changeset 7997:5601e440e5e7

8130150: Implement BigInteger.montgomeryMultiply intrinsic Reviewed-by: kvn, mdoerr
author vkempik
date Fri, 04 Mar 2016 16:15:48 +0300
parents 51c505229e71
children 4abc54f62213
files src/cpu/x86/vm/sharedRuntime_x86_64.cpp src/cpu/x86/vm/stubGenerator_x86_64.cpp src/cpu/x86/vm/vm_version_x86.cpp src/share/vm/classfile/vmSymbols.hpp src/share/vm/opto/c2_globals.hpp src/share/vm/opto/escape.cpp src/share/vm/opto/library_call.cpp src/share/vm/opto/runtime.cpp src/share/vm/opto/runtime.hpp src/share/vm/runtime/sharedRuntime.hpp src/share/vm/runtime/stubRoutines.cpp src/share/vm/runtime/stubRoutines.hpp test/compiler/intrinsics/montgomerymultiply/MontgomeryMultiplyTest.java
diffstat 13 files changed, 775 insertions(+), 9 deletions(-) [+]
line wrap: on
line diff
--- a/src/cpu/x86/vm/sharedRuntime_x86_64.cpp	Wed Feb 17 13:40:12 2016 +0300
+++ b/src/cpu/x86/vm/sharedRuntime_x86_64.cpp	Fri Mar 04 16:15:48 2016 +0300
@@ -23,6 +23,9 @@
  */
 
 #include "precompiled.hpp"
+#ifndef _WINDOWS
+#include "alloca.h"
+#endif
 #include "asm/macroAssembler.hpp"
 #include "asm/macroAssembler.inline.hpp"
 #include "code/debugInfoRec.hpp"
@@ -3966,6 +3969,256 @@
 }
 
