class Float

Returns self modulo other as a float.

For float f and real number r, these expressions are equivalent:

f % r f-r*(f/r).floor f.divmod(r)[1] 

See Numeric#divmod.

Examples:

10.0 % 2 # => 0.0 10.0 % 3 # => 1.0 10.0 % 4 # => 2.0 10.0 % -2 # => 0.0 10.0 % -3 # => -2.0 10.0 % -4 # => -2.0 10.0 % 4.0 # => 2.0 10.0 % Rational(4, 1) # => 2.0 

static VALUE flo_mod(VALUE x, VALUE y) { double fy; if (FIXNUM_P(y)) { fy = (double)FIX2LONG(y); } else if (RB_BIGNUM_TYPE_P(y)) { fy = rb_big2dbl(y); } else if (RB_FLOAT_TYPE_P(y)) { fy = RFLOAT_VALUE(y); } else { return rb_num_coerce_bin(x, y, '%'); } return DBL2NUM(ruby_float_mod(RFLOAT_VALUE(x), fy)); }

Returns a new Float which is the product of self and other:

f = 3.14 f * 2 # => 6.28 f * 2.0 # => 6.28 f * Rational(1, 2) # => 1.57 f * Complex(2, 0) # => (6.28+0.0i) 

VALUE rb_float_mul(VALUE x, VALUE y) { if (FIXNUM_P(y)) { return DBL2NUM(RFLOAT_VALUE(x) * (double)FIX2LONG(y)); } else if (RB_BIGNUM_TYPE_P(y)) { return DBL2NUM(RFLOAT_VALUE(x) * rb_big2dbl(y)); } else if (RB_FLOAT_TYPE_P(y)) { return DBL2NUM(RFLOAT_VALUE(x) * RFLOAT_VALUE(y)); } else { return rb_num_coerce_bin(x, y, '*'); } }

Raises self to the power of other:

f = 3.14 f ** 2 # => 9.8596 f ** -2 # => 0.1014239928597509 f ** 2.1 # => 11.054834900588839 f ** Rational(2, 1) # => 9.8596 f ** Complex(2, 0) # => (9.8596+0i) 

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 (FIXNUM_P(y)) { dx = RFLOAT_VALUE(x); dy = (double)FIX2LONG(y); } else if (RB_BIGNUM_TYPE_P(y)) { dx = RFLOAT_VALUE(x); dy = rb_big2dbl(y); } else if (RB_FLOAT_TYPE_P(y)) { 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)); }

Returns a new Float which is the sum of self and other:

f = 3.14 f + 1 # => 4.140000000000001 f + 1.0 # => 4.140000000000001 f + Rational(1, 1) # => 4.140000000000001 f + Complex(1, 0) # => (4.140000000000001+0i) 

VALUE rb_float_plus(VALUE x, VALUE y) { if (FIXNUM_P(y)) { return DBL2NUM(RFLOAT_VALUE(x) + (double)FIX2LONG(y)); } else if (RB_BIGNUM_TYPE_P(y)) { return DBL2NUM(RFLOAT_VALUE(x) + rb_big2dbl(y)); } else if (RB_FLOAT_TYPE_P(y)) { return DBL2NUM(RFLOAT_VALUE(x) + RFLOAT_VALUE(y)); } else { return rb_num_coerce_bin(x, y, '+'); } }

Returns a new Float which is the difference of self and other:

f = 3.14 f - 1 # => 2.14 f - 1.0 # => 2.14 f - Rational(1, 1) # => 2.14 f - Complex(1, 0) # => (2.14+0i) 

VALUE rb_float_minus(VALUE x, VALUE y) { if (FIXNUM_P(y)) { return DBL2NUM(RFLOAT_VALUE(x) - (double)FIX2LONG(y)); } else if (RB_BIGNUM_TYPE_P(y)) { return DBL2NUM(RFLOAT_VALUE(x) - rb_big2dbl(y)); } else if (RB_FLOAT_TYPE_P(y)) { return DBL2NUM(RFLOAT_VALUE(x) - RFLOAT_VALUE(y)); } else { return rb_num_coerce_bin(x, y, '-'); } }

Returns self, negated.

