@@ -745,4 +745,38 @@ static inline bool ne128(uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1)
return a0 != b0 || a1 != b1;
}
+/*
+ * Similarly, comparisons of 192-bit values.
+ */
+
+static inline bool eq192(uint64_t a0, uint64_t a1, uint64_t a2,
+ uint64_t b0, uint64_t b1, uint64_t b2)
+{
+ return ((a0 ^ b0) | (a1 ^ b1) | (a2 ^ b2)) == 0;
+}
+
+static inline bool le192(uint64_t a0, uint64_t a1, uint64_t a2,
+ uint64_t b0, uint64_t b1, uint64_t b2)
+{
+ if (a0 != b0) {
+ return a0 < b0;
+ }
+ if (a1 != b1) {
+ return a1 < b1;
+ }
+ return a2 <= b2;
+}
+
+static inline bool lt192(uint64_t a0, uint64_t a1, uint64_t a2,
+ uint64_t b0, uint64_t b1, uint64_t b2)
+{
+ if (a0 != b0) {
+ return a0 < b0;
+ }
+ if (a1 != b1) {
+ return a1 < b1;
+ }
+ return a2 < b2;
+}
+
#endif
@@ -401,60 +401,6 @@ float64_gen2(float64 xa, float64 xb, float_status *s,
return soft(ua.s, ub.s, s);
}
-/*----------------------------------------------------------------------------
-| Returns the fraction bits of the single-precision floating-point value `a'.
-*----------------------------------------------------------------------------*/
-
-static inline uint32_t extractFloat32Frac(float32 a)
-{
- return float32_val(a) & 0x007FFFFF;
-}
-
-/*----------------------------------------------------------------------------
-| Returns the exponent bits of the single-precision floating-point value `a'.
-*----------------------------------------------------------------------------*/
-
-static inline int extractFloat32Exp(float32 a)
-{
- return (float32_val(a) >> 23) & 0xFF;
-}
-
-/*----------------------------------------------------------------------------
-| Returns the sign bit of the single-precision floating-point value `a'.
-*----------------------------------------------------------------------------*/
-
-static inline bool extractFloat32Sign(float32 a)
-{
- return float32_val(a) >> 31;
-}
-
-/*----------------------------------------------------------------------------
-| Returns the fraction bits of the double-precision floating-point value `a'.
-*----------------------------------------------------------------------------*/
-
-static inline uint64_t extractFloat64Frac(float64 a)
-{
- return float64_val(a) & UINT64_C(0x000FFFFFFFFFFFFF);
-}
-
-/*----------------------------------------------------------------------------
-| Returns the exponent bits of the double-precision floating-point value `a'.
-*----------------------------------------------------------------------------*/
-
-static inline int extractFloat64Exp(float64 a)
-{
- return (float64_val(a) >> 52) & 0x7FF;
-}
-
-/*----------------------------------------------------------------------------
-| Returns the sign bit of the double-precision floating-point value `a'.
-*----------------------------------------------------------------------------*/
-
-static inline bool extractFloat64Sign(float64 a)
-{
- return float64_val(a) >> 63;
-}
-
/*
* Classify a floating point number. Everything above float_class_qnan
* is a NaN so cls >= float_class_qnan is any NaN.
@@ -845,6 +791,14 @@ static FloatParts128 *parts128_div(FloatParts128 *a, FloatParts128 *b,
#define parts_div(A, B, S) \
PARTS_GENERIC_64_128(div, A)(A, B, S)
+static FloatParts64 *parts64_modrem(FloatParts64 *a, FloatParts64 *b,
+ uint64_t *mod_quot, float_status *s);
+static FloatParts128 *parts128_modrem(FloatParts128 *a, FloatParts128 *b,
+ uint64_t *mod_quot, float_status *s);
+
+#define parts_modrem(A, B, Q, S) \
+ PARTS_GENERIC_64_128(modrem, A)(A, B, Q, S)
+
static void parts64_sqrt(FloatParts64 *a, float_status *s, const FloatFmt *f);
static void parts128_sqrt(FloatParts128 *a, float_status *s, const FloatFmt *f);
@@ -1229,6 +1183,186 @@ static int frac256_normalize(FloatParts256 *a)
#define frac_normalize(A) FRAC_GENERIC_64_128_256(normalize, A)(A)
+static void frac64_modrem(FloatParts64 *a, FloatParts64 *b, uint64_t *mod_quot)
+{
+ uint64_t a0, a1, b0, t0, t1, q, quot;
+ int exp_diff = a->exp - b->exp;
+ int shift;
+
+ a0 = a->frac;
+ a1 = 0;
+
+ if (exp_diff < -1) {
+ if (mod_quot) {
+ *mod_quot = 0;
+ }
+ return;
+ }
+ if (exp_diff == -1) {
+ a0 >>= 1;
+ exp_diff = 0;
+ }
+
+ b0 = b->frac;
+ quot = q = b0 <= a0;
+ if (q) {
+ a0 -= b0;
+ }
+
+ exp_diff -= 64;
+ while (exp_diff > 0) {
+ q = estimateDiv128To64(a0, a1, b0);
+ q = q > 2 ? q - 2 : 0;
+ mul64To128(b0, q, &t0, &t1);
+ sub128(a0, a1, t0, t1, &a0, &a1);
+ shortShift128Left(a0, a1, 62, &a0, &a1);
+ exp_diff -= 62;
+ quot = (quot << 62) + q;
+ }
+
+ exp_diff += 64;
+ if (exp_diff > 0) {
+ q = estimateDiv128To64(a0, a1, b0);
+ q = q > 2 ? (q - 2) >> (64 - exp_diff) : 0;
+ mul64To128(b0, q << (64 - exp_diff), &t0, &t1);
+ sub128(a0, a1, t0, t1, &a0, &a1);
+ shortShift128Left(0, b0, 64 - exp_diff, &t0, &t1);
+ while (le128(t0, t1, a0, a1)) {
+ ++q;
+ sub128(a0, a1, t0, t1, &a0, &a1);
+ }
+ quot = (exp_diff < 64 ? quot << exp_diff : 0) + q;
+ } else {
+ t0 = b0;
+ t1 = 0;
+ }
+
+ if (mod_quot) {
+ *mod_quot = quot;
+ } else {
+ sub128(t0, t1, a0, a1, &t0, &t1);
+ if (lt128(t0, t1, a0, a1) ||
+ (eq128(t0, t1, a0, a1) && (q & 1))) {
+ a0 = t0;
+ a1 = t1;
+ a->sign = !a->sign;
+ }
+ }
+
+ if (likely(a0)) {
