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authorAndrew Waterman <waterman@s141.Millennium.Berkeley.EDU>2011-06-19 20:47:29 -0700
committerAndrew Waterman <waterman@s141.Millennium.Berkeley.EDU>2011-06-19 20:47:29 -0700
commit77452a26e7d95d29dbaa797595ae683f03a3345b (patch)
treee7aaae682f73a20ceb4d3366528b0cd38378f49d /softfloat/primitives.h
parent740f981cfd55604d46598144dccac26dd53f643c (diff)
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+
+/*============================================================================
+
+This C source fragment is part of the SoftFloat IEC/IEEE Floating-point
+Arithmetic Package, Release 3.
+
+*** UPDATE
+
+Written by John R. Hauser. This work was made possible in part by the
+International Computer Science Institute, located at Suite 600, 1947 Center
+Street, Berkeley, California 94704. Funding was partially provided by the
+National Science Foundation under grant MIP-9311980. The original version
+of this code was written as part of a project to build a fixed-point vector
+processor in collaboration with the University of California at Berkeley,
+overseen by Profs. Nelson Morgan and John Wawrzynek. More information
+is available through the Web page `http://www.cs.berkeley.edu/~jhauser/
+arithmetic/SoftFloat.html'.
+
+THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort has
+been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT TIMES
+RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO PERSONS
+AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ALL LOSSES,
+COSTS, OR OTHER PROBLEMS THEY INCUR DUE TO THE SOFTWARE, AND WHO FURTHERMORE
+EFFECTIVELY INDEMNIFY JOHN HAUSER AND THE INTERNATIONAL COMPUTER SCIENCE
+INSTITUTE (possibly via similar legal notice) AGAINST ALL LOSSES, COSTS, OR
+OTHER PROBLEMS INCURRED BY THEIR CUSTOMERS AND CLIENTS DUE TO THE SOFTWARE.
+
+Derivative works are acceptable, even for commercial purposes, so long as
+(1) the source code for the derivative work includes prominent notice that
+the work is derivative, and (2) the source code includes prominent notice with
+these four paragraphs for those parts of this code that are retained.
+
+=============================================================================*/
+
+#include <stdbool.h>
+#include <stdint.h>
+
+/*** CHANGE TO USE `fast' INTEGER TYPES? ***/
+/*** ADD 80-BIT FUNCTIONS? ***/
+
+#ifdef LITTLEENDIAN
+struct uintx80 { uint64_t v0; uint16_t v64; };
+struct uint128 { uint64_t v0, v64; };
+struct uint192 { uint64_t v0, v64, v128; };
+struct uint256 { uint64_t v0, v64, v128, v192; };
+#else
+struct uintx80 { uint16_t v64; uint64_t v0; };
+struct uint128 { uint64_t v64, v0; };
+struct uint192 { uint64_t v128, v64, v0; };
+struct uint256 { uint64_t v256, v128, v64, v0; };
+#endif
+
+struct uint64_extra { uint64_t v, extra; };
+struct uint128_extra { uint64_t v64; uint64_t v0; uint64_t extra; };
+
+
+/*** SHIFT COUNTS CANNOT BE ZERO. MUST CHECK BEFORE CALLING! ***/
+
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the 128-bit value formed by concatenating `a0' and `a1'
+| is equal to the 128-bit value formed by concatenating `b0' and `b1'.
+| Otherwise, returns 0.
+*----------------------------------------------------------------------------*/
+#if defined INLINE_LEVEL && ( 1 <= INLINE_LEVEL )
+INLINE bool
+ softfloat_eq128( uint64_t a64, uint64_t a0, uint64_t b64, uint64_t b0 )
+ { return ( a64 == b64 ) && ( a0 == b0 ); }
+#else
+bool softfloat_eq128( uint64_t, uint64_t, uint64_t, uint64_t );
+#endif
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is less
+| than or equal to the 128-bit value formed by concatenating `b0' and `b1'.
+| Otherwise, returns 0.
