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authorMilo Yip <miloyip@gmail.com>2014-07-16 22:26:20 +0400
committerMilo Yip <miloyip@gmail.com>2014-07-16 22:26:20 +0400
commit46eeb46a61872b6573a7d816ac5bdba82ac86075 (patch)
treedb7da459f729aa7fb08e9a05c432116bb90aaaee /test
parent8b963dc7ada1034e04ec40e3f419a01dfd20df78 (diff)
Implemented faster itoa with bit counting and reverse write
Diffstat (limited to 'test')
-rw-r--r--test/perftest/misctest.cpp558
1 files changed, 500 insertions, 58 deletions
diff --git a/test/perftest/misctest.cpp b/test/perftest/misctest.cpp
index 94c2ef2d..cc2cc339 100644
--- a/test/perftest/misctest.cpp
+++ b/test/perftest/misctest.cpp
@@ -3,14 +3,23 @@
#if TEST_MISC
#define __STDC_FORMAT_MACROS
+#include "rapidjson/stringbuffer.h"
+
+#ifdef _MSC_VER
+#pragma warning (push)
+#pragma warning (disable: 4996)
+#endif
#define strtk_no_tr1_or_boost
#include "strtk/strtk.hpp"
-#include "rapidjson/stringbuffer.h"
+
+#ifdef _MSC_VER
+#pragma warning (pop)
+#endif
#ifdef _MSC_VER
#pragma warning (push)
-#pragma warning (disable: 4245; disable: 4512)
+#pragma warning (disable: 4245; disable: 4512; disable: 4996)
#endif
#include "cppformat/format.h"
@@ -76,6 +85,154 @@ TEST_F(Misc, Hoehrmann_IsUTF8) {
}
}
+////////////////////////////////////////////////////////////////////////////////
+// CountDecimalDigit: Count number of decimal places
+
+inline unsigned CountDecimalDigit_naive(unsigned n) {
+ unsigned count = 1;
+ while (n >= 10) {
+ n /= 10;
+ count++;
+ }
+ return count;
+}
+
+inline unsigned CountDecimalDigit_enroll4(unsigned n) {
+ unsigned count = 1;
+ while (n >= 10000) {
+ n /= 10000u;
+ count += 4;
+ }
+ if (n < 10) return count;
+ if (n < 100) return count + 1;
+ if (n < 1000) return count + 2;
+ return count + 3;
+}
+
+inline unsigned CountDecimalDigit64_enroll4(uint64_t n) {
+ unsigned count = 1;
+ while (n >= 10000) {
+ n /= 10000u;
+ count += 4;
+ }
+ if (n < 10) return count;
+ if (n < 100) return count + 1;
+ if (n < 1000) return count + 2;
+ return count + 3;
+}
+
+inline unsigned CountDecimalDigit_fast(unsigned n) {
+ static const uint32_t powers_of_10[] = {
+ 0,
+ 10,
+ 100,
+ 1000,
+ 10000,
+ 100000,
+ 1000000,
+ 10000000,
+ 100000000,
+ 1000000000
+ };
+
+ unsigned long i = 0;
+ // uint32_t t = (32 - __builtin_clz(n | 1)) * 1233 >> 12;
+ _BitScanReverse(&i, n | 1);
+ uint32_t t = (i + 1) * 1233 >> 12;
+ return t - (n < powers_of_10[t]) + 1;
+}
+
+inline unsigned CountDecimalDigit64_fast(uint64_t n) {
+ static const uint64_t powers_of_10[] = {
+ 0,
+ 10,
+ 100,
+ 1000,
+ 10000,
+ 100000,
+ 1000000,
+ 10000000,
+ 100000000,
+ 1000000000,
+ 10000000000,
+ 100000000000,
+ 1000000000000,
+ 10000000000000,
+ 100000000000000,
+ 1000000000000000,
+ 10000000000000000,
+ 100000000000000000,
+ 1000000000000000000,
+ 10000000000000000000U
+ };
+
+ unsigned long i = 0;
+ // uint32_t t = (32 - __builtin_clz(n | 1)) * 1233 >> 12;
+
+#if _M_IX86
+ uint64_t m = n | 1;
+ if (_BitScanReverse(&i, m >> 32))
+ i += 32;
+ else
