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+
+/*============================================================================
+
+This C header file is part of the SoftFloat IEC/IEEE Floating-point Arithmetic
+Package, Release 2b.
+
+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 warning) 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.
+
+=============================================================================*/
+
+/*----------------------------------------------------------------------------
+| The macro `FLOATX80' must be defined to enable the extended double-precision
+| floating-point format `floatx80'. If this macro is not defined, the
+| `floatx80' type will not be defined, and none of the functions that either
+| input or output the `floatx80' type will be defined. The same applies to
+| the `FLOAT128' macro and the quadruple-precision format `float128'.
+*----------------------------------------------------------------------------*/
+#define FLOATX80
+#define FLOAT128
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE floating-point types.
+*----------------------------------------------------------------------------*/
+typedef bits32 float32;
+typedef bits64 float64;
+#ifdef FLOATX80
+typedef struct {
+ bits16 high;
+ bits64 low;
+} floatx80;
+#endif
+#ifdef FLOAT128
+typedef struct {
+ bits64 high, low;
+} float128;
+#endif
+
+/*----------------------------------------------------------------------------
+| Primitive arithmetic functions, including multi-word arithmetic, and
+| division and square root approximations. (Can be specialized to target if
+| desired.)
+*----------------------------------------------------------------------------*/
+#include "softfloat-macros"
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE floating-point underflow tininess-detection mode.
+*----------------------------------------------------------------------------*/
+extern int8 float_detect_tininess;
+enum {
+ float_tininess_after_rounding = 0,
+ float_tininess_before_rounding = 1
+};
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE floating-point rounding mode.
+*----------------------------------------------------------------------------*/
+extern int8 float_rounding_mode;
+enum {
+ float_round_nearest_even = 0,
+ float_round_to_zero = 1,
+ float_round_down = 2,
+ float_round_up = 3
+};
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE floating-point exception flags.
+*----------------------------------------------------------------------------*/
+extern int8 float_exception_flags;
+enum {
+ float_flag_invalid = 0x01, float_flag_denormal = 0x02, float_flag_divbyzero = 0x04, float_flag_overflow = 0x08,
+ float_flag_underflow = 0x10, float_flag_inexact = 0x20
+};
+
+/*----------------------------------------------------------------------------
+| Routine to raise any or all of the software IEC/IEEE floating-point
+| exception flags.
+*----------------------------------------------------------------------------*/
+void float_raise( int8 );
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE integer-to-floating-point conversion routines.
+*----------------------------------------------------------------------------*/
+float32 int32_to_float32( int32 );
+float64 int32_to_float64( int32 );
+#ifdef FLOATX80
+floatx80 int32_to_floatx80( int32 );
+#endif
+#ifdef FLOAT128
+float128 int32_to_float128( int32 );
+#endif
+float32 int64_to_float32( int64 );
+float64 int64_to_float64( int64 );
+#ifdef FLOATX80
+floatx80 int64_to_floatx80( int64 );
+#endif
+#ifdef FLOAT128
+float128 int64_to_float128( int64 );
+#endif
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE single-precision conversion routines.
+*----------------------------------------------------------------------------*/
+int32 float32_to_int32( float32 );
+int32 float32_to_int32_round_to_zero( float32 );
+int64 float32_to_int64( float32 );
+int64 float32_to_int64_round_to_zero( float32 );
+float64 float32_to_float64( float32 );
+#ifdef FLOATX80
+floatx80 float32_to_floatx80( float32 );
+#endif
+#ifdef FLOAT128
+float128 float32_to_float128( float32 );
+#endif
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE single-precision operations.
+*----------------------------------------------------------------------------*/
+float32 float32_round_to_int( float32 );
+float32 float32_add( float32, float32 );
+float32 float32_sub( float32, float32 );
+float32 float32_mul( float32, float32 );
+float32 float32_div( float32, float32 );
+float32 float32_rem( float32, float32 );
+float32 float32_sqrt( float32 );
+flag float32_eq( float32, float32 );
+flag float32_le( float32, float32 );
+flag float32_lt( float32, float32 );
+flag float32_eq_signaling( float32, float32 );
+flag float32_le_quiet( float32, float32 );
+flag float32_lt_quiet( float32, float32 );
+flag float32_is_signaling_nan( float32 );
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE double-precision conversion routines.
