math

package module
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 Go to latest Published: Oct 10, 2016 License: BSD-3-Clause Imports: 1 Imported by: 1

README

math

This was not written by the Engo project. The original author decided to remove the original project from GitHub, we were given permission to reupload the code as long as we did not credit them.

This library is a copy of the standard math library but for float32 (more common in computer graphics and games. Most of the function are simply casting the arguments as float64 and forwarding to the original math library (something you would have to do anyway, but slowly we are translating the original function to the float32 version.
ALL tests are passing, meaning whatever program you we're running using the 64 bit version should still be correct using this library (using the IEEE floating point definition of "correct").
I only care about i386 and amd64, but if I receive pull request for other architecture I will merge them (I can't test it so please send me proof that all test pass and benchmark are better :)

rewriten functions

The benchmark is based on my macbook pro, with an i386 processor but a x86_64 operating system. benchmark may produce different results on different computers. However if you see an architecture for which casting to float64, calling the standard lib then casting back to flaot32 is faster then my implementation please tell me.
✓ = Test passing.
✗ = Not implemented yet.
? = Implemented but not tested.
* = has no ASM implementation.

Abs status lux math casting std math accel
function name ✓, ✗, ? or * benchmark for float32 using lux math package benchmark for casting a var to float64, doing the op then casting back benchmark for float64 using standard math package accelleration between casting and lux math
Abs status lux math casting std math accel
software ✓
amd64 ✓ 2.10 ns/op 2.37 ns/op 2.08 ns/op +13%
386 ✓ 2.02 ns/op 2.24 ns/op 2.02 ns/op +11%
Sqrt status lux math casting std math accel
software ✓
amd64 ✓ 2.33 ns/op 4.70 ns/op 0.33 ns/op +102%
386 ✓ 2.33 ns/op 5.14 ns/op 4.74 ns/op +121%
Acosh status lux math casting std math accel
software ✓ 43.5 ns/op 75.8 ns/op 40.3 ns/op +74%
Asinh status lux math casting std math accel
software ✓ 47.3 ns/op 81.3 ns/op 46.1 ns/op +72%
Gamma status lux math casting std math accel
software ✓ 25.1 ns/op 38.5 ns/op 24.0 ns/op +53%
template status lux math casting std math accel
software ✓ ns/op ns/op ns/op %
amd64 ✓ ns/op ns/op ns/op %
i386 ✓ ns/op ns/op ns/op %

Documentation

Overview

Package math provides basic constants and mathematical functions.

Index

Constants

View Source 
const (
	Totalsize    = 32
	MantissaSize = 23
	ExponentSize = 8
	Signsize     = 1

	Uvnan = 0x7FC00001

	Uvinf = 0x7F800000

	Uvneginf = 0xFF800000

	//mask for exponent part
	Mask = 0xFF

	Shift = Totalsize - ExponentSize - Signsize

	//bias = (2 ^ (exponentSize - 1)) - 1
	Bias = 127
)

Constants used for various operations.

View Source 
const (
	E   = 2.71828182845904523536028747135266249775724709369995957496696763 // A001113
	Pi  = 3.14159265358979323846264338327950288419716939937510582097494459 // A000796
	Phi = 1.61803398874989484820458683436563811772030917980576286213544862 // A001622

	Sqrt2   = 1.41421356237309504880168872420969807856967187537694807317667974 // A002193
	SqrtE   = 1.64872127070012814684865078781416357165377610071014801157507931 // A019774
	SqrtPi  = 1.77245385090551602729816748334114518279754945612238712821380779 // A002161
	SqrtPhi = 1.27201964951406896425242246173749149171560804184009624861664038 // A139339

	Ln2     = 0.693147180559945309417232121458176568075500134360255254120680009 // A002162
	Log2E   = 1 / Ln2
	Ln10    = 2.30258509299404568401799145468436420760110148862877297603332790 // A002392
	Log10E  = 1 / Ln10
	Log10Ef = float32(1) / float32(Ln10)
)

Mathematical constants. Reference: http://oeis.org/Axxxxxx

View Source 
const (
	MaxFloat32             = 3.40282346638528859811704183484516925440e+38  // 2**127 * (2**24 - 1) / 2**23
	SmallestNonzeroFloat32 = 1.401298464324817070923729583289916131280e-45 // 1 / 2**(127 - 1 + 23)

	MaxFloat64             = 1.797693134862315708145274237317043567981e+308 // 2**1023 * (2**53 - 1) / 2**52
	SmallestNonzeroFloat64 = 4.940656458412465441765687928682213723651e-324 // 1 / 2**(1023 - 1 + 52)
)

Floating-point limit values. Max is the largest finite value representable by the type. SmallestNonzero is the smallest positive, non-zero value representable by the type.

