Change Details

Tested on amd64, i386 (qemu), big-endian powerpc64 (qemu). I spot-checked that the new implementation produces the same values as the old one. Below are timing differences for a program which generates 100000000 numbers from a random seed. The new implementation is faster in all cases, especially for drand48() and erand48(), which are implemented by converting the LCG output to a floating point number in the range [0, 1). ``` Using seed: 533733328 unmodified drand48: 1.05 real 1.05 user 0.00 sys 1.07 real 1.07 user 0.00 sys 1.04 real 1.04 user 0.00 sys 1.05 real 1.04 user 0.00 sys 1.07 real 1.07 user 0.00 sys modified drand48: 0.53 real 0.53 user 0.00 sys 0.56 real 0.56 user 0.00 sys 0.57 real 0.57 user 0.00 sys 0.53 real 0.53 user 0.00 sys 0.57 real 0.57 user 0.00 sys unmodified erand48: 1.09 real 1.09 user 0.00 sys 1.09 real 1.09 user 0.00 sys 1.09 real 1.09 user 0.00 sys 1.08 real 1.08 user 0.00 sys 1.07 real 1.07 user 0.00 sys modified erand48: 0.76 real 0.75 user 0.00 sys 0.75 real 0.75 user 0.00 sys 0.75 real 0.75 user 0.00 sys 0.76 real 0.76 user 0.00 sys 0.76 real 0.76 user 0.00 sys unmodified lrand48: 0.32 real 0.32 user 0.00 sys 0.32 real 0.32 user 0.00 sys 0.32 real 0.32 user 0.00 sys 0.33 real 0.33 user 0.00 sys 0.35 real 0.35 user 0.00 sys modified lrand48: 0.23 real 0.23 user 0.00 sys 0.24 real 0.24 user 0.00 sys 0.24 real 0.24 user 0.00 sys 0.22 real 0.22 user 0.00 sys 0.23 real 0.23 user 0.00 sys unmodified nrand48: 0.57 real 0.57 user 0.00 sys 0.59 real 0.59 user 0.00 sys 0.59 real 0.59 user 0.00 sys 0.54 real 0.54 user 0.00 sys 0.59 real 0.59 user 0.00 sys modified nrand48: 0.50 real 0.50 user 0.00 sys 0.54 real 0.54 user 0.00 sys 0.50 real 0.50 user 0.00 sys 0.50 real 0.50 user 0.00 sys 0.55 real 0.55 user 0.00 sys unmodified mrand48: 0.46 real 0.46 user 0.00 sys 0.48 real 0.48 user 0.00 sys 0.51 real 0.51 user 0.00 sys 0.46 real 0.46 user 0.00 sys 0.51 real 0.51 user 0.00 sys modified mrand48: 0.20 real 0.20 user 0.00 sys 0.23 real 0.23 user 0.00 sys 0.22 real 0.22 user 0.00 sys 0.23 real 0.23 user 0.00 sys 0.20 real 0.20 user 0.00 sys unmodified jrand48: 0.67 real 0.67 user 0.00 sys 0.76 real 0.76 user 0.00 sys 0.70 real 0.70 user 0.00 sys 0.69 real 0.69 user 0.00 sys 0.71 real 0.71 user 0.00 sys modified jrand48: 0.53 real 0.53 user 0.00 sys 0.49 real 0.49 user 0.00 sys 0.49 real 0.49 user 0.00 sys 0.51 real 0.51 user 0.00 sys 0.53 real 0.53 user 0.00 sys ```

