C reference implementation of the int64 helper functions.

In test_int64.c: don't test FP->int64 conversions when the FP argument is out of range.

15 files changed, 905 insertions, 0 deletions

diff --git a/runtime/c/i64.h b/runtime/c/i64.h
new file mode 100644
index 00000000..dd584533
--- /dev/null
+++ b/runtime/c/i64.h
@@ -0,0 +1,43 @@
+/*****************************************************************
+ *
+ *               The Compcert verified compiler
+ *
+ *           Xavier Leroy, INRIA Paris-Rocquencourt
+ *
+ * Copyright (c) 2013 Institut National de Recherche en Informatique et
+ *  en Automatique.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions are met:
+ *     * Redistributions of source code must retain the above copyright
+ *       notice, this list of conditions and the following disclaimer.
+ *     * Redistributions in binary form must reproduce the above copyright
+ *       notice, this list of conditions and the following disclaimer in the
+ *       documentation and/or other materials provided with the distribution.
+ *     * Neither the name of the <organization> nor the
+ *       names of its contributors may be used to endorse or promote products
+ *       derived from this software without specific prior written permission.
+ * 
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL <COPYRIGHT
+ * HOLDER> BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ *
+ **********************************************************************/
+
+/* Helper functions for 64-bit integer arithmetic. Reference C implementation */
+
+extern unsigned long long __i64_shl(unsigned long long x, int amount);
+extern unsigned long long __i64_shr(unsigned long long x, int amount);
+extern signed long long __i64_sar(signed long long x, int amount);
+
+extern unsigned long long __i64_udivmod(unsigned long long n,
+                                        unsigned long long d,
+                                        unsigned long long * rp);
diff --git a/runtime/c/i64_dtos.c b/runtime/c/i64_dtos.c
new file mode 100644
index 00000000..d428e744
--- /dev/null
+++ b/runtime/c/i64_dtos.c
@@ -0,0 +1,74 @@
+/*****************************************************************
+ *
+ *               The Compcert verified compiler
+ *
+ *           Xavier Leroy, INRIA Paris-Rocquencourt
+ *
+ * Copyright (c) 2013 Institut National de Recherche en Informatique et
+ *  en Automatique.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions are met:
+ *     * Redistributions of source code must retain the above copyright
+ *       notice, this list of conditions and the following disclaimer.
+ *     * Redistributions in binary form must reproduce the above copyright
+ *       notice, this list of conditions and the following disclaimer in the
+ *       documentation and/or other materials provided with the distribution.
+ *     * Neither the name of the <organization> nor the
+ *       names of its contributors may be used to endorse or promote products
+ *       derived from this software without specific prior written permission.
+ * 
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL <COPYRIGHT
+ * HOLDER> BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ *
+ **********************************************************************/
+
+/* Helper functions for 64-bit integer arithmetic. Reference C implementation */
+
+#include "i64.h"
+
+/* Conversion float64 -> signed int64 */
+
+long long __i64_dtos(double d)
+{
+  /* Extract bits of d's representation */
+  union { double d; unsigned long long i; } buf;
+  buf.d = d;
+  unsigned int h = buf.i >> 32;
+  /* Extract unbiased exponent */
+  int e = ((h & 0x7FF00000) >> 20) - (1023 + 52);
+  /* Check range of exponent */
+  if (e < -52) {
+    /* |d| is less than 1.0 */
+    return 0LL;
+  }
+  if (e >= 63 - 52) {
+    /* |d| is greater or equal to 2^63 */
+    if ((int) h < 0)
+      return -0x8000000000000000LL; /* min signed long long */
+    else
+      return  0x7FFFFFFFFFFFFFFFLL; /* max signed long long */
+  }
+  /* Extract true mantissa */
+  unsigned long long m =
+    (buf.i & ~0xFFF0000000000000LL) | 0x0010000000000000LL;
+  /* Shift it appropriately */
+  if (e >= 0)
+    m = __i64_shl(m, e);
+  else
+    m = __i64_shr(m, -e);
+  /* Apply sign to result */
+  if ((int) h < 0)
+    return -m;
+  else
+    return m;
+}
diff --git a/runtime/c/i64_dtou.c b/runtime/c/i64_dtou.c
new file mode 100644
index 00000000..c5f9df4d
--- /dev/null
+++ b/runtime/c/i64_dtou.c
@@ -0,0 +1,69 @@
+/*****************************************************************
+ *
+ *               The Compcert verified compiler
+ *
+ *           Xavier Leroy, INRIA Paris-Rocquencourt
+ *
+ * Copyright (c) 2013 Institut National de Recherche en Informatique et
+ *  en Automatique.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions are met:
+ *     * Redistributions of source code must retain the above copyright
+ *       notice, this list of conditions and the following disclaimer.