+ _BitScanReverse(&i, m & 0xFFFFFFFF);
+#elif _M_X64
+ _BitScanReverse64(&i, n | 1);
+#else
+#error
+#endif
+
+ uint32_t t = (i + 1) * 1233 >> 12;
+ return t - (n < powers_of_10[t]) + 1;
+}
+
+#if 0
+// Exhaustive, very slow
+TEST_F(Misc, CountDecimalDigit_Verify) {
+ unsigned i = 0;
+ do {
+ if (i % (65536 * 256) == 0)
+ printf("%u\n", i);
+ ASSERT_EQ(CountDecimalDigit_enroll4(i), CountDecimalDigit_fast(i));
+ i++;
+ } while (i != 0);
+}
+
+static const unsigned kDigits10Trial = 1000000000u;
+TEST_F(Misc, CountDecimalDigit_naive) {
+ unsigned sum = 0;
+ for (unsigned i = 0; i < kDigits10Trial; i++)
+ sum += CountDecimalDigit_naive(i);
+ printf("%u\n", sum);
+}
+
+TEST_F(Misc, CountDecimalDigit_enroll4) {
+ unsigned sum = 0;
+ for (unsigned i = 0; i < kDigits10Trial; i++)
+ sum += CountDecimalDigit_enroll4(i);
+ printf("%u\n", sum);
+}
+
+TEST_F(Misc, CountDecimalDigit_fast) {
+ unsigned sum = 0;
+ for (unsigned i = 0; i < kDigits10Trial; i++)
+ sum += CountDecimalDigit_fast(i);
+ printf("%u\n", sum);
+}
+#endif
+
+TEST_F(Misc, CountDecimalDigit64_VerifyFast) {
+ uint64_t i = 1, j;
+ do {
+ printf("%" PRIu64 "\n", i);
+ ASSERT_EQ(CountDecimalDigit64_enroll4(i), CountDecimalDigit64_fast(i));
+ j = i;
+ i *= 3;
+ } while (j < i);
+}
+
+////////////////////////////////////////////////////////////////////////////////
+// integer-to-string conversion
+
// https://gist.github.com/anonymous/7179097
static const int randval[] ={
936116, 369532, 453755, -72860, 209713, 268347, 435278, -360266, -416287, -182064,
@@ -185,6 +342,13 @@ static const int randval[] ={
static const size_t randvalCount = sizeof(randval) / sizeof(randval[0]);
static const size_t kItoaTrialCount = 10000;
+static const char digits[201] =
+"0001020304050607080910111213141516171819"
+"2021222324252627282930313233343536373839"
+"4041424344454647484950515253545556575859"
+"6061626364656667686970717273747576777879"
+"8081828384858687888990919293949596979899";
+
// Prevent code being optimized out
#define OUTPUT_LENGTH(length) printf("", length)
//#define OUTPUT_LENGTH(length) printf("%d\n", length)
@@ -250,12 +414,22 @@ private:
OutputStream* os_;
};
-static const char digits[201] =
- "0001020304050607080910111213141516171819"
- "2021222324252627282930313233343536373839"
- "4041424344454647484950515253545556575859"
- "6061626364656667686970717273747576777879"
- "8081828384858687888990919293949596979899";
+template<>
+inline bool Writer1<rapidjson::StringBuffer>::WriteUint(unsigned u) {
+ char buffer[10];
+ char* p = buffer;
+ do {
+ *p++ = char(u % 10) + '0';
+ u /= 10;
+ } while (u > 0);
+
+ char* d = os_->Allocate(p - buffer);
+ do {
+ --p;
+ *d++ = *p;
+ } while (p != buffer);
+ return true;
+}
// Using digits LUT to reduce divsion/modulo
template<typename OutputStream>
@@ -337,8 +511,254 @@ private:
OutputStream* os_;
};
+// First pass to count digits
+template<typename OutputStream>
+class Writer3 {
+public:
+ Writer3() : os_() {}
+ Writer3(OutputStream& os) : os_(&os) {}
+
+ void Reset(OutputStream& os) {
