std.math

Contains the elementary mathematical functions (powers, roots, and trigonometric functions), and low-level floating-point operations. Mathematical special functions are available in std.mathspecial.


Category	Members
Constants	E PI PI_2 PI_4 M_1_PI M_2_PI M_2_SQRTPI LN10 LN2 LOG2 LOG2E LOG2T LOG10E SQRT2 SQRT1_2
Classics	abs fabs sqrt cbrt hypot poly nextPow2 truncPow2
Trigonometry	sin cos tan asin acos atan atan2 sinh cosh tanh asinh acosh atanh
Rounding	ceil floor round lround trunc rint lrint nearbyint rndtol quantize
Exponentiation & Logarithms	pow exp exp2 expm1 ldexp frexp log log2 log10 logb ilogb log1p scalbn
Modulus	fmod modf remainder
Floating-point operations	approxEqual feqrel fdim fmax fmin fma isClose nextDown nextUp nextafter NaN getNaNPayload cmp
Introspection	isFinite isIdentical isInfinity isNaN isNormal isSubnormal signbit sgn copysign isPowerOf2
Hardware Control	IeeeFlags FloatingPointControl

The functionality closely follows the IEEE754-2008 standard for floating-point arithmetic, including the use of camelCase names rather than C99-style lower case names. All of these functions behave correctly when presented with an infinity or NaN.

The following IEEE 'real' formats are currently supported:

64 bit Big-endian 'double' (eg PowerPC)
128 bit Big-endian 'quadruple' (eg SPARC)
64 bit Little-endian 'double' (eg x86-SSE2)
80 bit Little-endian, with implied bit 'real80' (eg x87, Itanium)
128 bit Little-endian 'quadruple' (not implemented on any known processor!)
Non-IEEE 128 bit Big-endian 'doubledouble' (eg PowerPC) has partial support

Unlike C, there is no global 'errno' variable. Consequently, almost all of these functions are pure nothrow.

Public Imports

std.meta public import std.meta : AliasSeq;

Members

Aliases

FP_ILOGB0 alias FP_ILOGB0 = core.stdc.math.FP_ILOGB0
FP_ILOGBNAN alias FP_ILOGBNAN = core.stdc.math.FP_ILOGBNAN: Special return values of ilogb.