+ *     * Redistributions in binary form must reproduce the above copyright
+ *       notice, this list of conditions and the following disclaimer in the
+ *       documentation and/or other materials provided with the distribution.
+ *     * Neither the name of the <organization> nor the
+ *       names of its contributors may be used to endorse or promote products
+ *       derived from this software without specific prior written permission.
+ * 
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL <COPYRIGHT
+ * HOLDER> BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ *
+ **********************************************************************/
+
+/* Helper functions for 64-bit integer arithmetic. Reference C implementation */
+
+#include "i64.h"
+
+/* Conversion float64 -> unsigned int64 */
+
+unsigned long long __i64_dtou(double d)
+{
+  /* Extract bits of d's representation */
+  union { double d; unsigned long long i; } buf;
+  buf.d = d;
+  unsigned int h = buf.i >> 32;
+  /* Negative FP numbers convert to 0 */
+  if ((int) h < 0) return 0ULL;
+  /* Extract unbiased exponent */
+  int e = ((h & 0x7FF00000) >> 20) - (1023 + 52);
+  /* Check range of exponent */
+  if (e < -52) {
+    /* d is less than 1.0 */
+    return 0ULL;
+  }
+  if (e >= 64 - 52) {
+    /* d is greater or equal to 2^64 */
+    return 0xFFFFFFFFFFFFFFFFULL; /* max unsigned long long */
+  }
+  /* Extract true mantissa */
+  unsigned long long m =
+    (buf.i & ~0xFFF0000000000000LL) | 0x0010000000000000LL;
+  /* Shift it appropriately */
+  if (e >= 0)
+    return __i64_shl(m, e);
+  else
+    return __i64_shr(m, -e);
+
+}
diff --git a/runtime/c/i64_sar.c b/runtime/c/i64_sar.c
new file mode 100644
index 00000000..a5f3364a
--- /dev/null
+++ b/runtime/c/i64_sar.c
@@ -0,0 +1,56 @@
+/*****************************************************************
+ *
+ *               The Compcert verified compiler
+ *
+ *           Xavier Leroy, INRIA Paris-Rocquencourt
+ *
+ * Copyright (c) 2013 Institut National de Recherche en Informatique et
+ *  en Automatique.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions are met:
+ *     * Redistributions of source code must retain the above copyright
+ *       notice, this list of conditions and the following disclaimer.
+ *     * Redistributions in binary form must reproduce the above copyright
+ *       notice, this list of conditions and the following disclaimer in the
+ *       documentation and/or other materials provided with the distribution.
+ *     * Neither the name of the <organization> nor the
+ *       names of its contributors may be used to endorse or promote products
+ *       derived from this software without specific prior written permission.