+*----------------------------------------------------------------------------*/
+int32 float64_to_int32( float64 );
+int32 float64_to_int32_round_to_zero( float64 );
+int64 float64_to_int64( float64 );
+int64 float64_to_int64_round_to_zero( float64 );
+float32 float64_to_float32( float64 );
+#ifdef FLOATX80
+floatx80 float64_to_floatx80( float64 );
+#endif
+#ifdef FLOAT128
+float128 float64_to_float128( float64 );
+#endif
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE double-precision operations.
+*----------------------------------------------------------------------------*/
+float64 float64_round_to_int( float64 );
+float64 float64_add( float64, float64 );
+float64 float64_sub( float64, float64 );
+float64 float64_mul( float64, float64 );
+float64 float64_div( float64, float64 );
+float64 float64_rem( float64, float64 );
+float64 float64_sqrt( float64 );
+flag float64_eq( float64, float64 );
+flag float64_le( float64, float64 );
+flag float64_lt( float64, float64 );
+flag float64_eq_signaling( float64, float64 );
+flag float64_le_quiet( float64, float64 );
+flag float64_lt_quiet( float64, float64 );
+flag float64_is_signaling_nan( float64 );
+
+#ifdef FLOATX80
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE extended double-precision conversion routines.
+*----------------------------------------------------------------------------*/
+int32 floatx80_to_int32( floatx80 );
+int32 floatx80_to_int32_round_to_zero( floatx80 );
+int64 floatx80_to_int64( floatx80 );
+int64 floatx80_to_int64_round_to_zero( floatx80 );
+float32 floatx80_to_float32( floatx80 );
+float64 floatx80_to_float64( floatx80 );
+#ifdef FLOAT128
+float128 floatx80_to_float128( floatx80 );
+#endif
+floatx80 floatx80_scale(floatx80 a, floatx80 b);
+
+/*----------------------------------------------------------------------------
+| Packs the sign `zSign', exponent `zExp', and significand `zSig' into an
+| extended double-precision floating-point value, returning the result.
+*----------------------------------------------------------------------------*/
+
+INLINE floatx80 packFloatx80( flag zSign, int32 zExp, bits64 zSig )
+{
+ floatx80 z;
+
+ z.low = zSig;
+ z.high = ( ( (bits16) zSign )<<15 ) + zExp;
+ return z;
+
+}
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE extended double-precision rounding precision. Valid
+| values are 32, 64, and 80.
+*----------------------------------------------------------------------------*/
+extern int8 floatx80_rounding_precision;
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE extended double-precision operations.
+*----------------------------------------------------------------------------*/
+floatx80 floatx80_round_to_int( floatx80 );
+floatx80 floatx80_add( floatx80, floatx80 );
+floatx80 floatx80_sub( floatx80, floatx80 );
+floatx80 floatx80_mul( floatx80, floatx80 );
+floatx80 floatx80_div( floatx80, floatx80 );
+floatx80 floatx80_rem( floatx80, floatx80 );
+floatx80 floatx80_sqrt( floatx80 );
+flag floatx80_eq( floatx80, floatx80 );
+flag floatx80_le( floatx80, floatx80 );
+flag floatx80_lt( floatx80, floatx80 );
+flag floatx80_eq_signaling( floatx80, floatx80 );
+flag floatx80_le_quiet( floatx80, floatx80 );
+flag floatx80_lt_quiet( floatx80, floatx80 );
+flag floatx80_is_signaling_nan( floatx80 );
+
+int floatx80_fsin(floatx80 &a);
+int floatx80_fcos(floatx80 &a);
+int floatx80_ftan(floatx80 &a);
+
+floatx80 floatx80_flognp1(floatx80 a);
+floatx80 floatx80_flogn(floatx80 a);
+floatx80 floatx80_flog2(floatx80 a);
+floatx80 floatx80_flog10(floatx80 a);
+
+// roundAndPackFloatx80 used to be in softfloat-round-pack, is now in softfloat.c
+floatx80 roundAndPackFloatx80(int8 roundingPrecision, flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1);
+
+#endif
+
+#ifdef FLOAT128
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE quadruple-precision conversion routines.