+*----------------------------------------------------------------------------*/
+#if defined INLINE_LEVEL && ( 1 <= INLINE_LEVEL )
+INLINE bool
+ softfloat_le128( uint64_t a64, uint64_t a0, uint64_t b64, uint64_t b0 )
+ { return ( a64 < b64 ) || ( ( a64 == b64 ) && ( a0 <= b0 ) ); }
+#else
+bool softfloat_le128( uint64_t, uint64_t, uint64_t, uint64_t );
+#endif
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is less
+| than the 128-bit value formed by concatenating `b0' and `b1'. Otherwise,
+| returns 0.
+*----------------------------------------------------------------------------*/
+#if defined INLINE_LEVEL && ( 1 <= INLINE_LEVEL )
+INLINE bool
+ softfloat_lt128( uint64_t a64, uint64_t a0, uint64_t b64, uint64_t b0 )
+ { return ( a64 < b64 ) || ( ( a64 == b64 ) && ( a0 < b0 ) ); }
+#else
+bool softfloat_lt128( uint64_t, uint64_t, uint64_t, uint64_t );
+#endif
+
+/*----------------------------------------------------------------------------
+| Shifts the 128-bit value formed by concatenating `a0' and `a1' left by the
+| number of bits given in `count'. Any bits shifted off are lost. The value
+| of `count' must be less than 64. The result is broken into two 64-bit
+| pieces which are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
+*----------------------------------------------------------------------------*/
+#if defined INLINE_LEVEL && ( 2 <= INLINE_LEVEL )
+INLINE struct uint128
+ softfloat_shortShift128Left( uint64_t a64, uint64_t a0, unsigned int count )
+{
+ struct uint128 z;
+ z.v64 = a64<<count | a0>>( ( - count ) & 63 );
+ z.v0 = a0<<count;
+ return z;
+}
+#else
+struct uint128 softfloat_shortShift128Left( uint64_t, uint64_t, unsigned int );
+#endif
+
+/*----------------------------------------------------------------------------
+| Shifts the 192-bit value formed by concatenating `a0', `a1', and `a2' left
+| by the number of bits given in `count'. Any bits shifted off are lost.
+| The value of `count' must be less than 64. The result is broken into three
+| 64-bit pieces which are stored at the locations pointed to by `z0Ptr',
+| `z1Ptr', and `z2Ptr'.
+*----------------------------------------------------------------------------*/
+#if defined INLINE_LEVEL && ( 3 <= INLINE_LEVEL )
+INLINE struct uint192
+ softfloat_shortShift192Left(
+ uint64_t a128, uint64_t a64, uint64_t a0, unsigned int count )
+{
+ unsigned int negCount = - count;
+ struct uint192 z;
+ z.v128 = a128<<count | a64>>( negCount & 63 );
+ z.v64 = a64<<count | a0>>( negCount & 63 );
+ z.v0 = a0<<count;
+ return z;
+}
+#else
+struct uint192
+ softfloat_shortShift192Left( uint64_t, uint64_t, uint64_t, unsigned int );
+#endif
+
+/*----------------------------------------------------------------------------
+| Shifts `a' right by the number of bits given in `count'. If any nonzero
+| bits are shifted off, they are ``jammed'' into the least significant bit of
+| the result by setting the least significant bit to 1. The value of `count'
+| can be arbitrarily large; in particular, if `count' is greater than 32, the
+| result will be either 0 or 1, depending on whether `a' is zero or nonzero.
+| The result is stored in the location pointed to by `zPtr'.
+*----------------------------------------------------------------------------*/
+#if defined INLINE_LEVEL && ( 2 <= INLINE_LEVEL )
+INLINE uint32_t softfloat_shift32RightJam( uint32_t a, unsigned int count )
+{
+ return
+ ( count < 32 )
+ ? a>>count | ( (uint32_t) ( a<<( ( - count ) & 31 ) ) != 0 )
+ : ( a != 0 );
+}
+#else
+uint32_t softfloat_shift32RightJam( uint32_t, unsigned int );
+#endif
+
+/*----------------------------------------------------------------------------
+| Shift count is less than 32.
