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Maths

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Elementary mathematical functions and constants.


Functions

realbmath_cos (...)
realbmath_sin (...)
realbmath_tan (...)
realbmath_acos (...)
realbmath_asin (...)
realbmath_atan2 (...)
realbmath_sqrt (...)
realbmath_isqrt (...)
realbmath_log (...)
realbmath_log10 (...)
realbmath_exp (...)
realbmath_pow (...)
realbmath_abs (...)
realbmath_max (...)
realbmath_min (...)
realbmath_clamp (...)
realbmath_mod (...)
realbmath_modf (...)
uint32_tbmath_prec (...)
realbmath_round (...)
realbmath_round_step (...)
realbmath_floor (...)
realbmath_ceil (...)
uint32_tbmath_time_seed (void)
voidbmath_rand_seed (...)
realbmath_rand (...)
uint32_tbmath_randi (...)

Types and Constants

realkE
realkLN2
realkLN10
realkPI
realkSQRT2
realkSQRT3
realkDEG2RAD
realkRAD2DEG

kE

const real32_t kBMATH_Ef = 2.718281828459045f;

const real64_t kBMATH_Ed = 2.718281828459045;

const real BMath::kE;

Euler's number.


kLN2

const real32_t kBMATH_LN2f = 0.6931471805599453f;

const real64_t kBMATH_LN2d = 0.6931471805599453;

const real BMath::kLN2;

The natural logarithm of 2.


kLN10

const real32_t kBMATH_LN10f = 2.302585092994046f;

const real64_t kBMATH_LN10d = 2.302585092994046;

const real BMath::kLN10;

The natural logarithm of 10.


kPI

const real32_t kBMATH_PIf = 3.141592653589793f;

const real64_t kBMATH_PId = 3.141592653589793;

const real BMath::kPI;

The number Pi.


kSQRT2

const real32_t kBMATH_SQRT2f = 1.414213562373095f;

const real64_t kBMATH_SQRT2d = 1.414213562373095;

const real BMath::kSQRT2;

Square root of 2.


kSQRT3

const real32_t kBMATH_SQRT3f = 1.732050807568878f;

const real64_t kBMATH_SQRT3d = 1.732050807568878;

const real BMath::kSQRT3;

Square root of 3.


kDEG2RAD

const real32_t kBMATH_DEG2RADf = 0.017453292519943f;

const real64_t kBMATH_DEG2RADd = 0.017453292519943;

const real BMath::kDEG2RAD;

Conversion from one degree to radians.


kRAD2DEG

const real32_t kBMATH_RAD2DEGf = 57.2957795130823f;

const real64_t kBMATH_RAD2DEGd = 57.2957795130823;

const real BMath::kRAD2DEG;

Conversion of a radian to degrees.


bmath_cos ()

Get the cosine of an angle.

real32_t
bmath_cosf(const real32_t angle);

real64_t
bmath_cosd(const real64_t angle);

real
BMath::cos(const real angle);
angle

Angle in radians.

Return

The cosine of the angle.


bmath_sin ()

Get the sine of an angle.

real32_t
bmath_sinf(const real32_t angle);

real64_t
bmath_sind(const real64_t angle);

real
BMath::sin(const real angle);
angle

Angle in radians.

Return

The sine of the angle.


bmath_tan ()

Get the tangent of an angle.

real32_t
bmath_tanf(const real32_t angle);

real64_t
bmath_tand(const real64_t angle);

real
BMath::tan(const real angle);
angle

Angle in radians.

Return

The angle tangent.


bmath_acos ()

Get the cosine arc, or inverse cosine, which is the angle whose cosine is the value.

real32_t
bmath_acosf(const real32_t cos);

real64_t
bmath_acosd(const real64_t cos);

real
BMath::acos(const real cos);
cos

Cosine (-1, 1).

Return

The angle (0, Pi).


bmath_asin ()

Get the sine arc, or inverse sine, which is the angle whose sine is the value.

real32_t
bmath_asinf(const real32_t sin);

real64_t
bmath_asind(const real64_t sin);

real
BMath::asin(const real sin);
sin

Sine (-1, 1).

Return

The angle (0, Pi).


bmath_atan2 ()

Get the tangent arc, or inverse tangent. Es is the angle measured from the X axis to the line containing the origin (0, 0) and the point with the coordinates (x, y).

real32_t
bmath_atan2f(const real32_t y,
             const real32_t x);

real64_t
bmath_atan2d(const real64_t y,
             const real64_t x);

real
BMath::atan2(const real y,
             const real x);
y

Y coordinate.

x

Coordinate X.

Return

The angle (-Pi, Pi).


bmath_sqrt ()

Get the square root of a number.

real32_t
bmath_sqrtf(const real32_t value);

real64_t
bmath_sqrtd(const real64_t value);

real
BMath::sqrt(const real value);
value

The number.

Return

The square root.


bmath_isqrt ()

Get the inverse square root of a number (1/sqrt).

real32_t
bmath_isqrtf(const real32_t value);

real64_t
bmath_isqrtd(const real64_t value);

real
BMath::isqrt(const real value);
value

The number.

Return

The inverse square root.


bmath_log ()

Get the natural logarithm (base e) of a number.

real32_t
bmath_logf(const real32_t value);

real64_t
bmath_logd(const real64_t value);

real
BMath::log(const real value);
value

The number.

