Merge remote-tracking branch 'remotes/rth-gitlab/tags/pull-fpu-20210603' into staging

Finish conversion of float128 and floatx80 to FloatParts.
Implement float128_muladd and float128_{min,max}*.
Optimize int-to-float conversion with hard-float.

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# gpg:                issuer "richard.henderson@linaro.org"
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* remotes/rth-gitlab/tags/pull-fpu-20210603: (29 commits)
  softfloat: Use hard-float for {u}int64_to_float{32,64}
  tests/fp: Enable more tests
  softfloat: Convert modrem operations to FloatParts
  softfloat: Move floatN_log2 to softfloat-parts.c.inc
  softfloat: Convert float32_exp2 to FloatParts
  softfloat: Convert floatx80 compare to FloatParts
  softfloat: Convert floatx80_scalbn to FloatParts
  softfloat: Convert floatx80 to integer to FloatParts
  softfloat: Convert floatx80 float conversions to FloatParts
  softfloat: Convert integer to floatx80 to FloatParts
  softfloat: Convert floatx80_round_to_int to FloatParts
  softfloat: Convert floatx80_round to FloatParts
  softfloat: Convert floatx80_sqrt to FloatParts
  softfloat: Convert floatx80_div to FloatParts
  softfloat: Convert floatx80_mul to FloatParts
  softfloat: Convert floatx80_add/sub to FloatParts
  tests/fp/fp-test: Reverse order of floatx80 precision tests
  softfloat: Adjust parts_uncanon_normal for floatx80
  softfloat: Introduce Floatx80RoundPrec
  softfloat: Reduce FloatFmt
  ...

Signed-off-by: Peter Maydell <peter.maydell@linaro.org>

15 files changed, 2165 insertions, 3814 deletions

diff --git a/fpu/softfloat-parts.c.inc b/fpu/softfloat-parts.c.inc
index 7f69da1d8f..dddee92d6e 100644
--- a/fpu/softfloat-parts.c.inc
+++ b/fpu/softfloat-parts.c.inc
@@ -140,46 +140,28 @@ static void partsN(canonicalize)(FloatPartsN *p, float_status *status,
  * fraction; these bits will be removed. The exponent will be biased
  * by EXP_BIAS and must be bounded by [EXP_MAX-1, 0].
  */
-static void partsN(uncanon)(FloatPartsN *p, float_status *s,
-                            const FloatFmt *fmt)
+static void partsN(uncanon_normal)(FloatPartsN *p, float_status *s,
+                                   const FloatFmt *fmt)
 {
     const int exp_max = fmt->exp_max;
     const int frac_shift = fmt->frac_shift;
-    const uint64_t frac_lsb = fmt->frac_lsb;
-    const uint64_t frac_lsbm1 = fmt->frac_lsbm1;
     const uint64_t round_mask = fmt->round_mask;
-    const uint64_t roundeven_mask = fmt->roundeven_mask;
+    const uint64_t frac_lsb = round_mask + 1;
+    const uint64_t frac_lsbm1 = round_mask ^ (round_mask >> 1);
+    const uint64_t roundeven_mask = round_mask | frac_lsb;
     uint64_t inc;
-    bool overflow_norm;
+    bool overflow_norm = false;
     int exp, flags = 0;
 
-    if (unlikely(p->cls != float_class_normal)) {
-        switch (p->cls) {
-        case float_class_zero:
-            p->exp = 0;
-            frac_clear(p);
-            return;
-        case float_class_inf:
-            g_assert(!fmt->arm_althp);
-            p->exp = fmt->exp_max;
-            frac_clear(p);
-            return;
-        case float_class_qnan:
-        case float_class_snan:
-            g_assert(!fmt->arm_althp);
-            p->exp = fmt->exp_max;
-            frac_shr(p, fmt->frac_shift);
-            return;
-        default:
-            break;
-        }
-        g_assert_not_reached();
-    }
-
-    overflow_norm = false;
     switch (s->float_rounding_mode) {
     case float_round_nearest_even:
-        inc = ((p->frac_lo & roundeven_mask) != frac_lsbm1 ? frac_lsbm1 : 0);
+        if (N > 64 && frac_lsb == 0) {
+            inc = ((p->frac_hi & 1) || (p->frac_lo & round_mask) != frac_lsbm1
+                   ? frac_lsbm1 : 0);
+        } else {
+            inc = ((p->frac_lo & roundeven_mask) != frac_lsbm1
+                   ? frac_lsbm1 : 0);
+        }
         break;
     case float_round_ties_away:
         inc = frac_lsbm1;
@@ -200,7 +182,11 @@ static void partsN(uncanon)(FloatPartsN *p, float_status *s,
         overflow_norm = true;
         /* fall through */
     case float_round_to_odd_inf:
-        inc = p->frac_lo & frac_lsb ? 0 : round_mask;
+        if (N > 64 && frac_lsb == 0) {
+            inc = p->frac_hi & 1 ? 0 : round_mask;
+        } else {
+            inc = p->frac_lo & frac_lsb ? 0 : round_mask;
+        }
         break;
     default:
         g_assert_not_reached();
@@ -215,8 +201,8 @@ static void partsN(uncanon)(FloatPartsN *p, float_status *s,
                 p->frac_hi |= DECOMPOSED_IMPLICIT_BIT;
                 exp++;
             }
+            p->frac_lo &= ~round_mask;
         }
-        frac_shr(p, frac_shift);
 
         if (fmt->arm_althp) {
             /* ARM Alt HP eschews Inf and NaN for a wider exponent.  */
@@ -225,18 +211,21 @@ static void partsN(uncanon)(FloatPartsN *p, float_status *s,
                 flags = float_flag_invalid;
                 exp = exp_max;
                 frac_allones(p);
+                p->frac_lo &= ~round_mask;
             }
         } else if (unlikely(exp >= exp_max)) {
             flags |= float_flag_overflow | float_flag_inexact;
             if (overflow_norm) {
                 exp = exp_max - 1;
                 frac_allones(p);
+                p->frac_lo &= ~round_mask;
             } else {
                 p->cls = float_class_inf;
                 exp = exp_max;
                 frac_clear(p);
             }
         }
+        frac_shr(p, frac_shift);
     } else if (s->flush_to_zero) {
         flags |= float_flag_output_denormal;
         p->cls = float_class_zero;
@@ -256,18 +245,29 @@ static void partsN(uncanon)(FloatPartsN *p, float_status *s,
             /* Need to recompute round-to-even/round-to-odd. */
             switch (s->float_rounding_mode) {
             case float_round_nearest_even:
-                inc = ((p->frac_lo & roundeven_mask) != frac_lsbm1
-                       ? frac_lsbm1 : 0);
+                if (N > 64 && frac_lsb == 0) {
+                    inc = ((p->frac_hi & 1) ||
+                           (p->frac_lo & round_mask) != frac_lsbm1
+                           ? frac_lsbm1 : 0);
+                } else {
+                    inc = ((p->frac_lo & roundeven_mask) != frac_lsbm1
+                           ? frac_lsbm1 : 0);
+                }
                 break;
             case float_round_to_odd:
             case float_round_to_odd_inf:
-                inc = p->frac_lo & frac_lsb ? 0 : round_mask;
+                if (N > 64 && frac_lsb == 0) {
+                    inc = p->frac_hi & 1 ? 0 : round_mask;
+                } else {
+                    inc = p->frac_lo & frac_lsb ? 0 : round_mask;
+                }
                 break;
             default:
                 break;
             }
             flags |= float_flag_inexact;
             frac_addi(p, p, inc);
+            p->frac_lo &= ~round_mask;
         }
 
         exp = (p->frac_hi & DECOMPOSED_IMPLICIT_BIT) != 0;
@@ -284,6 +284,35 @@ static void partsN(uncanon)(FloatPartsN *p, float_status *s,
     float_raise(flags, s);
 }
 
+static void partsN(uncanon)(FloatPartsN *p, float_status *s,
+                            const FloatFmt *fmt)
+{
+    if (likely(p->cls == float_class_normal)) {
+        parts_uncanon_normal(p, s, fmt);
+    } else {
+        switch (p->cls) {
+        case float_class_zero:
+            p->exp = 0;
+            frac_clear(p);
+            return;
+        case float_class_inf:
+            g_assert(!fmt->arm_althp);
+            p->exp = fmt->exp_max;
+            frac_clear(p);
+            return;
+        case float_class_qnan:
+        case float_class_snan:
+            g_assert(!fmt->arm_althp);
+            p->exp = fmt->exp_max;
+            frac_shr(p, fmt->frac_shift);
+            return;
+        default:
+            break;
+        }
+        g_assert_not_reached();
+    }
+}
+
 /*
  * Returns the result of adding or subtracting the values of the
  * floating-point values `a' and `b'. The operation is performed
@@ -598,6 +627,246 @@ static FloatPartsN *partsN(div)(FloatPartsN *a, FloatPartsN *b,
 }
 
 /*
+ * 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
+ *
+ * The base algorithm is lifted from
+ * https://git.musl-libc.org/cgit/musl/tree/src/math/sqrtf.c
+ * https://git.musl-libc.org/cgit/musl/tree/src/math/sqrt.c
+ * https://git.musl-libc.org/cgit/musl/tree/src/math/sqrtl.c
+ * and is thus MIT licenced.
+ */
+static void partsN(sqrt)(FloatPartsN *a, float_status *status,
+                         const FloatFmt *fmt)
+{
+    const uint32_t three32 = 3u << 30;
+    const uint64_t three64 = 3ull << 62;
+    uint32_t d32, m32, r32, s32, u32;            /* 32-bit computation */
+    uint64_t d64, m64, r64, s64, u64;            /* 64-bit computation */
+    uint64_t dh, dl, rh, rl, sh, sl, uh, ul;     /* 128-bit computation */
+    uint64_t d0h, d0l, d1h, d1l, d2h, d2l;
+    uint64_t discard;
+    bool exp_odd;
+    size_t index;
+
+    if (unlikely(a->cls != float_class_normal)) {
+        switch (a->cls) {
+        case float_class_snan:
+        case float_class_qnan:
+            parts_return_nan(a, status);
+            return;
+        case float_class_zero:
+            return;
+        case float_class_inf:
+            if (unlikely(a->sign)) {
+                goto d_nan;
+            }
+            return;
+        default:
+            g_assert_not_reached();
+        }
+    }
+
+    if (unlikely(a->sign)) {
+        goto d_nan;
+    }
+
+    /*
+     * Argument reduction.
+     * x = 4^e frac; with integer e, and frac in [1, 4)
+     * m = frac fixed point at bit 62, since we're in base 4.
+     * If base-2 exponent is odd, exchange that for multiply by 2,
+     * which results in no shift.
+     */
+    exp_odd = a->exp & 1;
+    index = extract64(a->frac_hi, 57, 6) | (!exp_odd << 6);
+    if (!exp_odd) {
+        frac_shr(a, 1);
+    }
+
+    /*
+     * Approximate r ~= 1/sqrt(m) and s ~= sqrt(m) when m in [1, 4).
+     *
+     * Initial estimate:
+     * 7-bit lookup table (1-bit exponent and 6-bit significand).
+     *
+     * The relative error (e = r0*sqrt(m)-1) of a linear estimate
+     * (r0 = a*m + b) is |e| < 0.085955 ~ 0x1.6p-4 at best;
+     * a table lookup is faster and needs one less iteration.
+     * The 7-bit table gives |e| < 0x1.fdp-9.
+     *
+     * A Newton-Raphson iteration for r is
+     *   s = m*r
+     *   d = s*r
+     *   u = 3 - d
+     *   r = r*u/2
+     *
+     * Fixed point representations:
+     *   m, s, d, u, three are all 2.30; r is 0.32
+     */
+    m64 = a->frac_hi;
+    m32 = m64 >> 32;
+
+    r32 = rsqrt_tab[index] << 16;
+    /* |r*sqrt(m) - 1| < 0x1.FDp-9 */
+
+    s32 = ((uint64_t)m32 * r32) >> 32;
+    d32 = ((uint64_t)s32 * r32) >> 32;
+    u32 = three32 - d32;
+
+    if (N == 64) {
+        /* float64 or smaller */
+
+        r32 = ((uint64_t)r32 * u32) >> 31;
+        /* |r*sqrt(m) - 1| < 0x1.7Bp-16 */
+
+        s32 = ((uint64_t)m32 * r32) >> 32;
+        d32 = ((uint64_t)s32 * r32) >> 32;
+        u32 = three32 - d32;
+
+        if (fmt->frac_size <= 23) {
+            /* float32 or smaller */
+
+            s32 = ((uint64_t)s32 * u32) >> 32;  /* 3.29 */
+            s32 = (s32 - 1) >> 6;               /* 9.23 */
+            /* s < sqrt(m) < s + 0x1.08p-23 */
+
+            /* compute nearest rounded result to 2.23 bits */
+            uint32_t d0 = (m32 << 16) - s32 * s32;
+            uint32_t d1 = s32 - d0;
+            uint32_t d2 = d1 + s32 + 1;
+            s32 += d1 >> 31;
+            a->frac_hi = (uint64_t)s32 << (64 - 25);
+
+            /* increment or decrement for inexact */
+            if (d2 != 0) {
+                a->frac_hi += ((int32_t)(d1 ^ d2) < 0 ? -1 : 1);
+            }
+            goto done;
+        }
+
+        /* float64 */
+
+        r64 = (uint64_t)r32 * u32 * 2;
+        /* |r*sqrt(m) - 1| < 0x1.37-p29; convert to 64-bit arithmetic */
+        mul64To128(m64, r64, &s64, &discard);
+        mul64To128(s64, r64, &d64, &discard);
+        u64 = three64 - d64;
+
+        mul64To128(s64, u64, &s64, &discard);  /* 3.61 */
+        s64 = (s64 - 2) >> 9;                  /* 12.52 */
+
+        /* Compute nearest rounded result */
+        uint64_t d0 = (m64 << 42) - s64 * s64;
+        uint64_t d1 = s64 - d0;
+        uint64_t d2 = d1 + s64 + 1;
+        s64 += d1 >> 63;
+        a->frac_hi = s64 << (64 - 54);
+
+        /* increment or decrement for inexact */
+        if (d2 != 0) {
+            a->frac_hi += ((int64_t)(d1 ^ d2) < 0 ? -1 : 1);
+        }
+        goto done;
+    }
+
+    r64 = (uint64_t)r32 * u32 * 2;
+    /* |r*sqrt(m) - 1| < 0x1.7Bp-16; convert to 64-bit arithmetic */
+
+    mul64To128(m64, r64, &s64, &discard);
+    mul64To128(s64, r64, &d64, &discard);
+    u64 = three64 - d64;
+    mul64To128(u64, r64, &r64, &discard);
+    r64 <<= 1;
+    /* |r*sqrt(m) - 1| < 0x1.a5p-31 */
+
+    mul64To128(m64, r64, &s64, &discard);
+    mul64To128(s64, r64, &d64, &discard);
+    u64 = three64 - d64;
+    mul64To128(u64, r64, &rh, &rl);
+    add128(rh, rl, rh, rl, &rh, &rl);
+    /* |r*sqrt(m) - 1| < 0x1.c001p-59; change to 128-bit arithmetic */
+
+    mul128To256(a->frac_hi, a->frac_lo, rh, rl, &sh, &sl, &discard, &discard);
+    mul128To256(sh, sl, rh, rl, &dh, &dl, &discard, &discard);
+    sub128(three64, 0, dh, dl, &uh, &ul);
+    mul128To256(uh, ul, sh, sl, &sh, &sl, &discard, &discard);  /* 3.125 */
+    /* -0x1p-116 < s - sqrt(m) < 0x3.8001p-125 */
+
+    sub128(sh, sl, 0, 4, &sh, &sl);
+    shift128Right(sh, sl, 13, &sh, &sl);  /* 16.112 */
+    /* s < sqrt(m) < s + 1ulp */
+
+    /* Compute nearest rounded result */
+    mul64To128(sl, sl, &d0h, &d0l);
+    d0h += 2 * sh * sl;
+    sub128(a->frac_lo << 34, 0, d0h, d0l, &d0h, &d0l);
+    sub128(sh, sl, d0h, d0l, &d1h, &d1l);
+    add128(sh, sl, 0, 1, &d2h, &d2l);
+    add128(d2h, d2l, d1h, d1l, &d2h, &d2l);
+    add128(sh, sl, 0, d1h >> 63, &sh, &sl);
+    shift128Left(sh, sl, 128 - 114, &sh, &sl);
+
+    /* increment or decrement for inexact */
+    if (d2h | d2l) {
+        if ((int64_t)(d1h ^ d2h) < 0) {
+            sub128(sh, sl, 0, 1, &sh, &sl);
+        } else {
+            add128(sh, sl, 0, 1, &sh, &sl);
+        }
+    }
+    a->frac_lo = sl;
+    a->frac_hi = sh;
+
+ done:
+    /* Convert back from base 4 to base 2. */
+    a->exp >>= 1;
+    if (!(a->frac_hi & DECOMPOSED_IMPLICIT_BIT)) {
+        frac_add(a, a, a);
+    } else {
+        a->exp += 1;
+    }
+    return;
+
+ d_nan:
+    float_raise(float_flag_invalid, status);
+    parts_default_nan(a, status);
+}
+
+/*
  * Rounds the floating-point value `a' to an integer, and returns the
  * result as a floating-point value. The operation is performed
  * according to the IEC/IEEE Standard for Binary Floating-Point
@@ -763,7 +1032,7 @@ static void partsN(round_to_int)(FloatPartsN *a, FloatRoundMode rmode,
  * the largest positive integer is returned. Otherwise, if the
  * conversion overflows, the largest integer with the same sign as `a'
  * is returned.
-*/
+ */
 static int64_t partsN(float_to_sint)(FloatPartsN *p, FloatRoundMode rmode,
                                      int scale, int64_t min, int64_t max,
                                      float_status *s)
@@ -817,3 +1086,407 @@ static int64_t partsN(float_to_sint)(FloatPartsN *p, FloatRoundMode rmode,
     float_raise(flags, s);
     return r;
 }
+
+/*
+ *  Returns the result of converting the floating-point value `a' to
+ *  the unsigned integer format. The conversion is performed according
+ *  to the IEC/IEEE Standard for Binary Floating-Point
+ *  Arithmetic---which means in particular that the conversion is
+ *  rounded according to the current rounding mode. If `a' is a NaN,
+ *  the largest unsigned integer is returned. Otherwise, if the
+ *  conversion overflows, the largest unsigned integer is returned. If
+ *  the 'a' is negative, the result is rounded and zero is returned;
+ *  values that do not round to zero will raise the inexact exception
+ *  flag.
+ */
+static uint64_t partsN(float_to_uint)(FloatPartsN *p, FloatRoundMode rmode,
+                                      int scale, uint64_t max, float_status *s)
+{
+    int flags = 0;
+    uint64_t r;
+
+    switch (p->cls) {
+    case float_class_snan:
+    case float_class_qnan:
+        flags = float_flag_invalid;
+        r = max;
+        break;
+
+    case float_class_inf:
+        flags = float_flag_invalid;
+        r = p->sign ? 0 : max;
+        break;
+
+    case float_class_zero:
+        return 0;
+
+    case float_class_normal:
+        /* TODO: N - 2 is frac_size for rounding; could use input fmt. */
+        if (parts_round_to_int_normal(p, rmode, scale, N - 2)) {
+            flags = float_flag_inexact;
+            if (p->cls == float_class_zero) {
+                r = 0;
+                break;
+            }
+        }
+
+        if (p->sign) {
+            flags = float_flag_invalid;
+            r = 0;
+        } else if (p->exp > DECOMPOSED_BINARY_POINT) {
+            flags = float_flag_invalid;
+            r = max;
+        } else {
+            r = p->frac_hi >> (DECOMPOSED_BINARY_POINT - p->exp);
+            if (r > max) {
+                flags = float_flag_invalid;
+                r = max;
+            }
+        }
+        break;
+
+    default:
+        g_assert_not_reached();
+    }
+
+    float_raise(flags, s);
+    return r;
+}
+
+/*
+ * Integer to float conversions
+ *
+ * Returns the result of converting the two's complement integer `a'
+ * to the floating-point format. The conversion is performed according
+ * to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+ */
+static void partsN(sint_to_float)(FloatPartsN *p, int64_t a,
+                                  int scale, float_status *s)
+{
+    uint64_t f = a;
+    int shift;
+
+    memset(p, 0, sizeof(*p));
+
+    if (a == 0) {
+        p->cls = float_class_zero;
+        return;
+    }
+
+    p->cls = float_class_normal;
+    if (a < 0) {
+        f = -f;
+        p->sign = true;
+    }
+    shift = clz64(f);
+    scale = MIN(MAX(scale, -0x10000), 0x10000);
+
+    p->exp = DECOMPOSED_BINARY_POINT - shift + scale;
+    p->frac_hi = f << shift;
+}
+
+/*
+ * Unsigned Integer to float conversions
+ *
+ * Returns the result of converting the unsigned integer `a' to the
+ * floating-point format. The conversion is performed according to the
+ * IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+ */
+static void partsN(uint_to_float)(FloatPartsN *p, uint64_t a,
+                                  int scale, float_status *status)
+{
+    memset(p, 0, sizeof(*p));
+
+    if (a == 0) {
+        p->cls = float_class_zero;
+    } else {
+        int shift = clz64(a);
+        scale = MIN(MAX(scale, -0x10000), 0x10000);
+        p->cls = float_class_normal;
+        p->exp = DECOMPOSED_BINARY_POINT - shift + scale;
+        p->frac_hi = a << shift;
+    }
+}
+
+/*
+ * Float min/max.
+ */
+static FloatPartsN *partsN(minmax)(FloatPartsN *a, FloatPartsN *b,
+                                   float_status *s, int flags)
+{
+    int ab_mask = float_cmask(a->cls) | float_cmask(b->cls);
+    int a_exp, b_exp, cmp;
+
+    if (unlikely(ab_mask & float_cmask_anynan)) {
+        /*
+         * For minnum/maxnum, if one operand is a QNaN, and the other
+         * operand is numerical, then return numerical argument.
+         */
+        if ((flags & minmax_isnum)
+            && !(ab_mask & float_cmask_snan)
+            && (ab_mask & ~float_cmask_qnan)) {
+            return is_nan(a->cls) ? b : a;
+        }
+        return parts_pick_nan(a, b, s);
+    }
+
+    a_exp = a->exp;
+    b_exp = b->exp;
+
+    if (unlikely(ab_mask != float_cmask_normal)) {
+        switch (a->cls) {
+        case float_class_normal:
+            break;
+        case float_class_inf:
+            a_exp = INT16_MAX;
+            break;
+        case float_class_zero:
+            a_exp = INT16_MIN;
+            break;
+        default:
+            g_assert_not_reached();
+            break;
+        }
+        switch (b->cls) {
+        case float_class_normal:
+            break;
+        case float_class_inf:
+            b_exp = INT16_MAX;
+            break;
+        case float_class_zero:
+            b_exp = INT16_MIN;
+            break;
+        default:
+            g_assert_not_reached();
+            break;
+        }
+    }
+
+    /* Compare magnitudes. */
+    cmp = a_exp - b_exp;
+    if (cmp == 0) {
+        cmp = frac_cmp(a, b);
+    }
+
+    /*
+     * Take the sign into account.
+     * For ismag, only do this if the magnitudes are equal.
+     */
+    if (!(flags & minmax_ismag) || cmp == 0) {
+        if (a->sign != b->sign) {
+            /* For differing signs, the negative operand is less. */
+            cmp = a->sign ? -1 : 1;
+        } else if (a->sign) {
+            /* For two negative operands, invert the magnitude comparison. */
+            cmp = -cmp;
+        }
+    }
+
+    if (flags & minmax_ismin) {
+        cmp = -cmp;
+    }
+    return cmp < 0 ? b : a;
+}
+
+/*
+ * Floating point compare
+ */
+static FloatRelation partsN(compare)(FloatPartsN *a, FloatPartsN *b,
+                                     float_status *s, bool is_quiet)
+{
+    int ab_mask = float_cmask(a->cls) | float_cmask(b->cls);
+    int cmp;
+
+    if (likely(ab_mask == float_cmask_normal)) {
+        if (a->sign != b->sign) {
+            goto a_sign;
+        }
+        if (a->exp != b->exp) {
+            cmp = a->exp < b->exp ? -1 : 1;
+        } else {
+            cmp = frac_cmp(a, b);
+        }
+        if (a->sign) {
+            cmp = -cmp;
+        }
+        return cmp;
+    }
+
+    if (unlikely(ab_mask & float_cmask_anynan)) {
+        if (!is_quiet || (ab_mask & float_cmask_snan)) {
+            float_raise(float_flag_invalid, s);
+        }
+        return float_relation_unordered;
+    }
+
+    if (ab_mask & float_cmask_zero) {
+        if (ab_mask == float_cmask_zero) {
+            return float_relation_equal;
+        } else if (a->cls == float_class_zero) {
+            goto b_sign;
+        } else {
+            goto a_sign;
+        }
+    }
+
+    if (ab_mask == float_cmask_inf) {
+        if (a->sign == b->sign) {
+            return float_relation_equal;
+        }
+    } else if (b->cls == float_class_inf) {
+        goto b_sign;
+    } else {
+        g_assert(a->cls == float_class_inf);
+    }
+
+ a_sign:
+    return a->sign ? float_relation_less : float_relation_greater;
+ b_sign:
+    return b->sign ? float_relation_greater : float_relation_less;
+}
+
+/*
+ * Multiply A by 2 raised to the power N.
+ */
+static void partsN(scalbn)(FloatPartsN *a, int n, float_status *s)
+{
+    switch (a->cls) {
+    case float_class_snan:
+    case float_class_qnan:
+        parts_return_nan(a, s);
+        break;
+    case float_class_zero:
+    case float_class_inf:
+        break;
+    case float_class_normal:
+        a->exp += MIN(MAX(n, -0x10000), 0x10000);
+        break;
+    default:
+        g_assert_not_reached();
+    }
+}
+
+/*
+ * Return log2(A)
+ */
+static void partsN(log2)(FloatPartsN *a, float_status *s, const FloatFmt *fmt)
+{
+    uint64_t a0, a1, r, t, ign;
+    FloatPartsN f;
+    int i, n, a_exp, f_exp;
+
+    if (unlikely(a->cls != float_class_normal)) {
+        switch (a->cls) {
+        case float_class_snan:
+        case float_class_qnan:
+            parts_return_nan(a, s);
+            return;
+        case float_class_zero:
+            /* log2(0) = -inf */
+            a->cls = float_class_inf;
+            a->sign = 1;
+            return;
+        case float_class_inf:
+            if (unlikely(a->sign)) {
+                goto d_nan;
+            }
+            return;
+        default:
+            break;
+        }
+        g_assert_not_reached();
+    }
+    if (unlikely(a->sign)) {
+        goto d_nan;
+    }
+
+    /* TODO: This algorithm looses bits too quickly for float128. */
+    g_assert(N == 64);
+
+    a_exp = a->exp;
+    f_exp = -1;
+
+    r = 0;
+    t = DECOMPOSED_IMPLICIT_BIT;
+    a0 = a->frac_hi;
+    a1 = 0;
+
+    n = fmt->frac_size + 2;
+    if (unlikely(a_exp == -1)) {
+        /*
+         * When a_exp == -1, we're computing the log2 of a value [0.5,1.0).
+         * When the value is very close to 1.0, there are lots of 1's in
+         * the msb parts of the fraction.  At the end, when we subtract
+         * this value from -1.0, we can see a catastrophic loss of precision,
+         * as 0x800..000 - 0x7ff..ffx becomes 0x000..00y, leaving only the
+         * bits of y in the final result.  To minimize this, compute as many
+         * digits as we can.
+         * ??? This case needs another algorithm to avoid this.
+         */
+        n = fmt->frac_size * 2 + 2;
+        /* Don't compute a value overlapping the sticky bit */
+        n = MIN(n, 62);
+    }
+
+    for (i = 0; i < n; i++) {
+        if (a1) {
+            mul128To256(a0, a1, a0, a1, &a0, &a1, &ign, &ign);
+        } else if (a0 & 0xffffffffull) {
+            mul64To128(a0, a0, &a0, &a1);
+        } else if (a0 & ~DECOMPOSED_IMPLICIT_BIT) {
+            a0 >>= 32;
+            a0 *= a0;
+        } else {
+            goto exact;
+        }
+
+        if (a0 & DECOMPOSED_IMPLICIT_BIT) {
+            if (unlikely(a_exp == 0 && r == 0)) {
+                /*
+                 * When a_exp == 0, we're computing the log2 of a value
+                 * [1.0,2.0).  When the value is very close to 1.0, there
+                 * are lots of 0's in the msb parts of the fraction.
+                 * We need to compute more digits to produce a correct
+                 * result -- restart at the top of the fraction.
+                 * ??? This is likely to lose precision quickly, as for
+                 * float128; we may need another method.
+                 */
+                f_exp -= i;
+                t = r = DECOMPOSED_IMPLICIT_BIT;
+                i = 0;
+            } else {
+                r |= t;
+            }
+        } else {
+            add128(a0, a1, a0, a1, &a0, &a1);
+        }
+        t >>= 1;
+    }
+
+    /* Set sticky for inexact. */
+    r |= (a1 || a0 & ~DECOMPOSED_IMPLICIT_BIT);
+
+ exact:
+    parts_sint_to_float(a, a_exp, 0, s);
+    if (r == 0) {
+        return;
+    }
+
+    memset(&f, 0, sizeof(f));
+    f.cls = float_class_normal;
+    f.frac_hi = r;
+    f.exp = f_exp - frac_normalize(&f);
+
+    if (a_exp < 0) {
+        parts_sub_normal(a, &f);
+    } else if (a_exp > 0) {
+        parts_add_normal(a, &f);
+    } else {
+        *a = f;
+    }
+    return;
+
+ d_nan:
+    float_raise(float_flag_invalid, s);
+    parts_default_nan(a, s);
+}
diff --git a/fpu/softfloat-specialize.c.inc b/fpu/softfloat-specialize.c.inc
index c895733e79..12467bb9bb 100644
--- a/fpu/softfloat-specialize.c.inc
+++ b/fpu/softfloat-specialize.c.inc
@@ -257,14 +257,6 @@ const floatx80 floatx80_infinity
     = make_floatx80_init(floatx80_infinity_high, floatx80_infinity_low);
 