+ * 
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL <COPYRIGHT
+ * HOLDER> BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ *
+ **********************************************************************/
+
+/* Helper functions for 64-bit integer arithmetic. Reference C implementation */
+
+#include "i64.h"
+
+/* Shift right signed */
+
+signed long long __i64_sar(signed long long x, int amount)
+{
+  unsigned xl = x;
+  int xh = x >> 32;
+  amount = amount & 63;
+  if (amount == 0) {
+    return x;
+  }
+  else if (amount < 32) {
+    unsigned rl = (xl >> amount) | (xh << (32 - amount));
+    int rh = xh >> amount;
+    return rl | ((signed long long) rh << 32);
+  } else {
+    return (signed long long) (xh >> (amount - 32));
+  }
+}
diff --git a/runtime/c/i64_sdiv.c b/runtime/c/i64_sdiv.c
new file mode 100644
index 00000000..3f21d9b7
--- /dev/null
+++ b/runtime/c/i64_sdiv.c
@@ -0,0 +1,51 @@
+/*****************************************************************
+ *
+ *               The Compcert verified compiler
+ *
+ *           Xavier Leroy, INRIA Paris-Rocquencourt
+ *
+ * Copyright (c) 2013 Institut National de Recherche en Informatique et
+ *  en Automatique.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions are met:
+ *     * Redistributions of source code must retain the above copyright
+ *       notice, this list of conditions and the following disclaimer.
+ *     * Redistributions in binary form must reproduce the above copyright
+ *       notice, this list of conditions and the following disclaimer in the
+ *       documentation and/or other materials provided with the distribution.
+ *     * Neither the name of the <organization> nor the
+ *       names of its contributors may be used to endorse or promote products
+ *       derived from this software without specific prior written permission.
+ * 
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL <COPYRIGHT
+ * HOLDER> BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ *
+ **********************************************************************/
+
+/* Helper functions for 64-bit integer arithmetic. Reference C implementation */
+
+#include "i64.h"
+
+/* Signed division */
+
+signed long long __i64_sdiv(signed long long n, signed long long d)
+{
+  unsigned long long un, ud, uq, ur;
+  int nh = n >> 32, dh = d >> 32;
+  /* Take absolute values of n and d */
+  un = nh < 0 ? -n : n;
+  ud = dh < 0 ? -d : d;
+  uq = __i64_udivmod(un, ud, &ur);
+  /* Apply sign to quotient */
+  return (nh ^ dh) < 0 ? -uq : uq;
+}
diff --git a/runtime/c/i64_shl.c b/runtime/c/i64_shl.c
new file mode 100644
index 00000000..9b9aae57
--- /dev/null
+++ b/runtime/c/i64_shl.c
@@ -0,0 +1,55 @@
+/*****************************************************************
+ *
+ *               The Compcert verified compiler
+ *
+ *           Xavier Leroy, INRIA Paris-Rocquencourt
+ *
+ * Copyright (c) 2013 Institut National de Recherche en Informatique et
+ *  en Automatique.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions are met:
+ *     * Redistributions of source code must retain the above copyright
+ *       notice, this list of conditions and the following disclaimer.
+ *     * Redistributions in binary form must reproduce the above copyright
+ *       notice, this list of conditions and the following disclaimer in the
+ *       documentation and/or other materials provided with the distribution.
+ *     * Neither the name of the <organization> nor the
+ *       names of its contributors may be used to endorse or promote products
+ *       derived from this software without specific prior written permission.
+ * 
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL <COPYRIGHT
+ * HOLDER> BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ *
+ **********************************************************************/
+
+/* Helper functions for 64-bit integer arithmetic. Reference C implementation */
+
+#include "i64.h"
+
+/* Shift left */
+
+unsigned long long __i64_shl(unsigned long long x, int amount)
+{
+  unsigned xl = x, xh = x >> 32;
+  amount = amount & 63;
+  if (amount == 0) {
+    return x;
+  }
+  else if (amount < 32) {
+    unsigned rl = xl << amount;
+    unsigned rh = (xh << amount) | (xl >> (32 - amount));
+    return rl | ((unsigned long long) rh << 32);
+  } else {
+    return ((unsigned long long) (xl << (amount - 32))) << 32;
+  }
+}
diff --git a/runtime/c/i64_shr.c b/runtime/c/i64_shr.c
new file mode 100644
index 00000000..c1db2a5f
--- /dev/null
+++ b/runtime/c/i64_shr.c
@@ -0,0 +1,55 @@
+/*****************************************************************
+ *
+ *               The Compcert verified compiler
+ *
+ *           Xavier Leroy, INRIA Paris-Rocquencourt
+ *
+ * Copyright (c) 2013 Institut National de Recherche en Informatique et
+ *  en Automatique.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions are met:
+ *     * Redistributions of source code must retain the above copyright
+ *       notice, this list of conditions and the following disclaimer.