 
+//------------------------------Montgomery multiplication------------------------
+//
+
+#ifndef _WINDOWS
+
+#define ASM_SUBTRACT
+
+#ifdef ASM_SUBTRACT
+// Subtract 0:b from carry:a.  Return carry.
+static unsigned long
+sub(unsigned long a[], unsigned long b[], unsigned long carry, long len) {
+  long i = 0, cnt = len;
+  unsigned long tmp;
+  asm volatile("clc; "
+               "0: ; "
+               "mov (%[b], %[i], 8), %[tmp]; "
+               "sbb %[tmp], (%[a], %[i], 8); "
+               "inc %[i]; dec %[cnt]; "
+               "jne 0b; "
+               "mov %[carry], %[tmp]; sbb $0, %[tmp]; "
+               : [i]"+r"(i), [cnt]"+r"(cnt), [tmp]"=&r"(tmp)
+               : [a]"r"(a), [b]"r"(b), [carry]"r"(carry)
+               : "memory");
+  return tmp;
+}
+#else // ASM_SUBTRACT
+typedef int __attribute__((mode(TI))) int128;
+
+// Subtract 0:b from carry:a.  Return carry.
+static unsigned long
+sub(unsigned long a[], unsigned long b[], unsigned long carry, int len) {
+  int128 tmp = 0;
+  int i;
+  for (i = 0; i < len; i++) {
+    tmp += a[i];
+    tmp -= b[i];
+    a[i] = tmp;
+    tmp >>= 64;
+    assert(-1 <= tmp && tmp <= 0, "invariant");
+  }
+  return tmp + carry;
+}
+#endif // ! ASM_SUBTRACT
+
+// Multiply (unsigned) Long A by Long B, accumulating the double-
+// length result into the accumulator formed of T0, T1, and T2.
+#define MACC(A, B, T0, T1, T2)                                      \
+do {                                                                \
+  unsigned long hi, lo;                                             \
+  asm volatile("mul %5; add %%rax, %2; adc %%rdx, %3; adc $0, %4"   \
+           : "=&d"(hi), "=a"(lo), "+r"(T0), "+r"(T1), "+g"(T2)      \
+           : "r"(A), "a"(B) : "cc");                                \
+ } while(0)
+
+// As above, but add twice the double-length result into the
+// accumulator.
+#define MACC2(A, B, T0, T1, T2)                                     \
+do {                                                                \
+  unsigned long hi, lo;                                             \
+  asm volatile("mul %5; add %%rax, %2; adc %%rdx, %3; adc $0, %4;"  \
+           "add %%rax, %2; adc %%rdx, %3; adc $0, %4"               \
+           : "=&d"(hi), "=a"(lo), "+r"(T0), "+r"(T1), "+g"(T2)      \
+           : "r"(A), "a"(B) : "cc");                                \
+ } while(0)
+
+// Fast Montgomery multiplication.  The derivation of the algorithm is
+// in  A Cryptographic Library for the Motorola DSP56000,
+// Dusse and Kaliski, Proc. EUROCRYPT 90, pp. 230-237.
+
+static void __attribute__((noinline))
+montgomery_multiply(unsigned long a[], unsigned long b[], unsigned long n[],
+                    unsigned long m[], unsigned long inv, int len) {
+  unsigned long t0 = 0, t1 = 0, t2 = 0; // Triple-precision accumulator
+  int i;
+
+  assert(inv * n[0] == -1UL, "broken inverse in Montgomery multiply");
+
+  for (i = 0; i < len; i++) {
+    int j;
+    for (j = 0; j < i; j++) {
+      MACC(a[j], b[i-j], t0, t1, t2);
+      MACC(m[j], n[i-j], t0, t1, t2);
+    }
+    MACC(a[i], b[0], t0, t1, t2);
+    m[i] = t0 * inv;
+    MACC(m[i], n[0], t0, t1, t2);
+
+    assert(t0 == 0, "broken Montgomery multiply");
+
+    t0 = t1; t1 = t2; t2 = 0;
+  }
+
+  for (i = len; i < 2*len; i++) {
+    int j;
+    for (j = i-len+1; j < len; j++) {
+      MACC(a[j], b[i-j], t0, t1, t2);
+      MACC(m[j], n[i-j], t0, t1, t2);
+    }
+    m[i-len] = t0;
+    t0 = t1; t1 = t2; t2 = 0;
+  }
+
+  while (t0)
+    t0 = sub(m, n, t0, len);
+}
+
+// Fast Montgomery squaring.  This uses asymptotically 25% fewer
+// multiplies so it should be up to 25% faster than Montgomery
+// multiplication.  However, its loop control is more complex and it
+// may actually run slower on some machines.
+
+static void __attribute__((noinline))
+montgomery_square(unsigned long a[], unsigned long n[],
+                  unsigned long m[], unsigned long inv, int len) {
+  unsigned long t0 = 0, t1 = 0, t2 = 0; // Triple-precision accumulator
+  int i;
+
+  assert(inv * n[0] == -1UL, "broken inverse in Montgomery multiply");
+
+  for (i = 0; i < len; i++) {
+    int j;
+    int end = (i+1)/2;
+    for (j = 0; j < end; j++) {
+      MACC2(a[j], a[i-j], t0, t1, t2);
+      MACC(m[j], n[i-j], t0, t1, t2);
+    }
+    if ((i & 1) == 0) {
+      MACC(a[j], a[j], t0, t1, t2);
+    }
+    for (; j < i; j++) {
+      MACC(m[j], n[i-j], t0, t1, t2);
+    }
+    m[i] = t0 * inv;
+    MACC(m[i], n[0], t0, t1, t2);
+
+    assert(t0 == 0, "broken Montgomery square");
+
+    t0 = t1; t1 = t2; t2 = 0;
+  }
+
+  for (i = len; i < 2*len; i++) {
+    int start = i-len+1;
+    int end = start + (len - start)/2;
+    int j;
+    for (j = start; j < end; j++) {
+      MACC2(a[j], a[i-j], t0, t1, t2);
+      MACC(m[j], n[i-j], t0, t1, t2);
+    }
+    if ((i & 1) == 0) {
+      MACC(a[j], a[j], t0, t1, t2);
+    }
+    for (; j < len; j++) {
+      MACC(m[j], n[i-j], t0, t1, t2);
+    }
+    m[i-len] = t0;
+    t0 = t1; t1 = t2; t2 = 0;
+  }
+
+  while (t0)
+    t0 = sub(m, n, t0, len);
+}
+
+// Swap words in a longword.
+static unsigned long swap(unsigned long x) {
+  return (x << 32) | (x >> 32);
+}
+
+// Copy len longwords from s to d, word-swapping as we go.  The
+// destination array is reversed.
+static void reverse_words(unsigned long *s, unsigned long *d, int len) {
+  d += len;
+  while(len-- > 0) {
+    d--;
+    *d = swap(*s);
+    s++;
+  }
+}
+
+// The threshold at which squaring is advantageous was determined
+// experimentally on an i7-3930K (Ivy Bridge) CPU @ 3.5GHz.
+#define MONTGOMERY_SQUARING_THRESHOLD 64
+
+void SharedRuntime::montgomery_multiply(jint *a_ints, jint *b_ints, jint *n_ints,
+                                        jint len, jlong inv,
+                                        jint *m_ints) {
+  assert(len % 2 == 0, "array length in montgomery_multiply must be even");
+  int longwords = len/2;
+
+  // Make very sure we don't use so much space that the stack might
+  // overflow.  512 jints corresponds to an 16384-bit integer and
+  // will use here a total of 8k bytes of stack space.
+  int total_allocation = longwords * sizeof (unsigned long) * 4;
+  guarantee(total_allocation <= 8192, "must be");
+  unsigned long *scratch = (unsigned long *)alloca(total_allocation);
+
+  // Local scratch arrays
+  unsigned long
+    *a = scratch + 0 * longwords,
+    *b = scratch + 1 * longwords,
+    *n = scratch + 2 * longwords,
+    *m = scratch + 3 * longwords;
+
+  reverse_words((unsigned long *)a_ints, a, longwords);
+  reverse_words((unsigned long *)b_ints, b, longwords);
+  reverse_words((unsigned long *)n_ints, n, longwords);
+
+  ::montgomery_multiply(a, b, n, m, (unsigned long)inv, longwords);
+
+  reverse_words(m, (unsigned long *)m_ints, longwords);
+}
+
+void SharedRuntime::montgomery_square(jint *a_ints, jint *n_ints,
+                                      jint len, jlong inv,
+                                      jint *m_ints) {
+  assert(len % 2 == 0, "array length in montgomery_square must be even");
+  int longwords = len/2;
+
+  // Make very sure we don't use so much space that the stack might
+  // overflow.  512 jints corresponds to an 16384-bit integer and
+  // will use here a total of 6k bytes of stack space.
+  int total_allocation = longwords * sizeof (unsigned long) * 3;
+  guarantee(total_allocation <= 8192, "must be");
+  unsigned long *scratch = (unsigned long *)alloca(total_allocation);
+
+  // Local scratch arrays
+  unsigned long
+    *a = scratch + 0 * longwords,
+    *n = scratch + 1 * longwords,
+    *m = scratch + 2 * longwords;
+
+  reverse_words((unsigned long *)a_ints, a, longwords);
+  reverse_words((unsigned long *)n_ints, n, longwords);
+
+  //montgomery_square fails to pass BigIntegerTest on solaris amd64
+  //on jdk7 and jdk8.
+#ifndef SOLARIS
+  if (len >= MONTGOMERY_SQUARING_THRESHOLD) {
+#else
+  if (0) {
+#endif
+    ::montgomery_square(a, n, m, (unsigned long)inv, longwords);
+  } else {
+    ::montgomery_multiply(a, a, n, m, (unsigned long)inv, longwords);
+  }
+
+  reverse_words(m, (unsigned long *)m_ints, longwords);
+}
+
+#endif // WINDOWS
+
 #ifdef COMPILER2
 // This is here instead of runtime_x86_64.cpp because it uses SimpleRuntimeFrame
 //
--- a/src/cpu/x86/vm/stubGenerator_x86_64.cpp	Wed Feb 17 13:40:12 2016 +0300
+++ b/src/cpu/x86/vm/stubGenerator_x86_64.cpp	Fri Mar 04 16:15:48 2016 +0300
@@ -4094,7 +4094,18 @@
     if (UseMulAddIntrinsic) {
       StubRoutines::_mulAdd = generate_mulAdd();
     }
-#endif
+
+#ifndef _WINDOWS
+    if (UseMontgomeryMultiplyIntrinsic) {
+      StubRoutines::_montgomeryMultiply
+        = CAST_FROM_FN_PTR(address, SharedRuntime::montgomery_multiply);
+    }
+    if (UseMontgomerySquareIntrinsic) {
+      StubRoutines::_montgomerySquare
+        = CAST_FROM_FN_PTR(address, SharedRuntime::montgomery_square);
+    }
+#endif // WINDOWS
+#endif // COMPILER2
   }
 