+ shift = clz64(a0);
+ shortShift128Left(a0, a1, shift, &a0, &a1);
+ } else if (likely(a1)) {
+ shift = clz64(a1);
+ a0 = a1 << shift;
+ a1 = 0;
+ shift += 64;
+ } else {
+ a->cls = float_class_zero;
+ return;
+ }
+
+ a->exp = b->exp + exp_diff - shift;
+ a->frac = a0 | (a1 != 0);
+}
+
+static void frac128_modrem(FloatParts128 *a, FloatParts128 *b,
+ uint64_t *mod_quot)
+{
+ uint64_t a0, a1, a2, b0, b1, t0, t1, t2, q, quot;
+ int exp_diff = a->exp - b->exp;
+ int shift;
+
+ a0 = a->frac_hi;
+ a1 = a->frac_lo;
+ a2 = 0;
+
+ if (exp_diff < -1) {
+ if (mod_quot) {
+ *mod_quot = 0;
+ }
+ return;
+ }
+ if (exp_diff == -1) {
+ shift128Right(a0, a1, 1, &a0, &a1);
+ exp_diff = 0;
+ }
+
+ b0 = b->frac_hi;
+ b1 = b->frac_lo;
+
+ quot = q = le128(b0, b1, a0, a1);
+ if (q) {
+ sub128(a0, a1, b0, b1, &a0, &a1);
+ }
+
+ exp_diff -= 64;
+ while (exp_diff > 0) {
+ q = estimateDiv128To64(a0, a1, b0);
+ q = q > 4 ? q - 4 : 0;
+ mul128By64To192(b0, b1, q, &t0, &t1, &t2);
+ sub192(a0, a1, a2, t0, t1, t2, &a0, &a1, &a2);
+ shortShift192Left(a0, a1, a2, 61, &a0, &a1, &a2);
+ exp_diff -= 61;
+ quot = (quot << 61) + q;
+ }
+
+ exp_diff += 64;
+ if (exp_diff > 0) {
+ q = estimateDiv128To64(a0, a1, b0);
+ q = q > 4 ? (q - 4) >> (64 - exp_diff) : 0;
+ mul128By64To192(b0, b1, q << (64 - exp_diff), &t0, &t1, &t2);
+ sub192(a0, a1, a2, t0, t1, t2, &a0, &a1, &a2);
+ shortShift192Left(0, b0, b1, 64 - exp_diff, &t0, &t1, &t2);
+ while (le192(t0, t1, t2, a0, a1, a2)) {
+ ++q;
+ sub192(a0, a1, a2, t0, t1, t2, &a0, &a1, &a2);
+ }
+ quot = (exp_diff < 64 ? quot << exp_diff : 0) + q;
+ } else {
+ t0 = b0;
+ t1 = b1;
+ t2 = 0;
+ }
+
+ if (mod_quot) {
+ *mod_quot = quot;
+ } else {
+ sub192(t0, t1, t2, a0, a1, a2, &t0, &t1, &t2);
+ if (lt192(t0, t1, t2, a0, a1, a2) ||
+ (eq192(t0, t1, t2, a0, a1, a2) && (q & 1))) {
+ a0 = t0;
+ a1 = t1;
+ a2 = t2;
+ a->sign = !a->sign;
+ }
+ }
+
+ if (likely(a0)) {
+ shift = clz64(a0);
+ shortShift192Left(a0, a1, a2, shift, &a0, &a1, &a2);
+ } else if (likely(a1)) {
+ shift = clz64(a1);
+ shortShift128Left(a1, a2, shift, &a0, &a1);
+ a2 = 0;
+ shift += 64;
+ } else if (likely(a2)) {
+ shift = clz64(a2);
+ a0 = a2 << shift;
+ a1 = a2 = 0;
+ shift += 128;
+ } else {
+ a->cls = float_class_zero;
+ return;
+ }
+
+ a->exp = b->exp + exp_diff - shift;
+ a->frac_hi = a0;
+ a->frac_lo = a1 | (a2 != 0);
+}
+
+#define frac_modrem(A, B, Q) FRAC_GENERIC_64_128(modrem, A)(A, B, Q)
+
static void frac64_shl(FloatParts64 *a, int c)
{
a->frac <<= c;
@@ -2313,6 +2447,79 @@ floatx80 floatx80_div(floatx80 a, floatx80 b, float_status *status)
return floatx80_round_pack_canonical(pr, status);
}
+/*
+ * Remainder
+ */
+
+float32 float32_rem(float32 a, float32 b, float_status *status)
+{
+ FloatParts64 pa, pb, *pr;
+
+ float32_unpack_canonical(&pa, a, status);
+ float32_unpack_canonical(&pb, b, status);
+ pr = parts_modrem(&pa, &pb, NULL, status);
+
+ return float32_round_pack_canonical(pr, status);
+}
+
+float64 float64_rem(float64 a, float64 b, float_status *status)
+{
+ FloatParts64 pa, pb, *pr;
+
+ float64_unpack_canonical(&pa, a, status);
+ float64_unpack_canonical(&pb, b, status);
+ pr = parts_modrem(&pa, &pb, NULL, status);
+
+ return float64_round_pack_canonical(pr, status);
+}
+
+float128 float128_rem(float128 a, float128 b, float_status *status)
+{
+ FloatParts128 pa, pb, *pr;
+
+ float128_unpack_canonical(&pa, a, status);
+ float128_unpack_canonical(&pb, b, status);
+ pr = parts_modrem(&pa, &pb, NULL, status);
+
+ return float128_round_pack_canonical(pr, status);
+}
+
+/*
+ * Returns the remainder of the extended double-precision floating-point value
+ * `a' with respect to the corresponding value `b'.
+ * If 'mod' is false, the operation is performed according to the IEC/IEEE
+ * Standard for Binary Floating-Point Arithmetic. If 'mod' is true, return
+ * the remainder based on truncating the quotient toward zero instead and
+ * *quotient is set to the low 64 bits of the absolute value of the integer
+ * quotient.
+ */
+floatx80 floatx80_modrem(floatx80 a, floatx80 b, bool mod,
+ uint64_t *quotient, float_status *status)
+{
+ FloatParts128 pa, pb, *pr;
+
+ *quotient = 0;
+ if (!floatx80_unpack_canonical(&pa, a, status) ||
+ !floatx80_unpack_canonical(&pb, b, status)) {
+ return floatx80_default_nan(status);
+ }
+ pr = parts_modrem(&pa, &pb, mod ? quotient : NULL, status);
+
+ return floatx80_round_pack_canonical(pr, status);
+}
+
+floatx80 floatx80_rem(floatx80 a, floatx80 b, float_status *status)
+{
+ uint64_t quotient;
+ return floatx80_modrem(a, b, false, "ient, status);
+}
+
+floatx80 floatx80_mod(floatx80 a, floatx80 b, float_status *status)
+{
+ uint64_t quotient;
+ return floatx80_modrem(a, b, true, "ient, status);
+}
+
/*
* Float to Float conversions
*
@@ -4262,300 +4469,6 @@ bfloat16 bfloat16_squash_input_denormal(bfloat16 a, float_status *status)
return a;
}
-/*----------------------------------------------------------------------------
-| Normalizes the subnormal single-precision floating-point value represented
-| by the denormalized significand `aSig'. The normalized exponent and
-| significand are stored at the locations pointed to by `zExpPtr' and
-| `zSigPtr', respectively.
