is the absolute value of x, that is, 
if the sign of x is negative.
is the ceiling of x, the smallest integral value no less than x.
is the floor of x, the largest integral value no greater than x.
Abs returns
AddHalfTruncate returns
AddHalfTruncatetoLong returns the value
Annuity returns the value of the financial formula
Annuity raises invalid for rates less than -1. The case
ArcCos returns the inverse cosine in radians of its argument x. ArcCos raises invalid for
ArcCosh returns the inverse hyperbolic cosine of its argument x. ArcCosh raises invalid for
ArcSin returns the inverse sine in radians of its argument x. ArcSin raises invalid for
ArcSinh returns the inverse hyperbolic sine of its argument x. It raises inexact for all finite x except zero.
ArcTan returns the inverse tangent in radians of its argument x. It raises inexact for all x except zero.
When called as ArcTan(y, x), ArcTan returns the inverse tangent of
ArcTanh returns the hyperbolic arctangent of its argument x. ArcTanh raises invalid for
Ceiling returns
Compound returns the value of the financial formula
Compound raises invalid for
CopySign, called as CopySign(x, y), returns the floating-point value whose sign is that of y and whose exponent and significand are those of x. It raises no exceptions.
Cos returns the cosine of its argument x in radians. Cos raises inexact for all finite arguments except zero. It is periodic with period
Cosh returns the hyperbolic cosine of its argument x. Cosh is inexact for all finite arguments except zero.
Erf returns
Erfc returns
Exp returns
Exp2 returns
ExpMinus1 returns
Floor returns
FPClassify returns an element of the enumerated type EFPNumberKind indicating the nature of its argument x: kFPNaN, kFPInfinite, kFPNormal, kFPSubnormal, or kFPZero.
Gamma returns
Hash returns a long hash value corresponding to its argument x. Hash supports the use of tables of floating-point values.
Hypotenuse, called as Hypotenuse(x, y), returns
IsFinite returns true when its argument x is finite, that is, x is zero, subnormal, or normal. It returns false when x is infinite or a NaN. It raises no exceptions.
IsGreater, called as IsGreater(x, y), returns true when
IsGreaterEqual, called as IsGreaterEqual(x, y), returns true when
IsInfinite returns true when its argument x is
IsLess, called as IsLess(x, y), returns true when
IsLessEqual, called as IsLessEqual(x, y), returns true when
IsLessGreater, called as IsLessGreater(x, y), returns true when
IsNaN returns true when its argument x is a NaN. It returns false when x is zero, subnormal, normal, or infinite. It raises no exceptions.
IsNormal returns true when its argument x is normal. It returns false when x is zero, subnormal, infinite, or a NaN. It raises no exceptions.
IsSignNegative returns true when the sign bit of its argument x is 1; that is, x is
IsUnordered, called as IsUnordered(x, y), returns true when x and y are unordered and false when
kDegreesToRadians is the value
kDegreesToRadiansLongDouble is the value
kInfinity is the floating-point value
kNaN is a NaN.
kPi is the value
kPiLongDouble is the value
kRadiansToDegrees is the value
kRadiansToDegreesLongDouble is the value
Log returns the natural logarithm of its argument x. Log raises inexact for all positive, finite arguments except 1. Log raises invalid for all arguments
Log10 returns the logarithm base 10 of its argument x. Because
Log1Plus returns
Log2 returns the logarithm base 2 of its argument x. Because
Logb returns the integral value k such that
LogGamma returns
Max, called as Max(x, y), returns the larger of x and y. When one is a NaN, it returns the other. When both are NaNs it returns one of them. Max raises no flags.
Min, called as Min(x, y), returns the smaller of x and y. When one is a NaN, it returns the other. When both are NaNs it returns one of them. Min raises no flags.
NaN returns a NaN whose significand depends in a platform-dependent way on its TText argument.
NearbyInt returns the integral value nearest its argument x, according to the current rounding mode:
NextAfter, called as NextAfter(x, y), returns, in the format of x, the number adjacent to x toward y. When
NextDouble is a variant of NextAfter in which both arguments are of type double.
NextFloat is a variant of NextAfter in which both arguments are of type float.
NextLongDouble is a variant of NextAfter in which both arguments are of type long double.
