# 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:

- https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html
- https://github.com/rdp/ruby_tutorials_core/wiki/Ruby-Talk-FAQ#floats_imprecise
- https://en.wikipedia.org/wiki/Floating_point#Accuracy_problems
``````

## Constant Summary collapse

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 possible 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 =

:MIN. 0.0.next_float returns the smallest positive floating point number including denormalized numbers.

```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```
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 greater than 1.

Usually defaults to 2.2204460492503131e-16.

`DBL2NUM(DBL_EPSILON)`
INFINITY =

An expression representing positive infinity.

`DBL2NUM(HUGE_VAL)`
NAN =

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

`DBL2NUM(nan(""))`

## Instance Method Summary collapse

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

• 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 number greater than or equal to `float` with a precision of `ndigits` decimal digits (default: 0).

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

• Returns the denominator (always positive).

• See Numeric#divmod.

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

• Returns `true` if `float` is a valid IEEE floating point number, i.e.

• Returns the largest number less than or equal to `float` with a precision of `ndigits` decimal digits (default: 0).

• Returns a hash code for this float.

• Returns `nil`, -1, or 1 depending on whether the value is finite, `-Infinity`, or `+Infinity`.

• Returns the absolute value of `float`.

• Returns the modulo after division of `float` by `other`.

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

• Returns `true` if `float` is less than 0.

• Returns the next representable floating point number.

• Returns the numerator.

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

• Returns `true` if `float` is greater than 0.

• Returns the previous representable floating point number.

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

• Returns a simpler approximation of the value (flt-|eps| <= result <= flt+|eps|).

• Returns `float` rounded to the nearest value with a precision of `ndigits` decimal digits (default: 0).

• 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 `float` truncated (toward zero) to a precision of `ndigits` decimal digits (default: 0).

• Returns `true` if `float` is 0.0.

## Instance Method Details

### #%(other) ⇒ Float #modulo(other) ⇒ Float

Returns the modulo after division of `float` by `other`.

``````6543.21.modulo(137)      #=> 104.21000000000004
6543.21.modulo(137.24)   #=> 92.92999999999961
``````

 ``` 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273``` ```# File 'numeric.c', line 1255 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:

 ``` 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116``` ```# File 'numeric.c', line 1101 VALUE rb_float_mul(VALUE x, VALUE y) { if (RB_TYPE_P(y, T_FIXNUM)) { return DBL2NUM(RFLOAT_VALUE(x) * (double)FIX2LONG(y)); } else if (RB_TYPE_P(y, T_BIGNUM)) { return DBL2NUM(RFLOAT_VALUE(x) * rb_big2dbl(y)); } else if (RB_TYPE_P(y, T_FLOAT)) { return DBL2NUM(RFLOAT_VALUE(x) * RFLOAT_VALUE(y)); } else { return rb_num_coerce_bin(x, y, '*'); } }```

### #**(other) ⇒ Float

Raises `float` to the power of `other`.

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

Returns:

 ``` 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 1352 1353``` ```# File 'numeric.c', line 1327 VALUE rb_float_pow(VALUE x, VALUE y) { double dx, dy; if (y == INT2FIX(2)) { dx = RFLOAT_VALUE(x); return DBL2NUM(dx * dx); } else if (RB_TYPE_P(y, T_FIXNUM)) { dx = RFLOAT_VALUE(x); dy = (double)FIX2LONG(y); } else if (RB_TYPE_P(y, T_BIGNUM)) { dx = RFLOAT_VALUE(x); dy = rb_big2dbl(y); } else if (RB_TYPE_P(y, T_FLOAT)) { dx = RFLOAT_VALUE(x); dy = RFLOAT_VALUE(y); if (dx < 0 && dy != round(dy)) return rb_dbl_complex_new_polar_pi(pow(-dx, dy), dy); } else { return rb_num_coerce_bin(x, y, idPow); } return DBL2NUM(pow(dx, dy)); }```

### #+(other) ⇒ Float

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

Returns:

 ``` 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068``` ```# File 'numeric.c', line 1053 VALUE rb_float_plus(VALUE x, VALUE y) { if (RB_TYPE_P(y, T_FIXNUM)) { return DBL2NUM(RFLOAT_VALUE(x) + (double)FIX2LONG(y)); } else if (RB_TYPE_P(y, T_BIGNUM)) { return DBL2NUM(RFLOAT_VALUE(x) + rb_big2dbl(y)); } else if (RB_TYPE_P(y, T_FLOAT)) { return DBL2NUM(RFLOAT_VALUE(x) + RFLOAT_VALUE(y)); } else { return rb_num_coerce_bin(x, y, '+'); } }```