View Source 
const (
	MaxInt8   = 1<<7 - 1
	MinInt8   = -1 << 7
	MaxInt16  = 1<<15 - 1
	MinInt16  = -1 << 15
	MaxInt32  = 1<<31 - 1
	MinInt32  = -1 << 31
	MaxInt64  = 1<<63 - 1
	MinInt64  = -1 << 63
	MaxUint8  = 1<<8 - 1
	MaxUint16 = 1<<16 - 1
	MaxUint32 = 1<<32 - 1
	MaxUint64 = 1<<64 - 1
)

Integer limit values.

Variables

This section is empty.

Functions

func Abs 

func Abs(x float32) float32

Abs returns the absolute value of x.

Special cases are: 

Abs(±Inf) = +Inf
Abs(NaN) = NaN

func Acos 

func Acos(x float32) float32

Acos returns the arccosine, in radians, of x.

Special case is: 

Acos(x) = NaN if x < -1 or x > 1

func Acosh 

func Acosh(x float32) float32

Acosh returns the inverse hyperbolic cosine of x.

Special cases are: 

Acosh(+Inf) = +Inf
Acosh(x) = NaN if x < 1
Acosh(NaN) = NaN

func Asin 

func Asin(x float32) float32

Asin returns the arcsine, in radians, of x.

Special cases are: 

Asin(±0) = ±0
Asin(x) = NaN if x < -1 or x > 1

func Asinh 

func Asinh(x float32) float32

Asinh returns the inverse hyperbolic sine of x.

Special cases are: 

Asinh(±0) = ±0
Asinh(±Inf) = ±Inf
Asinh(NaN) = NaN

func Atan 

func Atan(x float32) float32

Atan returns the arctangent, in radians, of x.

Special cases are: 

Atan(±0) = ±0
Atan(±Inf) = ±Pi/2

func Atan2 

func Atan2(y, x float32) float32

Atan2 returns the arc tangent of y/x, using the signs of the two to determine the quadrant of the return value.

Special cases are (in order): 

Atan2(y, NaN) = NaN
Atan2(NaN, x) = NaN
Atan2(+0, x>=0) = +0
Atan2(-0, x>=0) = -0
Atan2(+0, x<=-0) = +Pi
Atan2(-0, x<=-0) = -Pi
Atan2(y>0, 0) = +Pi/2
Atan2(y<0, 0) = -Pi/2
Atan2(+Inf, +Inf) = +Pi/4
Atan2(-Inf, +Inf) = -Pi/4
Atan2(+Inf, -Inf) = 3Pi/4
Atan2(-Inf, -Inf) = -3Pi/4
Atan2(y, +Inf) = 0
Atan2(y>0, -Inf) = +Pi
Atan2(y<0, -Inf) = -Pi
Atan2(+Inf, x) = +Pi/2
Atan2(-Inf, x) = -Pi/2

func Atanh 

func Atanh(x float32) float32

Atanh returns the inverse hyperbolic tangent of x.

Special cases are: 

Atanh(1) = +Inf
Atanh(±0) = ±0
Atanh(-1) = -Inf
Atanh(x) = NaN if x < -1 or x > 1
Atanh(NaN) = NaN

func Cbrt 

func Cbrt(x float32) float32

Cbrt returns the cube root of x.

Special cases are: 

Cbrt(±0) = ±0
Cbrt(±Inf) = ±Inf
Cbrt(NaN) = NaN

func Ceil 

func Ceil(x float32) float32

Ceil returns the least integer value greater than or equal to x.

Special cases are: 

Ceil(±0) = ±0
Ceil(±Inf) = ±Inf
Ceil(NaN) = NaN

func Clamp 

func Clamp(f, low, high float32) float32

Clamp returns f clamped to [low, high]

func Copysign 

func Copysign(x, y float32) float32

Copysign returns a value with the magnitude of x and the sign of y.

func Cos 

func Cos(x float32) float32

Cos returns the cosine of the radian argument x.