 /*----------------------------------------------------------------------------
-| Internal canonical NaN format.
-*----------------------------------------------------------------------------*/
-typedef struct {
-    bool sign;
-    uint64_t high, low;
-} commonNaNT;
-
-/*----------------------------------------------------------------------------
 | Returns 1 if the half-precision floating-point value `a' is a quiet
 | NaN; otherwise returns 0.
 *----------------------------------------------------------------------------*/
@@ -380,46 +372,6 @@ bool float32_is_signaling_nan(float32 a_, float_status *status)
 }
 
 /*----------------------------------------------------------------------------
-| Returns the result of converting the single-precision floating-point NaN
-| `a' to the canonical NaN format.  If `a' is a signaling NaN, the invalid
-| exception is raised.
-*----------------------------------------------------------------------------*/
-
-static commonNaNT float32ToCommonNaN(float32 a, float_status *status)
-{
-    commonNaNT z;
-
-    if (float32_is_signaling_nan(a, status)) {
-        float_raise(float_flag_invalid, status);
-    }
-    z.sign = float32_val(a) >> 31;
-    z.low = 0;
-    z.high = ((uint64_t)float32_val(a)) << 41;
-    return z;
-}
-
-/*----------------------------------------------------------------------------
-| Returns the result of converting the canonical NaN `a' to the single-
-| precision floating-point format.
-*----------------------------------------------------------------------------*/
-
-static float32 commonNaNToFloat32(commonNaNT a, float_status *status)
-{
-    uint32_t mantissa = a.high >> 41;
-
-    if (status->default_nan_mode) {
-        return float32_default_nan(status);
-    }
-
-    if (mantissa) {
-        return make_float32(
-            (((uint32_t)a.sign) << 31) | 0x7F800000 | (a.high >> 41));
-    } else {
-        return float32_default_nan(status);
-    }
-}
-
-/*----------------------------------------------------------------------------
 | Select which NaN to propagate for a two-input operation.
 | IEEE754 doesn't specify all the details of this, so the
 | algorithm is target-specific.
@@ -690,62 +642,6 @@ static int pickNaNMulAdd(FloatClass a_cls, FloatClass b_cls, FloatClass c_cls,
 }
 
 /*----------------------------------------------------------------------------
-| 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.
 *----------------------------------------------------------------------------*/
@@ -786,104 +682,6 @@ bool float64_is_signaling_nan(float64 a_, float_status *status)
 }
 
 /*----------------------------------------------------------------------------
-| Returns the result of converting the double-precision floating-point NaN
-| `a' to the canonical NaN format.  If `a' is a signaling NaN, the invalid
-| exception is raised.
-*----------------------------------------------------------------------------*/
-
-static commonNaNT float64ToCommonNaN(float64 a, float_status *status)
-{
-    commonNaNT z;
-
-    if (float64_is_signaling_nan(a, status)) {
-        float_raise(float_flag_invalid, status);
-    }
-    z.sign = float64_val(a) >> 63;
-    z.low = 0;
-    z.high = float64_val(a) << 12;
-    return z;
-}
-
-/*----------------------------------------------------------------------------
-| Returns the result of converting the canonical NaN `a' to the double-
-| precision floating-point format.
-*----------------------------------------------------------------------------*/
-
-static float64 commonNaNToFloat64(commonNaNT a, float_status *status)
-{
-    uint64_t mantissa = a.high >> 12;
-
-    if (status->default_nan_mode) {
-        return float64_default_nan(status);
-    }
-
-    if (mantissa) {
-        return make_float64(
-              (((uint64_t) a.sign) << 63)
-            | UINT64_C(0x7FF0000000000000)
-            | (a.high >> 12));
-    } else {
-        return float64_default_nan(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
 | function for other types as floatx80 has an explicit bit.
@@ -947,55 +745,6 @@ floatx80 floatx80_silence_nan(floatx80 a, float_status *status)
 }
 
 /*----------------------------------------------------------------------------
-| Returns the result of converting the extended double-precision floating-
-| point NaN `a' to the canonical NaN format.  If `a' is a signaling NaN, the
-| invalid exception is raised.
-*----------------------------------------------------------------------------*/
-
-static commonNaNT floatx80ToCommonNaN(floatx80 a, float_status *status)
-{
-    floatx80 dflt;
-    commonNaNT z;
-
-    if (floatx80_is_signaling_nan(a, status)) {
-        float_raise(float_flag_invalid, status);
-    }
-    if (a.low >> 63) {
-        z.sign = a.high >> 15;
-        z.low = 0;
-        z.high = a.low << 1;
-    } else {
-        dflt = floatx80_default_nan(status);
-        z.sign = dflt.high >> 15;
-        z.low = 0;
-        z.high = dflt.low << 1;
-    }
-    return z;
-}
-
-/*----------------------------------------------------------------------------
-| Returns the result of converting the canonical NaN `a' to the extended
-| double-precision floating-point format.
-*----------------------------------------------------------------------------*/
-
-static floatx80 commonNaNToFloatx80(commonNaNT a, float_status *status)
-{
-    floatx80 z;
-
-    if (status->default_nan_mode) {
-        return floatx80_default_nan(status);
-    }
-
-    if (a.high >> 1) {
-        z.low = UINT64_C(0x8000000000000000) | a.high >> 1;
-        z.high = (((uint16_t)a.sign) << 15) | 0x7FFF;
-    } else {
-        z = floatx80_default_nan(status);
-    }
-    return z;
-}
-
-/*----------------------------------------------------------------------------
 | Takes two extended 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.
@@ -1086,92 +835,3 @@ bool float128_is_signaling_nan(float128 a, float_status *status)
         }
     }
 }
-
-/*----------------------------------------------------------------------------
-| Returns the result of converting the quadruple-precision floating-point NaN
-| `a' to the canonical NaN format.  If `a' is a signaling NaN, the invalid
-| exception is raised.
-*----------------------------------------------------------------------------*/
-
-static commonNaNT float128ToCommonNaN(float128 a, float_status *status)
-{
-    commonNaNT z;
-
-    if (float128_is_signaling_nan(a, status)) {
-        float_raise(float_flag_invalid, status);
-    }
-    z.sign = a.high >> 63;
-    shortShift128Left(a.high, a.low, 16, &z.high, &z.low);
-    return z;
-}
-
-/*----------------------------------------------------------------------------
-| Returns the result of converting the canonical NaN `a' to the quadruple-
-| precision floating-point format.
-*----------------------------------------------------------------------------*/
-
-static float128 commonNaNToFloat128(commonNaNT a, float_status *status)
-{
-    float128 z;
-
-    if (status->default_nan_mode) {
-        return float128_default_nan(status);
-    }
-
-    shift128Right(a.high, a.low, 16, &z.high, &z.low);
-    z.high |= (((uint64_t)a.sign) << 63) | UINT64_C(0x7FFF000000000000);
-    return z;
-}
-
-/*----------------------------------------------------------------------------
-| 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;
-    }
-}
diff --git a/fpu/softfloat.c b/fpu/softfloat.c
index 0dc2203477..1cb162882b 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.
@@ -482,6 +428,15 @@ enum {
     float_cmask_anynan  = float_cmask_qnan | float_cmask_snan,
 };
 
+/* Flags for parts_minmax. */
+enum {
+    /* Set for minimum; clear for maximum. */
+    minmax_ismin = 1,
+    /* Set for the IEEE 754-2008 minNum() and maxNum() operations. */
+    minmax_isnum = 2,
+    /* Set for the IEEE 754-2008 minNumMag() and minNumMag() operations. */
+    minmax_ismag = 4,
+};
 
 /* Simple helpers for checking if, or what kind of, NaN we have */
 static inline __attribute__((unused)) bool is_nan(FloatClass c)
@@ -554,9 +509,7 @@ typedef struct {
  *   frac_size: the size of the fraction field
  *   frac_shift: shift to normalise the fraction with DECOMPOSED_BINARY_POINT
  * The following are computed based the size of fraction
- *   frac_lsb: least significant bit of fraction
- *   frac_lsbm1: the bit below the least significant bit (for rounding)
- *   round_mask/roundeven_mask: masks used for rounding
+ *   round_mask: bits below lsb which must be rounded
  * The following optional modifiers are available:
  *   arm_althp: handle ARM Alternative Half Precision
  */
@@ -566,24 +519,21 @@ typedef struct {
     int exp_max;
     int frac_size;
     int frac_shift;
-    uint64_t frac_lsb;
-    uint64_t frac_lsbm1;
-    uint64_t round_mask;
-    uint64_t roundeven_mask;
     bool arm_althp;
+    uint64_t round_mask;
 } FloatFmt;
 
 /* Expand fields based on the size of exponent and fraction */
-#define FLOAT_PARAMS(E, F)                                           \
-    .exp_size       = E,                                             \
-    .exp_bias       = ((1 << E) - 1) >> 1,                           \
-    .exp_max        = (1 << E) - 1,                                  \
-    .frac_size      = F,                                             \
-    .frac_shift     = (-F - 1) & 63,                                 \
-    .frac_lsb       = 1ull << ((-F - 1) & 63),                       \
-    .frac_lsbm1     = 1ull << ((-F - 2) & 63),                       \
-    .round_mask     = (1ull << ((-F - 1) & 63)) - 1,                 \
-    .roundeven_mask = (2ull << ((-F - 1) & 63)) - 1
+#define FLOAT_PARAMS_(E)                                \
+    .exp_size       = E,                                \
+    .exp_bias       = ((1 << E) - 1) >> 1,              \
+    .exp_max        = (1 << E) - 1
+
+#define FLOAT_PARAMS(E, F)                              \
+    FLOAT_PARAMS_(E),                                   \
+    .frac_size      = F,                                \
+    .frac_shift     = (-F - 1) & 63,                    \
+    .round_mask     = (1ull << ((-F - 1) & 63)) - 1
 
 static const FloatFmt float16_params = {
     FLOAT_PARAMS(5, 10)
@@ -610,6 +560,18 @@ static const FloatFmt float128_params = {
     FLOAT_PARAMS(15, 112)
 };
 
+#define FLOATX80_PARAMS(R)              \
+    FLOAT_PARAMS_(15),                  \
+    .frac_size = R == 64 ? 63 : R,      \
+    .frac_shift = 0,                    \
+    .round_mask = R == 64 ? -1 : (1ull << ((-R - 1) & 63)) - 1
+
+static const FloatFmt floatx80_params[3] = {
+    [floatx80_precision_s] = { FLOATX80_PARAMS(23) },
+    [floatx80_precision_d] = { FLOATX80_PARAMS(52) },
+    [floatx80_precision_x] = { FLOATX80_PARAMS(64) },
+};
+
 /* Unpack a float to parts, but do not canonicalize.  */
 static void unpack_raw64(FloatParts64 *r, const FloatFmt *fmt, uint64_t raw)
 {
@@ -644,6 +606,16 @@ static inline void float64_unpack_raw(FloatParts64 *p, float64 f)
     unpack_raw64(p, &float64_params, f);
 }
 
+static void floatx80_unpack_raw(FloatParts128 *p, floatx80 f)
+{
+    *p = (FloatParts128) {
+        .cls = float_class_unclassified,
+        .sign = extract32(f.high, 15, 1),
+        .exp = extract32(f.high, 0, 15),
+        .frac_hi = f.low
+    };
+}
+
 static void float128_unpack_raw(FloatParts128 *p, float128 f)
 {
     const int f_size = float128_params.frac_size - 64;
@@ -755,6 +727,14 @@ static void parts128_canonicalize(FloatParts128 *p, float_status *status,
 #define parts_canonicalize(A, S, F) \
     PARTS_GENERIC_64_128(canonicalize, A)(A, S, F)
 
+static void parts64_uncanon_normal(FloatParts64 *p, float_status *status,
+                                   const FloatFmt *fmt);
+static void parts128_uncanon_normal(FloatParts128 *p, float_status *status,
+                                    const FloatFmt *fmt);
+
+#define parts_uncanon_normal(A, S, F) \
+    PARTS_GENERIC_64_128(uncanon_normal, A)(A, S, F)
+
 static void parts64_uncanon(FloatParts64 *p, float_status *status,
                             const FloatFmt *fmt);
 static void parts128_uncanon(FloatParts128 *p, float_status *status,
@@ -811,6 +791,20 @@ 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);
+
+#define parts_sqrt(A, S, F) \
+    PARTS_GENERIC_64_128(sqrt, A)(A, S, F)
+
 static bool parts64_round_to_int_normal(FloatParts64 *a, FloatRoundMode rm,
                                         int scale, int frac_size);
 static bool parts128_round_to_int_normal(FloatParts128 *a, FloatRoundMode r,
@@ -839,6 +833,60 @@ static int64_t parts128_float_to_sint(FloatParts128 *p, FloatRoundMode rmode,
 #define parts_float_to_sint(P, R, Z, MN, MX, S) \
     PARTS_GENERIC_64_128(float_to_sint, P)(P, R, Z, MN, MX, S)
 
+static uint64_t parts64_float_to_uint(FloatParts64 *p, FloatRoundMode rmode,
+                                      int scale, uint64_t max,
+                                      float_status *s);
+static uint64_t parts128_float_to_uint(FloatParts128 *p, FloatRoundMode rmode,
+                                       int scale, uint64_t max,
+                                       float_status *s);
+
+#define parts_float_to_uint(P, R, Z, M, S) \
+    PARTS_GENERIC_64_128(float_to_uint, P)(P, R, Z, M, S)
+
+static void parts64_sint_to_float(FloatParts64 *p, int64_t a,
+                                  int scale, float_status *s);
+static void parts128_sint_to_float(FloatParts128 *p, int64_t a,
+                                   int scale, float_status *s);
+
+#define parts_sint_to_float(P, I, Z, S) \
+    PARTS_GENERIC_64_128(sint_to_float, P)(P, I, Z, S)
+
+static void parts64_uint_to_float(FloatParts64 *p, uint64_t a,
+                                  int scale, float_status *s);
+static void parts128_uint_to_float(FloatParts128 *p, uint64_t a,
+                                   int scale, float_status *s);
+
+#define parts_uint_to_float(P, I, Z, S) \
+    PARTS_GENERIC_64_128(uint_to_float, P)(P, I, Z, S)
+
+static FloatParts64 *parts64_minmax(FloatParts64 *a, FloatParts64 *b,
+                                    float_status *s, int flags);
+static FloatParts128 *parts128_minmax(FloatParts128 *a, FloatParts128 *b,
+                                      float_status *s, int flags);
+
+#define parts_minmax(A, B, S, F) \
+    PARTS_GENERIC_64_128(minmax, A)(A, B, S, F)
+
+static int parts64_compare(FloatParts64 *a, FloatParts64 *b,
+                           float_status *s, bool q);
+static int parts128_compare(FloatParts128 *a, FloatParts128 *b,
+                            float_status *s, bool q);
+
+#define parts_compare(A, B, S, Q) \
+    PARTS_GENERIC_64_128(compare, A)(A, B, S, Q)
+
+static void parts64_scalbn(FloatParts64 *a, int n, float_status *s);
+static void parts128_scalbn(FloatParts128 *a, int n, float_status *s);
+
+#define parts_scalbn(A, N, S) \
+    PARTS_GENERIC_64_128(scalbn, A)(A, N, S)
+
+static void parts64_log2(FloatParts64 *a, float_status *s, const FloatFmt *f);
+static void parts128_log2(FloatParts128 *a, float_status *s, const FloatFmt *f);
+
+#define parts_log2(A, S, F) \
+    PARTS_GENERIC_64_128(log2, A)(A, S, F)
+
 /*
  * Helper functions for softfloat-parts.c.inc, per-size operations.
  */
@@ -1135,6 +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;
@@ -1329,6 +1557,30 @@ static void frac128_widen(FloatParts256 *r, FloatParts128 *a)
 
 #define frac_widen(A, B)  FRAC_GENERIC_64_128(widen, B)(A, B)
 
+/*
+ * Reciprocal sqrt table.  1 bit of exponent, 6-bits of mantessa.
+ * From https://git.musl-libc.org/cgit/musl/tree/src/math/sqrt_data.c
+ * and thus MIT licenced.
+ */
+static const uint16_t rsqrt_tab[128] = {
+    0xb451, 0xb2f0, 0xb196, 0xb044, 0xaef9, 0xadb6, 0xac79, 0xab43,
+    0xaa14, 0xa8eb, 0xa7c8, 0xa6aa, 0xa592, 0xa480, 0xa373, 0xa26b,
+    0xa168, 0xa06a, 0x9f70, 0x9e7b, 0x9d8a, 0x9c9d, 0x9bb5, 0x9ad1,
+    0x99f0, 0x9913, 0x983a, 0x9765, 0x9693, 0x95c4, 0x94f8, 0x9430,
+    0x936b, 0x92a9, 0x91ea, 0x912e, 0x9075, 0x8fbe, 0x8f0a, 0x8e59,
+    0x8daa, 0x8cfe, 0x8c54, 0x8bac, 0x8b07, 0x8a64, 0x89c4, 0x8925,
+    0x8889, 0x87ee, 0x8756, 0x86c0, 0x862b, 0x8599, 0x8508, 0x8479,
+    0x83ec, 0x8361, 0x82d8, 0x8250, 0x81c9, 0x8145, 0x80c2, 0x8040,
+    0xff02, 0xfd0e, 0xfb25, 0xf947, 0xf773, 0xf5aa, 0xf3ea, 0xf234,
+    0xf087, 0xeee3, 0xed47, 0xebb3, 0xea27, 0xe8a3, 0xe727, 0xe5b2,
+    0xe443, 0xe2dc, 0xe17a, 0xe020, 0xdecb, 0xdd7d, 0xdc34, 0xdaf1,
+    0xd9b3, 0xd87b, 0xd748, 0xd61a, 0xd4f1, 0xd3cd, 0xd2ad, 0xd192,
+    0xd07b, 0xcf69, 0xce5b, 0xcd51, 0xcc4a, 0xcb48, 0xca4a, 0xc94f,
+    0xc858, 0xc764, 0xc674, 0xc587, 0xc49d, 0xc3b7, 0xc2d4, 0xc1f4,
+    0xc116, 0xc03c, 0xbf65, 0xbe90, 0xbdbe, 0xbcef, 0xbc23, 0xbb59,
+    0xba91, 0xb9cc, 0xb90a, 0xb84a, 0xb78c, 0xb6d0, 0xb617, 0xb560,
+};
+
 #define partsN(NAME)   glue(glue(glue(parts,N),_),NAME)
 #define FloatPartsN    glue(FloatParts,N)
 #define FloatPartsW    glue(FloatParts,W)
@@ -1446,6 +1698,92 @@ static float128 float128_round_pack_canonical(FloatParts128 *p,
     return float128_pack_raw(p);
 }
 
+/* Returns false if the encoding is invalid. */
+static bool floatx80_unpack_canonical(FloatParts128 *p, floatx80 f,
+                                      float_status *s)
+{
+    /* Ensure rounding precision is set before beginning. */
+    switch (s->floatx80_rounding_precision) {
+    case floatx80_precision_x:
+    case floatx80_precision_d:
+    case floatx80_precision_s:
+        break;
+    default:
+        g_assert_not_reached();
+    }
+
+    if (unlikely(floatx80_invalid_encoding(f))) {
+        float_raise(float_flag_invalid, s);
+        return false;
+    }
+
+    floatx80_unpack_raw(p, f);
+
+    if (likely(p->exp != floatx80_params[floatx80_precision_x].exp_max)) {
+        parts_canonicalize(p, s, &floatx80_params[floatx80_precision_x]);
+    } else {
+        /* The explicit integer bit is ignored, after invalid checks. */
+        p->frac_hi &= MAKE_64BIT_MASK(0, 63);
+        p->cls = (p->frac_hi == 0 ? float_class_inf
+                  : parts_is_snan_frac(p->frac_hi, s)
+                  ? float_class_snan : float_class_qnan);
+    }
+    return true;
+}
+
+static floatx80 floatx80_round_pack_canonical(FloatParts128 *p,
+                                              float_status *s)
+{
+    const FloatFmt *fmt = &floatx80_params[s->floatx80_rounding_precision];
+    uint64_t frac;
+    int exp;
+
+    switch (p->cls) {
+    case float_class_normal:
+        if (s->floatx80_rounding_precision == floatx80_precision_x) {
+            parts_uncanon_normal(p, s, fmt);
+            frac = p->frac_hi;
+            exp = p->exp;
+        } else {
+            FloatParts64 p64;
+
+            p64.sign = p->sign;
+            p64.exp = p->exp;
+            frac_truncjam(&p64, p);
+            parts_uncanon_normal(&p64, s, fmt);
+            frac = p64.frac;
+            exp = p64.exp;
+        }
+        if (exp != fmt->exp_max) {
+            break;
+        }
+        /* rounded to inf -- fall through to set frac correctly */
+
+    case float_class_inf:
+        /* x86 and m68k differ in the setting of the integer bit. */
+        frac = floatx80_infinity_low;
+        exp = fmt->exp_max;
+        break;
+
+    case float_class_zero:
+        frac = 0;
+        exp = 0;
+        break;
+
+    case float_class_snan:
+    case float_class_qnan:
+        /* NaNs have the integer bit set. */
+        frac = p->frac_hi | (1ull << 63);
+        exp = fmt->exp_max;
+        break;
+
+    default:
+        g_assert_not_reached();
+    }
+
+    return packFloatx80(p->sign, exp, frac);
+}
+
 /*
  * Addition and subtraction
  */
@@ -1635,6 +1973,30 @@ float128 float128_sub(float128 a, float128 b, float_status *status)
     return float128_addsub(a, b, status, true);
 }
 
+static floatx80 QEMU_FLATTEN
+floatx80_addsub(floatx80 a, floatx80 b, float_status *status, bool subtract)
+{
+    FloatParts128 pa, pb, *pr;
+
+    if (!floatx80_unpack_canonical(&pa, a, status) ||
+        !floatx80_unpack_canonical(&pb, b, status)) {
+        return floatx80_default_nan(status);
+    }
+
+    pr = parts_addsub(&pa, &pb, status, subtract);
+    return floatx80_round_pack_canonical(pr, status);
+}
+
+floatx80 floatx80_add(floatx80 a, floatx80 b, float_status *status)
+{
+    return floatx80_addsub(a, b, status, false);
+}
+
+floatx80 floatx80_sub(floatx80 a, floatx80 b, float_status *status)
+{
+    return floatx80_addsub(a, b, status, true);
+}
+
 /*
  * Multiplication
  */
@@ -1722,6 +2084,20 @@ float128_mul(float128 a, float128 b, float_status *status)
     return float128_round_pack_canonical(pr, status);
 }
 
+floatx80 QEMU_FLATTEN
+floatx80_mul(floatx80 a, floatx80 b, float_status *status)
+{
+    FloatParts128 pa, pb, *pr;
+
+    if (!floatx80_unpack_canonical(&pa, a, status) ||
+        !floatx80_unpack_canonical(&pb, b, status)) {
+        return floatx80_default_nan(status);
+    }
+
+    pr = parts_mul(&pa, &pb, status);
+    return floatx80_round_pack_canonical(pr, status);
+}
+
 /*
  * Fused multiply-add
  */
@@ -2058,6 +2434,92 @@ float128_div(float128 a, float128 b, float_status *status)
     return float128_round_pack_canonical(pr, status);
 }
 
+floatx80 floatx80_div(floatx80 a, floatx80 b, float_status *status)
+{
+    FloatParts128 pa, pb, *pr;
+
+    if (!floatx80_unpack_canonical(&pa, a, status) ||
+        !floatx80_unpack_canonical(&pb, b, status)) {
+        return floatx80_default_nan(status);
+    }
+
+    pr = parts_div(&pa, &pb, 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, &quotient, status);
+}
+
+floatx80 floatx80_mod(floatx80 a, floatx80 b, float_status *status)
+{
+    uint64_t quotient;
+    return floatx80_modrem(a, b, true, &quotient, status);
+}
+
 /*
  * Float to Float conversions
  *
@@ -2312,6 +2774,73 @@ float128 float64_to_float128(float64 a, float_status *s)
     return float128_round_pack_canonical(&p128, s);
 }
 
+float32 floatx80_to_float32(floatx80 a, float_status *s)
+{
+    FloatParts64 p64;
+    FloatParts128 p128;
+
+    if (floatx80_unpack_canonical(&p128, a, s)) {
+        parts_float_to_float_narrow(&p64, &p128, s);
+    } else {
+        parts_default_nan(&p64, s);
+    }
+    return float32_round_pack_canonical(&p64, s);
+}
+
+float64 floatx80_to_float64(floatx80 a, float_status *s)
+{
+    FloatParts64 p64;
+    FloatParts128 p128;
+
+    if (floatx80_unpack_canonical(&p128, a, s)) {
+        parts_float_to_float_narrow(&p64, &p128, s);
+    } else {
+        parts_default_nan(&p64, s);
+    }
+    return float64_round_pack_canonical(&p64, s);
+}
+
+float128 floatx80_to_float128(floatx80 a, float_status *s)
+{
+    FloatParts128 p;
+
+    if (floatx80_unpack_canonical(&p, a, s)) {
+        parts_float_to_float(&p, s);
+    } else {
+        parts_default_nan(&p, s);
+    }
+    return float128_round_pack_canonical(&p, s);
+}
+
+floatx80 float32_to_floatx80(float32 a, float_status *s)
+{
+    FloatParts64 p64;
+    FloatParts128 p128;
+
+    float32_unpack_canonical(&p64, a, s);
+    parts_float_to_float_widen(&p128, &p64, s);
+    return floatx80_round_pack_canonical(&p128, s);
+}
+
+floatx80 float64_to_floatx80(float64 a, float_status *s)
+{
+    FloatParts64 p64;
+    FloatParts128 p128;
+
+    float64_unpack_canonical(&p64, a, s);
+    parts_float_to_float_widen(&p128, &p64, s);
+    return floatx80_round_pack_canonical(&p128, s);
+}
+
+floatx80 float128_to_floatx80(float128 a, float_status *s)
+{
+    FloatParts128 p;
+
+    float128_unpack_canonical(&p, a, s);
+    parts_float_to_float(&p, s);
+    return floatx80_round_pack_canonical(&p, s);
+}
+
 /*
  * Round to integral value
  */
@@ -2361,6 +2890,19 @@ float128 float128_round_to_int(float128 a, float_status *s)
     return float128_round_pack_canonical(&p, s);
 }
 
