CRC32 Power Optimization Changes

Summary:
Support for PowerPC Architecture
Detecting AltiVec Support
Closes https://github.com/facebook/rocksdb/pull/2353

Differential Revision: D5210948

Pulled By: siying

fbshipit-source-id: 859a8c063d37697addd89ba2b8a14e5efd5d24bf

Makefile

@@ -96,6 +96,18 @@ OPT += -momit-leaf-frame-pointer
 endif
 endif
 
+ifeq (,$(shell $(CXX) -fsyntax-only -maltivec -xc /dev/null 2>&1))
+CXXFLAGS += -DHAS_ALTIVEC
+CFLAGS += -DHAS_ALTIVEC
+HAS_ALTIVEC=1
+endif
+
+ifeq (,$(shell $(CXX) -fsyntax-only -mcpu=power8 -xc /dev/null 2>&1))
+CXXFLAGS += -DHAVE_POWER8
+CFLAGS +=  -DHAVE_POWER8
+HAVE_POWER8=1
+endif
+
 # if we're compiling for release, compile without debug code (-DNDEBUG) and
 # don't treat warnings as errors
 ifeq ($(DEBUG_LEVEL),0)
@@ -305,9 +317,9 @@ util/build_version.cc: FORCE
 	else mv -f $@-t $@; fi
 endif
 
-LIBOBJECTS = $(LIB_SOURCES:.cc=.o)
-LIBOBJECTS += $(TOOL_LIB_SOURCES:.cc=.o)
-MOCKOBJECTS = $(MOCK_LIB_SOURCES:.cc=.o)
+LIBOBJECTS = $(LIB_SOURCES:.cc=.cc.o) $(LIB_SOURCES_C:.c=.c.o) $(LIB_SOURCES_ASM:.S=.S.o)
+LIBOBJECTS += $(TOOL_LIB_SOURCES:.cc=.cc.o)
+MOCKOBJECTS = $(MOCK_LIB_SOURCES:.cc=.cc.o)
 
 GTEST = $(GTEST_DIR)/gtest/gtest-all.o
 TESTUTIL = ./util/testutil.o
@@ -555,14 +567,27 @@ $(SHARED2): $(SHARED4)
 $(SHARED3): $(SHARED4)
 	ln -fs $(SHARED4) $(SHARED3)
 endif
+SHARED_CC_OBJECTS = $(LIB_SOURCES:.cc=.cc.o)
+SHARED_C_OBJECTS = $(LIB_SOURCES_C:.c=.c.o)
+SHARED_ASM_OBJECTS = $(LIB_SOURCES_ASM:.S=.S.o)
 
-shared_libobjects = $(patsubst %,shared-objects/%,$(LIBOBJECTS))
+SHARED_CC_LIBOBJECTS = $(patsubst %.cc.o,shared-objects/%.cc.o,$(SHARED_CC_OBJECTS))
+SHARED_C_LIBOBJECTS = $(patsubst %.c.o,shared-objects/%.c.o,$(SHARED_C_OBJECTS))
+SHARED_ASM_LIBOBJECTS = $(patsubst %.S.o,shared-objects/%.S.o,$(SHARED_ASM_OBJECTS))
+
+shared_libobjects = $(SHARED_CC_LIBOBJECTS) $(SHARED_C_LIBOBJECTS) $(SHARED_ASM_LIBOBJECTS)
 CLEAN_FILES += shared-objects
 
-$(shared_libobjects): shared-objects/%.o: %.cc
+$(SHARED_CC_LIBOBJECTS): shared-objects/%.cc.o: %.cc 
+	$(AM_V_CC)mkdir -p $(@D) && $(CXX) $(CXXFLAGS) $(PLATFORM_SHARED_CFLAGS) -c $< -o $@
+
+$(SHARED_C_LIBOBJECTS): shared-objects/%.c.o: %.c
 	$(AM_V_CC)mkdir -p $(@D) && $(CXX) $(CXXFLAGS) $(PLATFORM_SHARED_CFLAGS) -c $< -o $@
 
-$(SHARED4): $(shared_libobjects)
+$(SHARED_ASM_LIBOBJECTS): shared-objects/%.S.o: %.S
+	$(AM_V_CC)mkdir -p $(@D) && $(CXX) $(CXXFLAGS) $(PLATFORM_SHARED_CFLAGS) -c $< -o $@
+
+$(SHARED4): $(shared_libobjects) 
 	$(CXX) $(PLATFORM_SHARED_LDFLAGS)$(SHARED3) $(CXXFLAGS) $(PLATFORM_SHARED_CFLAGS) $(shared_libobjects) $(LDFLAGS) -o $@
 
 endif  # PLATFORM_SHARED_EXT
@@ -1642,12 +1667,26 @@ rocksdbjavastaticpublishcentral:
 	mvn gpg:sign-and-deploy-file -Durl=https://oss.sonatype.org/service/local/staging/deploy/maven2/ -DrepositoryId=sonatype-nexus-staging -DpomFile=java/rocksjni.pom -Dfile=java/target/rocksdbjni-$(ROCKSDB_MAJOR).$(ROCKSDB_MINOR).$(ROCKSDB_PATCH).jar
 
 # A version of each $(LIBOBJECTS) compiled with -fPIC
-java_libobjects = $(patsubst %,jl/%,$(LIBOBJECTS))
+JAVA_CC_OBJECTS = $(SHARED_CC_OBJECTS)
+JAVA_C_OBJECTS = $(SHARED_C_OBJECTS)
+JAVA_ASM_OBJECTS = $(SHARED_ASM_OBJECTS)
+
+JAVA_CC_LIBOBJECTS = $(patsubst %.cc.o,jl/%.cc.o,$(JAVA_CC_OBJECTS))
+JAVA_C_LIBOBJECTS = $(patsubst %.c.o,jl/%.c.o,$(JAVA_C_OBJECTS))
+JAVA_ASM_LIBOBJECTS = $(patsubst %.S.o,jl/%.S.o,$(JAVA_ASM_OBJECTS))
+java_libobjects = $(JAVA_CC_LIBOBJECTS) $(JAVA_C_LIBOBJECTS) $(JAVA_ASM_LIBOBJECTS)
 CLEAN_FILES += jl
 
-$(java_libobjects): jl/%.o: %.cc
+$(JAVA_CC_LIBOBJECTS): jl/%.cc.o:  %.cc
+	$(AM_V_CC)mkdir -p $(@D) && $(CXX) $(CXXFLAGS) -fPIC -c $< -o $@ $(COVERAGEFLAGS)
+
+$(JAVA_C_LIBOBJECTS): jl/%.c.o:  %.c
+	$(AM_V_CC)mkdir -p $(@D) && $(CXX) $(CXXFLAGS) -fPIC -c $< -o $@ $(COVERAGEFLAGS)
+
+$(JAVA_ASM_LIBOBJECTS): jl/%.S.o:  %.S
 	$(AM_V_CC)mkdir -p $(@D) && $(CXX) $(CXXFLAGS) -fPIC -c $< -o $@ $(COVERAGEFLAGS)
 
+
 rocksdbjava: $(java_libobjects)
 	$(AM_V_GEN)cd java;$(MAKE) javalib;
 	$(AM_V_at)rm -f ./java/target/$(ROCKSDBJNILIB)
@@ -1703,19 +1742,24 @@ IOSVERSION=$(shell defaults read $(PLATFORMSROOT)/iPhoneOS.platform/version CFBu
 	lipo ios-x86/$@ ios-arm/$@ -create -output $@
 
 else
-.cc.o:
+%.cc.o: %.cc
 	$(AM_V_CC)$(CXX) $(CXXFLAGS) -c $< -o $@ $(COVERAGEFLAGS)
 
-.c.o:
+%.c.o:  %.c
+	$(AM_V_CC)$(CC) $(CFLAGS) -c $< -o $@
+
+%.S.o:  %.S
 	$(AM_V_CC)$(CC) $(CFLAGS) -c $< -o $@
-endif
 
+endif
 # ---------------------------------------------------------------------------
 #  	Source files dependencies detection
 # ---------------------------------------------------------------------------
 
 all_sources = $(LIB_SOURCES) $(MAIN_SOURCES) $(MOCK_LIB_SOURCES) $(TOOL_LIB_SOURCES) $(BENCH_LIB_SOURCES) $(TEST_LIB_SOURCES) $(EXP_LIB_SOURCES)
 DEPFILES = $(all_sources:.cc=.d)
+DEPFILES_C = $(LIB_SOURCES_C:.c=.d)
+DEPFILES_ASM = $(LIB_SOURCES_ASM:.S=.d)
 
 # Add proper dependency support so changing a .h file forces a .cc file to
 # rebuild.
@@ -1726,7 +1770,16 @@ $(DEPFILES): %.d: %.cc
 	@$(CXX) $(CXXFLAGS) $(PLATFORM_SHARED_CFLAGS) \
 	  -MM -MT'$@' -MT'$(<:.cc=.o)' "$<" -o '$@'
 
-depend: $(DEPFILES)
+$(DEPFILES_C): %.d: %.c
+	@$(CXX) $(CXXFLAGS) $(PLATFORM_SHARED_CFLAGS) \
+	  -MM -MT'$@' -MT'$(<:.c=.o)' "$<" -o '$@'
+
+$(DEPFILES_ASM): %.d: %.S
+	@$(CXX) $(CXXFLAGS) $(PLATFORM_SHARED_CFLAGS) \
+	  -MM -MT'$@' -MT'$(<:.S=.o)' "$<" -o '$@'
+
+
+depend: $(DEPFILES) $(DEPFILES_C) $(DEPFILES_ASM)
 
 # if the make goal is either "clean" or "format", we shouldn't
 # try to import the *.d files.

db/db_test_util.cc

@@ -277,12 +277,11 @@ Options DBTestBase::GetOptions(
   Options options = default_options;
   BlockBasedTableOptions table_options;
   bool set_block_based_table_factory = true;
-#if !defined(OS_MACOSX) && !defined(OS_WIN) && !defined(OS_SOLARIS) &&  \
-  !defined(OS_AIX)
+#if !defined(OS_MACOSX) && !defined(OS_WIN) && !defined(OS_SOLARIS) && \
+    !defined(OS_AIX)
   rocksdb::SyncPoint::GetInstance()->ClearCallBack(
       "NewRandomAccessFile:O_DIRECT");
-  rocksdb::SyncPoint::GetInstance()->ClearCallBack(
-      "NewWritableFile:O_DIRECT");
+  rocksdb::SyncPoint::GetInstance()->ClearCallBack("NewWritableFile:O_DIRECT");
 #endif
 
   bool can_allow_mmap = IsMemoryMappedAccessSupported();

src.mk

@@ -204,6 +204,16 @@ LIB_SOURCES =                                                   \
   utilities/write_batch_with_index/write_batch_with_index.cc    \
   utilities/write_batch_with_index/write_batch_with_index_internal.cc    \
 
+ifeq (,$(shell $(CXX) -fsyntax-only -maltivec -xc /dev/null 2>&1))
+LIB_SOURCES_ASM =\
+  util/crc32c_ppc_asm.S
+LIB_SOURCES_C = \
+  util/crc32c_ppc.c
+else
+LIB_SOURCES_ASM =
+LIB_SOURCES_C =
+endif
+
 TOOL_LIB_SOURCES = \
   tools/ldb_cmd.cc                                               \
   tools/ldb_tool.cc                                              \

tools/db_stress.cc

@@ -2370,15 +2370,15 @@ int main(int argc, char** argv) {
 #if !defined(NDEBUG) && !defined(OS_MACOSX) && !defined(OS_WIN) && \
   !defined(OS_SOLARIS) && !defined(OS_AIX)
   rocksdb::SyncPoint::GetInstance()->SetCallBack(
-    "NewWritableFile:O_DIRECT", [&](void* arg) {
-      int* val = static_cast<int*>(arg);
-      *val &= ~O_DIRECT;
-    });
+      "NewWritableFile:O_DIRECT", [&](void* arg) {
+        int* val = static_cast<int*>(arg);
+        *val &= ~O_DIRECT;
+      });
   rocksdb::SyncPoint::GetInstance()->SetCallBack(
-    "NewRandomAccessFile:O_DIRECT", [&](void* arg) {
-      int* val = static_cast<int*>(arg);
-      *val &= ~O_DIRECT;
-    });
+      "NewRandomAccessFile:O_DIRECT", [&](void* arg) {
+        int* val = static_cast<int*>(arg);
+        *val &= ~O_DIRECT;
+      });
   rocksdb::SyncPoint::GetInstance()->EnableProcessing();
 #endif
 

util/crc32c.cc

@@ -18,9 +18,32 @@
 #endif
 #include "util/coding.h"
 