+*----------------------------------------------------------------------------*/
+int32 float128_to_int32( float128 );
+int32 float128_to_int32_round_to_zero( float128 );
+int64 float128_to_int64( float128 );
+int64 float128_to_int64_round_to_zero( float128 );
+float32 float128_to_float32( float128 );
+float64 float128_to_float64( float128 );
+#ifdef FLOATX80
+floatx80 float128_to_floatx80( float128 );
+#endif
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE quadruple-precision operations.
+*----------------------------------------------------------------------------*/
+float128 float128_round_to_int( float128 );
+float128 float128_add( float128, float128 );
+float128 float128_sub( float128, float128 );
+float128 float128_mul( float128, float128 );
+float128 float128_div( float128, float128 );
+float128 float128_rem( float128, float128 );
+float128 float128_sqrt( float128 );
+flag float128_eq( float128, float128 );
+flag float128_le( float128, float128 );
+flag float128_lt( float128, float128 );
+flag float128_eq_signaling( float128, float128 );
+flag float128_le_quiet( float128, float128 );
+flag float128_lt_quiet( float128, float128 );
+flag float128_is_signaling_nan( float128 );
+
+/*----------------------------------------------------------------------------
+| Packs the sign `zSign', the exponent `zExp', and the significand formed
+| by the concatenation of `zSig0' and `zSig1' into a quadruple-precision
+| floating-point value, returning the result. After being shifted into the
+| proper positions, the three fields `zSign', `zExp', and `zSig0' are simply
+| added together to form the most significant 32 bits of the result. This
+| means that any integer portion of `zSig0' will be added into the exponent.
+| Since a properly normalized significand will have an integer portion equal
+| to 1, the `zExp' input should be 1 less than the desired result exponent
+| whenever `zSig0' and `zSig1' concatenated form a complete, normalized
+| significand.
+*----------------------------------------------------------------------------*/
+
+INLINE float128
+ packFloat128( flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1 )
+{
+ float128 z;
+
+ z.low = zSig1;
+ z.high = ( ( (bits64) zSign )<<63 ) + ( ( (bits64) zExp )<<48 ) + zSig0;
+ return z;
+
+}
+
+/*----------------------------------------------------------------------------
+| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
+| and extended significand formed by the concatenation of `zSig0', `zSig1',
+| and `zSig2', and returns the proper quadruple-precision floating-point value
+| corresponding to the abstract input. Ordinarily, the abstract value is
+| simply rounded and packed into the quadruple-precision format, with the
+| inexact exception raised if the abstract input cannot be represented
+| exactly. However, if the abstract value is too large, the overflow and
+| inexact exceptions are raised and an infinity or maximal finite value is
+| returned. If the abstract value is too small, the input value is rounded to
+| a subnormal number, and the underflow and inexact exceptions are raised if
+| the abstract input cannot be represented exactly as a subnormal quadruple-
+| precision floating-point number.
