mathlib.qh File Reference

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Macros
#define	M_PI   3.14159265358979323846 /* pi */

Functions
float	acosh (float e)
float	asinh (float e)
float	atanh (float e)
float	cbrt (float e)
float	copysign (float e, float f)
float	cosh (float e)
float	erf (float e)
float	erfc (float e)
float	exp (float e)
float	exp2 (float e)
float	expm1 (float e)
float	fdim (float e, float f)
float	fma (float e, float f, float g)
float	fmax (float e, float f)
float	fmin (float e, float f)
float	fmod (float e, float f)
int	fpclassify (float e)
vector	frexp (float e)
float	hypot (float e, float f)
int	ilogb (float e)
bool	isfinite (float e)
int	isgreater (float e, float f)
int	isgreaterequal (float e, float f)
bool	isinf (float e)
int	isless (float e, float f)
int	islessequal (float e, float f)
int	islessgreater (float e, float f)
bool	isnan (float e)
bool	isnormal (float e)
int	isunordered (float e, float f)
float	ldexp (float e, int e)
vector	lgamma (float e)
float	log10 (float e)
float	log1p (float e)
float	log2 (float e)
float	logb (float e)
float	logn (float e, float base)
vector	modf (float f)
float	nan (string tag)
float	nearbyint (float e)
float	nextafter (float e, float f)
float	nexttoward (float e, float f)
float	pymod (float e, float f)
	Pythonic mod: TODO: %% operator? More...
float	remainder (float e, float f)
vector	remquo (float e, float f)
float	scalbn (float e, int n)
bool	signbit (float e)
float	sinh (float e)
float	tanh (float e)
float	tgamma (float e)
float	trunc (float e)

Variables
const int	FP_INFINITE = 1
const int	FP_NAN = 0
const int	FP_NORMAL = 4
const int	FP_SUBNORMAL = 3
const int	FP_ZERO = 2
const float	M_1_PI = 0.31830988618379067154
const float	M_2_PI = 0.63661977236758134308
const float	M_2_SQRTPI = 1.12837916709551257390
const float	M_E = 2.7182818284590452354
const float	M_LN10 = 2.30258509299404568402
const float	M_LN2 = 0.69314718055994530942
const float	M_LOG10E = 0.43429448190325182765
const float	M_LOG2E = 1.4426950408889634074
const float	M_PI_2 = 1.57079632679489661923
const float	M_PI_4 = 0.78539816339744830962
const float	M_SQRT1_2 = 0.70710678118654752440
const float	M_SQRT2 = 1.41421356237309504880

Macro Definition Documentation

M_PI

#define M_PI   3.14159265358979323846 /* pi */

Definition at line 108 of file mathlib.qh.

Function Documentation

acosh()

float acosh

(

float

e

)

Definition at line 48 of file mathlib.qc.

References log(), and sqrt().

{
    return log(e + sqrt(e*e - 1));
}

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asinh()

float asinh

(

float

e

)

Definition at line 52 of file mathlib.qc.

References log(), and sqrt().

{
    return log(e + sqrt(e*e + 1));
}

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atanh()

float atanh

(

float

e

)

Definition at line 56 of file mathlib.qc.

References log().

{
    return 0.5 * log((1+e) / (1-e));
}

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cbrt()

float cbrt

(

float

e

)

Definition at line 132 of file mathlib.qc.

References copysign(), fabs(), and pow().

Referenced by solve_cubic_pq().

{
    return copysign(pow(fabs(e), (1.0/3.0)), e);
}

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copysign()

float copysign	(	float	e,
		float	f
	)

Definition at line 225 of file mathlib.qc.

References fabs().

Referenced by AdjustAirAccelQW(), cbrt(), erf(), and lgamma().

{
    return fabs(e) * ((f>0) ? 1 : -1);
}

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cosh()

float cosh

(

float

e

)

Definition at line 60 of file mathlib.qc.

References exp().

Referenced by tanh().

{
    return 0.5 * (exp(e) + exp(-e));
}

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erf()

float erf

(

float

e

)

Definition at line 141 of file mathlib.qc.

References copysign(), exp(), and sqrt().

Referenced by erfc().

{
    // approximation taken from wikipedia
    float f;
    f = e*e;
    return copysign(sqrt(1 - exp(-f * (1.273239544735163 + 0.14001228868667 * f) / (1 + 0.14001228868667 * f))), e);
}

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erfc()

float erfc

(

float

e

)

Definition at line 148 of file mathlib.qc.

