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X-Received-From: 2a00:1450:400c:c0c::230 Subject: [Qemu-devel] [PATCH v4 22/22] fpu/softfloat: re-factor sqrt X-BeenThere: qemu-devel@nongnu.org X-Mailman-Version: 2.1.21 Precedence: list List-Id: List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , Cc: =?utf-8?q?Alex_Benn=C3=A9e?= , qemu-devel@nongnu.org, Aurelien Jarno Errors-To: qemu-devel-bounces+patch=linaro.org@nongnu.org Sender: "Qemu-devel" This is a little bit of a departure from softfloat's original approach as we skip the estimate step in favour of a straight iteration. Suggested-by: Richard Henderson Signed-off-by: Alex Bennée --- v3 - added to series - fixed renames of structs v4 - fix up comments - use is_nan - use return_nan instead of pick_nan(a,a) --- fpu/softfloat.c | 201 ++++++++++++++++++++++-------------------------- include/fpu/softfloat.h | 1 + 2 files changed, 91 insertions(+), 111 deletions(-) -- 2.15.1 Reviewed-by: Peter Maydell Reviewed-by: Richard Henderson diff --git a/fpu/softfloat.c b/fpu/softfloat.c index 8fc1c2a8d9..80301d8e04 100644 --- a/fpu/softfloat.c +++ b/fpu/softfloat.c @@ -1897,6 +1897,96 @@ float64 float64_scalbn(float64 a, int n, float_status *status) return float64_round_pack_canonical(pr, status); } +/* + * Square Root + * + * The old softfloat code did an approximation step before zeroing in + * on the final result. However for simpleness we just compute the + * square root by iterating down from the implicit bit to enough extra + * bits to ensure we get a correctly rounded result. + */ + +static FloatParts sqrt_float(FloatParts a, float_status *s, const FloatFmt *p) +{ + uint64_t a_frac, r_frac, s_frac; + int bit, last_bit; + + if (is_nan(a.cls)) { + return return_nan(a, s); + } + if (a.cls == float_class_zero) { + return a; /* sqrt(+-0) = +-0 */ + } + if (a.sign) { + s->float_exception_flags |= float_flag_invalid; + a.cls = float_class_dnan; + return a; + } + if (a.cls == float_class_inf) { + return a; /* sqrt(+inf) = +inf */ + } + + assert(a.cls == float_class_normal); + + /* We need two overflow bits at the top. Adding room for that is + a right shift. If the exponent is odd, we can discard the low + bit by multiplying the fraction by 2; that's a left shift. + Combine those and we shift right if the exponent is even. */ + a_frac = a.frac; + if (!(a.exp & 1)) { + a_frac >>= 1; + } + a.exp >>= 1; + + /* Bit-by-bit computation of sqrt. */ + r_frac = 0; + s_frac = 0; + + /* Iterate from implicit bit down to the 3 extra bits to compute a + * properly rounded result. Remember we've inserted one more bit + * at the top, so these positions are one less. */ + bit = DECOMPOSED_BINARY_POINT - 1; + last_bit = MAX(p->frac_shift - 4, 0); + do { + uint64_t q = 1ULL << bit; + uint64_t t_frac = s_frac + q; + if (t_frac <= a_frac) { + s_frac = t_frac + q; + a_frac -= t_frac; + r_frac += q; + } + a_frac <<= 1; + } while (--bit >= last_bit); + + /* Undo the right shift done above. If there is any remaining + fraction, the result is inexact. Set the sticky bit. */ + a.frac = (r_frac << 1) + (a_frac != 0); + + return a; +} + +float16 float16_sqrt(float16 a, float_status *status) +{ + FloatParts pa = float16_unpack_canonical(a, status); + FloatParts pr = sqrt_float(pa, status, &float16_params); + return float16_round_pack_canonical(pr, status); +} + +float32 float32_sqrt(float32 a, float_status *status) +{ + FloatParts pa = float32_unpack_canonical(a, status); + FloatParts pr = sqrt_float(pa, status, &float32_params); + return float32_round_pack_canonical(pr, status); +} + +float64 float64_sqrt(float64 a, float_status *status) +{ + FloatParts pa = float64_unpack_canonical(a, status); + FloatParts pr = sqrt_float(pa, status, &float64_params); + return float64_round_pack_canonical(pr, status); +} + + /*---------------------------------------------------------------------------- | Takes a 64-bit fixed-point value `absZ' with binary point between bits 6 | and 7, and returns the properly rounded 32-bit integer corresponding to the @@ -3304,62 +3394,6 @@ float32 float32_rem(float32 a, float32 b, float_status *status) } -/*---------------------------------------------------------------------------- -| Returns the square root of the single-precision floating-point value `a'. -| The