Brickworks > API documentation > bw_math
A collection of mathematical routines that strive to be better suited to DSP than, e.g., those supplied by your C standard library.
Such a goal is hopefully accomplished by:
0.f and -0.f.In practice they should guarantee fast and consistent performance, but always do your own benchmarking.
All functions in this module are reentrant, RT-safe, thread-safe, and have no side effects.
Module type: utility
Version: 1.0.1
Requires:
static inline int32_t bw_signfilli32(
int32_t x);
Returns ~0 if x is negative, 0 otherwise.
static inline int32_t bw_mini32(
int32_t a,
int32_t b);
Returns the minimum of a and b.
static inline int32_t bw_maxi32(
int32_t a,
int32_t b);
Returns the maximum of a and b.
static inline int32_t bw_clipi32(
int32_t x,
int32_t m,
int32_t M);
Returns x unless it is smaller than m, in which case it returns m, or bigger than M, in which case it returns M.
static inline uint32_t bw_minu32(
uint32_t a,
uint32_t b);
Returns the minimum of a and b.
static inline uint32_t bw_maxu32(
uint32_t a,
uint32_t b);
Returns the maximum of a and b.
static inline uint32_t bw_clipu32(
uint32_t x,
uint32_t m,
uint32_t M);
Returns x unless it is smaller than m, in which case it returns m, or bigger than M, in which case it returns M.
static inline float bw_copysignf(
float x,
float y);
Returns a value that has the absolute value of x and the sign of y.
static inline float bw_signf(
float x);
Returns 1.f if x > 0.f, -1.f if x < 0.f and 0.f if x == 0.f.
static inline float bw_absf(
float x);
Returns the absolute value of x.
static inline float bw_min0f(
float x);
Returns the minimum of 0.f and x.
static inline float bw_max0f(
float x);
Returns the maximum of 0.f and x.
static inline float bw_minf(
float a,
float b);
Returns the minimum of a and b.
static inline float bw_maxf(
float a,
float b);
Returns the maximum of a and b.
static inline float bw_clipf(
float x,
float m,
float M);
Returns x unless it is smaller than m, in which case it returns m, or bigger than M, in which case it returns M.
M must be greater than or equal to m.
static inline float bw_truncf(
float x);
Returns x with its fractional part set to zero (i.e., rounded towards zero).
x must be finite.
static inline float bw_roundf(
float x);
Returns x rounded to the nearest integer.
Halfway cases are rounded away from zero. E.g., bw_roundf(0.5f) gives 1.f and bw_roundf(-0.5f) gives -1.f.
x must be finite.
static inline float bw_floorf(
float x);
Returns the biggest integer less or equal than x (i.e., x is rounded down).
x must be finite.
static inline float bw_ceilf(
float x);
Returns the smallest integer greater or equal than x (i.e., x is rounded up).
x must be finite.
static inline void bw_intfracf(
float x,
float * BW_RESTRICT i,
float * BW_RESTRICT f);
Puts the integer part (floor) of x in i and the fractional part in f.
x must be finite.
static inline float bw_rcpf(
float x);
Returns the reciprocal of x (i.e., 1.f / x).
|x| must be in [8.077935669463161e-28f, 1.237940039285380e+27].
Relative error < 0.0013%.
static inline float bw_sin2pif(
float x);
Returns an approximation of the sine of 2 * pi * x, where x is given in radians.
x must be finite.
Absolute error < 0.011 or relative error < 1.7%, whatever is worse.
static inline float bw_sinf(
float x);
Returns an approximation of the sine of x, where x is given in radians.
x must be finite.
Absolute error < 0.011 or relative error < 1.7%, whatever is worse.
static inline float bw_cos2pif(
float x);
Returns an approximation of the cosine of 2 * pi * x, where x is given in radians.
x must be finite.
Absolute error < 0.011 or relative error < 1.7%, whatever is worse.
static inline float bw_cosf(
float x);
Returns an approximation of the cosine of x, where x is given in radians.
x must be finite.
Absolute error < 0.011 or relative error < 1.7%, whatever is worse.
static inline float bw_tan2pif(
float x);
Returns an approximation of the tangent of 2 * pi * x, where x is given in radians.
x must be finite and in [-1/4 + 5e-4f / pi, 1/4 - 5e-4f / pi] + k / 2, where k is any integer number.
