@@ -377,46 +377,6 @@ float16 float16_maybe_silence_nan(float16 a, float_status *status)
return a;
}
-/*----------------------------------------------------------------------------
-| Returns the result of converting the half-precision floating-point NaN
-| `a' to the canonical NaN format. If `a' is a signaling NaN, the invalid
-| exception is raised.
-*----------------------------------------------------------------------------*/
-
-static commonNaNT float16ToCommonNaN(float16 a, float_status *status)
-{
- commonNaNT z;
-
- if (float16_is_signaling_nan(a, status)) {
- float_raise(float_flag_invalid, status);
- }
- z.sign = float16_val(a) >> 15;
- z.low = 0;
- z.high = ((uint64_t) float16_val(a)) << 54;
- return z;
-}
-
-/*----------------------------------------------------------------------------
-| Returns the result of converting the canonical NaN `a' to the half-
-| precision floating-point format.
-*----------------------------------------------------------------------------*/
-
-static float16 commonNaNToFloat16(commonNaNT a, float_status *status)
-{
- uint16_t mantissa = a.high >> 54;
-
- if (status->default_nan_mode) {
- return float16_default_nan(status);
- }
-
- if (mantissa) {
- return make_float16(((((uint16_t) a.sign) << 15)
- | (0x1F << 10) | mantissa));
- } else {
- return float16_default_nan(status);
- }
-}
-
/*----------------------------------------------------------------------------
| Returns 1 if the single-precision floating-point value `a' is a quiet
| NaN; otherwise returns 0.
@@ -211,10 +211,10 @@ float128 uint64_to_float128(uint64_t, float_status *status);
/*----------------------------------------------------------------------------
| Software half-precision conversion routines.
*----------------------------------------------------------------------------*/
-float16 float32_to_float16(float32, flag, float_status *status);
-float32 float16_to_float32(float16, flag, float_status *status);
-float16 float64_to_float16(float64 a, flag ieee, float_status *status);
-float64 float16_to_float64(float16 a, flag ieee, float_status *status);
+float16 float32_to_float16(float32, bool ieee, float_status *status);
+float32 float16_to_float32(float16, bool ieee, float_status *status);
+float16 float64_to_float16(float64 a, bool ieee, float_status *status);
+float64 float16_to_float64(float16 a, bool ieee, float_status *status);
int16_t float16_to_int16(float16, float_status *status);
uint16_t float16_to_uint16(float16 a, float_status *status);
int16_t float16_to_int16_round_to_zero(float16, float_status *status);
@@ -113,15 +113,6 @@ static inline int extractFloat16Exp(float16 a)
return (float16_val(a) >> 10) & 0x1f;
}
-/*----------------------------------------------------------------------------
-| Returns the sign bit of the single-precision floating-point value `a'.
-*----------------------------------------------------------------------------*/
-
-static inline flag extractFloat16Sign(float16 a)
-{
- return float16_val(a)>>15;
-}
-
/*----------------------------------------------------------------------------
| Returns the fraction bits of the single-precision floating-point value `a'.
*----------------------------------------------------------------------------*/
@@ -1168,6 +1159,75 @@ float64 float64_div(float64 a, float64 b, float_status *status)
return float64_round_pack_canonical(pr, status);
}
+/*
+ * Float to Float conversions
+ *
+ * Returns the result of converting one float format to another. The
+ * conversion is performed according to the IEC/IEEE Standard for
+ * Binary Floating-Point Arithmetic.
+ *
+ * The float_to_float helper only needs to take care of raising
+ * invalid exceptions and handling the conversion on NaNs.