+*----------------------------------------------------------------------------*/
+#if defined INLINE
+INLINE uint32_t softfloat_shortShift32Right1Jam( uint32_t a )
+ { return a>>1 | ( a & 1 ); }
+#else
+uint32_t softfloat_shortShift32Right1Jam( uint32_t );
+#endif
+
+/*----------------------------------------------------------------------------
+| Shifts `a' right by the number of bits given in `count'. If any nonzero
+| bits are shifted off, they are ``jammed'' into the least significant bit of
+| the result by setting the least significant bit to 1. The value of `count'
+| can be arbitrarily large; in particular, if `count' is greater than 64, the
+| result will be either 0 or 1, depending on whether `a' is zero or nonzero.
+| The result is stored in the location pointed to by `zPtr'.
+*----------------------------------------------------------------------------*/
+#if defined INLINE_LEVEL && ( 3 <= INLINE_LEVEL )
+INLINE uint64_t softfloat_shift64RightJam( uint64_t a, unsigned int count )
+{
+ return
+ ( count < 64 )
+ ? a>>count | ( (uint64_t) ( a<<( ( - count ) & 63 ) ) != 0 )
+ : ( a != 0 );
+}
+#else
+uint64_t softfloat_shift64RightJam( uint64_t, unsigned int );
+#endif
+
+/*----------------------------------------------------------------------------
+| Shift count is less than 64.
+*----------------------------------------------------------------------------*/
+#if defined INLINE_LEVEL && ( 2 <= INLINE_LEVEL )
+INLINE uint64_t
+ softfloat_shortShift64RightJam( uint64_t a, unsigned int count )
+ { return a>>count | ( ( a & ( ( (uint64_t) 1<<count ) - 1 ) ) != 0 ); }
+#else
+uint64_t softfloat_shortShift64RightJam( uint64_t, unsigned int );
+#endif
+
+/*----------------------------------------------------------------------------
+| Shifts the 128-bit value formed by concatenating `a0' and `a1' right by 64
+| _plus_ the number of bits given in `count'. The shifted result is at most
+| 64 nonzero bits; this is stored at the location pointed to by `z0Ptr'. The
+| bits shifted off form a second 64-bit result as follows: The _last_ bit
+| shifted off is the most-significant bit of the extra result, and the other
+| 63 bits of the extra result are all zero if and only if _all_but_the_last_
+| bits shifted off were all zero. This extra result is stored in the location
+| pointed to by `z1Ptr'. The value of `count' can be arbitrarily large.
+| (This routine makes more sense if `a0' and `a1' are considered to form
+| a fixed-point value with binary point between `a0' and `a1'. This fixed-
+| point value is shifted right by the number of bits given in `count', and
+| the integer part of the result is returned at the location pointed to by
+| `z0Ptr'. The fractional part of the result may be slightly corrupted as
+| described above, and is returned at the location pointed to by `z1Ptr'.)
+*----------------------------------------------------------------------------*/
+#if defined INLINE_LEVEL && ( 3 <= INLINE_LEVEL )
+INLINE struct uint64_extra
+ softfloat_shift64ExtraRightJam(
+ uint64_t a, uint64_t extra, unsigned int count )
+{
+ struct uint64_extra z;
+ if ( count < 64 ) {
+ z.v = a>>count;
+ z.extra = a<<( ( - count ) & 63 );
+ } else {
+ z.v = 0;
+ z.extra = ( count == 64 ) ? a : ( a != 0 );
+ }
+ z.extra |= ( extra != 0 );
+ return z;
+}
+#else
+struct uint64_extra
+ softfloat_shift64ExtraRightJam( uint64_t, uint64_t, unsigned int );
+#endif
+
+/*----------------------------------------------------------------------------
+| Shift count is less than 64.