### #-(other) ⇒ Float

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

Returns:

 ``` 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092``` ```# File 'numeric.c', line 1077 VALUE rb_float_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:

 ``` 1040 1041 1042 1043 1044``` ```# File 'numeric.c', line 1040 VALUE rb_float_uminus(VALUE flt) { return DBL2NUM(-RFLOAT_VALUE(flt)); }```

### #/(other) ⇒ Float

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

Returns:

 ``` 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177``` ```# File 'numeric.c', line 1155 VALUE rb_float_div(VALUE x, VALUE y) { double num = RFLOAT_VALUE(x); double den; double ret; if (RB_TYPE_P(y, T_FIXNUM)) { den = FIX2LONG(y); } else if (RB_TYPE_P(y, T_BIGNUM)) { den = rb_big2dbl(y); } else if (RB_TYPE_P(y, T_FLOAT)) { den = RFLOAT_VALUE(y); } else { return rb_num_coerce_bin(x, y, '/'); } ret = double_div_double(num, den); return DBL2NUM(ret); }```

### #<(real) ⇒ Boolean

Returns `true` if `float` is less than `real`.

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

Returns:

• (Boolean)
 ``` 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``` ```# File 'numeric.c', line 1610 static VALUE flo_lt(VALUE x, VALUE y) { double a, b; a = RFLOAT_VALUE(x); if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) { VALUE rel = rb_integer_float_cmp(y, x); if (FIXNUM_P(rel)) return -FIX2LONG(rel) < 0 ? Qtrue : Qfalse; return Qfalse; } else if (RB_TYPE_P(y, T_FLOAT)) { b = RFLOAT_VALUE(y); #if MSC_VERSION_BEFORE(1300) if (isnan(b)) return Qfalse; #endif } else { return rb_num_coerce_relop(x, y, '<'); } #if MSC_VERSION_BEFORE(1300) if (isnan(a)) return Qfalse; #endif return (a < b)?Qtrue:Qfalse; }```

### #<=(real) ⇒ Boolean

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

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

Returns:

• (Boolean)
 ``` 1647 1648 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668 1669 1670 1671 1672``` ```# File 'numeric.c', line 1647 static VALUE flo_le(VALUE x, VALUE y) { double a, b; a = RFLOAT_VALUE(x); if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) { VALUE rel = rb_integer_float_cmp(y, x); if (FIXNUM_P(rel)) return -FIX2LONG(rel) <= 0 ? Qtrue : Qfalse; return Qfalse; } else if (RB_TYPE_P(y, T_FLOAT)) { b = RFLOAT_VALUE(y); #if MSC_VERSION_BEFORE(1300) if (isnan(b)) return Qfalse; #endif } else { return rb_num_coerce_relop(x, y, idLE); } #if MSC_VERSION_BEFORE(1300) if (isnan(a)) return Qfalse; #endif return (a <= b)?Qtrue:Qfalse; }```

### #<=>(real) ⇒ -1, ...

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

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

`nil` is returned if the two values are incomparable.

Returns:

• (-1, 0, +1, nil)
 ``` 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518``` ```# File 'numeric.c', line 1488 static VALUE flo_cmp(VALUE x, VALUE y) { double a, b; VALUE i; a = RFLOAT_VALUE(x); if (isnan(a)) return Qnil; if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) { VALUE rel = rb_integer_float_cmp(y, x); if (FIXNUM_P(rel)) return LONG2FIX(-FIX2LONG(rel)); return rel; } else if (RB_TYPE_P(y, T_FLOAT)) { b = RFLOAT_VALUE(y); } else { if (isinf(a) && (i = rb_check_funcall(y, rb_intern("infinite?"), 0, 0)) != Qundef) { if (RTEST(i)) { int j = rb_cmpint(i, x, y); j = (a > 0.0) ? (j > 0 ? 0 : +1) : (j < 0 ? 0 : -1); return INT2FIX(j); } if (a > 0.0) return INT2FIX(1); return INT2FIX(-1); } return rb_num_coerce_cmp(x, y, id_cmp); } return rb_dbl_cmp(a, b); }```

### #>(real) ⇒ Boolean

Returns `true` if `float` is greater than `real`.

