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:
The minimum number of significant decimal digits in a double-precision floating point.
Usually defaults to 15.
The difference between 1 and the smallest double-precision floating point number greater than 1.
Usually defaults to 2.2204460492503131e-16.
An expression representing positive infinity.
The number of base digits for the double data type.
Usually defaults to 53.
The largest possible integer in a double-precision floating point number.
Usually defaults to 1.7976931348623157e+308.
The largest positive exponent in a double-precision floating point where 10 raised to this power minus 1.
Usually defaults to 308.
The largest possible exponent value in a double-precision floating point.
Usually defaults to 1024.
The smallest positive normalized number in a double-precision floating point.
Usually defaults to 2.2250738585072014e-308.
If the platform supports denormalized numbers, there are numbers between zero and Float::MIN. 0.0.next_float returns the smallest positive floating point number including denormalized numbers.
The smallest negative exponent in a double-precision floating point where 10 raised to this power minus 1.
Usually defaults to -307.
The smallest possible exponent value in a double-precision floating point.
Usually defaults to -1021.
An expression representing a value which is "not a number".
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.
Represents the rounding mode for floating point addition.
Usually defaults to 1, rounding to the nearest number.
Other modes include:
Indeterminable
Rounding towards zero
Rounding to the nearest number
Rounding towards positive infinity
Rounding towards negative infinity
Returns the modulo after division of float by other.
6543.21.modulo(137) #=> 104.21000000000004 6543.21.modulo(137.24) #=> 92.92999999999961
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));
}
Returns a new Float which is the product of float and other.
static VALUE
flo_mul(VALUE x, VALUE y)
{
if (RB_TYPE_P(y, T_FIXNUM)) {
return DBL2NUM(RFLOAT_VALUE(x) * (double)FIX2LONG(y));
}
else if (RB_TYPE_P(y, T_BIGNUM)) {
return DBL2NUM(RFLOAT_VALUE(x) * rb_big2dbl(y));
}
else if (RB_TYPE_P(y, T_FLOAT)) {
return DBL2NUM(RFLOAT_VALUE(x) * RFLOAT_VALUE(y));
}
else {
return rb_num_coerce_bin(x, y, '*');
}
}
Raises float to the power of other.
2.0**3 #=> 8.0
VALUE
rb_float_pow(VALUE x, VALUE y)
{
double dx, dy;
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 num_funcall1(rb_complex_raw1(x), idPow, y);
}
else {
return rb_num_coerce_bin(x, y, idPow);
}
return DBL2NUM(pow(dx, dy));
}
Returns a new Float which is the sum of float and other.
static VALUE
flo_plus(VALUE x, VALUE y)
{
if (RB_TYPE_P(y, T_FIXNUM)) {
return DBL2NUM(RFLOAT_VALUE(x) + (double)FIX2LONG(y));
}
else if (RB_TYPE_P(y, T_BIGNUM)) {
return DBL2NUM(RFLOAT_VALUE(x) + rb_big2dbl(y));
}
else if (RB_TYPE_P(y, T_FLOAT)) {
return DBL2NUM(RFLOAT_VALUE(x) + RFLOAT_VALUE(y));
}
else {
return rb_num_coerce_bin(x, y, '+');
}
}
Returns a new Float which is the difference of float and other.
static VALUE
flo_minus(VALUE x, VALUE y)
{
if (RB_TYPE_P(y, T_FIXNUM)) {
return DBL2NUM(RFLOAT_VALUE(x) - (double)FIX2LONG(y));
}
else if (RB_TYPE_P(y, T_BIGNUM)) {
return DBL2NUM(RFLOAT_VALUE(x) - rb_big2dbl(y));
}
else if (RB_TYPE_P(y, T_FLOAT)) {
return DBL2NUM(RFLOAT_VALUE(x) - RFLOAT_VALUE(y));
}
else {
return rb_num_coerce_bin(x, y, '-');
}
}
Returns float, negated.
VALUE
rb_float_uminus(VALUE flt)
{
return DBL2NUM(-RFLOAT_VALUE(flt));
}
Returns a new Float which is the result of dividing float by other.
static VALUE
flo_div(VALUE x, VALUE y)
{
long f_y;
double d;
if (RB_TYPE_P(y, T_FIXNUM)) {
f_y = FIX2LONG(y);
return DBL2NUM(RFLOAT_VALUE(x) / (double)f_y);
}
else if (RB_TYPE_P(y, T_BIGNUM)) {
d = rb_big2dbl(y);
return DBL2NUM(RFLOAT_VALUE(x) / d);
}
else if (RB_TYPE_P(y, T_FLOAT)) {
return DBL2NUM(RFLOAT_VALUE(x) / RFLOAT_VALUE(y));
}
else {
return rb_num_coerce_bin(x, y, '/');
}
}
Returns true if float is less than real.