+ os_ = &os;
+ }
+
+ bool WriteInt(int i) {
+ if (i < 0) {
+ os_->Put('-');
+ i = -i;
+ }
+ return WriteUint((unsigned)i);
+ }
+
+ bool WriteUint(unsigned u) {
+ char buffer[10];
+ char *p = buffer;
+ do {
+ *p++ = char(u % 10) + '0';
+ u /= 10;
+ } while (u > 0);
+
+ do {
+ --p;
+ os_->Put(*p);
+ } while (p != buffer);
+ return true;
+ }
+
+ bool WriteInt64(int64_t i64) {
+ if (i64 < 0) {
+ os_->Put('-');
+ i64 = -i64;
+ }
+ WriteUint64((uint64_t)i64);
+ return true;
+ }
+
+ bool WriteUint64(uint64_t u64) {
+ char buffer[20];
+ char *p = buffer;
+ do {
+ *p++ = char(u64 % 10) + '0';
+ u64 /= 10;
+ } while (u64 > 0);
+
+ do {
+ --p;
+ os_->Put(*p);
+ } while (p != buffer);
+ return true;
+ }
+
+private:
+ void WriteUintReverse(char* d, unsigned u) {
+ do {
+ *--d = char(u % 10) + '0';
+ u /= 10;
+ } while (u > 0);
+ }
+
+ void WriteUint64Reverse(char* d, uint64_t u) {
+ do {
+ *--d = char(u % 10) + '0';
+ u /= 10;
+ } while (u > 0);
+ }
+
+ OutputStream* os_;
+};
+
+template<>
+inline bool Writer3<rapidjson::StringBuffer>::WriteUint(unsigned u) {
+ unsigned digit = CountDecimalDigit_fast(u);
+ WriteUintReverse(os_->Allocate(digit) + digit, u);
+ return true;
+}
+
+template<>
+inline bool Writer3<rapidjson::InsituStringStream>::WriteUint(unsigned u) {
+ unsigned digit = CountDecimalDigit_fast(u);
+ WriteUintReverse(os_->Allocate(digit) + digit, u);
+ return true;
+}
+
+template<>
+inline bool Writer3<rapidjson::StringBuffer>::WriteUint64(uint64_t u) {
+ unsigned digit = CountDecimalDigit64_fast(u);
+ WriteUint64Reverse(os_->Allocate(digit) + digit, u);
+ return true;
+}
+
+template<>
+inline bool Writer3<rapidjson::InsituStringStream>::WriteUint64(uint64_t u) {
+ unsigned digit = CountDecimalDigit64_fast(u);
+ WriteUint64Reverse(os_->Allocate(digit) + digit, u);
+ return true;
+}
+
+// Using digits LUT to reduce divsion/modulo, two passes
+template<typename OutputStream>
+class Writer4 {
+public:
+ Writer4() : os_() {}
+ Writer4(OutputStream& os) : os_(&os) {}
+
+ void Reset(OutputStream& os) {
+ os_ = &os;
+ }
+
+ bool WriteInt(int i) {
+ if (i < 0) {
+ os_->Put('-');
+ i = -i;
+ }
+ return WriteUint((unsigned)i);
+ }
+
+ bool WriteUint(unsigned u) {
+ char buffer[10];
+ char* p = buffer;
+ while (u >= 100) {
+ const unsigned i = (u % 100) << 1;
+ u /= 100;
+ *p++ = digits[i + 1];
+ *p++ = digits[i];
+ }
+ if (u < 10)
+ *p++ = char(u) + '0';
+ else {
+ const unsigned i = u << 1;
+ *p++ = digits[i + 1];
+ *p++ = digits[i];
+ }
+
+ do {
+ --p;
+ os_->Put(*p);
+ } while (p != buffer);
+ return true;
+ }
+
+ bool WriteInt64(int64_t i64) {
+ if (i64 < 0) {
+ os_->Put('-');
+ i64 = -i64;
+ }
+ WriteUint64((uint64_t)i64);
+ return true;
+ }
+
+ bool WriteUint64(uint64_t u64) {
+ char buffer[20];
+ char* p = buffer;
+ while (u64 >= 100) {
+ const unsigned i = static_cast<unsigned>(u64 % 100) << 1;
+ u64 /= 100;
+ *p++ = digits[i + 1];
+ *p++ = digits[i];
+ }
+ if (u64 < 10)
+ *p++ = char(u64) + '0';
+ else {
+ const unsigned i = static_cast<unsigned>(u64) << 1;