+ */
+
+static FloatParts float_to_float(FloatParts a,
+ const FloatFmt *srcf, const FloatFmt *dstf,
+ float_status *s)
+{
+ if (is_nan(a.cls)) {
+ if (is_snan(a.cls)) {
+ s->float_exception_flags |= float_flag_invalid;
+ a = parts_silence_nan(a, s);
+ }
+ if (s->default_nan_mode) {
+ return parts_default_nan(s);
+ }
+ }
+ return a;
+}
+
+float32 float16_to_float32(float16 a, bool ieee, float_status *s)
+{
+ FloatParts p = float16_unpack_canonical(a, s);
+ FloatParts pr = float_to_float(p, &float16_params, &float32_params, s);
+ return float32_round_pack_canonical(pr, s);
+}
+
+float64 float16_to_float64(float16 a, bool ieee, float_status *s)
+{
+ FloatParts p = float16_unpack_canonical(a, s);
+ FloatParts pr = float_to_float(p, &float16_params, &float64_params, s);
+ return float64_round_pack_canonical(pr, s);
+}
+
+float16 float32_to_float16(float32 a, bool ieee, float_status *s)
+{
+ FloatParts p = float32_unpack_canonical(a, s);
+ FloatParts pr = float_to_float(p, &float32_params, &float16_params, s);
+ return float16_round_pack_canonical(pr, s);
+}
+
+float64 float32_to_float64(float32 a, float_status *s)
+{
+ FloatParts p = float32_unpack_canonical(a, s);
+ FloatParts pr = float_to_float(p, &float32_params, &float64_params, s);
+ return float64_round_pack_canonical(pr, s);
+}
+
+float16 float64_to_float16(float64 a, bool ieee, float_status *s)
+{
+ FloatParts p = float64_unpack_canonical(a, s);
+ FloatParts pr = float_to_float(p, &float64_params, &float16_params, s);
+ return float16_round_pack_canonical(pr, s);
+}
+
+float32 float64_to_float32(float64 a, float_status *s)
+{
+ FloatParts p = float64_unpack_canonical(a, s);
+ FloatParts pr = float_to_float(p, &float64_params, &float32_params, s);
+ return float32_round_pack_canonical(pr, s);
+}
+
/*
* Rounds the floating-point value `a' to an integer, and returns the
* result as a floating-point value. The operation is performed
@@ -3111,41 +3171,6 @@ float128 uint64_to_float128(uint64_t a, float_status *status)
return normalizeRoundAndPackFloat128(0, 0x406E, a, 0, status);
}
-
-
-
-/*----------------------------------------------------------------------------
-| Returns the result of converting the single-precision floating-point value
-| `a' to the double-precision floating-point format. The conversion is
-| performed according to the IEC/IEEE Standard for Binary Floating-Point
-| Arithmetic.
-*----------------------------------------------------------------------------*/
-
-float64 float32_to_float64(float32 a, float_status *status)
-{
- flag aSign;
- int aExp;
- uint32_t aSig;
- a = float32_squash_input_denormal(a, status);
-
- aSig = extractFloat32Frac( a );
- aExp = extractFloat32Exp( a );
- aSign = extractFloat32Sign( a );
- if ( aExp == 0xFF ) {
- if (aSig) {
- return commonNaNToFloat64(float32ToCommonNaN(a, status), status);
- }
- return packFloat64( aSign, 0x7FF, 0 );
- }
- if ( aExp == 0 ) {
- if ( aSig == 0 ) return packFloat64( aSign, 0, 0 );
- normalizeFloat32Subnormal( aSig, &aExp, &aSig );
- --aExp;
- }
- return packFloat64( aSign, aExp + 0x380, ( (uint64_t) aSig )<<29 );
-
-}
-
/*----------------------------------------------------------------------------
| Returns the result of converting the single-precision floating-point value
| `a' to the extended double-precision floating-point format. The conversion
@@ -3664,173 +3689,6 @@ int float32_unordered_quiet(float32 a, float32 b, float_status *status)
return 0;
}
-
-/*----------------------------------------------------------------------------
-| Returns the result of converting the double-precision floating-point value
-| `a' to the single-precision floating-point format. The conversion is
-| performed according to the IEC/IEEE Standard for Binary Floating-Point
-| Arithmetic.
-*----------------------------------------------------------------------------*/
-
-float32 float64_to_float32(float64 a, float_status *status)
-{
- flag aSign;
- int aExp;
- uint64_t aSig;
- uint32_t zSig;
- a = float64_squash_input_denormal(a, status);
-
- aSig = extractFloat64Frac( a );
- aExp = extractFloat64Exp( a );
- aSign = extractFloat64Sign( a );
- if ( aExp == 0x7FF ) {
- if (aSig) {
- return commonNaNToFloat32(float64ToCommonNaN(a, status), status);
- }
- return packFloat32( aSign, 0xFF, 0 );
- }
- shift64RightJamming( aSig, 22, &aSig );
- zSig = aSig;
- if ( aExp || zSig ) {
- zSig |= 0x40000000;
- aExp -= 0x381;
- }
- return roundAndPackFloat32(aSign, aExp, zSig, status);
-
-}
-
-
-/*----------------------------------------------------------------------------
-| Packs the sign `zSign', exponent `zExp', and significand `zSig' into a
-| half-precision floating-point value, returning the result. After being
-| shifted into the proper positions, the three fields are simply added
-| together to form the result. This means that any integer portion of `zSig'
-| 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 `zSig' is a complete, normalized
-| significand.
