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:
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
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.
The number of base digits for the double data type.
Usually defaults to 53.
The minimum number of significant decimal digits in a double-precision floating point.
Usually defaults to 15.
The smallest possible exponent value in a double-precision floating point.
Usually defaults to -1021.
The largest possible exponent value in a double-precision floating point.
Usually defaults to 1024.
The smallest negative exponent in a double-precision floating point where 10 raised to this power minus 1.
Usually defaults to -307.
The largest positive exponent in a double-precision floating point where 10 raised to this power minus 1.
Usually defaults to 308.
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 largest possible integer in a double-precision floating point number.
Usually defaults to 1.7976931348623157e+308.
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.
An expression representing a value which is “not a number”.
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 the modulo after division of float by other.
6543.21.modulo(137) #=> 104.21000000000004 6543.21.modulo(137.24) #=> 92.92999999999961
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, '*');
}
}
Returns a new Float which is the product of float and other.
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));
}
Raises float to the power of other.
2.0**3 #=> 8.0
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 sum 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 a new Float which is the difference of float and other.
VALUE
rb_float_uminus(VALUE flt)
{
return DBL2NUM(-RFLOAT_VALUE(flt));
}
Returns float, negated.
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 a new Float which is the result of dividing float by other.
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 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 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_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 -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.
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_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 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 true if float is greater than or equal to real.
The result of NaN >= NaN is undefined, so an implementation-dependent value is returned.
VALUE
rb_float_abs(VALUE flt)
{
double val = fabs(RFLOAT_VALUE(flt));
return DBL2NUM(val);
}
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.
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
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 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_coerce(VALUE x, VALUE y)
{
return rb_assoc_new(rb_Float(y), x);
}
# File tmp/rubies/ruby-2.5.9/lib/rexml/xpath_parser.rb, line 28
def dclone ; self ; end
provides a unified clone operation, for REXML::XPathParser to use across multiple Object types
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);
}
Returns the denominator (always positive). The result is machine dependent.
See also Float#numerator.
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);
}
See Numeric#divmod.
42.0.divmod(6) #=> [7, 0.0] 42.0.divmod(5) #=> [8, 2.0]
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;
}
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 true if float is a valid IEEE floating point number, i.e. it is not infinite and Float#nan? is false.
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 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_hash(VALUE num)
{
return rb_dbl_hash(RFLOAT_VALUE(num));
}
Returns a hash code for this float.
See also Object#hash.
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 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
static VALUE
flo_is_nan_p(VALUE num)
{
double value = RFLOAT_VALUE(num);
return isnan(value) ? Qtrue : Qfalse;
}
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_negative_p(VALUE num)
{
double f = RFLOAT_VALUE(num);
return f < 0.0 ? Qtrue : Qfalse;
}
Returns true if float is less than 0.
static VALUE
flo_next_float(VALUE vx)
{
double x, y;
x = NUM2DBL(vx);
y = nextafter(x, INFINITY);
return DBL2NUM(y);
}
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
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 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
flo_positive_p(VALUE num)
{
double f = RFLOAT_VALUE(num);
return f > 0.0 ? Qtrue : Qfalse;
}
Returns true if float is greater than 0.
static VALUE
flo_prev_float(VALUE vx)
{
double x, y;
x = NUM2DBL(vx);
y = nextafter(x, -INFINITY);
return DBL2NUM(y);
}
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_quo(VALUE x, VALUE y)
{
return num_funcall1(x, '/', y);
}
Returns float / numeric, same as Float#/.
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 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
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;
}
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
# File tmp/rubies/ruby-2.5.9/ext/bigdecimal/lib/bigdecimal/util.rb, line 45
def to_d(precision=nil)
BigDecimal(self, precision || Float::DIG)
end
Returns the value of float as a BigDecimal. The precision parameter is used to determine the number of significant digits for the result (the default is Float::DIG).
require 'bigdecimal' require 'bigdecimal/util' 0.5.to_d # => 0.5e0 1.234.to_d(2) # => 0.12e1
See also BigDecimal::new.
static VALUE
flo_to_f(VALUE num)
{
return num;
}
Since float is already a Float, returns self.
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);
}
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 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
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 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_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 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_zero_p(VALUE num)
{
if (RFLOAT_VALUE(num) == 0.0) {
return Qtrue;
}
return Qfalse;
}
Returns true if float is 0.0.