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

Returns:

• (Boolean)
 ``` 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561``` ```# File 'numeric.c', line 1536 VALUE rb_float_gt(VALUE x, VALUE y) { double a, b; a = RFLOAT_VALUE(x); if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) { VALUE rel = rb_integer_float_cmp(y, x); if (FIXNUM_P(rel)) return -FIX2LONG(rel) > 0 ? Qtrue : Qfalse; return Qfalse; } else if (RB_TYPE_P(y, T_FLOAT)) { b = RFLOAT_VALUE(y); #if MSC_VERSION_BEFORE(1300) if (isnan(b)) return Qfalse; #endif } else { return rb_num_coerce_relop(x, y, '>'); } #if MSC_VERSION_BEFORE(1300) if (isnan(a)) return Qfalse; #endif return (a > b)?Qtrue:Qfalse; }```

### #>=(real) ⇒ Boolean

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

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

Returns:

• (Boolean)
 ``` 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598``` ```# File 'numeric.c', line 1573 static VALUE flo_ge(VALUE x, VALUE y) { double a, b; a = RFLOAT_VALUE(x); if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) { VALUE rel = rb_integer_float_cmp(y, x); if (FIXNUM_P(rel)) return -FIX2LONG(rel) >= 0 ? Qtrue : Qfalse; return Qfalse; } else if (RB_TYPE_P(y, T_FLOAT)) { b = RFLOAT_VALUE(y); #if MSC_VERSION_BEFORE(1300) if (isnan(b)) return Qfalse; #endif } else { return rb_num_coerce_relop(x, y, idGE); } #if MSC_VERSION_BEFORE(1300) if (isnan(a)) return Qfalse; #endif return (a >= b)?Qtrue:Qfalse; }```

### #abs ⇒ Float #magnitude ⇒ Float

Returns the absolute value of `float`.

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

Float#magnitude is an alias for Float#abs.

 ``` 1731 1732 1733 1734 1735 1736``` ```# File 'numeric.c', line 1731 VALUE rb_float_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.

 ``` 2278 2279 2280 2281 2282 2283 2284 2285 2286``` ```# File 'complex.c', line 2278 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.

 ``` 2278 2279 2280 2281 2282 2283 2284 2285 2286``` ```# File 'complex.c', line 2278 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([ndigits]) ⇒ Integer, Float

Returns the smallest number greater than or equal to `float` with a precision of `ndigits` decimal digits (default: 0).

When the precision is negative, the returned value is an integer with at least `ndigits.abs` trailing zeros.

Returns a floating point number when `ndigits` is positive, otherwise returns an integer.

``````1.2.ceil      #=> 2
2.0.ceil      #=> 2
(-1.2).ceil   #=> -1
(-2.0).ceil   #=> -2

1.234567.ceil(2)   #=> 1.24
1.234567.ceil(3)   #=> 1.235
1.234567.ceil(4)   #=> 1.2346
1.234567.ceil(5)   #=> 1.23457

34567.89.ceil(-5)  #=> 100000
34567.89.ceil(-4)  #=> 40000
34567.89.ceil(-3)  #=> 35000
34567.89.ceil(-2)  #=> 34600
34567.89.ceil(-1)  #=> 34570
34567.89.ceil(0)   #=> 34568
34567.89.ceil(1)   #=> 34567.9
34567.89.ceil(2)   #=> 34567.89
34567.89.ceil(3)   #=> 34567.89
``````

Note that the limited precision of floating point arithmetic might lead to surprising results:

``````(2.1 / 0.7).ceil  #=> 4 (!)
``````

Returns:

 ``` 2047 2048 2049 2050 2051 2052 2053 2054 2055 2056``` ```# File 'numeric.c', line 2047 static VALUE flo_ceil(int argc, VALUE *argv, VALUE num) { int ndigits = 0; if (rb_check_arity(argc, 0, 1)) { ndigits = NUM2INT(argv[0]); } return rb_float_ceil(num, ndigits); }```

### #coerce(numeric) ⇒ Array

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

This is achieved by converting `numeric` to a Float.

``````1.2.coerce(3)       #=> [3.0, 1.2]
2.5.coerce(1.1)     #=> [1.1, 2.5]
``````

Returns:

 ``` 1027 1028 1029 1030 1031``` ```# File 'numeric.c', line 1027 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.

Returns:

 ``` 2111 2112 2113 2114 2115 2116 2117 2118 2119 2120``` ```# File 'rational.c', line 2111 VALUE rb_float_denominator(VALUE self) { double d = RFLOAT_VALUE(self); VALUE r; if (isinf(d) || isnan(d)) return INT2FIX(1); r = float_to_r(self); return nurat_denominator(r); }```

### #divmod(numeric) ⇒ Array

See Numeric#divmod.