+ *     * Redistributions in binary form must reproduce the above copyright
+ *       notice, this list of conditions and the following disclaimer in the
+ *       documentation and/or other materials provided with the distribution.
+ *     * Neither the name of the <organization> nor the
+ *       names of its contributors may be used to endorse or promote products
+ *       derived from this software without specific prior written permission.
+ * 
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL <COPYRIGHT
+ * HOLDER> BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ *
+ **********************************************************************/
+
+/* Helper functions for 64-bit integer arithmetic. Reference C implementation */
+
+#include "i64.h"
+
+/* Shift right unsigned */
+
+unsigned long long __i64_shr(unsigned long long x, int amount)
+{
+  unsigned xl = x, xh = x >> 32;
+  amount = amount & 63;
+  if (amount == 0) {
+    return x;
+  }
+  else if (amount < 32) {
+    unsigned rl = (xl >> amount) | (xh << (32 - amount));
+    unsigned rh = xh >> amount;
+    return rl | ((unsigned long long) rh << 32);
+  } else {
+    return (unsigned long long) (xh >> (amount - 32));
+  }
+}
diff --git a/runtime/c/i64_smod.c b/runtime/c/i64_smod.c
new file mode 100644
index 00000000..ab15b6e6
--- /dev/null
+++ b/runtime/c/i64_smod.c
@@ -0,0 +1,51 @@
+/*****************************************************************
+ *
+ *               The Compcert verified compiler
+ *
+ *           Xavier Leroy, INRIA Paris-Rocquencourt
+ *
+ * Copyright (c) 2013 Institut National de Recherche en Informatique et
+ *  en Automatique.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions are met:
+ *     * Redistributions of source code must retain the above copyright
+ *       notice, this list of conditions and the following disclaimer.
+ *     * Redistributions in binary form must reproduce the above copyright
+ *       notice, this list of conditions and the following disclaimer in the
+ *       documentation and/or other materials provided with the distribution.
+ *     * Neither the name of the <organization> nor the
+ *       names of its contributors may be used to endorse or promote products
+ *       derived from this software without specific prior written permission.
+ * 
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL <COPYRIGHT
+ * HOLDER> BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ *
+ **********************************************************************/
+
+/* Helper functions for 64-bit integer arithmetic. Reference C implementation */
+
+#include "i64.h"
+
+/* Signed remainder */
+
+signed long long __i64_smod(signed long long n, signed long long d)
+{
+  unsigned long long un, ud, ur;
+  int nh = n >> 32, dh = d >> 32;
+  /* Take absolute values of n and d */
+  un = nh < 0 ? -n : n;
+  ud = dh < 0 ? -d : d;
+  (void) __i64_udivmod(un, ud, &ur);
+  /* Apply sign to remainder */
+  return nh < 0 ? -ur : ur;
+}
diff --git a/runtime/c/i64_stod.c b/runtime/c/i64_stod.c
new file mode 100644
index 00000000..158b6892
--- /dev/null
+++ b/runtime/c/i64_stod.c
@@ -0,0 +1,46 @@
+/*****************************************************************
+ *
+ *               The Compcert verified compiler
+ *
+ *           Xavier Leroy, INRIA Paris-Rocquencourt
+ *
+ * Copyright (c) 2013 Institut National de Recherche en Informatique et
+ *  en Automatique.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions are met:
+ *     * Redistributions of source code must retain the above copyright
+ *       notice, this list of conditions and the following disclaimer.