+#ifdef __powerpc64__
+#include "util/crc32c_ppc.h"
+#include "util/crc32c_ppc_constants.h"
+
+#if __linux__
+#include <sys/auxv.h>
+
+#ifndef PPC_FEATURE2_VEC_CRYPTO
+#define PPC_FEATURE2_VEC_CRYPTO 0x02000000
+#endif
+
+#ifndef AT_HWCAP2
+#define AT_HWCAP2 26
+#endif
+
+#endif /* __linux__ */
+
+#endif
+
 namespace rocksdb {
 namespace crc32c {
 
+#ifdef __powerpc64__
+static int arch_ppc_crc32 = 0;
+#endif
+
 static const uint32_t table0_[256] = {
   0x00000000, 0xf26b8303, 0xe13b70f7, 0x1350f3f4,
   0xc79a971f, 0x35f1141c, 0x26a1e7e8, 0xd4ca64eb,
@@ -371,6 +394,7 @@ uint32_t ExtendImpl(uint32_t crc, const char* buf, size_t size) {
 }
 
 // Detect if SS42 or not.
+#ifndef HAVE_POWER8
 static bool isSSE42() {
 #ifndef HAVE_SSE42
   return false;
@@ -387,15 +411,58 @@ static bool isSSE42() {
   return false;
 #endif
 }
+#endif
 
 typedef uint32_t (*Function)(uint32_t, const char*, size_t);
 
+#if defined(HAVE_POWER8) && defined(HAS_ALTIVEC)
+uint32_t ExtendPPCImpl(uint32_t crc, const char *buf, size_t size) {
+  return crc32c_ppc(crc, (const unsigned char *)buf, size);
+}
+
+#if __linux__
+static int arch_ppc_probe(void) {
+  arch_ppc_crc32 = 0;
+
+#if defined(__powerpc64__)
+  if (getauxval(AT_HWCAP2) & PPC_FEATURE2_VEC_CRYPTO) arch_ppc_crc32 = 1;
+#endif /* __powerpc64__ */
+
+  return arch_ppc_crc32;
+}
+#endif  // __linux__
+
+static bool isAltiVec() {
+  if (arch_ppc_probe()) {
+    return true;
+  } else {
+    return false;
+  }
+}
+#endif
+
 static inline Function Choose_Extend() {
+#ifndef HAVE_POWER8
   return isSSE42() ? ExtendImpl<Fast_CRC32> : ExtendImpl<Slow_CRC32>;
+#else
+  return isAltiVec() ? ExtendPPCImpl : ExtendImpl<Slow_CRC32>;
+#endif
 }
 
 bool IsFastCrc32Supported() {
-  return isSSE42();
+  bool has_fast_crc = false;
+#ifdef HAVE_POWER8
+#ifdef HAS_ALTIVEC
+  if (arch_ppc_probe()) {
+    has_fast_crc = true;
+  }
+#else
+  has_fast_crc = false;
+#endif
+#else
+  has_fast_crc = isSSE42();
+#endif
+  return has_fast_crc;
 }
 
 Function ChosenExtend = Choose_Extend();

util/crc32c_ppc.c

@@ -0,0 +1,95 @@
+//  Copyright (c) 2017 International Business Machines Corp.
+//  All rights reserved.
+//  This source code is licensed under the BSD-style license found in the
+//  LICENSE file in the root directory of this source tree. An additional grant
+//  of patent rights can be found in the PATENTS file in the same directory.
+//  This source code is also licensed under the GPLv2 license found in the
+//  COPYING file in the root directory of this source tree.
+
+#define CRC_TABLE
+#include <inttypes.h>
+#include <stdlib.h>
+#include <strings.h>
+#include "util/crc32c_ppc_constants.h"
+
+#define VMX_ALIGN 16
+#define VMX_ALIGN_MASK (VMX_ALIGN - 1)
+
+#ifdef REFLECT
+static unsigned int crc32_align(unsigned int crc, unsigned char const *p,
+                                unsigned long len) {
+  while (len--) crc = crc_table[(crc ^ *p++) & 0xff] ^ (crc >> 8);
+  return crc;
+}
+#endif
+
+#ifdef HAVE_POWER8
+unsigned int __crc32_vpmsum(unsigned int crc, unsigned char const *p,
+                            unsigned long len);
+
+static uint32_t crc32_vpmsum(uint32_t crc, unsigned char const *data,
+                             unsigned len) {
+  unsigned int prealign;
+  unsigned int tail;
+
+#ifdef CRC_XOR
+  crc ^= 0xffffffff;
+#endif
+
+  if (len < VMX_ALIGN + VMX_ALIGN_MASK) {
+    crc = crc32_align(crc, data, (unsigned long)len);
+    goto out;
+  }
+
+  if ((unsigned long)data & VMX_ALIGN_MASK) {
+    prealign = VMX_ALIGN - ((unsigned long)data & VMX_ALIGN_MASK);
+    crc = crc32_align(crc, data, prealign);
+    len -= prealign;
+    data += prealign;
+  }
+
+  crc = __crc32_vpmsum(crc, data, (unsigned long)len & ~VMX_ALIGN_MASK);
+
+  tail = len & VMX_ALIGN_MASK;
+  if (tail) {
+    data += len & ~VMX_ALIGN_MASK;
+    crc = crc32_align(crc, data, tail);
+  }
+
+out:
+#ifdef CRC_XOR
+  crc ^= 0xffffffff;
+#endif
+
+  return crc;
+}
+
+/* This wrapper function works around the fact that crc32_vpmsum
+ * does not gracefully handle the case where the data pointer is NULL.  There
+ * may be room for performance improvement here.
+ */
+uint32_t crc32c_ppc(uint32_t crc, unsigned char const *data, unsigned len) {
+  unsigned char *buf2;
+
+  if (!data) {
+    buf2 = (unsigned char *)malloc(len);
+    bzero(buf2, len);
+    crc = crc32_vpmsum(crc, buf2, len);
+    free(buf2);
+  } else {
+    crc = crc32_vpmsum(crc, data, (unsigned long)len);
+  }
+  return crc;
+}
+
+#else /* HAVE_POWER8 */
+
+/* This symbol has to exist on non-ppc architectures (and on legacy
+ * ppc systems using power7 or below) in order to compile properly
+ * there, even though it won't be called.
+ */
+uint32_t crc32c_ppc(uint32_t crc, unsigned char const *data, unsigned len) {
+  return 0;
+}
+
+#endif /* HAVE_POWER8 */

util/crc32c_ppc.h

@@ -0,0 +1,23 @@
+//  Copyright (c) 2017 International Business Machines Corp.
+//  All rights reserved.
+//  This source code is licensed under the BSD-style license found in the
+//  LICENSE file in the root directory of this source tree. An additional grant
+//  of patent rights can be found in the PATENTS file in the same directory.
+//  This source code is also licensed under the GPLv2 license found in the
+//  COPYING file in the root directory of this source tree.
+
+#ifndef CRC32C_PPC_H
+#define CRC32C_PPC_H
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+extern uint32_t crc32c_ppc(uint32_t crc, unsigned char const *buffer,
+                           unsigned len);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif

