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 <richard.hender...@linaro.org>
Signed-off-by: Alex Bennée <alex.ben...@linaro.org>
---
v3
- added to series
- fixed renames of structs
---
fpu/softfloat.c | 205 ++++++++++++++++++++++--------------------------
include/fpu/softfloat.h | 1 +
2 files changed, 95 insertions(+), 111 deletions(-)
diff --git a/fpu/softfloat.c b/fpu/softfloat.c
index 8ee110abba..d0c91d5a9a 100644
--- a/fpu/softfloat.c
+++ b/fpu/softfloat.c
@@ -1886,6 +1886,100 @@ float64 float64_scalbn(float64 a, int n, float_status
*status)
return float64_round_pack_canonical(pr, status);
}
+/* sqrt */
+
+/*
+ * Returns an approximation to the square root of the fraction given
+ * by `a'. Considered as an integer, `a' must be at least 2^31. If bit
+ * 0 of `aExp' (the least significant bit) is 1, the integer returned
+ * approximates 2^31*sqrt(`a'/2^31), where `a' is considered an
+ * integer. If bit 0 of `aExp' is 0, the integer returned approximates
+ * 2^31*sqrt(`a'/2^30). In either case, the approximation returned
+ * lies strictly within +/-2 of the exact value.
+ */
+
+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 (a.cls >= float_class_qnan) {
+ return pick_nan_parts(a, 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
@@ -3293,62 +3387,6 @@ 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
@@ -4192,61 +4230,6 @@ 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);
--
2.15.1