+ *     * Redistributions in binary form must reproduce the above copyright
+ *       notice, this list of conditions and the following disclaimer in the
+ *       documentation and/or other materials provided with the distribution.
+ *     * Neither the name of the <organization> nor the
+ *       names of its contributors may be used to endorse or promote products
+ *       derived from this software without specific prior written permission.
+ * 
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL <COPYRIGHT
+ * HOLDER> BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ *
+ **********************************************************************/
+
+/* Helper functions for 64-bit integer arithmetic. Reference C implementation */
+
+#include "i64.h"
+
+/* Conversion from signed int64 to float64 */
+
+double __i64_stod(signed long long x)
+{
+  unsigned xl = x;
+  signed xh = x >> 32;
+  return (double) xl + 0x1p+32 * (double) xh;
+}
diff --git a/runtime/c/i64_stof.c b/runtime/c/i64_stof.c
new file mode 100644
index 00000000..8410ba13
--- /dev/null
+++ b/runtime/c/i64_stof.c
@@ -0,0 +1,56 @@
+/*****************************************************************
+ *
+ *               The Compcert verified compiler
+ *
+ *           Xavier Leroy, INRIA Paris-Rocquencourt
+ *
+ * Copyright (c) 2013 Institut National de Recherche en Informatique et
+ *  en Automatique.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions are met:
+ *     * Redistributions of source code must retain the above copyright
+ *       notice, this list of conditions and the following disclaimer.
+ *     * Redistributions in binary form must reproduce the above copyright
+ *       notice, this list of conditions and the following disclaimer in the
+ *       documentation and/or other materials provided with the distribution.
+ *     * Neither the name of the <organization> nor the
+ *       names of its contributors may be used to endorse or promote products
+ *       derived from this software without specific prior written permission.
+ * 
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL <COPYRIGHT
+ * HOLDER> BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ *
+ **********************************************************************/
+
+/* Helper functions for 64-bit integer arithmetic. Reference C implementation */
+
+#include "i64.h"
+
+/* Conversion from signed int64 to float32 */
+
+float __i64_stof(signed long long x)
+{
+  if (x < -(1LL << 53) || x >= (1LL << 53)) {
+    /* x is large enough that double rounding can occur.
+       Nudge x away from the points where double rounding occurs
+       (the "round to odd" technique) */
+    unsigned delta = ((unsigned) x & 0x7FF) + 0x7FF;
+    x = (x | delta) & ~0x7FFLL;
+  }
+  /* Convert to double */
+  unsigned xl = x;
+  signed xh = x >> 32;
+  double r = (double) xl + 0x1.0p32 * (double) xh;
+  /* Round to single */
+  return (float) r;
+}
diff --git a/runtime/c/i64_udiv.c b/runtime/c/i64_udiv.c
new file mode 100644
index 00000000..91fbf6e4
--- /dev/null
+++ b/runtime/c/i64_udiv.c
@@ -0,0 +1,45 @@
+/*****************************************************************
+ *
+ *               The Compcert verified compiler
+ *
+ *           Xavier Leroy, INRIA Paris-Rocquencourt
+ *
+ * Copyright (c) 2013 Institut National de Recherche en Informatique et
+ *  en Automatique.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions are met:
+ *     * Redistributions of source code must retain the above copyright
+ *       notice, this list of conditions and the following disclaimer.
+ *     * Redistributions in binary form must reproduce the above copyright
+ *       notice, this list of conditions and the following disclaimer in the
+ *       documentation and/or other materials provided with the distribution.
+ *     * Neither the name of the <organization> nor the
+ *       names of its contributors may be used to endorse or promote products
+ *       derived from this software without specific prior written permission.