+ *p++ = digits[i + 1];
+ *p++ = digits[i];
+ }
+
+ do {
+ --p;
+ os_->Put(*p);
+ } while (p != buffer);
+ return true;
+ }
+
+private:
+ void WriteUintReverse(char* d, unsigned u) {
+ while (u >= 100) {
+ const unsigned i = (u % 100) << 1;
+ u /= 100;
+ *--d = digits[i + 1];
+ *--d = digits[i];
+ }
+ if (u < 10) {
+ *--d = char(u) + '0';
+ }
+ else {
+ const unsigned i = u << 1;
+ *--d = digits[i + 1];
+ *--d = digits[i];
+ }
+ }
+
+ void WriteUint64Reverse(char* d, uint64_t u) {
+ while (u >= 100) {
+ const unsigned i = (u % 100) << 1;
+ u /= 100;
+ *--d = digits[i + 1];
+ *--d = digits[i];
+ }
+ if (u < 10) {
+ *--d = char(u) + '0';
+ }
+ else {
+ const unsigned i = u << 1;
+ *--d = digits[i + 1];
+ *--d = digits[i];
+ }
+ }
+
+ OutputStream* os_;
+};
+
+template<>
+inline bool Writer4<rapidjson::StringBuffer>::WriteUint(unsigned u) {
+ unsigned digit = CountDecimalDigit_fast(u);
+ WriteUintReverse(os_->Allocate(digit) + digit, u);
+ return true;
+}
+
+template<>
+inline bool Writer4<rapidjson::InsituStringStream>::WriteUint(unsigned u) {
+ unsigned digit = CountDecimalDigit_fast(u);
+ WriteUintReverse(os_->Allocate(digit) + digit, u);
+ return true;
+}
+
+template<>
+inline bool Writer4<rapidjson::StringBuffer>::WriteUint64(uint64_t u) {
+ unsigned digit = CountDecimalDigit64_fast(u);
+ WriteUint64Reverse(os_->Allocate(digit) + digit, u);
+ return true;
+}
+
+template<>
+inline bool Writer4<rapidjson::InsituStringStream>::WriteUint64(uint64_t u) {
+ unsigned digit = CountDecimalDigit64_fast(u);
+ WriteUint64Reverse(os_->Allocate(digit) + digit, u);
+ return true;
+}
+
template <typename Writer>
-void itoa_Writer_Verify() {
+void itoa_Writer_StringBufferVerify() {
rapidjson::StringBuffer sb;
Writer writer(sb);
for (int j = 0; j < randvalCount; j++) {
@@ -351,6 +771,23 @@ void itoa_Writer_Verify() {
}
template <typename Writer>
+void itoa_Writer_InsituStringStreamVerify() {
+ Writer writer;
+ for (int j = 0; j < randvalCount; j++) {
+ char buffer[32];
+ sprintf(buffer, "%d", randval[j]);
+ char buffer2[32];
+ rapidjson::InsituStringStream ss(buffer2);
+ writer.Reset(ss);
+ char* begin = ss.PutBegin();
+ writer.WriteInt(randval[j]);
+ ss.Put('\0');
+ ss.PutEnd(begin);
+ ASSERT_STREQ(buffer, buffer2);
+ }
+}
+
+template <typename Writer>
void itoa_Writer_StringBuffer() {
size_t length = 0;
@@ -386,7 +823,7 @@ void itoa_Writer_InsituStringStream() {
};
template <typename Writer>
-void itoa64_Writer_Verify() {
+void itoa64_Writer_StringBufferVerify() {
rapidjson::StringBuffer sb;
Writer writer(sb);
for (int j = 0; j < randvalCount; j++) {
@@ -400,6 +837,24 @@ void itoa64_Writer_Verify() {
}
template <typename Writer>
+void itoa64_Writer_InsituStringStreamVerify() {
+ Writer writer;
+ for (int j = 0; j < randvalCount; j++) {
+ char buffer[32];
+ int64_t x = randval[j] * randval[j];
+ sprintf(buffer, "%" PRIi64, x);
+ char buffer2[32];
+ rapidjson::InsituStringStream ss(buffer2);
+ writer.Reset(ss);
+ char* begin = ss.PutBegin();
+ writer.WriteInt64(x);