util/crc32c_ppc_asm.S

@@ -0,0 +1,753 @@
+//  Copyright (c) 2015 Anton Blanchard <anton@au.ibm.com>, IBM
+//  Copyright (c) 2017 International Business Machines Corp.
+//  All rights reserved.
+//  This source code is licensed under the BSD-style license found in the
+//  LICENSE file in the root directory of this source tree. An additional grant
+//  of patent rights can be found in the PATENTS file in the same directory.
+//  This source code is also licensed under the GPLv2 license found in the
+//  COPYING file in the root directory of this source tree.
+
+#include <ppc-asm.h>
+#include "ppc-opcode.h"
+
+#undef toc
+
+#ifndef r1
+#define r1 1
+#endif
+
+#ifndef r2
+#define r2 2
+#endif
+
+	.section	.rodata
+.balign 16
+
+.byteswap_constant:
+	/* byte reverse permute constant */
+	.octa 0x0F0E0D0C0B0A09080706050403020100
+
+#define __ASSEMBLY__
+#include "crc32c_ppc_constants.h"
+
+	.text
+
+#if defined(__BIG_ENDIAN__) && defined(REFLECT)
+#define BYTESWAP_DATA
+#elif defined(__LITTLE_ENDIAN__) && !defined(REFLECT)
+#define BYTESWAP_DATA
+#else
+#undef BYTESWAP_DATA
+#endif
+
+#define off16		r25
+#define off32		r26
+#define off48		r27
+#define off64		r28
+#define off80		r29
+#define off96		r30
+#define off112		r31
+
+#define const1		v24
+#define const2		v25
+
+#define byteswap	v26
+#define	mask_32bit	v27
+#define	mask_64bit	v28
+#define zeroes		v29
+
+#ifdef BYTESWAP_DATA
+#define VPERM(A, B, C, D) vperm	A, B, C, D
+#else
+#define VPERM(A, B, C, D)
+#endif
+
+/* unsigned int __crc32_vpmsum(unsigned int crc, void *p, unsigned long len) */
+FUNC_START(__crc32_vpmsum)
+	std	r31,-8(r1)
+	std	r30,-16(r1)
+	std	r29,-24(r1)
+	std	r28,-32(r1)
+	std	r27,-40(r1)
+	std	r26,-48(r1)
+	std	r25,-56(r1)
+
+	li	off16,16
+	li	off32,32
+	li	off48,48
+	li	off64,64
+	li	off80,80
+	li	off96,96
+	li	off112,112
+	li	r0,0
+
+	/* Enough room for saving 10 non volatile VMX registers */
+	subi	r6,r1,56+10*16
+	subi	r7,r1,56+2*16
+
+	stvx	v20,0,r6
+	stvx	v21,off16,r6
+	stvx	v22,off32,r6
+	stvx	v23,off48,r6
+	stvx	v24,off64,r6
+	stvx	v25,off80,r6
+	stvx	v26,off96,r6
+	stvx	v27,off112,r6
+	stvx	v28,0,r7
+	stvx	v29,off16,r7
+
+	mr	r10,r3
+
+	vxor	zeroes,zeroes,zeroes
+	vspltisw v0,-1
+
+	vsldoi	mask_32bit,zeroes,v0,4
+	vsldoi	mask_64bit,zeroes,v0,8
+
+	/* Get the initial value into v8 */
+	vxor	v8,v8,v8
+	MTVRD(v8, r3)
+#ifdef REFLECT
+	vsldoi	v8,zeroes,v8,8	/* shift into bottom 32 bits */
+#else
+	vsldoi	v8,v8,zeroes,4	/* shift into top 32 bits */
+#endif
+
+#ifdef BYTESWAP_DATA
+	addis	r3,r2,.byteswap_constant@toc@ha
+	addi	r3,r3,.byteswap_constant@toc@l
+
+	lvx	byteswap,0,r3
+	addi	r3,r3,16
+#endif
+
+	cmpdi	r5,256
+	blt	.Lshort
+
+	rldicr	r6,r5,0,56
+
+	/* Checksum in blocks of MAX_SIZE */
+1:	lis	r7,MAX_SIZE@h
+	ori	r7,r7,MAX_SIZE@l
+	mr	r9,r7
+	cmpd	r6,r7
+	bgt	2f
+	mr	r7,r6
+2:	subf	r6,r7,r6
+
+	/* our main loop does 128 bytes at a time */
+	srdi	r7,r7,7
+
+	/*
+	 * Work out the offset into the constants table to start at. Each
+	 * constant is 16 bytes, and it is used against 128 bytes of input
+	 * data - 128 / 16 = 8
+	 */
+	sldi	r8,r7,4
+	srdi	r9,r9,3
+	subf	r8,r8,r9
+
+	/* We reduce our final 128 bytes in a separate step */
+	addi	r7,r7,-1
+	mtctr	r7
+
+	addis	r3,r2,.constants@toc@ha
+	addi	r3,r3,.constants@toc@l
+
+	/* Find the start of our constants */
+	add	r3,r3,r8
+
+	/* zero v0-v7 which will contain our checksums */
+	vxor	v0,v0,v0
+	vxor	v1,v1,v1
+	vxor	v2,v2,v2
+	vxor	v3,v3,v3
+	vxor	v4,v4,v4
+	vxor	v5,v5,v5
+	vxor	v6,v6,v6
+	vxor	v7,v7,v7
+
+	lvx	const1,0,r3
+
+	/*
+	 * If we are looping back to consume more data we use the values
+	 * already in v16-v23.
+	 */
+	cmpdi	r0,1
+	beq	2f
+
+	/* First warm up pass */
+	lvx	v16,0,r4
+	lvx	v17,off16,r4
+	VPERM(v16,v16,v16,byteswap)
+	VPERM(v17,v17,v17,byteswap)
+	lvx	v18,off32,r4
+	lvx	v19,off48,r4
+	VPERM(v18,v18,v18,byteswap)
+	VPERM(v19,v19,v19,byteswap)
+	lvx	v20,off64,r4
+	lvx	v21,off80,r4
+	VPERM(v20,v20,v20,byteswap)
+	VPERM(v21,v21,v21,byteswap)
+	lvx	v22,off96,r4
+	lvx	v23,off112,r4
+	VPERM(v22,v22,v22,byteswap)
+	VPERM(v23,v23,v23,byteswap)
+	addi	r4,r4,8*16
+
+	/* xor in initial value */
+	vxor	v16,v16,v8
+
+2:	bdz	.Lfirst_warm_up_done
+
+	addi	r3,r3,16
+	lvx	const2,0,r3
+
+	/* Second warm up pass */
+	VPMSUMD(v8,v16,const1)
+	lvx	v16,0,r4
+	VPERM(v16,v16,v16,byteswap)
+	ori	r2,r2,0
+
+	VPMSUMD(v9,v17,const1)
+	lvx	v17,off16,r4
+	VPERM(v17,v17,v17,byteswap)
+	ori	r2,r2,0
+
+	VPMSUMD(v10,v18,const1)
+	lvx	v18,off32,r4
+	VPERM(v18,v18,v18,byteswap)
+	ori	r2,r2,0
+
+	VPMSUMD(v11,v19,const1)
+	lvx	v19,off48,r4
+	VPERM(v19,v19,v19,byteswap)
+	ori	r2,r2,0
+
+	VPMSUMD(v12,v20,const1)
+	lvx	v20,off64,r4
+	VPERM(v20,v20,v20,byteswap)
+	ori	r2,r2,0
+
+	VPMSUMD(v13,v21,const1)
+	lvx	v21,off80,r4
+	VPERM(v21,v21,v21,byteswap)
+	ori	r2,r2,0
+
+	VPMSUMD(v14,v22,const1)
+	lvx	v22,off96,r4
+	VPERM(v22,v22,v22,byteswap)
+	ori	r2,r2,0
+
+	VPMSUMD(v15,v23,const1)
+	lvx	v23,off112,r4
+	VPERM(v23,v23,v23,byteswap)
+
+	addi	r4,r4,8*16
+
+	bdz	.Lfirst_cool_down
+
+	/*
+	 * main loop. We modulo schedule it such that it takes three iterations
+	 * to complete - first iteration load, second iteration vpmsum, third
+	 * iteration xor.
+	 */
+	.balign	16
+4:	lvx	const1,0,r3
+	addi	r3,r3,16
+	ori	r2,r2,0
+
+	vxor	v0,v0,v8
+	VPMSUMD(v8,v16,const2)
+	lvx	v16,0,r4
+	VPERM(v16,v16,v16,byteswap)
+	ori	r2,r2,0
+
+	vxor	v1,v1,v9
+	VPMSUMD(v9,v17,const2)
+	lvx	v17,off16,r4
+	VPERM(v17,v17,v17,byteswap)
+	ori	r2,r2,0
+
+	vxor	v2,v2,v10
+	VPMSUMD(v10,v18,const2)
+	lvx	v18,off32,r4
+	VPERM(v18,v18,v18,byteswap)
+	ori	r2,r2,0
+
+	vxor	v3,v3,v11
+	VPMSUMD(v11,v19,const2)
+	lvx	v19,off48,r4
+	VPERM(v19,v19,v19,byteswap)
+	lvx	const2,0,r3
+	ori	r2,r2,0
+
+	vxor	v4,v4,v12
+	VPMSUMD(v12,v20,const1)
+	lvx	v20,off64,r4
+	VPERM(v20,v20,v20,byteswap)
+	ori	r2,r2,0
+
+	vxor	v5,v5,v13
+	VPMSUMD(v13,v21,const1)
+	lvx	v21,off80,r4
+	VPERM(v21,v21,v21,byteswap)
+	ori	r2,r2,0
+
+	vxor	v6,v6,v14
+	VPMSUMD(v14,v22,const1)
+	lvx	v22,off96,r4
+	VPERM(v22,v22,v22,byteswap)
+	ori	r2,r2,0
+
+	vxor	v7,v7,v15
+	VPMSUMD(v15,v23,const1)
+	lvx	v23,off112,r4
+	VPERM(v23,v23,v23,byteswap)
+
+	addi	r4,r4,8*16
+
+	bdnz	4b
+
+.Lfirst_cool_down:
+	/* First cool down pass */
+	lvx	const1,0,r3
+	addi	r3,r3,16
+
+	vxor	v0,v0,v8
+	VPMSUMD(v8,v16,const1)
+	ori	r2,r2,0
+
+	vxor	v1,v1,v9
+	VPMSUMD(v9,v17,const1)
+	ori	r2,r2,0
+
+	vxor	v2,v2,v10
+	VPMSUMD(v10,v18,const1)
+	ori	r2,r2,0
+
+	vxor	v3,v3,v11
+	VPMSUMD(v11,v19,const1)
+	ori	r2,r2,0
+
+	vxor	v4,v4,v12
+	VPMSUMD(v12,v20,const1)
+	ori	r2,r2,0
+
+	vxor	v5,v5,v13
+	VPMSUMD(v13,v21,const1)
+	ori	r2,r2,0
+
+	vxor	v6,v6,v14
+	VPMSUMD(v14,v22,const1)
+	ori	r2,r2,0
+
+	vxor	v7,v7,v15
+	VPMSUMD(v15,v23,const1)
+	ori	r2,r2,0
+
+.Lsecond_cool_down:
+	/* Second cool down pass */
+	vxor	v0,v0,v8
+	vxor	v1,v1,v9
+	vxor	v2,v2,v10
+	vxor	v3,v3,v11
+	vxor	v4,v4,v12
+	vxor	v5,v5,v13
+	vxor	v6,v6,v14
+	vxor	v7,v7,v15
+
+#ifdef REFLECT
+	/*
+	 * vpmsumd produces a 96 bit result in the least significant bits
+	 * of the register. Since we are bit reflected we have to shift it
+	 * left 32 bits so it occupies the least significant bits in the
+	 * bit reflected domain.
+	 */
+	vsldoi	v0,v0,zeroes,4
+	vsldoi	v1,v1,zeroes,4
+	vsldoi	v2,v2,zeroes,4
+	vsldoi	v3,v3,zeroes,4
+	vsldoi	v4,v4,zeroes,4
+	vsldoi	v5,v5,zeroes,4
+	vsldoi	v6,v6,zeroes,4
+	vsldoi	v7,v7,zeroes,4
+#endif
+
+	/* xor with last 1024 bits */
+	lvx	v8,0,r4
+	lvx	v9,off16,r4
+	VPERM(v8,v8,v8,byteswap)
+	VPERM(v9,v9,v9,byteswap)
+	lvx	v10,off32,r4
+	lvx	v11,off48,r4
+	VPERM(v10,v10,v10,byteswap)
+	VPERM(v11,v11,v11,byteswap)
+	lvx	v12,off64,r4
+	lvx	v13,off80,r4
+	VPERM(v12,v12,v12,byteswap)
+	VPERM(v13,v13,v13,byteswap)
+	lvx	v14,off96,r4
+	lvx	v15,off112,r4
+	VPERM(v14,v14,v14,byteswap)
+	VPERM(v15,v15,v15,byteswap)
+
+	addi	r4,r4,8*16
+
+	vxor	v16,v0,v8
+	vxor	v17,v1,v9
+	vxor	v18,v2,v10
+	vxor	v19,v3,v11
+	vxor	v20,v4,v12
+	vxor	v21,v5,v13
+	vxor	v22,v6,v14
+	vxor	v23,v7,v15
+
+	li	r0,1
+	cmpdi	r6,0
+	addi	r6,r6,128
+	bne	1b
+
+	/* Work out how many bytes we have left */
+	andi.	r5,r5,127
+
+	/* Calculate where in the constant table we need to start */
+	subfic	r6,r5,128
+	add	r3,r3,r6
+
+	/* How many 16 byte chunks are in the tail */
+	srdi	r7,r5,4
+	mtctr	r7
+
+	/*
+	 * Reduce the previously calculated 1024 bits to 64 bits, shifting
+	 * 32 bits to include the trailing 32 bits of zeros
+	 */
+	lvx	v0,0,r3
+	lvx	v1,off16,r3
+	lvx	v2,off32,r3
+	lvx	v3,off48,r3
+	lvx	v4,off64,r3
+	lvx	v5,off80,r3
+	lvx	v6,off96,r3
+	lvx	v7,off112,r3
+	addi	r3,r3,8*16
+
+	VPMSUMW(v0,v16,v0)
+	VPMSUMW(v1,v17,v1)
+	VPMSUMW(v2,v18,v2)
+	VPMSUMW(v3,v19,v3)
+	VPMSUMW(v4,v20,v4)
+	VPMSUMW(v5,v21,v5)
+	VPMSUMW(v6,v22,v6)
+	VPMSUMW(v7,v23,v7)
+
+	/* Now reduce the tail (0 - 112 bytes) */
+	cmpdi	r7,0
+	beq	1f
+
+	lvx	v16,0,r4
+	lvx	v17,0,r3
+	VPERM(v16,v16,v16,byteswap)
+	VPMSUMW(v16,v16,v17)
+	vxor	v0,v0,v16
+	bdz	1f
+
+	lvx	v16,off16,r4
+	lvx	v17,off16,r3
+	VPERM(v16,v16,v16,byteswap)
+	VPMSUMW(v16,v16,v17)
+	vxor	v0,v0,v16
+	bdz	1f
+
+	lvx	v16,off32,r4
+	lvx	v17,off32,r3
+	VPERM(v16,v16,v16,byteswap)
+	VPMSUMW(v16,v16,v17)
+	vxor	v0,v0,v16
+	bdz	1f
+
+	lvx	v16,off48,r4
+	lvx	v17,off48,r3
+	VPERM(v16,v16,v16,byteswap)
+	VPMSUMW(v16,v16,v17)
+	vxor	v0,v0,v16
+	bdz	1f
+
+	lvx	v16,off64,r4
+	lvx	v17,off64,r3
+	VPERM(v16,v16,v16,byteswap)
+	VPMSUMW(v16,v16,v17)
+	vxor	v0,v0,v16
+	bdz	1f
+
+	lvx	v16,off80,r4
+	lvx	v17,off80,r3
+	VPERM(v16,v16,v16,byteswap)
+	VPMSUMW(v16,v16,v17)
+	vxor	v0,v0,v16
+	bdz	1f
+
+	lvx	v16,off96,r4
+	lvx	v17,off96,r3
+	VPERM(v16,v16,v16,byteswap)
+	VPMSUMW(v16,v16,v17)
+	vxor	v0,v0,v16
+
+	/* Now xor all the parallel chunks together */
+1:	vxor	v0,v0,v1
+	vxor	v2,v2,v3
+	vxor	v4,v4,v5
+	vxor	v6,v6,v7
+
+	vxor	v0,v0,v2
+	vxor	v4,v4,v6
+
+	vxor	v0,v0,v4
+
+.Lbarrett_reduction:
+	/* Barrett constants */
+	addis	r3,r2,.barrett_constants@toc@ha
+	addi	r3,r3,.barrett_constants@toc@l
+
+	lvx	const1,0,r3
+	lvx	const2,off16,r3
+
+	vsldoi	v1,v0,v0,8
+	vxor	v0,v0,v1		/* xor two 64 bit results together */
+
+#ifdef REFLECT
+	/* shift left one bit */
+	vspltisb v1,1
+	vsl	v0,v0,v1
+#endif
+
+	vand	v0,v0,mask_64bit
+
+#ifndef REFLECT
+	/*
+	 * Now for the Barrett reduction algorithm. The idea is to calculate q,
+	 * the multiple of our polynomial that we need to subtract. By
+	 * doing the computation 2x bits higher (ie 64 bits) and shifting the
+	 * result back down 2x bits, we round down to the nearest multiple.
+	 */
+	VPMSUMD(v1,v0,const1)	/* ma */
+	vsldoi	v1,zeroes,v1,8	/* q = floor(ma/(2^64)) */
+	VPMSUMD(v1,v1,const2)	/* qn */
+	vxor	v0,v0,v1	/* a - qn, subtraction is xor in GF(2) */
+
+	/*
+	 * Get the result into r3. We need to shift it left 8 bytes:
+	 * V0 [ 0 1 2 X ]
+	 * V0 [ 0 X 2 3 ]
+	 */
+	vsldoi	v0,v0,zeroes,8	/* shift result into top 64 bits */
+#else
+	/*
+	 * The reflected version of Barrett reduction. Instead of bit
+	 * reflecting our data (which is expensive to do), we bit reflect our
+	 * constants and our algorithm, which means the intermediate data in
+	 * our vector registers goes from 0-63 instead of 63-0. We can reflect
+	 * the algorithm because we don't carry in mod 2 arithmetic.
+	 */
+	vand	v1,v0,mask_32bit	/* bottom 32 bits of a */
+	VPMSUMD(v1,v1,const1)		/* ma */
+	vand	v1,v1,mask_32bit	/* bottom 32bits of ma */
+	VPMSUMD(v1,v1,const2)		/* qn */
+	vxor	v0,v0,v1		/* a - qn, subtraction is xor in GF(2) */
+
+	/*
+	 * Since we are bit reflected, the result (ie the low 32 bits) is in
+	 * the high 32 bits. We just need to shift it left 4 bytes
+	 * V0 [ 0 1 X 3 ]
+	 * V0 [ 0 X 2 3 ]
+	 */
+	vsldoi	v0,v0,zeroes,4		/* shift result into top 64 bits of */
+#endif
+
+	/* Get it into r3 */
+	MFVRD(r3, v0)
+
+.Lout:
+	subi	r6,r1,56+10*16
+	subi	r7,r1,56+2*16
+
+	lvx	v20,0,r6
+	lvx	v21,off16,r6
+	lvx	v22,off32,r6
+	lvx	v23,off48,r6
+	lvx	v24,off64,r6
+	lvx	v25,off80,r6
+	lvx	v26,off96,r6
+	lvx	v27,off112,r6
+	lvx	v28,0,r7
+	lvx	v29,off16,r7
+
+	ld	r31,-8(r1)
+	ld	r30,-16(r1)
+	ld	r29,-24(r1)
+	ld	r28,-32(r1)
+	ld	r27,-40(r1)
+	ld	r26,-48(r1)
+	ld	r25,-56(r1)
+
+	blr
+
+.Lfirst_warm_up_done:
+	lvx	const1,0,r3
+	addi	r3,r3,16
+
+	VPMSUMD(v8,v16,const1)
+	VPMSUMD(v9,v17,const1)
+	VPMSUMD(v10,v18,const1)
+	VPMSUMD(v11,v19,const1)
+	VPMSUMD(v12,v20,const1)
+	VPMSUMD(v13,v21,const1)
+	VPMSUMD(v14,v22,const1)
+	VPMSUMD(v15,v23,const1)
+
+	b	.Lsecond_cool_down
+
+.Lshort:
+	cmpdi	r5,0
+	beq	.Lzero
+
+	addis	r3,r2,.short_constants@toc@ha
+	addi	r3,r3,.short_constants@toc@l
+
+	/* Calculate where in the constant table we need to start */
+	subfic	r6,r5,256
+	add	r3,r3,r6
+
+	/* How many 16 byte chunks? */
+	srdi	r7,r5,4
+	mtctr	r7
+
+	vxor	v19,v19,v19
+	vxor	v20,v20,v20
+
+	lvx	v0,0,r4
+	lvx	v16,0,r3
+	VPERM(v0,v0,v16,byteswap)
+	vxor	v0,v0,v8	/* xor in initial value */
+	VPMSUMW(v0,v0,v16)
+	bdz	.Lv0
+
+	lvx	v1,off16,r4
+	lvx	v17,off16,r3
+	VPERM(v1,v1,v17,byteswap)
+	VPMSUMW(v1,v1,v17)
+	bdz	.Lv1
+
+	lvx	v2,off32,r4
+	lvx	v16,off32,r3
+	VPERM(v2,v2,v16,byteswap)
+	VPMSUMW(v2,v2,v16)
+	bdz	.Lv2
+
+	lvx	v3,off48,r4
+	lvx	v17,off48,r3
+	VPERM(v3,v3,v17,byteswap)
+	VPMSUMW(v3,v3,v17)
+	bdz	.Lv3
+
+	lvx	v4,off64,r4
+	lvx	v16,off64,r3
+	VPERM(v4,v4,v16,byteswap)
+	VPMSUMW(v4,v4,v16)
+	bdz	.Lv4
+
+	lvx	v5,off80,r4
+	lvx	v17,off80,r3
+	VPERM(v5,v5,v17,byteswap)
+	VPMSUMW(v5,v5,v17)
+	bdz	.Lv5
+
+	lvx	v6,off96,r4
+	lvx	v16,off96,r3
+	VPERM(v6,v6,v16,byteswap)
+	VPMSUMW(v6,v6,v16)
+	bdz	.Lv6
+
+	lvx	v7,off112,r4
+	lvx	v17,off112,r3
+	VPERM(v7,v7,v17,byteswap)
+	VPMSUMW(v7,v7,v17)
+	bdz	.Lv7
+
+	addi	r3,r3,128
+	addi	r4,r4,128
+
+	lvx	v8,0,r4
+	lvx	v16,0,r3
+	VPERM(v8,v8,v16,byteswap)
+	VPMSUMW(v8,v8,v16)
+	bdz	.Lv8
+
+	lvx	v9,off16,r4
+	lvx	v17,off16,r3
+	VPERM(v9,v9,v17,byteswap)
+	VPMSUMW(v9,v9,v17)
+	bdz	.Lv9
+
+	lvx	v10,off32,r4
+	lvx	v16,off32,r3
+	VPERM(v10,v10,v16,byteswap)
+	VPMSUMW(v10,v10,v16)
+	bdz	.Lv10
+
+	lvx	v11,off48,r4
+	lvx	v17,off48,r3
+	VPERM(v11,v11,v17,byteswap)
+	VPMSUMW(v11,v11,v17)
+	bdz	.Lv11
+
+	lvx	v12,off64,r4
+	lvx	v16,off64,r3
+	VPERM(v12,v12,v16,byteswap)
+	VPMSUMW(v12,v12,v16)
+	bdz	.Lv12
+
+	lvx	v13,off80,r4
+	lvx	v17,off80,r3
+	VPERM(v13,v13,v17,byteswap)
+	VPMSUMW(v13,v13,v17)
+	bdz	.Lv13
+
+	lvx	v14,off96,r4
+	lvx	v16,off96,r3
+	VPERM(v14,v14,v16,byteswap)
+	VPMSUMW(v14,v14,v16)
+	bdz	.Lv14
+
+	lvx	v15,off112,r4
+	lvx	v17,off112,r3
+	VPERM(v15,v15,v17,byteswap)
+	VPMSUMW(v15,v15,v17)
+
+.Lv15:	vxor	v19,v19,v15
+.Lv14:	vxor	v20,v20,v14
+.Lv13:	vxor	v19,v19,v13
+.Lv12:	vxor	v20,v20,v12
+.Lv11:	vxor	v19,v19,v11
+.Lv10:	vxor	v20,v20,v10
+.Lv9:	vxor	v19,v19,v9
+.Lv8:	vxor	v20,v20,v8
+.Lv7:	vxor	v19,v19,v7
+.Lv6:	vxor	v20,v20,v6
+.Lv5:	vxor	v19,v19,v5
+.Lv4:	vxor	v20,v20,v4
+.Lv3:	vxor	v19,v19,v3
+.Lv2:	vxor	v20,v20,v2
+.Lv1:	vxor	v19,v19,v1
+.Lv0:	vxor	v20,v20,v0
+
+	vxor	v0,v19,v20
+
+	b	.Lbarrett_reduction
+
+.Lzero:
+	mr	r3,r10
+	b	.Lout
+
+FUNC_END(__crc32_vpmsum)