+ * 
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL <COPYRIGHT
+ * HOLDER> BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ *
+ **********************************************************************/
+
+/* Helper functions for 64-bit integer arithmetic. Reference C implementation */
+
+#include "i64.h"
+
+/* Unsigned division */
+
+unsigned long long __i64_udiv(unsigned long long n, unsigned long long d)
+{
+  unsigned long long r;
+  return __i64_udivmod(n, d, &r);
+}
diff --git a/runtime/c/i64_udivmod.c b/runtime/c/i64_udivmod.c
new file mode 100644
index 00000000..d8f5073a
--- /dev/null
+++ b/runtime/c/i64_udivmod.c
@@ -0,0 +1,158 @@
+/*****************************************************************
+ *
+ *               The Compcert verified compiler
+ *
+ *           Xavier Leroy, INRIA Paris-Rocquencourt
+ *
+ * Copyright (c) 2013 Institut National de Recherche en Informatique et
+ *  en Automatique.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions are met:
+ *     * Redistributions of source code must retain the above copyright
+ *       notice, this list of conditions and the following disclaimer.
+ *     * Redistributions in binary form must reproduce the above copyright
+ *       notice, this list of conditions and the following disclaimer in the
+ *       documentation and/or other materials provided with the distribution.
+ *     * Neither the name of the <organization> nor the
+ *       names of its contributors may be used to endorse or promote products
+ *       derived from this software without specific prior written permission.
+ * 
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL <COPYRIGHT
+ * HOLDER> BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ *
+ **********************************************************************/
+
+/* Helper functions for 64-bit integer arithmetic. Reference C implementation */
+
+#include <stddef.h>
+#include "i64.h"
+
+static unsigned __i64_udiv6432(unsigned u1, unsigned u0,
+                               unsigned v, unsigned *r);
+static int __i64_nlz(unsigned x);
+
+/* Unsigned division and remainder */
+
+unsigned long long __i64_udivmod(unsigned long long n,
+                                 unsigned long long d,
+                                 unsigned long long * rp)
+{
+  unsigned dh = d >> 32;
+  if (dh == 0) {
+    unsigned nh = n >> 32;
+    if (nh == 0) {
+      /* Special case 32 / 32 */
+      unsigned nl = n;
+      unsigned dl = d; 
+      *rp = (unsigned long long) (nl % dl);
+      return (unsigned long long) (nl / dl);
+    } else {
+      /* Special case 64 / 32 */
+      unsigned nl = n;
+      unsigned dl = d; 
+      unsigned qh = nh / dl;
+      unsigned rl;
+      unsigned ql = __i64_udiv6432(nh % dl, nl, dl, &rl);
+      *rp = (unsigned long long) rl; /* high word of remainder is 0 */
+      return ((unsigned long long) qh) << 32 | ql;
+    }
+  } else {
+    /* General case 64 / 64 */
+    unsigned dl = d;
+    /* Scale N and D down, giving N' and D' such that 2^31 <= D' < 2^32 */
+    int s = 32 - __i64_nlz(dh);  /* shift amount, between 1 and 32 */
+    unsigned long long np = __i64_shr(n, s);
+    unsigned dp = (unsigned) __i64_shr(d, s);
+    /* Divide N' by D' to get an approximate quotient Q */
+    unsigned q = __i64_udiv6432(np >> 32, np, dp, NULL);
+  again: ;
+    /* Tentative quotient Q is either correct or one too high */
+    /* Compute Q * D, checking for overflow */
+    unsigned long long p1 = (unsigned long long) dl * q;
+    unsigned long long p2 = (unsigned long long) (dh * q) << 32;
+    unsigned long long p = p1 + p2;
+    if (p < p1) {
+      /* Overflow occurred: adjust Q down by 1 and redo check */
+      q = q - 1; goto again;
+    }
+    /* Compute remainder R */
+    unsigned long long r = n - p;
+    if (n < p) {
+      /* Q is one too high, adjust Q down by 1 and R up by D */
+      q = q - 1; r = r + d;
+    }
+    *rp = r;
+    return (unsigned long long) q;
+  }
+}
+
+/* Unsigned division and remainder for 64 bits divided by 32 bits. */
+/* This is algorithm "divlu" from _Hacker's Delight_, fig 9.3 */
+
+static unsigned __i64_udiv6432(unsigned u1, unsigned u0,
+                               unsigned v, unsigned *r)
+{
+  const unsigned b = 65536; // Number base (16 bits).