+floatx80 floatx80_round_to_int(floatx80 a, float_status *status)
+{
+    FloatParts128 p;
+
+    if (!floatx80_unpack_canonical(&p, a, status)) {
+        return floatx80_default_nan(status);
+    }
+
+    parts_round_to_int(&p, status->float_rounding_mode, 0, status,
+                       &floatx80_params[status->floatx80_rounding_precision]);
+    return floatx80_round_pack_canonical(&p, status);
+}
+
 /*
  * Floating-point to signed integer conversions
  */
@@ -2500,6 +3042,28 @@ static int64_t float128_to_int64_scalbn(float128 a, FloatRoundMode rmode,
     return parts_float_to_sint(&p, rmode, scale, INT64_MIN, INT64_MAX, s);
 }
 
+static int32_t floatx80_to_int32_scalbn(floatx80 a, FloatRoundMode rmode,
+                                        int scale, float_status *s)
+{
+    FloatParts128 p;
+
+    if (!floatx80_unpack_canonical(&p, a, s)) {
+        parts_default_nan(&p, s);
+    }
+    return parts_float_to_sint(&p, rmode, scale, INT32_MIN, INT32_MAX, s);
+}
+
+static int64_t floatx80_to_int64_scalbn(floatx80 a, FloatRoundMode rmode,
+                                        int scale, float_status *s)
+{
+    FloatParts128 p;
+
+    if (!floatx80_unpack_canonical(&p, a, s)) {
+        parts_default_nan(&p, s);
+    }
+    return parts_float_to_sint(&p, rmode, scale, INT64_MIN, INT64_MAX, s);
+}
+
 int8_t float16_to_int8(float16 a, float_status *s)
 {
     return float16_to_int8_scalbn(a, s->float_rounding_mode, 0, s);
@@ -2560,6 +3124,16 @@ int64_t float128_to_int64(float128 a, float_status *s)
     return float128_to_int64_scalbn(a, s->float_rounding_mode, 0, s);
 }
 
+int32_t floatx80_to_int32(floatx80 a, float_status *s)
+{
+    return floatx80_to_int32_scalbn(a, s->float_rounding_mode, 0, s);
+}
+
+int64_t floatx80_to_int64(floatx80 a, float_status *s)
+{
+    return floatx80_to_int64_scalbn(a, s->float_rounding_mode, 0, s);
+}
+
 int16_t float16_to_int16_round_to_zero(float16 a, float_status *s)
 {
     return float16_to_int16_scalbn(a, float_round_to_zero, 0, s);
@@ -2615,6 +3189,16 @@ int64_t float128_to_int64_round_to_zero(float128 a, float_status *s)
     return float128_to_int64_scalbn(a, float_round_to_zero, 0, s);
 }
 
+int32_t floatx80_to_int32_round_to_zero(floatx80 a, float_status *s)
+{
+    return floatx80_to_int32_scalbn(a, float_round_to_zero, 0, s);
+}
+
+int64_t floatx80_to_int64_round_to_zero(floatx80 a, float_status *s)
+{
+    return floatx80_to_int64_scalbn(a, float_round_to_zero, 0, s);
+}
+
 int16_t bfloat16_to_int16(bfloat16 a, float_status *s)
 {
     return bfloat16_to_int16_scalbn(a, s->float_rounding_mode, 0, s);
@@ -2646,80 +3230,16 @@ int64_t bfloat16_to_int64_round_to_zero(bfloat16 a, float_status *s)
 }
 
 /*
- *  Returns the result of converting the floating-point value `a' to
- *  the unsigned integer format. The conversion is performed according
- *  to the IEC/IEEE Standard for Binary Floating-Point
- *  Arithmetic---which means in particular that the conversion is
- *  rounded according to the current rounding mode. If `a' is a NaN,
- *  the largest unsigned integer is returned. Otherwise, if the
- *  conversion overflows, the largest unsigned integer is returned. If
- *  the 'a' is negative, the result is rounded and zero is returned;
- *  values that do not round to zero will raise the inexact exception
- *  flag.
+ * Floating-point to unsigned integer conversions
  */
 
-static uint64_t round_to_uint_and_pack(FloatParts64 p, FloatRoundMode rmode,
-                                       int scale, uint64_t max,
-                                       float_status *s)
-{
-    int flags = 0;
-    uint64_t r;
-
-    switch (p.cls) {
-    case float_class_snan:
-    case float_class_qnan:
-        flags = float_flag_invalid;
-        r = max;
-        break;
-
-    case float_class_inf:
-        flags = float_flag_invalid;
-        r = p.sign ? 0 : max;
-        break;
-
-    case float_class_zero:
-        return 0;
-
-    case float_class_normal:
-        /* TODO: 62 = N - 2, frac_size for rounding */
-        if (parts_round_to_int_normal(&p, rmode, scale, 62)) {
-            flags = float_flag_inexact;
-            if (p.cls == float_class_zero) {
-                r = 0;
-                break;
-            }
-        }
-
-        if (p.sign) {
-            flags = float_flag_invalid;
-            r = 0;
-        } else if (p.exp > DECOMPOSED_BINARY_POINT) {
-            flags = float_flag_invalid;
-            r = max;
-        } else {
-            r = p.frac >> (DECOMPOSED_BINARY_POINT - p.exp);
-            if (r > max) {
-                flags = float_flag_invalid;
-                r = max;
-            }
-        }
-        break;
-
-    default:
-        g_assert_not_reached();
-    }
-
-    float_raise(flags, s);
-    return r;
-}
-
 uint8_t float16_to_uint8_scalbn(float16 a, FloatRoundMode rmode, int scale,
                                 float_status *s)
 {
     FloatParts64 p;
 
     float16_unpack_canonical(&p, a, s);
-    return round_to_uint_and_pack(p, rmode, scale, UINT8_MAX, s);
+    return parts_float_to_uint(&p, rmode, scale, UINT8_MAX, s);
 }
 
 uint16_t float16_to_uint16_scalbn(float16 a, FloatRoundMode rmode, int scale,
@@ -2728,7 +3248,7 @@ uint16_t float16_to_uint16_scalbn(float16 a, FloatRoundMode rmode, int scale,
     FloatParts64 p;
 
     float16_unpack_canonical(&p, a, s);
-    return round_to_uint_and_pack(p, rmode, scale, UINT16_MAX, s);
+    return parts_float_to_uint(&p, rmode, scale, UINT16_MAX, s);
 }
 
 uint32_t float16_to_uint32_scalbn(float16 a, FloatRoundMode rmode, int scale,
@@ -2737,7 +3257,7 @@ uint32_t float16_to_uint32_scalbn(float16 a, FloatRoundMode rmode, int scale,
     FloatParts64 p;
 
     float16_unpack_canonical(&p, a, s);
-    return round_to_uint_and_pack(p, rmode, scale, UINT32_MAX, s);
+    return parts_float_to_uint(&p, rmode, scale, UINT32_MAX, s);
 }
 
 uint64_t float16_to_uint64_scalbn(float16 a, FloatRoundMode rmode, int scale,
@@ -2746,7 +3266,7 @@ uint64_t float16_to_uint64_scalbn(float16 a, FloatRoundMode rmode, int scale,
     FloatParts64 p;
 
     float16_unpack_canonical(&p, a, s);
-    return round_to_uint_and_pack(p, rmode, scale, UINT64_MAX, s);
+    return parts_float_to_uint(&p, rmode, scale, UINT64_MAX, s);
 }
 
 uint16_t float32_to_uint16_scalbn(float32 a, FloatRoundMode rmode, int scale,
@@ -2755,7 +3275,7 @@ uint16_t float32_to_uint16_scalbn(float32 a, FloatRoundMode rmode, int scale,
     FloatParts64 p;
 
     float32_unpack_canonical(&p, a, s);
-    return round_to_uint_and_pack(p, rmode, scale, UINT16_MAX, s);
+    return parts_float_to_uint(&p, rmode, scale, UINT16_MAX, s);
 }
 
 uint32_t float32_to_uint32_scalbn(float32 a, FloatRoundMode rmode, int scale,
@@ -2764,7 +3284,7 @@ uint32_t float32_to_uint32_scalbn(float32 a, FloatRoundMode rmode, int scale,
     FloatParts64 p;
 
     float32_unpack_canonical(&p, a, s);
-    return round_to_uint_and_pack(p, rmode, scale, UINT32_MAX, s);
+    return parts_float_to_uint(&p, rmode, scale, UINT32_MAX, s);
 }
 
 uint64_t float32_to_uint64_scalbn(float32 a, FloatRoundMode rmode, int scale,
@@ -2773,7 +3293,7 @@ uint64_t float32_to_uint64_scalbn(float32 a, FloatRoundMode rmode, int scale,
     FloatParts64 p;
 
     float32_unpack_canonical(&p, a, s);
-    return round_to_uint_and_pack(p, rmode, scale, UINT64_MAX, s);
+    return parts_float_to_uint(&p, rmode, scale, UINT64_MAX, s);
 }
 
 uint16_t float64_to_uint16_scalbn(float64 a, FloatRoundMode rmode, int scale,
@@ -2782,7 +3302,7 @@ uint16_t float64_to_uint16_scalbn(float64 a, FloatRoundMode rmode, int scale,
     FloatParts64 p;
 
     float64_unpack_canonical(&p, a, s);
-    return round_to_uint_and_pack(p, rmode, scale, UINT16_MAX, s);
+    return parts_float_to_uint(&p, rmode, scale, UINT16_MAX, s);
 }
 
 uint32_t float64_to_uint32_scalbn(float64 a, FloatRoundMode rmode, int scale,
@@ -2791,7 +3311,7 @@ uint32_t float64_to_uint32_scalbn(float64 a, FloatRoundMode rmode, int scale,
     FloatParts64 p;
 
     float64_unpack_canonical(&p, a, s);
-    return round_to_uint_and_pack(p, rmode, scale, UINT32_MAX, s);
+    return parts_float_to_uint(&p, rmode, scale, UINT32_MAX, s);
 }
 
 uint64_t float64_to_uint64_scalbn(float64 a, FloatRoundMode rmode, int scale,
@@ -2800,7 +3320,52 @@ uint64_t float64_to_uint64_scalbn(float64 a, FloatRoundMode rmode, int scale,
     FloatParts64 p;
 
     float64_unpack_canonical(&p, a, s);
-    return round_to_uint_and_pack(p, rmode, scale, UINT64_MAX, s);
+    return parts_float_to_uint(&p, rmode, scale, UINT64_MAX, s);
+}
+
+uint16_t bfloat16_to_uint16_scalbn(bfloat16 a, FloatRoundMode rmode,
+                                   int scale, float_status *s)
+{
+    FloatParts64 p;
+
+    bfloat16_unpack_canonical(&p, a, s);
+    return parts_float_to_uint(&p, rmode, scale, UINT16_MAX, s);
+}
+
+uint32_t bfloat16_to_uint32_scalbn(bfloat16 a, FloatRoundMode rmode,
+                                   int scale, float_status *s)
+{
+    FloatParts64 p;
+
+    bfloat16_unpack_canonical(&p, a, s);
+    return parts_float_to_uint(&p, rmode, scale, UINT32_MAX, s);
+}
+
+uint64_t bfloat16_to_uint64_scalbn(bfloat16 a, FloatRoundMode rmode,
+                                   int scale, float_status *s)
+{
+    FloatParts64 p;
+
+    bfloat16_unpack_canonical(&p, a, s);
+    return parts_float_to_uint(&p, rmode, scale, UINT64_MAX, s);
+}
+
+static uint32_t float128_to_uint32_scalbn(float128 a, FloatRoundMode rmode,
+                                          int scale, float_status *s)
+{
+    FloatParts128 p;
+
+    float128_unpack_canonical(&p, a, s);
+    return parts_float_to_uint(&p, rmode, scale, UINT32_MAX, s);
+}
+
+static uint64_t float128_to_uint64_scalbn(float128 a, FloatRoundMode rmode,
+                                          int scale, float_status *s)
+{
+    FloatParts128 p;
+
+    float128_unpack_canonical(&p, a, s);
+    return parts_float_to_uint(&p, rmode, scale, UINT64_MAX, s);
 }
 
 uint8_t float16_to_uint8(float16 a, float_status *s)
@@ -2853,6 +3418,16 @@ uint64_t float64_to_uint64(float64 a, float_status *s)
     return float64_to_uint64_scalbn(a, s->float_rounding_mode, 0, s);
 }
 
+uint32_t float128_to_uint32(float128 a, float_status *s)
+{
+    return float128_to_uint32_scalbn(a, s->float_rounding_mode, 0, s);
+}
+
+uint64_t float128_to_uint64(float128 a, float_status *s)
+{
+    return float128_to_uint64_scalbn(a, s->float_rounding_mode, 0, s);
+}
+
 uint16_t float16_to_uint16_round_to_zero(float16 a, float_status *s)
 {
     return float16_to_uint16_scalbn(a, float_round_to_zero, 0, s);
@@ -2898,36 +3473,14 @@ uint64_t float64_to_uint64_round_to_zero(float64 a, float_status *s)
     return float64_to_uint64_scalbn(a, float_round_to_zero, 0, s);
 }
 
-/*
- *  Returns the result of converting the bfloat16 value `a' to
- *  the unsigned integer format.
- */
-
-uint16_t bfloat16_to_uint16_scalbn(bfloat16 a, FloatRoundMode rmode,
-                                   int scale, float_status *s)
-{
-    FloatParts64 p;
-
-    bfloat16_unpack_canonical(&p, a, s);
-    return round_to_uint_and_pack(p, rmode, scale, UINT16_MAX, s);
-}
-
-uint32_t bfloat16_to_uint32_scalbn(bfloat16 a, FloatRoundMode rmode,
-                                   int scale, float_status *s)
+uint32_t float128_to_uint32_round_to_zero(float128 a, float_status *s)
 {
-    FloatParts64 p;
-
-    bfloat16_unpack_canonical(&p, a, s);
-    return round_to_uint_and_pack(p, rmode, scale, UINT32_MAX, s);
+    return float128_to_uint32_scalbn(a, float_round_to_zero, 0, s);
 }
 
-uint64_t bfloat16_to_uint64_scalbn(bfloat16 a, FloatRoundMode rmode,
-                                   int scale, float_status *s)
+uint64_t float128_to_uint64_round_to_zero(float128 a, float_status *s)
 {
-    FloatParts64 p;
-
-    bfloat16_unpack_canonical(&p, a, s);
-    return round_to_uint_and_pack(p, rmode, scale, UINT64_MAX, s);
+    return float128_to_uint64_scalbn(a, float_round_to_zero, 0, s);
 }
 
 uint16_t bfloat16_to_uint16(bfloat16 a, float_status *s)
@@ -2961,42 +3514,15 @@ uint64_t bfloat16_to_uint64_round_to_zero(bfloat16 a, float_status *s)
 }
 
 /*
- * Integer to float conversions
- *
- * Returns the result of converting the two's complement integer `a'
- * to the floating-point format. The conversion is performed according
- * to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+ * Signed integer to floating-point conversions
  */
 
-static FloatParts64 int_to_float(int64_t a, int scale, float_status *status)
-{
-    FloatParts64 r = { .sign = false };
-
-    if (a == 0) {
-        r.cls = float_class_zero;
-    } else {
-        uint64_t f = a;
-        int shift;
-
-        r.cls = float_class_normal;
-        if (a < 0) {
-            f = -f;
-            r.sign = true;
-        }
-        shift = clz64(f);
-        scale = MIN(MAX(scale, -0x10000), 0x10000);
-
-        r.exp = DECOMPOSED_BINARY_POINT - shift + scale;
-        r.frac = f << shift;
-    }
-
-    return r;
-}
-
 float16 int64_to_float16_scalbn(int64_t a, int scale, float_status *status)
 {
-    FloatParts64 pa = int_to_float(a, scale, status);
-    return float16_round_pack_canonical(&pa, status);
+    FloatParts64 p;
+
+    parts_sint_to_float(&p, a, scale, status);
+    return float16_round_pack_canonical(&p, status);
 }
 
 float16 int32_to_float16_scalbn(int32_t a, int scale, float_status *status)
@@ -3031,8 +3557,17 @@ float16 int8_to_float16(int8_t a, float_status *status)
 
 float32 int64_to_float32_scalbn(int64_t a, int scale, float_status *status)
 {
-    FloatParts64 pa = int_to_float(a, scale, status);
-    return float32_round_pack_canonical(&pa, status);
+    FloatParts64 p;
+
+    /* Without scaling, there are no overflow concerns. */
+    if (likely(scale == 0) && can_use_fpu(status)) {
+        union_float32 ur;
+        ur.h = a;
+        return ur.s;
+    }
+
+    parts64_sint_to_float(&p, a, scale, status);
+    return float32_round_pack_canonical(&p, status);
 }
 
 float32 int32_to_float32_scalbn(int32_t a, int scale, float_status *status)
@@ -3062,8 +3597,17 @@ float32 int16_to_float32(int16_t a, float_status *status)
 
 float64 int64_to_float64_scalbn(int64_t a, int scale, float_status *status)
 {
-    FloatParts64 pa = int_to_float(a, scale, status);
-    return float64_round_pack_canonical(&pa, status);
+    FloatParts64 p;
+
+    /* Without scaling, there are no overflow concerns. */
+    if (likely(scale == 0) && can_use_fpu(status)) {
+        union_float64 ur;
+        ur.h = a;
+        return ur.s;
+    }
+
+    parts_sint_to_float(&p, a, scale, status);
+    return float64_round_pack_canonical(&p, status);
 }
 
 float64 int32_to_float64_scalbn(int32_t a, int scale, float_status *status)
@@ -3091,15 +3635,12 @@ float64 int16_to_float64(int16_t a, float_status *status)
     return int64_to_float64_scalbn(a, 0, status);
 }
 
-/*
- * Returns the result of converting the two's complement integer `a'
- * to the bfloat16 format.
- */
-
 bfloat16 int64_to_bfloat16_scalbn(int64_t a, int scale, float_status *status)
 {
-    FloatParts64 pa = int_to_float(a, scale, status);
-    return bfloat16_round_pack_canonical(&pa, status);
+    FloatParts64 p;
+
+    parts_sint_to_float(&p, a, scale, status);
+    return bfloat16_round_pack_canonical(&p, status);
 }
 
 bfloat16 int32_to_bfloat16_scalbn(int32_t a, int scale, float_status *status)
@@ -3127,36 +3668,42 @@ bfloat16 int16_to_bfloat16(int16_t a, float_status *status)
     return int64_to_bfloat16_scalbn(a, 0, status);
 }
 
-/*
- * Unsigned Integer to float conversions
- *
- * Returns the result of converting the unsigned integer `a' to the
- * floating-point format. The conversion is performed according to the
- * IEC/IEEE Standard for Binary Floating-Point Arithmetic.
- */
+float128 int64_to_float128(int64_t a, float_status *status)
+{
+    FloatParts128 p;
 
-static FloatParts64 uint_to_float(uint64_t a, int scale, float_status *status)
+    parts_sint_to_float(&p, a, 0, status);
+    return float128_round_pack_canonical(&p, status);
+}
+
+float128 int32_to_float128(int32_t a, float_status *status)
 {
-    FloatParts64 r = { .sign = false };
-    int shift;
+    return int64_to_float128(a, status);
+}
 
-    if (a == 0) {
-        r.cls = float_class_zero;
-    } else {
-        scale = MIN(MAX(scale, -0x10000), 0x10000);
-        shift = clz64(a);
-        r.cls = float_class_normal;
-        r.exp = DECOMPOSED_BINARY_POINT - shift + scale;
-        r.frac = a << shift;
-    }
+floatx80 int64_to_floatx80(int64_t a, float_status *status)
+{
+    FloatParts128 p;
 
-    return r;
+    parts_sint_to_float(&p, a, 0, status);
+    return floatx80_round_pack_canonical(&p, status);
+}
+
+floatx80 int32_to_floatx80(int32_t a, float_status *status)
+{
+    return int64_to_floatx80(a, status);
 }
 
+/*
+ * Unsigned Integer to floating-point conversions
+ */
+
 float16 uint64_to_float16_scalbn(uint64_t a, int scale, float_status *status)
 {
-    FloatParts64 pa = uint_to_float(a, scale, status);
-    return float16_round_pack_canonical(&pa, status);
+    FloatParts64 p;
+
+    parts_uint_to_float(&p, a, scale, status);
+    return float16_round_pack_canonical(&p, status);
 }
 
 float16 uint32_to_float16_scalbn(uint32_t a, int scale, float_status *status)
@@ -3191,8 +3738,17 @@ float16 uint8_to_float16(uint8_t a, float_status *status)
 
 float32 uint64_to_float32_scalbn(uint64_t a, int scale, float_status *status)
 {
-    FloatParts64 pa = uint_to_float(a, scale, status);
-    return float32_round_pack_canonical(&pa, status);
+    FloatParts64 p;
+
+    /* Without scaling, there are no overflow concerns. */
+    if (likely(scale == 0) && can_use_fpu(status)) {
+        union_float32 ur;
+        ur.h = a;
+        return ur.s;
+    }
+
+    parts_uint_to_float(&p, a, scale, status);
+    return float32_round_pack_canonical(&p, status);
 }
 
 float32 uint32_to_float32_scalbn(uint32_t a, int scale, float_status *status)
@@ -3222,8 +3778,17 @@ float32 uint16_to_float32(uint16_t a, float_status *status)
 
 float64 uint64_to_float64_scalbn(uint64_t a, int scale, float_status *status)
 {
-    FloatParts64 pa = uint_to_float(a, scale, status);
-    return float64_round_pack_canonical(&pa, status);
+    FloatParts64 p;
+
+    /* Without scaling, there are no overflow concerns. */
+    if (likely(scale == 0) && can_use_fpu(status)) {
+        union_float64 ur;
+        ur.h = a;
+        return ur.s;
+    }
+
+    parts_uint_to_float(&p, a, scale, status);
+    return float64_round_pack_canonical(&p, status);
 }
 
 float64 uint32_to_float64_scalbn(uint32_t a, int scale, float_status *status)
@@ -3251,15 +3816,12 @@ float64 uint16_to_float64(uint16_t a, float_status *status)
     return uint64_to_float64_scalbn(a, 0, status);
 }
 
-/*
- * Returns the result of converting the unsigned integer `a' to the
- * bfloat16 format.
- */
-
 bfloat16 uint64_to_bfloat16_scalbn(uint64_t a, int scale, float_status *status)
 {
-    FloatParts64 pa = uint_to_float(a, scale, status);
-    return bfloat16_round_pack_canonical(&pa, status);
+    FloatParts64 p;
+
+    parts_uint_to_float(&p, a, scale, status);
+    return bfloat16_round_pack_canonical(&p, status);
 }
 
 bfloat16 uint32_to_bfloat16_scalbn(uint32_t a, int scale, float_status *status)
@@ -3287,232 +3849,132 @@ bfloat16 uint16_to_bfloat16(uint16_t a, float_status *status)
     return uint64_to_bfloat16_scalbn(a, 0, status);
 }
 
-/* Float Min/Max */
-/* min() and max() functions. These can't be implemented as
- * 'compare and pick one input' because that would mishandle
- * NaNs and +0 vs -0.
- *
- * minnum() and maxnum() functions. These are similar to the min()
- * and max() functions but if one of the arguments is a QNaN and
- * the other is numerical then the numerical argument is returned.
- * SNaNs will get quietened before being returned.
- * minnum() and maxnum correspond to the IEEE 754-2008 minNum()
- * and maxNum() operations. min() and max() are the typical min/max
- * semantics provided by many CPUs which predate that specification.
- *
- * minnummag() and maxnummag() functions correspond to minNumMag()
- * and minNumMag() from the IEEE-754 2008.
+float128 uint64_to_float128(uint64_t a, float_status *status)
+{
+    FloatParts128 p;
+
+    parts_uint_to_float(&p, a, 0, status);
+    return float128_round_pack_canonical(&p, status);
+}
+
+/*
+ * Minimum and maximum
  */
-static FloatParts64 minmax_floats(FloatParts64 a, FloatParts64 b, bool ismin,
-                                bool ieee, bool ismag, float_status *s)
-{
-    if (unlikely(is_nan(a.cls) || is_nan(b.cls))) {
-        if (ieee) {
-            /* Takes two 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.
-             */
-            if (is_snan(a.cls) || is_snan(b.cls)) {
-                return *parts_pick_nan(&a, &b, s);
-            } else if (is_nan(a.cls) && !is_nan(b.cls)) {
-                return b;
-            } else if (is_nan(b.cls) && !is_nan(a.cls)) {
-                return a;
-            }
-        }
-        return *parts_pick_nan(&a, &b, s);
-    } else {
-        int a_exp, b_exp;
 
-        switch (a.cls) {
-        case float_class_normal:
-            a_exp = a.exp;
-            break;
-        case float_class_inf:
-            a_exp = INT_MAX;
-            break;
-        case float_class_zero:
-            a_exp = INT_MIN;
-            break;
-        default:
-            g_assert_not_reached();
-            break;
-        }
-        switch (b.cls) {
-        case float_class_normal:
-            b_exp = b.exp;
-            break;
-        case float_class_inf:
-            b_exp = INT_MAX;
-            break;
-        case float_class_zero:
-            b_exp = INT_MIN;
-            break;
-        default:
-            g_assert_not_reached();
-            break;
-        }
+static float16 float16_minmax(float16 a, float16 b, float_status *s, int flags)
+{
+    FloatParts64 pa, pb, *pr;
 
-        if (ismag && (a_exp != b_exp || a.frac != b.frac)) {
-            bool a_less = a_exp < b_exp;
-            if (a_exp == b_exp) {
-                a_less = a.frac < b.frac;
-            }
-            return a_less ^ ismin ? b : a;
-        }
+    float16_unpack_canonical(&pa, a, s);
+    float16_unpack_canonical(&pb, b, s);
+    pr = parts_minmax(&pa, &pb, s, flags);
 
-        if (a.sign == b.sign) {
-            bool a_less = a_exp < b_exp;
-            if (a_exp == b_exp) {
-                a_less = a.frac < b.frac;
-            }
-            return a.sign ^ a_less ^ ismin ? b : a;
-        } else {
-            return a.sign ^ ismin ? b : a;
-        }
-    }
+    return float16_round_pack_canonical(pr, s);
 }
 
-#define MINMAX(sz, name, ismin, isiee, ismag)                           \
-float ## sz float ## sz ## _ ## name(float ## sz a, float ## sz b,      \
-                                     float_status *s)                   \
-{                                                                       \
-    FloatParts64 pa, pb, pr;                                            \
-    float ## sz ## _unpack_canonical(&pa, a, s);                        \
-    float ## sz ## _unpack_canonical(&pb, b, s);                        \
-    pr = minmax_floats(pa, pb, ismin, isiee, ismag, s);                 \
-    return float ## sz ## _round_pack_canonical(&pr, s);                \
-}
-
-MINMAX(16, min, true, false, false)
-MINMAX(16, minnum, true, true, false)
-MINMAX(16, minnummag, true, true, true)
-MINMAX(16, max, false, false, false)
-MINMAX(16, maxnum, false, true, false)
-MINMAX(16, maxnummag, false, true, true)
-
-MINMAX(32, min, true, false, false)
-MINMAX(32, minnum, true, true, false)
-MINMAX(32, minnummag, true, true, true)
-MINMAX(32, max, false, false, false)
-MINMAX(32, maxnum, false, true, false)
-MINMAX(32, maxnummag, false, true, true)
-
-MINMAX(64, min, true, false, false)
-MINMAX(64, minnum, true, true, false)
-MINMAX(64, minnummag, true, true, true)
-MINMAX(64, max, false, false, false)
-MINMAX(64, maxnum, false, true, false)
-MINMAX(64, maxnummag, false, true, true)
-
-#undef MINMAX
-
-#define BF16_MINMAX(name, ismin, isiee, ismag)                          \
-bfloat16 bfloat16_ ## name(bfloat16 a, bfloat16 b, float_status *s)     \
-{                                                                       \
-    FloatParts64 pa, pb, pr;                                            \
-    bfloat16_unpack_canonical(&pa, a, s);                               \
-    bfloat16_unpack_canonical(&pb, b, s);                               \
-    pr = minmax_floats(pa, pb, ismin, isiee, ismag, s);                 \
-    return bfloat16_round_pack_canonical(&pr, s);                       \
-}
-
-BF16_MINMAX(min, true, false, false)
-BF16_MINMAX(minnum, true, true, false)
-BF16_MINMAX(minnummag, true, true, true)
-BF16_MINMAX(max, false, false, false)
-BF16_MINMAX(maxnum, false, true, false)
-BF16_MINMAX(maxnummag, false, true, true)
-
-#undef BF16_MINMAX
-
-/* Floating point compare */
-static FloatRelation compare_floats(FloatParts64 a, FloatParts64 b, bool is_quiet,
-                                    float_status *s)
-{
-    if (is_nan(a.cls) || is_nan(b.cls)) {
-        if (!is_quiet ||
-            a.cls == float_class_snan ||
-            b.cls == float_class_snan) {
-            float_raise(float_flag_invalid, s);
-        }
-        return float_relation_unordered;
-    }
+static bfloat16 bfloat16_minmax(bfloat16 a, bfloat16 b,
+                                float_status *s, int flags)
+{
+    FloatParts64 pa, pb, *pr;
 