# File ruby_3_4_1/numeric.rb, line 380 def -@ Primitive.attr! :leaf Primitive.cexpr! 'rb_float_uminus(self)' end

Returns a new Float which is the result of dividing self by other:

f = 3.14 f / 2 # => 1.57 f / 2.0 # => 1.57 f / Rational(2, 1) # => 1.57 f / Complex(2, 0) # => (1.57+0.0i) 

VALUE rb_float_div(VALUE x, VALUE y) { double num = RFLOAT_VALUE(x); double den; double ret; if (FIXNUM_P(y)) { den = FIX2LONG(y); } else if (RB_BIGNUM_TYPE_P(y)) { den = rb_big2dbl(y); } else if (RB_FLOAT_TYPE_P(y)) { den = RFLOAT_VALUE(y); } else { return rb_num_coerce_bin(x, y, '/'); } ret = double_div_double(num, den); return DBL2NUM(ret); }

Returns true if self is numerically less than other:

2.0 < 3 # => true 2.0 < 3.0 # => true 2.0 < Rational(3, 1) # => true 2.0 < 2.0 # => false 

Float::NAN < Float::NAN returns an implementation-dependent value.

static VALUE flo_lt(VALUE x, VALUE y) { double a, b; a = RFLOAT_VALUE(x); if (RB_INTEGER_TYPE_P(y)) { VALUE rel = rb_integer_float_cmp(y, x); if (FIXNUM_P(rel)) return RBOOL(-FIX2LONG(rel) < 0); return Qfalse; } else if (RB_FLOAT_TYPE_P(y)) { 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 RBOOL(a < b); }

Returns true if self is numerically less than or equal to other:

2.0 <= 3 # => true 2.0 <= 3.0 # => true 2.0 <= Rational(3, 1) # => true 2.0 <= 2.0 # => true 2.0 <= 1.0 # => false 

Float::NAN <= Float::NAN returns an implementation-dependent value.

static VALUE flo_le(VALUE x, VALUE y) { double a, b; a = RFLOAT_VALUE(x); if (RB_INTEGER_TYPE_P(y)) { VALUE rel = rb_integer_float_cmp(y, x); if (FIXNUM_P(rel)) return RBOOL(-FIX2LONG(rel) <= 0); return Qfalse; } else if (RB_FLOAT_TYPE_P(y)) { 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 RBOOL(a <= b); }

Returns a value that depends on the numeric relation between self and other:

• -1, if self is less than other.

• 0, if self is equal to other.

• 1, if self is greater than other.

• nil, if the two values are incommensurate.

Examples:

2.0 <=> 2 # => 0 2.0 <=> 2.0 # => 0 2.0 <=> Rational(2, 1) # => 0 2.0 <=> Complex(2, 0) # => 0 2.0 <=> 1.9 # => 1 2.0 <=> 2.1 # => -1 2.0 <=> 'foo' # => nil 

This is the basis for the tests in the Comparable module.

Float::NAN <=> Float::NAN returns an implementation-dependent value.

static VALUE flo_cmp(VALUE x, VALUE y) { double a, b; VALUE i; a = RFLOAT_VALUE(x); if (isnan(a)) return Qnil; if (RB_INTEGER_TYPE_P(y)) { VALUE rel = rb_integer_float_cmp(y, x); if (FIXNUM_P(rel)) return LONG2FIX(-FIX2LONG(rel)); return rel; } else if (RB_FLOAT_TYPE_P(y)) { b = RFLOAT_VALUE(y); } else { if (isinf(a) && !UNDEF_P(i = rb_check_funcall(y, rb_intern("infinite?"), 0, 0))) { 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); }

Returns true if other has the same value as self, false otherwise:

2.0 == 2 # => true 2.0 == 2.0 # => true 2.0 == Rational(2, 1) # => true 2.0 == Complex(2, 0) # => true 

Float::NAN == Float::NAN returns an implementation-dependent value.