  public:
--- a/src/cpu/x86/vm/vm_version_x86.cpp	Wed Feb 17 13:40:12 2016 +0300
+++ b/src/cpu/x86/vm/vm_version_x86.cpp	Fri Mar 04 16:15:48 2016 +0300
@@ -709,6 +709,12 @@
   if (FLAG_IS_DEFAULT(UseMulAddIntrinsic)) {
     UseMulAddIntrinsic = true;
   }
+  if (FLAG_IS_DEFAULT(UseMontgomeryMultiplyIntrinsic)) {
+    UseMontgomeryMultiplyIntrinsic = true;
+  }
+  if (FLAG_IS_DEFAULT(UseMontgomerySquareIntrinsic)) {
+    UseMontgomerySquareIntrinsic = true;
+  }
 #else
   if (UseMultiplyToLenIntrinsic) {
     if (!FLAG_IS_DEFAULT(UseMultiplyToLenIntrinsic)) {
@@ -728,6 +734,18 @@
     }
     FLAG_SET_DEFAULT(UseMulAddIntrinsic, false);
   }
+  if (UseMontgomeryMultiplyIntrinsic) {
+    if (!FLAG_IS_DEFAULT(UseMontgomeryMultiplyIntrinsic)) {
+      warning("montgomeryMultiply intrinsic is not available in 32-bit VM");
+    }
+    FLAG_SET_DEFAULT(UseMontgomeryMultiplyIntrinsic, false);
+  }
+  if (UseMontgomerySquareIntrinsic) {
+    if (!FLAG_IS_DEFAULT(UseMontgomerySquareIntrinsic)) {
+      warning("montgomerySquare intrinsic is not available in 32-bit VM");
+    }
+    FLAG_SET_DEFAULT(UseMontgomerySquareIntrinsic, false);
+  }
 #endif
 #endif // COMPILER2
 
