[Qemu-devel] [PATCH v2 1/4] softfloat: Fix division

[Richard Henderson <richard.henderson@linaro.org>]

The __udiv_qrnnd primitive that we nicked from gmp requires its
inputs to be normalized.  We were not doing that.  Because the
inputs are nearly normalized already, finishing that is trivial.

Replace div128to64 with a "proper" udiv_qrnnd, so that this
remains a reusable primitive.

Fixes: cf07323d494
Fixes: https://bugs.launchpad.net/qemu/+bug/1793119
Signed-off-by: Richard Henderson <richard.henderson@linaro.org>
---
 include/fpu/softfloat-macros.h |  7 ++++---
 fpu/softfloat.c                | 35 ++++++++++++++++++++++++++--------
 2 files changed, 31 insertions(+), 11 deletions(-)

diff --git a/include/fpu/softfloat-macros.h b/include/fpu/softfloat-macros.h
index edc682139e..03312471b2 100644
--- a/include/fpu/softfloat-macros.h
+++ b/include/fpu/softfloat-macros.h
@@ -619,7 +619,8 @@ static inline uint64_t estimateDiv128To64(uint64_t a0, uint64_t a1, uint64_t b)
  *
  * Licensed under the GPLv2/LGPLv3
  */
-static inline uint64_t div128To64(uint64_t n0, uint64_t n1, uint64_t d)
+static inline uint64_t udiv_qrnnd(uint64_t *r, uint64_t n1,
+                                  uint64_t n0, uint64_t d)
 {
     uint64_t d0, d1, q0, q1, r1, r0, m;
 
@@ -658,8 +659,8 @@ static inline uint64_t div128To64(uint64_t n0, uint64_t n1, uint64_t d)
     }
     r0 -= m;
 
-    /* Return remainder in LSB */
-    return (q1 << 32) | q0 | (r0 != 0);
+    *r = r0;
+    return (q1 << 32) | q0;
 }
 
 /*----------------------------------------------------------------------------
diff --git a/fpu/softfloat.c b/fpu/softfloat.c
index a06b6ef7e4..97ef66d570 100644
--- a/fpu/softfloat.c
+++ b/fpu/softfloat.c
@@ -1112,19 +1112,38 @@ static FloatParts div_floats(FloatParts a, FloatParts b, float_status *s)
     bool sign = a.sign ^ b.sign;
 
     if (a.cls == float_class_normal && b.cls == float_class_normal) {
-        uint64_t temp_lo, temp_hi;
+        uint64_t n0, n1, q, r;
         int exp = a.exp - b.exp;
+
+        /*
+         * We want a 2*N / N-bit division to produce exactly an N-bit
+         * result, so that we do not lose any precision and so that we
+         * do not have to renormalize afterward.  If A.frac < B.frac,
+         * then division would produce an (N-1)-bit result; shift A left
+         * by one to produce the an N-bit result, and decrement the
+         * exponent to match.
+         *
+         * The udiv_qrnnd algorithm that we're using requires normalization,
+         * i.e. the msb of the denominator must be set.  Since we know that
+         * DECOMPOSED_BINARY_POINT is msb-1, the inputs must be shifted left
+         * by one (more), and the remainder must be shifted right by one.
+         */
         if (a.frac < b.frac) {
             exp -= 1;
-            shortShift128Left(0, a.frac, DECOMPOSED_BINARY_POINT + 1,
-                              &temp_hi, &temp_lo);
+            shortShift128Left(0, a.frac, DECOMPOSED_BINARY_POINT + 2, &n1, &n0);
         } else {
-            shortShift128Left(0, a.frac, DECOMPOSED_BINARY_POINT,
-                              &temp_hi, &temp_lo);
+            shortShift128Left(0, a.frac, DECOMPOSED_BINARY_POINT + 1, &n1, &n0);
         }
-        /* LSB of quot is set if inexact which roundandpack will use
-         * to set flags. Yet again we re-use a for the result */
-        a.frac = div128To64(temp_lo, temp_hi, b.frac);
+        q = udiv_qrnnd(&r, n1, n0, b.frac << 1);
+
+        /*
+         * Set lsb if there is a remainder, to set inexact.
+         * As mentioned above, to find the actual value of the remainder we
+         * would need to shift right, but (1) we are only concerned about
+         * non-zero-ness, and (2) the remainder will always be even because
+         * both inputs to the division primitive are even.
+         */
+        a.frac = q | (r != 0);
         a.sign = sign;
         a.exp = exp;
         return a;
-- 
2.17.1