The result of NaN < NaN is undefined, so an implementation-dependent value is returned.
static VALUE
flo_lt(VALUE x, VALUE y)
{
double a, b;
a = RFLOAT_VALUE(x);
if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) {
VALUE rel = rb_integer_float_cmp(y, x);
if (FIXNUM_P(rel))
return -FIX2INT(rel) < 0 ? Qtrue : Qfalse;
return Qfalse;
}
else if (RB_TYPE_P(y, T_FLOAT)) {
b = RFLOAT_VALUE(y);
#if defined(_MSC_VER) && _MSC_VER < 1300
if (isnan(b)) return Qfalse;
#endif
}
else {
return rb_num_coerce_relop(x, y, '<');
}
#if defined(_MSC_VER) && _MSC_VER < 1300
if (isnan(a)) return Qfalse;
#endif
return (a < b)?Qtrue:Qfalse;
}
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.
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, idLE);
}
#if defined(_MSC_VER) && _MSC_VER < 1300
if (isnan(a)) return Qfalse;
#endif
return (a <= b)?Qtrue:Qfalse;
}
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.
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);
}
Returns true only if obj has the same value as float. Contrast this with Float#eql?, which requires obj to be a Float.
1.0 == 1 #=> true
The result of NaN == NaN is undefined, so an implementation-dependent value is returned.
VALUE
rb_float_equal(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;
}
Returns true only if obj has the same value as float. Contrast this with Float#eql?, which requires obj to be a Float.
1.0 == 1 #=> true
The result of NaN == NaN is undefined, so an implementation-dependent value is returned.
VALUE
rb_float_equal(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;
}
Returns true if float is greater than real.
The result of NaN > NaN is undefined, so an implementation-dependent value is returned.
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 -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;
}
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.
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, idGE);
}
#if defined(_MSC_VER) && _MSC_VER < 1300
if (isnan(a)) return Qfalse;
#endif
return (a >= b)?Qtrue:Qfalse;
}
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.
VALUE
rb_float_abs(VALUE flt)
{
double val = fabs(RFLOAT_VALUE(flt));
return DBL2NUM(val);
}
Returns 0 if the value is positive, 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 0 if the value is positive, 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 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 (!)
static VALUE
flo_ceil(int argc, VALUE *argv, VALUE num)
{
double number, f;
int ndigits = 0;
if (rb_check_arity(argc, 0, 1)) {
ndigits = NUM2INT(argv[0]);
}
number = RFLOAT_VALUE(num);
if (number == 0.0) {
return ndigits > 0 ? DBL2NUM(number) : INT2FIX(0);
}
if (ndigits > 0) {
int binexp;
frexp(number, &binexp);
if (float_round_overflow(ndigits, binexp)) return num;
if (number < 0.0 && float_round_underflow(ndigits, binexp))
return DBL2NUM(0.0);
f = pow(10, ndigits);
f = ceil(number * f) / f;
return DBL2NUM(f);
}
else {
num = dbl2ival(ceil(number));
if (ndigits < 0) num = rb_int_ceil(num, ndigits);
return num;
}
}
Returns the denominator (always positive). The result is machine dependent.
See also Float#numerator.
static VALUE
float_denominator(VALUE self)
{
double d = RFLOAT_VALUE(self);
VALUE r;
if (isinf(d) || isnan(d))
return INT2FIX(1);
r = float_to_r(self);
if (canonicalization && k_integer_p(r)) {
return ONE;
}
return nurat_denominator(r);
}
See Numeric#divmod.
42.0.divmod(6) #=> [7, 0.0] 42.0.divmod(5) #=> [8, 2.0]
static VALUE
flo_divmod(VALUE x, VALUE y)
{
double fy, div, mod;
volatile VALUE a, b;
if (RB_TYPE_P(y, T_FIXNUM)) {
fy = (double)FIX2LONG(y);
}
else if (RB_TYPE_P(y, T_BIGNUM)) {
fy = rb_big2dbl(y);
}
else if (RB_TYPE_P(y, T_FLOAT)) {
fy = RFLOAT_VALUE(y);
}
else {
return rb_num_coerce_bin(x, y, id_divmod);
}
flodivmod(RFLOAT_VALUE(x), fy, &div, &mod);
a = dbl2ival(div);
b = DBL2NUM(mod);
return rb_assoc_new(a, b);
}
Returns true only if obj is a Float with the same value as float. Contrast this with Float#==, which performs type conversions.
1.0.eql?(1) #=> false
The result of NaN.eql?(NaN) is undefined, so an implementation-dependent value is returned.