Related: Float#eql? (requires other to be a Float).

VALUE rb_float_equal(VALUE x, VALUE y) { volatile double a, b; if (RB_INTEGER_TYPE_P(y)) { return rb_integer_float_eq(y, x); } else if (RB_FLOAT_TYPE_P(y)) { b = RFLOAT_VALUE(y); #if MSC_VERSION_BEFORE(1300) if (isnan(b)) return Qfalse; #endif } else { return num_equal(x, y); } a = RFLOAT_VALUE(x); #if MSC_VERSION_BEFORE(1300) if (isnan(a)) return Qfalse; #endif return RBOOL(a == b); }

Returns true if self is numerically greater than other:

2.0 > 1 # => true 2.0 > 1.0 # => true 2.0 > Rational(1, 2) # => true 2.0 > 2.0 # => false 

Float::NAN > Float::NAN returns an implementation-dependent value.

VALUE rb_float_gt(VALUE x, VALUE y) { double a, b; a = RFLOAT_VALUE(x); if (RB_INTEGER_TYPE_P(y)) { VALUE rel = rb_integer_float_cmp(y, x); if (FIXNUM_P(rel)) return RBOOL(-FIX2LONG(rel) > 0); return Qfalse; } else if (RB_FLOAT_TYPE_P(y)) { 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 RBOOL(a > b); }

Returns true if self is numerically greater than or equal to other:

2.0 >= 1 # => true 2.0 >= 1.0 # => true 2.0 >= Rational(1, 2) # => true 2.0 >= 2.0 # => true 2.0 >= 2.1 # => false 

Float::NAN >= Float::NAN returns an implementation-dependent value.

static VALUE flo_ge(VALUE x, VALUE y) { double a, b; a = RFLOAT_VALUE(x); if (RB_TYPE_P(y, T_FIXNUM) || RB_BIGNUM_TYPE_P(y)) { VALUE rel = rb_integer_float_cmp(y, x); if (FIXNUM_P(rel)) return RBOOL(-FIX2LONG(rel) >= 0); return Qfalse; } else if (RB_FLOAT_TYPE_P(y)) { 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 RBOOL(a >= b); }

Returns the absolute value of self:

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

# File ruby_3_4_1/numeric.rb, line 368 def abs Primitive.attr! :leaf Primitive.cexpr! 'rb_float_abs(self)' end

Returns 0 if self is positive, Math::PI otherwise.

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); }

Returns a numeric that is a “ceiling” value for self, as specified by the given ndigits, which must be an integer-convertible object.

When ndigits is positive, returns a Float with ndigits decimal digits after the decimal point (as available, but no fewer than 1):

f = 12345.6789 f.ceil(1) # => 12345.7 f.ceil(3) # => 12345.679 f.ceil(30) # => 12345.6789 f = -12345.6789 f.ceil(1) # => -12345.6 f.ceil(3) # => -12345.678 f.ceil(30) # => -12345.6789 f = 0.0 f.ceil(1) # => 0.0 f.ceil(100) # => 0.0 

When ndigits is non-positive, returns an Integer based on a computed granularity:

• The granularity is 10 ** ndigits.abs.

• The returned value is the largest multiple of the granularity that is less than or equal to self.

Examples with positive self:

Examples with negative self:

When self is zero and ndigits is non-positive, returns Integer zero:

0.0.ceil(0) # => 0 0.0.ceil(-1) # => 0 0.0.ceil(-2) # => 0 

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

(2.1 / 0.7).ceil #=> 4 # Not 3 (because 2.1 / 0.7 # => 3.0000000000000004, not 3.0) 

Related: Float#floor.

static VALUE flo_ceil(int argc, VALUE *argv, VALUE num) { int ndigits = flo_ndigits(argc, argv); return rb_float_ceil(num, ndigits); }

Returns a 2-element array containing other converted to a Float and self:

f = 3.14 # => 3.14 f.coerce(2) # => [2.0, 3.14] f.coerce(2.0) # => [2.0, 3.14] f.coerce(Rational(1, 2)) # => [0.5, 3.14] f.coerce(Complex(1, 0)) # => [1.0, 3.14] 

Raises an exception if a type conversion fails.

static VALUE flo_coerce(VALUE x, VALUE y) { return rb_assoc_new(rb_Float(y), x); }

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

See also Float#numerator.