-*----------------------------------------------------------------------------*/
-static float16 packFloat16(flag zSign, int zExp, uint16_t zSig)
-{
- return make_float16(
- (((uint32_t)zSign) << 15) + (((uint32_t)zExp) << 10) + zSig);
-}
-
-/*----------------------------------------------------------------------------
-| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
-| and significand `zSig', and returns the proper half-precision floating-
-| point value corresponding to the abstract input. Ordinarily, the abstract
-| value is simply rounded and packed into the half-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 half-
-| precision floating-point number.
-| The `ieee' flag indicates whether to use IEEE standard half precision, or
-| ARM-style "alternative representation", which omits the NaN and Inf
-| encodings in order to raise the maximum representable exponent by one.
-| The input significand `zSig' has its binary point between bits 22
-| and 23, which is 13 bits to the left of the usual location. This shifted
-| significand must be normalized or smaller. If `zSig' 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 `zSig' is
-| normalized, `zExp' must be 1 less than the ``true'' floating-point exponent.
-| Note the slightly odd position of the binary point in zSig compared with the
-| other roundAndPackFloat functions. This should probably be fixed if we
-| need to implement more float16 routines than just conversion.
-| The handling of underflow and overflow follows the IEC/IEEE Standard for
-| Binary Floating-Point Arithmetic.
-*----------------------------------------------------------------------------*/
-
-static float16 roundAndPackFloat16(flag zSign, int zExp,
- uint32_t zSig, flag ieee,
- float_status *status)
-{
- int maxexp = ieee ? 29 : 30;
- uint32_t mask;
- uint32_t increment;
- bool rounding_bumps_exp;
- bool is_tiny = false;
-
- /* Calculate the mask of bits of the mantissa which are not
- * representable in half-precision and will be lost.
- */
- if (zExp < 1) {
- /* Will be denormal in halfprec */
- mask = 0x00ffffff;
- if (zExp >= -11) {
- mask >>= 11 + zExp;
- }
- } else {
- /* Normal number in halfprec */
- mask = 0x00001fff;
- }
-
- switch (status->float_rounding_mode) {
- case float_round_nearest_even:
- increment = (mask + 1) >> 1;
- if ((zSig & mask) == increment) {
- increment = zSig & (increment << 1);
- }
- break;
- case float_round_ties_away:
- increment = (mask + 1) >> 1;
- break;
- case float_round_up:
- increment = zSign ? 0 : mask;
- break;
- case float_round_down:
- increment = zSign ? mask : 0;
- break;
- default: /* round_to_zero */
- increment = 0;
- break;
- }
-
- rounding_bumps_exp = (zSig + increment >= 0x01000000);
-
- if (zExp > maxexp || (zExp == maxexp && rounding_bumps_exp)) {
- if (ieee) {
- float_raise(float_flag_overflow | float_flag_inexact, status);
- return packFloat16(zSign, 0x1f, 0);
- } else {
- float_raise(float_flag_invalid, status);
- return packFloat16(zSign, 0x1f, 0x3ff);
- }
- }
-
- if (zExp < 0) {
- /* Note that flush-to-zero does not affect half-precision results */
- is_tiny =
- (status->float_detect_tininess == float_tininess_before_rounding)
- || (zExp < -1)
- || (!rounding_bumps_exp);
- }
- if (zSig & mask) {
- float_raise(float_flag_inexact, status);
- if (is_tiny) {
- float_raise(float_flag_underflow, status);
- }
- }
-
- zSig += increment;
- if (rounding_bumps_exp) {
- zSig >>= 1;
- zExp++;
- }
-
- if (zExp < -10) {
- return packFloat16(zSign, 0, 0);
- }
- if (zExp < 0) {
- zSig >>= -zExp;
- zExp = 0;
- }
- return packFloat16(zSign, zExp, zSig >> 13);
-}
-
/*----------------------------------------------------------------------------
| If `a' is denormal and we are in flush-to-zero mode then set the
| input-denormal exception and return zero. Otherwise just return the value.
@@ -3846,163 +3704,6 @@ float16 float16_squash_input_denormal(float16 a, float_status *status)
return a;
}
-static void normalizeFloat16Subnormal(uint32_t aSig, int *zExpPtr,
- uint32_t *zSigPtr)
-{
- int8_t shiftCount = countLeadingZeros32(aSig) - 21;
- *zSigPtr = aSig << shiftCount;
- *zExpPtr = 1 - shiftCount;
-}
-
-/* Half precision floats come in two formats: standard IEEE and "ARM" format.