util/crc32c_ppc_constants.h

@@ -0,0 +1,893 @@
+//  Copyright (C) 2015, 2017 International Business Machines Corp.
+//  All rights reserved.
+//  This source code is licensed under the BSD-style license found in the
+//  LICENSE file in the root directory of this source tree. An additional grant
+//  of patent rights can be found in the PATENTS file in the same directory.
+//  This source code is also licensed under the GPLv2 license found in the
+//  COPYING file in the root directory of this source tree.
+#ifndef CRC32C_PPC_CONST_H
+#define CRC32C_PPC_CONST_H
+#define CRC 0x1edc6f41
+#define REFLECT
+#define CRC_XOR
+
+#ifndef __ASSEMBLY__
+#ifdef CRC_TABLE
+static const unsigned int crc_table[] = {
+    0x00000000, 0xf26b8303, 0xe13b70f7, 0x1350f3f4, 0xc79a971f, 0x35f1141c,
+    0x26a1e7e8, 0xd4ca64eb, 0x8ad958cf, 0x78b2dbcc, 0x6be22838, 0x9989ab3b,
+    0x4d43cfd0, 0xbf284cd3, 0xac78bf27, 0x5e133c24, 0x105ec76f, 0xe235446c,
+    0xf165b798, 0x030e349b, 0xd7c45070, 0x25afd373, 0x36ff2087, 0xc494a384,
+    0x9a879fa0, 0x68ec1ca3, 0x7bbcef57, 0x89d76c54, 0x5d1d08bf, 0xaf768bbc,
+    0xbc267848, 0x4e4dfb4b, 0x20bd8ede, 0xd2d60ddd, 0xc186fe29, 0x33ed7d2a,
+    0xe72719c1, 0x154c9ac2, 0x061c6936, 0xf477ea35, 0xaa64d611, 0x580f5512,
+    0x4b5fa6e6, 0xb93425e5, 0x6dfe410e, 0x9f95c20d, 0x8cc531f9, 0x7eaeb2fa,
+    0x30e349b1, 0xc288cab2, 0xd1d83946, 0x23b3ba45, 0xf779deae, 0x05125dad,
+    0x1642ae59, 0xe4292d5a, 0xba3a117e, 0x4851927d, 0x5b016189, 0xa96ae28a,
+    0x7da08661, 0x8fcb0562, 0x9c9bf696, 0x6ef07595, 0x417b1dbc, 0xb3109ebf,
+    0xa0406d4b, 0x522bee48, 0x86e18aa3, 0x748a09a0, 0x67dafa54, 0x95b17957,
+    0xcba24573, 0x39c9c670, 0x2a993584, 0xd8f2b687, 0x0c38d26c, 0xfe53516f,
+    0xed03a29b, 0x1f682198, 0x5125dad3, 0xa34e59d0, 0xb01eaa24, 0x42752927,
+    0x96bf4dcc, 0x64d4cecf, 0x77843d3b, 0x85efbe38, 0xdbfc821c, 0x2997011f,
+    0x3ac7f2eb, 0xc8ac71e8, 0x1c661503, 0xee0d9600, 0xfd5d65f4, 0x0f36e6f7,
+    0x61c69362, 0x93ad1061, 0x80fde395, 0x72966096, 0xa65c047d, 0x5437877e,
+    0x4767748a, 0xb50cf789, 0xeb1fcbad, 0x197448ae, 0x0a24bb5a, 0xf84f3859,
+    0x2c855cb2, 0xdeeedfb1, 0xcdbe2c45, 0x3fd5af46, 0x7198540d, 0x83f3d70e,
+    0x90a324fa, 0x62c8a7f9, 0xb602c312, 0x44694011, 0x5739b3e5, 0xa55230e6,
+    0xfb410cc2, 0x092a8fc1, 0x1a7a7c35, 0xe811ff36, 0x3cdb9bdd, 0xceb018de,
+    0xdde0eb2a, 0x2f8b6829, 0x82f63b78, 0x709db87b, 0x63cd4b8f, 0x91a6c88c,
+    0x456cac67, 0xb7072f64, 0xa457dc90, 0x563c5f93, 0x082f63b7, 0xfa44e0b4,
+    0xe9141340, 0x1b7f9043, 0xcfb5f4a8, 0x3dde77ab, 0x2e8e845f, 0xdce5075c,
+    0x92a8fc17, 0x60c37f14, 0x73938ce0, 0x81f80fe3, 0x55326b08, 0xa759e80b,
+    0xb4091bff, 0x466298fc, 0x1871a4d8, 0xea1a27db, 0xf94ad42f, 0x0b21572c,
+    0xdfeb33c7, 0x2d80b0c4, 0x3ed04330, 0xccbbc033, 0xa24bb5a6, 0x502036a5,
+    0x4370c551, 0xb11b4652, 0x65d122b9, 0x97baa1ba, 0x84ea524e, 0x7681d14d,
+    0x2892ed69, 0xdaf96e6a, 0xc9a99d9e, 0x3bc21e9d, 0xef087a76, 0x1d63f975,
+    0x0e330a81, 0xfc588982, 0xb21572c9, 0x407ef1ca, 0x532e023e, 0xa145813d,
+    0x758fe5d6, 0x87e466d5, 0x94b49521, 0x66df1622, 0x38cc2a06, 0xcaa7a905,
+    0xd9f75af1, 0x2b9cd9f2, 0xff56bd19, 0x0d3d3e1a, 0x1e6dcdee, 0xec064eed,
+    0xc38d26c4, 0x31e6a5c7, 0x22b65633, 0xd0ddd530, 0x0417b1db, 0xf67c32d8,
+    0xe52cc12c, 0x1747422f, 0x49547e0b, 0xbb3ffd08, 0xa86f0efc, 0x5a048dff,
+    0x8ecee914, 0x7ca56a17, 0x6ff599e3, 0x9d9e1ae0, 0xd3d3e1ab, 0x21b862a8,
+    0x32e8915c, 0xc083125f, 0x144976b4, 0xe622f5b7, 0xf5720643, 0x07198540,
+    0x590ab964, 0xab613a67, 0xb831c993, 0x4a5a4a90, 0x9e902e7b, 0x6cfbad78,
+    0x7fab5e8c, 0x8dc0dd8f, 0xe330a81a, 0x115b2b19, 0x020bd8ed, 0xf0605bee,
+    0x24aa3f05, 0xd6c1bc06, 0xc5914ff2, 0x37faccf1, 0x69e9f0d5, 0x9b8273d6,
+    0x88d28022, 0x7ab90321, 0xae7367ca, 0x5c18e4c9, 0x4f48173d, 0xbd23943e,
+    0xf36e6f75, 0x0105ec76, 0x12551f82, 0xe03e9c81, 0x34f4f86a, 0xc69f7b69,
+    0xd5cf889d, 0x27a40b9e, 0x79b737ba, 0x8bdcb4b9, 0x988c474d, 0x6ae7c44e,
+    0xbe2da0a5, 0x4c4623a6, 0x5f16d052, 0xad7d5351,
+};
+
+#endif
+
+#else
+#define MAX_SIZE 32768
+.constants :
+
+    /* Reduce 262144 kbits to 1024 bits */
+    /* x^261120 mod p(x)` << 1, x^261184 mod p(x)` << 1 */
+    .octa 0x00000000b6ca9e20000000009c37c408
+
+    /* x^260096 mod p(x)` << 1, x^260160 mod p(x)` << 1 */
+    .octa 0x00000000350249a800000001b51df26c
+
+    /* x^259072 mod p(x)` << 1, x^259136 mod p(x)` << 1 */
+    .octa 0x00000001862dac54000000000724b9d0
+
+    /* x^258048 mod p(x)` << 1, x^258112 mod p(x)` << 1 */
+    .octa 0x00000001d87fb48c00000001c00532fe
+
+    /* x^257024 mod p(x)` << 1, x^257088 mod p(x)` << 1 */
+    .octa 0x00000001f39b699e00000000f05a9362
+
+    /* x^256000 mod p(x)` << 1, x^256064 mod p(x)` << 1 */
+    .octa 0x0000000101da11b400000001e1007970
+
+    /* x^254976 mod p(x)` << 1, x^255040 mod p(x)` << 1 */
+    .octa 0x00000001cab571e000000000a57366ee
+
+    /* x^253952 mod p(x)` << 1, x^254016 mod p(x)` << 1 */
+    .octa 0x00000000c7020cfe0000000192011284
+
+    /* x^252928 mod p(x)` << 1, x^252992 mod p(x)` << 1 */
+    .octa 0x00000000cdaed1ae0000000162716d9a
+
+    /* x^251904 mod p(x)` << 1, x^251968 mod p(x)` << 1 */
+    .octa 0x00000001e804effc00000000cd97ecde
+
+    /* x^250880 mod p(x)` << 1, x^250944 mod p(x)` << 1 */
+    .octa 0x0000000077c3ea3a0000000058812bc0
+
+    /* x^249856 mod p(x)` << 1, x^249920 mod p(x)` << 1 */
+    .octa 0x0000000068df31b40000000088b8c12e
+
+    /* x^248832 mod p(x)` << 1, x^248896 mod p(x)` << 1 */
+    .octa 0x00000000b059b6c200000001230b234c
+
+    /* x^247808 mod p(x)` << 1, x^247872 mod p(x)` << 1 */
+    .octa 0x0000000145fb8ed800000001120b416e
+
+    /* x^246784 mod p(x)` << 1, x^246848 mod p(x)` << 1 */
+    .octa 0x00000000cbc0916800000001974aecb0
+
+    /* x^245760 mod p(x)` << 1, x^245824 mod p(x)` << 1 */
+    .octa 0x000000005ceeedc2000000008ee3f226
+
+    /* x^244736 mod p(x)` << 1, x^244800 mod p(x)` << 1 */
+    .octa 0x0000000047d74e8600000001089aba9a
+
+    /* x^243712 mod p(x)` << 1, x^243776 mod p(x)` << 1 */
+    .octa 0x00000001407e9e220000000065113872
+
+    /* x^242688 mod p(x)` << 1, x^242752 mod p(x)` << 1 */
+    .octa 0x00000001da967bda000000005c07ec10
+
+    /* x^241664 mod p(x)` << 1, x^241728 mod p(x)` << 1 */
+    .octa 0x000000006c8983680000000187590924
+
+    /* x^240640 mod p(x)` << 1, x^240704 mod p(x)` << 1 */
+    .octa 0x00000000f2d14c9800000000e35da7c6
+
+    /* x^239616 mod p(x)` << 1, x^239680 mod p(x)` << 1 */
+    .octa 0x00000001993c6ad4000000000415855a
+
+    /* x^238592 mod p(x)` << 1, x^238656 mod p(x)` << 1 */
+    .octa 0x000000014683d1ac0000000073617758
+
+    /* x^237568 mod p(x)` << 1, x^237632 mod p(x)` << 1 */
+    .octa 0x00000001a7c93e6c0000000176021d28
+
+    /* x^236544 mod p(x)` << 1, x^236608 mod p(x)` << 1 */
+    .octa 0x000000010211e90a00000001c358fd0a
+
+    /* x^235520 mod p(x)` << 1, x^235584 mod p(x)` << 1 */
+    .octa 0x000000001119403e00000001ff7a2c18
+
+    /* x^234496 mod p(x)` << 1, x^234560 mod p(x)` << 1 */
+    .octa 0x000000001c3261aa00000000f2d9f7e4
+
+    /* x^233472 mod p(x)` << 1, x^233536 mod p(x)` << 1 */
+    .octa 0x000000014e37a634000000016cf1f9c8
+
+    /* x^232448 mod p(x)` << 1, x^232512 mod p(x)` << 1 */
+    .octa 0x0000000073786c0c000000010af9279a
+
+    /* x^231424 mod p(x)` << 1, x^231488 mod p(x)` << 1 */
+    .octa 0x000000011dc037f80000000004f101e8
+
+    /* x^230400 mod p(x)` << 1, x^230464 mod p(x)` << 1 */
+    .octa 0x0000000031433dfc0000000070bcf184
+
+    /* x^229376 mod p(x)` << 1, x^229440 mod p(x)` << 1 */
+    .octa 0x000000009cde8348000000000a8de642
+
+    /* x^228352 mod p(x)` << 1, x^228416 mod p(x)` << 1 */
+    .octa 0x0000000038d3c2a60000000062ea130c
+
+    /* x^227328 mod p(x)` << 1, x^227392 mod p(x)` << 1 */
+    .octa 0x000000011b25f26000000001eb31cbb2
+
+    /* x^226304 mod p(x)` << 1, x^226368 mod p(x)` << 1 */
+    .octa 0x000000001629e6f00000000170783448
+
+    /* x^225280 mod p(x)` << 1, x^225344 mod p(x)` << 1 */
+    .octa 0x0000000160838b4c00000001a684b4c6
+
+    /* x^224256 mod p(x)` << 1, x^224320 mod p(x)` << 1 */
+    .octa 0x000000007a44011c00000000253ca5b4
+
+    /* x^223232 mod p(x)` << 1, x^223296 mod p(x)` << 1 */
+    .octa 0x00000000226f417a0000000057b4b1e2
+
+    /* x^222208 mod p(x)` << 1, x^222272 mod p(x)` << 1 */
+    .octa 0x0000000045eb2eb400000000b6bd084c
+
+    /* x^221184 mod p(x)` << 1, x^221248 mod p(x)` << 1 */
+    .octa 0x000000014459d70c0000000123c2d592
+
+    /* x^220160 mod p(x)` << 1, x^220224 mod p(x)` << 1 */
