From: Bill Zorn <bill.zorn@gmail.com>
Date: Fri, 3 Aug 2018 02:31:19 +0000 (-0700)
Subject: update posit interface
X-Git-Url: https://git.libre-soc.org/?a=commitdiff_plain;h=613fd66860992ec270d1515a4cd92b4468bc6280;p=sfpy.git

update posit interface
---

diff --git a/sfpy/cposit.pxd b/sfpy/cposit.pxd
index c7c4c3e..ad205d3 100644
--- a/sfpy/cposit.pxd
+++ b/sfpy/cposit.pxd
@@ -1,30 +1,60 @@
 from libc.stdint cimport *
 
+# As far as I can tell, this is never enabled when the library is comiled...
+# The option will have to be synced manually, as by the time Cython's c is
+# compiled the library will already be stored as a .a file and any compile-time
+# options used to build it will be long gone.
+DEF SOFTPOSIT_EXACT = 0
+
 cdef extern from '../SoftPosit/source/include/softposit.h':
 
-    ctypedef struct posit8_t:
-        pass
+    # Transparent types so we can have access to the raw bits.
+
+    IF SOFTPOSIT_EXACT:
+
+        ctypedef struct posit8_t:
+            uint8_t v;
+            bint exact;
+
+        ctypedef struct quire8_t:
+            uint32_t v;
+            bint exact;
+
+        ctypedef struct posit16_t:
+            uint16_t v;
+            bint exact;
 
-    ctypedef struct posit16_t:
-        pass
+        ctypedef struct quire16_t:
+            uint64_t v[2];
+            bint exact;
 
-    ctypedef struct posit32_t:
-        pass
+        ctypedef struct posit32_t:
+            uint32_t v;
+            bint exact;
 
-    ctypedef struct posit64_t:
-        pass
+        ctypedef struct quire32_t:
+            uint64_t v[8];
+            bint exact;
 
-    ctypedef struct posit128_t:
-        pass
+    ELSE:
 
-    ctypedef struct quire8_t:
-        pass
+        ctypedef struct posit8_t:
+            uint8_t v;
 
-    ctypedef struct quire16_t:
-        pass
+        ctypedef struct posit16_t:
+            uint16_t v;
 
-    ctypedef struct quire32_t:
-        pass
+        ctypedef struct posit32_t:
+            uint32_t v;
+
+        ctypedef struct quire8_t:
+            uint32_t v;
+
+        ctypedef struct quire16_t:
+            uint64_t v[2];
+
+        ctypedef struct quire32_t:
+            uint64_t v[8];
 
     # /*----------------------------------------------------------------------------
     # | Integer-to-posit conversion routines.
@@ -32,23 +62,23 @@ cdef extern from '../SoftPosit/source/include/softposit.h':
 
     posit8_t  ui32_to_p8( uint32_t );
     posit16_t ui32_to_p16( uint32_t );
-    posit32_t ui32_to_p32( uint32_t );
-    posit64_t ui32_to_p64( uint32_t );
+    # posit32_t ui32_to_p32( uint32_t );
+    # posit64_t ui32_to_p64( uint32_t );
 
     posit8_t  ui64_to_p8( uint64_t );
     posit16_t ui64_to_p16( uint64_t );
-    posit32_t ui64_to_p32( uint64_t );
-    posit64_t ui64_to_p64( uint64_t );
+    # posit32_t ui64_to_p32( uint64_t );
+    # posit64_t ui64_to_p64( uint64_t );
 
     posit8_t  i32_to_p8( int32_t );
     posit16_t i32_to_p16( int32_t );
-    posit32_t i32_to_p32( int32_t );
-    posit64_t i32_to_p64( int32_t );
+    # posit32_t i32_to_p32( int32_t );
+    # posit64_t i32_to_p64( int32_t );
 
     posit8_t  i64_to_p8( int64_t );
     posit16_t i64_to_p16( int64_t );
-    posit32_t i64_to_p32( int64_t );
-    posit64_t i64_to_p64( int64_t );
+    # posit32_t i64_to_p32( int64_t );
+    # posit64_t i64_to_p64( int64_t );
 