+ ss.Put('\0');
+ ss.PutEnd(begin);
+ ASSERT_STREQ(buffer, buffer2);
+ }
+}
+
+template <typename Writer>
void itoa64_Writer_StringBuffer() {
size_t length = 0;
@@ -434,53 +889,39 @@ void itoa64_Writer_InsituStringStream() {
OUTPUT_LENGTH(length);
};
-TEST_F(Misc, itoa_Writer1_Verify) {
- itoa_Writer_Verify<Writer1<rapidjson::StringBuffer> >();
-}
-
-TEST_F(Misc, itoa_Writer2_Verify) {
- itoa_Writer_Verify<Writer1<rapidjson::StringBuffer> >();
-}
-
-TEST_F(Misc, itoa_Writer1_StringBuffer) {
- itoa_Writer_StringBuffer<Writer1<rapidjson::StringBuffer> >();
-}
-
-TEST_F(Misc, itoa_Writer1_InsituStringStream) {
- itoa_Writer_InsituStringStream<Writer1<rapidjson::InsituStringStream> >();
-}
-
-TEST_F(Misc, itoa_Writer2_StringBuffer) {
- itoa_Writer_StringBuffer<Writer2<rapidjson::StringBuffer> >();
-}
-
-TEST_F(Misc, itoa_Writer2_InsituStringStream) {
- itoa_Writer_InsituStringStream<Writer2<rapidjson::InsituStringStream> >();
-}
-
-TEST_F(Misc, itoa64_Writer1_Verify) {
- itoa64_Writer_Verify<Writer1<rapidjson::StringBuffer> >();
-}
-
-TEST_F(Misc, itoa64_Writer2_Verify) {
- itoa64_Writer_Verify<Writer1<rapidjson::StringBuffer> >();
-}
-
-TEST_F(Misc, itoa64_Writer1_StringBuffer) {
- itoa64_Writer_StringBuffer<Writer1<rapidjson::StringBuffer> >();
-}
-
-TEST_F(Misc, itoa64_Writer1_InsituStringStream) {
- itoa64_Writer_InsituStringStream<Writer1<rapidjson::InsituStringStream> >();
-}
-
-TEST_F(Misc, itoa64_Writer2_StringBuffer) {
- itoa64_Writer_StringBuffer<Writer2<rapidjson::StringBuffer> >();
-}
-
-TEST_F(Misc, itoa64_Writer2_InsituStringStream) {
- itoa64_Writer_InsituStringStream<Writer2<rapidjson::InsituStringStream> >();
-}
+TEST_F(Misc, itoa_Writer1_StringBufferVerify) { itoa_Writer_StringBufferVerify<Writer1<rapidjson::StringBuffer> >(); }
+TEST_F(Misc, itoa_Writer2_StringBufferVerify) { itoa_Writer_StringBufferVerify<Writer2<rapidjson::StringBuffer> >(); }
+TEST_F(Misc, itoa_Writer3_StringBufferVerify) { itoa_Writer_StringBufferVerify<Writer3<rapidjson::StringBuffer> >(); }
+TEST_F(Misc, itoa_Writer4_StringBufferVerify) { itoa_Writer_StringBufferVerify<Writer4<rapidjson::StringBuffer> >(); }
+TEST_F(Misc, itoa_Writer1_InsituStringStreamVerify) { itoa_Writer_InsituStringStreamVerify<Writer1<rapidjson::InsituStringStream> >(); }
+TEST_F(Misc, itoa_Writer2_InsituStringStreamVerify) { itoa_Writer_InsituStringStreamVerify<Writer2<rapidjson::InsituStringStream> >(); }
+TEST_F(Misc, itoa_Writer3_InsituStringStreamVerify) { itoa_Writer_InsituStringStreamVerify<Writer3<rapidjson::InsituStringStream> >(); }
+TEST_F(Misc, itoa_Writer4_InsituStringStreamVerify) { itoa_Writer_InsituStringStreamVerify<Writer4<rapidjson::InsituStringStream> >(); }
+TEST_F(Misc, itoa_Writer1_StringBuffer) { itoa_Writer_StringBuffer<Writer1<rapidjson::StringBuffer> >(); }
+TEST_F(Misc, itoa_Writer2_StringBuffer) { itoa_Writer_StringBuffer<Writer2<rapidjson::StringBuffer> >(); }
+TEST_F(Misc, itoa_Writer3_StringBuffer) { itoa_Writer_StringBuffer<Writer3<rapidjson::StringBuffer> >(); }