-*----------------------------------------------------------------------------*/
-
-static void
- normalizeFloat32Subnormal(uint32_t aSig, int *zExpPtr, uint32_t *zSigPtr)
-{
- int8_t shiftCount;
-
- shiftCount = clz32(aSig) - 8;
- *zSigPtr = aSig<<shiftCount;
- *zExpPtr = 1 - shiftCount;
-
-}
-
-/*----------------------------------------------------------------------------
-| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
-| and significand `zSig', and returns the proper single-precision floating-
-| point value corresponding to the abstract input. Ordinarily, the abstract
-| value is simply rounded and packed into the single-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 single-
-| precision floating-point number.
-| The input significand `zSig' has its binary point between bits 30
-| and 29, which is 7 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.
-| The handling of underflow and overflow follows the IEC/IEEE Standard for
-| Binary Floating-Point Arithmetic.
-*----------------------------------------------------------------------------*/
-
-static float32 roundAndPackFloat32(bool zSign, int zExp, uint32_t zSig,
- float_status *status)
-{
- int8_t roundingMode;
- bool roundNearestEven;
- int8_t roundIncrement, roundBits;
- bool isTiny;
-
- roundingMode = status->float_rounding_mode;
- roundNearestEven = ( roundingMode == float_round_nearest_even );
- switch (roundingMode) {
- case float_round_nearest_even:
- case float_round_ties_away:
- roundIncrement = 0x40;
- break;
- case float_round_to_zero:
- roundIncrement = 0;
- break;
- case float_round_up:
- roundIncrement = zSign ? 0 : 0x7f;
- break;
- case float_round_down:
- roundIncrement = zSign ? 0x7f : 0;
- break;
- case float_round_to_odd:
- roundIncrement = zSig & 0x80 ? 0 : 0x7f;
- break;
- default:
- abort();
- break;
- }
- roundBits = zSig & 0x7F;
- if ( 0xFD <= (uint16_t) zExp ) {
- if ( ( 0xFD < zExp )
- || ( ( zExp == 0xFD )
- && ( (int32_t) ( zSig + roundIncrement ) < 0 ) )
- ) {
- bool overflow_to_inf = roundingMode != float_round_to_odd &&
- roundIncrement != 0;
- float_raise(float_flag_overflow | float_flag_inexact, status);
- return packFloat32(zSign, 0xFF, -!overflow_to_inf);
- }
- if ( zExp < 0 ) {
- if (status->flush_to_zero) {
- float_raise(float_flag_output_denormal, status);
- return packFloat32(zSign, 0, 0);
- }
- isTiny = status->tininess_before_rounding
- || (zExp < -1)
- || (zSig + roundIncrement < 0x80000000);
- shift32RightJamming( zSig, - zExp, &zSig );
- zExp = 0;
- roundBits = zSig & 0x7F;
- if (isTiny && roundBits) {
- float_raise(float_flag_underflow, status);
- }
- if (roundingMode == float_round_to_odd) {
- /*
- * For round-to-odd case, the roundIncrement depends on
- * zSig which just changed.
- */
- roundIncrement = zSig & 0x80 ? 0 : 0x7f;
- }
- }
- }
- if (roundBits) {
- float_raise(float_flag_inexact, status);
- }
- zSig = ( zSig + roundIncrement )>>7;
- if (!(roundBits ^ 0x40) && roundNearestEven) {
- zSig &= ~1;
- }
- if ( zSig == 0 ) zExp = 0;
- return packFloat32( zSign, zExp, zSig );
-
-}
-
-/*----------------------------------------------------------------------------
-| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
-| and significand `zSig', and returns the proper single-precision floating-
-| point value corresponding to the abstract input. This routine is just like
-| `roundAndPackFloat32' except that `zSig' does not have to be normalized.
-| Bit 31 of `zSig' must be zero, and `zExp' must be 1 less than the ``true''
-| floating-point exponent.
-*----------------------------------------------------------------------------*/
-
-static float32
- normalizeRoundAndPackFloat32(bool zSign, int zExp, uint32_t zSig,
- float_status *status)
-{
- int8_t shiftCount;
-
- shiftCount = clz32(zSig) - 1;
- return roundAndPackFloat32(zSign, zExp - shiftCount, zSig<<shiftCount,
- status);
-
-}
-
-/*----------------------------------------------------------------------------
-| Normalizes the subnormal double-precision floating-point value represented
-| by the denormalized significand `aSig'. The normalized exponent and
-| significand are stored at the locations pointed to by `zExpPtr' and
-| `zSigPtr', respectively.
-*----------------------------------------------------------------------------*/
-
-static void
- normalizeFloat64Subnormal(uint64_t aSig, int *zExpPtr, uint64_t *zSigPtr)
-{
- int8_t shiftCount;
-
- shiftCount = clz64(aSig) - 11;
- *zSigPtr = aSig<<shiftCount;
- *zExpPtr = 1 - shiftCount;
-
-}
-
-/*----------------------------------------------------------------------------
-| Packs the sign `zSign', exponent `zExp', and significand `zSig' into a
-| double-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 inline float64 packFloat64(bool zSign, int zExp, uint64_t zSig)
-{
-
- return make_float64(
- ( ( (uint64_t) zSign )<<63 ) + ( ( (uint64_t) zExp )<<52 ) + zSig);
-
-}
-
-/*----------------------------------------------------------------------------
-| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
-| and significand `zSig', and returns the proper double-precision floating-
-| point value corresponding to the abstract input. Ordinarily, the abstract
-| value is simply rounded and packed into the double-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 double-
-| precision floating-point number.
-| The input significand `zSig' has its binary point between bits 62
-| and 61, which is 10 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.
-| The handling of underflow and overflow follows the IEC/IEEE Standard for
-| Binary Floating-Point Arithmetic.
-*----------------------------------------------------------------------------*/
-
-static float64 roundAndPackFloat64(bool zSign, int zExp, uint64_t zSig,
- float_status *status)
-{
- int8_t roundingMode;
- bool roundNearestEven;
- int roundIncrement, roundBits;
- bool isTiny;
-
- roundingMode = status->float_rounding_mode;
- roundNearestEven = ( roundingMode == float_round_nearest_even );
- switch (roundingMode) {
- case float_round_nearest_even:
- case float_round_ties_away:
- roundIncrement = 0x200;
- break;
- case float_round_to_zero:
- roundIncrement = 0;
- break;
- case float_round_up:
- roundIncrement = zSign ? 0 : 0x3ff;
- break;
- case float_round_down:
- roundIncrement = zSign ? 0x3ff : 0;
- break;
- case float_round_to_odd:
- roundIncrement = (zSig & 0x400) ? 0 : 0x3ff;
- break;
- default:
- abort();
- }
- roundBits = zSig & 0x3FF;
- if ( 0x7FD <= (uint16_t) zExp ) {
- if ( ( 0x7FD < zExp )
- || ( ( zExp == 0x7FD )
- && ( (int64_t) ( zSig + roundIncrement ) < 0 ) )
- ) {
- bool overflow_to_inf = roundingMode != float_round_to_odd &&
- roundIncrement != 0;
- float_raise(float_flag_overflow | float_flag_inexact, status);
- return packFloat64(zSign, 0x7FF, -(!overflow_to_inf));
- }
- if ( zExp < 0 ) {
- if (status->flush_to_zero) {
- float_raise(float_flag_output_denormal, status);
- return packFloat64(zSign, 0, 0);
- }
- isTiny = status->tininess_before_rounding
- || (zExp < -1)
- || (zSig + roundIncrement < UINT64_C(0x8000000000000000));
- shift64RightJamming( zSig, - zExp, &zSig );
- zExp = 0;
- roundBits = zSig & 0x3FF;
- if (isTiny && roundBits) {
- float_raise(float_flag_underflow, status);
- }
- if (roundingMode == float_round_to_odd) {
- /*
- * For round-to-odd case, the roundIncrement depends on
- * zSig which just changed.