-    if (a.cls == float_class_zero) {
-        if (b.cls == float_class_zero) {
-            return float_relation_equal;
-        }
-        return b.sign ? float_relation_greater : float_relation_less;
-    } else if (b.cls == float_class_zero) {
-        return a.sign ? float_relation_less : float_relation_greater;
-    }
+    bfloat16_unpack_canonical(&pa, a, s);
+    bfloat16_unpack_canonical(&pb, b, s);
+    pr = parts_minmax(&pa, &pb, s, flags);
 
-    /* The only really important thing about infinity is its sign. If
-     * both are infinities the sign marks the smallest of the two.
-     */
-    if (a.cls == float_class_inf) {
-        if ((b.cls == float_class_inf) && (a.sign == b.sign)) {
-            return float_relation_equal;
-        }
-        return a.sign ? float_relation_less : float_relation_greater;
-    } else if (b.cls == float_class_inf) {
-        return b.sign ? float_relation_greater : float_relation_less;
-    }
+    return bfloat16_round_pack_canonical(pr, s);
+}
 
-    if (a.sign != b.sign) {
-        return a.sign ? float_relation_less : float_relation_greater;
-    }
+static float32 float32_minmax(float32 a, float32 b, float_status *s, int flags)
+{
+    FloatParts64 pa, pb, *pr;
 
-    if (a.exp == b.exp) {
-        if (a.frac == b.frac) {
-            return float_relation_equal;
-        }
-        if (a.sign) {
-            return a.frac > b.frac ?
-                float_relation_less : float_relation_greater;
-        } else {
-            return a.frac > b.frac ?
-                float_relation_greater : float_relation_less;
-        }
-    } else {
-        if (a.sign) {
-            return a.exp > b.exp ? float_relation_less : float_relation_greater;
-        } else {
-            return a.exp > b.exp ? float_relation_greater : float_relation_less;
-        }
-    }
+    float32_unpack_canonical(&pa, a, s);
+    float32_unpack_canonical(&pb, b, s);
+    pr = parts_minmax(&pa, &pb, s, flags);
+
+    return float32_round_pack_canonical(pr, s);
 }
 
-#define COMPARE(name, attr, sz)                                         \
-static int attr                                                         \
-name(float ## sz a, float ## sz b, bool is_quiet, float_status *s)      \
-{                                                                       \
-    FloatParts64 pa, pb;                                                \
-    float ## sz ## _unpack_canonical(&pa, a, s);                        \
-    float ## sz ## _unpack_canonical(&pb, b, s);                        \
-    return compare_floats(pa, pb, is_quiet, s);                         \
+static float64 float64_minmax(float64 a, float64 b, float_status *s, int flags)
+{
+    FloatParts64 pa, pb, *pr;
+
+    float64_unpack_canonical(&pa, a, s);
+    float64_unpack_canonical(&pb, b, s);
+    pr = parts_minmax(&pa, &pb, s, flags);
+
+    return float64_round_pack_canonical(pr, s);
 }
 
-COMPARE(soft_f16_compare, QEMU_FLATTEN, 16)
-COMPARE(soft_f32_compare, QEMU_SOFTFLOAT_ATTR, 32)
-COMPARE(soft_f64_compare, QEMU_SOFTFLOAT_ATTR, 64)
+static float128 float128_minmax(float128 a, float128 b,
+                                float_status *s, int flags)
+{
+    FloatParts128 pa, pb, *pr;
+
+    float128_unpack_canonical(&pa, a, s);
+    float128_unpack_canonical(&pb, b, s);
+    pr = parts_minmax(&pa, &pb, s, flags);
+
+    return float128_round_pack_canonical(pr, s);
+}
 
-#undef COMPARE
+#define MINMAX_1(type, name, flags) \
+    type type##_##name(type a, type b, float_status *s) \
+    { return type##_minmax(a, b, s, flags); }
+
+#define MINMAX_2(type) \
+    MINMAX_1(type, max, 0)                                      \
+    MINMAX_1(type, maxnum, minmax_isnum)                        \
+    MINMAX_1(type, maxnummag, minmax_isnum | minmax_ismag)      \
+    MINMAX_1(type, min, minmax_ismin)                           \
+    MINMAX_1(type, minnum, minmax_ismin | minmax_isnum)         \
+    MINMAX_1(type, minnummag, minmax_ismin | minmax_isnum | minmax_ismag)
+
+MINMAX_2(float16)
+MINMAX_2(bfloat16)
+MINMAX_2(float32)
+MINMAX_2(float64)
+MINMAX_2(float128)
+
+#undef MINMAX_1
+#undef MINMAX_2
+
+/*
+ * Floating point compare
+ */
+
+static FloatRelation QEMU_FLATTEN
+float16_do_compare(float16 a, float16 b, float_status *s, bool is_quiet)
+{
+    FloatParts64 pa, pb;
+
+    float16_unpack_canonical(&pa, a, s);
+    float16_unpack_canonical(&pb, b, s);
+    return parts_compare(&pa, &pb, s, is_quiet);
+}
 
 FloatRelation float16_compare(float16 a, float16 b, float_status *s)
 {
-    return soft_f16_compare(a, b, false, s);
+    return float16_do_compare(a, b, s, false);
 }
 
 FloatRelation float16_compare_quiet(float16 a, float16 b, float_status *s)
 {
-    return soft_f16_compare(a, b, true, s);
+    return float16_do_compare(a, b, s, true);
+}
+
+static FloatRelation QEMU_SOFTFLOAT_ATTR
+float32_do_compare(float32 a, float32 b, float_status *s, bool is_quiet)
+{
+    FloatParts64 pa, pb;
+
+    float32_unpack_canonical(&pa, a, s);
+    float32_unpack_canonical(&pb, b, s);
+    return parts_compare(&pa, &pb, s, is_quiet);
 }
 
 static FloatRelation QEMU_FLATTEN
-f32_compare(float32 xa, float32 xb, bool is_quiet, float_status *s)
+float32_hs_compare(float32 xa, float32 xb, float_status *s, bool is_quiet)
 {
     union_float32 ua, ub;
 
@@ -3533,25 +3995,36 @@ f32_compare(float32 xa, float32 xb, bool is_quiet, float_status *s)
     if (likely(isless(ua.h, ub.h))) {
         return float_relation_less;
     }
-    /* The only condition remaining is unordered.
+    /*
+     * The only condition remaining is unordered.
      * Fall through to set flags.
      */
  soft:
-    return soft_f32_compare(ua.s, ub.s, is_quiet, s);
+    return float32_do_compare(ua.s, ub.s, s, is_quiet);
 }
 
 FloatRelation float32_compare(float32 a, float32 b, float_status *s)
 {
-    return f32_compare(a, b, false, s);
+    return float32_hs_compare(a, b, s, false);
 }
 
 FloatRelation float32_compare_quiet(float32 a, float32 b, float_status *s)
 {
-    return f32_compare(a, b, true, s);
+    return float32_hs_compare(a, b, s, true);
+}
+
+static FloatRelation QEMU_SOFTFLOAT_ATTR
+float64_do_compare(float64 a, float64 b, float_status *s, bool is_quiet)
+{
+    FloatParts64 pa, pb;
+
+    float64_unpack_canonical(&pa, a, s);
+    float64_unpack_canonical(&pb, b, s);
+    return parts_compare(&pa, &pb, s, is_quiet);
 }
 
 static FloatRelation QEMU_FLATTEN
-f64_compare(float64 xa, float64 xb, bool is_quiet, float_status *s)
+float64_hs_compare(float64 xa, float64 xb, float_status *s, bool is_quiet)
 {
     union_float64 ua, ub;
 
@@ -3572,196 +4045,177 @@ f64_compare(float64 xa, float64 xb, bool is_quiet, float_status *s)
     if (likely(isless(ua.h, ub.h))) {
         return float_relation_less;
     }
-    /* The only condition remaining is unordered.
+    /*
+     * The only condition remaining is unordered.
      * Fall through to set flags.
      */
  soft:
-    return soft_f64_compare(ua.s, ub.s, is_quiet, s);
+    return float64_do_compare(ua.s, ub.s, s, is_quiet);
 }
 
 FloatRelation float64_compare(float64 a, float64 b, float_status *s)
 {
-    return f64_compare(a, b, false, s);
+    return float64_hs_compare(a, b, s, false);
 }
 
 FloatRelation float64_compare_quiet(float64 a, float64 b, float_status *s)
 {
-    return f64_compare(a, b, true, s);
+    return float64_hs_compare(a, b, s, true);
 }
 
 static FloatRelation QEMU_FLATTEN
-soft_bf16_compare(bfloat16 a, bfloat16 b, bool is_quiet, float_status *s)
+bfloat16_do_compare(bfloat16 a, bfloat16 b, float_status *s, bool is_quiet)
 {
     FloatParts64 pa, pb;
 
     bfloat16_unpack_canonical(&pa, a, s);
     bfloat16_unpack_canonical(&pb, b, s);
-    return compare_floats(pa, pb, is_quiet, s);
+    return parts_compare(&pa, &pb, s, is_quiet);
 }
 
 FloatRelation bfloat16_compare(bfloat16 a, bfloat16 b, float_status *s)
 {
-    return soft_bf16_compare(a, b, false, s);
+    return bfloat16_do_compare(a, b, s, false);
 }
 
 FloatRelation bfloat16_compare_quiet(bfloat16 a, bfloat16 b, float_status *s)
 {
-    return soft_bf16_compare(a, b, true, s);
+    return bfloat16_do_compare(a, b, s, true);
 }
 
-/* Multiply A by 2 raised to the power N.  */
-static FloatParts64 scalbn_decomposed(FloatParts64 a, int n, float_status *s)
+static FloatRelation QEMU_FLATTEN
+float128_do_compare(float128 a, float128 b, float_status *s, bool is_quiet)
 {
-    if (unlikely(is_nan(a.cls))) {
-        parts_return_nan(&a, s);
-    }
-    if (a.cls == float_class_normal) {
-        /* The largest float type (even though not supported by FloatParts64)
-         * is float128, which has a 15 bit exponent.  Bounding N to 16 bits
-         * still allows rounding to infinity, without allowing overflow
-         * within the int32_t that backs FloatParts64.exp.
-         */
-        n = MIN(MAX(n, -0x10000), 0x10000);
-        a.exp += n;
-    }
-    return a;
+    FloatParts128 pa, pb;
+
+    float128_unpack_canonical(&pa, a, s);
+    float128_unpack_canonical(&pb, b, s);
+    return parts_compare(&pa, &pb, s, is_quiet);
 }
 
-float16 float16_scalbn(float16 a, int n, float_status *status)
+FloatRelation float128_compare(float128 a, float128 b, float_status *s)
 {
-    FloatParts64 pa, pr;
-
-    float16_unpack_canonical(&pa, a, status);
-    pr = scalbn_decomposed(pa, n, status);
-    return float16_round_pack_canonical(&pr, status);
+    return float128_do_compare(a, b, s, false);
 }
 
-float32 float32_scalbn(float32 a, int n, float_status *status)
+FloatRelation float128_compare_quiet(float128 a, float128 b, float_status *s)
 {
-    FloatParts64 pa, pr;
-
-    float32_unpack_canonical(&pa, a, status);
-    pr = scalbn_decomposed(pa, n, status);
-    return float32_round_pack_canonical(&pr, status);
+    return float128_do_compare(a, b, s, true);
 }
 
-float64 float64_scalbn(float64 a, int n, float_status *status)
+static FloatRelation QEMU_FLATTEN
+floatx80_do_compare(floatx80 a, floatx80 b, float_status *s, bool is_quiet)
 {
-    FloatParts64 pa, pr;
+    FloatParts128 pa, pb;
 
-    float64_unpack_canonical(&pa, a, status);
-    pr = scalbn_decomposed(pa, n, status);
-    return float64_round_pack_canonical(&pr, status);
+    if (!floatx80_unpack_canonical(&pa, a, s) ||
+        !floatx80_unpack_canonical(&pb, b, s)) {
+        return float_relation_unordered;
+    }
+    return parts_compare(&pa, &pb, s, is_quiet);
 }
 
-bfloat16 bfloat16_scalbn(bfloat16 a, int n, float_status *status)
+FloatRelation floatx80_compare(floatx80 a, floatx80 b, float_status *s)
 {
-    FloatParts64 pa, pr;
+    return floatx80_do_compare(a, b, s, false);
+}
 
-    bfloat16_unpack_canonical(&pa, a, status);
-    pr = scalbn_decomposed(pa, n, status);
-    return bfloat16_round_pack_canonical(&pr, status);
+FloatRelation floatx80_compare_quiet(floatx80 a, floatx80 b, float_status *s)
+{
+    return floatx80_do_compare(a, b, s, true);
 }
 
 /*
- * 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.
- *
- * This does mean however the calculation is slower than before,
- * especially for 64 bit floats.
+ * Scale by 2**N
  */
 
-static FloatParts64 sqrt_float(FloatParts64 a, float_status *s, const FloatFmt *p)
+float16 float16_scalbn(float16 a, int n, float_status *status)
 {
-    uint64_t a_frac, r_frac, s_frac;
-    int bit, last_bit;
+    FloatParts64 p;
 
-    if (is_nan(a.cls)) {
-        parts_return_nan(&a, s);
-        return a;
-    }
-    if (a.cls == float_class_zero) {
-        return a;  /* sqrt(+-0) = +-0 */
-    }
-    if (a.sign) {
-        float_raise(float_flag_invalid, s);
-        parts_default_nan(&a, s);
-        return a;
-    }
-    if (a.cls == float_class_inf) {
-        return a;  /* sqrt(+inf) = +inf */
-    }
+    float16_unpack_canonical(&p, a, status);
+    parts_scalbn(&p, n, status);
+    return float16_round_pack_canonical(&p, status);
+}
 
-    assert(a.cls == float_class_normal);
+float32 float32_scalbn(float32 a, int n, float_status *status)
+{
+    FloatParts64 p;
 
-    /* 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 by 1 if the exponent is odd, otherwise 2.
-     */
-    a_frac = a.frac >> (2 - (a.exp & 1));
-    a.exp >>= 1;
+    float32_unpack_canonical(&p, a, status);
+    parts_scalbn(&p, n, status);
+    return float32_round_pack_canonical(&p, status);
+}
 
-    /* Bit-by-bit computation of sqrt.  */
-    r_frac = 0;
-    s_frac = 0;
+float64 float64_scalbn(float64 a, int n, float_status *status)
+{
+    FloatParts64 p;
 
-    /* Iterate from implicit bit down to the 3 extra bits to compute a
-     * properly rounded result. Remember we've inserted two more bits
-     * at the top, so these positions are two less.
-     */
-    bit = DECOMPOSED_BINARY_POINT - 2;
-    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);
+    float64_unpack_canonical(&p, a, status);
+    parts_scalbn(&p, n, status);
+    return float64_round_pack_canonical(&p, status);
+}
 
-    /* Undo the right shift done above. If there is any remaining
-     * fraction, the result is inexact. Set the sticky bit.
-     */
-    a.frac = (r_frac << 2) + (a_frac != 0);
+bfloat16 bfloat16_scalbn(bfloat16 a, int n, float_status *status)
+{
+    FloatParts64 p;
 
-    return a;
+    bfloat16_unpack_canonical(&p, a, status);
+    parts_scalbn(&p, n, status);
+    return bfloat16_round_pack_canonical(&p, status);
+}
+
+float128 float128_scalbn(float128 a, int n, float_status *status)
+{
+    FloatParts128 p;
+
+    float128_unpack_canonical(&p, a, status);
+    parts_scalbn(&p, n, status);
+    return float128_round_pack_canonical(&p, status);
+}
+
+floatx80 floatx80_scalbn(floatx80 a, int n, float_status *status)
+{
+    FloatParts128 p;
+
+    if (!floatx80_unpack_canonical(&p, a, status)) {
+        return floatx80_default_nan(status);
+    }
+    parts_scalbn(&p, n, status);
+    return floatx80_round_pack_canonical(&p, status);
 }
 
+/*
+ * Square Root
+ */
+
 float16 QEMU_FLATTEN float16_sqrt(float16 a, float_status *status)
 {
-    FloatParts64 pa, pr;
+    FloatParts64 p;
 
-    float16_unpack_canonical(&pa, a, status);
-    pr = sqrt_float(pa, status, &float16_params);
-    return float16_round_pack_canonical(&pr, status);
+    float16_unpack_canonical(&p, a, status);
+    parts_sqrt(&p, status, &float16_params);
+    return float16_round_pack_canonical(&p, status);
 }
 
 static float32 QEMU_SOFTFLOAT_ATTR
 soft_f32_sqrt(float32 a, float_status *status)
 {
-    FloatParts64 pa, pr;
+    FloatParts64 p;
 
-    float32_unpack_canonical(&pa, a, status);
-    pr = sqrt_float(pa, status, &float32_params);
-    return float32_round_pack_canonical(&pr, status);
+    float32_unpack_canonical(&p, a, status);
+    parts_sqrt(&p, status, &float32_params);
+    return float32_round_pack_canonical(&p, status);
 }
 
 static float64 QEMU_SOFTFLOAT_ATTR
 soft_f64_sqrt(float64 a, float_status *status)
 {
-    FloatParts64 pa, pr;
+    FloatParts64 p;
 
-    float64_unpack_canonical(&pa, a, status);
-    pr = sqrt_float(pa, status, &float64_params);
-    return float64_round_pack_canonical(&pr, status);
+    float64_unpack_canonical(&p, a, status);
+    parts_sqrt(&p, status, &float64_params);
+    return float64_round_pack_canonical(&p, status);
 }
 
 float32 QEMU_FLATTEN float32_sqrt(float32 xa, float_status *s)
@@ -3820,11 +4274,52 @@ float64 QEMU_FLATTEN float64_sqrt(float64 xa, float_status *s)
 
 bfloat16 QEMU_FLATTEN bfloat16_sqrt(bfloat16 a, float_status *status)
 {
-    FloatParts64 pa, pr;
+    FloatParts64 p;
 
-    bfloat16_unpack_canonical(&pa, a, status);
-    pr = sqrt_float(pa, status, &bfloat16_params);
-    return bfloat16_round_pack_canonical(&pr, status);
+    bfloat16_unpack_canonical(&p, a, status);
+    parts_sqrt(&p, status, &bfloat16_params);
+    return bfloat16_round_pack_canonical(&p, status);
+}
+
+float128 QEMU_FLATTEN float128_sqrt(float128 a, float_status *status)
+{
+    FloatParts128 p;
+
+    float128_unpack_canonical(&p, a, status);
+    parts_sqrt(&p, status, &float128_params);
+    return float128_round_pack_canonical(&p, status);
+}
+
+floatx80 floatx80_sqrt(floatx80 a, float_status *s)
+{
+    FloatParts128 p;
+
+    if (!floatx80_unpack_canonical(&p, a, s)) {
+        return floatx80_default_nan(s);
+    }
+    parts_sqrt(&p, s, &floatx80_params[s->floatx80_rounding_precision]);
+    return floatx80_round_pack_canonical(&p, s);
+}
+
+/*
+ * log2
+ */
+float32 float32_log2(float32 a, float_status *status)
+{
+    FloatParts64 p;
+
+    float32_unpack_canonical(&p, a, status);
+    parts_log2(&p, status, &float32_params);
+    return float32_round_pack_canonical(&p, status);
+}
+
+float64 float64_log2(float64 a, float_status *status)
+{
+    FloatParts64 p;
+
+    float64_unpack_canonical(&p, a, status);
+    parts_log2(&p, status, &float64_params);
+    return float64_round_pack_canonical(&p, status);
 }
 
 /*----------------------------------------------------------------------------
@@ -4003,481 +4498,6 @@ bfloat16 bfloat16_squash_input_denormal(bfloat16 a, float_status *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
-| input.  If `zSign' is 1, the input is negated before being converted to an
-| integer.  Bit 63 of `absZ' must be zero.  Ordinarily, the fixed-point input
-| is simply rounded to an integer, with the inexact exception raised if the
-| input cannot be represented exactly as an integer.  However, if the fixed-
-| point input is too large, the invalid exception is raised and the largest
-| positive or negative integer is returned.
-*----------------------------------------------------------------------------*/
-
-static int32_t roundAndPackInt32(bool zSign, uint64_t absZ,
-                                 float_status *status)
-{
-    int8_t roundingMode;
-    bool roundNearestEven;
-    int8_t roundIncrement, roundBits;
-    int32_t z;
-
-    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 = absZ & 0x80 ? 0 : 0x7f;
-        break;
-    default:
-        abort();
-    }
-    roundBits = absZ & 0x7F;
-    absZ = ( absZ + roundIncrement )>>7;
-    if (!(roundBits ^ 0x40) && roundNearestEven) {
-        absZ &= ~1;
-    }
-    z = absZ;
-    if ( zSign ) z = - z;
-    if ( ( absZ>>32 ) || ( z && ( ( z < 0 ) ^ zSign ) ) ) {
-        float_raise(float_flag_invalid, status);
-        return zSign ? INT32_MIN : INT32_MAX;
-    }
-    if (roundBits) {
-        float_raise(float_flag_inexact, status);
-    }
-    return z;
-
-}
-
-/*----------------------------------------------------------------------------
-| Takes the 128-bit fixed-point value formed by concatenating `absZ0' and
-| `absZ1', with binary point between bits 63 and 64 (between the input words),
-| and returns the properly rounded 64-bit integer corresponding to the input.
-| If `zSign' is 1, the input is negated before being converted to an integer.
-| Ordinarily, the fixed-point input is simply rounded to an integer, with
-| the inexact exception raised if the input cannot be represented exactly as
-| an integer.  However, if the fixed-point input is too large, the invalid
-| exception is raised and the largest positive or negative integer is
-| returned.
-*----------------------------------------------------------------------------*/
-
-static int64_t roundAndPackInt64(bool zSign, uint64_t absZ0, uint64_t absZ1,
-                               float_status *status)
-{
-    int8_t roundingMode;
-    bool roundNearestEven, increment;
-    int64_t z;
-
-    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) absZ1 < 0);
-        break;
-    case float_round_to_zero:
-        increment = 0;
-        break;
-    case float_round_up:
-        increment = !zSign && absZ1;
-        break;
-    case float_round_down:
-        increment = zSign && absZ1;
-        break;
-    case float_round_to_odd:
-        increment = !(absZ0 & 1) && absZ1;
-        break;
-    default:
-        abort();
-    }
-    if ( increment ) {
-        ++absZ0;
-        if ( absZ0 == 0 ) goto overflow;
-        if (!(absZ1 << 1) && roundNearestEven) {
-            absZ0 &= ~1;
-        }
-    }
-    z = absZ0;
-    if ( zSign ) z = - z;
-    if ( z && ( ( z < 0 ) ^ zSign ) ) {
- overflow:
-        float_raise(float_flag_invalid, status);
-        return zSign ? INT64_MIN : INT64_MAX;
-    }
-    if (absZ1) {
-        float_raise(float_flag_inexact, status);
-    }
-    return z;
-
-}
-
-/*----------------------------------------------------------------------------
-| Takes the 128-bit fixed-point value formed by concatenating `absZ0' and
-| `absZ1', with binary point between bits 63 and 64 (between the input words),
-| and returns the properly rounded 64-bit unsigned integer corresponding to the
-| input.  Ordinarily, the fixed-point input is simply rounded to an integer,
-| with the inexact exception raised if the input cannot be represented exactly
-| as an integer.  However, if the fixed-point input is too large, the invalid
-| exception is raised and the largest unsigned integer is returned.
-*----------------------------------------------------------------------------*/
-
-static int64_t roundAndPackUint64(bool zSign, uint64_t absZ0,
-                                uint64_t absZ1, float_status *status)
-{
-    int8_t roundingMode;
-    bool roundNearestEven, increment;
-
-    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)absZ1 < 0);
-        break;
-    case float_round_to_zero:
-        increment = 0;
-        break;
-    case float_round_up:
-        increment = !zSign && absZ1;
-        break;
-    case float_round_down:
-        increment = zSign && absZ1;
-        break;
-    case float_round_to_odd:
-        increment = !(absZ0 & 1) && absZ1;
-        break;
-    default:
-        abort();
-    }
-    if (increment) {
-        ++absZ0;
-        if (absZ0 == 0) {
-            float_raise(float_flag_invalid, status);
-            return UINT64_MAX;
-        }
-        if (!(absZ1 << 1) && roundNearestEven) {
-            absZ0 &= ~1;
-        }
-    }
-
-    if (zSign && absZ0) {
-        float_raise(float_flag_invalid, status);
-        return 0;
-    }
-
-    if (absZ1) {
-        float_raise(float_flag_inexact, status);
-    }
-    return absZ0;
-}
-
-/*----------------------------------------------------------------------------
-| 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
@@ -4507,10 +4527,10 @@ void normalizeFloatx80Subnormal(uint64_t aSig, int32_t *zExpPtr,
 | a subnormal number, and the underflow and inexact exceptions are raised if
 | the abstract input cannot be represented exactly as a subnormal extended
 | double-precision floating-point number.
-|     If `roundingPrecision' is 32 or 64, the result is rounded to the same
-| number of bits as single or double precision, respectively.  Otherwise, the
-| result is rounded to the full precision of the extended double-precision
-| format.
+|     If `roundingPrecision' is floatx80_precision_s or floatx80_precision_d,
+| the result is rounded to the same number of bits as single or double
+| precision, respectively.  Otherwise, the result is rounded to the full
+| precision of the extended double-precision format.
 |     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.  The
@@ -4518,27 +4538,29 @@ void normalizeFloatx80Subnormal(uint64_t aSig, int32_t *zExpPtr,
 | Floating-Point Arithmetic.
 *----------------------------------------------------------------------------*/
 
-floatx80 roundAndPackFloatx80(int8_t roundingPrecision, bool zSign,
+floatx80 roundAndPackFloatx80(FloatX80RoundPrec roundingPrecision, bool zSign,
                               int32_t zExp, uint64_t zSig0, uint64_t zSig1,
                               float_status *status)
 {
-    int8_t roundingMode;
+    FloatRoundMode roundingMode;
     bool roundNearestEven, increment, isTiny;
     int64_t roundIncrement, roundMask, roundBits;
 
     roundingMode = status->float_rounding_mode;
     roundNearestEven = ( roundingMode == float_round_nearest_even );
-    if ( roundingPrecision == 80 ) goto precision80;
-    if ( roundingPrecision == 64 ) {
+    switch (roundingPrecision) {
+    case floatx80_precision_x:
+        goto precision80;
+    case floatx80_precision_d:
         roundIncrement = UINT64_C(0x0000000000000400);
         roundMask = UINT64_C(0x00000000000007FF);
-    }
-    else if ( roundingPrecision == 32 ) {
+        break;
+    case floatx80_precision_s:
         roundIncrement = UINT64_C(0x0000008000000000);
         roundMask = UINT64_C(0x000000FFFFFFFFFF);
-    }
-    else {
-        goto precision80;
+        break;
+    default:
+        g_assert_not_reached();
     }
     zSig0 |= ( zSig1 != 0 );
     switch (roundingMode) {
@@ -4715,7 +4737,7 @@ floatx80 roundAndPackFloatx80(int8_t roundingPrecision, bool zSign,
 | normalized.
 *----------------------------------------------------------------------------*/
 