VALUE rb_float_denominator(VALUE self) { double d = RFLOAT_VALUE(self); VALUE r; if (!isfinite(d)) return INT2FIX(1); r = float_to_r(self); return nurat_denominator(r); }

Returns a 2-element array [q, r], where

q = (self/other).floor # Quotient r = self % other # Remainder 

Examples:

11.0.divmod(4) # => [2, 3.0] 11.0.divmod(-4) # => [-3, -1.0] -11.0.divmod(4) # => [-3, 1.0] -11.0.divmod(-4) # => [2, -3.0] 12.0.divmod(4) # => [3, 0.0] 12.0.divmod(-4) # => [-3, 0.0] -12.0.divmod(4) # => [-3, -0.0] -12.0.divmod(-4) # => [3, -0.0] 13.0.divmod(4.0) # => [3, 1.0] 13.0.divmod(Rational(4, 1)) # => [3, 1.0] 

static VALUE flo_divmod(VALUE x, VALUE y) { double fy, div, mod; volatile VALUE a, b; if (FIXNUM_P(y)) { fy = (double)FIX2LONG(y); } else if (RB_BIGNUM_TYPE_P(y)) { fy = rb_big2dbl(y); } else if (RB_FLOAT_TYPE_P(y)) { 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 true if other is a Float with the same value as self, false otherwise:

2.0.eql?(2.0) # => true 2.0.eql?(1.0) # => false 2.0.eql?(1) # => false 2.0.eql?(Rational(2, 1)) # => false 2.0.eql?(Complex(2, 0)) # => false 

Float::NAN.eql?(Float::NAN) returns an implementation-dependent value.

Related: Float#== (performs type conversions).

VALUE rb_float_eql(VALUE x, VALUE y) { if (RB_FLOAT_TYPE_P(y)) { double a = RFLOAT_VALUE(x); double b = RFLOAT_VALUE(y); #if MSC_VERSION_BEFORE(1300) if (isnan(a) || isnan(b)) return Qfalse; #endif return RBOOL(a == b); } return Qfalse; }

Returns true if self is not Infinity, -Infinity, or NaN, false otherwise:

f = 2.0 # => 2.0 f.finite? # => true f = 1.0/0.0 # => Infinity f.finite? # => false f = -1.0/0.0 # => -Infinity f.finite? # => false f = 0.0/0.0 # => NaN f.finite? # => false 

VALUE rb_flo_is_finite_p(VALUE num) { double value = RFLOAT_VALUE(num); return RBOOL(isfinite(value)); }

Returns a float or integer that is a “floor” value for self, as specified by ndigits, which must be an integer-convertible object.

When self is zero, returns a zero value: a float if ndigits is positive, an integer otherwise:

f = 0.0 # => 0.0 f.floor(20) # => 0.0 f.floor(0) # => 0 f.floor(-20) # => 0 

When self is non-zero and ndigits is positive, returns a float with ndigits digits after the decimal point (as available):

f = 12345.6789 f.floor(1) # => 12345.6 f.floor(3) # => 12345.678 f.floor(30) # => 12345.6789 f = -12345.6789 f.floor(1) # => -12345.7 f.floor(3) # => -12345.679 f.floor(30) # => -12345.6789 

When self is non-zero and ndigits is non-positive, returns an integer value based on a computed granularity:

• The granularity is 10 ** ndigits.abs.

• The returned value is the largest multiple of the granularity that is less than or equal to self.