+*----------------------------------------------------------------------------*/
+#if defined INLINE_LEVEL && ( 2 <= INLINE_LEVEL )
+INLINE struct uint64_extra
+ softfloat_shortShift64ExtraRightJam(
+ uint64_t a, uint64_t extra, unsigned int count )
+{
+ struct uint64_extra z;
+ z.v = a>>count;
+ z.extra = a<<( ( - count ) & 63 ) | ( extra != 0 );
+ return z;
+}
+#else
+struct uint64_extra
+ softfloat_shortShift64ExtraRightJam( uint64_t, uint64_t, unsigned int );
+#endif
+
+/*----------------------------------------------------------------------------
+| Shifts the 128-bit value formed by concatenating `a0' and `a1' right by the
+| number of bits given in `count'. Any bits shifted off are lost. The value
+| of `count' can be arbitrarily large; in particular, if `count' is greater
+| than 128, the result will be 0. The result is broken into two 64-bit pieces
+| which are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
+*----------------------------------------------------------------------------*/
+/*----------------------------------------------------------------------------
+| Shift count is less than 64.
+*----------------------------------------------------------------------------*/
+#if defined INLINE_LEVEL && ( 2 <= INLINE_LEVEL )
+INLINE struct uint128
+ softfloat_shortShift128Right( uint64_t a64, uint64_t a0, unsigned int count )
+{
+ struct uint128 z;
+ z.v64 = a64>>count;
+ z.v0 = a64<<( ( - count ) & 63 ) | a0>>count;
+ return z;
+}
+#else
+struct uint128
+ softfloat_shortShift128Right( uint64_t, uint64_t, unsigned int );
+#endif
+
+/*----------------------------------------------------------------------------
+| Shifts the 128-bit value formed by concatenating `a0' and `a1' right by the
+| number of bits given in `count'. If any nonzero bits are shifted off, they
+| are ``jammed'' into the least significant bit of the result by setting the
+| least significant bit to 1. The value of `count' can be arbitrarily large;
+| in particular, if `count' is greater than 128, the result will be either
+| 0 or 1, depending on whether the concatenation of `a0' and `a1' is zero or
+| nonzero. The result is broken into two 64-bit pieces which are stored at
+| the locations pointed to by `z0Ptr' and `z1Ptr'.
+*----------------------------------------------------------------------------*/
+#if defined INLINE_LEVEL && ( 4 <= INLINE_LEVEL )
+INLINE struct uint128
+ softfloat_shift128RightJam( uint64_t a64, uint64_t a0, unsigned int count )
+{
+ unsigned int negCount;
+ struct uint128 z;
+ if ( count < 64 ) {
+ negCount = - count;
+ z.v64 = a64>>( count & 63 );
+ z.v0 =
+ a64<<( negCount & 63 ) | a0>>count
+ | ( (uint64_t) ( a0<<( negCount & 63 ) ) != 0 );
+ } else {
+ z.v64 = 0;
+ z.v0 =
+ ( count < 128 )
+ ? a64>>( count & 63 )
+ | ( ( ( a64 & ( ( (uint64_t) 1<<( count & 63 ) ) - 1 ) )
+ | a0 )
+ != 0 )
+ : ( ( a64 | a0 ) != 0 );
+ }
+ return z;
+}
+#else
+struct uint128
+ softfloat_shift128RightJam( uint64_t, uint64_t, unsigned int );
+#endif
+
+/*----------------------------------------------------------------------------
+| Shifts the 192-bit value formed by concatenating `a0', `a1', and `a2' right
+| by 64 _plus_ the number of bits given in `count'. The shifted result is
+| at most 128 nonzero bits; these are broken into two 64-bit pieces which are
+| stored at the locations pointed to by `z0Ptr' and `z1Ptr'. The bits shifted
+| off form a third 64-bit result as follows: The _last_ bit shifted off is
+| the most-significant bit of the extra result, and the other 63 bits of the
+| extra result are all zero if and only if _all_but_the_last_ bits shifted off
+| were all zero. This extra result is stored in the location pointed to by
+| `z2Ptr'. The value of `count' can be arbitrarily large.
+| (This routine makes more sense if `a0', `a1', and `a2' are considered
+| to form a fixed-point value with binary point between `a1' and `a2'. This
+| fixed-point value is shifted right by the number of bits given in `count',
+| and the integer part of the result is returned at the locations pointed to
+| by `z0Ptr' and `z1Ptr'. The fractional part of the result may be slightly
+| corrupted as described above, and is returned at the location pointed to by
+| `z2Ptr'.)