     # /*----------------------------------------------------------------------------
     # | 8-bit (quad-precision) posit operations.
@@ -62,8 +92,8 @@ cdef extern from '../SoftPosit/source/include/softposit.h':
     int_fast64_t p8_to_i64( posit8_t );
 
     posit16_t p8_to_p16( posit8_t );
-    #posit32_t p8_to_p32( posit8_t );
-    #posit64_t p8_to_p64( posit8_t );
+    # posit32_t p8_to_p32( posit8_t );
+    # posit64_t p8_to_p64( posit8_t );
 
     posit8_t p8_roundToInt( posit8_t );
     posit8_t p8_add( posit8_t, posit8_t );
@@ -98,14 +128,14 @@ cdef extern from '../SoftPosit/source/include/softposit.h':
     # *----------------------------------------------------------------------------*/
 
     bint isNaRP16UI( uint16_t );
-    
+
     uint_fast32_t p16_to_ui32( posit16_t );
     uint_fast64_t p16_to_ui64( posit16_t );
     int_fast32_t p16_to_i32( posit16_t);
     int_fast64_t p16_to_i64( posit16_t );
     posit8_t p16_to_p8( posit16_t );
-    #posit32_t p16_to_p32( posit16_t );
-    #posit64_t p16_to_p64( posit16_t );
+    # posit32_t p16_to_p32( posit16_t );
+    # posit64_t p16_to_p64( posit16_t );
 
     posit16_t p16_roundToInt( posit16_t);
     posit16_t p16_add( posit16_t, posit16_t );
@@ -118,18 +148,18 @@ cdef extern from '../SoftPosit/source/include/softposit.h':
     bint p16_le( posit16_t, posit16_t );
     bint p16_lt( posit16_t, posit16_t );
 
-    #Quire 16
+    # Quire 16
     quire16_t q16_fdp_add( quire16_t, posit16_t, posit16_t );
     quire16_t q16_fdp_sub( quire16_t, posit16_t, posit16_t );
-    #posit16_t convertQ16ToP16( quire16_t );
+    # posit16_t convertQ16ToP16( quire16_t );
     posit16_t q16_to_p16( quire16_t );
 
     bint isNaRQ16( quire16_t );
     bint isQ16Zero( quire16_t );
-    #quire16_t q16_TwosComplement( quire16_t );
+    # quire16_t q16_TwosComplement( quire16_t );
 
-    #void printBinary( uint64_t*, int );
-    #void printHex( uint64_t );
+    # void printBinary( uint64_t*, int );
+    # void printHex( uint64_t );
 
     quire16_t q16_clr( quire16_t );
     quire16_t castQ16( uint16_t, uint16_t );
@@ -139,5 +169,5 @@ cdef extern from '../SoftPosit/source/include/softposit.h':
 
     # Helper
     double convertP16ToDouble( posit16_t );
-    #posit16_t convertFloatToP16( float );
+    # posit16_t convertFloatToP16( float );
     posit16_t convertDoubleToP16( double );
diff --git a/sfpy/posit.pyx b/sfpy/posit.pyx
index ce3888c..d09b603 100644
--- a/sfpy/posit.pyx
+++ b/sfpy/posit.pyx
@@ -1,5 +1,13 @@
+from libc.stdint cimport *
 cimport cposit
 
+
+# special values needed for some initializations
+
+cdef posit8_one = cposit.ui32_to_p8(1)
+cdef posit16_one = cposit.ui32_to_p16(1)
+
+
 cdef class Posit8:
 
     # the wrapped posit value
@@ -17,16 +25,16 @@ cdef class Posit8:
         return obj
 
     @staticmethod
-    def from_bits(int value):
+    def from_bits(uint8_t value):
         """Factory function to create a Posit8 object from a bit pattern
         represented as an integer.
         """
         cdef Posit8 obj = Posit8.__new__(Posit8)
-        obj._c_posit = cposit.castP8(value)
+        obj._c_posit.v = value
         return obj
 
     @staticmethod
-    def from_double(float value):
+    def from_double(double value):
         """Factory function to create a Posit8 object from a double.
         """
         cdef Posit8 obj = Posit8.__new__(Posit8)
@@ -37,119 +45,128 @@ cdef class Posit8:
 
     def __init__(self, value):
         if isinstance(value, int):
-            self._c_posit = cposit.castP8(value)
+            self._c_posit.v = value
         else:
             f = float(value)
             self._c_posit = cposit.convertDoubleToP8(f)
 
+    def __float__(self):
+        return cposit.convertP8ToDouble(self._c_posit)
+
+    def __int__(self):
+        return int(cposit.convertP8ToDouble(self._c_posit))
+
     def __str__(self):
         return repr(cposit.convertP8ToDouble(self._c_posit))
 
     def __repr__(self):
         return 'Posit8(' + repr(cposit.convertP8ToDouble(self._c_posit)) + ')'
 
-    cpdef get_bits(self):
-        cdef int u = cposit.castUI8(self._c_posit)
-        return u
+    cpdef uint8_t get_bits(self):
+        return self._c_posit.v
     bits = property(get_bits)
 
     # arithmetic
 
-    cpdef round(self):
+    cpdef Posit8 round(self):
         cdef cposit.posit8_t f = cposit.p8_roundToInt(self._c_posit)
         return Posit8.from_c_posit(f)
 