- */
- roundIncrement = (zSig & 0x400) ? 0 : 0x3ff;
- }
- }
- }
- if (roundBits) {
- float_raise(float_flag_inexact, status);
- }
- zSig = ( zSig + roundIncrement )>>10;
- if (!(roundBits ^ 0x200) && roundNearestEven) {
- zSig &= ~1;
- }
- if ( zSig == 0 ) zExp = 0;
- return packFloat64( zSign, zExp, zSig );
-
-}
-
-/*----------------------------------------------------------------------------
-| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
-| and significand `zSig', and returns the proper double-precision floating-
-| point value corresponding to the abstract input. This routine is just like
-| `roundAndPackFloat64' except that `zSig' does not have to be normalized.
-| Bit 63 of `zSig' must be zero, and `zExp' must be 1 less than the ``true''
-| floating-point exponent.
-*----------------------------------------------------------------------------*/
-
-static float64
- normalizeRoundAndPackFloat64(bool zSign, int zExp, uint64_t zSig,
- float_status *status)
-{
- int8_t shiftCount;
-
- shiftCount = clz64(zSig) - 1;
- return roundAndPackFloat64(zSign, zExp - shiftCount, zSig<<shiftCount,
- status);
-
-}
-
/*----------------------------------------------------------------------------
| Normalizes the subnormal extended double-precision floating-point value
| represented by the denormalized significand `aSig'. The normalized exponent
@@ -4816,388 +4729,6 @@ floatx80 normalizeRoundAndPackFloatx80(FloatX80RoundPrec roundingPrecision,
}
-/*----------------------------------------------------------------------------
-| Returns the least-significant 64 fraction bits of the quadruple-precision
-| floating-point value `a'.
-*----------------------------------------------------------------------------*/
-
-static inline uint64_t extractFloat128Frac1( float128 a )
-{
-
- return a.low;
-
-}
-
-/*----------------------------------------------------------------------------
-| Returns the most-significant 48 fraction bits of the quadruple-precision
-| floating-point value `a'.
-*----------------------------------------------------------------------------*/
-
-static inline uint64_t extractFloat128Frac0( float128 a )
-{
-
- return a.high & UINT64_C(0x0000FFFFFFFFFFFF);
-
-}
-
-/*----------------------------------------------------------------------------
-| Returns the exponent bits of the quadruple-precision floating-point value
-| `a'.
-*----------------------------------------------------------------------------*/
-
-static inline int32_t extractFloat128Exp( float128 a )
-{
-
- return ( a.high>>48 ) & 0x7FFF;
-
-}
-
-/*----------------------------------------------------------------------------
-| Returns the sign bit of the quadruple-precision floating-point value `a'.
-*----------------------------------------------------------------------------*/
-
-static inline bool extractFloat128Sign(float128 a)
-{
- return a.high >> 63;
-}
-
-/*----------------------------------------------------------------------------
-| Normalizes the subnormal quadruple-precision floating-point value
-| represented by the denormalized significand formed by the concatenation of
-| `aSig0' and `aSig1'. The normalized exponent is stored at the location
-| pointed to by `zExpPtr'. The most significant 49 bits of the normalized
-| significand are stored at the location pointed to by `zSig0Ptr', and the
-| least significant 64 bits of the normalized significand are stored at the
-| location pointed to by `zSig1Ptr'.
-*----------------------------------------------------------------------------*/
-
-static void
- normalizeFloat128Subnormal(
- uint64_t aSig0,
- uint64_t aSig1,
- int32_t *zExpPtr,
- uint64_t *zSig0Ptr,
- uint64_t *zSig1Ptr
- )
-{
- int8_t shiftCount;
-
- if ( aSig0 == 0 ) {
- shiftCount = clz64(aSig1) - 15;
- if ( shiftCount < 0 ) {
- *zSig0Ptr = aSig1>>( - shiftCount );
- *zSig1Ptr = aSig1<<( shiftCount & 63 );
- }
- else {
- *zSig0Ptr = aSig1<<shiftCount;
- *zSig1Ptr = 0;
- }
- *zExpPtr = - shiftCount - 63;
- }
- else {
- shiftCount = clz64(aSig0) - 15;
- shortShift128Left( aSig0, aSig1, shiftCount, zSig0Ptr, zSig1Ptr );
- *zExpPtr = 1 - shiftCount;
- }
-
-}
-
-/*----------------------------------------------------------------------------
-| 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.
-*----------------------------------------------------------------------------*/
-
-static inline float128
-packFloat128(bool zSign, int32_t zExp, uint64_t zSig0, uint64_t zSig1)
-{
- float128 z;
-
- z.low = zSig1;
- z.high = ((uint64_t)zSign << 63) + ((uint64_t)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.