-floatx80 normalizeRoundAndPackFloatx80(int8_t roundingPrecision,
+floatx80 normalizeRoundAndPackFloatx80(FloatX80RoundPrec roundingPrecision,
                                        bool zSign, int32_t zExp,
                                        uint64_t zSig0, uint64_t zSig1,
                                        float_status *status)
@@ -4736,538 +4758,6 @@ floatx80 normalizeRoundAndPackFloatx80(int8_t 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 result of converting the 32-bit two's complement integer `a'
-| to the extended double-precision floating-point format.  The conversion
-| is performed according to the IEC/IEEE Standard for Binary Floating-Point
-| Arithmetic.
-*----------------------------------------------------------------------------*/
-
-floatx80 int32_to_floatx80(int32_t a, float_status *status)
-{
-    bool zSign;
-    uint32_t absA;
-    int8_t shiftCount;
-    uint64_t zSig;
-
-    if ( a == 0 ) return packFloatx80( 0, 0, 0 );
-    zSign = ( a < 0 );
-    absA = zSign ? - a : a;
-    shiftCount = clz32(absA) + 32;
-    zSig = absA;
-    return packFloatx80( zSign, 0x403E - shiftCount, zSig<<shiftCount );
-
-}
-
-/*----------------------------------------------------------------------------
-| Returns the result of converting the 32-bit two's complement integer `a' to
-| the quadruple-precision floating-point format.  The conversion is performed
-| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
-*----------------------------------------------------------------------------*/
-
-float128 int32_to_float128(int32_t a, float_status *status)
-{
-    bool zSign;
-    uint32_t absA;
-    int8_t shiftCount;
-    uint64_t zSig0;
-
-    if ( a == 0 ) return packFloat128( 0, 0, 0, 0 );
-    zSign = ( a < 0 );
-    absA = zSign ? - a : a;
-    shiftCount = clz32(absA) + 17;
-    zSig0 = absA;
-    return packFloat128( zSign, 0x402E - shiftCount, zSig0<<shiftCount, 0 );
-
-}
-
-/*----------------------------------------------------------------------------
-| Returns the result of converting the 64-bit two's complement integer `a'
-| to the extended double-precision floating-point format.  The conversion
-| is performed according to the IEC/IEEE Standard for Binary Floating-Point
-| Arithmetic.
-*----------------------------------------------------------------------------*/
-
-floatx80 int64_to_floatx80(int64_t a, float_status *status)
-{
-    bool zSign;
-    uint64_t absA;
-    int8_t shiftCount;
-
-    if ( a == 0 ) return packFloatx80( 0, 0, 0 );
-    zSign = ( a < 0 );
-    absA = zSign ? - a : a;
-    shiftCount = clz64(absA);
-    return packFloatx80( zSign, 0x403E - shiftCount, absA<<shiftCount );
-
-}
-
-/*----------------------------------------------------------------------------
-| Returns the result of converting the 64-bit two's complement integer `a' to
-| the quadruple-precision floating-point format.  The conversion is performed
-| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
-*----------------------------------------------------------------------------*/
-
-float128 int64_to_float128(int64_t a, float_status *status)
-{
-    bool zSign;
-    uint64_t absA;
-    int8_t shiftCount;
-    int32_t zExp;
-    uint64_t zSig0, zSig1;
-
-    if ( a == 0 ) return packFloat128( 0, 0, 0, 0 );
-    zSign = ( a < 0 );
-    absA = zSign ? - a : a;
-    shiftCount = clz64(absA) + 49;
-    zExp = 0x406E - shiftCount;
-    if ( 64 <= shiftCount ) {
-        zSig1 = 0;
-        zSig0 = absA;
-        shiftCount -= 64;
-    }
-    else {
-        zSig1 = absA;
-        zSig0 = 0;
-    }
-    shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 );
-    return packFloat128( zSign, zExp, zSig0, zSig1 );
-
-}
-
-/*----------------------------------------------------------------------------
-| Returns the result of converting the 64-bit unsigned integer `a'
-| to the quadruple-precision floating-point format.  The conversion is performed
-| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
-*----------------------------------------------------------------------------*/
-
-float128 uint64_to_float128(uint64_t a, float_status *status)
-{
-    if (a == 0) {
-        return float128_zero;
-    }
-    return normalizeRoundAndPackFloat128(0, 0x406E, 0, a, status);
-}
-
-/*----------------------------------------------------------------------------
-| Returns the result of converting the single-precision floating-point value
-| `a' to the extended double-precision floating-point format.  The conversion
-| is performed according to the IEC/IEEE Standard for Binary Floating-Point
-| Arithmetic.
-*----------------------------------------------------------------------------*/
-
-floatx80 float32_to_floatx80(float32 a, float_status *status)
-{
-    bool aSign;
-    int aExp;
-    uint32_t aSig;
-
-    a = float32_squash_input_denormal(a, status);
-    aSig = extractFloat32Frac( a );
-    aExp = extractFloat32Exp( a );
-    aSign = extractFloat32Sign( a );
-    if ( aExp == 0xFF ) {
-        if (aSig) {
-            floatx80 res = commonNaNToFloatx80(float32ToCommonNaN(a, status),
-                                               status);
-            return floatx80_silence_nan(res, status);
-        }
-        return packFloatx80(aSign,
-                            floatx80_infinity_high,
-                            floatx80_infinity_low);
-    }
-    if ( aExp == 0 ) {
-        if ( aSig == 0 ) return packFloatx80( aSign, 0, 0 );
-        normalizeFloat32Subnormal( aSig, &aExp, &aSig );
-    }
-    aSig |= 0x00800000;
-    return packFloatx80( aSign, aExp + 0x3F80, ( (uint64_t) aSig )<<40 );
-
-}
-
-/*----------------------------------------------------------------------------
-| 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.
@@ -5306,542 +4796,40 @@ static const float64 float32_exp2_coefficients[15] =
 
 float32 float32_exp2(float32 a, float_status *status)
 {
-    bool aSign;
-    int aExp;
-    uint32_t aSig;
-    float64 r, x, xn;
+    FloatParts64 xp, xnp, tp, rp;
     int i;
-    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);
+    float32_unpack_canonical(&xp, a, status);
+    if (unlikely(xp.cls != float_class_normal)) {
+        switch (xp.cls) {
+        case float_class_snan:
+        case float_class_qnan:
+            parts_return_nan(&xp, status);
+            return float32_round_pack_canonical(&xp, status);
+        case float_class_inf:
+            return xp.sign ? float32_zero : a;
+        case float_class_zero:
+            return float32_one;
+        default:
+            break;
         }
-        return (aSign) ? float32_zero : a;
-    }
-    if (aExp == 0) {
-        if (aSig == 0) return float32_one;
+        g_assert_not_reached();
     }
 
     float_raise(float_flag_inexact, status);
 
-    /* ******************************* */
-    /* using float64 for approximation */
-    /* ******************************* */
-    x = float32_to_float64(a, status);
-    x = float64_mul(x, float64_ln2, status);
+    float64_unpack_canonical(&xnp, float64_ln2, status);
+    xp = *parts_mul(&xp, &tp, status);
+    xnp = xp;
 
-    xn = x;
-    r = float64_one;
+    float64_unpack_canonical(&rp, float64_one, status);
     for (i = 0 ; i < 15 ; i++) {
-        float64 f;
-
-        f = float64_mul(xn, float32_exp2_coefficients[i], status);
-        r = float64_add(r, f, status);
-
-        xn = float64_mul(xn, x, status);
-    }
-
-    return float64_to_float32(r, status);
-}
-
-/*----------------------------------------------------------------------------
-| Returns the binary log 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_log2(float32 a, float_status *status)
-{
-    bool aSign, zSign;
-    int aExp;
-    uint32_t aSig, zSig, i;
-
-    a = float32_squash_input_denormal(a, status);
-    aSig = extractFloat32Frac( a );
-    aExp = extractFloat32Exp( a );
-    aSign = extractFloat32Sign( a );
-
-    if ( aExp == 0 ) {
-        if ( aSig == 0 ) return packFloat32( 1, 0xFF, 0 );
-        normalizeFloat32Subnormal( aSig, &aExp, &aSig );
-    }
-    if ( aSign ) {
-        float_raise(float_flag_invalid, status);
-        return float32_default_nan(status);
-    }
-    if ( aExp == 0xFF ) {
-        if (aSig) {
-            return propagateFloat32NaN(a, float32_zero, status);
-        }
-        return a;
-    }
-
-    aExp -= 0x7F;
-    aSig |= 0x00800000;
-    zSign = aExp < 0;
-    zSig = aExp << 23;
-
-    for (i = 1 << 22; i > 0; i >>= 1) {
-        aSig = ( (uint64_t)aSig * aSig ) >> 23;
-        if ( aSig & 0x01000000 ) {
-            aSig >>= 1;
-            zSig |= i;
-        }
-    }
-
-    if ( zSign )
-        zSig = -zSig;
-
-    return normalizeRoundAndPackFloat32(zSign, 0x85, zSig, status);
-}
-
-/*----------------------------------------------------------------------------
-| Returns the result of converting the double-precision floating-point value
-| `a' to the extended double-precision floating-point format.  The conversion
-| is performed according to the IEC/IEEE Standard for Binary Floating-Point
-| Arithmetic.
-*----------------------------------------------------------------------------*/
-
-floatx80 float64_to_floatx80(float64 a, float_status *status)
-{
-    bool aSign;
-    int aExp;
-    uint64_t aSig;
-
-    a = float64_squash_input_denormal(a, status);
-    aSig = extractFloat64Frac( a );
-    aExp = extractFloat64Exp( a );
-    aSign = extractFloat64Sign( a );
-    if ( aExp == 0x7FF ) {
-        if (aSig) {
-            floatx80 res = commonNaNToFloatx80(float64ToCommonNaN(a, status),
-                                               status);
-            return floatx80_silence_nan(res, status);
-        }
-        return packFloatx80(aSign,
-                            floatx80_infinity_high,
-                            floatx80_infinity_low);
-    }
-    if ( aExp == 0 ) {
-        if ( aSig == 0 ) return packFloatx80( aSign, 0, 0 );
-        normalizeFloat64Subnormal( aSig, &aExp, &aSig );
-    }
-    return
-        packFloatx80(
-            aSign, aExp + 0x3C00, (aSig | UINT64_C(0x0010000000000000)) << 11);
-
-}
-
-/*----------------------------------------------------------------------------
-| 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);
-
-}
-
-/*----------------------------------------------------------------------------
-| Returns the binary log 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_log2(float64 a, float_status *status)
-{
-    bool aSign, zSign;
-    int aExp;
-    uint64_t aSig, aSig0, aSig1, zSig, i;
-    a = float64_squash_input_denormal(a, status);
-
-    aSig = extractFloat64Frac( a );
-    aExp = extractFloat64Exp( a );
-    aSign = extractFloat64Sign( a );
-
-    if ( aExp == 0 ) {
-        if ( aSig == 0 ) return packFloat64( 1, 0x7FF, 0 );
-        normalizeFloat64Subnormal( aSig, &aExp, &aSig );
-    }
-    if ( aSign ) {
-        float_raise(float_flag_invalid, status);
-        return float64_default_nan(status);
-    }
-    if ( aExp == 0x7FF ) {
-        if (aSig) {
-            return propagateFloat64NaN(a, float64_zero, status);
-        }
-        return a;
-    }
-
-    aExp -= 0x3FF;
-    aSig |= UINT64_C(0x0010000000000000);
-    zSign = aExp < 0;
-    zSig = (uint64_t)aExp << 52;
-    for (i = 1LL << 51; i > 0; i >>= 1) {
-        mul64To128( aSig, aSig, &aSig0, &aSig1 );
-        aSig = ( aSig0 << 12 ) | ( aSig1 >> 52 );
-        if ( aSig & UINT64_C(0x0020000000000000) ) {
-            aSig >>= 1;
-            zSig |= i;
-        }
-    }
-
-    if ( zSign )
-        zSig = -zSig;
-    return normalizeRoundAndPackFloat64(zSign, 0x408, zSig, status);
-}
-
-/*----------------------------------------------------------------------------
-| Returns the result of converting the extended double-precision floating-
-| point value `a' to the 32-bit two's complement integer format.  The
-| conversion is performed according to the IEC/IEEE Standard for Binary
-| Floating-Point Arithmetic---which means in particular that the conversion
-| is rounded according to the current rounding mode.  If `a' is a NaN, the
-| largest positive integer is returned.  Otherwise, if the conversion
-| overflows, the largest integer with the same sign as `a' is returned.
-*----------------------------------------------------------------------------*/
-
-int32_t floatx80_to_int32(floatx80 a, float_status *status)
-{
-    bool aSign;
-    int32_t aExp, shiftCount;
-    uint64_t aSig;
-
-    if (floatx80_invalid_encoding(a)) {
-        float_raise(float_flag_invalid, status);
-        return 1 << 31;
-    }
-    aSig = extractFloatx80Frac( a );
-    aExp = extractFloatx80Exp( a );
-    aSign = extractFloatx80Sign( a );
-    if ( ( aExp == 0x7FFF ) && (uint64_t) ( aSig<<1 ) ) aSign = 0;
-    shiftCount = 0x4037 - aExp;
-    if ( shiftCount <= 0 ) shiftCount = 1;
-    shift64RightJamming( aSig, shiftCount, &aSig );
-    return roundAndPackInt32(aSign, aSig, status);
-
-}
-
-/*----------------------------------------------------------------------------
-| Returns the result of converting the extended double-precision floating-
-| point value `a' to the 32-bit two's complement integer format.  The
-| conversion is performed according to the IEC/IEEE Standard for Binary
-| Floating-Point Arithmetic, except that the conversion is always rounded
-| toward zero.  If `a' is a NaN, the largest positive integer is returned.
-| Otherwise, if the conversion overflows, the largest integer with the same
-| sign as `a' is returned.
-*----------------------------------------------------------------------------*/
-
-int32_t floatx80_to_int32_round_to_zero(floatx80 a, float_status *status)
-{
-    bool aSign;
-    int32_t aExp, shiftCount;
-    uint64_t aSig, savedASig;
-    int32_t z;
-
-    if (floatx80_invalid_encoding(a)) {
-        float_raise(float_flag_invalid, status);
-        return 1 << 31;
-    }
-    aSig = extractFloatx80Frac( a );
-    aExp = extractFloatx80Exp( a );
-    aSign = extractFloatx80Sign( a );
-    if ( 0x401E < aExp ) {
-        if ( ( aExp == 0x7FFF ) && (uint64_t) ( aSig<<1 ) ) aSign = 0;
-        goto invalid;
-    }
-    else if ( aExp < 0x3FFF ) {
-        if (aExp || aSig) {
-            float_raise(float_flag_inexact, status);
-        }
-        return 0;
-    }
-    shiftCount = 0x403E - aExp;
-    savedASig = aSig;
-    aSig >>= shiftCount;
-    z = aSig;
-    if ( aSign ) z = - z;
-    if ( ( z < 0 ) ^ aSign ) {
- invalid:
-        float_raise(float_flag_invalid, status);
-        return aSign ? (int32_t) 0x80000000 : 0x7FFFFFFF;
-    }
-    if ( ( aSig<<shiftCount ) != savedASig ) {
-        float_raise(float_flag_inexact, status);
-    }
-    return z;
-
-}
-
-/*----------------------------------------------------------------------------
-| Returns the result of converting the extended double-precision floating-
-| point value `a' to the 64-bit two's complement integer format.  The
-| conversion is performed according to the IEC/IEEE Standard for Binary
-| Floating-Point Arithmetic---which means in particular that the conversion
-| is rounded according to the current rounding mode.  If `a' is a NaN,
-| the largest positive integer is returned.  Otherwise, if the conversion
-| overflows, the largest integer with the same sign as `a' is returned.
-*----------------------------------------------------------------------------*/
-
-int64_t floatx80_to_int64(floatx80 a, float_status *status)
-{
-    bool aSign;
-    int32_t aExp, shiftCount;
-    uint64_t aSig, aSigExtra;
-
-    if (floatx80_invalid_encoding(a)) {
-        float_raise(float_flag_invalid, status);
-        return 1ULL << 63;
-    }
-    aSig = extractFloatx80Frac( a );
-    aExp = extractFloatx80Exp( a );
-    aSign = extractFloatx80Sign( a );
-    shiftCount = 0x403E - aExp;
-    if ( shiftCount <= 0 ) {
-        if ( shiftCount ) {
-            float_raise(float_flag_invalid, status);
-            if (!aSign || floatx80_is_any_nan(a)) {
-                return INT64_MAX;
-            }
-            return INT64_MIN;
-        }
-        aSigExtra = 0;
-    }
-    else {
-        shift64ExtraRightJamming( aSig, 0, shiftCount, &aSig, &aSigExtra );
-    }
-    return roundAndPackInt64(aSign, aSig, aSigExtra, status);
-
-}
-
-/*----------------------------------------------------------------------------
-| Returns the result of converting the extended double-precision floating-
-| point value `a' to the 64-bit two's complement integer format.  The
-| conversion is performed according to the IEC/IEEE Standard for Binary
-| Floating-Point Arithmetic, except that the conversion is always rounded
-| toward zero.  If `a' is a NaN, the largest positive integer is returned.
-| Otherwise, if the conversion overflows, the largest integer with the same
-| sign as `a' is returned.
-*----------------------------------------------------------------------------*/
-
-int64_t floatx80_to_int64_round_to_zero(floatx80 a, float_status *status)
-{
-    bool aSign;
-    int32_t aExp, shiftCount;
-    uint64_t aSig;
-    int64_t z;
-
-    if (floatx80_invalid_encoding(a)) {
-        float_raise(float_flag_invalid, status);
-        return 1ULL << 63;
-    }
-    aSig = extractFloatx80Frac( a );
-    aExp = extractFloatx80Exp( a );
-    aSign = extractFloatx80Sign( a );
-    shiftCount = aExp - 0x403E;
-    if ( 0 <= shiftCount ) {
-        aSig &= UINT64_C(0x7FFFFFFFFFFFFFFF);
-        if ( ( a.high != 0xC03E ) || aSig ) {
-            float_raise(float_flag_invalid, status);
-            if ( ! aSign || ( ( aExp == 0x7FFF ) && aSig ) ) {
-                return INT64_MAX;
-            }
-        }
-        return INT64_MIN;
-    }
-    else if ( aExp < 0x3FFF ) {
-        if (aExp | aSig) {
-            float_raise(float_flag_inexact, status);
-        }
-        return 0;
+        float64_unpack_canonical(&tp, float32_exp2_coefficients[i], status);
+        rp = *parts_muladd(&tp, &xp, &rp, 0, status);
+        xnp = *parts_mul(&xnp, &xp, status);
     }
-    z = aSig>>( - shiftCount );
-    if ( (uint64_t) ( aSig<<( shiftCount & 63 ) ) ) {
-        float_raise(float_flag_inexact, status);
-    }
-    if ( aSign ) z = - z;
-    return z;
-
-}
-
-/*----------------------------------------------------------------------------
-| Returns the result of converting the extended double-precision floating-
-| point value `a' to the single-precision floating-point format.  The
-| conversion is performed according to the IEC/IEEE Standard for Binary
-| Floating-Point Arithmetic.
-*----------------------------------------------------------------------------*/
-
-float32 floatx80_to_float32(floatx80 a, float_status *status)
-{
-    bool aSign;
-    int32_t aExp;
-    uint64_t aSig;
-
-    if (floatx80_invalid_encoding(a)) {
-        float_raise(float_flag_invalid, status);
-        return float32_default_nan(status);
-    }
-    aSig = extractFloatx80Frac( a );
-    aExp = extractFloatx80Exp( a );
-    aSign = extractFloatx80Sign( a );
-    if ( aExp == 0x7FFF ) {
-        if ( (uint64_t) ( aSig<<1 ) ) {
-            float32 res = commonNaNToFloat32(floatx80ToCommonNaN(a, status),
-                                             status);
-            return float32_silence_nan(res, status);
-        }
-        return packFloat32( aSign, 0xFF, 0 );
-    }
-    shift64RightJamming( aSig, 33, &aSig );
-    if ( aExp || aSig ) aExp -= 0x3F81;
-    return roundAndPackFloat32(aSign, aExp, aSig, status);
-
-}
-
-/*----------------------------------------------------------------------------
-| Returns the result of converting the extended double-precision floating-
-| point value `a' to the double-precision floating-point format.  The
-| conversion is performed according to the IEC/IEEE Standard for Binary
-| Floating-Point Arithmetic.
-*----------------------------------------------------------------------------*/
-
-float64 floatx80_to_float64(floatx80 a, float_status *status)
-{
-    bool aSign;
-    int32_t aExp;
-    uint64_t aSig, zSig;
-
-    if (floatx80_invalid_encoding(a)) {
-        float_raise(float_flag_invalid, status);
-        return float64_default_nan(status);
-    }
-    aSig = extractFloatx80Frac( a );
-    aExp = extractFloatx80Exp( a );
-    aSign = extractFloatx80Sign( a );
-    if ( aExp == 0x7FFF ) {
-        if ( (uint64_t) ( aSig<<1 ) ) {
-            float64 res = commonNaNToFloat64(floatx80ToCommonNaN(a, status),
-                                             status);
-            return float64_silence_nan(res, status);
-        }
-        return packFloat64( aSign, 0x7FF, 0 );
-    }
-    shift64RightJamming( aSig, 1, &zSig );
-    if ( aExp || aSig ) aExp -= 0x3C01;
-    return roundAndPackFloat64(aSign, aExp, zSig, status);
-
-}
-
-/*----------------------------------------------------------------------------
-| Returns the result of converting the extended double-precision floating-
-| point value `a' to the quadruple-precision floating-point format.  The
-| conversion is performed according to the IEC/IEEE Standard for Binary
-| Floating-Point Arithmetic.
-*----------------------------------------------------------------------------*/
-
-float128 floatx80_to_float128(floatx80 a, float_status *status)
-{
-    bool aSign;
-    int aExp;
-    uint64_t aSig, zSig0, zSig1;
-
-    if (floatx80_invalid_encoding(a)) {
-        float_raise(float_flag_invalid, status);
-        return float128_default_nan(status);
-    }
-    aSig = extractFloatx80Frac( a );
-    aExp = extractFloatx80Exp( a );
-    aSign = extractFloatx80Sign( a );
-    if ( ( aExp == 0x7FFF ) && (uint64_t) ( aSig<<1 ) ) {
-        float128 res = commonNaNToFloat128(floatx80ToCommonNaN(a, status),
-                                           status);
-        return float128_silence_nan(res, status);
-    }
-    shift128Right( aSig<<1, 0, 16, &zSig0, &zSig1 );
-    return packFloat128( aSign, aExp, zSig0, zSig1 );
 
+    return float32_round_pack_canonical(&rp, status);
 }
 
 /*----------------------------------------------------------------------------
@@ -5854,1195 +4842,12 @@ float128 floatx80_to_float128(floatx80 a, float_status *status)
 
