XS3 Math Types¶
Scalar Types¶
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typedef int exponent_t¶
An exponent.
Many places in this API make use of integers representing the exponent associated with some floating-point value or block floating-point vector.
For a floating-point value \(x \cdot 2^p\), \(p\) is the exponent, and may usually be positive or negative.
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typedef unsigned headroom_t¶
Headroom of some integer or integer array.
Represents the headroom of a signed or unsigned integer, complex integer or channel pair, or the headroom of the mantissa array of a block floating-point vector.
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typedef int right_shift_t¶
A rightwards arithmetic bit-shift.
Represents a right bit-shift to be applied to an integer. May be signed or unsigned, depending on context. If signed, negative values represent leftward bit-shifts.
See also
-
typedef int left_shift_t¶
A leftwards arithmetic bit-shift.
Represents a left bit-shift to be applied to an integer. May be signed or unsigned, depending on context. If signed, negative values represent rightward bit-shifts.
See also
-
typedef int32_t fixed_s32_t¶
A 32-bit fixed-point scalar.
Represents a 32-bit fixed-point scalar with a Q-format implied by the context in which it occurs. Typically this type will be used for fixed-point function parameters as a hint to the user to check the documentation for the required Q-format.
If a function has a
fixed_s32_t
parameter ending with_qXX
(where theX
are digits), theXX
typically indicates the number of fractional bits. For example, afixed_s32_t
parameter calledcoef_q30
would imply 30 fractional bits and an associated exponent of -30. This is just a convention, however, and this interpretation should be verified in the function’s documentation.
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typedef int16_t fixed_s16_t¶
A 16-bit fixed-point scalar.
Represents a 16-bit fixed-point scalar with a Q-format implied by the context in which it occurs. Typically this type will be used for fixed-point function parameters as a hint to the user to check the documentation for the required Q-format.
If a function has a
fixed_s16_t
parameter ending with_qXX
(where theX
are digits), theXX
typically indicates the number of fractional bits. For example, afixed_s16_t
parameter calledcoef_q14
would imply 14 fractional bits and an associated exponent of -14. This is just a convention, however, and this interpretation should be verified in the function’s documentation.
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struct complex_s64_t¶
- #include <xs3_math_types.h>
A complex number with a 64-bit real part and 64-bit imaginary part.
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struct complex_s32_t¶
- #include <xs3_math_types.h>
A complex number with a 32-bit real part and 32-bit imaginary part.
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struct complex_s16_t¶
- #include <xs3_math_types.h>
A complex number with a 16-bit real part and 16-bit imaginary part.
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struct float_s32_t¶
- #include <xs3_math_types.h>
A floating-point scalar with a 32-bit mantissa.
Represents a (non-standard) floating-point value given by \( M \cdot 2^{x} \), where \(M\) is the 32-bit mantissa
mant
, and \(x\) is the exponentexp
.To convert a
float_s32_t
to a standard IEEE754 single-precision floating-point value (which may result in a loss of precision):float to_ieee_float(float_s32_t x) { return ldexpf(x.mant, x.exp); }
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struct float_s64_t¶
- #include <xs3_math_types.h>
A floating-point scalar with a 64-bit mantissa.
Represents a (non-standard) floating-point value given by \( M \cdot 2^{x} \), where \(M\) is the 64-bit mantissa
mant
, and \(x\) is the exponentexp
.To convert a
float_s64_t
to a standard IEEE754 double-precision floating-point value (which may result in a loss of precision):double to_ieee_float(float_s64_t x) { return ldexp(x.mant, x.exp); }
-
struct float_complex_s16_t¶
- #include <xs3_math_types.h>
A complex floating-point scalar with a complex 16-bit mantissa.
Represents a (non-standard) complex floating-point value given by \( A + j\cdot B \cdot 2^{x} \), where \(A\) is
mant.re
, the 16-bit real part of the mantissa, \(B\) ismant.im
, the 16-bit imaginary part of the mantissa, and \(x\) is the exponentexp
.
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struct float_complex_s32_t¶
- #include <xs3_math_types.h>
A complex floating-point scalar with a complex 32-bit mantissa.
Represents a (non-standard) complex floating-point value given by \( A + j\cdot B \cdot 2^{x} \), where \(A\) is
mant.re
, the 32-bit real part of the mantissa, \(B\) ismant.im
, the 32-bit imaginary part of the mantissa, and \(x\) is the exponentexp
.
-
struct float_complex_s64_t¶
- #include <xs3_math_types.h>
A complex floating-point scalar with a complex 64-bit mantissa.
Represents a (non-standard) complex floating-point value given by \( A + j\cdot B \cdot 2^{x} \), where \(A\) is
mant.re
, the 64-bit real part of the mantissa, \(B\) ismant.im
, the 64-bit imaginary part of the mantissa, and \(x\) is the exponentexp
.
Block Floating-Point Types¶
-
enum bfp_flags_e¶
(Opaque) Flags field for BFP vectors.
