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31 .Nd fixed-point math library based on the
39 data types and APIs support fixed-point math based on the
66 .Bq 2, 4, 6, 8, 16, 32, 48
67 bits of precision after the binary radix point,
72 The number of bits available for the integral component is not explicitly
73 specified, and implicitly consumes the remaining available bits of the chosen Q
79 None of the operations is affected by the floating-point environment.
86 .Bl -column "isgreaterequal" "bessel function of the second kind of the order 0"
124 .Xr Q_PRECEQ 3 compare bits
134 .Ss Functions which manipulate the control/sign data bits
140 .Xr Q_GCRAW 3 raw control bits
141 .Xr Q_GCVAL 3 value of control bits
142 .Xr Q_SCVAL 3 set control bits
144 .Ss Functions which manipulate the combined integer/fractional data bits
147 .Xr Q_IFVALIMASK 3 value of integer bits
148 .Xr Q_IFVALFMASK 3 value of fractional bits
149 .Xr Q_GIFRAW 3 raw integer/fractional bits
150 .Xr Q_GIFABSVAL 3 absolute value of fractional bits
151 .Xr Q_GIFVAL 3 real value of fractional bits
152 .Xr Q_SIFVAL 3 set integer/fractional bits
155 .Ss Functions which manipulate the integer data bits
158 .Xr Q_GIRAW 3 raw integer bits
159 .Xr Q_GIABSVAL 3 absolute value of integer bits
160 .Xr Q_GIVAL 3 real value of integer bits
161 .Xr Q_SIVAL 3 set integer bits
163 .Ss Functions which manipulate the fractional data bits
166 .Xr Q_GFRAW 3 raw fractional bits
167 .Xr Q_GFABSVAL 3 absolute value of fractional bits
168 .Xr Q_GFVAL 3 real value of fractional bits
169 .Xr Q_SFVAL 3 set fractional bits
173 .Xr Q_NCBITS 3 number of reserved control bits
176 .Xr Q_NTBITS 3 number of total bits
177 .Xr Q_NFCBITS 3 number of control-encoded fractional bits
178 .Xr Q_MAXNFBITS 3 number of maximum fractional bits
179 .Xr Q_NFBITS 3 number of effective fractional bits
180 .Xr Q_NIBITS 3 number of integer bits
185 .Xr Q_SHL 3 left-shifted value
186 .Xr Q_SHR 3 right-shifted value
193 data types and APIs support fixed-point math based on the
200 specifies the number of bits for integral data
204 specifies the number of bits for fractional data.
207 .Bd -literal -offset indent
231 The 3 least significant bits
234 .Bl -dash
236 bits 1-2 specify the binary radix point shift index operand, with 00,01,10,11 ==
246 .Bq 2,4,6,8,16,32,48,64
247 bits of precision after the binary radix point.
248 The number of bits available for the integral component is not explicitly
249 specified, and implicitly consumes the remaining available bits of the chosen Q
273 .Bd -literal -offset indent
284 Important bit counts are: total, control, control-encoded fractional, maximum
285 fractional, effective fractional and integer bits.
287 The count of total bits is derived from the size of the q_t data type.
288 For example, a s32q_t has 32 total bits.
290 The count of control-encoded fractional bits is derived from calculating the
291 number of fractional bits per the control bit encoding scheme.
292 For example, the control bits binary value of 101 encodes a fractional bit
293 count of 2 x 16 = 32 fractional bits.
295 The count of maximum fractional bits is derived from the difference between the
296 counts of total bits and control/sign bits.
297 For example, a s32q_t has a maximum of 32 - 3 - 1 = 28 fractional bits.
299 The count of effective fractional bits is derived from the minimum of the
300 control-encoded fractional bits and the maximum fractional bits.
301 For example, a s32q_t with 32 control-encoded fractional bits is effectively
302 limited to 28 fractional bits.
304 The count of integer bits is derived from the difference between the counts of
305 total bits and all other non-integer data bits
306 .Pq the sum of control, fractional and sign bits.
307 For example, a s32q_t with 8 effective fractional bits has 32 - 3 - 8 - 1 = 20 integer
308 bits.
309 The count of integer bits can be zero if all available numeric data bits have
310 been reserved for fractional data, e.g., when the number of control-encoded
311 fractional bits is greater than or equal to the underlying Q data type's maximum
312 fractional bits.
315 .Bd -literal -offset indent
317 char buf[32]
327 Q_TOSTR(a, -1, 10, buf, sizeof(buf));
333 initialise it with the fixed-point value for 5/3, and render a debugging
335 .Pq including its full precision decimal C-string representation ,
337 .Bd -literal -offset indent
342 Q_TOSTR(s32, -1, 10, buf, sizeof(buf));
347 .Bd -literal -offset indent
348 "s32"@0x7fffffffe7d4
382 .An -nosplit