--- a/src/share/vm/classfile/vmSymbols.hpp	Wed Feb 17 13:40:12 2016 +0300
+++ b/src/share/vm/classfile/vmSymbols.hpp	Fri Mar 04 16:15:48 2016 +0300
@@ -789,7 +789,7 @@
    do_signature(encodeISOArray_signature,                        "([CI[BII)I")                                          \
                                                                                                                         \
   do_class(java_math_BigInteger,                      "java/math/BigInteger")                                           \
-  do_intrinsic(_multiplyToLen,      java_math_BigInteger, multiplyToLen_name, multiplyToLen_signature, F_R)             \
+  do_intrinsic(_multiplyToLen,      java_math_BigInteger, multiplyToLen_name, multiplyToLen_signature, F_S)             \
    do_name(     multiplyToLen_name,                             "multiplyToLen")                                        \
    do_signature(multiplyToLen_signature,                        "([II[II[I)[I")                                         \
                                                                                                                         \
@@ -801,6 +801,14 @@
    do_name(     mulAdd_name,                                  "implMulAdd")                                             \
    do_signature(mulAdd_signature,                             "([I[IIII)I")                                             \
                                                                                                                         \
+  do_intrinsic(_montgomeryMultiply,      java_math_BigInteger, montgomeryMultiply_name, montgomeryMultiply_signature, F_S) \
+   do_name(     montgomeryMultiply_name,                             "implMontgomeryMultiply")                          \
+   do_signature(montgomeryMultiply_signature,                        "([I[I[IIJ[I)[I")                                  \
+                                                                                                                        \
+  do_intrinsic(_montgomerySquare,      java_math_BigInteger, montgomerySquare_name, montgomerySquare_signature, F_S)    \
+   do_name(     montgomerySquare_name,                             "implMontgomerySquare")                              \
+   do_signature(montgomerySquare_signature,                        "([I[IIJ[I)[I")                                      \
+                                                                                                                        \
   /* java/lang/ref/Reference */                                                                                         \
   do_intrinsic(_Reference_get,            java_lang_ref_Reference, get_name,    void_object_signature, F_R)             \
                                                                                                                         \
--- a/src/share/vm/opto/c2_globals.hpp	Wed Feb 17 13:40:12 2016 +0300
+++ b/src/share/vm/opto/c2_globals.hpp	Fri Mar 04 16:15:48 2016 +0300
@@ -665,6 +665,12 @@
   product(bool, UseMulAddIntrinsic, false,                                  \
           "Enables intrinsification of BigInteger.mulAdd()")                \
                                                                             \
+  product(bool, UseMontgomeryMultiplyIntrinsic, false,                      \
+          "Enables intrinsification of BigInteger.montgomeryMultiply()")    \
+                                                                            \
+  product(bool, UseMontgomerySquareIntrinsic, false,                        \
+          "Enables intrinsification of BigInteger.montgomerySquare()")      \
+                                                                            \
   product(bool, UseTypeSpeculation, true,                                   \
           "Speculatively propagate types from profiles")                    \
                                                                             \
--- a/src/share/vm/opto/escape.cpp	Wed Feb 17 13:40:12 2016 +0300
+++ b/src/share/vm/opto/escape.cpp	Fri Mar 04 16:15:48 2016 +0300
@@ -960,8 +960,10 @@
                   strcmp(call->as_CallLeaf()->_name, "sha512_implCompressMB") == 0 ||
                   strcmp(call->as_CallLeaf()->_name, "multiplyToLen") == 0 ||
                   strcmp(call->as_CallLeaf()->_name, "squareToLen") == 0 ||
-                  strcmp(call->as_CallLeaf()->_name, "mulAdd") == 0)
-                  ))) {
+                  strcmp(call->as_CallLeaf()->_name, "mulAdd") == 0 ||
+                  strcmp(call->as_CallLeaf()->_name, "montgomery_multiply") == 0 ||
+                  strcmp(call->as_CallLeaf()->_name, "montgomery_square") == 0)
+                 ))) {
             call->dump();
             fatal(err_msg_res("EA unexpected CallLeaf %s", call->as_CallLeaf()->_name));
           }
--- a/src/share/vm/opto/library_call.cpp	Wed Feb 17 13:40:12 2016 +0300
+++ b/src/share/vm/opto/library_call.cpp	Fri Mar 04 16:15:48 2016 +0300
@@ -326,6 +326,8 @@
   bool inline_multiplyToLen();
   bool inline_squareToLen();
   bool inline_mulAdd();
+  bool inline_montgomeryMultiply();
+  bool inline_montgomerySquare();
 
   bool inline_profileBoolean();
 };
@@ -537,6 +539,13 @@
     if (!UseMulAddIntrinsic) return NULL;
     break;
 
+  case vmIntrinsics::_montgomeryMultiply:
+     if (!UseMontgomeryMultiplyIntrinsic) return NULL;
+    break;
+  case vmIntrinsics::_montgomerySquare:
+     if (!UseMontgomerySquareIntrinsic) return NULL;
+    break;
+
   case vmIntrinsics::_cipherBlockChaining_encryptAESCrypt:
   case vmIntrinsics::_cipherBlockChaining_decryptAESCrypt:
     if (!UseAESIntrinsics) return NULL;
@@ -943,6 +952,11 @@
   case vmIntrinsics::_mulAdd:
     return inline_mulAdd();
 
+  case vmIntrinsics::_montgomeryMultiply:
+    return inline_montgomeryMultiply();
+  case vmIntrinsics::_montgomerySquare:
+    return inline_montgomerySquare();
+
   case vmIntrinsics::_encodeISOArray:
     return inline_encodeISOArray();
 
@@ -5783,11 +5797,12 @@
 
   assert(callee()->signature()->size() == 5, "multiplyToLen has 5 parameters");
 
-  Node* x    = argument(1);
-  Node* xlen = argument(2);
-  Node* y    = argument(3);
-  Node* ylen = argument(4);
-  Node* z    = argument(5);
+  // no receiver because it is a static method
+  Node* x    = argument(0);
+  Node* xlen = argument(1);
+  Node* y    = argument(2);
+  Node* ylen = argument(3);
+  Node* z    = argument(4);
 
   const Type* x_type = x->Value(&_gvn);
   const Type* y_type = y->Value(&_gvn);
@@ -5966,6 +5981,121 @@
   return true;
 }
 