+*----------------------------------------------------------------------------*/
+#if defined INLINE_LEVEL && ( 5 <= INLINE_LEVEL )
+INLINE struct uint128_extra
+ softfloat_shift128ExtraRightJam(
+ uint64_t a64, uint64_t a0, uint64_t extra, unsigned int count )
+{
+ unsigned int negCount = - count;
+ struct uint128_extra z;
+ if ( count < 64 ) {
+ z.v64 = a64>>count;
+ z.v0 = a64<<( negCount & 63 ) | a0>>count;
+ z.extra = a0<<( negCount & 63 );
+ } else {
+ z.v64 = 0;
+ if ( count == 64 ) {
+ z.v0 = a64;
+ z.extra = a0;
+ } else {
+ extra |= a0;
+ if ( count < 128 ) {
+ z.v0 = a64>>( count & 63 );
+ z.extra = a64<<( negCount & 63 );
+ } else {
+ z.v0 = 0;
+ z.extra = ( count == 128 ) ? a64 : ( a64 != 0 );
+ }
+ }
+ }
+ z.extra |= ( extra != 0 );
+ return z;
+}
+#else
+struct uint128_extra
+ softfloat_shift128ExtraRightJam( uint64_t, uint64_t, uint64_t, unsigned int );
+#endif
+
+/*----------------------------------------------------------------------------
+| Shift count is less than 64.
+*----------------------------------------------------------------------------*/
+#if defined INLINE_LEVEL && ( 3 <= INLINE_LEVEL )
+INLINE struct uint128_extra
+ softfloat_shortShift128ExtraRightJam(
+ uint64_t a64, uint64_t a0, uint64_t extra, unsigned int count )
+{
+ unsigned int negCount = - count;
+ struct uint128_extra z;
+ z.v64 = a64>>count;
+ z.v0 = a64<<( negCount & 63 ) | a0>>count;
+ z.extra = a0<<( negCount & 63 ) | ( extra != 0 );
+ return z;
+}
+#else
+struct uint128_extra
+ softfloat_shortShift128ExtraRightJam(
+ uint64_t, uint64_t, uint64_t, unsigned int );
+#endif
+
+extern const uint8_t softfloat_countLeadingZeros8[ 256 ];
+
+/*----------------------------------------------------------------------------
+| Returns the number of leading 0 bits before the most-significant 1 bit of
+| `a'. If `a' is zero, 32 is returned.
+*----------------------------------------------------------------------------*/
+#if defined INLINE_LEVEL && ( 2 <= INLINE_LEVEL )
+INLINE int softfloat_countLeadingZeros32( uint32_t a )
+{
+ int count = 0;
+ if ( a < 0x10000 ) {
+ count = 16;
+ a <<= 16;
+ }
+ if ( a < 0x1000000 ) {
+ count += 8;
+ a <<= 8;
+ }
+ count += softfloat_countLeadingZeros8[ a>>24 ];
+ return count;
+}
+#else
+int softfloat_countLeadingZeros32( uint32_t );
+#endif
+
+/*----------------------------------------------------------------------------
+| Returns the number of leading 0 bits before the most-significant 1 bit of
+| `a'. If `a' is zero, 64 is returned.
+*----------------------------------------------------------------------------*/
+#if defined INLINE_LEVEL && ( 4 <= INLINE_LEVEL )
+INLINE int softfloat_countLeadingZeros64( uint64_t a )
+{
+ int count = 32;
+ uint32_t a32 = a;
+ if ( UINT64_C( 0x100000000 ) <= a ) {
+ count = 0;
+ a32 = a>>32;
+ }
+ /*------------------------------------------------------------------------
+ | From here, result is current count + count leading zeros of `a32'.