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

Returns:

 ``` 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316``` ```# File 'numeric.c', line 1294 static VALUE flo_divmod(VALUE x, VALUE y) { double fy, div, mod; volatile VALUE a, b; if (RB_TYPE_P(y, T_FIXNUM)) { fy = (double)FIX2LONG(y); } else if (RB_TYPE_P(y, T_BIGNUM)) { fy = rb_big2dbl(y); } else if (RB_TYPE_P(y, T_FLOAT)) { fy = RFLOAT_VALUE(y); } else { return rb_num_coerce_bin(x, y, id_divmod); } flodivmod(RFLOAT_VALUE(x), fy, &div, &mod); a = dbl2ival(div); b = DBL2NUM(mod); return rb_assoc_new(a, b); }```

Returns:

• (Boolean)

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

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

 ``` 1187 1188 1189 1190 1191``` ```# File 'numeric.c', line 1187 static VALUE flo_quo(VALUE x, VALUE y) { return num_funcall1(x, '/', y); }```

### #finite? ⇒ Boolean

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

Returns:

• (Boolean)
 ``` 1803 1804 1805 1806 1807 1808 1809 1810 1811 1812 1813 1814 1815 1816 1817``` ```# File 'numeric.c', line 1803 VALUE rb_flo_is_finite_p(VALUE num) { double value = RFLOAT_VALUE(num); #ifdef HAVE_ISFINITE if (!isfinite(value)) return Qfalse; #else if (isinf(value) || isnan(value)) return Qfalse; #endif return Qtrue; }```

### #floor([ndigits]) ⇒ Integer, Float

Returns the largest number less than or equal to `float` with a precision of `ndigits` decimal digits (default: 0).

When the precision is negative, the returned value is an integer with at least `ndigits.abs` trailing zeros.

Returns a floating point number when `ndigits` is positive, otherwise returns an integer.

``````1.2.floor      #=> 1
2.0.floor      #=> 2
(-1.2).floor   #=> -2
(-2.0).floor   #=> -2

1.234567.floor(2)   #=> 1.23
1.234567.floor(3)   #=> 1.234
1.234567.floor(4)   #=> 1.2345
1.234567.floor(5)   #=> 1.23456

34567.89.floor(-5)  #=> 0
34567.89.floor(-4)  #=> 30000
34567.89.floor(-3)  #=> 34000
34567.89.floor(-2)  #=> 34500
34567.89.floor(-1)  #=> 34560
34567.89.floor(0)   #=> 34567
34567.89.floor(1)   #=> 34567.8
34567.89.floor(2)   #=> 34567.89
34567.89.floor(3)   #=> 34567.89
``````

Note that the limited precision of floating point arithmetic might lead to surprising results:

``````(0.3 / 0.1).floor  #=> 2 (!)
``````

Returns:

 ``` 1998 1999 2000 2001 2002 2003 2004 2005 2006``` ```# File 'numeric.c', line 1998 static VALUE flo_floor(int argc, VALUE *argv, VALUE num) { int ndigits = 0; if (rb_check_arity(argc, 0, 1)) { ndigits = NUM2INT(argv[0]); } return rb_float_floor(num, ndigits); }```

### #hash ⇒ Integer

Returns a hash code for this float.

Returns:

 ``` 1452 1453 1454 1455 1456``` ```# File 'numeric.c', line 1452 static VALUE flo_hash(VALUE num) { return rb_dbl_hash(RFLOAT_VALUE(num)); }```

### #infinite? ⇒ -1, ...

Returns `nil`, -1, or 1 depending on whether the value is finite, `-Infinity`, or `+Infinity`.

``````(0.0).infinite?        #=> nil
(-1.0/0.0).infinite?   #=> -1
(+1.0/0.0).infinite?   #=> 1
``````

Returns:

• (-1, 1, nil)
 ``` 1783 1784 1785 1786 1787 1788 1789 1790 1791 1792 1793``` ```# File 'numeric.c', line 1783 VALUE rb_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
34.56.abs      #=> 34.56
``````

Float#magnitude is an alias for Float#abs.