References erf().

{
    return 1.0 - erf(e);
}

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exp()

float exp

(

float

e

)

Definition at line 73 of file mathlib.qc.

References M_E, and pow().

Referenced by anticheat_physics(), cosh(), erf(), expm1(), fromDecibelOfSquare(), GenericCommand_rpn(), GetCurrentFov(), ListBox_draw(), sinh(), tgamma(), and toDecibelOfSquare().

{
    return pow(M_E, e);
}

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exp2()

float exp2

(

float

e

)

Definition at line 77 of file mathlib.qc.

References pow().

{
    return pow(2, e);
}

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expm1()

float expm1

(

float

e

)

Definition at line 81 of file mathlib.qc.

References exp().

{
    return exp(e) - 1;
}

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fdim()

float fdim	(	float	e,
		float	f
	)

Definition at line 260 of file mathlib.qc.

References max().

{
    return max(e-f, 0);
}

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fma()

float fma	(	float	e,
		float	f,
		float	g
	)

Definition at line 272 of file mathlib.qc.

{
    return e * f + g;
}

fmax()

float fmax	(	float	e,
		float	f
	)

Definition at line 264 of file mathlib.qc.

References max().

{
    return max(e, f);
}

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fmin()

float fmin	(	float	e,
		float	f
	)

Definition at line 268 of file mathlib.qc.

References min().

{
    return min(e, f);
}

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fmod()

float fmod	(	float	e,
		float	f
	)

Definition at line 208 of file mathlib.qc.

References trunc().

Referenced by CSQCModel_Effects_Apply().

{
    return e - f * trunc(e / f);
}

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fpclassify()

int fpclassify

(

float

e

)

Definition at line 7 of file mathlib.qc.

References FP_INFINITE, FP_NAN, FP_NORMAL, FP_ZERO, isinf(), and isnan().

{
    if(isnan(e))
        return FP_NAN;
    if(isinf(e))
        return FP_INFINITE;
    if(e == 0)
        return FP_ZERO;
    return FP_NORMAL;
}

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frexp()

vector frexp

(

float

e

)

Definition at line 86 of file mathlib.qc.

References ilogb(), pow(), v, and vector().

{
    vector v;
    v.z = 0;
    v.y = ilogb(e) + 1;
    v.x = e / pow(2, v.y);
    return v;
}

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hypot()

float hypot	(	float	e,
		float	f
	)

Definition at line 136 of file mathlib.qc.

References sqrt().

{
    return sqrt(e*e + f*f);
}

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ilogb()

int ilogb

(

float

e

)

Definition at line 94 of file mathlib.qc.

References fabs(), floor(), and log2().

Referenced by frexp().

{
    return floor(log2(fabs(e)));
}

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isfinite()

bool isfinite

(

float

e

)

Definition at line 17 of file mathlib.qc.

References isinf(), and isnan().

Referenced by isnormal(), and lgamma().

{
    return !(isnan(e) || isinf(e));
}

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isgreater()

int isgreater	(	float	e,
		float	f
	)

Definition at line 277 of file mathlib.qc.

{
    return e > f;
}

isgreaterequal()

int isgreaterequal	(	float	e,
		float	f
	)

Definition at line 281 of file mathlib.qc.

{
    return e >= f;
}

isinf()

bool isinf

(

float

e

)

Definition at line 21 of file mathlib.qc.

Referenced by fpclassify(), and isfinite().

{
    return (e != 0) && (e + e == e);
}

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isless()

int isless	(	float	e,
		float	f
	)

Definition at line 285 of file mathlib.qc.

{
    return e < f;
}

islessequal()

int islessequal	(	float	e,
		float	f
	)

Definition at line 289 of file mathlib.qc.

{
    return e <= f;
}

islessgreater()

int islessgreater	(	float	e,
		float	f
	)

Definition at line 293 of file mathlib.qc.

{
    return e < f || e > f;
}

isnan()

bool isnan

(

float

e

)

Definition at line 25 of file mathlib.qc.

References ftos().

Referenced by fpclassify(), is_all_nans(), and isfinite().

{
    // The sane way to detect NaN is this:
    // float f = e;
    // return (e != f);
    // but darkplaces used to be compiled with -ffinite-math-only which broke it.
    // DP is fixed now but until all clients update (so after 0.8.3) we have to use the following workaround
    // or they'd have issues when connecting to newer servers.