-    def __round__(self, Posit8 other):
-        return self.roundToInt(other)
+    def __round__(self):
+        return self.roundToInt()
 
-    cpdef add(self, Posit8 other):
+    cpdef Posit8 add(self, Posit8 other):
         cdef cposit.posit8_t f = cposit.p8_add(self._c_posit, other._c_posit)
         return Posit8.from_c_posit(f)
 
     def __add__(self, Posit8 other):
         return self.add(other)
 
-    cpdef sub(self, Posit8 other):
+    cpdef Posit8 sub(self, Posit8 other):
         cdef cposit.posit8_t f = cposit.p8_sub(self._c_posit, other._c_posit)
         return Posit8.from_c_posit(f)
 
     def __sub__(self, Posit8 other):
         return self.sub(other)
 
-    cpdef mul(self, Posit8 other):
+    cpdef Posit8 mul(self, Posit8 other):
         cdef cposit.posit8_t f = cposit.p8_mul(self._c_posit, other._c_posit)
         return Posit8.from_c_posit(f)
 
     def __mul__(self, Posit8 other):
         return self.mul(other)
 
-    cpdef fma(self, Posit8 a2, Posit8 a3):
-      cdef cposit.posit8_t f = cposit.p8_mulAdd(self._c_posit, a2._c_posit, a3._c_posit)
-      return Posit8.from_c_posit(f)
+    cpdef Posit8 fma(self, Posit8 a2, Posit8 a3):
+        cdef cposit.posit8_t f = cposit.p8_mulAdd(self._c_posit, a2._c_posit, a3._c_posit)
+        return Posit8.from_c_posit(f)
 
-    cpdef div(self, Posit8 other):
+    cpdef Posit8 qma(self, Posit8 a1, Posit8 a2):
+        cdef cposit.posit8_t f = cposit.p8_mulAdd(a1._c_posit, a2._c_posit, self._c_posit)
+        return Posit8.from_c_posit(f)
+
+    cpdef Posit8 div(self, Posit8 other):
         cdef cposit.posit8_t f = cposit.p8_div(self._c_posit, other._c_posit)
         return Posit8.from_c_posit(f)
 
     def __truediv__(self, Posit8 other):
         return self.div(other)
 
-    cpdef sqrt(self):
+    cpdef Posit8 sqrt(self):
         cdef cposit.posit8_t f = cposit.p8_sqrt(self._c_posit)
         return Posit8.from_c_posit(f)
 
     # in-place arithmetic
 
-    cpdef iround(self):
+    cpdef void iround(self):
         self._c_posit = cposit.p8_roundToInt(self._c_posit)
 
-    cpdef iadd(self, Posit8 other):
+    cpdef void iadd(self, Posit8 other):
         self._c_posit = cposit.p8_add(self._c_posit, other._c_posit)
 
     def __iadd__(self, Posit8 other):
         self.iadd(other)
         return self
 
-    cpdef isub(self, Posit8 other):
+    cpdef void isub(self, Posit8 other):
         self._c_posit = cposit.p8_sub(self._c_posit, other._c_posit)
 
     def __isub__(self, Posit8 other):
         self.isub(other)
         return self
 
-    cpdef imul(self, Posit8 other):
+    cpdef void imul(self, Posit8 other):
         self._c_posit = cposit.p8_mul(self._c_posit, other._c_posit)
 
     def __imul__(self, Posit8 other):
         self.imul(other)
         return self
 
-    cpdef ifma(self, Posit8 a2, Posit8 a3):
+    cpdef void ifma(self, Posit8 a2, Posit8 a3):
         self._c_posit = cposit.p8_mulAdd(self._c_posit, a2._c_posit, a3._c_posit)
 
-    cpdef idiv(self, Posit8 other):
+    cpdef void iqma(self, Posit8 a1, Posit8 a2):
+        self._c_posit = cposit.p8_mulAdd(a1._c_posit, a2._c_posit, self._c_posit)
+
+    cpdef void idiv(self, Posit8 other):
         self._c_posit = cposit.p8_div(self._c_posit, other._c_posit)
 
     def __itruediv__(self, Posit8 other):
         self.idiv(other)
         return self
 
-    cpdef isqrt(self):
+    cpdef void isqrt(self):
         self._c_posit = cposit.p8_sqrt(self._c_posit)
 
     # comparison
 
-    cpdef eq(self, Posit8 other):
-        cdef bint b = cposit.p8_eq(self._c_posit, other._c_posit)
-        return b
+    cpdef bint eq(self, Posit8 other):
+        return cposit.p8_eq(self._c_posit, other._c_posit)
 
-    cpdef le(self, Posit8 other):
-        cdef bint b = cposit.p8_le(self._c_posit, other._c_posit)
-        return b
+    cpdef bint le(self, Posit8 other):
+        return cposit.p8_le(self._c_posit, other._c_posit)
 