Special cases are: 

Cos(±Inf) = NaN
Cos(NaN) = NaN

func Cosh 

func Cosh(x float32) float32

Cosh returns the hyperbolic cosine of x.

Special cases are: 

Cosh(±0) = 1
Cosh(±Inf) = +Inf
Cosh(NaN) = NaN

func Dim 

func Dim(x, y float32) float32

Dim returns the maximum of x-y or 0.

Special cases are: 

Dim(+Inf, +Inf) = NaN
Dim(-Inf, -Inf) = NaN
Dim(x, NaN) = Dim(NaN, x) = NaN

func Erf 

func Erf(x float32) float32

Erf returns the error function of x.

Special cases are: 

Erf(+Inf) = 1
Erf(-Inf) = -1
Erf(NaN) = NaN

func Erfc 

func Erfc(x float32) float32

Erfc returns the complementary error function of x.

Special cases are: 

Erfc(+Inf) = 0
Erfc(-Inf) = 2
Erfc(NaN) = NaN

func Exp 

func Exp(x float32) float32

Exp returns e**x, the base-e exponential of x.

Special cases are: 

Exp(+Inf) = +Inf
Exp(NaN) = NaN

Very large values overflow to 0 or +Inf. Very small values underflow to 1.

func Exp2 

func Exp2(x float32) float32

Exp2 returns 2**x, the base-2 exponential of x.

Special cases are the same as Exp.

func Expm1 

func Expm1(x float32) float32

Expm1 returns e**x - 1, the base-e exponential of x minus 1. It is more accurate than Exp(x) - 1 when x is near zero.

Special cases are: 

Expm1(+Inf) = +Inf
Expm1(-Inf) = -1
Expm1(NaN) = NaN

Very large values overflow to -1 or +Inf.

func Float32bits 

func Float32bits(f float32) uint32

Float32bits returns the IEEE 754 binary representation of f.

func Float32frombits 

func Float32frombits(b uint32) float32

Float32frombits returns the floating point number corresponding to the IEEE 754 binary representation b.

func Float64bits 

func Float64bits(f float64) uint64

Float64bits returns the IEEE 754 binary representation of f.

func Float64frombits 

func Float64frombits(b uint64) float64

Float64frombits returns the floating point number corresponding the IEEE 754 binary representation b.

func Floor 

func Floor(x float32) float32

Floor returns the greatest integer value less than or equal to x.

Special cases are: 

Floor(±0) = ±0
Floor(±Inf) = ±Inf
Floor(NaN) = NaN

func Frexp 

func Frexp(f float32) (frac float32, exp int)

Frexp breaks f into a normalized fraction and an integral power of two. It returns frac and exp satisfying f == frac × 2**exp, with the absolute value of frac in the interval [½, 1).

Special cases are: 

Frexp(±0) = ±0, 0
Frexp(±Inf) = ±Inf, 0
Frexp(NaN) = NaN, 0

func Gamma 

func Gamma(x float32) float32

Gamma returns the Gamma function of x.

Special cases are: 

Gamma(+Inf) = +Inf
Gamma(+0) = +Inf
Gamma(-0) = -Inf
Gamma(x) = NaN for integer x < 0
Gamma(-Inf) = NaN
Gamma(NaN) = NaN

func Hypot 

func Hypot(p, q float32) float32

Hypot returns Sqrt(p*p + q*q), taking care to avoid unnecessary overflow and underflow.

Special cases are: 

Hypot(±Inf, q) = +Inf
Hypot(p, ±Inf) = +Inf
Hypot(NaN, q) = NaN
Hypot(p, NaN) = NaN

func Ilogb 

func Ilogb(x float32) int

Ilogb returns the binary exponent of x as an integer.

Special cases are: 

Ilogb(±Inf) = MaxInt32
Ilogb(0) = MinInt32
Ilogb(NaN) = MaxInt32

func Inf 

func Inf(sign int) float32

Inf returns positive infinity if sign >= 0, negative infinity if sign < 0.

func IsInf 

func IsInf(f float32, sign int) bool

IsInf reports whether f is an infinity, according to sign. If sign > 0, IsInf reports whether f is positive infinity. If sign < 0, IsInf reports whether f is negative infinity. If sign == 0, IsInf reports whether f is either infinity.

func IsNaN 

func IsNaN(f float32) (is bool)

IsNaN reports whether f is an IEEE 754 “not-a-number” value.

func J0 

func J0(x float32) float32

J0 returns the order-zero Bessel function of the first kind.