+| The input significand must be normalized or smaller. If the input
+| significand is not normalized, `zExp' must be 0; in that case, the result
+| returned is a subnormal number, and it must not require rounding. In the
+| usual case that the input significand is normalized, `zExp' must be 1 less
+| than the ``true'' floating-point exponent. The handling of underflow and
+| overflow follows the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+INLINE float128
+ roundAndPackFloat128(
+ flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1, bits64 zSig2 )
+{
+ int8 roundingMode;
+ flag roundNearestEven, increment, isTiny;
+
+ roundingMode = float_rounding_mode;
+ roundNearestEven = ( roundingMode == float_round_nearest_even );
+ increment = ( (sbits64) zSig2 < 0 );
+ if ( ! roundNearestEven ) {
+ if ( roundingMode == float_round_to_zero ) {
+ increment = 0;
+ }
+ else {
+ if ( zSign ) {
+ increment = ( roundingMode == float_round_down ) && zSig2;
+ }
+ else {
+ increment = ( roundingMode == float_round_up ) && zSig2;
+ }
+ }
+ }
+ if ( 0x7FFD <= (bits32) zExp ) {
+ if ( ( 0x7FFD < zExp )
+ || ( ( zExp == 0x7FFD )
+ && eq128(
+ LIT64( 0x0001FFFFFFFFFFFF ),
+ LIT64( 0xFFFFFFFFFFFFFFFF ),
+ zSig0,
+ zSig1
+ )
+ && increment
+ )
+ ) {
+ float_raise( float_flag_overflow | float_flag_inexact );
+ if ( ( roundingMode == float_round_to_zero )
+ || ( zSign && ( roundingMode == float_round_up ) )
+ || ( ! zSign && ( roundingMode == float_round_down ) )
+ ) {
+ return
+ packFloat128(
+ zSign,
+ 0x7FFE,
+ LIT64( 0x0000FFFFFFFFFFFF ),
+ LIT64( 0xFFFFFFFFFFFFFFFF )
+ );
+ }
+ return packFloat128( zSign, 0x7FFF, 0, 0 );
+ }
+ if ( zExp < 0 ) {
+ isTiny =
+ ( float_detect_tininess == float_tininess_before_rounding )
+ || ( zExp < -1 )
+ || ! increment
+ || lt128(
+ zSig0,
+ zSig1,
+ LIT64( 0x0001FFFFFFFFFFFF ),
+ LIT64( 0xFFFFFFFFFFFFFFFF )
+ );
+ shift128ExtraRightJamming(
+ zSig0, zSig1, zSig2, - zExp, &zSig0, &zSig1, &zSig2 );
+ zExp = 0;
+ if ( isTiny && zSig2 ) float_raise( float_flag_underflow );
+ if ( roundNearestEven ) {
+ increment = ( (sbits64) zSig2 < 0 );
+ }
+ else {
+ if ( zSign ) {
+ increment = ( roundingMode == float_round_down ) && zSig2;
+ }
+ else {
+ increment = ( roundingMode == float_round_up ) && zSig2;
+ }
+ }
+ }
+ }
+ if ( zSig2 ) float_exception_flags |= float_flag_inexact;
+ if ( increment ) {
+ add128( zSig0, zSig1, 0, 1, &zSig0, &zSig1 );
+ zSig1 &= ~ ( ( zSig2 + zSig2 == 0 ) & roundNearestEven );
+ }
+ else {
+ if ( ( zSig0 | zSig1 ) == 0 ) zExp = 0;
+ }
+ return packFloat128( zSign, zExp, zSig0, zSig1 );
+
+}
+
+/*----------------------------------------------------------------------------
+| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
+| and significand formed by the concatenation of `zSig0' and `zSig1', and
+| returns the proper quadruple-precision floating-point value corresponding
+| to the abstract input. This routine is just like `roundAndPackFloat128'
+| except that the input significand has fewer bits and does not have to be
+| normalized. In all cases, `zExp' must be 1 less than the ``true'' floating-
+| point exponent.
+*----------------------------------------------------------------------------*/
+
+INLINE float128
+ normalizeRoundAndPackFloat128(
+ flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1 )
+{
+ int8 shiftCount;
+ bits64 zSig2;
+
+ if ( zSig0 == 0 ) {
+ zSig0 = zSig1;
+ zSig1 = 0;
+ zExp -= 64;
+ }
+ shiftCount = countLeadingZeros64( zSig0 ) - 15;
+ if ( 0 <= shiftCount ) {
+ zSig2 = 0;
+ shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 );
+ }
+ else {
+ shift128ExtraRightJamming(
+ zSig0, zSig1, 0, - shiftCount, &zSig0, &zSig1, &zSig2 );
+ }
+ zExp -= shiftCount;
+ return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 );
+
+}
+#endif