Absolute error < 0.06 or relative error < 0.8%, whatever is worse.
static inline float bw_tanf(
float x);
Returns an approximation of the tangent of x, where x is given in radians.
x must be finite and in [-pi/2 + 1e-3f, pi/2 - 1e-3f] + k * pi, where k is any integer number.
Absolute error < 0.06 or relative error < 0.8%, whatever is worse.
static inline float bw_log2f(
float x);
Returns an approximation of the base-2 logarithm of x.
x must be finite and greater than or equal to 1.175494350822287e-38f.
Absolute error < 0.0055 or relative error < 1.2%, whatever is worse.
static inline float bw_logf(
float x);
Returns an approximation of the natural logarithm of x.
x must be finite and greater than or equal to 1.175494350822287e-38f.
Absolute error < 0.0038 or relative error < 1.2%, whatever is worse.
static inline float bw_log10f(
float x);
Returns an approximation of the base-10 logarithm of x.
x must be finite and greater than or equal to 1.175494350822287e-38f.
Absolute error < 0.0017 or relative error < 1.2%, whatever is worse.
static inline float bw_pow2f(
float x);
Returns an approximation of 2 raised to the power of x. For x < -126.f it just returns 0.f.
x must be less than or equal to 127.999f.
Relative error < 0.062%.
static inline float bw_expf(
float x);
Returns an approximation of e (Euler's number) raised to the power of x. For x < -87.3365447505531f it just returns 0.
x must be less than or equal to 88.722f.
Relative error < 0.062%.
static inline float bw_pow10f(
float x);
Returns an approximation of 10 raised to the power of x. For x < -37.92977945366162f it just returns 0.
x must be less than or equal to 38.531f.
Relative error < 0.062%.
static inline float bw_dB2linf(
float x);
Returns an approximation of 10 raised to the power of x / 20 (dB to linear ratio conversion). For x < -758.5955890732315f it just returns 0.f.
x must be less than or equal to 770.630f.
Relative error < 0.062%.
static inline float bw_lin2dBf(
float x);
Returns an approximation of 20 times the base-10 logarithm of x (linear ratio to dB conversion).
x must be finite and greater than or equal to 1.175494350822287e-38f.
Absolute error < 0.032 or relative error < 1.2%, whatever is worse.
static inline float bw_sqrtf(
float x);
Returns an approximation of the square root of x.
x must be finite and non-negative.
Absolute error < 1.09e-19 or relative error < 0.0007%, whatever is worse.
static inline float bw_tanhf(
float x);
Returns an approximation of the hyperbolic tangent of x.
Absolute error < 0.035 or relative error < 6.5%, whatever is worse.
static inline float bw_sinhf(
float x);
Returns an approximation of the hyperbolic sine of x.
|x| must less than or equal to 88.722f.
Absolute error < 1e-7 or relative error < 0.07%, whatever is worse.
static inline float bw_coshf(
float x);
Returns an approximation of the hyperbolic cosine of x.
|x| must less than or equal to 88.722f.
Relative error < 0.07%.
static inline float bw_asinhf(
float x);
Returns an approximation of the hyperbolic arcsine of x.
|x| must less than or equal to 8.507059173023462e+37f.
Absolute error < 0.004 or relative error < 1.2%, whatever is worse.
static inline float bw_acoshf(
float x);
Returns an approximation of the hyperbolic arccosine of x.
x must be in [1.f, 8.507059173023462e+37f].
Absolute error < 0.004 or relative error < 0.8%, whatever is worse.
BW_NULL.bw_truncf(), bw_roundf(), and bw_sqrtf().bw_min0xf() as bw_min0f() and bw_max0xf() as bw_max0f().bw_min0f(), bw_max0f(), bw_minf(), bw_maxf(), and bw_clipf().bw_roundf() when absolute value of input was in [0.5f, 1.f].bw_ceilf() for negative input values.bw_sqrtf() for very large input values and improved implementation.bw_asinhf() and bw_acoshf().BW_RESTRICT specifiers to input arguments of bw_intfracf().extern "C" to functions.bw_intfracf().bw_omega_3log() and bw_omega_3lognr().bw_pow10f_3() and bw_acoshf_3().bw_ceilf(), bw_intfracf(), bw_sinhf_3(), bw_coshf_3(), bw_asinhf_3(), and bw_acoshf_3().bw_log10f_3(), bw_pow10f_3(), bw_dB2linf_3(), and bw_lin2dBf_3().bw_sqrtf_2().bw_sin2pif_3(), bw_cos2pif_3(), bw_tan2pif_3(), bw_omega_3lognr(), and bw_tanhf_3().