Warning
Users should not manually modify fields of this type, as it is intended to be opaque.
Values:
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enumerator BFP_FLAG_DYNAMIC¶
Indicates that BFP vector’s mantissa buffer(s) were allocated dynamically
This flag lets the bfp_*_dealloc() functions know whether the mantissa vector must be free()ed.
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enumerator BFP_FLAG_DYNAMIC¶
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struct bfp_s32_t¶
- #include <xs3_math_types.h>
A block floating-point vector of 32-bit elements.
Initialized with the
bfp_s32_init()
function.The logical quantity represented by each element of this vector is:
data[i]*2^(exp)
where the multiplication and exponentiation are using real (non-modular) arithmetic.The BFP API keeps the
hr
field up-to-date with the current headroom ofdata[]
so as to minimize precision loss as elements become small. [bfp_s32_t]Public Members
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int32_t *data¶
Pointer to the underlying element buffer.
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exponent_t exp¶
Exponent associated with the vector.
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headroom_t hr¶
Current headroom in the
data[]
-
unsigned length¶
Current size of
data[]
, expressed in elements
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bfp_flags_e flags¶
BFP vector flags. Users should not normally modify these manually.
-
int32_t *data¶
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struct bfp_s16_t¶
- #include <xs3_math_types.h>
A block floating-point vector of 16-bit elements.
Initialized with the
bfp_s16_init()
function.The logical quantity represented by each element of this vector is:
data[i] * 2^(exp)
where the multiplication and exponentiation are using real (non-modular) arithmetic.The BFP API keeps the
hr
field up-to-date with the current headroom ofdata[]
so as to minimize precision loss as elements become small. [bfp_s16_t]Public Members
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int16_t *data¶
Pointer to the underlying element buffer.
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exponent_t exp¶
Exponent associated with the vector.
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headroom_t hr¶
Current headroom in the
data[]
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unsigned length¶
Current size of
data[]
, expressed in elements
-
bfp_flags_e flags¶
BFP vector flags. Users should not normally modify these manually.
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int16_t *data¶
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struct bfp_complex_s32_t¶
- #include <xs3_math_types.h>
A block floating-point vector of complex 32-bit elements.
Initialized with the
bfp_complex_s32_init()
function.The logical quantity represented by each element of this vector is:
data[k].re * 2^(exp) + i * data[k].im * 2^(exp)
where the multiplication and exponentiation are using real (non-modular) arithmetic, and i is sqrt(-1)The BFP API keeps the
hr
field up-to-date with the current headroom ofdata[]
so as to minimize precision loss as elements become small. [bfp_complex_s32_t]Public Members
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complex_s32_t *data¶
Pointer to the underlying element buffer.
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exponent_t exp¶
Exponent associated with the vector.
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headroom_t hr¶
Current headroom in the
data[]
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unsigned length¶
Current size of
data[]
, expressed in elements
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bfp_flags_e flags¶
BFP vector flags. Users should not normally modify these manually.
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complex_s32_t *data¶
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struct bfp_complex_s16_t¶
- #include <xs3_math_types.h>
A block floating-point vector of complex 16-bit elements.
Initialized with the
bfp_complex_s16_init()
function.The logical quantity represented by each element of this vector is:
data[k].re * 2^(exp) + i * data[k].im * 2^(exp)
where the multiplication and exponentiation are using real (non-modular) arithmetic, and i is sqrt(-1)The BFP API keeps the
hr
field up-to-date with the current headroom ofdata[]
so as to minimize precision loss as elements become small. [bfp_complex_s16_t]Public Members
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int16_t *real¶
Pointer to the underlying element buffer.
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int16_t *imag¶
Pointer to the underlying element buffer.
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exponent_t exp¶
Exponent associated with the vector.
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headroom_t hr¶
Current headroom in the
data[]
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unsigned length¶
Current size of
data[]
, expressed in elements
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bfp_flags_e flags¶
BFP vector flags. Users should not normally modify these manually.
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int16_t *real¶
Misc Types¶
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struct complex_float_t¶
- #include <xs3_math_types.h>
A complex number with a single-precision floating-point real part and a single-precision floating-point imaginary part.
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struct complex_double_t¶
- #include <xs3_math_types.h>
A complex number with a double-precision floating-point real part and a double-precision floating-point imaginary part.
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struct xs3_split_acc_s32_t¶
- #include <xs3_math_types.h>
Holds a set of sixteen 32-bit accumulators in the XS3 VPU’s internal format.
The XS3 VPU stores 32-bit accumulators with the most significant 16-bits stored in one 256-bit vector register (called vD), and the least significant 16-bit stored in another 256-bit register (called vR). This struct reflects that internal format, and is occasionally used to store intermediate results.
Note
vR
is unsigned. This reflects the fact that a signed 16-bit integer0xSTUVWXYZ
is always exactly0x0000WXYZ
larger than0xSTUV0000
. To combine the upper and lower 16-bits of an accumulator, use(((int32_t)vD[k]) << 16) + vR[k]
.