Examples with positive self:

Examples with negative self:

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

(0.3 / 0.1).floor # => 2 # Not 3, (because (0.3 / 0.1) # => 2.9999999999999996, not 3.0) 

Related: Float#ceil.

static VALUE flo_floor(int argc, VALUE *argv, VALUE num) { int ndigits = flo_ndigits(argc, argv); return rb_float_floor(num, ndigits); }

Returns the integer hash value for self.

See also Object#hash.

static VALUE flo_hash(VALUE num) { return rb_dbl_hash(RFLOAT_VALUE(num)); }

Returns:

• 1, if self is Infinity.

• -1 if self is -Infinity.

• nil, otherwise.

Examples:

f = 1.0/0.0 # => Infinity f.infinite? # => 1 f = -1.0/0.0 # => -Infinity f.infinite? # => -1 f = 1.0 # => 1.0 f.infinite? # => nil f = 0.0/0.0 # => NaN f.infinite? # => nil 

VALUE rb_flo_is_infinite_p(VALUE num) { double value = RFLOAT_VALUE(num); if (isinf(value)) { return INT2FIX( value < 0 ? -1 : 1 ); } return Qnil; }

Returns true if self is a NaN, false otherwise.

f = -1.0 #=> -1.0 f.nan? #=> false f = 0.0/0.0 #=> NaN f.nan? #=> true 

static VALUE flo_is_nan_p(VALUE num) { double value = RFLOAT_VALUE(num); return RBOOL(isnan(value)); }

Returns true if self is less than 0, false otherwise.

# File ruby_3_4_1/numeric.rb, line 407 def negative? Primitive.attr! :leaf Primitive.cexpr! 'RBOOL(RFLOAT_VALUE(self) < 0.0)' end

Returns the next-larger representable Float.

These examples show the internally stored values (64-bit hexadecimal) for each Float f and for the corresponding f.next_float:

f = 0.0 # 0x0000000000000000 f.next_float # 0x0000000000000001 f = 0.01 # 0x3f847ae147ae147b f.next_float # 0x3f847ae147ae147c 

In the remaining examples here, the output is shown in the usual way (result to_s):

0.01.next_float # => 0.010000000000000002 1.0.next_float # => 1.0000000000000002 100.0.next_float # => 100.00000000000001 f = 0.01 (0..3).each_with_index {|i| printf "%2d %-20a %s\n", i, f, f.to_s; f = f.next_float } 

Output:

 0 0x1.47ae147ae147bp-7 0.01 1 0x1.47ae147ae147cp-7 0.010000000000000002 2 0x1.47ae147ae147dp-7 0.010000000000000004 3 0x1.47ae147ae147ep-7 0.010000000000000005 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.

Related: Float#prev_float

static VALUE flo_next_float(VALUE vx) { return flo_nextafter(vx, HUGE_VAL); }

Returns the numerator. The result is machine dependent.

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

See also Float#denominator.

VALUE rb_float_numerator(VALUE self) { double d = RFLOAT_VALUE(self); VALUE r; if (!isfinite(d)) return self; r = float_to_r(self); return nurat_numerator(r); }

Returns true if self is greater than 0, false otherwise.

# File ruby_3_4_1/numeric.rb, line 398 def positive? Primitive.attr! :leaf Primitive.cexpr! 'RBOOL(RFLOAT_VALUE(self) > 0.0)' end

Returns the next-smaller representable Float.

These examples show the internally stored values (64-bit hexadecimal) for each Float f and for the corresponding f.pev_float:

f = 5e-324 # 0x0000000000000001 f.prev_float # 0x0000000000000000 f = 0.01 # 0x3f847ae147ae147b f.prev_float # 0x3f847ae147ae147a 

In the remaining examples here, the output is shown in the usual way (result to_s):

0.01.prev_float # => 0.009999999999999998 1.0.prev_float # => 0.9999999999999999 100.0.prev_float # => 99.99999999999999 f = 0.01 (0..3).each_with_index {|i| printf "%2d %-20a %s\n", i, f, f.to_s; f = f.prev_float } 

Output:

0 0x1.47ae147ae147bp-7 0.01 1 0x1.47ae147ae147ap-7 0.009999999999999998 2 0x1.47ae147ae1479p-7 0.009999999999999997 3 0x1.47ae147ae1478p-7 0.009999999999999995

Related: Float#next_float.

static VALUE flo_prev_float(VALUE vx) { return flo_nextafter(vx, -HUGE_VAL); }

Returns the quotient from dividing self by other:

f = 3.14 f.quo(2) # => 1.57 f.quo(-2) # => -1.57 f.quo(Rational(2, 1)) # => 1.57 f.quo(Complex(2, 0)) # => (1.57+0.0i) 

static VALUE flo_quo(VALUE x, VALUE y) { return num_funcall1(x, '/', y); }

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) 

See also Float#to_r.

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; }

Returns self rounded to the nearest value with a precision of ndigits decimal digits.

When ndigits is non-negative, returns a float with ndigits after the decimal point (as available):

f = 12345.6789 f.round(1) # => 12345.7 f.round(3) # => 12345.679 f = -12345.6789 f.round(1) # => -12345.7 f.round(3) # => -12345.679 

When ndigits is negative, returns an integer with at least ndigits.abs trailing zeros:

f = 12345.6789 f.round(0) # => 12346 f.round(-3) # => 12000 f = -12345.6789 f.round(0) # => -12346 f.round(-3) # => -12000 

If keyword argument half is given, and self is equidistant from the two candidate values, the rounding is according to the given half value:

• :up or nil: round away from zero:

  2.5.round(half: :up) # => 3 3.5.round(half: :up) # => 4 (-2.5).round(half: :up) # => -3 

• :down: round toward zero:

  2.5.round(half: :down) # => 2 3.5.round(half: :down) # => 3 (-2.5).round(half: :down) # => -2 

• :even: round toward the candidate whose last nonzero digit is even:

  2.5.round(half: :even) # => 2 3.5.round(half: :even) # => 4 (-2.5).round(half: :even) # => -2 

Raises and exception if the value for half is invalid.

Related: Float#truncate.

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); if (ndigits > 14) { /* In this case, pow(10, ndigits) may not be accurate. */ return rb_flo_round_by_rational(argc, argv, num); } f = pow(10, ndigits); x = ROUND_CALL(mode, round, (number, f)); return DBL2NUM(x / f); } return num; }

Returns self (which is already a Float).

# File ruby_3_4_1/numeric.rb, line 355 def to_f self end

Returns self truncated to an Integer.

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

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

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

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); }

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 

See also Float#rationalize.

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 }

Returns a string containing a representation of self; depending of the value of self, the string representation may contain:

• A fixed-point number.

  3.14.to_s # => "3.14" 

• A number in “scientific notation” (containing an exponent).

  (10.1**50).to_s # => "1.644631821843879e+50" 

• ‘Infinity’.

  (10.1**500).to_s # => "Infinity" 

• ‘-Infinity’.

  (-10.1**500).to_s # => "-Infinity" 

• ‘NaN’ (indicating not-a-number).

  (0.0/0.0).to_s # => "NaN" 

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 + roomof(decimal_mant, 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); free(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; }

Returns self truncated (toward zero) to a precision of ndigits decimal digits.

When ndigits is positive, returns a float with ndigits digits after the decimal point (as available):

f = 12345.6789 f.truncate(1) # => 12345.6 f.truncate(3) # => 12345.678 f = -12345.6789 f.truncate(1) # => -12345.6 f.truncate(3) # => -12345.678 

When ndigits is negative, returns an integer with at least ndigits.abs trailing zeros:

f = 12345.6789 f.truncate(0) # => 12345 f.truncate(-3) # => 12000 f = -12345.6789 f.truncate(0) # => -12345 f.truncate(-3) # => -12000 

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

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

Related: Float#round.

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); }

Returns true if self is 0.0, false otherwise.

# File ruby_3_4_1/numeric.rb, line 389 def zero? Primitive.attr! :leaf Primitive.cexpr! 'RBOOL(FLOAT_ZERO_P(self))' end