+ *------------------------------------------------------------------------*/
+ if ( a32 < 0x10000 ) {
+ count += 16;
+ a32 <<= 16;
+ }
+ if ( a32 < 0x1000000 ) {
+ count += 8;
+ a32 <<= 8;
+ }
+ count += softfloat_countLeadingZeros8[ a32>>24 ];
+ return count;
+}
+#else
+int softfloat_countLeadingZeros64( uint64_t );
+#endif
+
+/*----------------------------------------------------------------------------
+| Adds the 128-bit value formed by concatenating `a0' and `a1' to the 128-bit
+| value formed by concatenating `b0' and `b1'. Addition is modulo 2^128, so
+| any carry out is lost. The result is broken into two 64-bit pieces which
+| are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
+*----------------------------------------------------------------------------*/
+#if defined INLINE_LEVEL && ( 2 <= INLINE_LEVEL )
+INLINE struct uint128
+ softfloat_add128( uint64_t a64, uint64_t a0, uint64_t b64, uint64_t b0 )
+{
+ struct uint128 z;
+ z.v0 = a0 + b0;
+ z.v64 = a64 + b64;
+ z.v64 += ( z.v0 < a0 );
+ return z;
+}
+#else
+struct uint128 softfloat_add128( uint64_t, uint64_t, uint64_t, uint64_t );
+#endif
+
+/*----------------------------------------------------------------------------
+| Adds the 192-bit value formed by concatenating `a0', `a1', and `a2' to the
+| 192-bit value formed by concatenating `b0', `b1', and `b2'. Addition is
+| modulo 2^192, so any carry out is lost. The result is broken into three
+| 64-bit pieces which are stored at the locations pointed to by `z0Ptr',
+| `z1Ptr', and `z2Ptr'.
+*----------------------------------------------------------------------------*/
+#if defined INLINE_LEVEL && ( 3 <= INLINE_LEVEL )
+INLINE struct uint192
+ softfloat_add192(
+ uint64_t a128,
+ uint64_t a64,
+ uint64_t a0,
+ uint64_t b128,
+ uint64_t b64,
+ uint64_t b0
+ )
+{
+ struct uint192 z;
+ unsigned int carry64, carry128;
+ z.v0 = a0 + b0;
+ carry64 = ( z.v0 < a0 );
+ z.v64 = a64 + b64;
+ carry128 = ( z.v64 < a64 );
+ z.v128 = a128 + b128;
+ z.v64 += carry64;
+ carry128 += ( z.v64 < carry64 );
+ z.v128 += carry128;
+ return z;
+}
+#else
+struct uint192
+ softfloat_add192(
+ uint64_t, uint64_t, uint64_t, uint64_t, uint64_t, uint64_t );
+#endif
+
+/*----------------------------------------------------------------------------
+| Subtracts the 128-bit value formed by concatenating `b0' and `b1' from the
+| 128-bit value formed by concatenating `a0' and `a1'. Subtraction is modulo
+| 2^128, so any borrow out (carry out) is lost. The result is broken into two
+| 64-bit pieces which are stored at the locations pointed to by `z0Ptr' and
+| `z1Ptr'.
+*----------------------------------------------------------------------------*/
+#if defined INLINE_LEVEL && ( 2 <= INLINE_LEVEL )
+INLINE struct uint128
+ softfloat_sub128( uint64_t a64, uint64_t a0, uint64_t b64, uint64_t b0 )
+{
+ struct uint128 z;
+ z.v0 = a0 - b0;
+ z.v64 = a64 - b64;
+ z.v64 -= ( a0 < b0 );
+ return z;
+}
+#else
+struct uint128 softfloat_sub128( uint64_t, uint64_t, uint64_t, uint64_t );
+#endif
+
+/*----------------------------------------------------------------------------
+| Subtracts the 192-bit value formed by concatenating `b0', `b1', and `b2'
+| from the 192-bit value formed by concatenating `a0', `a1', and `a2'.
+| Subtraction is modulo 2^192, so any borrow out (carry out) is lost. The
+| result is broken into three 64-bit pieces which are stored at the locations
+| pointed to by `z0Ptr', `z1Ptr', and `z2Ptr'.