    // Negative NaN ("-nan") is much more common but plain "nan" can be created by negating *some* -nans so we need to check both.
    // DP's QCVM and GMQCC's QCVM behave differently - one needs ftos(-(0.0 / 0.0)), the other ftos(-sqrt(-1)).
    string s = ftos(e);
    return s == "nan" || s == "-nan";
}

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isnormal()

bool isnormal

(

float

e

)

Definition at line 39 of file mathlib.qc.

References isfinite().

{
    return isfinite(e);
}

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isunordered()

int isunordered	(	float	e,
		float	f
	)

Definition at line 297 of file mathlib.qc.

{
    return !(e < f || e == f || e > f);
}

ldexp()

float ldexp	(	float	e,
		int	e
	)

Definition at line 98 of file mathlib.qc.

References pow().

{
    return x * pow(2, e);
}

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lgamma()

vector lgamma

(

float

e

)

Definition at line 152 of file mathlib.qc.

References copysign(), fabs(), floor(), isfinite(), lgamma(), log(), M_PI, nan(), sin(), v, and vector().

Referenced by lgamma(), and tgamma().

{
    // TODO improve accuracy
    if(!isfinite(e))
        return fabs(e) * '1 0 0' + copysign(1, e) * '0 1 0';
    if(e < 1 && e == floor(e))
        return nan("gamma") * '1 1 1';
    if(e < 0.1)
    {
        vector v;
        v = lgamma(1.0 - e);
        // reflection formula:
        // gamma(1-z) * gamma(z) = pi / sin(pi*z)
        // lgamma(1-z) + lgamma(z) = log(pi) - log(sin(pi*z))
        // sign of gamma(1-z) = sign of gamma(z) * sign of sin(pi*z)
        v.z = sin(M_PI * e);
        v.x = log(M_PI) - log(fabs(v.z)) - v.x;
        if(v.z < 0)
            v.y = -v.y;
        v.z = 0;
        return v;
    }
    if(e < 1.1)
        return lgamma(e + 1) - log(e) * '1 0 0';
    e -= 1;
    return (0.5 * log(2 * M_PI * e) + e * (log(e) - 1)) * '1 0 0' + '0 1 0';
}

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log10()

float log10

(

float

e

)

Definition at line 106 of file mathlib.qc.

References log(), and M_LOG10E.

{
    return log(e) * M_LOG10E;
}

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log1p()

float log1p

(

float

e

)

Definition at line 110 of file mathlib.qc.

References log().

{
    return log(e + 1);
}

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log2()

float log2

(

float

e

)

Definition at line 114 of file mathlib.qc.

References log(), and M_LOG2E.

Referenced by ilogb(), and logb().

{
    return log(e) * M_LOG2E;
}

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logb()

float logb

(

float

e

)

Definition at line 118 of file mathlib.qc.

References fabs(), floor(), and log2().

{
    return floor(log2(fabs(e)));
}

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logn()

float logn	(	float	e,
		float	base
	)

Definition at line 102 of file mathlib.qc.

References log().

Referenced by buff_Inferno_CalculateTime().

{
    return log(e) / log(base);
}

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modf()

vector modf

(

float

f

)

Definition at line 122 of file mathlib.qc.

References trunc().

{
    return '1 0 0' * (f - trunc(f)) + '0 1 0' * trunc(f);
}

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nan()

float nan

(

string

tag

)

Definition at line 230 of file mathlib.qc.

References sqrt().

Referenced by lgamma(), and nextafter().

{
    return sqrt(-1);
}

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nearbyint()

float nearbyint

(

float

e

)

Definition at line 199 of file mathlib.qc.

References rint().

{
    return rint(e);
}

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nextafter()

float nextafter	(	float	e,
		float	f
	)

Definition at line 234 of file mathlib.qc.

References fabs(), max(), nan(), and nextafter().

Referenced by nextafter(), and nexttoward().

{
    // TODO very crude
    if(e == f)
        return nan("nextafter");
    if(e > f)
        return -nextafter(-e, -f);
    // now we know that e < f
    // so we need the next number > e
    float d, a, b;
    d = max(fabs(e), 0.00000000000000000000001);
    a = e + d;
    do
    {
        d *= 0.5;
        b = a;
        a = e + d;
    }
    while(a != e);
    return b;
}

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nexttoward()

float nexttoward	(	float	e,
		float	f
	)

Definition at line 255 of file mathlib.qc.