 floatx80 floatx80_round(floatx80 a, float_status *status)
 {
-    return roundAndPackFloatx80(status->floatx80_rounding_precision,
-                                extractFloatx80Sign(a),
-                                extractFloatx80Exp(a),
-                                extractFloatx80Frac(a), 0, status);
-}
-
-/*----------------------------------------------------------------------------
-| Rounds the extended double-precision floating-point value `a' to an integer,
-| and returns the result as an extended quadruple-precision floating-point
-| value.  The operation is performed according to the IEC/IEEE Standard for
-| Binary Floating-Point Arithmetic.
-*----------------------------------------------------------------------------*/
-
-floatx80 floatx80_round_to_int(floatx80 a, float_status *status)
-{
-    bool aSign;
-    int32_t aExp;
-    uint64_t lastBitMask, roundBitsMask;
-    floatx80 z;
-
-    if (floatx80_invalid_encoding(a)) {
-        float_raise(float_flag_invalid, status);
-        return floatx80_default_nan(status);
-    }
-    aExp = extractFloatx80Exp( a );
-    if ( 0x403E <= aExp ) {
-        if ( ( aExp == 0x7FFF ) && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) {
-            return propagateFloatx80NaN(a, a, status);
-        }
-        return a;
-    }
-    if ( aExp < 0x3FFF ) {
-        if (    ( aExp == 0 )
-             && ( (uint64_t) ( extractFloatx80Frac( a ) ) == 0 ) ) {
-            return a;
-        }
-        float_raise(float_flag_inexact, status);
-        aSign = extractFloatx80Sign( a );
-        switch (status->float_rounding_mode) {
-         case float_round_nearest_even:
-            if ( ( aExp == 0x3FFE ) && (uint64_t) ( extractFloatx80Frac( a )<<1 )
-               ) {
-                return
-                    packFloatx80( aSign, 0x3FFF, UINT64_C(0x8000000000000000));
-            }
-            break;
-        case float_round_ties_away:
-            if (aExp == 0x3FFE) {
-                return packFloatx80(aSign, 0x3FFF, UINT64_C(0x8000000000000000));
-            }
-            break;
-         case float_round_down:
-            return
-                  aSign ?
-                      packFloatx80( 1, 0x3FFF, UINT64_C(0x8000000000000000))
-                : packFloatx80( 0, 0, 0 );
-         case float_round_up:
-            return
-                  aSign ? packFloatx80( 1, 0, 0 )
-                : packFloatx80( 0, 0x3FFF, UINT64_C(0x8000000000000000));
-
-        case float_round_to_zero:
-            break;
-        default:
-            g_assert_not_reached();
-        }
-        return packFloatx80( aSign, 0, 0 );
-    }
-    lastBitMask = 1;
-    lastBitMask <<= 0x403E - aExp;
-    roundBitsMask = lastBitMask - 1;
-    z = a;
-    switch (status->float_rounding_mode) {
-    case float_round_nearest_even:
-        z.low += lastBitMask>>1;
-        if ((z.low & roundBitsMask) == 0) {
-            z.low &= ~lastBitMask;
-        }
-        break;
-    case float_round_ties_away:
-        z.low += lastBitMask >> 1;
-        break;
-    case float_round_to_zero:
-        break;
-    case float_round_up:
-        if (!extractFloatx80Sign(z)) {
-            z.low += roundBitsMask;
-        }
-        break;
-    case float_round_down:
-        if (extractFloatx80Sign(z)) {
-            z.low += roundBitsMask;
-        }
-        break;
-    default:
-        abort();
-    }
-    z.low &= ~ roundBitsMask;
-    if ( z.low == 0 ) {
-        ++z.high;
-        z.low = UINT64_C(0x8000000000000000);
-    }
-    if (z.low != a.low) {
-        float_raise(float_flag_inexact, status);
-    }
-    return z;
-
-}
-
-/*----------------------------------------------------------------------------
-| Returns the result of adding the absolute values of the extended double-
-| precision floating-point values `a' and `b'.  If `zSign' is 1, the sum is
-| negated before being returned.  `zSign' is ignored if the result is a NaN.
-| The addition is performed according to the IEC/IEEE Standard for Binary
-| Floating-Point Arithmetic.
-*----------------------------------------------------------------------------*/
-
-static floatx80 addFloatx80Sigs(floatx80 a, floatx80 b, bool zSign,
-                                float_status *status)
-{
-    int32_t aExp, bExp, zExp;
-    uint64_t aSig, bSig, zSig0, zSig1;
-    int32_t expDiff;
-
-    aSig = extractFloatx80Frac( a );
-    aExp = extractFloatx80Exp( a );
-    bSig = extractFloatx80Frac( b );
-    bExp = extractFloatx80Exp( b );
-    expDiff = aExp - bExp;
-    if ( 0 < expDiff ) {
-        if ( aExp == 0x7FFF ) {
-            if ((uint64_t)(aSig << 1)) {
-                return propagateFloatx80NaN(a, b, status);
-            }
-            return a;
-        }
-        if ( bExp == 0 ) --expDiff;
-        shift64ExtraRightJamming( bSig, 0, expDiff, &bSig, &zSig1 );
-        zExp = aExp;
-    }
-    else if ( expDiff < 0 ) {
-        if ( bExp == 0x7FFF ) {
-            if ((uint64_t)(bSig << 1)) {
-                return propagateFloatx80NaN(a, b, status);
-            }
-            return packFloatx80(zSign,
-                                floatx80_infinity_high,
-                                floatx80_infinity_low);
-        }
-        if ( aExp == 0 ) ++expDiff;
-        shift64ExtraRightJamming( aSig, 0, - expDiff, &aSig, &zSig1 );
-        zExp = bExp;
-    }
-    else {
-        if ( aExp == 0x7FFF ) {
-            if ( (uint64_t) ( ( aSig | bSig )<<1 ) ) {
-                return propagateFloatx80NaN(a, b, status);
-            }
-            return a;
-        }
-        zSig1 = 0;
-        zSig0 = aSig + bSig;
-        if ( aExp == 0 ) {
-            if ((aSig | bSig) & UINT64_C(0x8000000000000000) && zSig0 < aSig) {
-                /* At least one of the values is a pseudo-denormal,
-                 * and there is a carry out of the result.  */
-                zExp = 1;
-                goto shiftRight1;
-            }
-            if (zSig0 == 0) {
-                return packFloatx80(zSign, 0, 0);
-            }
-            normalizeFloatx80Subnormal( zSig0, &zExp, &zSig0 );
-            goto roundAndPack;
-        }
-        zExp = aExp;
-        goto shiftRight1;
-    }
-    zSig0 = aSig + bSig;
-    if ( (int64_t) zSig0 < 0 ) goto roundAndPack;
- shiftRight1:
-    shift64ExtraRightJamming( zSig0, zSig1, 1, &zSig0, &zSig1 );
-    zSig0 |= UINT64_C(0x8000000000000000);
-    ++zExp;
- roundAndPack:
-    return roundAndPackFloatx80(status->floatx80_rounding_precision,
-                                zSign, zExp, zSig0, zSig1, status);
-}
-
-/*----------------------------------------------------------------------------
-| Returns the result of subtracting the absolute values of the extended
-| double-precision floating-point values `a' and `b'.  If `zSign' is 1, the
-| difference is negated before being returned.  `zSign' is ignored if the
-| result is a NaN.  The subtraction is performed according to the IEC/IEEE
-| Standard for Binary Floating-Point Arithmetic.
-*----------------------------------------------------------------------------*/
-
-static floatx80 subFloatx80Sigs(floatx80 a, floatx80 b, bool zSign,
-                                float_status *status)
-{
-    int32_t aExp, bExp, zExp;
-    uint64_t aSig, bSig, zSig0, zSig1;
-    int32_t expDiff;
-
-    aSig = extractFloatx80Frac( a );
-    aExp = extractFloatx80Exp( a );
-    bSig = extractFloatx80Frac( b );
-    bExp = extractFloatx80Exp( b );
-    expDiff = aExp - bExp;
-    if ( 0 < expDiff ) goto aExpBigger;
-    if ( expDiff < 0 ) goto bExpBigger;
-    if ( aExp == 0x7FFF ) {
-        if ( (uint64_t) ( ( aSig | bSig )<<1 ) ) {
-            return propagateFloatx80NaN(a, b, status);
-        }
-        float_raise(float_flag_invalid, status);
-        return floatx80_default_nan(status);
-    }
-    if ( aExp == 0 ) {
-        aExp = 1;
-        bExp = 1;
-    }
-    zSig1 = 0;
-    if ( bSig < aSig ) goto aBigger;
-    if ( aSig < bSig ) goto bBigger;
-    return packFloatx80(status->float_rounding_mode == float_round_down, 0, 0);
- bExpBigger:
-    if ( bExp == 0x7FFF ) {
-        if ((uint64_t)(bSig << 1)) {
-            return propagateFloatx80NaN(a, b, status);
-        }
-        return packFloatx80(zSign ^ 1, floatx80_infinity_high,
-                            floatx80_infinity_low);
-    }
-    if ( aExp == 0 ) ++expDiff;
-    shift128RightJamming( aSig, 0, - expDiff, &aSig, &zSig1 );
- bBigger:
-    sub128( bSig, 0, aSig, zSig1, &zSig0, &zSig1 );
-    zExp = bExp;
-    zSign ^= 1;
-    goto normalizeRoundAndPack;
- aExpBigger:
-    if ( aExp == 0x7FFF ) {
-        if ((uint64_t)(aSig << 1)) {
-            return propagateFloatx80NaN(a, b, status);
-        }
-        return a;
-    }
-    if ( bExp == 0 ) --expDiff;
-    shift128RightJamming( bSig, 0, expDiff, &bSig, &zSig1 );
- aBigger:
-    sub128( aSig, 0, bSig, zSig1, &zSig0, &zSig1 );
-    zExp = aExp;
- normalizeRoundAndPack:
-    return normalizeRoundAndPackFloatx80(status->floatx80_rounding_precision,
-                                         zSign, zExp, zSig0, zSig1, status);
-}
-
-/*----------------------------------------------------------------------------
-| Returns the result of adding the extended double-precision floating-point
-| values `a' and `b'.  The operation is performed according to the IEC/IEEE
-| Standard for Binary Floating-Point Arithmetic.
-*----------------------------------------------------------------------------*/
-
-floatx80 floatx80_add(floatx80 a, floatx80 b, float_status *status)
-{
-    bool aSign, bSign;
-
-    if (floatx80_invalid_encoding(a) || floatx80_invalid_encoding(b)) {
-        float_raise(float_flag_invalid, status);
-        return floatx80_default_nan(status);
-    }
-    aSign = extractFloatx80Sign( a );
-    bSign = extractFloatx80Sign( b );
-    if ( aSign == bSign ) {
-        return addFloatx80Sigs(a, b, aSign, status);
-    }
-    else {
-        return subFloatx80Sigs(a, b, aSign, status);
-    }
-
-}
-
-/*----------------------------------------------------------------------------
-| Returns the result of subtracting the extended double-precision floating-
-| point values `a' and `b'.  The operation is performed according to the
-| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
-*----------------------------------------------------------------------------*/
-
-floatx80 floatx80_sub(floatx80 a, floatx80 b, float_status *status)
-{
-    bool aSign, bSign;
-
-    if (floatx80_invalid_encoding(a) || floatx80_invalid_encoding(b)) {
-        float_raise(float_flag_invalid, status);
-        return floatx80_default_nan(status);
-    }
-    aSign = extractFloatx80Sign( a );
-    bSign = extractFloatx80Sign( b );
-    if ( aSign == bSign ) {
-        return subFloatx80Sigs(a, b, aSign, status);
-    }
-    else {
-        return addFloatx80Sigs(a, b, aSign, status);
-    }
-
-}
-
-/*----------------------------------------------------------------------------
-| Returns the result of multiplying the extended double-precision floating-
-| point values `a' and `b'.  The operation is performed according to the
-| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
-*----------------------------------------------------------------------------*/
-
-floatx80 floatx80_mul(floatx80 a, floatx80 b, float_status *status)
-{
-    bool aSign, bSign, zSign;
-    int32_t aExp, bExp, zExp;
-    uint64_t aSig, bSig, zSig0, zSig1;
-
-    if (floatx80_invalid_encoding(a) || floatx80_invalid_encoding(b)) {
-        float_raise(float_flag_invalid, status);
-        return floatx80_default_nan(status);
-    }
-    aSig = extractFloatx80Frac( a );
-    aExp = extractFloatx80Exp( a );
-    aSign = extractFloatx80Sign( a );
-    bSig = extractFloatx80Frac( b );
-    bExp = extractFloatx80Exp( b );
-    bSign = extractFloatx80Sign( b );
-    zSign = aSign ^ bSign;
-    if ( aExp == 0x7FFF ) {
-        if (    (uint64_t) ( aSig<<1 )
-             || ( ( bExp == 0x7FFF ) && (uint64_t) ( bSig<<1 ) ) ) {
-            return propagateFloatx80NaN(a, b, status);
-        }
-        if ( ( bExp | bSig ) == 0 ) goto invalid;
-        return packFloatx80(zSign, floatx80_infinity_high,
-                                   floatx80_infinity_low);
-    }
-    if ( bExp == 0x7FFF ) {
-        if ((uint64_t)(bSig << 1)) {
-            return propagateFloatx80NaN(a, b, status);
-        }
-        if ( ( aExp | aSig ) == 0 ) {
- invalid:
-            float_raise(float_flag_invalid, status);
-            return floatx80_default_nan(status);
-        }
-        return packFloatx80(zSign, floatx80_infinity_high,
-                                   floatx80_infinity_low);
-    }
-    if ( aExp == 0 ) {
-        if ( aSig == 0 ) return packFloatx80( zSign, 0, 0 );
-        normalizeFloatx80Subnormal( aSig, &aExp, &aSig );
-    }
-    if ( bExp == 0 ) {
-        if ( bSig == 0 ) return packFloatx80( zSign, 0, 0 );
-        normalizeFloatx80Subnormal( bSig, &bExp, &bSig );
-    }
-    zExp = aExp + bExp - 0x3FFE;
-    mul64To128( aSig, bSig, &zSig0, &zSig1 );
-    if ( 0 < (int64_t) zSig0 ) {
-        shortShift128Left( zSig0, zSig1, 1, &zSig0, &zSig1 );
-        --zExp;
-    }
-    return roundAndPackFloatx80(status->floatx80_rounding_precision,
-                                zSign, zExp, zSig0, zSig1, status);
-}
-
-/*----------------------------------------------------------------------------
-| Returns the result of dividing the extended double-precision floating-point
-| value `a' by the corresponding value `b'.  The operation is performed
-| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
-*----------------------------------------------------------------------------*/
-
-floatx80 floatx80_div(floatx80 a, floatx80 b, float_status *status)
-{
-    bool aSign, bSign, zSign;
-    int32_t aExp, bExp, zExp;
-    uint64_t aSig, bSig, zSig0, zSig1;
-    uint64_t rem0, rem1, rem2, term0, term1, term2;
-
-    if (floatx80_invalid_encoding(a) || floatx80_invalid_encoding(b)) {
-        float_raise(float_flag_invalid, status);
-        return floatx80_default_nan(status);
-    }
-    aSig = extractFloatx80Frac( a );
-    aExp = extractFloatx80Exp( a );
-    aSign = extractFloatx80Sign( a );
-    bSig = extractFloatx80Frac( b );
-    bExp = extractFloatx80Exp( b );
-    bSign = extractFloatx80Sign( b );
-    zSign = aSign ^ bSign;
-    if ( aExp == 0x7FFF ) {
-        if ((uint64_t)(aSig << 1)) {
-            return propagateFloatx80NaN(a, b, status);
-        }
-        if ( bExp == 0x7FFF ) {
-            if ((uint64_t)(bSig << 1)) {
-                return propagateFloatx80NaN(a, b, status);
-            }
-            goto invalid;
-        }
-        return packFloatx80(zSign, floatx80_infinity_high,
-                                   floatx80_infinity_low);
-    }
-    if ( bExp == 0x7FFF ) {
-        if ((uint64_t)(bSig << 1)) {
-            return propagateFloatx80NaN(a, b, status);
-        }
-        return packFloatx80( zSign, 0, 0 );
-    }
-    if ( bExp == 0 ) {
-        if ( bSig == 0 ) {
-            if ( ( aExp | aSig ) == 0 ) {
- invalid:
-                float_raise(float_flag_invalid, status);
-                return floatx80_default_nan(status);
-            }
-            float_raise(float_flag_divbyzero, status);
-            return packFloatx80(zSign, floatx80_infinity_high,
-                                       floatx80_infinity_low);
-        }
-        normalizeFloatx80Subnormal( bSig, &bExp, &bSig );
-    }
-    if ( aExp == 0 ) {
-        if ( aSig == 0 ) return packFloatx80( zSign, 0, 0 );
-        normalizeFloatx80Subnormal( aSig, &aExp, &aSig );
-    }
-    zExp = aExp - bExp + 0x3FFE;
-    rem1 = 0;
-    if ( bSig <= aSig ) {
-        shift128Right( aSig, 0, 1, &aSig, &rem1 );
-        ++zExp;
-    }
-    zSig0 = estimateDiv128To64( aSig, rem1, bSig );
-    mul64To128( bSig, zSig0, &term0, &term1 );
-    sub128( aSig, rem1, term0, term1, &rem0, &rem1 );
-    while ( (int64_t) rem0 < 0 ) {
-        --zSig0;
-        add128( rem0, rem1, 0, bSig, &rem0, &rem1 );
-    }
-    zSig1 = estimateDiv128To64( rem1, 0, bSig );
-    if ( (uint64_t) ( zSig1<<1 ) <= 8 ) {
-        mul64To128( bSig, zSig1, &term1, &term2 );
-        sub128( rem1, 0, term1, term2, &rem1, &rem2 );
-        while ( (int64_t) rem1 < 0 ) {
-            --zSig1;
-            add128( rem1, rem2, 0, bSig, &rem1, &rem2 );
-        }
-        zSig1 |= ( ( rem1 | rem2 ) != 0 );
-    }
-    return roundAndPackFloatx80(status->floatx80_rounding_precision,
-                                zSign, zExp, zSig0, zSig1, 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(
-            80, 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, &quotient, 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, &quotient, status);
-}
-
-/*----------------------------------------------------------------------------
-| Returns the square root of the extended double-precision floating-point
-| value `a'.  The operation is performed according to the IEC/IEEE Standard
-| for Binary Floating-Point Arithmetic.
-*----------------------------------------------------------------------------*/
-
-floatx80 floatx80_sqrt(floatx80 a, float_status *status)
-{
-    bool aSign;
-    int32_t aExp, zExp;
-    uint64_t aSig0, aSig1, zSig0, zSig1, doubleZSig0;
-    uint64_t rem0, rem1, rem2, rem3, term0, term1, term2, term3;
-
-    if (floatx80_invalid_encoding(a)) {
-        float_raise(float_flag_invalid, status);
-        return floatx80_default_nan(status);
-    }
-    aSig0 = extractFloatx80Frac( a );
-    aExp = extractFloatx80Exp( a );
-    aSign = extractFloatx80Sign( a );
-    if ( aExp == 0x7FFF ) {
-        if ((uint64_t)(aSig0 << 1)) {
-            return propagateFloatx80NaN(a, a, status);
-        }
-        if ( ! aSign ) return a;
-        goto invalid;
-    }
-    if ( aSign ) {
-        if ( ( aExp | aSig0 ) == 0 ) return a;
- invalid:
-        float_raise(float_flag_invalid, status);
-        return floatx80_default_nan(status);
-    }
-    if ( aExp == 0 ) {
-        if ( aSig0 == 0 ) return packFloatx80( 0, 0, 0 );
-        normalizeFloatx80Subnormal( aSig0, &aExp, &aSig0 );
-    }
-    zExp = ( ( aExp - 0x3FFF )>>1 ) + 0x3FFF;
-    zSig0 = estimateSqrt32( aExp, aSig0>>32 );
-    shift128Right( aSig0, 0, 2 + ( aExp & 1 ), &aSig0, &aSig1 );
-    zSig0 = estimateDiv128To64( aSig0, aSig1, zSig0<<32 ) + ( zSig0<<30 );
-    doubleZSig0 = zSig0<<1;
-    mul64To128( zSig0, zSig0, &term0, &term1 );
-    sub128( aSig0, aSig1, term0, term1, &rem0, &rem1 );
-    while ( (int64_t) rem0 < 0 ) {
-        --zSig0;
-        doubleZSig0 -= 2;
-        add128( rem0, rem1, zSig0>>63, doubleZSig0 | 1, &rem0, &rem1 );
-    }
-    zSig1 = estimateDiv128To64( rem1, 0, doubleZSig0 );
-    if ( ( zSig1 & UINT64_C(0x3FFFFFFFFFFFFFFF) ) <= 5 ) {
-        if ( zSig1 == 0 ) zSig1 = 1;
-        mul64To128( doubleZSig0, zSig1, &term1, &term2 );
-        sub128( rem1, 0, term1, term2, &rem1, &rem2 );
-        mul64To128( zSig1, zSig1, &term2, &term3 );
-        sub192( rem1, rem2, 0, 0, term2, term3, &rem1, &rem2, &rem3 );
-        while ( (int64_t) rem1 < 0 ) {
-            --zSig1;
-            shortShift128Left( 0, zSig1, 1, &term2, &term3 );
-            term3 |= 1;
-            term2 |= doubleZSig0;
-            add192( rem1, rem2, rem3, 0, term2, term3, &rem1, &rem2, &rem3 );
-        }
-        zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 );
-    }
-    shortShift128Left( 0, zSig1, 1, &zSig0, &zSig1 );
-    zSig0 |= doubleZSig0;
-    return roundAndPackFloatx80(status->floatx80_rounding_precision,
-                                0, zExp, zSig0, zSig1, status);
-}
-
-/*----------------------------------------------------------------------------
-| Returns the result of converting the quadruple-precision floating-point value
-| `a' to the 64-bit unsigned integer format.  The conversion is
-| performed according to the IEC/IEEE Standard for Binary Floating-Point
-| Arithmetic---which means in particular that the conversion is rounded
-| according to the current rounding mode.  If `a' is a NaN, the largest
-| positive integer is returned.  If the conversion overflows, the
-| largest unsigned integer is returned.  If 'a' is negative, the value is
-| rounded and zero is returned; negative values that do not round to zero
-| will raise the inexact exception.
-*----------------------------------------------------------------------------*/
-
-uint64_t float128_to_uint64(float128 a, float_status *status)
-{
-    bool aSign;
-    int aExp;
-    int shiftCount;
-    uint64_t aSig0, aSig1;
-
-    aSig0 = extractFloat128Frac0(a);
-    aSig1 = extractFloat128Frac1(a);
-    aExp = extractFloat128Exp(a);
-    aSign = extractFloat128Sign(a);
-    if (aSign && (aExp > 0x3FFE)) {
-        float_raise(float_flag_invalid, status);
-        if (float128_is_any_nan(a)) {
-            return UINT64_MAX;
-        } else {
-            return 0;
-        }
-    }
-    if (aExp) {
-        aSig0 |= UINT64_C(0x0001000000000000);
-    }
-    shiftCount = 0x402F - aExp;
-    if (shiftCount <= 0) {
-        if (0x403E < aExp) {
-            float_raise(float_flag_invalid, status);
-            return UINT64_MAX;
-        }
-        shortShift128Left(aSig0, aSig1, -shiftCount, &aSig0, &aSig1);
-    } else {
-        shift64ExtraRightJamming(aSig0, aSig1, shiftCount, &aSig0, &aSig1);
-    }
-    return roundAndPackUint64(aSign, aSig0, aSig1, status);
-}
-
-uint64_t float128_to_uint64_round_to_zero(float128 a, float_status *status)
-{
-    uint64_t v;
-    signed char current_rounding_mode = status->float_rounding_mode;
-
-    set_float_rounding_mode(float_round_to_zero, status);
-    v = float128_to_uint64(a, status);
-    set_float_rounding_mode(current_rounding_mode, status);
-
-    return v;
-}
-
-/*----------------------------------------------------------------------------
-| Returns the result of converting the quadruple-precision floating-point
-| value `a' to the 32-bit unsigned integer format.  The conversion
-| is performed according to the IEC/IEEE Standard for Binary Floating-Point
-| Arithmetic except that the conversion is always rounded toward zero.
-| If `a' is a NaN, the largest positive integer is returned.  Otherwise,
-| if the conversion overflows, the largest unsigned integer is returned.
-| If 'a' is negative, the value is rounded and zero is returned; negative
-| values that do not round to zero will raise the inexact exception.
-*----------------------------------------------------------------------------*/
-
-uint32_t float128_to_uint32_round_to_zero(float128 a, float_status *status)
-{
-    uint64_t v;
-    uint32_t res;
-    int old_exc_flags = get_float_exception_flags(status);
-
-    v = float128_to_uint64_round_to_zero(a, status);
-    if (v > 0xffffffff) {
-        res = 0xffffffff;
-    } else {
-        return v;
-    }
-    set_float_exception_flags(old_exc_flags, status);
-    float_raise(float_flag_invalid, status);
-    return res;
-}
-
-/*----------------------------------------------------------------------------
-| Returns the result of converting the quadruple-precision floating-point value
-| `a' to the 32-bit unsigned integer format.  The conversion is
-| performed according to the IEC/IEEE Standard for Binary Floating-Point
-| Arithmetic---which means in particular that the conversion is rounded
-| according to the current rounding mode.  If `a' is a NaN, the largest
-| positive integer is returned.  If the conversion overflows, the
-| largest unsigned integer is returned.  If 'a' is negative, the value is
-| rounded and zero is returned; negative values that do not round to zero
-| will raise the inexact exception.
-*----------------------------------------------------------------------------*/
-
-uint32_t float128_to_uint32(float128 a, float_status *status)
-{
-    uint64_t v;
-    uint32_t res;
-    int old_exc_flags = get_float_exception_flags(status);
-
-    v = float128_to_uint64(a, status);
-    if (v > 0xffffffff) {
-        res = 0xffffffff;
-    } else {
-        return v;
-    }
-    set_float_exception_flags(old_exc_flags, status);
-    float_raise(float_flag_invalid, status);
-    return res;
-}
-
-/*----------------------------------------------------------------------------
-| Returns the result of converting the quadruple-precision floating-point
-| value `a' to the extended double-precision floating-point format.  The
-| conversion is performed according to the IEC/IEEE Standard for Binary
-| Floating-Point Arithmetic.
-*----------------------------------------------------------------------------*/
-
-floatx80 float128_to_floatx80(float128 a, float_status *status)
-{
-    bool aSign;
-    int32_t aExp;
-    uint64_t aSig0, aSig1;
-
-    aSig1 = extractFloat128Frac1( a );
-    aSig0 = extractFloat128Frac0( a );
-    aExp = extractFloat128Exp( a );
-    aSign = extractFloat128Sign( a );
-    if ( aExp == 0x7FFF ) {
-        if ( aSig0 | aSig1 ) {
-            floatx80 res = commonNaNToFloatx80(float128ToCommonNaN(a, status),
-                                               status);
-            return floatx80_silence_nan(res, status);
-        }
-        return packFloatx80(aSign, floatx80_infinity_high,
-                                   floatx80_infinity_low);
-    }
-    if ( aExp == 0 ) {
-        if ( ( aSig0 | aSig1 ) == 0 ) return packFloatx80( aSign, 0, 0 );
-        normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 );
-    }
-    else {
-        aSig0 |= UINT64_C(0x0001000000000000);
-    }
-    shortShift128Left( aSig0, aSig1, 15, &aSig0, &aSig1 );
-    return roundAndPackFloatx80(80, aSign, aExp, aSig0, aSig1, 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);
-}
-
-/*----------------------------------------------------------------------------
-| Returns the square root of the quadruple-precision floating-point value `a'.
-| The operation is performed according to the IEC/IEEE Standard for Binary
-| Floating-Point Arithmetic.
-*----------------------------------------------------------------------------*/
-
-float128 float128_sqrt(float128 a, float_status *status)
-{
-    bool aSign;
-    int32_t aExp, zExp;
-    uint64_t aSig0, aSig1, zSig0, zSig1, zSig2, doubleZSig0;
-    uint64_t rem0, rem1, rem2, rem3, term0, term1, term2, term3;
-
-    aSig1 = extractFloat128Frac1( a );
-    aSig0 = extractFloat128Frac0( a );
-    aExp = extractFloat128Exp( a );
-    aSign = extractFloat128Sign( a );
-    if ( aExp == 0x7FFF ) {
-        if (aSig0 | aSig1) {
-            return propagateFloat128NaN(a, a, status);
-        }
-        if ( ! aSign ) return a;
-        goto invalid;
-    }
-    if ( aSign ) {
-        if ( ( aExp | aSig0 | aSig1 ) == 0 ) return a;
- invalid:
-        float_raise(float_flag_invalid, status);
-        return float128_default_nan(status);
-    }
-    if ( aExp == 0 ) {
-        if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( 0, 0, 0, 0 );
-        normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 );
-    }
-    zExp = ( ( aExp - 0x3FFF )>>1 ) + 0x3FFE;
-    aSig0 |= UINT64_C(0x0001000000000000);
-    zSig0 = estimateSqrt32( aExp, aSig0>>17 );
-    shortShift128Left( aSig0, aSig1, 13 - ( aExp & 1 ), &aSig0, &aSig1 );
-    zSig0 = estimateDiv128To64( aSig0, aSig1, zSig0<<32 ) + ( zSig0<<30 );
-    doubleZSig0 = zSig0<<1;
-    mul64To128( zSig0, zSig0, &term0, &term1 );
-    sub128( aSig0, aSig1, term0, term1, &rem0, &rem1 );
-    while ( (int64_t) rem0 < 0 ) {
-        --zSig0;
-        doubleZSig0 -= 2;
-        add128( rem0, rem1, zSig0>>63, doubleZSig0 | 1, &rem0, &rem1 );
-    }
-    zSig1 = estimateDiv128To64( rem1, 0, doubleZSig0 );
-    if ( ( zSig1 & 0x1FFF ) <= 5 ) {
-        if ( zSig1 == 0 ) zSig1 = 1;
-        mul64To128( doubleZSig0, zSig1, &term1, &term2 );
-        sub128( rem1, 0, term1, term2, &rem1, &rem2 );
-        mul64To128( zSig1, zSig1, &term2, &term3 );
-        sub192( rem1, rem2, 0, 0, term2, term3, &rem1, &rem2, &rem3 );
-        while ( (int64_t) rem1 < 0 ) {
-            --zSig1;
-            shortShift128Left( 0, zSig1, 1, &term2, &term3 );
-            term3 |= 1;
-            term2 |= doubleZSig0;
-            add192( rem1, rem2, rem3, 0, term2, term3, &rem1, &rem2, &rem3 );
-        }
-        zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 );
-    }
-    shift128ExtraRightJamming( zSig0, zSig1, 0, 14, &zSig0, &zSig1, &zSig2 );
-    return roundAndPackFloat128(0, zExp, zSig0, zSig1, zSig2, status);
-
-}
-
-static inline FloatRelation
-floatx80_compare_internal(floatx80 a, floatx80 b, bool is_quiet,
-                          float_status *status)
-{
-    bool aSign, bSign;
-
-    if (floatx80_invalid_encoding(a) || floatx80_invalid_encoding(b)) {
-        float_raise(float_flag_invalid, status);
-        return float_relation_unordered;
-    }
-    if (( ( extractFloatx80Exp( a ) == 0x7fff ) &&
-          ( extractFloatx80Frac( a )<<1 ) ) ||
-        ( ( extractFloatx80Exp( b ) == 0x7fff ) &&
-          ( extractFloatx80Frac( b )<<1 ) )) {
-        if (!is_quiet ||
-            floatx80_is_signaling_nan(a, status) ||
-            floatx80_is_signaling_nan(b, status)) {
-            float_raise(float_flag_invalid, status);
-        }
-        return float_relation_unordered;
-    }
-    aSign = extractFloatx80Sign( a );
-    bSign = extractFloatx80Sign( b );
-    if ( aSign != bSign ) {
-
-        if ( ( ( (uint16_t) ( ( a.high | b.high ) << 1 ) ) == 0) &&
-             ( ( a.low | b.low ) == 0 ) ) {
-            /* zero case */
-            return float_relation_equal;
-        } else {
-            return 1 - (2 * aSign);
-        }
-    } else {
-        /* Normalize pseudo-denormals before comparison.  */
-        if ((a.high & 0x7fff) == 0 && a.low & UINT64_C(0x8000000000000000)) {
-            ++a.high;
-        }
-        if ((b.high & 0x7fff) == 0 && b.low & UINT64_C(0x8000000000000000)) {
-            ++b.high;
-        }
-        if (a.low == b.low && a.high == b.high) {
-            return float_relation_equal;
-        } else {
-            return 1 - 2 * (aSign ^ ( lt128( a.high, a.low, b.high, b.low ) ));
-        }
-    }
-}
-
-FloatRelation floatx80_compare(floatx80 a, floatx80 b, float_status *status)
-{
-    return floatx80_compare_internal(a, b, 0, status);
-}
-
-FloatRelation floatx80_compare_quiet(floatx80 a, floatx80 b,
-                                     float_status *status)
-{
-    return floatx80_compare_internal(a, b, 1, status);
-}
-
-static inline FloatRelation
-float128_compare_internal(float128 a, float128 b, bool is_quiet,
-                          float_status *status)
-{
-    bool aSign, bSign;
-
-    if (( ( extractFloat128Exp( a ) == 0x7fff ) &&
-          ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) ||
-        ( ( extractFloat128Exp( b ) == 0x7fff ) &&
-          ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) )) {
-        if (!is_quiet ||
-            float128_is_signaling_nan(a, status) ||
-            float128_is_signaling_nan(b, status)) {
-            float_raise(float_flag_invalid, status);
-        }
-        return float_relation_unordered;
-    }
-    aSign = extractFloat128Sign( a );
-    bSign = extractFloat128Sign( b );
-    if ( aSign != bSign ) {
-        if ( ( ( ( a.high | b.high )<<1 ) | a.low | b.low ) == 0 ) {
-            /* zero case */
-            return float_relation_equal;
-        } else {
-            return 1 - (2 * aSign);
-        }
-    } else {
-        if (a.low == b.low && a.high == b.high) {
-            return float_relation_equal;
-        } else {
-            return 1 - 2 * (aSign ^ ( lt128( a.high, a.low, b.high, b.low ) ));
-        }
-    }
-}
-
-FloatRelation float128_compare(float128 a, float128 b, float_status *status)
-{
-    return float128_compare_internal(a, b, 0, status);
-}
-
-FloatRelation float128_compare_quiet(float128 a, float128 b,
-                                     float_status *status)
-{
-    return float128_compare_internal(a, b, 1, status);
-}
-
-floatx80 floatx80_scalbn(floatx80 a, int n, float_status *status)
-{
-    bool aSign;
-    int32_t aExp;
-    uint64_t aSig;
+    FloatParts128 p;
 
