diff options
Diffstat (limited to 'fpu/softfloat.c')
| -rw-r--r-- | fpu/softfloat.c | 1339 |
1 files changed, 261 insertions, 1078 deletions
diff --git a/fpu/softfloat.c b/fpu/softfloat.c index c0fe191f4d..5026f518b0 100644 --- a/fpu/softfloat.c +++ b/fpu/softfloat.c @@ -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; @@ -2314,6 +2448,79 @@ floatx80 floatx80_div(floatx80 a, floatx80 b, float_status *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 * * Returns the result of converting one float format to another. The @@ -4263,300 +4470,6 @@ bfloat16 bfloat16_squash_input_denormal(bfloat16 a, float_status *status) } /*---------------------------------------------------------------------------- -| 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 | and significand are stored at the locations pointed to by `zExpPtr' and @@ -4817,388 +4730,6 @@ 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 | Binary Floating-Point Arithmetic. @@ -5274,94 +4805,6 @@ float32 float32_exp2(float32 a, float_status *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 | result as an extended double-precision floating-point value. @@ -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; |