-    cpdef lt(self, Posit8 other):
-        cdef bint b = cposit.p8_lt(self._c_posit, other._c_posit)
-        return b
+    cpdef bint lt(self, Posit8 other):
+        return cposit.p8_lt(self._c_posit, other._c_posit)
 
     def __lt__(self, Posit8 other):
         return self.lt(other)
@@ -175,16 +192,53 @@ cdef class Posit8:
         cdef cposit.posit16_t f = cposit.p8_to_p16(self._c_posit)
         return Posit16.from_c_posit(f)
 
+    cpdef to_quire(self):
+        cdef cposit.quire8_t f
+        cposit.q8_clr(f)
+        f = cposit.q8_fdp_add(f, self._c_posit, posit8_one)
+        return Quire8.from_c_quire(f)
+
 
 cdef class Quire8:
 
     # the wrapped quire value
     cdef cposit.quire8_t _c_quire
 
-    # limited interface for now
+    # factory function constructors that bypass init
 
-    def __cinit__(self):
-        cposit.q8_clr(self._c_quire)
+    @staticmethod
+    cdef Quire8 from_c_quire(cposit.quire8_t f):
+        """Factory function to create a Quire8 object directly from
+        a C quire8_t.
+        """
+        cdef Quire8 obj = Quire8.__new__(Quire8)
+        obj._c_quire = f
+        return obj
+
+    @staticmethod
+    def from_bits(uint32_t value):
+        """Factory function to create a Quire8 object from a bit pattern
+        represented as an integer.
+        """
+        cdef Quire8 obj = Quire8.__new__(Quire8)
+        obj._c_quire.v = value
+        return obj
+
+    # convenience interface for use inside Python
+
+    def __init__(self, value):
+        if isinstance(value, int):
+            self._c_quire.v = value
+        else:
+            f = float(value)
+            cposit.q8_clr(self._c_quire)
+            self._c_quire = cposit.q8_fdp_add(self._c_quire, cposit.convertDoubleToP8(f), posit8_one)
+
+    def __float__(self):
+        return cposit.convertP8ToDouble(cposit.q8_to_p8(self._c_quire))
+
+    def __int__(self):
+        return int(cposit.convertP8ToDouble(cposit.q8_to_p8(self._c_quire)))
 
     def __str__(self):
         return repr(cposit.convertP8ToDouble(cposit.q8_to_p8(self._c_quire)))
@@ -192,16 +246,100 @@ cdef class Quire8:
     def __repr__(self):
         return 'Quire8(' + repr(cposit.convertP8ToDouble(cposit.q8_to_p8(self._c_quire))) + ')'
 
-    cpdef fdp_add(self, Posit8 a2, Posit8 a3):
-        self._c_quire = cposit.q8_fdp_add(self._c_quire, a2._c_posit, a3._c_posit)
+    cpdef uint32_t get_bits(self):
+        return self._c_quire.v
+    bits = property(get_bits)
+
+    # arithmetic
+
+    cpdef Quire8 qma(self, Posit8 a1, Posit8 a2):
+        cdef cposit.quire8_t f = cposit.q8_fdp_add(self._c_quire, a1._c_posit, a2._c_posit)
+        return Quire8.from_c_quire(f)
+
+    cpdef Quire8 qms(self, Posit8 a1, Posit8 a2):
+        cdef cposit.quire8_t f = cposit.q8_fdp_sub(self._c_quire, a1._c_posit, a2._c_posit)
+        return Quire8.from_c_quire(f)
+
+    cpdef void iqma(self, Posit8 a1, Posit8 a2):
+        self._c_quire = cposit.q8_fdp_add(self._c_quire, a1._c_posit, a2._c_posit)
 
-    cpdef fdp_sub(self, Posit8 a2, Posit8 a3):
-        self._c_quire = cposit.q8_fdp_sub(self._c_quire, a2._c_posit, a3._c_posit)
+    cpdef void iqms(self, Posit8 a1, Posit8 a2):
+        self._c_quire = cposit.q8_fdp_sub(self._c_quire, a1._c_posit, a2._c_posit)
 