 ``` 1731 1732 1733 1734 1735 1736``` ```# File 'numeric.c', line 1731 VALUE rb_float_abs(VALUE flt) { double val = fabs(RFLOAT_VALUE(flt)); return DBL2NUM(val); }```

### #%(other) ⇒ Float #modulo(other) ⇒ Float

Returns the modulo after division of `float` by `other`.

``````6543.21.modulo(137)      #=> 104.21000000000004
6543.21.modulo(137.24)   #=> 92.92999999999961
``````

 ``` 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273``` ```# File 'numeric.c', line 1255 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)
 ``` 1763 1764 1765 1766 1767 1768 1769``` ```# File 'numeric.c', line 1763 static VALUE flo_is_nan_p(VALUE num) { double value = RFLOAT_VALUE(num); return isnan(value) ? Qtrue : Qfalse; }```

### #negative? ⇒ Boolean

Returns `true` if `float` is less than 0.

Returns:

• (Boolean)
 ``` 2461 2462 2463 2464 2465 2466``` ```# File 'numeric.c', line 2461 static VALUE flo_negative_p(VALUE num) { double f = RFLOAT_VALUE(num); return f < 0.0 ? 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:

``````0.01.next_float    #=> 0.010000000000000002
1.0.next_float     #=> 1.0000000000000002
100.0.next_float   #=> 100.00000000000001

0.01.next_float - 0.01     #=> 1.734723475976807e-18
1.0.next_float - 1.0       #=> 2.220446049250313e-16
100.0.next_float - 100.0   #=> 1.4210854715202004e-14

f = 0.01; 20.times { printf "%-20a %s\n", f, f.to_s; f = f.next_float }
#=> 0x1.47ae147ae147bp-7 0.01
#   0x1.47ae147ae147cp-7 0.010000000000000002
#   0x1.47ae147ae147dp-7 0.010000000000000004
#   0x1.47ae147ae147ep-7 0.010000000000000005
#   0x1.47ae147ae147fp-7 0.010000000000000007
#   0x1.47ae147ae148p-7  0.010000000000000009
#   0x1.47ae147ae1481p-7 0.01000000000000001
#   0x1.47ae147ae1482p-7 0.010000000000000012
#   0x1.47ae147ae1483p-7 0.010000000000000014
#   0x1.47ae147ae1484p-7 0.010000000000000016
#   0x1.47ae147ae1485p-7 0.010000000000000018
#   0x1.47ae147ae1486p-7 0.01000000000000002
#   0x1.47ae147ae1487p-7 0.010000000000000021
#   0x1.47ae147ae1488p-7 0.010000000000000023
#   0x1.47ae147ae1489p-7 0.010000000000000024
#   0x1.47ae147ae148ap-7 0.010000000000000026
#   0x1.47ae147ae148bp-7 0.010000000000000028
#   0x1.47ae147ae148cp-7 0.01000000000000003
#   0x1.47ae147ae148dp-7 0.010000000000000031
#   0x1.47ae147ae148ep-7 0.010000000000000033

f = 0.0
100.times { f += 0.1 }
f                           #=> 9.99999999999998       # should be 10.0 in the ideal world.
10-f                        #=> 1.9539925233402755e-14 # the floating point error.
10.0.next_float-10          #=> 1.7763568394002505e-15 # 1 ulp (unit in the last place).
(10-f)/(10.0.next_float-10) #=> 11.0                   # the error is 11 ulp.
(10-f)/(10*Float::EPSILON)  #=> 8.8                    # approximation of the above.
"%a" % 10                   #=> "0x1.4p+3"
"%a" % f                    #=> "0x1.3fffffffffff5p+3" # the last hex digit is 5.  16 - 5 = 11 ulp.
``````

Returns:

 ``` 1880 1881 1882 1883 1884``` ```# File 'numeric.c', line 1880 static VALUE flo_next_float(VALUE vx) { return flo_nextafter(vx, HUGE_VAL); }```

### #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:

 ``` 2091 2092 2093 2094 2095 2096 2097 2098 2099 2100``` ```# File 'rational.c', line 2091 VALUE rb_float_numerator(VALUE self) { double d = RFLOAT_VALUE(self); VALUE r; if (isinf(d) || isnan(d)) return self; r = float_to_r(self); return nurat_numerator(r); }```

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

Returns 0 if the value is positive, pi otherwise.

 ``` 2278 2279 2280 2281 2282 2283 2284 2285 2286``` ```# File 'complex.c', line 2278 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); }```

### #positive? ⇒ Boolean

Returns `true` if `float` is greater than 0.