Functions

NaN real NaN(ulong payload): Create a quiet NaN, storing an integer inside the payload.
abs auto abs(Num x): Calculates the absolute value of a number.
acos real acos(real x)
double acos(double x)
float acos(float x): Calculates the arc cosine of x, returning a value ranging from 0 to π.
acosh real acosh(real x)
double acosh(double x)
float acosh(float x): Calculates the inverse hyperbolic cosine of x.
approxEqual bool approxEqual(T value, U reference, V maxRelDiff, V maxAbsDiff): Computes whether a values is approximately equal to a reference value, admitting a maximum relative difference, and a maximum absolute difference.
asin real asin(real x)
double asin(double x)
float asin(float x): Calculates the arc sine of x, returning a value ranging from -π/2 to π/2.
asinh real asinh(real x)
double asinh(double x)
float asinh(float x): Calculates the inverse hyperbolic sine of x.
atan real atan(real x)
double atan(double x)
float atan(float x): Calculates the arc tangent of x, returning a value ranging from -π/2 to π/2.
atan2 real atan2(real y, real x)
double atan2(double y, double x)
float atan2(float y, float x): Calculates the arc tangent of y / x, returning a value ranging from -π to π.
atanh real atanh(real x)
double atanh(double x)
float atanh(float x): Calculates the inverse hyperbolic tangent of x, returning a value from ranging from -1 to 1.
cbrt real cbrt(real x): Calculates the cube root of x.
ceil float ceil(float x)
double ceil(double x): Returns the value of x rounded upward to the next integer (toward positive infinity).
ceil real ceil(real x): Returns the value of x rounded upward to the next integer (toward positive infinity).
cmp int cmp(const(T) x, const(T) y): Defines a total order on all floating-point numbers.
copysign R copysign(X to, R from)
copysign R copysign(R to, X from)
cos real cos(real x)
double cos(double x)
float cos(float x): Returns cosine of x. x is in radians.
cosh real cosh(real x)
double cosh(double x)
float cosh(float x): Calculates the hyperbolic cosine of x.
exp real exp(real x)
double exp(double x)
float exp(float x): Calculates e^x.
exp2 real exp2(real x)
double exp2(double x)
float exp2(float x): Calculates 2^x.
expm1 real expm1(real x)
double expm1(double x)
float expm1(float x): Calculates the value of the natural logarithm base (e) raised to the power of x, minus 1.
fabs float fabs(float f)
double fabs(double d): Returns |x|
fabs real fabs(real x): Returns |x|
fdim real fdim(real x, real y): Returns the positive difference between x and y.
feqrel int feqrel(X x, X y): To what precision is x equal to y?
floor float floor(float x)
double floor(double x): Returns the value of x rounded downward to the next integer (toward negative infinity).
floor real floor(real x): Returns the value of x rounded downward to the next integer (toward negative infinity).
fma real fma(real x, real y, real z): Returns (x * y) + z, rounding only once according to the current rounding mode.
fmax real fmax(real x, real y): Returns the larger of x and y.
fmin real fmin(real x, real y): Returns the smaller of x and y.
fmod real fmod(real x, real y): Calculates the remainder from the calculation x/y.
frexp T frexp(T value, int exp): Separate floating point value into significand and exponent.
getNaNPayload ulong getNaNPayload(real x): Extract an integral payload from a NaN.
hypot real hypot(real x, real y): Calculates the length of the hypotenuse of a right-angled triangle with sides of length x and y. The hypotenuse is the value of the square root of the sums of the squares of x and y:
ilogb int ilogb(T x): Extracts the exponent of x as a signed integral value.
ilogb int ilogb(T x): Extracts the exponent of x as a signed integral value.
isClose bool isClose(T lhs, U rhs, V maxRelDiff, V maxAbsDiff): Computes whether two values are approximately equal, admitting a maximum relative difference, and a maximum absolute difference.
isFinite bool isFinite(X x): Determines if x is finite.
isIdentical bool isIdentical(real x, real y): Is the binary representation of x identical to y?
isInfinity bool isInfinity(X x): Determines if x is ±∞.
isNaN bool isNaN(X x): Determines if x is NaN.
isNormal bool isNormal(X x): Determines if x is normalized.
isPowerOf2 bool isPowerOf2(X x): Check whether a number is an integer power of two.
isSubnormal bool isSubnormal(X x): Determines if x is subnormal.
ldexp real ldexp(real n, int exp)
double ldexp(double n, int exp)
float ldexp(float n, int exp): Compute n * 2^exp References: frexp
log real log(real x): Calculate the natural logarithm of x.
log10 real log10(real x): Calculate the base-10 logarithm of x.