Special cases are: 

J0(±Inf) = 0
J0(0) = 1
J0(NaN) = NaN

func J1 

func J1(x float32) float32

J1 returns the order-one Bessel function of the first kind.

Special cases are: 

J1(±Inf) = 0
J1(NaN) = NaN

func Jn 

func Jn(n int, x float32) float32

Jn returns the order-n Bessel function of the first kind.

Special cases are: 

Jn(n, ±Inf) = 0
Jn(n, NaN) = NaN

func Ldexp 

func Ldexp(frac float32, exp int) float32

Ldexp is the inverse of Frexp. It returns frac × 2**exp.

Special cases are: 

Ldexp(±0, exp) = ±0
Ldexp(±Inf, exp) = ±Inf
Ldexp(NaN, exp) = NaN

func Lgamma 

func Lgamma(x float32) (lgamma float32, sign int)

Lgamma returns the natural logarithm and sign (-1 or +1) of Gamma(x).

Special cases are: 

Lgamma(+Inf) = +Inf
Lgamma(0) = +Inf
Lgamma(-integer) = +Inf
Lgamma(-Inf) = -Inf
Lgamma(NaN) = NaN

func Log 

func Log(x float32) float32

Log returns the natural logarithm of x.

Special cases are: 

Log(+Inf) = +Inf
Log(0) = -Inf
Log(x < 0) = NaN
Log(NaN) = NaN

func Log10 

func Log10(x float32) float32

Log10 returns the decimal logarithm of x. The special cases are the same as for Log.

func Log1p 

func Log1p(x float32) float32

Log1p returns the natural logarithm of 1 plus its argument x. It is more accurate than Log(1 + x) when x is near zero.

Special cases are: 

Log1p(+Inf) = +Inf
Log1p(±0) = ±0
Log1p(-1) = -Inf
Log1p(x < -1) = NaN
Log1p(NaN) = NaN

func Log2 

func Log2(x float32) float32

Log2 returns the binary logarithm of x. The special cases are the same as for Log.

func Logb 

func Logb(x float32) float32

Logb returns the binary exponent of x.

Special cases are: 

Logb(±Inf) = +Inf
Logb(0) = -Inf
Logb(NaN) = NaN

func Max 

func Max(x, y float32) float32

Max returns the larger of x or y.

Special cases are: 

Max(x, +Inf) = Max(+Inf, x) = +Inf
Max(x, NaN) = Max(NaN, x) = NaN
Max(+0, ±0) = Max(±0, +0) = +0
Max(-0, -0) = -0

func Min 

func Min(x, y float32) float32

Min returns the smaller of x or y.

Special cases are: 

Min(x, -Inf) = Min(-Inf, x) = -Inf
Min(x, NaN) = Min(NaN, x) = NaN
Min(-0, ±0) = Min(±0, -0) = -0

func Mod 

func Mod(x, y float32) float32

Mod returns the floating-point remainder of x/y. The magnitude of the result is less than y and its sign agrees with that of x.

Special cases are: 

Mod(±Inf, y) = NaN
Mod(NaN, y) = NaN
Mod(x, 0) = NaN
Mod(x, ±Inf) = x
Mod(x, NaN) = NaN

func Modf 

func Modf(f float32) (int float32, frac float32)

Modf returns integer and fractional floating-point numbers that sum to f. Both values have the same sign as f.

Special cases are: 

Modf(±Inf) = ±Inf, NaN
Modf(NaN) = NaN, NaN

func NaN 

func NaN() float32

NaN returns an IEEE 754 “not-a-number” value.

func Nextafter 

func Nextafter(x, y float32) (r float32)

Nextafter returns the next representable float32 value after x towards y. Special cases: 

	Nextafter32(x, x)   = x
     Nextafter32(NaN, y) = NaN
     Nextafter32(x, NaN) = NaN

Since this is a float32 math package the 32 bit version has no number and the 64 bit version has the number in the method name.

func Nextafter64 

func Nextafter64(x, y float64) (r float64)

Nextafter64 returns the next representable float64 value after x towards y. Special cases: 

Nextafter64(x, x)   = x
Nextafter64(NaN, y) = NaN
Nextafter64(x, NaN) = NaN

Since this is a float32 math package the 32 bit version has no number and the 64 bit version has the number in the method name.

func Pow 

func Pow(x, y float32) float32

Pow returns x**y, the base-x exponential of y.