+//-------------inline_montgomeryMultiply-----------------------------------
+bool LibraryCallKit::inline_montgomeryMultiply() {
+  address stubAddr = StubRoutines::montgomeryMultiply();
+  if (stubAddr == NULL) {
+    return false; // Intrinsic's stub is not implemented on this platform
+  }
+
+  assert(UseMontgomeryMultiplyIntrinsic, "not implemented on this platform");
+  const char* stubName = "montgomery_square";
+
+  assert(callee()->signature()->size() == 7, "montgomeryMultiply has 7 parameters");
+
+  Node* a    = argument(0);
+  Node* b    = argument(1);
+  Node* n    = argument(2);
+  Node* len  = argument(3);
+  Node* inv  = argument(4);
+  Node* m    = argument(6);
+
+  const Type* a_type = a->Value(&_gvn);
+  const TypeAryPtr* top_a = a_type->isa_aryptr();
+  const Type* b_type = b->Value(&_gvn);
+  const TypeAryPtr* top_b = b_type->isa_aryptr();
+  const Type* n_type = a->Value(&_gvn);
+  const TypeAryPtr* top_n = n_type->isa_aryptr();
+  const Type* m_type = a->Value(&_gvn);
+  const TypeAryPtr* top_m = m_type->isa_aryptr();
+  if (top_a  == NULL || top_a->klass()  == NULL ||
+      top_b == NULL || top_b->klass()  == NULL ||
+      top_n == NULL || top_n->klass()  == NULL ||
+      top_m == NULL || top_m->klass()  == NULL) {
+    // failed array check
+    return false;
+  }
+
+  BasicType a_elem = a_type->isa_aryptr()->klass()->as_array_klass()->element_type()->basic_type();
+  BasicType b_elem = b_type->isa_aryptr()->klass()->as_array_klass()->element_type()->basic_type();
+  BasicType n_elem = n_type->isa_aryptr()->klass()->as_array_klass()->element_type()->basic_type();
+  BasicType m_elem = m_type->isa_aryptr()->klass()->as_array_klass()->element_type()->basic_type();
+  if (a_elem != T_INT || b_elem != T_INT || n_elem != T_INT || m_elem != T_INT) {
+    return false;
+  }
+
+  // Make the call
+  {
+    Node* a_start = array_element_address(a, intcon(0), a_elem);
+    Node* b_start = array_element_address(b, intcon(0), b_elem);
+    Node* n_start = array_element_address(n, intcon(0), n_elem);
+    Node* m_start = array_element_address(m, intcon(0), m_elem);
+
+    Node* call = make_runtime_call(RC_LEAF,
+                                   OptoRuntime::montgomeryMultiply_Type(),
+                                   stubAddr, stubName, TypePtr::BOTTOM,
+                                   a_start, b_start, n_start, len, inv, top(),
+                                   m_start);
+    set_result(m);
+  }
+
+  return true;
+}
+
+bool LibraryCallKit::inline_montgomerySquare() {
+  address stubAddr = StubRoutines::montgomerySquare();
+  if (stubAddr == NULL) {
+    return false; // Intrinsic's stub is not implemented on this platform
+  }
+
+  assert(UseMontgomerySquareIntrinsic, "not implemented on this platform");
+  const char* stubName = "montgomery_square";
+
+  assert(callee()->signature()->size() == 6, "montgomerySquare has 6 parameters");
+
+  Node* a    = argument(0);
+  Node* n    = argument(1);
+  Node* len  = argument(2);
+  Node* inv  = argument(3);
+  Node* m    = argument(5);
+
+  const Type* a_type = a->Value(&_gvn);
+  const TypeAryPtr* top_a = a_type->isa_aryptr();
+  const Type* n_type = a->Value(&_gvn);
+  const TypeAryPtr* top_n = n_type->isa_aryptr();
+  const Type* m_type = a->Value(&_gvn);
+  const TypeAryPtr* top_m = m_type->isa_aryptr();
+  if (top_a  == NULL || top_a->klass()  == NULL ||
+      top_n == NULL || top_n->klass()  == NULL ||
+      top_m == NULL || top_m->klass()  == NULL) {
+    // failed array check
+    return false;
+  }
+
+  BasicType a_elem = a_type->isa_aryptr()->klass()->as_array_klass()->element_type()->basic_type();
+  BasicType n_elem = n_type->isa_aryptr()->klass()->as_array_klass()->element_type()->basic_type();
+  BasicType m_elem = m_type->isa_aryptr()->klass()->as_array_klass()->element_type()->basic_type();
+  if (a_elem != T_INT || n_elem != T_INT || m_elem != T_INT) {
+    return false;
+  }
+
+  // Make the call
+  {
+    Node* a_start = array_element_address(a, intcon(0), a_elem);
+    Node* n_start = array_element_address(n, intcon(0), n_elem);
+    Node* m_start = array_element_address(m, intcon(0), m_elem);
+
+    Node* call = make_runtime_call(RC_LEAF,
+                                   OptoRuntime::montgomerySquare_Type(),
+                                   stubAddr, stubName, TypePtr::BOTTOM,
+                                   a_start, n_start, len, inv, top(),
+                                   m_start);
+    set_result(m);
+  }
+
+  return true;
+}
+
 
 /**
  * Calculate CRC32 for byte.
--- a/src/share/vm/opto/runtime.cpp	Wed Feb 17 13:40:12 2016 +0300
+++ b/src/share/vm/opto/runtime.cpp	Fri Mar 04 16:15:48 2016 +0300
@@ -998,6 +998,52 @@
   return TypeFunc::make(domain, range);
 }
 
+const TypeFunc* OptoRuntime::montgomeryMultiply_Type() {
+  // create input type (domain)
+  int num_args      = 7;
+  int argcnt = num_args;
+  const Type** fields = TypeTuple::fields(argcnt);
+  int argp = TypeFunc::Parms;
+  fields[argp++] = TypePtr::NOTNULL;    // a
+  fields[argp++] = TypePtr::NOTNULL;    // b
+  fields[argp++] = TypePtr::NOTNULL;    // n
+  fields[argp++] = TypeInt::INT;        // len
+  fields[argp++] = TypeLong::LONG;      // inv
+  fields[argp++] = Type::HALF;
+  fields[argp++] = TypePtr::NOTNULL;    // result
+  assert(argp == TypeFunc::Parms+argcnt, "correct decoding");
+  const TypeTuple* domain = TypeTuple::make(TypeFunc::Parms+argcnt, fields);
+
+  // result type needed
+  fields = TypeTuple::fields(1);
+  fields[TypeFunc::Parms+0] = TypePtr::NOTNULL;
+
+  const TypeTuple* range = TypeTuple::make(TypeFunc::Parms, fields);
+  return TypeFunc::make(domain, range);
+}
+
+const TypeFunc* OptoRuntime::montgomerySquare_Type() {
+  // create input type (domain)
+  int num_args      = 6;
+  int argcnt = num_args;
+  const Type** fields = TypeTuple::fields(argcnt);
+  int argp = TypeFunc::Parms;
+  fields[argp++] = TypePtr::NOTNULL;    // a
+  fields[argp++] = TypePtr::NOTNULL;    // n
+  fields[argp++] = TypeInt::INT;        // len
+  fields[argp++] = TypeLong::LONG;      // inv
+  fields[argp++] = Type::HALF;
+  fields[argp++] = TypePtr::NOTNULL;    // result
+  assert(argp == TypeFunc::Parms+argcnt, "correct decoding");
+  const TypeTuple* domain = TypeTuple::make(TypeFunc::Parms+argcnt, fields);
+
+  // result type needed
+  fields = TypeTuple::fields(1);
+  fields[TypeFunc::Parms+0] = TypePtr::NOTNULL;
+
+  const TypeTuple* range = TypeTuple::make(TypeFunc::Parms, fields);
+  return TypeFunc::make(domain, range);
+}
 
