real) ⇒ Boolean

Returns true if float is less than real.

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

Returns:

• (Boolean)
 ``` 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314``` ```# File 'numeric.c', line 1289 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; } ```

### #<=(real) ⇒ Boolean

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.

Returns:

• (Boolean)
 ``` 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351``` ```# File 'numeric.c', line 1326 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; } ```

### #<=>(real) ⇒ -1, ...

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.

Returns:

• (-1, 0, +1, nil)
 ``` 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203``` ```# File 'numeric.c', line 1173 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); } ```

### #==(obj) ⇒ Boolean

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
``````

Returns:

• (Boolean)
 ``` 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126``` ```# File 'numeric.c', line 1104 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; } ```

### #==(obj) ⇒ Boolean

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
``````

Returns:

• (Boolean)
 ``` 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126``` ```# File 'numeric.c', line 1104 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; } ```

### #>(real) ⇒ Boolean

Returns true if float is greater than real.

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

Returns:

• (Boolean)
 ``` 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240``` ```# File 'numeric.c', line 1215 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; } ```

### #>=(real) ⇒ Boolean

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.

Returns:

• (Boolean)
 ``` 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277``` ```# File 'numeric.c', line 1252 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; } ```

### #abs ⇒ Float #magnitude ⇒ Float

Returns the absolute value of float.

``````(-34.56).abs   #=> 34.56
-34.56.abs     #=> 34.56
``````

 ``` 1406 1407 1408 1409 1410 1411``` ```# File 'numeric.c', line 1406 static VALUE flo_abs(VALUE flt) { double val = fabs(RFLOAT_VALUE(flt)); return DBL2NUM(val); } ```

### #arg ⇒ 0, Float #angle ⇒ 0, Float #phase ⇒ 0, Float

Returns 0 if the value is positive, pi otherwise.

 ``` 2011 2012 2013 2014 2015 2016 2017 2018 2019``` ```# File 'complex.c', line 2011 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); } ```

### #arg ⇒ 0, Float #angle ⇒ 0, Float #phase ⇒ 0, Float

Returns 0 if the value is positive, pi otherwise.

 ``` 2011 2012 2013 2014 2015 2016 2017 2018 2019``` ```# File 'complex.c', line 2011 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); } ```

### #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
``````

Returns:

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

### #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]
``````

Returns:

 ``` 756 757 758 759 760``` ```# File 'numeric.c', line 756 static VALUE flo_coerce(VALUE x, VALUE y) { return rb_assoc_new(rb_Float(y), x); } ```

### #denominator ⇒ Integer

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

See numerator.

Returns:

 ``` 1906 1907 1908 1909 1910 1911 1912 1913``` ```# File 'rational.c', line 1906 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); } ```

### #divmod(numeric) ⇒ Array

See Numeric#divmod.

``````42.0.divmod 6 #=> [7, 0.0]
42.0.divmod 5 #=> [8, 2.0]
``````

Returns:

 ``` 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013``` ```# File 'numeric.c', line 991 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); } ```

### #eql?(obj) ⇒ Boolean

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
``````

Returns:

• (Boolean)

Returns:

• (Boolean)
 ``` 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379``` ```# File 'numeric.c', line 1366 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; } ```

### #fdiv(numeric) ⇒ Float #quo(numeric) ⇒ Float

Returns float / numeric, same as Float#/.

 ``` 884 885 886 887 888``` ```# File 'numeric.c', line 884 static VALUE flo_quo(VALUE x, VALUE y) { return rb_funcall(x, '/', 1, y); } ```

### #finite? ⇒ Boolean

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

Returns:

• (Boolean)

Returns:

• (Boolean)
 ``` 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502``` ```# File 'numeric.c', line 1488 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; } ```

### #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
``````

Returns:

 ``` 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640``` ```# File 'numeric.c', line 1629 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); } ```

### #hash ⇒ Integer

Returns a hash code for this float.

Returns:

 ``` 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148``` ```# File 'numeric.c', line 1137 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); } ```

### #infinite? ⇒ nil, ...

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
``````

Returns:

• (nil, -1, +1)

Returns:

• (Boolean)
 ``` 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477``` ```# File 'numeric.c', line 1467 static VALUE flo_is_infinite_p(VALUE num) { double value = RFLOAT_VALUE(num); if (isinf(value)) { return INT2FIX( value < 0 ? -1 : 1 ); } return Qnil; } ```

### #abs ⇒ Float #magnitude ⇒ Float

Returns the absolute value of float.

``````(-34.56).abs   #=> 34.56
-34.56.abs     #=> 34.56
``````

 ``` 1406 1407 1408 1409 1410 1411``` ```# File 'numeric.c', line 1406 static VALUE flo_abs(VALUE flt) { double val = fabs(RFLOAT_VALUE(flt)); return DBL2NUM(val); } ```

### #%(other) ⇒ 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
``````

 ``` 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969``` ```# File 'numeric.c', line 951 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)); } ```

### #nan? ⇒ Boolean

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
``````