-    cpdef get_p8(self):
+    cpdef void iclr(self):
+        cposit.q8_clr(self._c_quire)
+
+    # conversion back to posit
+
+    cpdef Posit8 to_posit(self):
         cpdef cposit.posit8_t f = cposit.q8_to_p8(self._c_quire)
         return Posit8.from_c_posit(f)
-    p8 = property(get_p8)
+
+
+# external, non-method arithmetic
+
+cpdef Posit8 p8_round(Posit8 a1):
+    cdef cposit.posit8_t f = cposit.p8_roundToInt(a1._c_posit)
+    return Posit8.from_c_posit(f)
+
+cpdef Posit8 p8_add(Posit8 a1, Posit8 a2):
+    cdef cposit.posit8_t f = cposit.p8_add(a1._c_posit, a2._c_posit)
+    return Posit8.from_c_posit(f)
+
+cpdef Posit8 p8_sub(Posit8 a1, Posit8 a2):
+    cdef cposit.posit8_t f = cposit.p8_sub(a1._c_posit, a2._c_posit)
+    return Posit8.from_c_posit(f)
+
+cpdef Posit8 p8_mul(Posit8 a1, Posit8 a2):
+    cdef cposit.posit8_t f = cposit.p8_mul(a1._c_posit, a2._c_posit)
+    return Posit8.from_c_posit(f)
+
+cpdef Posit8 p8_fma(Posit8 a1, Posit8 a2, Posit8 a3):
+    cdef cposit.posit8_t f = cposit.p8_mulAdd(a1._c_posit, a2._c_posit, a3._c_posit)
+    return Posit8.from_c_posit(f)
+
+cpdef Posit8 p8_qma(Posit8 a3, Posit8 a1, Posit8 a2):
+    cdef cposit.posit8_t f = cposit.p8_mulAdd(a1._c_posit, a2._c_posit, a3._c_posit)
+    return Posit8.from_c_posit(f)
+
+cpdef Posit8 p8_div(Posit8 a1, Posit8 a2):
+    cdef cposit.posit8_t f = cposit.p8_div(a1._c_posit, a2._c_posit)
+    return Posit8.from_c_posit(f)
+
+cpdef Posit8 p8_sqrt(Posit8 a1):
+    cdef cposit.posit8_t f = cposit.p8_sqrt(a1._c_posit)
+    return Posit8.from_c_posit(f)
+
+cpdef bint p8_eq(Posit8 a1, Posit8 a2):
+    return cposit.p8_eq(a1._c_posit, a2._c_posit)
+
+cpdef bint p8_le(Posit8 a1, Posit8 a2):
+    return cposit.p8_le(a1._c_posit, a2._c_posit)
+
+cpdef bint p8_lt(Posit8 a1, Posit8 a2):
+    return cposit.p8_lt(a1._c_posit, a2._c_posit)
+
+cpdef Posit16 p8_to_p16(Posit8 a1):
+    cdef cposit.posit16_t f = cposit.p8_to_p16(a1._c_posit)
+    return Posit16.from_c_posit(f)
+
+cpdef Quire8 p8_to_q8(Posit8 a1):
+    cdef cposit.quire8_t f
+    cposit.q8_clr(f)
+    f = cposit.q8_fdp_add(f, a1._c_posit, posit8_one)
+    return Quire8.from_c_quire(f)
+
+cpdef Quire8 q8_qma(Quire8 a3, Posit8 a1, Posit8 a2):
+    cdef cposit.quire8_t f = cposit.q8_fdp_add(a3._c_quire, a1._c_posit, a2._c_posit)
+    return Quire8.from_c_quire(f)
+
+cpdef Quire8 q8_qms(Quire8 a3, Posit8 a1, Posit8 a2):
+    cdef cposit.quire8_t f = cposit.q8_fdp_sub(a3._c_quire, a1._c_posit, a2._c_posit)
+    return Quire8.from_c_quire(f)
+
+cpdef Posit8 q8_to_p8(Quire8 a1):
+    cpdef cposit.posit8_t f = cposit.q8_to_p8(a1._c_quire)
+    return Posit8.from_c_posit(f)
 
 
 cdef class Posit16:
@@ -221,16 +359,16 @@ cdef class Posit16:
         return obj
 
     @staticmethod
-    def from_bits(int value):
+    def from_bits(uint16_t value):
         """Factory function to create a Posit16 object from a bit pattern
         represented as an integer.
         """
         cdef Posit16 obj = Posit16.__new__(Posit16)
-        obj._c_posit = cposit.castP16(value)
+        obj._c_posit.v = value
         return obj
 
     @staticmethod
-    def from_double(float value):
+    def from_double(double value):
         """Factory function to create a Posit16 object from a double.
         """
         cdef Posit16 obj = Posit16.__new__(Posit16)
@@ -241,119 +379,128 @@ cdef class Posit16:
 
     def __init__(self, value):
         if isinstance(value, int):
-            self._c_posit = cposit.castP16(value)
+            self._c_posit.v = value
         else:
             f = float(value)
             self._c_posit = cposit.convertDoubleToP16(f)
 
+    def __float__(self):
+        return cposit.convertP16ToDouble(self._c_posit)
+
+    def __int__(self):
+        return int(cposit.convertP16ToDouble(self._c_posit))
+
     def __str__(self):
         return repr(cposit.convertP16ToDouble(self._c_posit))
 
     def __repr__(self):
         return 'Posit16(' + repr(cposit.convertP16ToDouble(self._c_posit)) + ')'
 