 
 //------------- Interpreter state access for on stack replacement
--- a/src/share/vm/opto/runtime.hpp	Wed Feb 17 13:40:12 2016 +0300
+++ b/src/share/vm/opto/runtime.hpp	Fri Mar 04 16:15:48 2016 +0300
@@ -308,6 +308,8 @@
   static const TypeFunc* squareToLen_Type();
 
   static const TypeFunc* mulAdd_Type();
+  static const TypeFunc* montgomeryMultiply_Type();
+  static const TypeFunc* montgomerySquare_Type();
 
   static const TypeFunc* updateBytesCRC32_Type();
 
--- a/src/share/vm/runtime/sharedRuntime.hpp	Wed Feb 17 13:40:12 2016 +0300
+++ b/src/share/vm/runtime/sharedRuntime.hpp	Fri Mar 04 16:15:48 2016 +0300
@@ -145,6 +145,12 @@
   static double dsqrt(double f);
 #endif
 
+  // Montgomery multiplication
+  static void montgomery_multiply(jint *a_ints, jint *b_ints, jint *n_ints,
+                                  jint len, jlong inv, jint *m_ints);
+  static void montgomery_square(jint *a_ints, jint *n_ints,
+                                jint len, jlong inv, jint *m_ints);
+
 #ifdef __SOFTFP__
   // C++ compiler generates soft float instructions as well as passing
   // float and double in registers.
--- a/src/share/vm/runtime/stubRoutines.cpp	Wed Feb 17 13:40:12 2016 +0300
+++ b/src/share/vm/runtime/stubRoutines.cpp	Fri Mar 04 16:15:48 2016 +0300
@@ -138,6 +138,8 @@
 address StubRoutines::_multiplyToLen = NULL;
 address StubRoutines::_squareToLen = NULL;
 address StubRoutines::_mulAdd = NULL;
+address StubRoutines::_montgomeryMultiply = NULL;
+address StubRoutines::_montgomerySquare = NULL;
 
 double (* StubRoutines::_intrinsic_log   )(double) = NULL;
 double (* StubRoutines::_intrinsic_log10 )(double) = NULL;
--- a/src/share/vm/runtime/stubRoutines.hpp	Wed Feb 17 13:40:12 2016 +0300
+++ b/src/share/vm/runtime/stubRoutines.hpp	Fri Mar 04 16:15:48 2016 +0300
@@ -211,6 +211,8 @@
   static address _multiplyToLen;
   static address _squareToLen;
   static address _mulAdd;
+  static address _montgomeryMultiply;
+  static address _montgomerySquare;
 
   // These are versions of the java.lang.Math methods which perform
   // the same operations as the intrinsic version.  They are used for
@@ -371,6 +373,8 @@
   static address multiplyToLen()       {return _multiplyToLen; }
   static address squareToLen()         {return _squareToLen; }
   static address mulAdd()              {return _mulAdd; }
+  static address montgomeryMultiply()  { return _montgomeryMultiply; }
+  static address montgomerySquare()    { return _montgomerySquare; }
 
   static address select_fill_function(BasicType t, bool aligned, const char* &name);
 