+  unsigned un1, un0,        // Norm. dividend LSD's.
+           vn1, vn0,        // Norm. divisor digits.
+           q1, q0,          // Quotient digits.
+           un32, un21, un10,// Divided digit pairs.
+           rhat;            // A remainder.
+  int s;                    // Shift amount for norm.
+
+  if (u1 >= v) {            // If overflow,
+    if (r != NULL) *r = 0xFFFFFFFFU; // set rem to an impossible value,
+    return 0xFFFFFFFFU;              // and return largest possible quotient.
+  }
+  s = __i64_nlz(v);          // 0 <= s <= 31.
+  v = v << s;                // Normalize divisor.
+  vn1 = v >> 16;             // Break divisor up into
+  vn0 = v & 0xFFFF;          // two 16-bit digits.
+  un32 = (u1 << s) | ((u0 >> (32 - s)) & (-s >> 31));
+  un10 = u0 << s;            // Shift dividend left.
+  un1 = un10 >> 16;          // Break right half of
+  un0 = un10 & 0xFFFF;       // dividend into two digits.
+  q1 = un32/vn1;             // Compute the first quotient digit, q1.
+  rhat = un32 - q1*vn1;
+ again1:
+  if (q1 >= b || q1*vn0 > b*rhat + un1) {
+    q1 = q1 - 1;
+    rhat = rhat + vn1;
+    if (rhat < b) goto again1;
+  }
+  un21 = un32*b + un1 - q1*v; // Multiply and subtract.
+  q0 = un21/vn1;              // Compute the second quotient digit, q0
+  rhat = un21 - q0*vn1;
+again2:
+  if (q0 >= b || q0*vn0 > b*rhat + un0) {
+    q0 = q0 - 1;
+    rhat = rhat + vn1;
+    if (rhat < b) goto again2;
+  }
+  if (r != NULL) *r = (un21*b + un0 - q0*v) >> s;
+  return q1*b + q0;
+}
+
+/* Number of leading zeroes */
+
+static int __i64_nlz(unsigned x)
+{
+  if (x == 0) return 32;
+  int n = 0;
+  if (x <= 0x0000FFFF) { n += 16; x <<= 16; }
+  if (x <= 0x00FFFFFF) { n += 8; x <<= 8; }
+  if (x <= 0x0FFFFFFF) { n += 4; x <<= 4; }
+  if (x <= 0x3FFFFFFF) { n += 2; x <<= 2; }
+  if (x <= 0x7FFFFFFF) { n += 1; x <<= 1; }
+  return n;
+}
diff --git a/runtime/c/i64_umod.c b/runtime/c/i64_umod.c
new file mode 100644
index 00000000..d30e29c4
--- /dev/null
+++ b/runtime/c/i64_umod.c
@@ -0,0 +1,46 @@
+/*****************************************************************
+ *
+ *               The Compcert verified compiler
+ *
+ *           Xavier Leroy, INRIA Paris-Rocquencourt
+ *
+ * Copyright (c) 2013 Institut National de Recherche en Informatique et
+ *  en Automatique.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions are met:
+ *     * Redistributions of source code must retain the above copyright
+ *       notice, this list of conditions and the following disclaimer.
+ *     * Redistributions in binary form must reproduce the above copyright
+ *       notice, this list of conditions and the following disclaimer in the
+ *       documentation and/or other materials provided with the distribution.
