(Mozzi is a sound synthesis toolkit for the Arduino)
The naming of the fixed-point types is based on the Qm.f-notation ("the unambiguous form") as described in the notation section of the wikipedia article on fixed-point arithmetic, replacing . with n.[^ Since `.` does not work in C.]
There are no automatic conversions.
For every fixed-point type with fractional part there is a floating point conversion method
float_to_Q<a>n<b>
Q<a>n<b>_to_floatAdditionally, there are conversion methods as displayed in the below graphics (and listed in the dedicated section below).
Converting a fixed-point number to another type by casting works as long as
- it has the same amount of fractional bits and
- the number of used integer bits in the old representation is less or equal to the number of integer bits available in the new representation.
Representation of the closest approximation of 1:
// unsigned
Q0n16_FIX1;
Q0n32_FIX1;
Q1n15_FIX1;
Q8n8_FIX1;
Q16n16_FIX1;
Q8n24_FIX1;
Q15n16_FIX1;
Q23n8_FIX1;
// signed
Q0n7_FIX1;
Q0n15_FIX1;
Q1n14_FIX1;
Q7n8_FIX1;
Q15n0_FIX1;Representation of the closest approximation of PI resp. 2PI:
// signed
Q16n16_PI
Q16n16_2PI
// signed
Q3n13_2PI.ffffffff // [0.0 ... 0.996]
Unsigned fractional number with 8 fractional bits.
Conversion to
Q8n24_to_Q0n8
Q24n8_to_Q0n8Conversion from
// unsigned
Q0n8_to_Q1n15
Q0n8_to_Q8n8
Q0n8_to_Q16n16
Q0n8_to_Q8n24
Q0n8_to_Q24n8
// signed
Q0n8_to_Q15n16
Conversion to
// unsigned
Q16n16_to_Q0n8.ffffffffffffffff // [0.0 ... 0.999]
Unsigned fractional number with 16 fractional bits.
Conversion to
// unsigned
Q16n16_to_Q0n8.ffffffffffffffffffffffffffffffff // [0 ... 0.999999999767169]
Unsigned fractional number with 0 integer bits and 32 fractional bits.
i.fffffffffffffff // [0 ... 1.999]
Unsigned fractional number with 1 integer bit and 15 fractional bits.
Conversion methods to
Q0n8_to_Q1n15Conversion methods from
Q1n15_to_Q0n8iii.fffffffffffff // [0 ... 7.999]
Unsigned fractional number with 3 integer bits and 13 fractional bits.
iiiiiiii.ffffffff // [0 ... 255.996]
Unsigned fractional number with 8 integer bits and 8 fractional bits.
Conversion methods to
Q0n8_to_Q8n8Conversion methods from
Q8n8_to_Q8n0
Q8n8_to_Q16n16`iiiiiiiiiiiiiiii.ffffffffffffffff // [0 ... 65535.999]
Unsigned fractional number with 16 integer bits and 16 fractional bits.
Conversion methods to
// unsigned
Q0n8_to_Q16n16
Q8n0_to_Q16n16
Q8n8_to_Q16n16
Q16n0_to_Q16n16
Q24n8_to_Q16n16Conversion methods from
// unsigned
Q16n16_to_Q0n8
Q16n16_to_Q16n0
Q16n16_to_Q24n8Usage:
int i_val = 127; // e.g from int
Q16n16 q_val = Q16n0_to_Q16n16(i_val);Q8n24 -- signed fractional number with 8 integer bits and 24 fractional bits.
[0 ... 255.999]
Conversion methods to
Q0n8_to_Q8n24Conversion methods from
Q8n24_to_Q0n8iiiiiiiiiiiiiiiiiiiiiiii.ffffffff // [0 ... 16777215]
unsigned fractional number with 24 integer bits and 8 fractional bits. [0 to represents 0 to 16777215.
// e.g. read from an analog input.
// could also be ints and unsigned ints, as long as they are positive
long i_val = 127;
Q24n8 q_val = Q16n0_to_Q24n8(i_val);Conversion methods to Q24n8 are:
// unsigned
Q0n8_to_Q24n8(a);
Q16n16_to_Q24n8(a);
Q16n0_to_Q24n8(a);Conversion methods from Q24n8 are:
// unsigned
Q24n8_to_Q0n8
Q24n8_to_Q16n16
Q24n8_to_Q16n0
Q24n8_to_Q32n0 calculate fractions for amplitude or frequency modulation and use it to set the frequency of an oscillator
Q24n8 q_freq = q_val / 10 + 100;
aOsc.setFreq(q_freq);iiiiiiii. // [0.0 ... 255.0]
Same as unsigned char.