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/test/compiler/intrinsics/montgomerymultiply/MontgomeryMultiplyTest.java	Fri Mar 04 16:15:48 2016 +0300
@@ -0,0 +1,278 @@
+//
+// Copyright (c) 2000, 2015, Oracle and/or its affiliates. All rights reserved.
+// Copyright (c) 2015, Red Hat Inc. All rights reserved.
+// DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
+//
+// This code is free software; you can redistribute it and/or modify it
+// under the terms of the GNU General Public License version 2 only, as
+// published by the Free Software Foundation.
+//
+// This code is distributed in the hope that it will be useful, but WITHOUT
+// ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+// FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
+// version 2 for more details (a copy is included in the LICENSE file that
+// accompanied this code).
+//
+// You should have received a copy of the GNU General Public License version
+// 2 along with this work; if not, write to the Free Software Foundation,
+// Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
+//
+// Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
+// or visit www.oracle.com if you need additional information or have any
+// questions.
+//
+//
+
+import java.lang.invoke.MethodHandle;
+import java.lang.invoke.MethodHandles;
+import java.lang.invoke.MethodType;
+import java.lang.reflect.Constructor;
+import java.lang.reflect.Field;
+import java.lang.reflect.Method;
+import java.math.BigInteger;
+import java.util.Arrays;
+import java.util.Random;
+
+/**
+ * @test
+ * @bug 8130150
+ * @library /testlibrary
+ * @requires (os.simpleArch == "x64") & (os.family != "windows")
+ * @summary Verify that the Montgomery multiply intrinsic works and correctly checks its arguments.
+ */
+
+public class MontgomeryMultiplyTest {
+
+    static final MethodHandles.Lookup lookup = MethodHandles.lookup();
+
+    static final MethodHandle montgomeryMultiplyHandle, montgomerySquareHandle;
+    static final MethodHandle bigIntegerConstructorHandle;
+    static final Field bigIntegerMagField;
+
+    static {
+       // Use reflection to gain access to the methods we want to test.
+        try {
+            Method m = BigInteger.class.getDeclaredMethod("montgomeryMultiply",
+                /*a*/int[].class, /*b*/int[].class, /*n*/int[].class, /*len*/int.class,
+                /*inv*/long.class, /*product*/int[].class);
+            m.setAccessible(true);
+            montgomeryMultiplyHandle = lookup.unreflect(m);
+
+            m = BigInteger.class.getDeclaredMethod("montgomerySquare",
+                /*a*/int[].class, /*n*/int[].class, /*len*/int.class,
+                /*inv*/long.class, /*product*/int[].class);
+            m.setAccessible(true);
+            montgomerySquareHandle = lookup.unreflect(m);
+
+            Constructor c
+                = BigInteger.class.getDeclaredConstructor(int.class, int[].class);
+            c.setAccessible(true);
+            bigIntegerConstructorHandle = lookup.unreflectConstructor(c);
+
+            bigIntegerMagField = BigInteger.class.getDeclaredField("mag");
+            bigIntegerMagField.setAccessible(true);
+
+        } catch (Throwable ex) {
+            throw new RuntimeException(ex);
+        }
+    }
+
+    // Invoke either BigInteger.montgomeryMultiply or BigInteger.montgomerySquare.
+    int[] montgomeryMultiply(int[] a, int[] b, int[] n, int len, long inv,
+                             int[] product) throws Throwable {
+        int[] result =
+            (a == b) ? (int[]) montgomerySquareHandle.invokeExact(a, n, len, inv, product)
+                     : (int[]) montgomeryMultiplyHandle.invokeExact(a, b, n, len, inv, product);
+        return Arrays.copyOf(result, len);
+    }
+
+    // Invoke the private constructor BigInteger(int[]).
+    BigInteger newBigInteger(int[] val) throws Throwable {
+        return (BigInteger) bigIntegerConstructorHandle.invokeExact(1, val);
+    }
+
+    // Get the private field BigInteger.mag
+    int[] mag(BigInteger n) {
+        try {
+            return (int[]) bigIntegerMagField.get(n);
+        } catch (Exception ex) {
+            throw new RuntimeException(ex);
+        }
+    }
+
+    // Montgomery multiplication
+    // Calculate a * b * r^-1 mod n)
+    //
+    // R is a power of the word size
+    // N' = R^-1 mod N
+    //
+    // T := ab
+    // m := (T mod R)N' mod R [so 0 <= m < R]
+    // t := (T + mN)/R
+    // if t >= N then return t - N else return t
+    //
+    BigInteger montgomeryMultiply(BigInteger a, BigInteger b, BigInteger N,
+            int len, BigInteger n_prime)
+            throws Throwable {
+        BigInteger T = a.multiply(b);
+        BigInteger R = BigInteger.ONE.shiftLeft(len*32);
+        BigInteger mask = R.subtract(BigInteger.ONE);
+        BigInteger m = (T.and(mask)).multiply(n_prime);
+        m = m.and(mask); // i.e. m.mod(R)
+        T = T.add(m.multiply(N));
+        T = T.shiftRight(len*32); // i.e. T.divide(R)
+        if (T.compareTo(N) > 0) {
+            T = T.subtract(N);
+        }
+        return T;
+    }
+
+    // Call the Montgomery multiply intrinsic.
+    BigInteger montgomeryMultiply(int[] a_words, int[] b_words, int[] n_words,
+            int len, BigInteger inv)
+            throws Throwable {
+        BigInteger t = montgomeryMultiply(
+                newBigInteger(a_words),
+                newBigInteger(b_words),
+                newBigInteger(n_words),
+                len, inv);
+        return t;
+    }
+
+    // Check that the Montgomery multiply intrinsic returns the same
+    // result as the longhand calculation.
+    void check(int[] a_words, int[] b_words, int[] n_words, int len, BigInteger inv)
+            throws Throwable {
+        BigInteger n = newBigInteger(n_words);
+        BigInteger slow = montgomeryMultiply(a_words, b_words, n_words, len, inv);
+        BigInteger fast
+            = newBigInteger(montgomeryMultiply
+                            (a_words, b_words, n_words, len, inv.longValue(), null));