+ *     * Neither the name of the <organization> nor the
+ *       names of its contributors may be used to endorse or promote products
+ *       derived from this software without specific prior written permission.
+ * 
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL <COPYRIGHT
+ * HOLDER> BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ *
+ **********************************************************************/
+
+/* Helper functions for 64-bit integer arithmetic. Reference C implementation */
+
+#include "i64.h"
+
+/* Unsigned remainder */
+
+unsigned long long __i64_umod(unsigned long long n, unsigned long long d)
+{
+  unsigned long long r;
+  (void) __i64_udivmod(n, d, &r);
+  return r;
+}
diff --git a/runtime/c/i64_utod.c b/runtime/c/i64_utod.c
new file mode 100644
index 00000000..e70820a9
--- /dev/null
+++ b/runtime/c/i64_utod.c
@@ -0,0 +1,45 @@
+/*****************************************************************
+ *
+ *               The Compcert verified compiler
+ *
+ *           Xavier Leroy, INRIA Paris-Rocquencourt
+ *
+ * Copyright (c) 2013 Institut National de Recherche en Informatique et
+ *  en Automatique.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions are met:
+ *     * Redistributions of source code must retain the above copyright
+ *       notice, this list of conditions and the following disclaimer.
+ *     * Redistributions in binary form must reproduce the above copyright
+ *       notice, this list of conditions and the following disclaimer in the
+ *       documentation and/or other materials provided with the distribution.
+ *     * Neither the name of the <organization> nor the
+ *       names of its contributors may be used to endorse or promote products
+ *       derived from this software without specific prior written permission.
+ * 
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL <COPYRIGHT
+ * HOLDER> BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ *
+ **********************************************************************/
+
+/* Helper functions for 64-bit integer arithmetic. Reference C implementation */
+
+#include "i64.h"
+
+/* Conversion from unsigned int64 to float64 */
+
+double __i64_utod(unsigned long long x)
+{
+  unsigned xl = x, xh = x >> 32;
+  return (double) xl + 0x1.0p32 * (double) xh;
+}
diff --git a/runtime/c/i64_utof.c b/runtime/c/i64_utof.c
new file mode 100644
index 00000000..87b85bfc
--- /dev/null
+++ b/runtime/c/i64_utof.c
@@ -0,0 +1,55 @@
+/*****************************************************************
+ *
+ *               The Compcert verified compiler
+ *
+ *           Xavier Leroy, INRIA Paris-Rocquencourt
+ *
+ * Copyright (c) 2013 Institut National de Recherche en Informatique et
+ *  en Automatique.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions are met:
+ *     * Redistributions of source code must retain the above copyright
+ *       notice, this list of conditions and the following disclaimer.
+ *     * Redistributions in binary form must reproduce the above copyright
+ *       notice, this list of conditions and the following disclaimer in the
+ *       documentation and/or other materials provided with the distribution.
+ *     * Neither the name of the <organization> nor the
+ *       names of its contributors may be used to endorse or promote products
+ *       derived from this software without specific prior written permission.
+ * 
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL <COPYRIGHT
+ * HOLDER> BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ *
+ **********************************************************************/
+
+/* Helper functions for 64-bit integer arithmetic. Reference C implementation */
+
+#include "i64.h"
+
+/* Conversion from unsigned int64 to float32 */
+
+float __i64_utof(unsigned long long x)
+{
+  if (x >= 1ULL << 53) {
+    /* x is large enough that double rounding can occur.
+       Nudge x away from the points where double rounding occurs
+       (the "round to odd" technique) */
+    unsigned delta = ((unsigned) x & 0x7FF) + 0x7FF;
+    x = (x | delta) & ~0x7FFULL;
+  }
+  /* Convert to double */
+  unsigned xl = x, xh = x >> 32;
+  double r = (double) xl + 0x1.0p32 * (double) xh;
+  /* Round to single */
+  return (float) r;
+}