VALUE
rb_float_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;
}
Returns float / numeric, same as Float#/.
static VALUE
flo_quo(VALUE x, VALUE y)
{
return num_funcall1(x, '/', y);
}
Returns true if float is a valid IEEE floating point number, i.e. it is not infinite and Float#nan? is false.
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;
}
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 (!)
static VALUE
flo_floor(int argc, VALUE *argv, VALUE num)
{
double number, f;
int ndigits = 0;
if (rb_check_arity(argc, 0, 1)) {
ndigits = NUM2INT(argv[0]);
}
number = RFLOAT_VALUE(num);
if (number == 0.0) {
return ndigits > 0 ? DBL2NUM(number) : INT2FIX(0);
}
if (ndigits > 0) {
int binexp;
frexp(number, &binexp);
if (float_round_overflow(ndigits, binexp)) return num;
if (number > 0.0 && float_round_underflow(ndigits, binexp))
return DBL2NUM(0.0);
f = pow(10, ndigits);
f = floor(number * f) / f;
return DBL2NUM(f);
}
else {
num = dbl2ival(floor(number));
if (ndigits < 0) num = rb_int_floor(num, ndigits);
return num;
}
}
Returns a hash code for this float.
See also Object#hash.
static VALUE
flo_hash(VALUE num)
{
return rb_dbl_hash(RFLOAT_VALUE(num));
}
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
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 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.
VALUE
rb_float_abs(VALUE flt)
{
double val = fabs(RFLOAT_VALUE(flt));
return DBL2NUM(val);
}
Returns the modulo after division of float by other.
6543.21.modulo(137) #=> 104.21000000000004 6543.21.modulo(137.24) #=> 92.92999999999961
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));
}
Returns true if float is an invalid IEEE floating point number.
a = -1.0 #=> -1.0 a.nan? #=> false a = 0.0/0.0 #=> NaN a.nan? #=> true
static VALUE
flo_is_nan_p(VALUE num)
{
double value = RFLOAT_VALUE(num);
return isnan(value) ? Qtrue : Qfalse;
}
Returns true if float is less than 0.
static VALUE
flo_negative_p(VALUE num)
{
double f = RFLOAT_VALUE(num);
return f < 0.0 ? Qtrue : Qfalse;
}
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.
static VALUE
flo_next_float(VALUE vx)
{
double x, y;
x = NUM2DBL(vx);
y = nextafter(x, INFINITY);
return DBL2NUM(y);
}
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.
static VALUE
float_numerator(VALUE self)
{
double d = RFLOAT_VALUE(self);
VALUE r;
if (isinf(d) || isnan(d))
return self;
r = float_to_r(self);
if (canonicalization && k_integer_p(r)) {
return r;
}
return nurat_numerator(r);
}
Returns 0 if the value is positive, 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 true if float is greater than 0.
static VALUE
flo_positive_p(VALUE num)
{
double f = RFLOAT_VALUE(num);
return f > 0.0 ? Qtrue : Qfalse;
}
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
static VALUE
flo_prev_float(VALUE vx)
{
double x, y;
x = NUM2DBL(vx);
y = nextafter(x, -INFINITY);
return DBL2NUM(y);
}
Returns float / numeric, same as Float#/.
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)
{
VALUE e;
double d = RFLOAT_VALUE(self);
if (d < 0.0)
return rb_rational_uminus(float_rationalize(argc, argv, DBL2NUM(-d)));
rb_scan_args(argc, argv, "01", &e);
if (argc != 0) {
return rb_flt_rationalize_with_prec(self, e);
}
else {
return rb_flt_rationalize(self);
}
}
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
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;
}
Since float is already a Float, returns self.
static VALUE
flo_to_f(VALUE num)
{
return num;
}
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 (!)
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 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 (!)
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, n;
float_decode_internal(self, &f, &n);
#if FLT_RADIX == 2
{
long ln = FIX2LONG(n);
if (ln == 0)
return rb_rational_new1(f);
if (ln > 0)
return rb_rational_new1(rb_int_lshift(f, n));
ln = -ln;
return rb_rational_new2(f, rb_int_lshift(ONE, INT2FIX(ln)));
}
#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. As well as a fixed or exponential form of the float, the call may return NaN, Infinity, and -Infinity.
static VALUE
flo_to_s(VALUE flt)
{
enum {decimal_mant = DBL_MANT_DIG-DBL_DIG};
enum {float_dig = DBL_DIG+1};
char buf[float_dig + (decimal_mant + CHAR_BIT - 1) / CHAR_BIT + 10];
double value = RFLOAT_VALUE(flt);
VALUE s;
char *p, *e;
int sign, decpt, digs;
if (isinf(value)) {
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 {
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 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 (!)
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 float is 0.0.
static VALUE
flo_zero_p(VALUE num)
{
if (RFLOAT_VALUE(num) == 0.0) {
return Qtrue;
}
return Qfalse;
}