rtm/scalard.h¶

#include "rtm/scalard.h"

scalar_set¶

scalard scalar_set(double xyzw)

Creates a scalar from a floating point value.

scalar_store¶

void scalar_store(double input, double* output)

Writes a scalar to memory.

scalar_cast¶

double scalar_cast(scalard input)

Casts a scalar into a floating point value.

scalar_floor¶

double scalar_floor(double input)

Returns the largest integer value not greater than the input (round towards negative infinity). scalar_floor(1.8) = 1.0 scalar_floor(-1.8) = -2.0

scalar_ceil¶

double scalar_ceil(double input)

Returns the smallest integer value not less than the input (round towards positive infinity). scalar_ceil(1.8) = 2.0 scalar_ceil(-1.8) = -1.0

scalar_clamp¶

double scalar_clamp(double input, double min, double max)

Returns the input if it is within the min/max values otherwise the exceeded boundary is returned.

scalar_abs¶

double scalar_abs(double input)

Returns the absolute value of the input.

scalar_sqrt¶

double scalar_sqrt(double input)

Returns the square root of the input.

scalar_sqrt_reciprocal¶

double scalar_sqrt_reciprocal(double input)

Returns the reciprocal square root of the input.

scalar_reciprocal¶

constexpr double scalar_reciprocal(double input)

Returns the reciprocal of the input.

scalar_add¶

constexpr double scalar_add(double lhs, double rhs)

Returns the addition of the two scalar inputs.

scalar_sub¶

constexpr double scalar_sub(double lhs, double rhs)

Returns the subtraction of the two scalar inputs.

scalar_mul¶

constexpr double scalar_mul(double lhs, double rhs)

Returns the multiplication of the two scalar inputs.

scalar_div¶

constexpr double scalar_div(double lhs, double rhs)

Returns the division of the two scalar inputs.

scalar_mul_add¶

double scalar_mul_add(double s0, double s1, double s2)

Returns the multiplication/addition of the three inputs: s2 + (s0 * s1).

scalar_neg_mul_sub¶

constexpr double scalar_neg_mul_sub(double s0, double s1, double s2)

Returns the negative multiplication/subtraction of the three inputs: -((s0 * s1) - s2) This is mathematically equivalent to: s2 - (s0 * s1)

scalar_lerp¶

double scalar_lerp(double start, double end, double alpha)

Returns the linear interpolation of the two inputs at the specified alpha. The formula used is: ((1.0 - alpha) * start) + (alpha * end). Interpolation is stable and will return 'start' when alpha is 0.0 and 'end' when it is 1.0. This is the same instruction count when FMA is present but it might be slightly slower due to the extra multiplication compared to: start + (alpha * (end - start)).

scalar_exp¶

double scalar_exp(double input)

Returns the natural exponential of the input: e^input. The function uses the same algorithm as vector_exp(..): for the same input, the results are equal.

scalar_log¶

double scalar_log(double input)

Returns the natural logarithm of the input. The function uses the same algorithm as vector_log(..): for the same input, the results are equal. The result is -inf when the input is zero, and NaN when the input is negative.

scalar_eerp¶

double scalar_eerp(double start, double end, double alpha)

Returns the exponential interpolation of the two inputs at the specified alpha. The formula used is: start * (end / start)^alpha. For equal steps of alpha, the result changes by the same ratio. Use it to interpolate a scale. The result is 'start' when alpha is 0.0. It is approximately 'end' when alpha is 1.0. The two inputs must have the same sign and must not be zero. Otherwise, the result is undefined.

scalar_min¶

double scalar_min(double left, double right)

Returns the smallest of the two inputs.

scalar_max¶

double scalar_max(double left, double right)

Returns the largest of the two inputs.

scalar_equal¶

constexpr bool scalar_equal(double lhs, double rhs)

Returns true if both inputs are equal, false otherwise.

scalar_lower_than¶

constexpr bool scalar_lower_than(double lhs, double rhs)

Returns true if lhs < rhs, false otherwise.

scalar_lower_equal¶

constexpr bool scalar_lower_equal(double lhs, double rhs)

Returns true if lhs <= rhs, false otherwise.

scalar_greater_than¶

constexpr bool scalar_greater_than(double lhs, double rhs)

Returns true if lhs > rhs, false otherwise.

scalar_greater_equal¶

constexpr bool scalar_greater_equal(double lhs, double rhs)

Returns true if lhs >= rhs, false otherwise.

scalar_near_equal¶

bool scalar_near_equal(double lhs, double rhs, double threshold)

Returns true if both inputs are nearly equal, otherwise false: abs(lhs - rhs) <= threshold.

scalar_is_finite¶

bool scalar_is_finite(double input)

Returns true if the input is finite (not NaN or Inf), false otherwise.

scalar_round_symmetric¶

double scalar_round_symmetric(double input)

Returns the rounded input using a symmetric algorithm. scalar_round_symmetric(1.5) = 2.0 scalar_round_symmetric(1.2) = 1.0 scalar_round_symmetric(-1.5) = -2.0 scalar_round_symmetric(-1.2) = -1.0

scalar_round_bankers¶

double scalar_round_bankers(double input)

Returns the rounded input using banker's rounding (half to even). scalar_round_bankers(2.5) = 2.0 scalar_round_bankers(1.5) = 2.0 scalar_round_bankers(1.2) = 1.0 scalar_round_bankers(-2.5) = -2.0 scalar_round_bankers(-1.5) = -2.0 scalar_round_bankers(-1.2) = -1.0

scalar_fraction¶

double scalar_fraction(double value)

Returns the fractional part of the input.

scalar_safe_to_double¶

template<typename SrcIntegralType>
double scalar_safe_to_double(SrcIntegralType input)

Safely casts an integral input into a float64 output.

scalar_load¶

double scalar_load(const double* input)

Loads a scalar from memory.

scalar_load_as_scalar¶

scalard scalar_load_as_scalar(const double* input)

Loads a scalar from memory.

Trigonometric functions¶

scalar_sin¶

double scalar_sin(double angle)

Returns the sine of the input angle.

scalar_cos¶

double scalar_cos(double angle)

Returns the cosine of the input angle.

scalar_sincos¶

vector4d scalar_sincos(double angle)

Returns both sine and cosine of the input angle. The result's [x] component contains sin(angle). The result's [y] component contains cos(angle). [zw] are undefined.

void scalar_sincos(double angle, double& out_sin, double& out_cos)

Returns both sine and cosine of the input angle.

scalar_asin¶

double scalar_asin(double value)

Returns the arc-sine of the input. Input value must be in the range [-1.0, 1.0].

scalar_acos¶

double scalar_acos(double value)

Returns the arc-cosine of the input. Input value must be in the range [-1.0, 1.0].

scalar_tan¶

double scalar_tan(double angle)

Returns the tangent of the input angle.

scalar_atan¶

double scalar_atan(double value)

Returns the arc-tangent of the input. Note that due to the sign ambiguity, atan cannot determine which quadrant the value resides in. See scalar_atan2.

scalar_atan2¶

double scalar_atan2(double y, double x)

Returns the arc-tangent of [y/x] using the sign of the arguments to determine the correct quadrant. Y represents the proportion of the y-coordinate. X represents the proportion of the x-coordinate.

scalar_deg_to_rad¶

constexpr double scalar_deg_to_rad(double deg)

Converts degrees into radians.

scalar_rad_to_deg¶

constexpr double scalar_rad_to_deg(double rad)

Converts radians into degrees.