+    .octa 0x00000001d406ed8200000000159dafce
+
+    /* x^219136 mod p(x)` << 1, x^219200 mod p(x)` << 1 */
+    .octa 0x0000000160c8e1a80000000127e1a64e
+
+    /* x^218112 mod p(x)` << 1, x^218176 mod p(x)` << 1 */
+    .octa 0x0000000027ba80980000000056860754
+
+    /* x^217088 mod p(x)` << 1, x^217152 mod p(x)` << 1 */
+    .octa 0x000000006d92d01800000001e661aae8
+
+    /* x^216064 mod p(x)` << 1, x^216128 mod p(x)` << 1 */
+    .octa 0x000000012ed7e3f200000000f82c6166
+
+    /* x^215040 mod p(x)` << 1, x^215104 mod p(x)` << 1 */
+    .octa 0x000000002dc8778800000000c4f9c7ae
+
+    /* x^214016 mod p(x)` << 1, x^214080 mod p(x)` << 1 */
+    .octa 0x0000000018240bb80000000074203d20
+
+    /* x^212992 mod p(x)` << 1, x^213056 mod p(x)` << 1 */
+    .octa 0x000000001ad381580000000198173052
+
+    /* x^211968 mod p(x)` << 1, x^212032 mod p(x)` << 1 */
+    .octa 0x00000001396b78f200000001ce8aba54
+
+    /* x^210944 mod p(x)` << 1, x^211008 mod p(x)` << 1 */
+    .octa 0x000000011a68133400000001850d5d94
+
+    /* x^209920 mod p(x)` << 1, x^209984 mod p(x)` << 1 */
+    .octa 0x000000012104732e00000001d609239c
+
+    /* x^208896 mod p(x)` << 1, x^208960 mod p(x)` << 1 */
+    .octa 0x00000000a140d90c000000001595f048
+
+    /* x^207872 mod p(x)` << 1, x^207936 mod p(x)` << 1 */
+    .octa 0x00000001b7215eda0000000042ccee08
+
+    /* x^206848 mod p(x)` << 1, x^206912 mod p(x)` << 1 */
+    .octa 0x00000001aaf1df3c000000010a389d74
+
+    /* x^205824 mod p(x)` << 1, x^205888 mod p(x)` << 1 */
+    .octa 0x0000000029d15b8a000000012a840da6
+
+    /* x^204800 mod p(x)` << 1, x^204864 mod p(x)` << 1 */
+    .octa 0x00000000f1a96922000000001d181c0c
+
+    /* x^203776 mod p(x)` << 1, x^203840 mod p(x)` << 1 */
+    .octa 0x00000001ac80d03c0000000068b7d1f6
+
+    /* x^202752 mod p(x)` << 1, x^202816 mod p(x)` << 1 */
+    .octa 0x000000000f11d56a000000005b0f14fc
+
+    /* x^201728 mod p(x)` << 1, x^201792 mod p(x)` << 1 */
+    .octa 0x00000001f1c022a20000000179e9e730
+
+    /* x^200704 mod p(x)` << 1, x^200768 mod p(x)` << 1 */
+    .octa 0x0000000173d00ae200000001ce1368d6
+
+    /* x^199680 mod p(x)` << 1, x^199744 mod p(x)` << 1 */
+    .octa 0x00000001d4ffe4ac0000000112c3a84c
+
+    /* x^198656 mod p(x)` << 1, x^198720 mod p(x)` << 1 */
+    .octa 0x000000016edc5ae400000000de940fee
+
+    /* x^197632 mod p(x)` << 1, x^197696 mod p(x)` << 1 */
+    .octa 0x00000001f1a0214000000000fe896b7e
+
+    /* x^196608 mod p(x)` << 1, x^196672 mod p(x)` << 1 */
+    .octa 0x00000000ca0b28a000000001f797431c
+
+    /* x^195584 mod p(x)` << 1, x^195648 mod p(x)` << 1 */
+    .octa 0x00000001928e30a20000000053e989ba
+
+    /* x^194560 mod p(x)` << 1, x^194624 mod p(x)` << 1 */
+    .octa 0x0000000097b1b002000000003920cd16
+
+    /* x^193536 mod p(x)` << 1, x^193600 mod p(x)` << 1 */
+    .octa 0x00000000b15bf90600000001e6f579b8
+
+    /* x^192512 mod p(x)` << 1, x^192576 mod p(x)` << 1 */
+    .octa 0x00000000411c5d52000000007493cb0a
+
+    /* x^191488 mod p(x)` << 1, x^191552 mod p(x)` << 1 */
+    .octa 0x00000001c36f330000000001bdd376d8
+
+    /* x^190464 mod p(x)` << 1, x^190528 mod p(x)` << 1 */
+    .octa 0x00000001119227e0000000016badfee6
+
+    /* x^189440 mod p(x)` << 1, x^189504 mod p(x)` << 1 */
+    .octa 0x00000000114d47020000000071de5c58
+
+    /* x^188416 mod p(x)` << 1, x^188480 mod p(x)` << 1 */
+    .octa 0x00000000458b5b9800000000453f317c
+
+    /* x^187392 mod p(x)` << 1, x^187456 mod p(x)` << 1 */
+    .octa 0x000000012e31fb8e0000000121675cce
+
+    /* x^186368 mod p(x)` << 1, x^186432 mod p(x)` << 1 */
+    .octa 0x000000005cf619d800000001f409ee92
+
+    /* x^185344 mod p(x)` << 1, x^185408 mod p(x)` << 1 */
+    .octa 0x0000000063f4d8b200000000f36b9c88
+
+    /* x^184320 mod p(x)` << 1, x^184384 mod p(x)` << 1 */
+    .octa 0x000000004138dc8a0000000036b398f4
+
+    /* x^183296 mod p(x)` << 1, x^183360 mod p(x)` << 1 */
+    .octa 0x00000001d29ee8e000000001748f9adc
+
+    /* x^182272 mod p(x)` << 1, x^182336 mod p(x)` << 1 */
+    .octa 0x000000006a08ace800000001be94ec00
+
+    /* x^181248 mod p(x)` << 1, x^181312 mod p(x)` << 1 */
+    .octa 0x0000000127d4201000000000b74370d6
+
+    /* x^180224 mod p(x)` << 1, x^180288 mod p(x)` << 1 */
+    .octa 0x0000000019d76b6200000001174d0b98
+
+    /* x^179200 mod p(x)` << 1, x^179264 mod p(x)` << 1 */
+    .octa 0x00000001b1471f6e00000000befc06a4
+
+    /* x^178176 mod p(x)` << 1, x^178240 mod p(x)` << 1 */
+    .octa 0x00000001f64c19cc00000001ae125288
+
+    /* x^177152 mod p(x)` << 1, x^177216 mod p(x)` << 1 */
+    .octa 0x00000000003c0ea00000000095c19b34
+
+    /* x^176128 mod p(x)` << 1, x^176192 mod p(x)` << 1 */
+    .octa 0x000000014d73abf600000001a78496f2
+
+    /* x^175104 mod p(x)` << 1, x^175168 mod p(x)` << 1 */
+    .octa 0x00000001620eb84400000001ac5390a0
+
+    /* x^174080 mod p(x)` << 1, x^174144 mod p(x)` << 1 */
+    .octa 0x0000000147655048000000002a80ed6e
+
+    /* x^173056 mod p(x)` << 1, x^173120 mod p(x)` << 1 */
+    .octa 0x0000000067b5077e00000001fa9b0128
+
+    /* x^172032 mod p(x)` << 1, x^172096 mod p(x)` << 1 */
+    .octa 0x0000000010ffe20600000001ea94929e
+
+    /* x^171008 mod p(x)` << 1, x^171072 mod p(x)` << 1 */
+    .octa 0x000000000fee8f1e0000000125f4305c
+
+    /* x^169984 mod p(x)` << 1, x^170048 mod p(x)` << 1 */
+    .octa 0x00000001da26fbae00000001471e2002
+
+    /* x^168960 mod p(x)` << 1, x^169024 mod p(x)` << 1 */
+    .octa 0x00000001b3a8bd880000000132d2253a
+
+    /* x^167936 mod p(x)` << 1, x^168000 mod p(x)` << 1 */
+    .octa 0x00000000e8f3898e00000000f26b3592
+
+    /* x^166912 mod p(x)` << 1, x^166976 mod p(x)` << 1 */
+    .octa 0x00000000b0d0d28c00000000bc8b67b0
+
+    /* x^165888 mod p(x)` << 1, x^165952 mod p(x)` << 1 */
+    .octa 0x0000000030f2a798000000013a826ef2
+
+    /* x^164864 mod p(x)` << 1, x^164928 mod p(x)` << 1 */
+    .octa 0x000000000fba10020000000081482c84
+
+    /* x^163840 mod p(x)` << 1, x^163904 mod p(x)` << 1 */
+    .octa 0x00000000bdb9bd7200000000e77307c2
+
+    /* x^162816 mod p(x)` << 1, x^162880 mod p(x)` << 1 */
+    .octa 0x0000000075d3bf5a00000000d4a07ec8
+
+    /* x^161792 mod p(x)` << 1, x^161856 mod p(x)` << 1 */
+    .octa 0x00000000ef1f98a00000000017102100
+
+    /* x^160768 mod p(x)` << 1, x^160832 mod p(x)` << 1 */
+    .octa 0x00000000689c760200000000db406486
+
+    /* x^159744 mod p(x)` << 1, x^159808 mod p(x)` << 1 */
+    .octa 0x000000016d5fa5fe0000000192db7f88
+
+    /* x^158720 mod p(x)` << 1, x^158784 mod p(x)` << 1 */
+    .octa 0x00000001d0d2b9ca000000018bf67b1e
+
+    /* x^157696 mod p(x)` << 1, x^157760 mod p(x)` << 1 */
+    .octa 0x0000000041e7b470000000007c09163e
+
+    /* x^156672 mod p(x)` << 1, x^156736 mod p(x)` << 1 */
+    .octa 0x00000001cbb6495e000000000adac060
+
+    /* x^155648 mod p(x)` << 1, x^155712 mod p(x)` << 1 */
+    .octa 0x000000010052a0b000000000bd8316ae
+
+    /* x^154624 mod p(x)` << 1, x^154688 mod p(x)` << 1 */
+    .octa 0x00000001d8effb5c000000019f09ab54
+
+    /* x^153600 mod p(x)` << 1, x^153664 mod p(x)` << 1 */
+    .octa 0x00000001d969853c0000000125155542
+
+    /* x^152576 mod p(x)` << 1, x^152640 mod p(x)` << 1 */
+    .octa 0x00000000523ccce2000000018fdb5882
+
+    /* x^151552 mod p(x)` << 1, x^151616 mod p(x)` << 1 */
+    .octa 0x000000001e2436bc00000000e794b3f4
+
+    /* x^150528 mod p(x)` << 1, x^150592 mod p(x)` << 1 */
+    .octa 0x00000000ddd1c3a2000000016f9bb022
+
+    /* x^149504 mod p(x)` << 1, x^149568 mod p(x)` << 1 */
+    .octa 0x0000000019fcfe3800000000290c9978
+
+    /* x^148480 mod p(x)` << 1, x^148544 mod p(x)` << 1 */
+    .octa 0x00000001ce95db640000000083c0f350
+
+    /* x^147456 mod p(x)` << 1, x^147520 mod p(x)` << 1 */
+    .octa 0x00000000af5828060000000173ea6628
+
+    /* x^146432 mod p(x)` << 1, x^146496 mod p(x)` << 1 */
+    .octa 0x00000001006388f600000001c8b4e00a
+
+    /* x^145408 mod p(x)` << 1, x^145472 mod p(x)` << 1 */
+    .octa 0x0000000179eca00a00000000de95d6aa
+
+    /* x^144384 mod p(x)` << 1, x^144448 mod p(x)` << 1 */
+    .octa 0x0000000122410a6a000000010b7f7248
+
+    /* x^143360 mod p(x)` << 1, x^143424 mod p(x)` << 1 */
+    .octa 0x000000004288e87c00000001326e3a06
+
+    /* x^142336 mod p(x)` << 1, x^142400 mod p(x)` << 1 */
+    .octa 0x000000016c5490da00000000bb62c2e6
+
+    /* x^141312 mod p(x)` << 1, x^141376 mod p(x)` << 1 */
+    .octa 0x00000000d1c71f6e0000000156a4b2c2
+
+    /* x^140288 mod p(x)` << 1, x^140352 mod p(x)` << 1 */
+    .octa 0x00000001b4ce08a6000000011dfe763a