+        // The intrinsic may not return the same value as the longhand
+        // calculation but they must have the same residue mod N.
+        if (!slow.mod(n).equals(fast.mod(n))) {
+            throw new RuntimeException();
+        }
+    }
+
+    Random rnd = new Random(0);
+
+    // Return a random value of length <= bits in an array of even length
+    int[] random_val(int bits) {
+        int len = (bits+63)/64;  // i.e. length in longs
+        int[] val = new int[len*2];
+        for (int i = 0; i < val.length; i++)
+            val[i] = rnd.nextInt();
+        int leadingZeros = 64 - (bits & 64);
+        if (leadingZeros >= 32) {
+            val[0] = 0;
+            val[1] &= ~(-1l << (leadingZeros & 31));
+        } else {
+            val[0] &= ~(-1l << leadingZeros);
+        }
+        return val;
+    }
+
+    void testOneLength(int lenInBits, int lenInInts) throws Throwable {
+        BigInteger mod = new BigInteger(lenInBits, 2, rnd);
+        BigInteger r = BigInteger.ONE.shiftLeft(lenInInts * 32);
+        BigInteger n_prime = mod.modInverse(r).negate();
+
+        // Make n.length even, padding with a zero if necessary
+        int[] n = mag(mod);
+        if (n.length < lenInInts) {
+            int[] x = new int[lenInInts];
+            System.arraycopy(n, 0, x, lenInInts-n.length, n.length);
+            n = x;
+        }
+
+        for (int i = 0; i < 10000; i++) {
+            // multiply
+            check(random_val(lenInBits), random_val(lenInBits), n, lenInInts, n_prime);
+            // square
+            int[] tmp = random_val(lenInBits);
+            check(tmp, tmp, n, lenInInts, n_prime);
+        }
+    }
+
+    // Test the Montgomery multiply intrinsic with a bunch of random
+    // values of varying lengths.  Do this for long enough that the
+    // caller of the intrinsic is C2-compiled.
+    void testResultValues() throws Throwable {
+        // Test a couple of interesting edge cases.
+        testOneLength(1024, 32);
+        testOneLength(1025, 34);
+        for (int j = 10; j > 0; j--) {
+            // Construct a random prime whose length in words is even
+            int lenInBits = rnd.nextInt(2048) + 64;
+            int lenInInts = (lenInBits + 63)/64*2;
+            testOneLength(lenInBits, lenInInts);
+        }
+    }
+
+    // Range checks
+    void testOneMontgomeryMultiplyCheck(int[] a, int[] b, int[] n, int len, long inv,
+                                        int[] product, Class klass) {
+        try {
+            montgomeryMultiply(a, b, n, len, inv, product);
+        } catch (Throwable ex) {
+            if (klass.isAssignableFrom(ex.getClass()))
+                return;
+            throw new RuntimeException(klass + " expected, " + ex + " was thrown");
+        }
+        throw new RuntimeException(klass + " expected, was not thrown");
+    }
+
+    void testOneMontgomeryMultiplyCheck(int[] a, int[] b, BigInteger n, int len, BigInteger inv,
+            Class klass) {
+        testOneMontgomeryMultiplyCheck(a, b, mag(n), len, inv.longValue(), null, klass);
+    }
+
+    void testOneMontgomeryMultiplyCheck(int[] a, int[] b, BigInteger n, int len, BigInteger inv,
+            int[] product, Class klass) {
+        testOneMontgomeryMultiplyCheck(a, b, mag(n), len, inv.longValue(), product, klass);
+    }
+
+    void testMontgomeryMultiplyChecks() {
+        int[] blah = random_val(40);
+        int[] small = random_val(39);
+        BigInteger mod = new BigInteger(40*32 , 2, rnd);
+        BigInteger r = BigInteger.ONE.shiftLeft(40*32);
+        BigInteger n_prime = mod.modInverse(r).negate();
+
+        // Length out of range: square
+        testOneMontgomeryMultiplyCheck(blah, blah, mod, 41, n_prime, IllegalArgumentException.class);
+        testOneMontgomeryMultiplyCheck(blah, blah, mod, 0, n_prime, IllegalArgumentException.class);
+        testOneMontgomeryMultiplyCheck(blah, blah, mod, -1, n_prime, IllegalArgumentException.class);
+        // As above, but for multiply
+        testOneMontgomeryMultiplyCheck(blah, blah.clone(), mod, 41, n_prime, IllegalArgumentException.class);
+        testOneMontgomeryMultiplyCheck(blah, blah.clone(), mod, 0, n_prime, IllegalArgumentException.class);
+        testOneMontgomeryMultiplyCheck(blah, blah.clone(), mod, 0, n_prime, IllegalArgumentException.class);
+
+        // Length odd
+        testOneMontgomeryMultiplyCheck(small, small, mod, 39, n_prime, IllegalArgumentException.class);
+        testOneMontgomeryMultiplyCheck(small, small, mod, 0, n_prime, IllegalArgumentException.class);
+        testOneMontgomeryMultiplyCheck(small, small, mod, -1, n_prime, IllegalArgumentException.class);
+        // As above, but for multiply
+        testOneMontgomeryMultiplyCheck(small, small.clone(), mod, 39, n_prime, IllegalArgumentException.class);
+        testOneMontgomeryMultiplyCheck(small, small.clone(), mod, 0, n_prime, IllegalArgumentException.class);
+        testOneMontgomeryMultiplyCheck(small, small.clone(), mod, -1, n_prime, IllegalArgumentException.class);
+
+        // array too small
+        testOneMontgomeryMultiplyCheck(blah, blah, mod, 40, n_prime, small, IllegalArgumentException.class);
+        testOneMontgomeryMultiplyCheck(blah, blah.clone(), mod, 40, n_prime, small, IllegalArgumentException.class);
+        testOneMontgomeryMultiplyCheck(small, blah, mod, 40, n_prime, blah, IllegalArgumentException.class);
+        testOneMontgomeryMultiplyCheck(blah, small, mod, 40, n_prime, blah, IllegalArgumentException.class);
+        testOneMontgomeryMultiplyCheck(blah, blah, mod, 40, n_prime, small, IllegalArgumentException.class);
+        testOneMontgomeryMultiplyCheck(small, small, mod, 40, n_prime, blah, IllegalArgumentException.class);
+    }
+
+    public static void main(String args[]) {
+        try {
+            new MontgomeryMultiplyTest().testMontgomeryMultiplyChecks();
+            new MontgomeryMultiplyTest().testResultValues();
+        } catch (Throwable ex) {
+            throw new RuntimeException(ex);
+        }
+     }
+}