-    cpdef get_bits(self):
-        cdef int u = cposit.castUI16(self._c_posit)
-        return u
+    cpdef uint16_t get_bits(self):
+        return self._c_posit.v
     bits = property(get_bits)
 
     # arithmetic
 
-    cpdef round(self):
+    cpdef Posit16 round(self):
         cdef cposit.posit16_t f = cposit.p16_roundToInt(self._c_posit)
         return Posit16.from_c_posit(f)
 
-    def __round__(self, Posit16 other):
-        return self.roundToInt(other)
+    def __round__(self):
+        return self.roundToInt()
 
-    cpdef add(self, Posit16 other):
+    cpdef Posit16 add(self, Posit16 other):
         cdef cposit.posit16_t f = cposit.p16_add(self._c_posit, other._c_posit)
         return Posit16.from_c_posit(f)
 
     def __add__(self, Posit16 other):
         return self.add(other)
 
-    cpdef sub(self, Posit16 other):
+    cpdef Posit16 sub(self, Posit16 other):
         cdef cposit.posit16_t f = cposit.p16_sub(self._c_posit, other._c_posit)
         return Posit16.from_c_posit(f)
 
     def __sub__(self, Posit16 other):
         return self.sub(other)
 
-    cpdef mul(self, Posit16 other):
+    cpdef Posit16 mul(self, Posit16 other):
         cdef cposit.posit16_t f = cposit.p16_mul(self._c_posit, other._c_posit)
         return Posit16.from_c_posit(f)
 
     def __mul__(self, Posit16 other):
         return self.mul(other)
 
-    cpdef fma(self, Posit16 a2, Posit16 a3):
-      cdef cposit.posit16_t f = cposit.p16_mulAdd(self._c_posit, a2._c_posit, a3._c_posit)
-      return Posit16.from_c_posit(f)
+    cpdef Posit16 fma(self, Posit16 a2, Posit16 a3):
+        cdef cposit.posit16_t f = cposit.p16_mulAdd(self._c_posit, a2._c_posit, a3._c_posit)
+        return Posit16.from_c_posit(f)
+
+    cpdef Posit16 qma(self, Posit16 a1, Posit16 a2):
+        cdef cposit.posit16_t f = cposit.p16_mulAdd(a1._c_posit, a2._c_posit, self._c_posit)
+        return Posit16.from_c_posit(f)
 
-    cpdef div(self, Posit16 other):
+    cpdef Posit16 div(self, Posit16 other):
         cdef cposit.posit16_t f = cposit.p16_div(self._c_posit, other._c_posit)
         return Posit16.from_c_posit(f)
 
     def __truediv__(self, Posit16 other):
         return self.div(other)
 
-    cpdef sqrt(self):
+    cpdef Posit16 sqrt(self):
         cdef cposit.posit16_t f = cposit.p16_sqrt(self._c_posit)
         return Posit16.from_c_posit(f)
 
     # in-place arithmetic
 
-    cpdef iround(self):
+    cpdef void iround(self):
         self._c_posit = cposit.p16_roundToInt(self._c_posit)
 
-    cpdef iadd(self, Posit16 other):
+    cpdef void iadd(self, Posit16 other):
         self._c_posit = cposit.p16_add(self._c_posit, other._c_posit)
 
     def __iadd__(self, Posit16 other):
         self.iadd(other)
         return self
 
-    cpdef isub(self, Posit16 other):
+    cpdef void isub(self, Posit16 other):
         self._c_posit = cposit.p16_sub(self._c_posit, other._c_posit)
 
     def __isub__(self, Posit16 other):
         self.isub(other)
         return self
 
-    cpdef imul(self, Posit16 other):
+    cpdef void imul(self, Posit16 other):
         self._c_posit = cposit.p16_mul(self._c_posit, other._c_posit)
 
     def __imul__(self, Posit16 other):
         self.imul(other)
         return self
 
-    cpdef ifma(self, Posit16 a2, Posit16 a3):
+    cpdef void ifma(self, Posit16 a2, Posit16 a3):
         self._c_posit = cposit.p16_mulAdd(self._c_posit, a2._c_posit, a3._c_posit)
 
-    cpdef idiv(self, Posit16 other):
+    cpdef void iqma(self, Posit16 a1, Posit16 a2):
+        self._c_posit = cposit.p16_mulAdd(a1._c_posit, a2._c_posit, self._c_posit)
+
+    cpdef void idiv(self, Posit16 other):
         self._c_posit = cposit.p16_div(self._c_posit, other._c_posit)
 
     def __itruediv__(self, Posit16 other):
         self.idiv(other)
         return self
 
