List of implemented functions

Q16.16 Fixed point functions

These functions operate on 32-bit numbers, fix16_t, which have 16 bit integer part and 16 bit fractional part.

Conversion functions

Conversion from integers and floating point values. These conversions retain the numeric value and perform rounding where necessary.

• fix16_from_int(a) Simply multiplies a by fix16_one = 65536
• fix16_to_int(a) Divides by fix16_one and rounds to nearest integer.
• fix16_from_float(a) Multiplies by fix16_one and rounds to nearest value.
• fix16_to_float(a) Divides by fix16_one. Rounding is according to the current floating point mode.
• fix16_from_dbl(a) Multiplies by fix16_one and rounds to nearest value.
• fix16_to_dbl(a) Divides by fix16_one. All fix16_t values fit into a double, so no rounding happens.
• fix16_from_str(buf) Converts from string to fix16_t.
• fix16_to_str(value, buf, decimals) Converts from fix16_t to string.

Accuracy: all non-trivial ones are covered by tests and accurate up to datatype limits.

Basic arithmetic

These functions perform rounding and detect overflows, unless disabled with CompilationOptions. When overflow is detected, they return fix16_overflow as a marker value.

• fix16_add(a,b) Addition
  • Implementation 1: just C's + operator
  • Implementation 2: with overflow detection
• fix16_sub(a,b) Subtraction.
  • Implementation 1: just C's - operator
  • Implementation 2: with overflow detection
• fix16_mul(a,b) Multiplication .
  • Implementation 1: using int32_t * int32_t -> int64_t
  • Implementation 2: using (u)int16_t * (u)int16_t -> (u)int32_t
  • Implementation 3: using uint8_t * uint8_t -> int16_t
• fix16_div(a,b) Division.
  • Implementation 1: using uint32_t / uint32_t
  • Implementation 2: performing division manually with uint32_t

Accuracy: these functions are covered by UnitTests and are accurate to Fix16Limits.

Saturating arithmetic

Functions for basic arithmetic that saturate instead of overflowing. They are based around the functions listed above, but add extra logic to convert fix16_overflow to either fix16_min or fix16_max.

• fix16_sadd(a,b) Saturating addition
• fix16_ssub(a,b) Saturating subtraction
• fix16_smul(a,b) Saturating multiplication
• fix16_sdiv(a,b) Saturating division

Accuracy: these functions are not yet covered by tests.

Transcendental functions

Roots, exponents & similar.

• fix16_sqrt(a) Square root. Performs rounding and is accurate to Fix16Limits.
• fix16_exp(a) Exponential function using power series approximation. Accuracy depends on range, worst case +-40 absolute for negative inputs and +-0.003% for positive inputs. Average error is +-1 for neg and +-0.0003% for pos.
• fix16_log(a) Natural logarithm using Newton approximation and fix16_exp(). Worst case error +-3 absolute, average error less than 1 unit.

These functions are covered by UnitTests.

Trigonometric functions

Functions for sin, tan etc.

• fix16_sin(a) Sine for angle in radians
• fix16_sin_parabola(a) Alternative sine implementation.
• fix16_cos(a) Cosine for angle in radians
• fix16_tan(a) Tangent for angle in radians
• fix16_asin(a) Inverse of sine, output in radians
• fix16_acos(a) Inverse of cosine, output in radians
• fix16_atan(a) Inverse of tangent, output in radians
• fix16_atan2(a,b) Inverse of tangent with automatic sign handling. Output in radians.

Accuracy: these functions are not yet covered by tests.