-*----------------------------------------------------------------------------*/
-
-static float128 roundAndPackFloat128(bool zSign, int32_t zExp,
- uint64_t zSig0, uint64_t zSig1,
- uint64_t zSig2, float_status *status)
-{
- int8_t roundingMode;
- bool roundNearestEven, increment, isTiny;
-
- roundingMode = status->float_rounding_mode;
- roundNearestEven = ( roundingMode == float_round_nearest_even );
- switch (roundingMode) {
- case float_round_nearest_even:
- case float_round_ties_away:
- increment = ((int64_t)zSig2 < 0);
- break;
- case float_round_to_zero:
- increment = 0;
- break;
- case float_round_up:
- increment = !zSign && zSig2;
- break;
- case float_round_down:
- increment = zSign && zSig2;
- break;
- case float_round_to_odd:
- increment = !(zSig1 & 0x1) && zSig2;
- break;
- default:
- abort();
- }
- if ( 0x7FFD <= (uint32_t) zExp ) {
- if ( ( 0x7FFD < zExp )
- || ( ( zExp == 0x7FFD )
- && eq128(
- UINT64_C(0x0001FFFFFFFFFFFF),
- UINT64_C(0xFFFFFFFFFFFFFFFF),
- zSig0,
- zSig1
- )
- && increment
- )
- ) {
- float_raise(float_flag_overflow | float_flag_inexact, status);
- if ( ( roundingMode == float_round_to_zero )
- || ( zSign && ( roundingMode == float_round_up ) )
- || ( ! zSign && ( roundingMode == float_round_down ) )
- || (roundingMode == float_round_to_odd)
- ) {
- return
- packFloat128(
- zSign,
- 0x7FFE,
- UINT64_C(0x0000FFFFFFFFFFFF),
- UINT64_C(0xFFFFFFFFFFFFFFFF)
- );
- }
- return packFloat128( zSign, 0x7FFF, 0, 0 );
- }
- if ( zExp < 0 ) {
- if (status->flush_to_zero) {
- float_raise(float_flag_output_denormal, status);
- return packFloat128(zSign, 0, 0, 0);
- }
- isTiny = status->tininess_before_rounding
- || (zExp < -1)
- || !increment
- || lt128(zSig0, zSig1,
- UINT64_C(0x0001FFFFFFFFFFFF),
- UINT64_C(0xFFFFFFFFFFFFFFFF));
- shift128ExtraRightJamming(
- zSig0, zSig1, zSig2, - zExp, &zSig0, &zSig1, &zSig2 );
- zExp = 0;
- if (isTiny && zSig2) {
- float_raise(float_flag_underflow, status);
- }
- switch (roundingMode) {
- case float_round_nearest_even:
- case float_round_ties_away:
- increment = ((int64_t)zSig2 < 0);
- break;
- case float_round_to_zero:
- increment = 0;
- break;
- case float_round_up:
- increment = !zSign && zSig2;
- break;
- case float_round_down:
- increment = zSign && zSig2;
- break;
- case float_round_to_odd:
- increment = !(zSig1 & 0x1) && zSig2;
- break;
- default:
- abort();
- }
- }
- }
- if (zSig2) {
- float_raise(float_flag_inexact, status);
- }
- if ( increment ) {
- add128( zSig0, zSig1, 0, 1, &zSig0, &zSig1 );
- if ((zSig2 + zSig2 == 0) && roundNearestEven) {
- zSig1 &= ~1;
- }
- }
- 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.
-*----------------------------------------------------------------------------*/
-
-static float128 normalizeRoundAndPackFloat128(bool zSign, int32_t zExp,
- uint64_t zSig0, uint64_t zSig1,
- float_status *status)
-{
- int8_t shiftCount;
- uint64_t zSig2;
-
- if ( zSig0 == 0 ) {
- zSig0 = zSig1;
- zSig1 = 0;
- zExp -= 64;
- }
- shiftCount = clz64(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, status);
-
-}
-
-/*----------------------------------------------------------------------------
-| Returns the remainder of the single-precision floating-point value `a'
-| with respect to the corresponding value `b'. The operation is performed
-| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
-*----------------------------------------------------------------------------*/
-
-float32 float32_rem(float32 a, float32 b, float_status *status)
-{
- bool aSign, zSign;
- int aExp, bExp, expDiff;
- uint32_t aSig, bSig;
- uint32_t q;
- uint64_t aSig64, bSig64, q64;
- uint32_t alternateASig;
- int32_t sigMean;
- a = float32_squash_input_denormal(a, status);
- b = float32_squash_input_denormal(b, status);
-
- aSig = extractFloat32Frac( a );
- aExp = extractFloat32Exp( a );
- aSign = extractFloat32Sign( a );
- bSig = extractFloat32Frac( b );
- bExp = extractFloat32Exp( b );
- if ( aExp == 0xFF ) {
- if ( aSig || ( ( bExp == 0xFF ) && bSig ) ) {
- return propagateFloat32NaN(a, b, status);
- }
- float_raise(float_flag_invalid, status);
- return float32_default_nan(status);
- }
- if ( bExp == 0xFF ) {
- if (bSig) {
- return propagateFloat32NaN(a, b, status);
- }
- return a;
- }
- if ( bExp == 0 ) {
- if ( bSig == 0 ) {
- float_raise(float_flag_invalid, status);
- return float32_default_nan(status);
- }
- normalizeFloat32Subnormal( bSig, &bExp, &bSig );
- }
- if ( aExp == 0 ) {
- if ( aSig == 0 ) return a;
- normalizeFloat32Subnormal( aSig, &aExp, &aSig );
- }
- expDiff = aExp - bExp;
- aSig |= 0x00800000;
- bSig |= 0x00800000;
- if ( expDiff < 32 ) {
- aSig <<= 8;
- bSig <<= 8;
- if ( expDiff < 0 ) {
- if ( expDiff < -1 ) return a;
- aSig >>= 1;
- }
- q = ( bSig <= aSig );
- if ( q ) aSig -= bSig;
- if ( 0 < expDiff ) {
- q = ( ( (uint64_t) aSig )<<32 ) / bSig;
- q >>= 32 - expDiff;
- bSig >>= 2;
- aSig = ( ( aSig>>1 )<<( expDiff - 1 ) ) - bSig * q;
- }
- else {
- aSig >>= 2;
- bSig >>= 2;
- }
- }
- else {
- if ( bSig <= aSig ) aSig -= bSig;
- aSig64 = ( (uint64_t) aSig )<<40;
- bSig64 = ( (uint64_t) bSig )<<40;
- expDiff -= 64;
- while ( 0 < expDiff ) {
- q64 = estimateDiv128To64( aSig64, 0, bSig64 );
- q64 = ( 2 < q64 ) ? q64 - 2 : 0;
- aSig64 = - ( ( bSig * q64 )<<38 );
- expDiff -= 62;
- }
- expDiff += 64;
- q64 = estimateDiv128To64( aSig64, 0, bSig64 );
- q64 = ( 2 < q64 ) ? q64 - 2 : 0;
- q = q64>>( 64 - expDiff );
- bSig <<= 6;
- aSig = ( ( aSig64>>33 )<<( expDiff - 1 ) ) - bSig * q;
- }
- do {
- alternateASig = aSig;
- ++q;
- aSig -= bSig;
- } while ( 0 <= (int32_t) aSig );
- sigMean = aSig + alternateASig;