operation is performed according to the IEC/IEEE Standard for Binary -| Floating-Point Arithmetic. -*----------------------------------------------------------------------------*/ - -float32 float32_sqrt(float32 a, float_status *status) -{ - flag aSign; - int aExp, zExp; - uint32_t aSig, zSig; - uint64_t rem, term; - a = float32_squash_input_denormal(a, status); - - aSig = extractFloat32Frac( a ); - aExp = extractFloat32Exp( a ); - aSign = extractFloat32Sign( a ); - if ( aExp == 0xFF ) { - if (aSig) { - return propagateFloat32NaN(a, float32_zero, status); - } - if ( ! aSign ) return a; - float_raise(float_flag_invalid, status); - return float32_default_nan(status); - } - if ( aSign ) { - if ( ( aExp | aSig ) == 0 ) return a; - float_raise(float_flag_invalid, status); - return float32_default_nan(status); - } - if ( aExp == 0 ) { - if ( aSig == 0 ) return float32_zero; - normalizeFloat32Subnormal( aSig, &aExp, &aSig ); - } - zExp = ( ( aExp - 0x7F )>>1 ) + 0x7E; - aSig = ( aSig | 0x00800000 )<<8; - zSig = estimateSqrt32( aExp, aSig ) + 2; - if ( ( zSig & 0x7F ) <= 5 ) { - if ( zSig < 2 ) { - zSig = 0x7FFFFFFF; - goto roundAndPack; - } - aSig >>= aExp & 1; - term = ( (uint64_t) zSig ) * zSig; - rem = ( ( (uint64_t) aSig )<<32 ) - term; - while ( (int64_t) rem < 0 ) { - --zSig; - rem += ( ( (uint64_t) zSig )<<1 ) | 1; - } - zSig |= ( rem != 0 ); - } - shift32RightJamming( zSig, 1, &zSig ); - roundAndPack: - return roundAndPackFloat32(0, zExp, zSig, status); - -} /*---------------------------------------------------------------------------- | Returns the binary exponential of the single-precision floating-point value @@ -4203,61 +4237,6 @@ float64 float64_rem(float64 a, float64 b, float_status *status) } - -/*---------------------------------------------------------------------------- -| Returns the square root of the double-precision floating-point value `a'. -| The operation is performed according to the IEC/IEEE Standard for Binary -| Floating-Point Arithmetic. -*----------------------------------------------------------------------------*/ - -float64 float64_sqrt(float64 a, float_status *status) -{ - flag aSign; - int aExp, zExp; - uint64_t aSig, zSig, doubleZSig; - uint64_t rem0, rem1, term0, term1; - a = float64_squash_input_denormal(a, status); - - aSig = extractFloat64Frac( a ); - aExp = extractFloat64Exp( a ); - aSign = extractFloat64Sign( a ); - if ( aExp == 0x7FF ) { - if (aSig) { - return propagateFloat64NaN(a, a, status); - } - if ( ! aSign ) return a; - float_raise(float_flag_invalid, status); - return float64_default_nan(status); - } - if ( aSign ) { - if ( ( aExp | aSig ) == 0 ) return a; - float_raise(float_flag_invalid, status); - return float64_default_nan(status); - } - if ( aExp == 0 ) { - if ( aSig == 0 ) return float64_zero; - normalizeFloat64Subnormal( aSig, &aExp, &aSig ); - } - zExp = ( ( aExp - 0x3FF )>>1 ) + 0x3FE; - aSig |= LIT64( 0x0010000000000000 ); - zSig = estimateSqrt32( aExp, aSig>>21 ); - aSig <<= 9 - ( aExp & 1 ); - zSig = estimateDiv128To64( aSig, 0, zSig<<32 ) + ( zSig<<30 ); - if ( ( zSig & 0x1FF ) <= 5 ) { - doubleZSig = zSig<<1; - mul64To128( zSig, zSig, &term0, &term1 ); - sub128( aSig, 0, term0, term1, &rem0, &rem1 ); - while ( (int64_t) rem0 < 0 ) { - --zSig; - doubleZSig -= 2; - add128( rem0, rem1, zSig>>63, doubleZSig | 1, &rem0, &rem1 ); - } - zSig |= ( ( rem0 | rem1 ) != 0 ); - } - return roundAndPackFloat64(0, zExp, zSig, status); - -} - /*---------------------------------------------------------------------------- | Returns the binary log of the double-precision floating-point value `a'. | The operation is performed according to the IEC/IEEE Standard for Binary diff --git a/include/fpu/softfloat.h b/include/fpu/softfloat.h index cebe37b716..9b7b5e34e2 100644 --- a/include/fpu/softfloat.h +++ b/include/fpu/softfloat.h @@ -251,6 +251,7 @@ float16 float16_minnum(float16, float16, float_status *status); float16 float16_maxnum(float16, float16, float_status *status); float16 float16_minnummag(float16, float16, float_status *status); float16 float16_maxnummag(float16, float16, float_status *status); +float16 float16_sqrt(float16, float_status *status); int float16_compare(float16, float16, float_status *status); int float16_compare_quiet(float16, float16, float_status *status);