Returns:

• (Boolean)

Returns:

• (Boolean)
 ``` 1442 1443 1444 1445 1446 1447 1448``` ```# File 'numeric.c', line 1442 static VALUE flo_is_nan_p(VALUE num) { double value = RFLOAT_VALUE(num); return isnan(value) ? Qtrue : Qfalse; } ```

### #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.
``````

Returns:

 ``` 1556 1557 1558 1559 1560 1561 1562 1563``` ```# File 'numeric.c', line 1556 static VALUE flo_next_float(VALUE vx) { double x, y; x = NUM2DBL(vx); y = nextafter(x, INFINITY); return DBL2NUM(y); } ```

### #numerator ⇒ Integer

Returns the numerator. The result is machine dependent.

``````n = 0.3.numerator    #=> 5404319552844595
d = 0.3.denominator  #=> 18014398509481984
n.fdiv(d)            #=> 0.3
``````

Returns:

 ``` 1888 1889 1890 1891 1892 1893 1894 1895``` ```# File 'rational.c', line 1888 static VALUE float_numerator(VALUE self) { double d = RFLOAT_VALUE(self); if (isinf(d) || isnan(d)) return self; return rb_call_super(0, 0); } ```

### #arg ⇒ 0, Float #angle ⇒ 0, Float #phase ⇒ 0, Float

Returns 0 if the value is positive, pi otherwise.

 ``` 2011 2012 2013 2014 2015 2016 2017 2018 2019``` ```# File 'complex.c', line 2011 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); } ```

### #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
``````

Returns:

 ``` 1608 1609 1610 1611 1612 1613 1614 1615``` ```# File 'numeric.c', line 1608 static VALUE flo_prev_float(VALUE vx) { double x, y; x = NUM2DBL(vx); y = nextafter(x, -INFINITY); return DBL2NUM(y); } ```

### #fdiv(numeric) ⇒ Float #quo(numeric) ⇒ Float

Returns float / numeric, same as Float#/.

 ``` 884 885 886 887 888``` ```# File 'numeric.c', line 884 static VALUE flo_quo(VALUE x, VALUE y) { return rb_funcall(x, '/', 1, y); } ```

### #rationalize([eps]) ⇒ Object

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.

 ``` 2103 2104 2105 2106 2107 2108 2109 2110 2111 2112 2113 2114 2115 2116 2117 2118 2119``` ```# File 'rational.c', line 2103 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); } } ```

### #round([ndigits]) ⇒ Integer, 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
``````

Returns:

 ``` 1740 1741 1742 1743 1744 1745 1746 1747 1748 1749 1750 1751 1752 1753 1754 1755 1756 1757 1758 1759 1760 1761 1762 1763 1764 1765 1766 1767 1768 1769 1770 1771 1772 1773 1774 1775 1776 1777 1778 1779 1780 1781 1782 1783 1784 1785 1786 1787``` ```# File 'numeric.c', line 1740 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); } ```

### #to_f ⇒ self

Since float is already a float, returns self.

Returns:

• (self)
 ``` 1388 1389 1390 1391 1392``` ```# File 'numeric.c', line 1388 static VALUE flo_to_f(VALUE num) { return num; } ```

### #to_i ⇒ Integer #to_int ⇒ Integer #truncate ⇒ Integer

Returns the float truncated to an Integer.

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

 ``` 1800 1801 1802 1803 1804 1805 1806 1807 1808 1809 1810 1811 1812 1813 1814``` ```# File 'numeric.c', line 1800 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); } ```

### #to_i ⇒ Integer #to_int ⇒ Integer #truncate ⇒ Integer

Returns the float truncated to an Integer.

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

 ``` 1800 1801 1802 1803 1804 1805 1806 1807 1808 1809 1810 1811 1812 1813 1814``` ```# File 'numeric.c', line 1800 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); } ```

### #to_r ⇒ Object

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.

 ``` 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033``` ```# File 'rational.c', line 2013 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 } ```

### #to_s ⇒ StringAlso 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.

Returns:

 ``` 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741``` ```# File 'numeric.c', line 675 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; } ```

### #to_i ⇒ Integer #to_int ⇒ Integer #truncate ⇒ Integer

Returns the float truncated to an Integer.

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

 ``` 1800 1801 1802 1803 1804 1805 1806 1807 1808 1809 1810 1811 1812 1813 1814``` ```# File 'numeric.c', line 1800 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); } ```

### #zero? ⇒ Boolean

Returns true if float is 0.0.

Returns:

• (Boolean)

Returns:

• (Boolean)
 ``` 1421 1422 1423 1424 1425 1426 1427 1428``` ```# File 'numeric.c', line 1421 static VALUE flo_zero_p(VALUE num) { if (RFLOAT_VALUE(num) == 0.0) { return Qtrue; } return Qfalse; } ```