-    cpdef isqrt(self):
+    cpdef void isqrt(self):
         self._c_posit = cposit.p16_sqrt(self._c_posit)
 
     # comparison
 
-    cpdef eq(self, Posit16 other):
-        cdef bint b = cposit.p16_eq(self._c_posit, other._c_posit)
-        return b
+    cpdef bint eq(self, Posit16 other):
+        return cposit.p16_eq(self._c_posit, other._c_posit)
 
-    cpdef le(self, Posit16 other):
-        cdef bint b = cposit.p16_le(self._c_posit, other._c_posit)
-        return b
+    cpdef bint le(self, Posit16 other):
+        return cposit.p16_le(self._c_posit, other._c_posit)
 
-    cpdef lt(self, Posit16 other):
-        cdef bint b = cposit.p16_lt(self._c_posit, other._c_posit)
-        return b
+    cpdef bint lt(self, Posit16 other):
+        return cposit.p16_lt(self._c_posit, other._c_posit)
 
     def __lt__(self, Posit16 other):
         return self.lt(other)
@@ -379,16 +526,67 @@ cdef class Posit16:
         cdef cposit.posit8_t f = cposit.p16_to_p8(self._c_posit)
         return Posit8.from_c_posit(f)
 
+    cpdef to_quire(self):
+        cdef cposit.quire16_t f
+        cposit.q16_clr(f)
+        f = cposit.q16_fdp_add(f, self._c_posit, posit16_one)
+        return Quire16.from_c_quire(f)
+
 
 cdef class Quire16:
 
     # the wrapped quire value
     cdef cposit.quire16_t _c_quire
 
-    # limited interface for now
+    # factory function constructors that bypass init
 
-    def __cinit__(self):
-        cposit.q16_clr(self._c_quire)
+    @staticmethod
+    cdef Quire16 from_c_quire(cposit.quire16_t f):
+        """Factory function to create a Quire16 object directly from
+        a C quire16_t.
+        """
+        cdef Quire16 obj = Quire16.__new__(Quire16)
+        obj._c_quire = f
+        return obj
+
+    @staticmethod
+    def from_bits(value):
+        """Factory function to create a Quire16 object from a bit pattern
+        represented as an integer.
+        """
+        cdef Quire16 obj = Quire16.__new__(Quire16)
+
+        if not isinstance(value, int):
+            raise TypeError('expecting int, got {}'.format(repr(value)))
+
+        for idx in range(1, -1, -1):
+            obj._c_quire.v[idx] = value & 0xffffffffffffffff
+            value >>= 64
+
+        if not (value == 0):
+            raise OverflowError('value too large to fit in uint64_t[2]')
+
+        return obj
+
+    # convenience interface for use inside Python
+
+    def __init__(self, value):
+        if isinstance(value, int):
+            for idx in range(1, -1, -1):
+                self._c_quire.v[idx] = value & 0xffffffffffffffff
+                value >>= 64
+            if not (value == 0):
+                raise OverflowError('value too large to fit in uint64_t[2]')
+        else:
+            f = float(value)
+            cposit.q16_clr(self._c_quire)
+            self._c_quire = cposit.q16_fdp_add(self._c_quire, cposit.convertDoubleToP16(f), posit16_one)
+
+    def __float__(self):
+        return cposit.convertP16ToDouble(cposit.q16_to_p16(self._c_quire))
+
+    def __int__(self):
+        return int(cposit.convertP16ToDouble(cposit.q16_to_p16(self._c_quire)))
 
     def __str__(self):
         return repr(cposit.convertP16ToDouble(cposit.q16_to_p16(self._c_quire)))
@@ -396,13 +594,101 @@ cdef class Quire16:
     def __repr__(self):
         return 'Quire16(' + repr(cposit.convertP16ToDouble(cposit.q16_to_p16(self._c_quire))) + ')'
 
-    cpdef fdp_add(self, Posit16 a2, Posit16 a3):
-        self._c_quire = cposit.q16_fdp_add(self._c_quire, a2._c_posit, a3._c_posit)
+    def get_bits(self):
+        b = 0
+        for u in self._c_quire.v:
+            b <<= 64
+            b |= u
+        return b
+    bits = property(get_bits)
+
+    # arithmetic
+
+    cpdef Quire16 qma(self, Posit16 a1, Posit16 a2):
+        cdef cposit.quire16_t f = cposit.q16_fdp_add(self._c_quire, a1._c_posit, a2._c_posit)
+        return Quire16.from_c_quire(f)
+
+    cpdef Quire16 qms(self, Posit16 a1, Posit16 a2):
+        cdef cposit.quire16_t f = cposit.q16_fdp_sub(self._c_quire, a1._c_posit, a2._c_posit)
+        return Quire16.from_c_quire(f)
+
+    cpdef void iqma(self, Posit16 a1, Posit16 a2):
+        self._c_quire = cposit.q16_fdp_add(self._c_quire, a1._c_posit, a2._c_posit)
 