Unsigned number with 0 fractional bits.
Conversion methods to
Q8n8_to_Q8n0Conversion methods from
// unsigned
Q8n0_to_Q7n8
Q8n0_to_Q8n8
Q8n0_to_Q16n16
// signed
Q8n0_to_Q15n16iiiiiiiiiiiiiiii // [0 ... 65536.0]
Unsigned number with 16 integer bits and 0 fractional bits.
Conversion methods to
// unsigned
Q24n8_to_Q16n0
// signed
Q23n8_to_Q16n0Conversion methods from
// unsigned
Q16n0_to_Q16n16
Q16n0_to_Q24n8
// signed
Q16n0_to_Q15n16
Q16n0_to_Q23n8iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii // [0 ... 4294967295]
Same as unsigned long int.
Unsigned number with 32 integer bits and 0 fractional bits.
Conversion methods to
// unsigned
Q24n8_to_Q32n0[+|-] .fffffff // [-0.5 ... 0.496]
Signed fractional number with 7 fractional bits.
Conversion methods to
Q1n14_to_Q0n7Conversion methods from
Q0n7_to_Q1n14
Q0n7_to_Q15n16
[+|-] .fffffffffffffff // [-0.32768 ... 0.32767]
Signed fractional number with 0 integer bits and 15 fractional bits.
[+|-] .fffffffffffffffffffffffffffffff // [-32768 ... 32767]
Signed fractional number with 0 integer bits and 31 fractional bits.
[+|-] i.ffffffffffffff // [-1.999 ... 1.999]
Signed fractional number with 1 integer bit and 14 fractional bits.
Conversion methods to
Q0n7_to_Q1n14()Conversion methods from
Q1n14_to_Q0n7[+|-] iiiiiii.ffffffff // [-127.996 ... 127.996]
Signed fractional number with 7 integer bits and 8 fractional bits.
Conversion methods to
// unsigned
Q8n0_to_Q7n8
// signed
Q15n16_to_Q7n8
Q23n8_to_Q7n8
Q7n0_to_Q7n8Conversion methods from
// signed
Q7n8_to_Q7n0
Q7n8_to_Q15n16[+|-] iiiiiiiiiiiiiiiiiiiiiii.ffffffff // [-8388607.996 ... 8388607.996]
Signed fractional number with 23 integer bits and 8 fractional bits.
Conversion methods to
// unsigned
Q16n0_to_Q23n8
Q15n16_to_Q23n8Conversion methods from
// unsigned
Q23n8_to_Q16n0
// signed
Q23n8_to_Q7n8
Q23n8_to_Q15n0
Q23n8_to_Q31n0[+|-] iiiiiiiiiiiiiii.ffffffffffffffff // [-32767.999 ... 32767.999]
Signed fractional number with 15 integer bits and 16 fractional bits.
Conversion methods to
// unsigned
Q0n8_to_Q15n16
Q8n0_to_Q15n16
// signed
Q0n7_to_Q15n16
Q7n8_to_Q15n16
Q7n0_to_Q15n16
Q15n0_to_Q15n16Conversion methods from
// unsigned
Q15n16_to_Q0n8
// signed
Q15n16_to_Q7n8
Q15n16_to_Q23n8
Q15n16_to_Q15n0[+|-] . // [-128 ... 127]
Same as char.
Signed fractional number with 7 integer bits 0 fractional bits.
// unsigned
Q16n0_to_Q15n16
// signed
Q7n0_to_Q7n8
Q7n0_to_Q15n16
[+|-] fffffffffffffff. // [-2147483648 ... 2147483647]
Signed number with 15 integer bits and 0 fractional bits.
Conversion methods to
Q15n0_to_Q15n16Conversion methods from
Q15n16_to_Q15n0[+|-] iiiiiiiiiiiiiiiiiiiiiiiiiiiiiii. // [-2147483648 ... 2147483647]
Signed (normal long int) number with 31 integer bits and 0 fractional bits.
Conversion methods to
Q23n8_to_Q31n0