+
+    /* x^139264 mod p(x)` << 1, x^139328 mod p(x)` << 1 */
+    .octa 0x00000001466ba60c000000007bcca8e2
+
+    /* x^138240 mod p(x)` << 1, x^138304 mod p(x)` << 1 */
+    .octa 0x00000001f6c488a40000000186118faa
+
+    /* x^137216 mod p(x)` << 1, x^137280 mod p(x)` << 1 */
+    .octa 0x000000013bfb06820000000111a65a88
+
+    /* x^136192 mod p(x)` << 1, x^136256 mod p(x)` << 1 */
+    .octa 0x00000000690e9e54000000003565e1c4
+
+    /* x^135168 mod p(x)` << 1, x^135232 mod p(x)` << 1 */
+    .octa 0x00000000281346b6000000012ed02a82
+
+    /* x^134144 mod p(x)` << 1, x^134208 mod p(x)` << 1 */
+    .octa 0x000000015646402400000000c486ecfc
+
+    /* x^133120 mod p(x)` << 1, x^133184 mod p(x)` << 1 */
+    .octa 0x000000016063a8dc0000000001b951b2
+
+    /* x^132096 mod p(x)` << 1, x^132160 mod p(x)` << 1 */
+    .octa 0x0000000116a663620000000048143916
+
+    /* x^131072 mod p(x)` << 1, x^131136 mod p(x)` << 1 */
+    .octa 0x000000017e8aa4d200000001dc2ae124
+
+    /* x^130048 mod p(x)` << 1, x^130112 mod p(x)` << 1 */
+    .octa 0x00000001728eb10c00000001416c58d6
+
+    /* x^129024 mod p(x)` << 1, x^129088 mod p(x)` << 1 */
+    .octa 0x00000001b08fd7fa00000000a479744a
+
+    /* x^128000 mod p(x)` << 1, x^128064 mod p(x)` << 1 */
+    .octa 0x00000001092a16e80000000096ca3a26
+
+    /* x^126976 mod p(x)` << 1, x^127040 mod p(x)` << 1 */
+    .octa 0x00000000a505637c00000000ff223d4e
+
+    /* x^125952 mod p(x)` << 1, x^126016 mod p(x)` << 1 */
+    .octa 0x00000000d94869b2000000010e84da42
+
+    /* x^124928 mod p(x)` << 1, x^124992 mod p(x)` << 1 */
+    .octa 0x00000001c8b203ae00000001b61ba3d0
+
+    /* x^123904 mod p(x)` << 1, x^123968 mod p(x)` << 1 */
+    .octa 0x000000005704aea000000000680f2de8
+
+    /* x^122880 mod p(x)` << 1, x^122944 mod p(x)` << 1 */
+    .octa 0x000000012e295fa2000000008772a9a8
+
+    /* x^121856 mod p(x)` << 1, x^121920 mod p(x)` << 1 */
+    .octa 0x000000011d0908bc0000000155f295bc
+
+    /* x^120832 mod p(x)` << 1, x^120896 mod p(x)` << 1 */
+    .octa 0x0000000193ed97ea00000000595f9282
+
+    /* x^119808 mod p(x)` << 1, x^119872 mod p(x)` << 1 */
+    .octa 0x000000013a0f1c520000000164b1c25a
+
+    /* x^118784 mod p(x)` << 1, x^118848 mod p(x)` << 1 */
+    .octa 0x000000010c2c40c000000000fbd67c50
+
+    /* x^117760 mod p(x)` << 1, x^117824 mod p(x)` << 1 */
+    .octa 0x00000000ff6fac3e0000000096076268
+
+    /* x^116736 mod p(x)` << 1, x^116800 mod p(x)` << 1 */
+    .octa 0x000000017b3609c000000001d288e4cc
+
+    /* x^115712 mod p(x)` << 1, x^115776 mod p(x)` << 1 */
+    .octa 0x0000000088c8c92200000001eaac1bdc
+
+    /* x^114688 mod p(x)` << 1, x^114752 mod p(x)` << 1 */
+    .octa 0x00000001751baae600000001f1ea39e2
+
+    /* x^113664 mod p(x)` << 1, x^113728 mod p(x)` << 1 */
+    .octa 0x000000010795297200000001eb6506fc
+
+    /* x^112640 mod p(x)` << 1, x^112704 mod p(x)` << 1 */
+    .octa 0x0000000162b00abe000000010f806ffe
+
+    /* x^111616 mod p(x)` << 1, x^111680 mod p(x)` << 1 */
+    .octa 0x000000000d7b404c000000010408481e
+
+    /* x^110592 mod p(x)` << 1, x^110656 mod p(x)` << 1 */
+    .octa 0x00000000763b13d40000000188260534
+
+    /* x^109568 mod p(x)` << 1, x^109632 mod p(x)` << 1 */
+    .octa 0x00000000f6dc22d80000000058fc73e0
+
+    /* x^108544 mod p(x)` << 1, x^108608 mod p(x)` << 1 */
+    .octa 0x000000007daae06000000000391c59b8
+
+    /* x^107520 mod p(x)` << 1, x^107584 mod p(x)` << 1 */
+    .octa 0x000000013359ab7c000000018b638400
+
+    /* x^106496 mod p(x)` << 1, x^106560 mod p(x)` << 1 */
+    .octa 0x000000008add438a000000011738f5c4
+
+    /* x^105472 mod p(x)` << 1, x^105536 mod p(x)` << 1 */
+    .octa 0x00000001edbefdea000000008cf7c6da
+
+    /* x^104448 mod p(x)` << 1, x^104512 mod p(x)` << 1 */
+    .octa 0x000000004104e0f800000001ef97fb16
+
+    /* x^103424 mod p(x)` << 1, x^103488 mod p(x)` << 1 */
+    .octa 0x00000000b48a82220000000102130e20
+
+    /* x^102400 mod p(x)` << 1, x^102464 mod p(x)` << 1 */
+    .octa 0x00000001bcb4684400000000db968898
+
+    /* x^101376 mod p(x)` << 1, x^101440 mod p(x)` << 1 */
+    .octa 0x000000013293ce0a00000000b5047b5e
+
+    /* x^100352 mod p(x)` << 1, x^100416 mod p(x)` << 1 */
+    .octa 0x00000001710d0844000000010b90fdb2
+
+    /* x^99328 mod p(x)` << 1, x^99392 mod p(x)` << 1 */
+    .octa 0x0000000117907f6e000000004834a32e
+
+    /* x^98304 mod p(x)` << 1, x^98368 mod p(x)` << 1 */
+    .octa 0x0000000087ddf93e0000000059c8f2b0
+
+    /* x^97280 mod p(x)` << 1, x^97344 mod p(x)` << 1 */
+    .octa 0x000000005970e9b00000000122cec508
+
+    /* x^96256 mod p(x)` << 1, x^96320 mod p(x)` << 1 */
+    .octa 0x0000000185b2b7d0000000000a330cda
+
+    /* x^95232 mod p(x)` << 1, x^95296 mod p(x)` << 1 */
+    .octa 0x00000001dcee0efc000000014a47148c
+
+    /* x^94208 mod p(x)` << 1, x^94272 mod p(x)` << 1 */
+    .octa 0x0000000030da27220000000042c61cb8
+
+    /* x^93184 mod p(x)` << 1, x^93248 mod p(x)` << 1 */
+    .octa 0x000000012f925a180000000012fe6960
+
+    /* x^92160 mod p(x)` << 1, x^92224 mod p(x)` << 1 */
+    .octa 0x00000000dd2e357c00000000dbda2c20
+
+    /* x^91136 mod p(x)` << 1, x^91200 mod p(x)` << 1 */
+    .octa 0x00000000071c80de000000011122410c
+
+    /* x^90112 mod p(x)` << 1, x^90176 mod p(x)` << 1 */
+    .octa 0x000000011513140a00000000977b2070
+
+    /* x^89088 mod p(x)` << 1, x^89152 mod p(x)` << 1 */
+    .octa 0x00000001df876e8e000000014050438e
+
+    /* x^88064 mod p(x)` << 1, x^88128 mod p(x)` << 1 */
+    .octa 0x000000015f81d6ce0000000147c840e8
+
+    /* x^87040 mod p(x)` << 1, x^87104 mod p(x)` << 1 */
+    .octa 0x000000019dd94dbe00000001cc7c88ce
+
+    /* x^86016 mod p(x)` << 1, x^86080 mod p(x)` << 1 */
+    .octa 0x00000001373d206e00000001476b35a4
+
+    /* x^84992 mod p(x)` << 1, x^85056 mod p(x)` << 1 */
+    .octa 0x00000000668ccade000000013d52d508
+
+    /* x^83968 mod p(x)` << 1, x^84032 mod p(x)` << 1 */
+    .octa 0x00000001b192d268000000008e4be32e
+
+    /* x^82944 mod p(x)` << 1, x^83008 mod p(x)` << 1 */
+    .octa 0x00000000e30f3a7800000000024120fe
+
+    /* x^81920 mod p(x)` << 1, x^81984 mod p(x)` << 1 */
+    .octa 0x000000010ef1f7bc00000000ddecddb4
+
+    /* x^80896 mod p(x)` << 1, x^80960 mod p(x)` << 1 */
+    .octa 0x00000001f5ac738000000000d4d403bc
+
+    /* x^79872 mod p(x)` << 1, x^79936 mod p(x)` << 1 */
+    .octa 0x000000011822ea7000000001734b89aa
+
+    /* x^78848 mod p(x)` << 1, x^78912 mod p(x)` << 1 */
+    .octa 0x00000000c3a33848000000010e7a58d6
+
+    /* x^77824 mod p(x)` << 1, x^77888 mod p(x)` << 1 */
+    .octa 0x00000001bd151c2400000001f9f04e9c
+
+    /* x^76800 mod p(x)` << 1, x^76864 mod p(x)` << 1 */
+    .octa 0x0000000056002d7600000000b692225e
+
+    /* x^75776 mod p(x)` << 1, x^75840 mod p(x)` << 1 */
+    .octa 0x000000014657c4f4000000019b8d3f3e
+
+    /* x^74752 mod p(x)` << 1, x^74816 mod p(x)` << 1 */
+    .octa 0x0000000113742d7c00000001a874f11e
+
+    /* x^73728 mod p(x)` << 1, x^73792 mod p(x)` << 1 */
+    .octa 0x000000019c5920ba000000010d5a4254
+
+    /* x^72704 mod p(x)` << 1, x^72768 mod p(x)` << 1 */
+    .octa 0x000000005216d2d600000000bbb2f5d6
+
+    /* x^71680 mod p(x)` << 1, x^71744 mod p(x)` << 1 */
+    .octa 0x0000000136f5ad8a0000000179cc0e36
+
+    /* x^70656 mod p(x)` << 1, x^70720 mod p(x)` << 1 */
+    .octa 0x000000018b07beb600000001dca1da4a
+
+    /* x^69632 mod p(x)` << 1, x^69696 mod p(x)` << 1 */
+    .octa 0x00000000db1e93b000000000feb1a192
+
+    /* x^68608 mod p(x)` << 1, x^68672 mod p(x)` << 1 */
+    .octa 0x000000000b96fa3a00000000d1eeedd6
+
+    /* x^67584 mod p(x)` << 1, x^67648 mod p(x)` << 1 */
+    .octa 0x00000001d9968af0000000008fad9bb4
+
+    /* x^66560 mod p(x)` << 1, x^66624 mod p(x)` << 1 */
+    .octa 0x000000000e4a77a200000001884938e4
+
+    /* x^65536 mod p(x)` << 1, x^65600 mod p(x)` << 1 */
+    .octa 0x00000000508c2ac800000001bc2e9bc0
+
+    /* x^64512 mod p(x)` << 1, x^64576 mod p(x)` << 1 */
+    .octa 0x0000000021572a8000000001f9658a68
+
+    /* x^63488 mod p(x)` << 1, x^63552 mod p(x)` << 1 */
+    .octa 0x00000001b859daf2000000001b9224fc
+
+    /* x^62464 mod p(x)` << 1, x^62528 mod p(x)` << 1 */
+    .octa 0x000000016f7884740000000055b2fb84
+
+    /* x^61440 mod p(x)` << 1, x^61504 mod p(x)` << 1 */
+    .octa 0x00000001b438810e000000018b090348
+
+    /* x^60416 mod p(x)` << 1, x^60480 mod p(x)` << 1 */
+    .octa 0x0000000095ddc6f2000000011ccbd5ea
+
+    /* x^59392 mod p(x)` << 1, x^59456 mod p(x)` << 1 */
+    .octa 0x00000001d977c20c0000000007ae47f8
+