-    if (floatx80_invalid_encoding(a)) {
-        float_raise(float_flag_invalid, status);
+    if (!floatx80_unpack_canonical(&p, a, status)) {
         return floatx80_default_nan(status);
     }
-    aSig = extractFloatx80Frac( a );
-    aExp = extractFloatx80Exp( a );
-    aSign = extractFloatx80Sign( a );
-
-    if ( aExp == 0x7FFF ) {
-        if ( aSig<<1 ) {
-            return propagateFloatx80NaN(a, a, status);
-        }
-        return a;
-    }
-
-    if (aExp == 0) {
-        if (aSig == 0) {
-            return a;
-        }
-        aExp++;
-    }
-
-    if (n > 0x10000) {
-        n = 0x10000;
-    } else if (n < -0x10000) {
-        n = -0x10000;
-    }
-
-    aExp += n;
-    return normalizeRoundAndPackFloatx80(status->floatx80_rounding_precision,
-                                         aSign, aExp, aSig, 0, status);
-}
-
-float128 float128_scalbn(float128 a, int n, float_status *status)
-{
-    bool aSign;
-    int32_t aExp;
-    uint64_t aSig0, aSig1;
-
-    aSig1 = extractFloat128Frac1( a );
-    aSig0 = extractFloat128Frac0( a );
-    aExp = extractFloat128Exp( a );
-    aSign = extractFloat128Sign( a );
-    if ( aExp == 0x7FFF ) {
-        if ( aSig0 | aSig1 ) {
-            return propagateFloat128NaN(a, a, status);
-        }
-        return a;
-    }
-    if (aExp != 0) {
-        aSig0 |= UINT64_C(0x0001000000000000);
-    } else if (aSig0 == 0 && aSig1 == 0) {
-        return a;
-    } else {
-        aExp++;
-    }
-
-    if (n > 0x10000) {
-        n = 0x10000;
-    } else if (n < -0x10000) {
-        n = -0x10000;
-    }
-
-    aExp += n - 1;
-    return normalizeRoundAndPackFloat128( aSign, aExp, aSig0, aSig1
-                                         , status);
-
+    return floatx80_round_pack_canonical(&p, status);
 }
 
 static void __attribute__((constructor)) softfloat_init(void)
diff --git a/include/fpu/softfloat-helpers.h b/include/fpu/softfloat-helpers.h
index 2f0674fbdd..34f4cf92ae 100644
--- a/include/fpu/softfloat-helpers.h
+++ b/include/fpu/softfloat-helpers.h
@@ -69,7 +69,7 @@ static inline void set_float_exception_flags(int val, float_status *status)
     status->float_exception_flags = val;
 }
 
-static inline void set_floatx80_rounding_precision(int val,
+static inline void set_floatx80_rounding_precision(FloatX80RoundPrec val,
                                                    float_status *status)
 {
     status->floatx80_rounding_precision = val;
@@ -120,7 +120,8 @@ static inline int get_float_exception_flags(float_status *status)
     return status->float_exception_flags;
 }
 
-static inline int get_floatx80_rounding_precision(float_status *status)
+static inline FloatX80RoundPrec
+get_floatx80_rounding_precision(float_status *status)
 {
     return status->floatx80_rounding_precision;
 }
diff --git a/include/fpu/softfloat-macros.h b/include/fpu/softfloat-macros.h
index ec4e27a595..81c3fe8256 100644
--- a/include/fpu/softfloat-macros.h
+++ b/include/fpu/softfloat-macros.h
@@ -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
diff --git a/include/fpu/softfloat-types.h b/include/fpu/softfloat-types.h
index 3b757c3d6a..5bcbd041f7 100644
--- a/include/fpu/softfloat-types.h
+++ b/include/fpu/softfloat-types.h
@@ -154,6 +154,14 @@ enum {
     float_flag_output_denormal = 128
 };
 
+/*
+ * Rounding precision for floatx80.
+ */
+typedef enum __attribute__((__packed__)) {
+    floatx80_precision_x,
+    floatx80_precision_d,
+    floatx80_precision_s,
+} FloatX80RoundPrec;
 
 /*
  * Floating Point Status. Individual architectures may maintain
@@ -165,7 +173,7 @@ enum {
 typedef struct float_status {
     FloatRoundMode float_rounding_mode;
     uint8_t     float_exception_flags;
-    signed char floatx80_rounding_precision;
+    FloatX80RoundPrec floatx80_rounding_precision;
     bool tininess_before_rounding;
     /* should denormalised results go to zero and set the inexact flag? */
     bool flush_to_zero;
diff --git a/include/fpu/softfloat.h b/include/fpu/softfloat.h
index 53f2c2ea3c..ec7dca0960 100644
--- a/include/fpu/softfloat.h
+++ b/include/fpu/softfloat.h
@@ -1152,7 +1152,7 @@ floatx80 propagateFloatx80NaN(floatx80 a, floatx80 b, float_status *status);
 | Floating-Point Arithmetic.
 *----------------------------------------------------------------------------*/
 
-floatx80 roundAndPackFloatx80(int8_t roundingPrecision, bool zSign,
+floatx80 roundAndPackFloatx80(FloatX80RoundPrec roundingPrecision, bool zSign,
                               int32_t zExp, uint64_t zSig0, uint64_t zSig1,
                               float_status *status);
 
@@ -1165,7 +1165,7 @@ floatx80 roundAndPackFloatx80(int8_t roundingPrecision, bool zSign,
 | normalized.
 *----------------------------------------------------------------------------*/
 
-floatx80 normalizeRoundAndPackFloatx80(int8_t roundingPrecision,
+floatx80 normalizeRoundAndPackFloatx80(FloatX80RoundPrec roundingPrecision,
                                        bool zSign, int32_t zExp,
                                        uint64_t zSig0, uint64_t zSig1,
                                        float_status *status);
@@ -1204,6 +1204,12 @@ float128 float128_rem(float128, float128, float_status *status);
 float128 float128_sqrt(float128, float_status *status);
 FloatRelation float128_compare(float128, float128, float_status *status);
 FloatRelation float128_compare_quiet(float128, float128, float_status *status);
+float128 float128_min(float128, float128, float_status *status);
+float128 float128_max(float128, float128, float_status *status);
+float128 float128_minnum(float128, float128, float_status *status);
+float128 float128_maxnum(float128, float128, float_status *status);
+float128 float128_minnummag(float128, float128, float_status *status);
+float128 float128_maxnummag(float128, float128, float_status *status);
 bool float128_is_quiet_nan(float128, float_status *status);
 bool float128_is_signaling_nan(float128, float_status *status);
 float128 float128_silence_nan(float128, float_status *status);
diff --git a/linux-user/arm/nwfpe/fpa11.c b/linux-user/arm/nwfpe/fpa11.c
index f6f8163eab..9a93610d24 100644
--- a/linux-user/arm/nwfpe/fpa11.c
+++ b/linux-user/arm/nwfpe/fpa11.c
@@ -97,37 +97,38 @@ void SetRoundingMode(const unsigned int opcode)
 
 void SetRoundingPrecision(const unsigned int opcode)
 {
-    int rounding_precision;
-   FPA11 *fpa11 = GET_FPA11();
+    FloatX80RoundPrec rounding_precision;
+    FPA11 *fpa11 = GET_FPA11();
 #ifdef MAINTAIN_FPCR
-   fpa11->fpcr &= ~MASK_ROUNDING_PRECISION;
+    fpa11->fpcr &= ~MASK_ROUNDING_PRECISION;
 #endif
-   switch (opcode & MASK_ROUNDING_PRECISION)
-   {
-      case ROUND_SINGLE:
-         rounding_precision = 32;
+    switch (opcode & MASK_ROUNDING_PRECISION) {
+    case ROUND_SINGLE:
+        rounding_precision = floatx80_precision_s;
 #ifdef MAINTAIN_FPCR
-         fpa11->fpcr |= ROUND_SINGLE;
+        fpa11->fpcr |= ROUND_SINGLE;
 #endif
-      break;
+        break;
 
-      case ROUND_DOUBLE:
-         rounding_precision = 64;
+    case ROUND_DOUBLE:
+        rounding_precision = floatx80_precision_d;
 #ifdef MAINTAIN_FPCR
-         fpa11->fpcr |= ROUND_DOUBLE;
+        fpa11->fpcr |= ROUND_DOUBLE;
 #endif
-      break;
+        break;
 
-      case ROUND_EXTENDED:
-         rounding_precision = 80;
+    case ROUND_EXTENDED:
+        rounding_precision = floatx80_precision_x;
 #ifdef MAINTAIN_FPCR
-         fpa11->fpcr |= ROUND_EXTENDED;
+        fpa11->fpcr |= ROUND_EXTENDED;
 #endif
-      break;
+        break;
 
-      default: rounding_precision = 80;
-  }
-   set_floatx80_rounding_precision(rounding_precision, &fpa11->fp_status);
+    default:
+        rounding_precision = floatx80_precision_x;
+        break;
+    }
+    set_floatx80_rounding_precision(rounding_precision, &fpa11->fp_status);
 }
 
 /* Emulate the instruction in the opcode. */
diff --git a/target/i386/tcg/fpu_helper.c b/target/i386/tcg/fpu_helper.c
index 1b30f1bb73..4e11965067 100644
--- a/target/i386/tcg/fpu_helper.c
+++ b/target/i386/tcg/fpu_helper.c
@@ -673,38 +673,40 @@ uint32_t helper_fnstcw(CPUX86State *env)
 
 void update_fp_status(CPUX86State *env)
 {
-    int rnd_type;
+    FloatRoundMode rnd_mode;
+    FloatX80RoundPrec rnd_prec;
 
     /* set rounding mode */
     switch (env->fpuc & FPU_RC_MASK) {
     default:
     case FPU_RC_NEAR:
-        rnd_type = float_round_nearest_even;
+        rnd_mode = float_round_nearest_even;
         break;
     case FPU_RC_DOWN:
-        rnd_type = float_round_down;
+        rnd_mode = float_round_down;
         break;
     case FPU_RC_UP:
-        rnd_type = float_round_up;
+        rnd_mode = float_round_up;
         break;
     case FPU_RC_CHOP:
-        rnd_type = float_round_to_zero;
+        rnd_mode = float_round_to_zero;
         break;
     }
-    set_float_rounding_mode(rnd_type, &env->fp_status);
+    set_float_rounding_mode(rnd_mode, &env->fp_status);
+
     switch ((env->fpuc >> 8) & 3) {
     case 0:
-        rnd_type = 32;
+        rnd_prec = floatx80_precision_s;
         break;
     case 2:
-        rnd_type = 64;
+        rnd_prec = floatx80_precision_d;
         break;
     case 3:
     default:
-        rnd_type = 80;
+        rnd_prec = floatx80_precision_x;
         break;
     }
-    set_floatx80_rounding_precision(rnd_type, &env->fp_status);
+    set_floatx80_rounding_precision(rnd_prec, &env->fp_status);
 }
 
 void helper_fldcw(CPUX86State *env, uint32_t val)
@@ -1074,7 +1076,8 @@ void helper_f2xm1(CPUX86State *env)
                             &sig2);
             /* This result is inexact.  */
             sig1 |= 1;
-            ST0 = normalizeRoundAndPackFloatx80(80, sign, exp, sig0, sig1,
+            ST0 = normalizeRoundAndPackFloatx80(floatx80_precision_x,
+                                                sign, exp, sig0, sig1,
                                                 &env->fp_status);
         }
     } else {
@@ -1083,9 +1086,10 @@ void helper_f2xm1(CPUX86State *env)
         int32_t n, aexp, bexp;
         uint64_t asig0, asig1, asig2, bsig0, bsig1;
         FloatRoundMode save_mode = env->fp_status.float_rounding_mode;
-        signed char save_prec = env->fp_status.floatx80_rounding_precision;
+        FloatX80RoundPrec save_prec =
+            env->fp_status.floatx80_rounding_precision;
         env->fp_status.float_rounding_mode = float_round_nearest_even;
-        env->fp_status.floatx80_rounding_precision = 80;
+        env->fp_status.floatx80_rounding_precision = floatx80_precision_x;
 
         /* Find the nearest multiple of 1/32 to the argument.  */
         tmp = floatx80_scalbn(ST0, 5, &env->fp_status);
@@ -1183,7 +1187,8 @@ void helper_f2xm1(CPUX86State *env)
             env->fp_status.float_rounding_mode = save_mode;
             /* This result is inexact.  */
             asig1 |= 1;
-            ST0 = normalizeRoundAndPackFloatx80(80, asign, aexp, asig0, asig1,
+            ST0 = normalizeRoundAndPackFloatx80(floatx80_precision_x,
+                                                asign, aexp, asig0, asig1,
                                                 &env->fp_status);
         }
 
@@ -1301,8 +1306,9 @@ void helper_fpatan(CPUX86State *env)
          * division is exact, the result of fpatan is still inexact
          * (and underflowing where appropriate).
          */
-        signed char save_prec = env->fp_status.floatx80_rounding_precision;
-        env->fp_status.floatx80_rounding_precision = 80;
+        FloatX80RoundPrec save_prec =
+            env->fp_status.floatx80_rounding_precision;
+        env->fp_status.floatx80_rounding_precision = floatx80_precision_x;
         ST1 = floatx80_div(ST1, ST0, &env->fp_status);
         env->fp_status.floatx80_rounding_precision = save_prec;
         if (!floatx80_is_zero(ST1) &&
@@ -1321,7 +1327,8 @@ void helper_fpatan(CPUX86State *env)
             if (exp == 0) {
                 normalizeFloatx80Subnormal(sig, &exp, &sig);
             }
-            ST1 = normalizeRoundAndPackFloatx80(80, sign, exp, sig - 1,
+            ST1 = normalizeRoundAndPackFloatx80(floatx80_precision_x,
+                                                sign, exp, sig - 1,
                                                 -1, &env->fp_status);
         }
     } else {
@@ -1377,9 +1384,10 @@ void helper_fpatan(CPUX86State *env)
             uint64_t azsig2, azsig3, axsig0, axsig1;
             floatx80 x8;
             FloatRoundMode save_mode = env->fp_status.float_rounding_mode;
-            signed char save_prec = env->fp_status.floatx80_rounding_precision;
+            FloatX80RoundPrec save_prec =
+                env->fp_status.floatx80_rounding_precision;
             env->fp_status.float_rounding_mode = float_round_nearest_even;
-            env->fp_status.floatx80_rounding_precision = 80;
+            env->fp_status.floatx80_rounding_precision = floatx80_precision_x;
 
             if (arg0_exp == 0) {
                 normalizeFloatx80Subnormal(arg0_sig, &arg0_exp, &arg0_sig);
@@ -1448,7 +1456,8 @@ void helper_fpatan(CPUX86State *env)
              * Split x as x = t + y, where t = n/8 is the nearest
              * multiple of 1/8 to x.
              */
-            x8 = normalizeRoundAndPackFloatx80(80, false, xexp + 3, xsig0,
+            x8 = normalizeRoundAndPackFloatx80(floatx80_precision_x,
+                                               false, xexp + 3, xsig0,
                                                xsig1, &env->fp_status);
             n = floatx80_to_int32(x8, &env->fp_status);
             if (n == 0) {
@@ -1569,7 +1578,7 @@ void helper_fpatan(CPUX86State *env)
                 /* Compute z^2.  */
                 mul128To256(zsig0, zsig1, zsig0, zsig1,
                             &z2sig0, &z2sig1, &z2sig2, &z2sig3);
-                z2 = normalizeRoundAndPackFloatx80(80, false,
+                z2 = normalizeRoundAndPackFloatx80(floatx80_precision_x, false,
                                                    zexp + zexp - 0x3ffe,
                                                    z2sig0, z2sig1,
                                                    &env->fp_status);
@@ -1689,7 +1698,7 @@ void helper_fpatan(CPUX86State *env)
         }
         /* This result is inexact.  */
         rsig1 |= 1;
-        ST1 = normalizeRoundAndPackFloatx80(80, rsign, rexp,
+        ST1 = normalizeRoundAndPackFloatx80(floatx80_precision_x, rsign, rexp,
                                             rsig0, rsig1, &env->fp_status);
     }
 
@@ -1890,7 +1899,8 @@ static void helper_fyl2x_common(CPUX86State *env, floatx80 arg, int32_t *exp,
      */
     mul128To256(tsig0, tsig1, tsig0, tsig1,
                 &t2sig0, &t2sig1, &t2sig2, &t2sig3);
-    t2 = normalizeRoundAndPackFloatx80(80, false, texp + texp - 0x3ffe,
+    t2 = normalizeRoundAndPackFloatx80(floatx80_precision_x, false,
+                                       texp + texp - 0x3ffe,
                                        t2sig0, t2sig1, &env->fp_status);
 
     /* Compute the lower parts of the polynomial expansion.  */
@@ -2004,15 +2014,17 @@ void helper_fyl2xp1(CPUX86State *env)
         exp += arg1_exp - 0x3ffe;
         /* This result is inexact.  */
         sig1 |= 1;
-        ST1 = normalizeRoundAndPackFloatx80(80, arg0_sign ^ arg1_sign, exp,
+        ST1 = normalizeRoundAndPackFloatx80(floatx80_precision_x,
+                                            arg0_sign ^ arg1_sign, exp,
                                             sig0, sig1, &env->fp_status);
     } else {
         int32_t aexp;
         uint64_t asig0, asig1, asig2;
         FloatRoundMode save_mode = env->fp_status.float_rounding_mode;
-        signed char save_prec = env->fp_status.floatx80_rounding_precision;
+        FloatX80RoundPrec save_prec =
+            env->fp_status.floatx80_rounding_precision;
         env->fp_status.float_rounding_mode = float_round_nearest_even;
-        env->fp_status.floatx80_rounding_precision = 80;
+        env->fp_status.floatx80_rounding_precision = floatx80_precision_x;
 
         helper_fyl2x_common(env, ST0, &aexp, &asig0, &asig1);
         /*
@@ -2027,7 +2039,8 @@ void helper_fyl2xp1(CPUX86State *env)
         /* This result is inexact.  */
         asig1 |= 1;
         env->fp_status.float_rounding_mode = save_mode;
-        ST1 = normalizeRoundAndPackFloatx80(80, arg0_sign ^ arg1_sign, aexp,
+        ST1 = normalizeRoundAndPackFloatx80(floatx80_precision_x,
+                                            arg0_sign ^ arg1_sign, aexp,
                                             asig0, asig1, &env->fp_status);
         env->fp_status.floatx80_rounding_precision = save_prec;
     }
@@ -2111,9 +2124,10 @@ void helper_fyl2x(CPUX86State *env)
         int32_t int_exp;
         floatx80 arg0_m1;
         FloatRoundMode save_mode = env->fp_status.float_rounding_mode;
-        signed char save_prec = env->fp_status.floatx80_rounding_precision;
+        FloatX80RoundPrec save_prec =
+            env->fp_status.floatx80_rounding_precision;
         env->fp_status.float_rounding_mode = float_round_nearest_even;
-        env->fp_status.floatx80_rounding_precision = 80;
+        env->fp_status.floatx80_rounding_precision = floatx80_precision_x;
 
         if (arg0_exp == 0) {
             normalizeFloatx80Subnormal(arg0_sig, &arg0_exp, &arg0_sig);
@@ -2170,7 +2184,8 @@ void helper_fyl2x(CPUX86State *env)
             /* This result is inexact.  */
             asig1 |= 1;
             env->fp_status.float_rounding_mode = save_mode;
-            ST1 = normalizeRoundAndPackFloatx80(80, asign ^ arg1_sign, aexp,
+            ST1 = normalizeRoundAndPackFloatx80(floatx80_precision_x,
+                                                asign ^ arg1_sign, aexp,
                                                 asig0, asig1, &env->fp_status);
         }
 
@@ -2252,12 +2267,12 @@ void helper_fscale(CPUX86State *env)
         }
     } else {
         int n;
-        signed char save = env->fp_status.floatx80_rounding_precision;
+        FloatX80RoundPrec save = env->fp_status.floatx80_rounding_precision;
         uint8_t save_flags = get_float_exception_flags(&env->fp_status);
         set_float_exception_flags(0, &env->fp_status);
         n = floatx80_to_int32_round_to_zero(ST1, &env->fp_status);
         set_float_exception_flags(save_flags, &env->fp_status);
-        env->fp_status.floatx80_rounding_precision = 80;
+        env->fp_status.floatx80_rounding_precision = floatx80_precision_x;
         ST0 = floatx80_scalbn(ST0, n, &env->fp_status);
         env->fp_status.floatx80_rounding_precision = save;
     }
diff --git a/target/m68k/fpu_helper.c b/target/m68k/fpu_helper.c
index 797000e748..fdc4937e29 100644
--- a/target/m68k/fpu_helper.c
+++ b/target/m68k/fpu_helper.c
@@ -94,13 +94,13 @@ static void m68k_restore_precision_mode(CPUM68KState *env)
 {
     switch (env->fpcr & FPCR_PREC_MASK) {
     case FPCR_PREC_X: /* extended */
-        set_floatx80_rounding_precision(80, &env->fp_status);
+        set_floatx80_rounding_precision(floatx80_precision_x, &env->fp_status);
         break;
     case FPCR_PREC_S: /* single */
-        set_floatx80_rounding_precision(32, &env->fp_status);
+        set_floatx80_rounding_precision(floatx80_precision_s, &env->fp_status);
         break;
     case FPCR_PREC_D: /* double */
-        set_floatx80_rounding_precision(64, &env->fp_status);
+        set_floatx80_rounding_precision(floatx80_precision_d, &env->fp_status);
         break;
     case FPCR_PREC_U: /* undefined */
     default:
@@ -111,9 +111,9 @@ static void m68k_restore_precision_mode(CPUM68KState *env)
 static void cf_restore_precision_mode(CPUM68KState *env)
 {
     if (env->fpcr & FPCR_PREC_S) { /* single */
-        set_floatx80_rounding_precision(32, &env->fp_status);
+        set_floatx80_rounding_precision(floatx80_precision_s, &env->fp_status);
     } else { /* double */
-        set_floatx80_rounding_precision(64, &env->fp_status);
+        set_floatx80_rounding_precision(floatx80_precision_d, &env->fp_status);
     }
 }
 
@@ -166,8 +166,8 @@ void HELPER(set_fpcr)(CPUM68KState *env, uint32_t val)
 
 #define PREC_BEGIN(prec)                                        \
     do {                                                        \
-        int old;                                                \
-        old = get_floatx80_rounding_precision(&env->fp_status); \
+        FloatX80RoundPrec old =                                 \
+            get_floatx80_rounding_precision(&env->fp_status);   \
         set_floatx80_rounding_precision(prec, &env->fp_status)  \
 
 #define PREC_END()                                              \
@@ -176,14 +176,14 @@ void HELPER(set_fpcr)(CPUM68KState *env, uint32_t val)
 
 void HELPER(fsround)(CPUM68KState *env, FPReg *res, FPReg *val)
 {
-    PREC_BEGIN(32);
+    PREC_BEGIN(floatx80_precision_s);
     res->d = floatx80_round(val->d, &env->fp_status);
     PREC_END();
 }
 
 void HELPER(fdround)(CPUM68KState *env, FPReg *res, FPReg *val)
 {
-    PREC_BEGIN(64);
+    PREC_BEGIN(floatx80_precision_d);
     res->d = floatx80_round(val->d, &env->fp_status);
     PREC_END();
 }
@@ -195,14 +195,14 @@ void HELPER(fsqrt)(CPUM68KState *env, FPReg *res, FPReg *val)
 
 void HELPER(fssqrt)(CPUM68KState *env, FPReg *res, FPReg *val)
 {
-    PREC_BEGIN(32);
+    PREC_BEGIN(floatx80_precision_s);
     res->d = floatx80_sqrt(val->d, &env->fp_status);
     PREC_END();
 }
 
 void HELPER(fdsqrt)(CPUM68KState *env, FPReg *res, FPReg *val)
 {
-    PREC_BEGIN(64);
+    PREC_BEGIN(floatx80_precision_d);
     res->d = floatx80_sqrt(val->d, &env->fp_status);
     PREC_END();
 }
@@ -214,14 +214,14 @@ void HELPER(fabs)(CPUM68KState *env, FPReg *res, FPReg *val)
 
 void HELPER(fsabs)(CPUM68KState *env, FPReg *res, FPReg *val)
 {
-    PREC_BEGIN(32);
+    PREC_BEGIN(floatx80_precision_s);
     res->d = floatx80_round(floatx80_abs(val->d), &env->fp_status);
     PREC_END();
 }
 
 void HELPER(fdabs)(CPUM68KState *env, FPReg *res, FPReg *val)
 {
-    PREC_BEGIN(64);
+    PREC_BEGIN(floatx80_precision_d);
     res->d = floatx80_round(floatx80_abs(val->d), &env->fp_status);
     PREC_END();
 }
@@ -233,14 +233,14 @@ void HELPER(fneg)(CPUM68KState *env, FPReg *res, FPReg *val)
 
 void HELPER(fsneg)(CPUM68KState *env, FPReg *res, FPReg *val)
 {
-    PREC_BEGIN(32);
+    PREC_BEGIN(floatx80_precision_s);
     res->d = floatx80_round(floatx80_chs(val->d), &env->fp_status);
     PREC_END();
 }
 
 void HELPER(fdneg)(CPUM68KState *env, FPReg *res, FPReg *val)
 {
-    PREC_BEGIN(64);
+    PREC_BEGIN(floatx80_precision_d);
     res->d = floatx80_round(floatx80_chs(val->d), &env->fp_status);
     PREC_END();
 }
@@ -252,14 +252,14 @@ void HELPER(fadd)(CPUM68KState *env, FPReg *res, FPReg *val0, FPReg *val1)
 
 void HELPER(fsadd)(CPUM68KState *env, FPReg *res, FPReg *val0, FPReg *val1)
 {
-    PREC_BEGIN(32);
+    PREC_BEGIN(floatx80_precision_s);
     res->d = floatx80_add(val0->d, val1->d, &env->fp_status);
     PREC_END();
 }
 
 void HELPER(fdadd)(CPUM68KState *env, FPReg *res, FPReg *val0, FPReg *val1)
 {
-    PREC_BEGIN(64);
+    PREC_BEGIN(floatx80_precision_d);
     res->d = floatx80_add(val0->d, val1->d, &env->fp_status);
     PREC_END();
 }
@@ -271,14 +271,14 @@ void HELPER(fsub)(CPUM68KState *env, FPReg *res, FPReg *val0, FPReg *val1)
 
 void HELPER(fssub)(CPUM68KState *env, FPReg *res, FPReg *val0, FPReg *val1)
 {
-    PREC_BEGIN(32);
+    PREC_BEGIN(floatx80_precision_s);
     res->d = floatx80_sub(val1->d, val0->d, &env->fp_status);
     PREC_END();
 }
 
 void HELPER(fdsub)(CPUM68KState *env, FPReg *res, FPReg *val0, FPReg *val1)
 {
-    PREC_BEGIN(64);
+    PREC_BEGIN(floatx80_precision_d);
     res->d = floatx80_sub(val1->d, val0->d, &env->fp_status);
     PREC_END();
 }
@@ -290,14 +290,14 @@ void HELPER(fmul)(CPUM68KState *env, FPReg *res, FPReg *val0, FPReg *val1)
 
 void HELPER(fsmul)(CPUM68KState *env, FPReg *res, FPReg *val0, FPReg *val1)
 {
-    PREC_BEGIN(32);
+    PREC_BEGIN(floatx80_precision_s);
     res->d = floatx80_mul(val0->d, val1->d, &env->fp_status);
     PREC_END();
 }
 
 void HELPER(fdmul)(CPUM68KState *env, FPReg *res, FPReg *val0, FPReg *val1)
 {
-    PREC_BEGIN(64);
+    PREC_BEGIN(floatx80_precision_d);
     res->d = floatx80_mul(val0->d, val1->d, &env->fp_status);
     PREC_END();
 }
@@ -307,7 +307,7 @@ void HELPER(fsglmul)(CPUM68KState *env, FPReg *res, FPReg *val0, FPReg *val1)
     FloatRoundMode rounding_mode = get_float_rounding_mode(&env->fp_status);
     floatx80 a, b;
 