-    cpdef fdp_sub(self, Posit16 a2, Posit16 a3):
-        self._c_quire = cposit.q16_fdp_sub(self._c_quire, a2._c_posit, a3._c_posit)
+    cpdef void iqms(self, Posit16 a1, Posit16 a2):
+        self._c_quire = cposit.q16_fdp_sub(self._c_quire, a1._c_posit, a2._c_posit)
 
-    cpdef get_p16(self):
+    cpdef void iclr(self):
+        cposit.q16_clr(self._c_quire)
+
+    # conversion back to posit
+
+    cpdef Posit16 to_posit(self):
         cpdef cposit.posit16_t f = cposit.q16_to_p16(self._c_quire)
         return Posit16.from_c_posit(f)
-    p16 = property(get_p16)
+
+
+# external, non-method arithmetic
+
+cpdef Posit16 p16_round(Posit16 a1):
+    cdef cposit.posit16_t f = cposit.p16_roundToInt(a1._c_posit)
+    return Posit16.from_c_posit(f)
+
+cpdef Posit16 p16_add(Posit16 a1, Posit16 a2):
+    cdef cposit.posit16_t f = cposit.p16_add(a1._c_posit, a2._c_posit)
+    return Posit16.from_c_posit(f)
+
+cpdef Posit16 p16_sub(Posit16 a1, Posit16 a2):
+    cdef cposit.posit16_t f = cposit.p16_sub(a1._c_posit, a2._c_posit)
+    return Posit16.from_c_posit(f)
+
+cpdef Posit16 p16_mul(Posit16 a1, Posit16 a2):
+    cdef cposit.posit16_t f = cposit.p16_mul(a1._c_posit, a2._c_posit)
+    return Posit16.from_c_posit(f)
+
+cpdef Posit16 p16_fma(Posit16 a1, Posit16 a2, Posit16 a3):
+    cdef cposit.posit16_t f = cposit.p16_mulAdd(a1._c_posit, a2._c_posit, a3._c_posit)
+    return Posit16.from_c_posit(f)
+
+cpdef Posit16 p16_qma(Posit16 a3, Posit16 a1, Posit16 a2):
+    cdef cposit.posit16_t f = cposit.p16_mulAdd(a1._c_posit, a2._c_posit, a3._c_posit)
+    return Posit16.from_c_posit(f)
+
+cpdef Posit16 p16_div(Posit16 a1, Posit16 a2):
+    cdef cposit.posit16_t f = cposit.p16_div(a1._c_posit, a2._c_posit)
+    return Posit16.from_c_posit(f)
+
+cpdef Posit16 p16_sqrt(Posit16 a1):
+    cdef cposit.posit16_t f = cposit.p16_sqrt(a1._c_posit)
+    return Posit16.from_c_posit(f)
+
+cpdef bint p16_eq(Posit16 a1, Posit16 a2):
+    return cposit.p16_eq(a1._c_posit, a2._c_posit)
+
+cpdef bint p16_le(Posit16 a1, Posit16 a2):
+    return cposit.p16_le(a1._c_posit, a2._c_posit)
+
+cpdef bint p16_lt(Posit16 a1, Posit16 a2):
+    return cposit.p16_lt(a1._c_posit, a2._c_posit)
+
+cpdef Posit8 p16_to_p8(Posit16 a1):
+    cdef cposit.posit8_t f = cposit.p16_to_p8(a1._c_posit)
+    return Posit8.from_c_posit(f)
+
+cpdef Quire16 p16_to_q16(Posit16 a1):
+    cdef cposit.quire16_t f
+    cposit.q16_clr(f)
+    f = cposit.q16_fdp_add(f, a1._c_posit, posit16_one)
+    return Quire16.from_c_quire(f)
+
+cpdef Quire16 q16_qma(Quire16 a3, Posit16 a1, Posit16 a2):
+    cdef cposit.quire16_t f = cposit.q16_fdp_add(a3._c_quire, a1._c_posit, a2._c_posit)
+    return Quire16.from_c_quire(f)
+
+cpdef Quire16 q16_qms(Quire16 a3, Posit16 a1, Posit16 a2):
+    cdef cposit.quire16_t f = cposit.q16_fdp_sub(a3._c_quire, a1._c_posit, a2._c_posit)
+    return Quire16.from_c_quire(f)
+
+cpdef Posit16 q16_to_p16(Quire16 a1):
+    cpdef cposit.posit16_t f = cposit.q16_to_p16(a1._c_quire)
+    return Posit16.from_c_posit(f)