+*----------------------------------------------------------------------------*/
+#if defined INLINE_LEVEL && ( 3 <= INLINE_LEVEL )
+INLINE struct uint192
+ softfloat_sub192(
+ uint64_t a128,
+ uint64_t a64,
+ uint64_t a0,
+ uint64_t b128,
+ uint64_t b64,
+ uint64_t b0
+ )
+{
+ struct uint192 z;
+ unsigned int borrow64, borrow128;
+ z.v0 = a0 - b0;
+ borrow64 = ( a0 < b0 );
+ z.v64 = a64 - b64;
+ borrow128 = ( a64 < b64 );
+ z.v128 = a128 - b128;
+ borrow128 += ( z.v64 < borrow64 );
+ z.v64 -= borrow64;
+ z.v128 -= borrow128;
+ return z;
+}
+#else
+struct uint192
+ softfloat_sub192(
+ uint64_t, uint64_t, uint64_t, uint64_t, uint64_t, uint64_t );
+#endif
+
+/*----------------------------------------------------------------------------
+| Multiplies `a' by `b' to obtain a 128-bit product. The product is broken
+| into two 64-bit pieces which are stored at the locations pointed to by
+| `z0Ptr' and `z1Ptr'.
+*----------------------------------------------------------------------------*/
+#if defined INLINE_LEVEL && ( 4 <= INLINE_LEVEL )
+INLINE struct uint128 softfloat_mul64To128( uint64_t a, uint64_t b )
+{
+ uint32_t a32 = a>>32;
+ uint32_t a0 = a;
+ uint32_t b32 = b>>32;
+ uint32_t b0 = b;
+ struct uint128 z;
+ uint64_t mid1, mid2, mid;
+ z.v0 = (uint64_t) a0 * b0;
+ mid1 = (uint64_t) a32 * b0;
+ mid2 = (uint64_t) a0 * b32;
+ z.v64 = (uint64_t) a32 * b32;
+ mid = mid1 + mid2;
+ z.v64 += ( (uint64_t) ( mid < mid1 ) )<<32 | mid>>32;
+ mid <<= 32;
+ z.v0 += mid;
+ z.v64 += ( z.v0 < mid );
+ return z;
+}
+#else
+struct uint128 softfloat_mul64To128( uint64_t, uint64_t );
+#endif
+
+/*----------------------------------------------------------------------------
+| Multiplies the 128-bit value formed by concatenating `a0' and `a1' by
+| `b' to obtain a 192-bit product. The product is broken into three 64-bit
+| pieces which are stored at the locations pointed to by `z0Ptr', `z1Ptr', and
+| `z2Ptr'.
+*----------------------------------------------------------------------------*/
+struct uint192 softfloat_mul128By64To192( uint64_t, uint64_t, uint64_t );
+/*----------------------------------------------------------------------------
+| Multiplies the 128-bit value formed by concatenating `a0' and `a1' to the
+| 128-bit value formed by concatenating `b0' and `b1' to obtain a 256-bit
+| product. The product is broken into four 64-bit pieces which are stored at
+| the locations pointed to by `z0Ptr', `z1Ptr', `z2Ptr', and `z3Ptr'.
+*----------------------------------------------------------------------------*/
+struct uint256 softfloat_mul128To256( uint64_t, uint64_t, uint64_t, uint64_t );
+
+/*----------------------------------------------------------------------------
+| Returns an approximation to the 64-bit integer quotient obtained by dividing
+| `b' into the 128-bit value formed by concatenating `a0' and `a1'. The
+| divisor `b' must be at least 2^63. If q is the exact quotient truncated
+| toward zero, the approximation returned lies between q and q + 2 inclusive.
+| If the exact quotient q is larger than 64 bits, the maximum positive 64-bit
+| unsigned integer is returned.
+*----------------------------------------------------------------------------*/
+uint64_t softfloat_estimateDiv128To64( uint64_t, uint64_t, uint64_t );
+
+/*----------------------------------------------------------------------------
+| Returns an approximation to the square root of the 32-bit significand given
+| by `a'. Considered as an integer, `a' must be at least 2^31. If bit 0 of
+| `aExp' (the least significant bit) is 1, the integer returned approximates
+| 2^31*sqrt(`a'/2^31), where `a' is considered an integer. If bit 0 of `aExp'
+| is 0, the integer returned approximates 2^31*sqrt(`a'/2^30). In either
+| case, the approximation returned lies strictly within +/-2 of the exact
+| value.
+*----------------------------------------------------------------------------*/
+uint32_t softfloat_estimateSqrt32( unsigned int, uint32_t );
+