+TEST_F(Misc, itoa_Writer4_StringBuffer) { itoa_Writer_StringBuffer<Writer4<rapidjson::StringBuffer> >(); }
+TEST_F(Misc, itoa_Writer1_InsituStringStream) { itoa_Writer_InsituStringStream<Writer1<rapidjson::InsituStringStream> >(); }
+TEST_F(Misc, itoa_Writer2_InsituStringStream) { itoa_Writer_InsituStringStream<Writer2<rapidjson::InsituStringStream> >(); }
+TEST_F(Misc, itoa_Writer3_InsituStringStream) { itoa_Writer_InsituStringStream<Writer3<rapidjson::InsituStringStream> >(); }
+TEST_F(Misc, itoa_Writer4_InsituStringStream) { itoa_Writer_InsituStringStream<Writer4<rapidjson::InsituStringStream> >(); }
+
+TEST_F(Misc, itoa64_Writer1_StringBufferVerify) { itoa64_Writer_StringBufferVerify<Writer1<rapidjson::StringBuffer> >(); }
+TEST_F(Misc, itoa64_Writer2_StringBufferVerify) { itoa64_Writer_StringBufferVerify<Writer2<rapidjson::StringBuffer> >(); }
+TEST_F(Misc, itoa64_Writer3_StringBufferVerify) { itoa64_Writer_StringBufferVerify<Writer3<rapidjson::StringBuffer> >(); }
+TEST_F(Misc, itoa64_Writer4_StringBufferVerify) { itoa64_Writer_StringBufferVerify<Writer4<rapidjson::StringBuffer> >(); }
+TEST_F(Misc, itoa64_Writer1_InsituStringStreamVerify) { itoa64_Writer_InsituStringStreamVerify<Writer1<rapidjson::InsituStringStream> >(); }
+TEST_F(Misc, itoa64_Writer2_InsituStringStreamVerify) { itoa64_Writer_InsituStringStreamVerify<Writer2<rapidjson::InsituStringStream> >(); }
+TEST_F(Misc, itoa64_Writer3_InsituStringStreamVerify) { itoa64_Writer_InsituStringStreamVerify<Writer3<rapidjson::InsituStringStream> >(); }
+TEST_F(Misc, itoa64_Writer4_InsituStringStreamVerify) { itoa64_Writer_InsituStringStreamVerify<Writer4<rapidjson::InsituStringStream> >(); }
+TEST_F(Misc, itoa64_Writer1_StringBuffer) { itoa64_Writer_StringBuffer<Writer1<rapidjson::StringBuffer> >(); }
+TEST_F(Misc, itoa64_Writer2_StringBuffer) { itoa64_Writer_StringBuffer<Writer2<rapidjson::StringBuffer> >(); }
+TEST_F(Misc, itoa64_Writer3_StringBuffer) { itoa64_Writer_StringBuffer<Writer3<rapidjson::StringBuffer> >(); }
+TEST_F(Misc, itoa64_Writer4_StringBuffer) { itoa64_Writer_StringBuffer<Writer4<rapidjson::StringBuffer> >(); }
+TEST_F(Misc, itoa64_Writer1_InsituStringStream) { itoa64_Writer_InsituStringStream<Writer1<rapidjson::InsituStringStream> >(); }
+TEST_F(Misc, itoa64_Writer2_InsituStringStream) { itoa64_Writer_InsituStringStream<Writer2<rapidjson::InsituStringStream> >(); }
+TEST_F(Misc, itoa64_Writer3_InsituStringStream) { itoa64_Writer_InsituStringStream<Writer3<rapidjson::InsituStringStream> >(); }
+TEST_F(Misc, itoa64_Writer4_InsituStringStream) { itoa64_Writer_InsituStringStream<Writer4<rapidjson::InsituStringStream> >(); }
TEST_F(Misc, itoa_sprintf) {
size_t length = 0;
@@ -498,7 +939,8 @@ TEST_F(Misc, itoa64_sprintf) {
for (int i = 0; i < kItoaTrialCount; i++) {
for (int j = 0; j < randvalCount; j++) {
char buffer[32];
- length += sprintf(buffer, "%" PRIi64, randval[j] * randval[j]);
+ int64_t x = randval[j] * randval[j];
+ length += sprintf(buffer, "%" PRIi64, x);
}
}
OUTPUT_LENGTH(length);