PositiveDifference, called as PositiveDifference(x, y), returns
Power, called as Power(x, y), returns
Remainder, called as Remainder(x, y), returns the exact difference
Called as Remainder(x, y, &q), Remainder returns its result as above along with several low-order bits of the quotient n through the reference argument q. These bits are useful for some forms of argument reduction. See the example "Sin(huge)" on page 228.
Rint is a pseudonym for RoundIEEE.
RintToLong is a pseudonym for RoundToLongIEEE.
Round is a pseudonym for AddHalfTruncate.
RoundIEEE is identical to NearbyInt, except that it raises inexact when its result differs from its argument x.
RoundToLong is a pseudonym for AddHalfTruncateToLong.
RoundToLongIEEE returns the integral value nearest its argument x, converted to a long, according to the current rounding mode:
Scalb, called as Scalb(x, n), returns
Sin returns the sine of its argument x in radians. Sin raises inexact for all finite arguments except zero. It is periodic with period
Sinh returns the hyperbolic sine of its argument x. Sinh raises inexact for all finite arguments except zero.
Square returns
SquareRoot returns
Tan returns the tangent of the radian measure of its argument x. It is periodic with period
Tanh returns the hyperbolic tangent of its argument x.
Truncate returns
, the absolute value of its argument, by forcing it to have a positive sign. It raises no exceptions.
, where s is the sign of the argument x. It raises inexact when its result differs from x.
, where s is the sign of the argument x, converted to a long. It raises inexact when its result differs from x because of rounding. It raises invalid when the mathematical result cannot be held exactly in the long format.
. It is called as Annuity(r, n), where r is the rate and n the number of periods. Annuity is robust and accurate over the full range of mathematically meaningful r and n, regardless of the financial interpretation.
depends on n:
Otherwise, 
for 
.
.
and raises divide-by-zero for 
.
, and, when 
, 
. Annuity raises inexact in all other cases. Annuity can raise overflow or underflow.
or 
. It raises inexact for all values except 1. ArcCos returns values between zero and 
.
. It raises inexact for finite x except 1. 
, but ArcCosh never overflows. Its value at the largest double number is
approximately 710.
or 
. It raises inexact for all values except zero and raises underflow for x near zero. ArcSin returns values between 
and 
.
and 
. ArcSinh raises underflow for x near 0.
and 
. ArcTan returns values between 
and 
. It raises underflow for x near 0.
, using the algebraic signs of the arguments to determine the quadrant of the return value. In this case, ArcTan returns results in the range 
to 
.
or 
. It raises inexact for all valid arguments except zero. 
and 
. Although ArcTanh is steeply sloped and asymptotic with the lines 
and 
, it never raises overflow. For example, ArcTanh(NextDouble(1.0, 0.0)) is less than 19.
, the smallest integral value no less than its argument x. It raises inexact when its result differs from x.
. It is called in the form Compound(r, n), where r is the rate and n the number of periods. Compound is robust and accurate over the full range of mathematically meaningful r and n, regardless of the financial interpretation.
. The case 
depends on n:
Otherwise, 
and raises divide-by-zero for 
.
.
for 
.
. 
. When 
and n is infinite, Compound raises invalid. Compound can raise inexact, underflow, or overflow.
, rounded to the precision of the computation. Cos raises invalid when x is infinite.
. Cosh raises overflow for finite values of large magnitude.
, the error function of its argument x. Erf raises inexact for all finite arguments except zero, where its value is zero. 
and 
. Erf raises underflow for x near zero.
, the complementary error function of its argument x. Erfc raises inexact for all finite arguments except zero, where its value is 1. 
and 
. Erfc raises underflow for x near 
.
, the exponential of its argument x. Exp is inexact for finite arguments other than zero. 
and 
. Exp raises overflow for large, positive, finite x and underflow for large, negative, finite x.
, two raised to the power of its argument x. Because 
, Exp2 shares the limiting properties of Exp. Exp2 is inexact for finite arguments other than zero (and, perhaps, integer values for which Exp2 neither underflows nor overflows). 
and 
. Exp2 raises overflow for large, positive, finite x and underflow for large, negative, finite x.