Returns:

• (Boolean)
 ``` 2447 2448 2449 2450 2451 2452``` ```# File 'numeric.c', line 2447 static VALUE flo_positive_p(VALUE num) { double f = RFLOAT_VALUE(num); return f > 0.0 ? Qtrue : Qfalse; }```

### #prev_float ⇒ Float

Returns the previous representable floating point number.

(-Float::MAX).prev_float and (-Float::INFINITY).prev_float is -Float::INFINITY.

Float::NAN.prev_float is Float::NAN.

For example:

``````0.01.prev_float    #=> 0.009999999999999998
1.0.prev_float     #=> 0.9999999999999999
100.0.prev_float   #=> 99.99999999999999

0.01 - 0.01.prev_float     #=> 1.734723475976807e-18
1.0 - 1.0.prev_float       #=> 1.1102230246251565e-16
100.0 - 100.0.prev_float   #=> 1.4210854715202004e-14

f = 0.01; 20.times { printf "%-20a %s\n", f, f.to_s; f = f.prev_float }
#=> 0x1.47ae147ae147bp-7 0.01
#   0x1.47ae147ae147ap-7 0.009999999999999998
#   0x1.47ae147ae1479p-7 0.009999999999999997
#   0x1.47ae147ae1478p-7 0.009999999999999995
#   0x1.47ae147ae1477p-7 0.009999999999999993
#   0x1.47ae147ae1476p-7 0.009999999999999992
#   0x1.47ae147ae1475p-7 0.00999999999999999
#   0x1.47ae147ae1474p-7 0.009999999999999988
#   0x1.47ae147ae1473p-7 0.009999999999999986
#   0x1.47ae147ae1472p-7 0.009999999999999985
#   0x1.47ae147ae1471p-7 0.009999999999999983
#   0x1.47ae147ae147p-7  0.009999999999999981
#   0x1.47ae147ae146fp-7 0.00999999999999998
#   0x1.47ae147ae146ep-7 0.009999999999999978
#   0x1.47ae147ae146dp-7 0.009999999999999976
#   0x1.47ae147ae146cp-7 0.009999999999999974
#   0x1.47ae147ae146bp-7 0.009999999999999972
#   0x1.47ae147ae146ap-7 0.00999999999999997
#   0x1.47ae147ae1469p-7 0.009999999999999969
#   0x1.47ae147ae1468p-7 0.009999999999999967
``````

Returns:

 ``` 1928 1929 1930 1931 1932``` ```# File 'numeric.c', line 1928 static VALUE flo_prev_float(VALUE vx) { return flo_nextafter(vx, -HUGE_VAL); }```

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

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

 ``` 1187 1188 1189 1190 1191``` ```# File 'numeric.c', line 1187 static VALUE flo_quo(VALUE x, VALUE y) { return num_funcall1(x, '/', y); }```

### #rationalize([eps]) ⇒ Object

Returns a simpler approximation of the value (flt-|eps| <= result <= flt+|eps|). If the optional argument `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)
``````

 ``` 2293 2294 2295 2296 2297 2298 2299 2300 2301 2302 2303 2304 2305 2306 2307 2308 2309``` ```# File 'rational.c', line 2293 static VALUE float_rationalize(int argc, VALUE *argv, VALUE self) { double d = RFLOAT_VALUE(self); VALUE rat; int neg = d < 0.0; if (neg) self = DBL2NUM(-d); if (rb_check_arity(argc, 0, 1)) { rat = rb_flt_rationalize_with_prec(self, argv[0]); } else { rat = rb_flt_rationalize(self); } if (neg) RATIONAL_SET_NUM(rat, rb_int_uminus(RRATIONAL(rat)->num)); return rat; }```

### #round([ndigits][, half: mode]) ⇒ Integer, Float

Returns `float` rounded to the nearest value with a precision of `ndigits` decimal digits (default: 0).

When the precision is negative, the returned value is an integer with at least `ndigits.abs` trailing zeros.

Returns a floating point number when `ndigits` is positive, otherwise returns an integer.