+    /* x^58368 mod p(x)` << 1, x^58432 mod p(x)` << 1 */
+    .octa 0x00000000ebedb99a0000000172acbec0
+
+    /* x^57344 mod p(x)` << 1, x^57408 mod p(x)` << 1 */
+    .octa 0x00000001df9e9e9200000001c6e3ff20
+
+    /* x^56320 mod p(x)` << 1, x^56384 mod p(x)` << 1 */
+    .octa 0x00000001a4a3f95200000000e1b38744
+
+    /* x^55296 mod p(x)` << 1, x^55360 mod p(x)` << 1 */
+    .octa 0x00000000e2f5122000000000791585b2
+
+    /* x^54272 mod p(x)` << 1, x^54336 mod p(x)` << 1 */
+    .octa 0x000000004aa01f3e00000000ac53b894
+
+    /* x^53248 mod p(x)` << 1, x^53312 mod p(x)` << 1 */
+    .octa 0x00000000b3e90a5800000001ed5f2cf4
+
+    /* x^52224 mod p(x)` << 1, x^52288 mod p(x)` << 1 */
+    .octa 0x000000000c9ca2aa00000001df48b2e0
+
+    /* x^51200 mod p(x)` << 1, x^51264 mod p(x)` << 1 */
+    .octa 0x000000015168231600000000049c1c62
+
+    /* x^50176 mod p(x)` << 1, x^50240 mod p(x)` << 1 */
+    .octa 0x0000000036fce78c000000017c460c12
+
+    /* x^49152 mod p(x)` << 1, x^49216 mod p(x)` << 1 */
+    .octa 0x000000009037dc10000000015be4da7e
+
+    /* x^48128 mod p(x)` << 1, x^48192 mod p(x)` << 1 */
+    .octa 0x00000000d3298582000000010f38f668
+
+    /* x^47104 mod p(x)` << 1, x^47168 mod p(x)` << 1 */
+    .octa 0x00000001b42e8ad60000000039f40a00
+
+    /* x^46080 mod p(x)` << 1, x^46144 mod p(x)` << 1 */
+    .octa 0x00000000142a983800000000bd4c10c4
+
+    /* x^45056 mod p(x)` << 1, x^45120 mod p(x)` << 1 */
+    .octa 0x0000000109c7f1900000000042db1d98
+
+    /* x^44032 mod p(x)` << 1, x^44096 mod p(x)` << 1 */
+    .octa 0x0000000056ff931000000001c905bae6
+
+    /* x^43008 mod p(x)` << 1, x^43072 mod p(x)` << 1 */
+    .octa 0x00000001594513aa00000000069d40ea
+
+    /* x^41984 mod p(x)` << 1, x^42048 mod p(x)` << 1 */
+    .octa 0x00000001e3b5b1e8000000008e4fbad0
+
+    /* x^40960 mod p(x)` << 1, x^41024 mod p(x)` << 1 */
+    .octa 0x000000011dd5fc080000000047bedd46
+
+    /* x^39936 mod p(x)` << 1, x^40000 mod p(x)` << 1 */
+    .octa 0x00000001675f0cc20000000026396bf8
+
+    /* x^38912 mod p(x)` << 1, x^38976 mod p(x)` << 1 */
+    .octa 0x00000000d1c8dd4400000000379beb92
+
+    /* x^37888 mod p(x)` << 1, x^37952 mod p(x)` << 1 */
+    .octa 0x0000000115ebd3d8000000000abae54a
+
+    /* x^36864 mod p(x)` << 1, x^36928 mod p(x)` << 1 */
+    .octa 0x00000001ecbd0dac0000000007e6a128
+
+    /* x^35840 mod p(x)` << 1, x^35904 mod p(x)` << 1 */
+    .octa 0x00000000cdf67af2000000000ade29d2
+
+    /* x^34816 mod p(x)` << 1, x^34880 mod p(x)` << 1 */
+    .octa 0x000000004c01ff4c00000000f974c45c
+
+    /* x^33792 mod p(x)` << 1, x^33856 mod p(x)` << 1 */
+    .octa 0x00000000f2d8657e00000000e77ac60a
+
+    /* x^32768 mod p(x)` << 1, x^32832 mod p(x)` << 1 */
+    .octa 0x000000006bae74c40000000145895816
+
+    /* x^31744 mod p(x)` << 1, x^31808 mod p(x)` << 1 */
+    .octa 0x0000000152af8aa00000000038e362be
+
+    /* x^30720 mod p(x)` << 1, x^30784 mod p(x)` << 1 */
+    .octa 0x0000000004663802000000007f991a64
+
+    /* x^29696 mod p(x)` << 1, x^29760 mod p(x)` << 1 */
+    .octa 0x00000001ab2f5afc00000000fa366d3a
+
+    /* x^28672 mod p(x)` << 1, x^28736 mod p(x)` << 1 */
+    .octa 0x0000000074a4ebd400000001a2bb34f0
+
+    /* x^27648 mod p(x)` << 1, x^27712 mod p(x)` << 1 */
+    .octa 0x00000001d7ab3a4c0000000028a9981e
+
+    /* x^26624 mod p(x)` << 1, x^26688 mod p(x)` << 1 */
+    .octa 0x00000001a8da60c600000001dbc672be
+
+    /* x^25600 mod p(x)` << 1, x^25664 mod p(x)` << 1 */
+    .octa 0x000000013cf6382000000000b04d77f6
+
+    /* x^24576 mod p(x)` << 1, x^24640 mod p(x)` << 1 */
+    .octa 0x00000000bec12e1e0000000124400d96
+
+    /* x^23552 mod p(x)` << 1, x^23616 mod p(x)` << 1 */
+    .octa 0x00000001c6368010000000014ca4b414
+
+    /* x^22528 mod p(x)` << 1, x^22592 mod p(x)` << 1 */
+    .octa 0x00000001e6e78758000000012fe2c938
+
+    /* x^21504 mod p(x)` << 1, x^21568 mod p(x)` << 1 */
+    .octa 0x000000008d7f2b3c00000001faed01e6
+
+    /* x^20480 mod p(x)` << 1, x^20544 mod p(x)` << 1 */
+    .octa 0x000000016b4a156e000000007e80ecfe
+
+    /* x^19456 mod p(x)` << 1, x^19520 mod p(x)` << 1 */
+    .octa 0x00000001c63cfeb60000000098daee94
+
+    /* x^18432 mod p(x)` << 1, x^18496 mod p(x)` << 1 */
+    .octa 0x000000015f902670000000010a04edea
+
+    /* x^17408 mod p(x)` << 1, x^17472 mod p(x)` << 1 */
+    .octa 0x00000001cd5de11e00000001c00b4524
+
+    /* x^16384 mod p(x)` << 1, x^16448 mod p(x)` << 1 */
+    .octa 0x000000001acaec540000000170296550
+
+    /* x^15360 mod p(x)` << 1, x^15424 mod p(x)` << 1 */
+    .octa 0x000000002bd0ca780000000181afaa48
+
+    /* x^14336 mod p(x)` << 1, x^14400 mod p(x)` << 1 */
+    .octa 0x0000000032d63d5c0000000185a31ffa
+
+    /* x^13312 mod p(x)` << 1, x^13376 mod p(x)` << 1 */
+    .octa 0x000000001c6d4e4c000000002469f608
+
+    /* x^12288 mod p(x)` << 1, x^12352 mod p(x)` << 1 */
+    .octa 0x0000000106a60b92000000006980102a
+
+    /* x^11264 mod p(x)` << 1, x^11328 mod p(x)` << 1 */
+    .octa 0x00000000d3855e120000000111ea9ca8
+
+    /* x^10240 mod p(x)` << 1, x^10304 mod p(x)` << 1 */
+    .octa 0x00000000e312563600000001bd1d29ce
+
+    /* x^9216 mod p(x)` << 1, x^9280 mod p(x)` << 1 */
+    .octa 0x000000009e8f7ea400000001b34b9580
+
+    /* x^8192 mod p(x)` << 1, x^8256 mod p(x)` << 1 */
+    .octa 0x00000001c82e562c000000003076054e
+
+    /* x^7168 mod p(x)` << 1, x^7232 mod p(x)` << 1 */
+    .octa 0x00000000ca9f09ce000000012a608ea4
+
+    /* x^6144 mod p(x)` << 1, x^6208 mod p(x)` << 1 */
+    .octa 0x00000000c63764e600000000784d05fe
+
+    /* x^5120 mod p(x)` << 1, x^5184 mod p(x)` << 1 */
+    .octa 0x0000000168d2e49e000000016ef0d82a
+
+    /* x^4096 mod p(x)` << 1, x^4160 mod p(x)` << 1 */
+    .octa 0x00000000e986c1480000000075bda454
+
+    /* x^3072 mod p(x)` << 1, x^3136 mod p(x)` << 1 */
+    .octa 0x00000000cfb65894000000003dc0a1c4
+
+    /* x^2048 mod p(x)` << 1, x^2112 mod p(x)` << 1 */
+    .octa 0x0000000111cadee400000000e9a5d8be
+
+    /* x^1024 mod p(x)` << 1, x^1088 mod p(x)` << 1 */
+    .octa 0x0000000171fb63ce00000001609bc4b4
+
+    .short_constants :
+
+    /* Reduce final 1024-2048 bits to 64 bits, shifting 32 bits to include the
+       trailing 32 bits of zeros */
+    /* x^1952 mod p(x)`, x^1984 mod p(x)`, x^2016 mod p(x)`, x^2048 mod p(x)` */
+    .octa 0x7fec2963e5bf80485cf015c388e56f72
+
+    /* x^1824 mod p(x)`, x^1856 mod p(x)`, x^1888 mod p(x)`, x^1920 mod p(x)` */
+    .octa 0x38e888d4844752a9963a18920246e2e6
+
+    /* x^1696 mod p(x)`, x^1728 mod p(x)`, x^1760 mod p(x)`, x^1792 mod p(x)` */
+    .octa 0x42316c00730206ad419a441956993a31
+
+    /* x^1568 mod p(x)`, x^1600 mod p(x)`, x^1632 mod p(x)`, x^1664 mod p(x)` */
+    .octa 0x543d5c543e65ddf9924752ba2b830011
+
+    /* x^1440 mod p(x)`, x^1472 mod p(x)`, x^1504 mod p(x)`, x^1536 mod p(x)` */
+    .octa 0x78e87aaf56767c9255bd7f9518e4a304
+
+    /* x^1312 mod p(x)`, x^1344 mod p(x)`, x^1376 mod p(x)`, x^1408 mod p(x)` */
+    .octa 0x8f68fcec1903da7f6d76739fe0553f1e
+
+    /* x^1184 mod p(x)`, x^1216 mod p(x)`, x^1248 mod p(x)`, x^1280 mod p(x)` */
+    .octa 0x3f4840246791d588c133722b1fe0b5c3
+
+    /* x^1056 mod p(x)`, x^1088 mod p(x)`, x^1120 mod p(x)`, x^1152 mod p(x)` */
+    .octa 0x34c96751b04de25a64b67ee0e55ef1f3
+
+    /* x^928 mod p(x)`, x^960 mod p(x)`, x^992 mod p(x)`, x^1024 mod p(x)` */
+    .octa 0x156c8e180b4a395b069db049b8fdb1e7
+
+    /* x^800 mod p(x)`, x^832 mod p(x)`, x^864 mod p(x)`, x^896 mod p(x)` */
+    .octa 0xe0b99ccbe661f7bea11bfaf3c9e90b9e
+
+    /* x^672 mod p(x)`, x^704 mod p(x)`, x^736 mod p(x)`, x^768 mod p(x)` */
+    .octa 0x041d37768cd75659817cdc5119b29a35
+
+    /* x^544 mod p(x)`, x^576 mod p(x)`, x^608 mod p(x)`, x^640 mod p(x)` */
+    .octa 0x3a0777818cfaa9651ce9d94b36c41f1c
+
+    /* x^416 mod p(x)`, x^448 mod p(x)`, x^480 mod p(x)`, x^512 mod p(x)` */
+    .octa 0x0e148e8252377a554f256efcb82be955
+
+    /* x^288 mod p(x)`, x^320 mod p(x)`, x^352 mod p(x)`, x^384 mod p(x)` */
+    .octa 0x9c25531d19e65ddeec1631edb2dea967
+
+    /* x^160 mod p(x)`, x^192 mod p(x)`, x^224 mod p(x)`, x^256 mod p(x)` */
+    .octa 0x790606ff9957c0a65d27e147510ac59a
+
+    /* x^32 mod p(x)`, x^64 mod p(x)`, x^96 mod p(x)`, x^128 mod p(x)` */
+    .octa 0x82f63b786ea2d55ca66805eb18b8ea18
+
+    .barrett_constants :
+    /* 33 bit reflected Barrett constant m - (4^32)/n */
+    .octa 0x000000000000000000000000dea713f1 /* x^64 div p(x)` */
+    /* 33 bit reflected Barrett constant n */
+    .octa 0x00000000000000000000000105ec76f1
+#endif
+
+#endif

