Marginal performance hacking in erand48.c.

Get rid of the multiplier and addend variables in favor of hard-wired
constants.  Do the multiply-and-add using uint64 arithmetic, rather
than manually combining several narrower multiplications and additions.
Make _dorand48 return the full-width new random value, and have its
callers use that directly (after suitable masking) rather than
reconstructing what they need from the unsigned short[] representation.

On my machine, this is good for a nearly factor-of-2 speedup of
pg_erand48(), probably mostly from needing just one call of ldexp()
rather than three.  The wins for the other functions are smaller
but measurable.  While none of the existing call sites are really
performance-critical, a cycle saved is a cycle earned; and besides
the machine code is smaller this way (at least on x86_64).

Patch by me, but the original idea to optimize this by switching
to int64 arithmetic is from Fabien Coelho.

Discussion: https://postgr.es/m/1551.1546018192@sss.pgh.pa.us

Author: tglsfdc

src/port/erand48.c

@@ -37,48 +37,46 @@
 
 #include <math.h>
 
+/* These values are specified by POSIX */
+#define RAND48_MULT		UINT64CONST(0x0005deece66d)
+#define RAND48_ADD		UINT64CONST(0x000b)
+
+/* POSIX specifies 0x330e's use in srand48, but the other bits are arbitrary */
 #define RAND48_SEED_0	(0x330e)
 #define RAND48_SEED_1	(0xabcd)
 #define RAND48_SEED_2	(0x1234)
-#define RAND48_MULT_0	(0xe66d)
-#define RAND48_MULT_1	(0xdeec)
-#define RAND48_MULT_2	(0x0005)
-#define RAND48_ADD		(0x000b)
 
 static unsigned short _rand48_seed[3] = {
 	RAND48_SEED_0,
 	RAND48_SEED_1,
 	RAND48_SEED_2
 };
-static unsigned short _rand48_mult[3] = {
-	RAND48_MULT_0,
-	RAND48_MULT_1,
-	RAND48_MULT_2
-};
-static unsigned short _rand48_add = RAND48_ADD;
 
 
 /*
  * Advance the 48-bit value stored in xseed[] to the next "random" number.
+ *
+ * Also returns the value of that number --- without masking it to 48 bits.
+ * If caller uses the result, it must mask off the bits it wants.
  */
-static void
+static uint64
 _dorand48(unsigned short xseed[3])
 {
-	unsigned long accu;
-	unsigned short temp[2];
-
-	accu = (unsigned long) _rand48_mult[0] * (unsigned long) xseed[0] +
-		(unsigned long) _rand48_add;
-	temp[0] = (unsigned short) accu;	/* lower 16 bits */
-	accu >>= sizeof(unsigned short) * 8;
-	accu += (unsigned long) _rand48_mult[0] * (unsigned long) xseed[1] +
-		(unsigned long) _rand48_mult[1] * (unsigned long) xseed[0];
-	temp[1] = (unsigned short) accu;	/* middle 16 bits */
-	accu >>= sizeof(unsigned short) * 8;
-	accu += _rand48_mult[0] * xseed[2] + _rand48_mult[1] * xseed[1] + _rand48_mult[2] * xseed[0];
-	xseed[0] = temp[0];
-	xseed[1] = temp[1];
-	xseed[2] = (unsigned short) accu;
+	/*
+	 * We do the arithmetic in uint64; any type wider than 48 bits would work.
+	 */
+	uint64		in;
+	uint64		out;
+
+	in = (uint64) xseed[2] << 32 | (uint64) xseed[1] << 16 | (uint64) xseed[0];
+
+	out = in * RAND48_MULT + RAND48_ADD;
+
+	xseed[0] = out & 0xFFFF;
+	xseed[1] = (out >> 16) & 0xFFFF;
+	xseed[2] = (out >> 32) & 0xFFFF;
+
+	return out;
 }
 
 
@@ -89,10 +87,9 @@ _dorand48(unsigned short xseed[3])
 double
 pg_erand48(unsigned short xseed[3])
 {
-	_dorand48(xseed);
-	return ldexp((double) xseed[0], -48) +
-		ldexp((double) xseed[1], -32) +
-		ldexp((double) xseed[2], -16);
+	uint64		x = _dorand48(xseed);
+
+	return ldexp((double) (x & UINT64CONST(0xFFFFFFFFFFFF)), -48);
 }
 
 /*
@@ -102,8 +99,9 @@ pg_erand48(unsigned short xseed[3])
 long
 pg_lrand48(void)
 {
-	_dorand48(_rand48_seed);
-	return ((long) _rand48_seed[2] << 15) + ((long) _rand48_seed[1] >> 1);
+	uint64		x = _dorand48(_rand48_seed);
+
+	return (x >> 17) & UINT64CONST(0x7FFFFFFF);
 }
 
 /*
@@ -113,8 +111,9 @@ pg_lrand48(void)
 long
 pg_jrand48(unsigned short xseed[3])
 {
-	_dorand48(xseed);
-	return (int32) (((uint32) xseed[2] << 16) + (uint32) xseed[1]);
+	uint64		x = _dorand48(xseed);
+
+	return (int32) ((x >> 16) & UINT64CONST(0xFFFFFFFF));
 }
 
 /*
@@ -134,8 +133,4 @@ pg_srand48(long seed)
 	_rand48_seed[0] = RAND48_SEED_0;
 	_rand48_seed[1] = (unsigned short) seed;
 	_rand48_seed[2] = (unsigned short) (seed >> 16);
-	_rand48_mult[0] = RAND48_MULT_0;
-	_rand48_mult[1] = RAND48_MULT_1;
-	_rand48_mult[2] = RAND48_MULT_2;
-	_rand48_add = RAND48_ADD;
 }