, given the argument x. While accurate for all arguments, ExpMinus1 avoids loss of accuracy when 
is nearly zero (and 
is nearly 1). ExpMinus1 is inexact for all finite arguments except zero. 
and 
. ExpMinus1 raises overflow for large, positive, finite x and underflow for x near zero.
, the greatest integral value less than or equal to its argument x. It raises inexact when its result differs from x.
, the gamma function applied to its argument x. Gamma raises inexact for all non-integral arguments. It raises invalid for non-positive integral arguments. 
for positive integral arguments, with 
defined to be 
. 
. Gamma can raise overflow.
, taking care to avoid spurious underflow and overflow. It can raise inexact, underflow, and overflow.
and false when 
or when x and y are unordered. IsGreater raises no exceptions.
and false when 
or when x and y are unordered. IsGreaterEqual raises no exceptions.
or 
. It returns false when x is zero, subnormal, normal, or a NaN. It raises no exceptions.
and false when 
or when x and y are unordered. IsLess raises no exceptions.
and false when 
or when x and y are unordered. IsLessEqual raises no exceptions.
or 
, and false when 
or when x and y are unordered. IsLessGreater raises no exceptions.
, 
, or x is a NaN with negative sign. It returns false when the sign bit of x is 0. It raises no exceptions.
or 
. IsUnordered raises no exceptions.
in the double_t format. When d is in units of degrees, 
has units of radians.
in the long double format.
.
in the double_t format.
in the long double format.
in the double_t format. When r is in units of radians, 
has units of degrees.
in the long double format.
. Although 
and 
, Log never underflows or overflows. Log(0) raises divide-by-zero.
, Log10 shares the computational properties of Log.
, given the argument x. While accurate for all values no less than 
, Log1Plus is devised to preserve accuracy when its argument is nearly zero--when explicitly performing the sum 
would sacrifice low-order bits of 
. Log1Plus raises inexact for all finite arguments greater than 
except 0. 
and raises divide-by-zero. 
. Log1Plus raises invalid for 
. Log1Plus raises underflow for x near zero.
, Log2 shares the computational properties of Log.
, for argument x. 
and raises divide-by-zero. 
.
, the log of the gamma function applied to its argument x. LogGamma raises inexact for all finite arguments. It raises divide-by-zero for non-positive integral arguments. Gamma can raise overflow; LogGamma cannot.
NearbyInt never raises a flag; it is the same as RoundIEEE except that RoundIEEE raises inexact when its result differs from x.
, where s is the sign of x
, return 
, return 
, NextAfter returns x. When x or y is a NaN, NextAfter returns one of the input NaNs. When x is finite but the result is infinite, NextAfter raises overflow and inexact. When the result is subnormal or zero, NextAfter raises underflow and inexact.
when 
and returns 
otherwise. It can raise inexact and overflow.
. When 
, Power raises invalid unless y is an integral value. It can raise inexact, underflow, overflow, and invalid.
, where n is the nearest mathematical integer to 
in the sense of rounding to nearest. Note that n can be huge--even thousands of bits wide--when x is much larger than y in magnitude. The result is no greater than 
in magnitude; when it is zero it has sign of x. Remainder raises invalid when y is zero or x is infinite. Remainder never raises inexact, underflow, or overflow.
RoundToLongIEEE raises inexact when its result differs from x. It raises invalid when the mathematical result cannot be held exactly in the long format.
, where s is the sign of x
, return 
, return 
. It avoids explicit computation of 
, and so avoids possible underflow or overflow in cases where the result is within range but 
isn't. Scalb can raise inexact, underflow, or overflow. Scalb and Logb are related as shown in "Manipulating numbers without arithmetic" on page 199: 
for finite, nonzero x.
. Sin raises invalid when x is infinite. Sin raises underflow for small x.
and 
. Sinh raises overflow for finite values of large magnitude. Sinh raises underflow for small x.
, the square of its argument x. It can raise inexact, underflow, or overflow.
, the square root of its argument x. It raises invalid for 
. It can raise inexact. 
.
. Tan raises invalid when x is infinite. Tan raises inexact for all finite, nonzero arguments, and raises underflow for values near zero.
and 
. It can raise inexact or underflow.
, where s is the sign of the argument x. It raises inexact when its result differs from x.
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