- if ( ( sigMean < 0 ) || ( ( sigMean == 0 ) && ( q & 1 ) ) ) {
- aSig = alternateASig;
- }
- zSign = ( (int32_t) aSig < 0 );
- if ( zSign ) aSig = - aSig;
- return normalizeRoundAndPackFloat32(aSign ^ zSign, bExp, aSig, status);
-}
-
-
-
/*----------------------------------------------------------------------------
| Returns the binary exponential of the single-precision floating-point value
| `a'. The operation is performed according to the IEC/IEEE Standard for
@@ -5273,94 +4804,6 @@ float32 float32_exp2(float32 a, float_status *status)
return float32_round_pack_canonical(&rp, status);
}
-/*----------------------------------------------------------------------------
-| Returns the remainder of the double-precision floating-point value `a'
-| with respect to the corresponding value `b'. The operation is performed
-| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
-*----------------------------------------------------------------------------*/
-
-float64 float64_rem(float64 a, float64 b, float_status *status)
-{
- bool aSign, zSign;
- int aExp, bExp, expDiff;
- uint64_t aSig, bSig;
- uint64_t q, alternateASig;
- int64_t sigMean;
-
- a = float64_squash_input_denormal(a, status);
- b = float64_squash_input_denormal(b, status);
- aSig = extractFloat64Frac( a );
- aExp = extractFloat64Exp( a );
- aSign = extractFloat64Sign( a );
- bSig = extractFloat64Frac( b );
- bExp = extractFloat64Exp( b );
- if ( aExp == 0x7FF ) {
- if ( aSig || ( ( bExp == 0x7FF ) && bSig ) ) {
- return propagateFloat64NaN(a, b, status);
- }
- float_raise(float_flag_invalid, status);
- return float64_default_nan(status);
- }
- if ( bExp == 0x7FF ) {
- if (bSig) {
- return propagateFloat64NaN(a, b, status);
- }
- return a;
- }
- if ( bExp == 0 ) {
- if ( bSig == 0 ) {
- float_raise(float_flag_invalid, status);
- return float64_default_nan(status);
- }
- normalizeFloat64Subnormal( bSig, &bExp, &bSig );
- }
- if ( aExp == 0 ) {
- if ( aSig == 0 ) return a;
- normalizeFloat64Subnormal( aSig, &aExp, &aSig );
- }
- expDiff = aExp - bExp;
- aSig = (aSig | UINT64_C(0x0010000000000000)) << 11;
- bSig = (bSig | UINT64_C(0x0010000000000000)) << 11;
- if ( expDiff < 0 ) {
- if ( expDiff < -1 ) return a;
- aSig >>= 1;
- }
- q = ( bSig <= aSig );
- if ( q ) aSig -= bSig;
- expDiff -= 64;
- while ( 0 < expDiff ) {
- q = estimateDiv128To64( aSig, 0, bSig );
- q = ( 2 < q ) ? q - 2 : 0;
- aSig = - ( ( bSig>>2 ) * q );
- expDiff -= 62;
- }
- expDiff += 64;
- if ( 0 < expDiff ) {
- q = estimateDiv128To64( aSig, 0, bSig );
- q = ( 2 < q ) ? q - 2 : 0;
- q >>= 64 - expDiff;
- bSig >>= 2;
- aSig = ( ( aSig>>1 )<<( expDiff - 1 ) ) - bSig * q;
- }
- else {
- aSig >>= 2;
- bSig >>= 2;
- }
- do {
- alternateASig = aSig;
- ++q;
- aSig -= bSig;
- } while ( 0 <= (int64_t) aSig );
- sigMean = aSig + alternateASig;
- if ( ( sigMean < 0 ) || ( ( sigMean == 0 ) && ( q & 1 ) ) ) {
- aSig = alternateASig;
- }
- zSign = ( (int64_t) aSig < 0 );
- if ( zSign ) aSig = - aSig;
- return normalizeRoundAndPackFloat64(aSign ^ zSign, bExp, aSig, status);
-
-}
-
/*----------------------------------------------------------------------------
| Rounds the extended double-precision floating-point value `a'
| to the precision provided by floatx80_rounding_precision and returns the
@@ -5379,266 +4822,6 @@ floatx80 floatx80_round(floatx80 a, float_status *status)
return floatx80_round_pack_canonical(&p, status);
}
-/*----------------------------------------------------------------------------
-| Returns the remainder of the extended double-precision floating-point value
-| `a' with respect to the corresponding value `b'. The operation is performed
-| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic,
-| if 'mod' is false; if 'mod' is true, return the remainder based on truncating
-| the quotient toward zero instead. '*quotient' is set to the low 64 bits of
-| the absolute value of the integer quotient.
-*----------------------------------------------------------------------------*/
-
-floatx80 floatx80_modrem(floatx80 a, floatx80 b, bool mod, uint64_t *quotient,
- float_status *status)
-{
- bool aSign, zSign;
- int32_t aExp, bExp, expDiff, aExpOrig;
- uint64_t aSig0, aSig1, bSig;
- uint64_t q, term0, term1, alternateASig0, alternateASig1;
-
- *quotient = 0;
- if (floatx80_invalid_encoding(a) || floatx80_invalid_encoding(b)) {
- float_raise(float_flag_invalid, status);
- return floatx80_default_nan(status);
- }
- aSig0 = extractFloatx80Frac( a );
- aExpOrig = aExp = extractFloatx80Exp( a );
- aSign = extractFloatx80Sign( a );
- bSig = extractFloatx80Frac( b );
- bExp = extractFloatx80Exp( b );
- if ( aExp == 0x7FFF ) {
- if ( (uint64_t) ( aSig0<<1 )
- || ( ( bExp == 0x7FFF ) && (uint64_t) ( bSig<<1 ) ) ) {
- return propagateFloatx80NaN(a, b, status);
- }
- goto invalid;
- }
- if ( bExp == 0x7FFF ) {
- if ((uint64_t)(bSig << 1)) {
- return propagateFloatx80NaN(a, b, status);
- }
- if (aExp == 0 && aSig0 >> 63) {
- /*
- * Pseudo-denormal argument must be returned in normalized
- * form.
- */
- return packFloatx80(aSign, 1, aSig0);
- }
- return a;
- }
- if ( bExp == 0 ) {
- if ( bSig == 0 ) {
- invalid:
- float_raise(float_flag_invalid, status);
- return floatx80_default_nan(status);
- }
- normalizeFloatx80Subnormal( bSig, &bExp, &bSig );
- }
- if ( aExp == 0 ) {
- if ( aSig0 == 0 ) return a;
- normalizeFloatx80Subnormal( aSig0, &aExp, &aSig0 );
- }
- zSign = aSign;
- expDiff = aExp - bExp;
- aSig1 = 0;
- if ( expDiff < 0 ) {
- if ( mod || expDiff < -1 ) {
- if (aExp == 1 && aExpOrig == 0) {
- /*
- * Pseudo-denormal argument must be returned in
- * normalized form.