util/ppc-opcode.h

@@ -0,0 +1,31 @@
+//  Copyright (c) 2017 International Business Machines Corp.
+//  All rights reserved.
+//  This source code is licensed under the BSD-style license found in the
+//  LICENSE file in the root directory of this source tree. An additional grant
+//  of patent rights can be found in the PATENTS file in the same directory.
+//  This source code is also licensed under the GPLv2 license found in the
+//  COPYING file in the root directory of this source tree.
+
+#ifndef __OPCODES_H
+#define __OPCODES_H
+
+#define __PPC_RA(a) (((a)&0x1f) << 16)
+#define __PPC_RB(b) (((b)&0x1f) << 11)
+#define __PPC_XA(a) ((((a)&0x1f) << 16) | (((a)&0x20) >> 3))
+#define __PPC_XB(b) ((((b)&0x1f) << 11) | (((b)&0x20) >> 4))
+#define __PPC_XS(s) ((((s)&0x1f) << 21) | (((s)&0x20) >> 5))
+#define __PPC_XT(s) __PPC_XS(s)
+#define VSX_XX3(t, a, b) (__PPC_XT(t) | __PPC_XA(a) | __PPC_XB(b))
+#define VSX_XX1(s, a, b) (__PPC_XS(s) | __PPC_RA(a) | __PPC_RB(b))
+
+#define PPC_INST_VPMSUMW 0x10000488
+#define PPC_INST_VPMSUMD 0x100004c8
+#define PPC_INST_MFVSRD 0x7c000066
+#define PPC_INST_MTVSRD 0x7c000166
+
+#define VPMSUMW(t, a, b) .long PPC_INST_VPMSUMW | VSX_XX3((t), a, b)
+#define VPMSUMD(t, a, b) .long PPC_INST_VPMSUMD | VSX_XX3((t), a, b)
+#define MFVRD(a, t) .long PPC_INST_MFVSRD | VSX_XX1((t) + 32, a, 0)
+#define MTVRD(t, a) .long PPC_INST_MTVSRD | VSX_XX1((t) + 32, a, 0)
+
+#endif