Return

The logarithm.


bmath_log10 ()

Get the logarithm in base 10 of a number.

real32_t
bmath_log10f(const real32_t value);

real64_t
bmath_log10d(const real64_t value);

real
BMath::log10(const real value);
value

The number.

Return

The logarithm.


bmath_exp ()

Get the number of Euler e (2.7182818) raised to a power.

real32_t
bmath_expf(const real32_t value);

real64_t
bmath_expd(const real64_t value);

real
BMath::exp(const real value);
value

The exponent.

Return

The exponential.


bmath_pow ()

Calculate a power, base raised to exponent.

real32_t
bmath_powf(const real32_t base,
           const real32_t exponent);

real64_t
bmath_powd(const real64_t base,
           const real64_t exponent);

real
BMath::pow(const real base,
           const real exponent);
base

Base.

exponent

Exponent.

Return

The result of the power.


bmath_abs ()

Get the absolute value of a number.

real32_t
bmath_absf(const real32_t value);

real64_t
bmath_absd(const real64_t value);

real
BMath::abs(const real value);
value

The number.

Return

The absolute value.


bmath_max ()

Get the maximum of two values.

real32_t
bmath_maxf(const real32_t value1,
           const real32_t value2);

real64_t
bmath_maxd(const real64_t value1,
           const real64_t value2);

real
BMath::max(const real value1,
           const real value2);
value1

First number.

value2

Second number.

Return

The maximum value.


bmath_min ()

Get the minimum of two values.

real32_t
bmath_minf(const real32_t value1,
           const real32_t value2);

real64_t
bmath_mind(const real64_t value1,
           const real64_t value2);

real
BMath::min(const real value1,
           const real value2);
value1

First number.

value2

Second number.

Return

The minimum value.


bmath_clamp ()

Restrict a value to a certain range.

real32_t
bmath_clampf(const real32_t value,
             const real32_t min,
             const real32_t max);

real64_t
bmath_clampd(const real64_t value,
             const real64_t min,
             const real64_t max);

real
BMath::clamp(const real value,
             const real min,
             const real max);
value

The number.

min

Minimum value of the range.

max

Maximum value of the range.

Return

The limited value.


bmath_mod ()

Get the module of divide num/den.

real32_t
bmath_modf(const real32_t num,
           const real32_t den);

real64_t
bmath_modd(const real64_t num,
           const real64_t den);

real
BMath::mod(const real num,
           const real den);
num

Numerator.

den

Denominator.

Return

The module.


bmath_modf ()

Get the integer and fraction part of a real number.

real32_t
bmath_modff(const real32_t value,
            real32_t *intpart);

real64_t
bmath_modfd(const real64_t value,
            real64_t *intpart);

real
BMath::modf(const real value,
            real *intpart);
value

The number.

intpart

Get the integer part.

Return

The fractional part [0,1).


bmath_prec ()

Get the number of decimals (precision) of a real number.

uint32_t
bmath_precf(const real32_t value);

uint32_t
bmath_precd(const real64_t value);

uint32_t
BMath::prec(const real value);
value

The number.

Return

The number of decimal places.


bmath_round ()

Rounds a number to the nearest integer (above or below).

real32_t
bmath_roundf(const real32_t value);

real64_t
bmath_roundd(const real64_t value);

real
BMath::round(const real value);
value

The number.

Return

The nearest whole.


bmath_round_step ()

Round a number to the nearest fraction.

real32_t
bmath_round_stepf(const real32_t value,
                  const real32_t step);

real64_t
bmath_round_stepd(const real64_t value,
                  const real64_t step);

real
BMath::round_step(const real value,
                  const real step);
value

The number.

step

The fraction.

Return

The nearest number.


bmath_floor ()

Rounds a number to the integer below.

real32_t
bmath_floorf(const real32_t value);

real64_t
bmath_floord(const real64_t value);

real
BMath::floor(const real value);
value

The number.

Return

The largest integer number, less than or equal to the number.


bmath_ceil ()

Round a number to the integer above.

real32_t
bmath_ceilf(const real32_t value);

real64_t
bmath_ceild(const real64_t value);

real
BMath::ceil(const real value);
value

The number.

Return

The smallest integer number, greater than or equal to the number.


bmath_time_seed ()

Gets a seed for random numbers, based on the system clock.

uint32_t
bmath_time_seed(void);

Return

The seed. Use it as a parameter of bmath_rand_seed to generate a different sequence of random numbers.


bmath_rand_seed ()

Establish a new seed of random numbers.

void
bmath_rand_seed(const uint32_t seed);
seed

The new seed.

Remarks

Each time the seed changes, a new sequence of random numbers begins. For the same seed, we will get the same sequence, so they are pseudo-random numbers. Similar seeds (eg. 4, 5 ) produce radically different sequences.


bmath_rand ()

Gets a random number, within an interval.

real32_t
bmath_randf(const real32_t from,
            const real32_t to);

real64_t
bmath_randd(const real64_t from,
            const real64_t to);

real
BMath::rand(const real from,
            const real to);
from

The lower limit of the interval.

to

The upper limit of the interval.

Return

The random number.


bmath_randi ()

Gets a random number, within an interval.

uint32_t
bmath_randi(const uint32_t from,
            const uint32_t to);
from

The lower limit of the interval.

to

The upper limit of the interval.

Return

The random number.

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