Special cases are (in order): 

Pow(x, ±0) = 1 for any x
Pow(1, y) = 1 for any y
Pow(x, 1) = x for any x
Pow(NaN, y) = NaN
Pow(x, NaN) = NaN
Pow(±0, y) = ±Inf for y an odd integer < 0
Pow(±0, -Inf) = +Inf
Pow(±0, +Inf) = +0
Pow(±0, y) = +Inf for finite y < 0 and not an odd integer
Pow(±0, y) = ±0 for y an odd integer > 0
Pow(±0, y) = +0 for finite y > 0 and not an odd integer
Pow(-1, ±Inf) = 1
Pow(x, +Inf) = +Inf for |x| > 1
Pow(x, -Inf) = +0 for |x| > 1
Pow(x, +Inf) = +0 for |x| < 1
Pow(x, -Inf) = +Inf for |x| < 1
Pow(+Inf, y) = +Inf for y > 0
Pow(+Inf, y) = +0 for y < 0
Pow(-Inf, y) = Pow(-0, -y)
Pow(x, y) = NaN for finite x < 0 and finite non-integer y

func Pow10 

func Pow10(e int) float32

Pow10 returns 10**e, the base-10 exponential of e.

Special cases are: 

Pow10(e) = +Inf for e > 309
Pow10(e) = 0 for e < -324

func Remainder 

func Remainder(x, y float32) float32

Remainder returns the IEEE 754 floating-point remainder of x/y.

Special cases are: 

Remainder(±Inf, y) = NaN
Remainder(NaN, y) = NaN
Remainder(x, 0) = NaN
Remainder(x, ±Inf) = x
Remainder(x, NaN) = NaN

func Signbit 

func Signbit(x float32) bool

Signbit returns true if x is negative or negative zero.

func Sin 

func Sin(x float32) float32

Sin returns the sine of the radian argument x.

Special cases are: 

Sin(±0) = ±0
Sin(±Inf) = NaN
Sin(NaN) = NaN

func Sincos 

func Sincos(x float32) (sin, cos float32)

Sincos returns Sin(x), Cos(x).

Special cases are: 

Sincos(±0) = ±0, 1
Sincos(±Inf) = NaN, NaN
Sincos(NaN) = NaN, NaN

func Sinh 

func Sinh(x float32) float32

Sinh returns the hyperbolic sine of x.

Special cases are: 

Sinh(±0) = ±0
Sinh(±Inf) = ±Inf
Sinh(NaN) = NaN

func Sqrt 

func Sqrt(x float32) float32

Sqrt returns the square root of x.

Special cases are: 

Sqrt(+Inf) = +Inf
Sqrt(±0) = ±0
Sqrt(x < 0) = NaN
Sqrt(NaN) = NaN

func Tan 

func Tan(x float32) float32

Tan returns the tangent of the radian argument x.

Special cases are: 

Tan(±0) = ±0
Tan(±Inf) = NaN
Tan(NaN) = NaN

func Tanh 

func Tanh(x float32) float32

Tanh returns the hyperbolic tangent of x.

Special cases are: 

Tanh(±0) = ±0
Tanh(±Inf) = ±1
Tanh(NaN) = NaN

func Trunc 

func Trunc(x float32) float32

Trunc returns the integer value of x.

Special cases are: 

Trunc(±0) = ±0
Trunc(±Inf) = ±Inf
Trunc(NaN) = NaN

func Y0 

func Y0(x float32) float32

Y0 returns the order-zero Bessel function of the second kind.

Special cases are: 

Y0(+Inf) = 0
Y0(0) = -Inf
Y0(x < 0) = NaN
Y0(NaN) = NaN

func Y1 

func Y1(x float32) float32

Y1 returns the order-one Bessel function of the second kind.

Special cases are: 

Y1(+Inf) = 0
Y1(0) = -Inf
Y1(x < 0) = NaN
Y1(NaN) = NaN

func Yn 

func Yn(n int, x float32) float32

Yn returns the order-n Bessel function of the second kind.

Special cases are: 

Yn(n, +Inf) = 0
Yn(n > 0, 0) = -Inf
Yn(n < 0, 0) = +Inf if n is odd, -Inf if n is even
Y1(n, x < 0) = NaN
Y1(n, NaN) = NaN

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