- */
- return packFloatx80(aSign, aExp, aSig0);
- }
- return a;
- }
- shift128Right( aSig0, 0, 1, &aSig0, &aSig1 );
- expDiff = 0;
- }
- *quotient = q = ( bSig <= aSig0 );
- if ( q ) aSig0 -= bSig;
- expDiff -= 64;
- while ( 0 < expDiff ) {
- q = estimateDiv128To64( aSig0, aSig1, bSig );
- q = ( 2 < q ) ? q - 2 : 0;
- mul64To128( bSig, q, &term0, &term1 );
- sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 );
- shortShift128Left( aSig0, aSig1, 62, &aSig0, &aSig1 );
- expDiff -= 62;
- *quotient <<= 62;
- *quotient += q;
- }
- expDiff += 64;
- if ( 0 < expDiff ) {
- q = estimateDiv128To64( aSig0, aSig1, bSig );
- q = ( 2 < q ) ? q - 2 : 0;
- q >>= 64 - expDiff;
- mul64To128( bSig, q<<( 64 - expDiff ), &term0, &term1 );
- sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 );
- shortShift128Left( 0, bSig, 64 - expDiff, &term0, &term1 );
- while ( le128( term0, term1, aSig0, aSig1 ) ) {
- ++q;
- sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 );
- }
- if (expDiff < 64) {
- *quotient <<= expDiff;
- } else {
- *quotient = 0;
- }
- *quotient += q;
- }
- else {
- term1 = 0;
- term0 = bSig;
- }
- if (!mod) {
- sub128( term0, term1, aSig0, aSig1, &alternateASig0, &alternateASig1 );
- if ( lt128( alternateASig0, alternateASig1, aSig0, aSig1 )
- || ( eq128( alternateASig0, alternateASig1, aSig0, aSig1 )
- && ( q & 1 ) )
- ) {
- aSig0 = alternateASig0;
- aSig1 = alternateASig1;
- zSign = ! zSign;
- ++*quotient;
- }
- }
- return
- normalizeRoundAndPackFloatx80(
- floatx80_precision_x, zSign, bExp + expDiff, aSig0, aSig1, status);
-
-}
-
-/*----------------------------------------------------------------------------
-| Returns the remainder of the extended double-precision floating-point value
-| `a' with respect to the corresponding value `b'. The operation is performed
-| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
-*----------------------------------------------------------------------------*/
-
-floatx80 floatx80_rem(floatx80 a, floatx80 b, float_status *status)
-{
- uint64_t quotient;
- return floatx80_modrem(a, b, false, "ient, status);
-}
-
-/*----------------------------------------------------------------------------
-| Returns the remainder of the extended double-precision floating-point value
-| `a' with respect to the corresponding value `b', with the quotient truncated
-| toward zero.
-*----------------------------------------------------------------------------*/
-
-floatx80 floatx80_mod(floatx80 a, floatx80 b, float_status *status)
-{
- uint64_t quotient;
- return floatx80_modrem(a, b, true, "ient, status);
-}
-
-/*----------------------------------------------------------------------------
-| Returns the remainder of the quadruple-precision floating-point value `a'
-| with respect to the corresponding value `b'. The operation is performed
-| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
-*----------------------------------------------------------------------------*/
-
-float128 float128_rem(float128 a, float128 b, float_status *status)
-{
- bool aSign, zSign;
- int32_t aExp, bExp, expDiff;
- uint64_t aSig0, aSig1, bSig0, bSig1, q, term0, term1, term2;
- uint64_t allZero, alternateASig0, alternateASig1, sigMean1;
- int64_t sigMean0;
-
- aSig1 = extractFloat128Frac1( a );
- aSig0 = extractFloat128Frac0( a );
- aExp = extractFloat128Exp( a );
- aSign = extractFloat128Sign( a );
- bSig1 = extractFloat128Frac1( b );
- bSig0 = extractFloat128Frac0( b );
- bExp = extractFloat128Exp( b );
- if ( aExp == 0x7FFF ) {
- if ( ( aSig0 | aSig1 )
- || ( ( bExp == 0x7FFF ) && ( bSig0 | bSig1 ) ) ) {
- return propagateFloat128NaN(a, b, status);
- }
- goto invalid;
- }
- if ( bExp == 0x7FFF ) {
- if (bSig0 | bSig1) {
- return propagateFloat128NaN(a, b, status);
- }
- return a;
- }
- if ( bExp == 0 ) {
- if ( ( bSig0 | bSig1 ) == 0 ) {
- invalid:
- float_raise(float_flag_invalid, status);
- return float128_default_nan(status);
- }
- normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 );
- }
- if ( aExp == 0 ) {
- if ( ( aSig0 | aSig1 ) == 0 ) return a;
- normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 );
- }
- expDiff = aExp - bExp;
- if ( expDiff < -1 ) return a;
- shortShift128Left(
- aSig0 | UINT64_C(0x0001000000000000),
- aSig1,
- 15 - ( expDiff < 0 ),
- &aSig0,
- &aSig1
- );
- shortShift128Left(
- bSig0 | UINT64_C(0x0001000000000000), bSig1, 15, &bSig0, &bSig1 );
- q = le128( bSig0, bSig1, aSig0, aSig1 );
- if ( q ) sub128( aSig0, aSig1, bSig0, bSig1, &aSig0, &aSig1 );
- expDiff -= 64;
- while ( 0 < expDiff ) {
- q = estimateDiv128To64( aSig0, aSig1, bSig0 );
- q = ( 4 < q ) ? q - 4 : 0;
- mul128By64To192( bSig0, bSig1, q, &term0, &term1, &term2 );
- shortShift192Left( term0, term1, term2, 61, &term1, &term2, &allZero );
- shortShift128Left( aSig0, aSig1, 61, &aSig0, &allZero );
- sub128( aSig0, 0, term1, term2, &aSig0, &aSig1 );
- expDiff -= 61;
- }
- if ( -64 < expDiff ) {
- q = estimateDiv128To64( aSig0, aSig1, bSig0 );
- q = ( 4 < q ) ? q - 4 : 0;
- q >>= - expDiff;
- shift128Right( bSig0, bSig1, 12, &bSig0, &bSig1 );
- expDiff += 52;
- if ( expDiff < 0 ) {
- shift128Right( aSig0, aSig1, - expDiff, &aSig0, &aSig1 );
- }
- else {
- shortShift128Left( aSig0, aSig1, expDiff, &aSig0, &aSig1 );
- }
- mul128By64To192( bSig0, bSig1, q, &term0, &term1, &term2 );
- sub128( aSig0, aSig1, term1, term2, &aSig0, &aSig1 );
- }
- else {
- shift128Right( aSig0, aSig1, 12, &aSig0, &aSig1 );
- shift128Right( bSig0, bSig1, 12, &bSig0, &bSig1 );
- }
- do {
- alternateASig0 = aSig0;
- alternateASig1 = aSig1;
- ++q;
- sub128( aSig0, aSig1, bSig0, bSig1, &aSig0, &aSig1 );
- } while ( 0 <= (int64_t) aSig0 );
- add128(
- aSig0, aSig1, alternateASig0, alternateASig1, (uint64_t *)&sigMean0, &sigMean1 );
- if ( ( sigMean0 < 0 )
- || ( ( ( sigMean0 | sigMean1 ) == 0 ) && ( q & 1 ) ) ) {
- aSig0 = alternateASig0;
- aSig1 = alternateASig1;
- }
- zSign = ( (int64_t) aSig0 < 0 );
- if ( zSign ) sub128( 0, 0, aSig0, aSig1, &aSig0, &aSig1 );
- return normalizeRoundAndPackFloat128(aSign ^ zSign, bExp - 4, aSig0, aSig1,
- status);
-}
static void __attribute__((constructor)) softfloat_init(void)
{
union_float64 ua, ub, uc, ur;
@@ -626,6 +626,40 @@ static FloatPartsN *partsN(div)(FloatPartsN *a, FloatPartsN *b,
return a;
}
+/*
+ * Floating point remainder, per IEC/IEEE, or modulus.