References nextafter().

{
    return nextafter(e, f);
}

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pymod()

float pymod	(	float	e,
		float	f
	)

Pythonic mod: TODO: %% operator?

1 % 2 == 1 -1 % 2 == 1 1 % -2 == -1 -1 % -2 == -1

Definition at line 194 of file mathlib.qc.

References floor().

{
    return e - f * floor(e / f);
}

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remainder()

float remainder	(	float	e,
		float	f
	)

Definition at line 212 of file mathlib.qc.

References rint().

Referenced by IsMoveInDirection().

{
    return e - f * rint(e / f);
}

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remquo()

vector remquo	(	float	e,
		float	f
	)

Definition at line 216 of file mathlib.qc.

References rint(), v, and vector().

{
    vector v;
    v.z = 0;
    v.y = rint(e / f);
    v.x = e - f * v.y;
    return v;
}

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scalbn()

float scalbn	(	float	e,
		int	n
	)

Definition at line 127 of file mathlib.qc.

References pow().

{
    return e * pow(2, n);
}

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signbit()

bool signbit

(

float

e

)

Definition at line 43 of file mathlib.qc.

{
    return (e < 0);
}

sinh()

float sinh

(

float

e

)

Definition at line 64 of file mathlib.qc.

References exp().

Referenced by tanh().

{
    return 0.5 * (exp(e) - exp(-e));
}

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tanh()

float tanh

(

float

e

)

Definition at line 68 of file mathlib.qc.

References cosh(), and sinh().

Referenced by ctf_CalculatePassVelocity().

{
    return sinh(e) / cosh(e);
}

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tgamma()

float tgamma

(

float

e

)

Definition at line 179 of file mathlib.qc.

References exp(), lgamma(), v, and vector().

{
    vector v = lgamma(e);
    return exp(v.x) * v.y;
}

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trunc()

float trunc

(

float

e

)

Definition at line 203 of file mathlib.qc.

References ceil(), and floor().

Referenced by fmod(), and modf().

{
    return (e>=0) ? floor(e) : ceil(e);
}

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Variable Documentation

FP_INFINITE

const int FP_INFINITE = 1

Definition at line 9 of file mathlib.qh.

Referenced by fpclassify().

FP_NAN

const int FP_NAN = 0

Definition at line 8 of file mathlib.qh.

Referenced by fpclassify().

FP_NORMAL

const int FP_NORMAL = 4

Definition at line 12 of file mathlib.qh.

Referenced by fpclassify().

FP_SUBNORMAL

const int FP_SUBNORMAL = 3

Definition at line 11 of file mathlib.qh.

FP_ZERO

const int FP_ZERO = 2

Definition at line 10 of file mathlib.qh.

Referenced by fpclassify().

M_1_PI

const float M_1_PI = 0.31830988618379067154

Definition at line 111 of file mathlib.qh.

M_2_PI

const float M_2_PI = 0.63661977236758134308

Definition at line 112 of file mathlib.qh.

M_2_SQRTPI

const float M_2_SQRTPI = 1.12837916709551257390

Definition at line 113 of file mathlib.qh.

M_E

const float M_E = 2.7182818284590452354

Definition at line 102 of file mathlib.qh.

Referenced by colormapPaletteColor_(), and exp().

M_LN10

const float M_LN10 = 2.30258509299404568402

Definition at line 106 of file mathlib.qh.

M_LN2

const float M_LN2 = 0.69314718055994530942

Definition at line 105 of file mathlib.qh.

M_LOG10E

const float M_LOG10E = 0.43429448190325182765

Definition at line 104 of file mathlib.qh.

Referenced by log10().

M_LOG2E

const float M_LOG2E = 1.4426950408889634074

Definition at line 103 of file mathlib.qh.

Referenced by log2().

M_PI_2

const float M_PI_2 = 1.57079632679489661923

Definition at line 109 of file mathlib.qh.

M_PI_4

const float M_PI_4 = 0.78539816339744830962

Definition at line 110 of file mathlib.qh.

M_SQRT1_2

const float M_SQRT1_2 = 0.70710678118654752440

Definition at line 115 of file mathlib.qh.

Referenced by MUTATOR_HOOKFUNCTION().

M_SQRT2

const float M_SQRT2 = 1.41421356237309504880

Definition at line 114 of file mathlib.qh.

Referenced by havocbot_movetogoal().