``````1.4.round      #=> 1
1.5.round      #=> 2
1.6.round      #=> 2
(-1.5).round   #=> -2

1.234567.round(2)   #=> 1.23
1.234567.round(3)   #=> 1.235
1.234567.round(4)   #=> 1.2346
1.234567.round(5)   #=> 1.23457

34567.89.round(-5)  #=> 0
34567.89.round(-4)  #=> 30000
34567.89.round(-3)  #=> 35000
34567.89.round(-2)  #=> 34600
34567.89.round(-1)  #=> 34570
34567.89.round(0)   #=> 34568
34567.89.round(1)   #=> 34567.9
34567.89.round(2)   #=> 34567.89
34567.89.round(3)   #=> 34567.89
``````

If the optional `half` keyword argument is given, numbers that are half-way between two possible rounded values will be rounded according to the specified tie-breaking `mode`:

• `:up` or `nil`: round half away from zero (default)

• `:down`: round half toward zero

• `:even`: round half toward the nearest even number

``````2.5.round(half: :up)      #=> 3
2.5.round(half: :down)    #=> 2
2.5.round(half: :even)    #=> 2
3.5.round(half: :up)      #=> 4
3.5.round(half: :down)    #=> 3
3.5.round(half: :even)    #=> 4
(-2.5).round(half: :up)   #=> -3
(-2.5).round(half: :down) #=> -2
(-2.5).round(half: :even) #=> -2
``````

Returns:

 ``` 2307 2308 2309 2310 2311 2312 2313 2314 2315 2316 2317 2318 2319 2320 2321 2322 2323 2324 2325 2326 2327 2328 2329 2330 2331 2332 2333 2334 2335 2336 2337 2338 2339 2340``` ```# File 'numeric.c', line 2307 static VALUE flo_round(int argc, VALUE *argv, VALUE num) { double number, f, x; VALUE nd, opt; int ndigits = 0; enum ruby_num_rounding_mode mode; if (rb_scan_args(argc, argv, "01:", &nd, &opt)) { ndigits = NUM2INT(nd); } mode = rb_num_get_rounding_option(opt); number = RFLOAT_VALUE(num); if (number == 0.0) { return ndigits > 0 ? DBL2NUM(number) : INT2FIX(0); } if (ndigits < 0) { return rb_int_round(flo_to_i(num), ndigits, mode); } if (ndigits == 0) { x = ROUND_CALL(mode, round, (number, 1.0)); return dbl2ival(x); } if (isfinite(number)) { int binexp; frexp(number, &binexp); if (float_round_overflow(ndigits, binexp)) return num; if (float_round_underflow(ndigits, binexp)) return DBL2NUM(0); f = pow(10, ndigits); x = ROUND_CALL(mode, round, (number, f)); return DBL2NUM(x / f); } return num; }```

### #to_f ⇒ self

Since `float` is already a Float, returns `self`.

Returns:

• (self)
 ``` 1711 1712 1713 1714 1715``` ```# File 'numeric.c', line 1711 static VALUE flo_to_f(VALUE num) { return num; }```

### #to_i ⇒ Integer #to_int ⇒ Integer

Returns the `float` truncated to an Integer.

``````1.2.to_i      #=> 1
(-1.2).to_i   #=> -1
``````

Note that the limited precision of floating point arithmetic might lead to surprising results:

``````(0.3 / 0.1).to_i  #=> 2 (!)
``````

#to_int is an alias for #to_i.

 ``` 2397 2398 2399 2400 2401 2402 2403 2404 2405 2406``` ```# File 'numeric.c', line 2397 static VALUE flo_to_i(VALUE num) { double f = RFLOAT_VALUE(num); if (f > 0.0) f = floor(f); if (f < 0.0) f = ceil(f); return dbl2ival(f); }```

### #to_i ⇒ Integer #to_int ⇒ Integer

Returns the `float` truncated to an Integer.

``````1.2.to_i      #=> 1
(-1.2).to_i   #=> -1
``````

Note that the limited precision of floating point arithmetic might lead to surprising results:

``````(0.3 / 0.1).to_i  #=> 2 (!)
``````

#to_int is an alias for #to_i.

 ``` 2397 2398 2399 2400 2401 2402 2403 2404 2405 2406``` ```# File 'numeric.c', line 2397 static VALUE flo_to_i(VALUE num) { double f = RFLOAT_VALUE(num); if (f > 0.0) f = floor(f); if (f < 0.0) f = ceil(f); return dbl2ival(f); }```

### #to_r ⇒ Object

Returns the value as a rational.

``````2.0.to_r    #=> (2/1)
2.5.to_r    #=> (5/2)
-0.75.to_r  #=> (-3/4)
0.0.to_r    #=> (0/1)
0.3.to_r    #=> (5404319552844595/18014398509481984)
``````

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.