+ */
+static FloatPartsN *partsN(modrem)(FloatPartsN *a, FloatPartsN *b,
+ uint64_t *mod_quot, float_status *s)
+{
+ int ab_mask = float_cmask(a->cls) | float_cmask(b->cls);
+
+ if (likely(ab_mask == float_cmask_normal)) {
+ frac_modrem(a, b, mod_quot);
+ return a;
+ }
+
+ if (mod_quot) {
+ *mod_quot = 0;
+ }
+
+ /* All the NaN cases */
+ if (unlikely(ab_mask & float_cmask_anynan)) {
+ return parts_pick_nan(a, b, s);
+ }
+
+ /* Inf % N; N % 0 */
+ if (a->cls == float_class_inf || b->cls == float_class_zero) {
+ float_raise(float_flag_invalid, s);
+ parts_default_nan(a, s);
+ return a;
+ }
+
+ /* N % Inf; 0 % N */
+ g_assert(b->cls == float_class_inf || a->cls == float_class_zero);
+ return a;
+}
+
/*
* Square Root
*
@@ -641,62 +641,6 @@ static int pickNaNMulAdd(FloatClass a_cls, FloatClass b_cls, FloatClass c_cls,
#endif
}
-/*----------------------------------------------------------------------------
-| Takes two single-precision floating-point values `a' and `b', one of which
-| is a NaN, and returns the appropriate NaN result. If either `a' or `b' is a
-| signaling NaN, the invalid exception is raised.
-*----------------------------------------------------------------------------*/
-
-static float32 propagateFloat32NaN(float32 a, float32 b, float_status *status)
-{
- bool aIsLargerSignificand;
- uint32_t av, bv;
- FloatClass a_cls, b_cls;
-
- /* This is not complete, but is good enough for pickNaN. */
- a_cls = (!float32_is_any_nan(a)
- ? float_class_normal
- : float32_is_signaling_nan(a, status)
- ? float_class_snan
- : float_class_qnan);
- b_cls = (!float32_is_any_nan(b)
- ? float_class_normal
- : float32_is_signaling_nan(b, status)
- ? float_class_snan
- : float_class_qnan);
-
- av = float32_val(a);
- bv = float32_val(b);
-
- if (is_snan(a_cls) || is_snan(b_cls)) {
- float_raise(float_flag_invalid, status);
- }
-
- if (status->default_nan_mode) {
- return float32_default_nan(status);
- }
-
- if ((uint32_t)(av << 1) < (uint32_t)(bv << 1)) {
- aIsLargerSignificand = 0;
- } else if ((uint32_t)(bv << 1) < (uint32_t)(av << 1)) {
- aIsLargerSignificand = 1;
- } else {
- aIsLargerSignificand = (av < bv) ? 1 : 0;
- }
-
- if (pickNaN(a_cls, b_cls, aIsLargerSignificand, status)) {
- if (is_snan(b_cls)) {
- return float32_silence_nan(b, status);
- }
- return b;
- } else {
- if (is_snan(a_cls)) {
- return float32_silence_nan(a, status);
- }
- return a;
- }
-}
-
/*----------------------------------------------------------------------------
| Returns 1 if the double-precision floating-point value `a' is a quiet
| NaN; otherwise returns 0.
@@ -737,62 +681,6 @@ bool float64_is_signaling_nan(float64 a_, float_status *status)
}
}
-/*----------------------------------------------------------------------------
-| Takes two double-precision floating-point values `a' and `b', one of which
-| is a NaN, and returns the appropriate NaN result. If either `a' or `b' is a
-| signaling NaN, the invalid exception is raised.
-*----------------------------------------------------------------------------*/
-
-static float64 propagateFloat64NaN(float64 a, float64 b, float_status *status)
-{
- bool aIsLargerSignificand;
- uint64_t av, bv;
- FloatClass a_cls, b_cls;
-
- /* This is not complete, but is good enough for pickNaN. */
- a_cls = (!float64_is_any_nan(a)
- ? float_class_normal
- : float64_is_signaling_nan(a, status)
- ? float_class_snan
- : float_class_qnan);
- b_cls = (!float64_is_any_nan(b)
- ? float_class_normal
- : float64_is_signaling_nan(b, status)
- ? float_class_snan
- : float_class_qnan);
-
- av = float64_val(a);
- bv = float64_val(b);
-
- if (is_snan(a_cls) || is_snan(b_cls)) {
- float_raise(float_flag_invalid, status);
- }
-
- if (status->default_nan_mode) {
- return float64_default_nan(status);
- }
-
- if ((uint64_t)(av << 1) < (uint64_t)(bv << 1)) {
- aIsLargerSignificand = 0;
- } else if ((uint64_t)(bv << 1) < (uint64_t)(av << 1)) {
- aIsLargerSignificand = 1;
- } else {
- aIsLargerSignificand = (av < bv) ? 1 : 0;
- }
-
- if (pickNaN(a_cls, b_cls, aIsLargerSignificand, status)) {
- if (is_snan(b_cls)) {
- return float64_silence_nan(b, status);
- }
- return b;
- } else {
- if (is_snan(a_cls)) {
- return float64_silence_nan(a, status);
- }
- return a;
- }
-}
-
/*----------------------------------------------------------------------------
| Returns 1 if the extended double-precision floating-point value `a' is a
| quiet NaN; otherwise returns 0. This slightly differs from the same
@@ -947,56 +835,3 @@ bool float128_is_signaling_nan(float128 a, float_status *status)
}
}
}
-
-/*----------------------------------------------------------------------------
-| Takes two quadruple-precision floating-point values `a' and `b', one of
-| which is a NaN, and returns the appropriate NaN result. If either `a' or
-| `b' is a signaling NaN, the invalid exception is raised.
-*----------------------------------------------------------------------------*/
-
-static float128 propagateFloat128NaN(float128 a, float128 b,
- float_status *status)
-{
- bool aIsLargerSignificand;
- FloatClass a_cls, b_cls;
-
- /* This is not complete, but is good enough for pickNaN. */
- a_cls = (!float128_is_any_nan(a)
- ? float_class_normal
- : float128_is_signaling_nan(a, status)
- ? float_class_snan
- : float_class_qnan);
- b_cls = (!float128_is_any_nan(b)
- ? float_class_normal
- : float128_is_signaling_nan(b, status)
- ? float_class_snan
- : float_class_qnan);
-
- if (is_snan(a_cls) || is_snan(b_cls)) {
- float_raise(float_flag_invalid, status);
- }
-
- if (status->default_nan_mode) {
- return float128_default_nan(status);
- }
-
- if (lt128(a.high << 1, a.low, b.high << 1, b.low)) {
- aIsLargerSignificand = 0;
- } else if (lt128(b.high << 1, b.low, a.high << 1, a.low)) {
- aIsLargerSignificand = 1;
- } else {
- aIsLargerSignificand = (a.high < b.high) ? 1 : 0;
- }
-
- if (pickNaN(a_cls, b_cls, aIsLargerSignificand, status)) {
- if (is_snan(b_cls)) {
- return float128_silence_nan(b, status);
- }
- return b;
- } else {
- if (is_snan(a_cls)) {
- return float128_silence_nan(a, status);
- }
- return a;
- }
-}