-    PREC_BEGIN(32);
+    PREC_BEGIN(floatx80_precision_s);
     set_float_rounding_mode(float_round_to_zero, &env->fp_status);
     a = floatx80_round(val0->d, &env->fp_status);
     b = floatx80_round(val1->d, &env->fp_status);
@@ -323,14 +323,14 @@ void HELPER(fdiv)(CPUM68KState *env, FPReg *res, FPReg *val0, FPReg *val1)
 
 void HELPER(fsdiv)(CPUM68KState *env, FPReg *res, FPReg *val0, FPReg *val1)
 {
-    PREC_BEGIN(32);
+    PREC_BEGIN(floatx80_precision_s);
     res->d = floatx80_div(val1->d, val0->d, &env->fp_status);
     PREC_END();
 }
 
 void HELPER(fddiv)(CPUM68KState *env, FPReg *res, FPReg *val0, FPReg *val1)
 {
-    PREC_BEGIN(64);
+    PREC_BEGIN(floatx80_precision_d);
     res->d = floatx80_div(val1->d, val0->d, &env->fp_status);
     PREC_END();
 }
@@ -340,7 +340,7 @@ void HELPER(fsgldiv)(CPUM68KState *env, FPReg *res, FPReg *val0, FPReg *val1)
     FloatRoundMode rounding_mode = get_float_rounding_mode(&env->fp_status);
     floatx80 a, b;
 
-    PREC_BEGIN(32);
+    PREC_BEGIN(floatx80_precision_s);
     set_float_rounding_mode(float_round_to_zero, &env->fp_status);
     a = floatx80_round(val1->d, &env->fp_status);
     b = floatx80_round(val0->d, &env->fp_status);
diff --git a/target/m68k/softfloat.c b/target/m68k/softfloat.c
index b6d0ed7acf..02dcc03d15 100644
--- a/target/m68k/softfloat.c
+++ b/target/m68k/softfloat.c
@@ -227,7 +227,8 @@ floatx80 floatx80_lognp1(floatx80 a, float_status *status)
     int32_t aExp;
     uint64_t aSig, fSig;
 
-    int8_t user_rnd_mode, user_rnd_prec;
+    FloatRoundMode user_rnd_mode;
+    FloatX80RoundPrec user_rnd_prec;
 
     int32_t compact, j, k;
     floatx80 fp0, fp1, fp2, fp3, f, logof2, klog2, saveu;
@@ -270,7 +271,7 @@ floatx80 floatx80_lognp1(floatx80 a, float_status *status)
     user_rnd_mode = status->float_rounding_mode;
     user_rnd_prec = status->floatx80_rounding_precision;
     status->float_rounding_mode = float_round_nearest_even;
-    status->floatx80_rounding_precision = 80;
+    status->floatx80_rounding_precision = floatx80_precision_x;
 
     compact = floatx80_make_compact(aExp, aSig);
 
@@ -426,7 +427,8 @@ floatx80 floatx80_logn(floatx80 a, float_status *status)
     int32_t aExp;
     uint64_t aSig, fSig;
 
-    int8_t user_rnd_mode, user_rnd_prec;
+    FloatRoundMode user_rnd_mode;
+    FloatX80RoundPrec user_rnd_prec;
 
     int32_t compact, j, k, adjk;
     floatx80 fp0, fp1, fp2, fp3, f, logof2, klog2, saveu;
@@ -469,7 +471,7 @@ floatx80 floatx80_logn(floatx80 a, float_status *status)
     user_rnd_mode = status->float_rounding_mode;
     user_rnd_prec = status->floatx80_rounding_precision;
     status->float_rounding_mode = float_round_nearest_even;
-    status->floatx80_rounding_precision = 80;
+    status->floatx80_rounding_precision = floatx80_precision_x;
 
     compact = floatx80_make_compact(aExp, aSig);
 
@@ -594,7 +596,8 @@ floatx80 floatx80_log10(floatx80 a, float_status *status)
     int32_t aExp;
     uint64_t aSig;
 
-    int8_t user_rnd_mode, user_rnd_prec;
+    FloatRoundMode user_rnd_mode;
+    FloatX80RoundPrec user_rnd_prec;
 
     floatx80 fp0, fp1;
 
@@ -626,7 +629,7 @@ floatx80 floatx80_log10(floatx80 a, float_status *status)
     user_rnd_mode = status->float_rounding_mode;
     user_rnd_prec = status->floatx80_rounding_precision;
     status->float_rounding_mode = float_round_nearest_even;
-    status->floatx80_rounding_precision = 80;
+    status->floatx80_rounding_precision = floatx80_precision_x;
 
     fp0 = floatx80_logn(a, status);
     fp1 = packFloatx80(0, 0x3FFD, UINT64_C(0xDE5BD8A937287195)); /* INV_L10 */
@@ -651,7 +654,8 @@ floatx80 floatx80_log2(floatx80 a, float_status *status)
     int32_t aExp;
     uint64_t aSig;
 
-    int8_t user_rnd_mode, user_rnd_prec;
+    FloatRoundMode user_rnd_mode;
+    FloatX80RoundPrec user_rnd_prec;
 
     floatx80 fp0, fp1;
 
@@ -686,7 +690,7 @@ floatx80 floatx80_log2(floatx80 a, float_status *status)
     user_rnd_mode = status->float_rounding_mode;
     user_rnd_prec = status->floatx80_rounding_precision;
     status->float_rounding_mode = float_round_nearest_even;
-    status->floatx80_rounding_precision = 80;
+    status->floatx80_rounding_precision = floatx80_precision_x;
 
     if (aSig == one_sig) { /* X is 2^k */
         status->float_rounding_mode = user_rnd_mode;
@@ -718,7 +722,8 @@ floatx80 floatx80_etox(floatx80 a, float_status *status)
     int32_t aExp;
     uint64_t aSig;
 
-    int8_t user_rnd_mode, user_rnd_prec;
+    FloatRoundMode user_rnd_mode;
+    FloatX80RoundPrec user_rnd_prec;
 
     int32_t compact, n, j, k, m, m1;
     floatx80 fp0, fp1, fp2, fp3, l2, scale, adjscale;
@@ -746,7 +751,7 @@ floatx80 floatx80_etox(floatx80 a, float_status *status)
     user_rnd_mode = status->float_rounding_mode;
     user_rnd_prec = status->floatx80_rounding_precision;
     status->float_rounding_mode = float_round_nearest_even;
-    status->floatx80_rounding_precision = 80;
+    status->floatx80_rounding_precision = floatx80_precision_x;
 
     adjflag = 0;
 
@@ -902,7 +907,8 @@ floatx80 floatx80_twotox(floatx80 a, float_status *status)
     int32_t aExp;
     uint64_t aSig;
 
-    int8_t user_rnd_mode, user_rnd_prec;
+    FloatRoundMode user_rnd_mode;
+    FloatX80RoundPrec user_rnd_prec;
 
     int32_t compact, n, j, l, m, m1;
     floatx80 fp0, fp1, fp2, fp3, adjfact, fact1, fact2;
@@ -929,7 +935,7 @@ floatx80 floatx80_twotox(floatx80 a, float_status *status)
     user_rnd_mode = status->float_rounding_mode;
     user_rnd_prec = status->floatx80_rounding_precision;
     status->float_rounding_mode = float_round_nearest_even;
-    status->floatx80_rounding_precision = 80;
+    status->floatx80_rounding_precision = floatx80_precision_x;
 
     fp0 = a;
 
@@ -1052,7 +1058,8 @@ floatx80 floatx80_tentox(floatx80 a, float_status *status)
     int32_t aExp;
     uint64_t aSig;
 
-    int8_t user_rnd_mode, user_rnd_prec;
+    FloatRoundMode user_rnd_mode;
+    FloatX80RoundPrec user_rnd_prec;
 
     int32_t compact, n, j, l, m, m1;
     floatx80 fp0, fp1, fp2, fp3, adjfact, fact1, fact2;
@@ -1079,7 +1086,7 @@ floatx80 floatx80_tentox(floatx80 a, float_status *status)
     user_rnd_mode = status->float_rounding_mode;
     user_rnd_prec = status->floatx80_rounding_precision;
     status->float_rounding_mode = float_round_nearest_even;
-    status->floatx80_rounding_precision = 80;
+    status->floatx80_rounding_precision = floatx80_precision_x;
 
     fp0 = a;
 
@@ -1207,7 +1214,8 @@ floatx80 floatx80_tan(floatx80 a, float_status *status)
     int32_t aExp, xExp;
     uint64_t aSig, xSig;
 
-    int8_t user_rnd_mode, user_rnd_prec;
+    FloatRoundMode user_rnd_mode;
+    FloatX80RoundPrec user_rnd_prec;
 
     int32_t compact, l, n, j;
     floatx80 fp0, fp1, fp2, fp3, fp4, fp5, invtwopi, twopi1, twopi2;
@@ -1233,7 +1241,7 @@ floatx80 floatx80_tan(floatx80 a, float_status *status)
     user_rnd_mode = status->float_rounding_mode;
     user_rnd_prec = status->floatx80_rounding_precision;
     status->float_rounding_mode = float_round_nearest_even;
-    status->floatx80_rounding_precision = 80;
+    status->floatx80_rounding_precision = floatx80_precision_x;
 
     compact = floatx80_make_compact(aExp, aSig);
 
@@ -1417,7 +1425,8 @@ floatx80 floatx80_sin(floatx80 a, float_status *status)
     int32_t aExp, xExp;
     uint64_t aSig, xSig;
 
-    int8_t user_rnd_mode, user_rnd_prec;
+    FloatRoundMode user_rnd_mode;
+    FloatX80RoundPrec user_rnd_prec;
 
     int32_t compact, l, n, j;
     floatx80 fp0, fp1, fp2, fp3, fp4, fp5, x, invtwopi, twopi1, twopi2;
@@ -1443,7 +1452,7 @@ floatx80 floatx80_sin(floatx80 a, float_status *status)
     user_rnd_mode = status->float_rounding_mode;
     user_rnd_prec = status->floatx80_rounding_precision;
     status->float_rounding_mode = float_round_nearest_even;
-    status->floatx80_rounding_precision = 80;
+    status->floatx80_rounding_precision = floatx80_precision_x;
 
     compact = floatx80_make_compact(aExp, aSig);
 
@@ -1656,7 +1665,8 @@ floatx80 floatx80_cos(floatx80 a, float_status *status)
     int32_t aExp, xExp;
     uint64_t aSig, xSig;
 
-    int8_t user_rnd_mode, user_rnd_prec;
+    FloatRoundMode user_rnd_mode;
+    FloatX80RoundPrec user_rnd_prec;
 
     int32_t compact, l, n, j;
     floatx80 fp0, fp1, fp2, fp3, fp4, fp5, x, invtwopi, twopi1, twopi2;
@@ -1682,7 +1692,7 @@ floatx80 floatx80_cos(floatx80 a, float_status *status)
     user_rnd_mode = status->float_rounding_mode;
     user_rnd_prec = status->floatx80_rounding_precision;
     status->float_rounding_mode = float_round_nearest_even;
-    status->floatx80_rounding_precision = 80;
+    status->floatx80_rounding_precision = floatx80_precision_x;
 
     compact = floatx80_make_compact(aExp, aSig);
 
@@ -1893,7 +1903,8 @@ floatx80 floatx80_atan(floatx80 a, float_status *status)
     int32_t aExp;
     uint64_t aSig;
 
-    int8_t user_rnd_mode, user_rnd_prec;
+    FloatRoundMode user_rnd_mode;
+    FloatX80RoundPrec user_rnd_prec;
 
     int32_t compact, tbl_index;
     floatx80 fp0, fp1, fp2, fp3, xsave;
@@ -1920,7 +1931,7 @@ floatx80 floatx80_atan(floatx80 a, float_status *status)
     user_rnd_mode = status->float_rounding_mode;
     user_rnd_prec = status->floatx80_rounding_precision;
     status->float_rounding_mode = float_round_nearest_even;
-    status->floatx80_rounding_precision = 80;
+    status->floatx80_rounding_precision = floatx80_precision_x;
 
     if (compact < 0x3FFB8000 || compact > 0x4002FFFF) {
         /* |X| >= 16 or |X| < 1/16 */
@@ -2090,7 +2101,8 @@ floatx80 floatx80_asin(floatx80 a, float_status *status)
     int32_t aExp;
     uint64_t aSig;
 
-    int8_t user_rnd_mode, user_rnd_prec;
+    FloatRoundMode user_rnd_mode;
+    FloatX80RoundPrec user_rnd_prec;
 
     int32_t compact;
     floatx80 fp0, fp1, fp2, one;
@@ -2124,7 +2136,7 @@ floatx80 floatx80_asin(floatx80 a, float_status *status)
     user_rnd_mode = status->float_rounding_mode;
     user_rnd_prec = status->floatx80_rounding_precision;
     status->float_rounding_mode = float_round_nearest_even;
-    status->floatx80_rounding_precision = 80;
+    status->floatx80_rounding_precision = floatx80_precision_x;
 
     one = packFloatx80(0, one_exp, one_sig);
     fp0 = a;
@@ -2155,7 +2167,8 @@ floatx80 floatx80_acos(floatx80 a, float_status *status)
     int32_t aExp;
     uint64_t aSig;
 
-    int8_t user_rnd_mode, user_rnd_prec;
+    FloatRoundMode user_rnd_mode;
+    FloatX80RoundPrec user_rnd_prec;
 
     int32_t compact;
     floatx80 fp0, fp1, one;
@@ -2193,7 +2206,7 @@ floatx80 floatx80_acos(floatx80 a, float_status *status)
     user_rnd_mode = status->float_rounding_mode;
     user_rnd_prec = status->floatx80_rounding_precision;
     status->float_rounding_mode = float_round_nearest_even;
-    status->floatx80_rounding_precision = 80;
+    status->floatx80_rounding_precision = floatx80_precision_x;
 
     one = packFloatx80(0, one_exp, one_sig);
     fp0 = a;
@@ -2224,7 +2237,8 @@ floatx80 floatx80_atanh(floatx80 a, float_status *status)
     int32_t aExp;
     uint64_t aSig;
 
-    int8_t user_rnd_mode, user_rnd_prec;
+    FloatRoundMode user_rnd_mode;
+    FloatX80RoundPrec user_rnd_prec;
 
     int32_t compact;
     floatx80 fp0, fp1, fp2, one;
@@ -2257,7 +2271,7 @@ floatx80 floatx80_atanh(floatx80 a, float_status *status)
     user_rnd_mode = status->float_rounding_mode;
     user_rnd_prec = status->floatx80_rounding_precision;
     status->float_rounding_mode = float_round_nearest_even;
-    status->floatx80_rounding_precision = 80;
+    status->floatx80_rounding_precision = floatx80_precision_x;
 
     one = packFloatx80(0, one_exp, one_sig);
     fp2 = packFloatx80(aSign, 0x3FFE, one_sig); /* SIGN(X) * (1/2) */
@@ -2289,7 +2303,8 @@ floatx80 floatx80_etoxm1(floatx80 a, float_status *status)
     int32_t aExp;
     uint64_t aSig;
 
-    int8_t user_rnd_mode, user_rnd_prec;
+    FloatRoundMode user_rnd_mode;
+    FloatX80RoundPrec user_rnd_prec;
 
     int32_t compact, n, j, m, m1;
     floatx80 fp0, fp1, fp2, fp3, l2, sc, onebysc;
@@ -2316,7 +2331,7 @@ floatx80 floatx80_etoxm1(floatx80 a, float_status *status)
     user_rnd_mode = status->float_rounding_mode;
     user_rnd_prec = status->floatx80_rounding_precision;
     status->float_rounding_mode = float_round_nearest_even;
-    status->floatx80_rounding_precision = 80;
+    status->floatx80_rounding_precision = floatx80_precision_x;
 
     if (aExp >= 0x3FFD) { /* |X| >= 1/4 */
         compact = floatx80_make_compact(aExp, aSig);
@@ -2541,7 +2556,8 @@ floatx80 floatx80_tanh(floatx80 a, float_status *status)
     int32_t aExp, vExp;
     uint64_t aSig, vSig;
 
-    int8_t user_rnd_mode, user_rnd_prec;
+    FloatRoundMode user_rnd_mode;
+    FloatX80RoundPrec user_rnd_prec;
 
     int32_t compact;
     floatx80 fp0, fp1;
@@ -2565,7 +2581,7 @@ floatx80 floatx80_tanh(floatx80 a, float_status *status)
     user_rnd_mode = status->float_rounding_mode;
     user_rnd_prec = status->floatx80_rounding_precision;
     status->float_rounding_mode = float_round_nearest_even;
-    status->floatx80_rounding_precision = 80;
+    status->floatx80_rounding_precision = floatx80_precision_x;
 
     compact = floatx80_make_compact(aExp, aSig);
 
@@ -2656,7 +2672,8 @@ floatx80 floatx80_sinh(floatx80 a, float_status *status)
     int32_t aExp;
     uint64_t aSig;
 
-    int8_t user_rnd_mode, user_rnd_prec;
+    FloatRoundMode user_rnd_mode;
+    FloatX80RoundPrec user_rnd_prec;
 
     int32_t compact;
     floatx80 fp0, fp1, fp2;
@@ -2681,7 +2698,7 @@ floatx80 floatx80_sinh(floatx80 a, float_status *status)
     user_rnd_mode = status->float_rounding_mode;
     user_rnd_prec = status->floatx80_rounding_precision;
     status->float_rounding_mode = float_round_nearest_even;
-    status->floatx80_rounding_precision = 80;
+    status->floatx80_rounding_precision = floatx80_precision_x;
 
     compact = floatx80_make_compact(aExp, aSig);
 
@@ -2744,7 +2761,8 @@ floatx80 floatx80_cosh(floatx80 a, float_status *status)
     int32_t aExp;
     uint64_t aSig;
 
-    int8_t user_rnd_mode, user_rnd_prec;
+    FloatRoundMode user_rnd_mode;
+    FloatX80RoundPrec user_rnd_prec;
 
     int32_t compact;
     floatx80 fp0, fp1;
@@ -2767,7 +2785,7 @@ floatx80 floatx80_cosh(floatx80 a, float_status *status)
     user_rnd_mode = status->float_rounding_mode;
     user_rnd_prec = status->floatx80_rounding_precision;
     status->float_rounding_mode = float_round_nearest_even;
-    status->floatx80_rounding_precision = 80;
+    status->floatx80_rounding_precision = floatx80_precision_x;
 
     compact = floatx80_make_compact(aExp, aSig);
 
diff --git a/tests/fp/fp-test-log2.c b/tests/fp/fp-test-log2.c
new file mode 100644
index 0000000000..4eae93eb7c
--- /dev/null
+++ b/tests/fp/fp-test-log2.c
@@ -0,0 +1,118 @@
+/*
+ * fp-test-log2.c - test QEMU's softfloat log2
+ *
+ * Copyright (C) 2020, Linaro, Ltd.
+ *
+ * License: GNU GPL, version 2 or later.
+ *   See the COPYING file in the top-level directory.
+ */
+#ifndef HW_POISON_H
+#error Must define HW_POISON_H to work around TARGET_* poisoning
+#endif
+
+#include "qemu/osdep.h"
+#include "qemu/cutils.h"
+#include <math.h>
+#include "fpu/softfloat.h"
+
+typedef union {
+    double d;
+    float64 i;
+} ufloat64;
+
+static int errors;
+
+static void compare(ufloat64 test, ufloat64 real, ufloat64 soft, bool exact)
+{
+    int msb;
+    uint64_t ulp = UINT64_MAX;
+
+    if (real.i == soft.i) {
+        return;
+    }
+    msb = 63 - __builtin_clzll(real.i ^ soft.i);
+
+    if (msb < 52) {
+        if (real.i > soft.i) {
+            ulp = real.i - soft.i;
+        } else {
+            ulp = soft.i - real.i;
+        }
+    }
+
+    /* glibc allows 3 ulp error in its libm-test-ulps; allow 4 here */
+    if (!exact && ulp <= 4) {
+        return;
+    }
+
+    printf("test: %016" PRIx64 "  %+.13a\n"
+           "  sf: %016" PRIx64 "  %+.13a\n"
+           "libm: %016" PRIx64 "  %+.13a\n",
+           test.i, test.d, soft.i, soft.d, real.i, real.d);
+
+    if (msb == 63) {
+        printf("Error in sign!\n\n");
+    } else if (msb >= 52) {
+        printf("Error in exponent: %d\n\n",
+               (int)(soft.i >> 52) - (int)(real.i >> 52));
+    } else {
+        printf("Error in fraction: %" PRIu64 " ulp\n\n", ulp);
+    }
+
+    if (++errors == 20) {
+        exit(1);
+    }
+}
+
+int main(int ac, char **av)
+{
+    ufloat64 test, real, soft;
+    float_status qsf = {0};
+    int i;
+
+    set_float_rounding_mode(float_round_nearest_even, &qsf);
+
+    test.d = 0.0;
+    real.d = -__builtin_inf();
+    soft.i = float64_log2(test.i, &qsf);
+    compare(test, real, soft, true);
+
+    test.d = 1.0;
+    real.d = 0.0;
+    soft.i = float64_log2(test.i, &qsf);
+    compare(test, real, soft, true);
+
+    test.d = 2.0;
+    real.d = 1.0;
+    soft.i = float64_log2(test.i, &qsf);
+    compare(test, real, soft, true);
+
+    test.d = 4.0;
+    real.d = 2.0;
+    soft.i = float64_log2(test.i, &qsf);
+    compare(test, real, soft, true);
+
+    test.d = 0x1p64;
+    real.d = 64.0;
+    soft.i = float64_log2(test.i, &qsf);
+    compare(test, real, soft, true);
+
+    test.d = __builtin_inf();
+    real.d = __builtin_inf();
+    soft.i = float64_log2(test.i, &qsf);
+    compare(test, real, soft, true);
+
+    for (i = 0; i < 10000; ++i) {
+        test.d = drand48() + 1.0;    /* [1.0, 2.0) */
+        real.d = log2(test.d);
+        soft.i = float64_log2(test.i, &qsf);
+        compare(test, real, soft, false);
+
+        test.d = drand48() * 100;    /* [0.0, 100) */
+        real.d = log2(test.d);
+        soft.i = float64_log2(test.i, &qsf);
+        compare(test, real, soft, false);
+    }
+
+    return 0;
+}
diff --git a/tests/fp/fp-test.c b/tests/fp/fp-test.c
index ff131afbde..352dd71c44 100644
--- a/tests/fp/fp-test.c
+++ b/tests/fp/fp-test.c
@@ -963,18 +963,21 @@ static void QEMU_NORETURN run_test(void)
             verCases_usesExact = !!(attrs & FUNC_ARG_EXACT);
 
             for (k = 0; k < 3; k++) {
-                int prec80 = 32;
+                FloatX80RoundPrec qsf_prec80 = floatx80_precision_x;
+                int prec80 = 80;
                 int l;
 
                 if (k == 1) {
                     prec80 = 64;
+                    qsf_prec80 = floatx80_precision_d;
                 } else if (k == 2) {
-                    prec80 = 80;
+                    prec80 = 32;
+                    qsf_prec80 = floatx80_precision_s;
                 }
 
                 verCases_roundingPrecision = 0;
                 slow_extF80_roundingPrecision = prec80;
-                qsf.floatx80_rounding_precision = prec80;
+                qsf.floatx80_rounding_precision = qsf_prec80;
 
                 if (attrs & FUNC_EFF_ROUNDINGPRECISION) {
                     verCases_roundingPrecision = prec80;
diff --git a/tests/fp/meson.build b/tests/fp/meson.build
index 1c3eee9955..07e2cdc8d2 100644
--- a/tests/fp/meson.build
+++ b/tests/fp/meson.build
@@ -556,7 +556,9 @@ softfloat_conv_tests = {
                       'extF80_to_f64 extF80_to_f128 ' +
                       'f128_to_f16',
     'int-to-float': 'i32_to_f16 i64_to_f16 i32_to_f32 i64_to_f32 ' +
-                    'i32_to_f64 i64_to_f64 i32_to_f128 i64_to_f128',
+                    'i32_to_f64 i64_to_f64 ' +
+                    'i32_to_extF80 i64_to_extF80 ' +
+                    'i32_to_f128 i64_to_f128',
     'uint-to-float': 'ui32_to_f16 ui64_to_f16 ui32_to_f32 ui64_to_f32 ' +
                      'ui32_to_f64 ui64_to_f64 ui64_to_f128 ' +
                      'ui32_to_extF80 ui64_to_extF80',
@@ -581,7 +583,7 @@ softfloat_conv_tests = {
                      'extF80_to_ui64 extF80_to_ui64_r_minMag ' +
                      'f128_to_ui64 f128_to_ui64_r_minMag',
     'round-to-integer': 'f16_roundToInt f32_roundToInt ' +
-                        'f64_roundToInt f128_roundToInt'
+                        'f64_roundToInt extF80_roundToInt f128_roundToInt'
 }
 softfloat_tests = {
     'eq_signaling' : 'compare',
@@ -602,24 +604,20 @@ fptest_args = ['-s', '-l', '1']
 fptest_rounding_args = ['-r', 'all']
 
 # Conversion Routines:
-# FIXME: i32_to_extF80 (broken), i64_to_extF80 (broken)
-#        extF80_roundToInt (broken)
 foreach k, v : softfloat_conv_tests
   test('fp-test-' + k, fptest,
        args: fptest_args + fptest_rounding_args + v.split(),
        suite: ['softfloat', 'softfloat-conv'])
 endforeach
 
-# FIXME: extF80_{lt_quiet, rem} (broken),
-#        extF80_{mulAdd} (missing)
 foreach k, v : softfloat_tests
-  extF80_broken = ['lt_quiet', 'rem'].contains(k)
   test('fp-test-' + k, fptest,
        args: fptest_args + fptest_rounding_args +
-             ['f16_' + k, 'f32_' + k, 'f64_' + k, 'f128_' + k] +
-             (extF80_broken ? [] : ['extF80_' + k]),
+             ['f16_' + k, 'f32_' + k, 'f64_' + k, 'f128_' + k, 'extF80_' + k],
        suite: ['softfloat', 'softfloat-' + v])
 endforeach
+
+# FIXME: extF80_{mulAdd} (missing)
 test('fp-test-mulAdd', fptest,
      # no fptest_rounding_args
      args: fptest_args +
@@ -634,3 +632,14 @@ fpbench = executable(
   include_directories: [sfinc, include_directories(tfdir)],
   c_args: fpcflags,
 )
+
+fptestlog2 = executable(
+  'fp-test-log2',
+  ['fp-test-log2.c', '../../fpu/softfloat.c'],
+  link_with: [libsoftfloat],
+  dependencies: [qemuutil],
+  include_directories: [sfinc],
+  c_args: fpcflags,
+)
+test('fp-test-log2', fptestlog2,
+     suite: ['softfloat', 'softfloat-ops'])
diff --git a/tests/fp/wrap.c.inc b/tests/fp/wrap.c.inc
index cb1bb77e4c..9ff884c140 100644
--- a/tests/fp/wrap.c.inc
+++ b/tests/fp/wrap.c.inc
@@ -643,7 +643,7 @@ WRAP_CMP80(qemu_extF80M_eq, floatx80_eq_quiet)
 WRAP_CMP80(qemu_extF80M_le, floatx80_le)
 WRAP_CMP80(qemu_extF80M_lt, floatx80_lt)
 WRAP_CMP80(qemu_extF80M_le_quiet, floatx80_le_quiet)
-WRAP_CMP80(qemu_extF80M_lt_quiet, floatx80_le_quiet)
+WRAP_CMP80(qemu_extF80M_lt_quiet, floatx80_lt_quiet)
 #undef WRAP_CMP80
 
 #define WRAP_CMP128(name, func)                                         \