``````0.3.to_r   == 3/10r  #=> false
"0.3".to_r == 3/10r  #=> true
``````

 ``` 2208 2209 2210 2211 2212 2213 2214 2215 2216 2217 2218 2219 2220 2221 2222 2223 2224 2225 2226 2227 2228``` ```# File 'rational.c', line 2208 static VALUE float_to_r(VALUE self) { VALUE f; int n; float_decode_internal(self, &f, &n); #if FLT_RADIX == 2 if (n == 0) return rb_rational_new1(f); if (n > 0) return rb_rational_new1(rb_int_lshift(f, INT2FIX(n))); n = -n; return rb_rational_new2(f, rb_int_lshift(ONE, INT2FIX(n))); #else f = rb_int_mul(f, rb_int_pow(INT2FIX(FLT_RADIX), n)); if (RB_TYPE_P(f, T_RATIONAL)) return f; return rb_rational_new1(f); #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:

 ``` 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012``` ```# File 'numeric.c', line 940 static VALUE flo_to_s(VALUE flt) { enum {decimal_mant = DBL_MANT_DIG-DBL_DIG}; enum {float_dig = DBL_DIG+1}; char buf[float_dig + (decimal_mant + CHAR_BIT - 1) / CHAR_BIT + 10]; double value = RFLOAT_VALUE(flt); VALUE s; char *p, *e; int sign, decpt, digs; if (isinf(value)) { static const char minf[] = "-Infinity"; const int pos = (value > 0); /* skip "-" */ return rb_usascii_str_new(minf+pos, strlen(minf)-pos); } else if (isnan(value)) return rb_usascii_str_new2("NaN"); p = ruby_dtoa(value, 0, 0, &decpt, &sign, &e); s = sign ? rb_usascii_str_new_cstr("-") : rb_usascii_str_new(0, 0); if ((digs = (int)(e - p)) >= (int)sizeof(buf)) digs = (int)sizeof(buf) - 1; memcpy(buf, p, digs); xfree(p); if (decpt > 0) { if (decpt < digs) { memmove(buf + decpt + 1, buf + decpt, digs - decpt); buf[decpt] = '.'; rb_str_cat(s, buf, digs + 1); } else if (decpt <= DBL_DIG) { long len; char *ptr; rb_str_cat(s, buf, digs); rb_str_resize(s, (len = RSTRING_LEN(s)) + decpt - digs + 2); ptr = RSTRING_PTR(s) + len; if (decpt > digs) { memset(ptr, '0', decpt - digs); ptr += decpt - digs; } memcpy(ptr, ".0", 2); } else { goto exp; } } else if (decpt > -4) { long len; char *ptr; rb_str_cat(s, "0.", 2); rb_str_resize(s, (len = RSTRING_LEN(s)) - decpt + digs); ptr = RSTRING_PTR(s); memset(ptr += len, '0', -decpt); memcpy(ptr -= decpt, buf, digs); } else { goto exp; } return s; exp: if (digs > 1) { memmove(buf + 2, buf + 1, digs - 1); } else { buf[2] = '0'; digs++; } buf[1] = '.'; rb_str_cat(s, buf, digs + 1); rb_str_catf(s, "e%+03d", decpt - 1); return s; }```

### #truncate([ndigits]) ⇒ Integer, Float

Returns `float` truncated (toward zero) to a precision of `ndigits` decimal digits (default: 0).

When the precision is negative, the returned value is an integer with at least `ndigits.abs` trailing zeros.

Returns a floating point number when `ndigits` is positive, otherwise returns an integer.

``````2.8.truncate           #=> 2
(-2.8).truncate        #=> -2
1.234567.truncate(2)   #=> 1.23
34567.89.truncate(-2)  #=> 34500
``````

Note that the limited precision of floating point arithmetic might lead to surprising results:

``````(0.3 / 0.1).truncate  #=> 2 (!)
``````

Returns:

 ``` 2431 2432 2433 2434 2435 2436 2437 2438``` ```# File 'numeric.c', line 2431 static VALUE flo_truncate(int argc, VALUE *argv, VALUE num) { if (signbit(RFLOAT_VALUE(num))) return flo_ceil(argc, argv, num); else return flo_floor(argc, argv, num); }```

### #zero? ⇒ Boolean

Returns `true` if `float` is 0.0.

Returns:

• (Boolean)
 ``` 1745 1746 1747 1748 1749``` ```# File 'numeric.c', line 1745 static VALUE flo_zero_p(VALUE num) { return flo_iszero(num) ? Qtrue : Qfalse; }```