log1p real log1p(real x): Calculates the natural logarithm of 1 + x.
log2 real log2(real x): Calculates the base-2 logarithm of x: log₂x
logb real logb(real x): Extracts the exponent of x as a signed integral value.
lrint long lrint(real x): Rounds x to the nearest integer value, using the current rounding mode.
lround long lround(real x): Return the value of x rounded to the nearest integer.
modf real modf(real x, real i): Breaks x into an integral part and a fractional part, each of which has the same sign as x. The integral part is stored in i.
nearbyint real nearbyint(real x): Rounds x to the nearest integer value, using the current rounding mode.
nextDown real nextDown(real x)
double nextDown(double x)
float nextDown(float x): Calculate the next smallest floating point value before x.
nextPow2 T nextPow2(T val): Gives the next power of two after val. T can be any built-in numerical type.
nextUp real nextUp(real x)
double nextUp(double x)
float nextUp(float x): Calculate the next largest floating point value after x.
nextafter T nextafter(T x, T y): Calculates the next representable value after x in the direction of y.
poly Unqual!(CommonType!(T1, T2)) poly(T1 x, T2[] A)
Unqual!(CommonType!(T1, T2)) poly(T1 x, T2[N] A): Evaluate polynomial A(x) = a₀ + a₁x + a₂x² + a₃x³; ...
pow Unqual!F pow(F x, G n): Compute the value of x ⁿ, where n is an integer
pow typeof(Unqual!(F).init * Unqual!(G).init) pow(F x, G n): Compute the power of two integral numbers.
pow real pow(I x, F y): Computes integer to floating point powers.
pow Unqual!(Largest!(F, G)) pow(F x, G y): Calculates x^y.
powmod Unqual!(Largest!(F, H)) powmod(F x, G n, H m): Computes the value of a positive integer x, raised to the power n, modulo m.
quantize Unqual!F quantize(F val, F unit): Round val to a multiple of unit. rfunc specifies the rounding function to use; by default this is rint, which uses the current rounding mode.
quantize Unqual!F quantize(F val, E exp)
Unqual!F quantize(F val): Round val to a multiple of pow(base, exp). rfunc specifies the rounding function to use; by default this is rint, which uses the current rounding mode.
remainder real remainder(real x, real y)
remquo real remquo(real x, real y, int n): Calculate the remainder x REM y, following IEC 60559.
resetIeeeFlags void resetIeeeFlags(): Set all of the floating-point status flags to false.
rint real rint(real x)
double rint(double x)
float rint(float x): Rounds x to the nearest integer value, using the current rounding mode.
rndtol long rndtol(float x)
long rndtol(double x): Returns x rounded to a long value using the current rounding mode. If the integer value of x is greater than long.max, the result is indeterminate.
rndtol long rndtol(real x): Returns x rounded to a long value using the current rounding mode. If the integer value of x is greater than long.max, the result is indeterminate.
rndtonl real rndtonl(real x): Deprecated. Please use round instead.
round auto round(real x): Return the value of x rounded to the nearest integer. If the fractional part of x is exactly 0.5, the return value is rounded away from zero.
scalbn real scalbn(real x, int n): Efficiently calculates x * 2ⁿ.
sgn F sgn(F x): Returns -1 if x < 0, x if x == 0, 1 if x > 0, and NaN if x==NaN.
signbit int signbit(X x): Return 1 if sign bit of e is set, 0 if not.
sin float sin(float x)
double sin(double x): Returns sine of x. x is in radians.
sin real sin(real x): Returns sine of x. x is in radians.
sinh float sinh(float x)
double sinh(double x): Calculates the hyperbolic sine of x.
sinh real sinh(real x): Calculates the hyperbolic sine of x.
sqrt real sqrt(real x)
double sqrt(double x): Compute square root of x.
sqrt float sqrt(float x): Compute square root of x.
tan float tan(float x)
double tan(double x): Returns tangent of x. x is in radians.
tan real tan(real x): Returns tangent of x. x is in radians.
tanh float tanh(float x)
double tanh(double x): Calculates the hyperbolic tangent of x.
tanh real tanh(real x): Calculates the hyperbolic tangent of x.
trunc real trunc(real x): Returns the integer portion of x, dropping the fractional portion. This is also known as "chop" rounding. pure on all platforms.
truncPow2 T truncPow2(T val): Gives the last power of two before val. $(T) can be any built-in numerical type.

Properties

ieeeFlags IeeeFlags ieeeFlags [@property getter]

Structs

FloatingPointControl struct FloatingPointControl: Control the Floating point hardware
IeeeFlags struct IeeeFlags: IEEE exception status flags ('sticky bits')

std.math

Public Imports

Members

Aliases

Functions

Properties

Structs

Meta

Source

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