- The latter gains extra exponent range by omitting the NaN/Inf encodings. */
-
-float32 float16_to_float32(float16 a, flag ieee, float_status *status)
-{
- flag aSign;
- int aExp;
- uint32_t aSig;
-
- aSign = extractFloat16Sign(a);
- aExp = extractFloat16Exp(a);
- aSig = extractFloat16Frac(a);
-
- if (aExp == 0x1f && ieee) {
- if (aSig) {
- return commonNaNToFloat32(float16ToCommonNaN(a, status), status);
- }
- return packFloat32(aSign, 0xff, 0);
- }
- if (aExp == 0) {
- if (aSig == 0) {
- return packFloat32(aSign, 0, 0);
- }
-
- normalizeFloat16Subnormal(aSig, &aExp, &aSig);
- aExp--;
- }
- return packFloat32( aSign, aExp + 0x70, aSig << 13);
-}
-
-float16 float32_to_float16(float32 a, flag ieee, float_status *status)
-{
- flag aSign;
- int aExp;
- uint32_t aSig;
-
- a = float32_squash_input_denormal(a, status);
-
- aSig = extractFloat32Frac( a );
- aExp = extractFloat32Exp( a );
- aSign = extractFloat32Sign( a );
- if ( aExp == 0xFF ) {
- if (aSig) {
- /* Input is a NaN */
- if (!ieee) {
- float_raise(float_flag_invalid, status);
- return packFloat16(aSign, 0, 0);
- }
- return commonNaNToFloat16(
- float32ToCommonNaN(a, status), status);
- }
- /* Infinity */
- if (!ieee) {
- float_raise(float_flag_invalid, status);
- return packFloat16(aSign, 0x1f, 0x3ff);
- }
- return packFloat16(aSign, 0x1f, 0);
- }
- if (aExp == 0 && aSig == 0) {
- return packFloat16(aSign, 0, 0);
- }
- /* Decimal point between bits 22 and 23. Note that we add the 1 bit
- * even if the input is denormal; however this is harmless because
- * the largest possible single-precision denormal is still smaller
- * than the smallest representable half-precision denormal, and so we
- * will end up ignoring aSig and returning via the "always return zero"
- * codepath.
- */
- aSig |= 0x00800000;
- aExp -= 0x71;
-
- return roundAndPackFloat16(aSign, aExp, aSig, ieee, status);
-}
-
-float64 float16_to_float64(float16 a, flag ieee, float_status *status)
-{
- flag aSign;
- int aExp;
- uint32_t aSig;
-
- aSign = extractFloat16Sign(a);
- aExp = extractFloat16Exp(a);
- aSig = extractFloat16Frac(a);
-
- if (aExp == 0x1f && ieee) {
- if (aSig) {
- return commonNaNToFloat64(
- float16ToCommonNaN(a, status), status);
- }
- return packFloat64(aSign, 0x7ff, 0);
- }
- if (aExp == 0) {
- if (aSig == 0) {
- return packFloat64(aSign, 0, 0);
- }
-
- normalizeFloat16Subnormal(aSig, &aExp, &aSig);
- aExp--;
- }
- return packFloat64(aSign, aExp + 0x3f0, ((uint64_t)aSig) << 42);
-}
-
-float16 float64_to_float16(float64 a, flag ieee, float_status *status)
-{
- flag aSign;
- int aExp;
- uint64_t aSig;
- uint32_t zSig;
-
- a = float64_squash_input_denormal(a, status);
-
- aSig = extractFloat64Frac(a);
- aExp = extractFloat64Exp(a);
- aSign = extractFloat64Sign(a);
- if (aExp == 0x7FF) {
- if (aSig) {
- /* Input is a NaN */
- if (!ieee) {
- float_raise(float_flag_invalid, status);
- return packFloat16(aSign, 0, 0);
- }
- return commonNaNToFloat16(
- float64ToCommonNaN(a, status), status);
- }
- /* Infinity */
- if (!ieee) {
- float_raise(float_flag_invalid, status);
- return packFloat16(aSign, 0x1f, 0x3ff);
- }
- return packFloat16(aSign, 0x1f, 0);
- }
- shift64RightJamming(aSig, 29, &aSig);
- zSig = aSig;
- if (aExp == 0 && zSig == 0) {
- return packFloat16(aSign, 0, 0);
- }
- /* Decimal point between bits 22 and 23. Note that we add the 1 bit
- * even if the input is denormal; however this is harmless because
- * the largest possible single-precision denormal is still smaller
- * than the smallest representable half-precision denormal, and so we
- * will end up ignoring aSig and returning via the "always return zero"
- * codepath.
- */
- zSig |= 0x00800000;
- aExp -= 0x3F1;
-
- return roundAndPackFloat16(aSign, aExp, zSig, ieee, status);
-}
-
/*----------------------------------------------------------------------------
| Returns the result of converting the double-precision floating-point value
| `a' to the extended double-precision floating-point format. The conversion