Tested on amd64, i386 (qemu), big-endian powerpc64 (qemu). I spot-checked that the new implementation produces the same values as the old one. Below are timing differences for a program which generates 100000000 numbers from a random seed. The new implementation is faster in all cases, especially for drand48() and erand48(), which are implemented by converting the LCG output to a floating point number in the range [0, 1). ``` Using seed: 160565650 x /tmp/drand48.unmodified + /tmp/drand48.modified +-----------------------------------------------------------------------------+ | + x x| | + x x| |+ + x x| |+ ++ x x| |+ ++ x x| | |_AM| |_A|| +-----------------------------------------------------------------------------+ N Min Max Median Avg Stddev x 10 1.06 1.08 1.07 1.07 0.010540926 + 10 0.54 0.57 0.565 0.559 0.013703203 Difference at 95.0% confidence -0.511 +/- 0.0114863 -47.757% +/- 0.917009% (Student's t, pooled s = 0.0122247) x /tmp/erand48.unmodified + /tmp/erand48.modified +-----------------------------------------------------------------------------+ |+ x| |+ x| |+ x| |+ x| |+ x| |+ x| |+ x| |+ x| |+ x| |+ x| |A A| +-----------------------------------------------------------------------------+ N Min Max Median Avg Stddev x 10 1.1 1.1 1.1 1.1 2.3405556e-16 + 10 0.75 0.75 0.75 0.75 0 Difference at 95.0% confidence -0.35 +/- 1.55505e-16 -31.8182% +/- 9.63875e-15% (Student's t, pooled s = 1.65502e-16) x /tmp/lrand48.unmodified + /tmp/lrand48.modified +-----------------------------------------------------------------------------+ |+ | |+ x | |+ x | |+ x | |+ x | |+ x | |+ x | |+ x | |+ x | |+ x x| |A |_A_| | +-----------------------------------------------------------------------------+ N Min Max Median Avg Stddev x 10 0.35 0.36 0.35 0.351 0.0031622777 + 10 0.24 0.24 0.24 0.24 5.8513891e-17 Difference at 95.0% confidence -0.111 +/- 0.002101 -31.6239% +/- 0.409282% (Student's t, pooled s = 0.00223607) x /tmp/nrand48.unmodified + /tmp/nrand48.modified +-----------------------------------------------------------------------------+ |+ x| |+ x| |+ x| |+ x| |+ x| |+ x| |+ x| |+ x| |+ x| |+ x| |A A| +-----------------------------------------------------------------------------+ N Min Max Median Avg Stddev x 10 0.6 0.6 0.6 0.6 1.1702778e-16 + 10 0.55 0.55 0.55 0.55 1.1702778e-16 Difference at 95.0% confidence -0.05 +/- 1.09959e-16 -8.33333% +/- 1.75795e-14% (Student's t, pooled s = 1.17028e-16) x /tmp/mrand48.unmodified + /tmp/mrand48.modified +-----------------------------------------------------------------------------+ |+ + x | |+ + x | |+ + x | |+ + x | |+ + x x| ||__A_| MA| | +-----------------------------------------------------------------------------+ N Min Max Median Avg Stddev x 10 0.51 0.52 0.51 0.511 0.0031622777 + 10 0.22 0.24 0.23 0.23 0.010540926 Difference at 95.0% confidence -0.281 +/- 0.00731169 -54.9902% +/- 1.38295% (Student's t, pooled s = 0.00778175) x /tmp/jrand48.unmodified + /tmp/jrand48.modified +-----------------------------------------------------------------------------+ |+ | |+ x | |+ x | |+ x | |+ x | |+ x | |+ x | |+ x | |+ x | |+ x x | |A |A|| +-----------------------------------------------------------------------------+ N Min Max Median Avg Stddev x 10 0.75 0.76 0.76 0.759 0.0031622777 + 10 0.53 0.53 0.53 0.53 1.1702778e-16 Difference at 95.0% confidence -0.229 +/- 0.002101 -30.1713% +/- 0.193294% (Student's t, pooled s = 0.00223607) ```

Tested on amd64, i386 (qemu), big-endian powerpc64 (qemu). I spot-checked that the new implementation produces the same values as the old one. Below are timing differences for a program which generates 100000000 numbers from a random seed. The new implementation is faster in all cases, especially for drand48() and erand48(), which are implemented by converting the LCG output to a floating point number in the range [0, 1). ``` Using seed: 533733328 unmodified drand48: 1.05 real 1.05 user 0.00 sys160565650 x /tmp/drand48.unmodified + /tmp/drand48.modified +-----------------------------------------------------------------------------+ | + 1.07 real 1.07 user 0.00 sys x x| | + 1.04 real 1.04 user 0.00 sys x x| |+ + 1.05 real 1.04 user 0.00 sys x x| |+ ++ 1.07 real 1.07 user 0.00 sys x x| modified drand48: |+ ++ 0.53 real 0.53 user 0.00 sysx x| | |_AM| 0.56 real 0.56 user 0.00 sys |_A|| 0.57 real 0.57 user 0.00 sys+-----------------------------------------------------------------------------+ N Min Max Median Avg Stddev x 10 1.06 1.08 1.07 1.07 0.010540926 + 10 0.54 0.57 0.565 0.559 0.013703203 Difference at 95.0% confidence 0.53 real-0.511 +/- 0.0114863 0.53 user 0.00 sys 0.57 real 0.57 user-47.757% +/- 0.917009% 0.00 sys unmodified erand48: 1.09 real 1.09 user 0.00 sys(Student's t, pooled s = 0.0122247) x /tmp/erand48.unmodified + /tmp/erand48.modified +-----------------------------------------------------------------------------+ |+ 1.09 real 1.09 user 0.00 sys x| |+ 1.09 real 1.09 user 0.00 sys x| |+ x| |+ x| |+ x| |+ x| |+ x| |+ x| |+ x| |+ x| |A A| +-----------------------------------------------------------------------------+ N Min Max Median Avg Stddev x 10 1.1 1.1 1.1 1.1 2.3405556e-16 + 10 0.75 0.75 0.75 0.75 0 Difference at 95.0% confidence 1.08 real-0.35 +/- 1.55505e-16 1.08 user 0.00 sys 1.07 real 1.07 user 0.00 sys modified erand48: -31.8182% +/- 9.63875e-15% 0.76 real 0.75 user 0.00 sys(Student's t, pooled s = 1.65502e-16) x /tmp/lrand48.unmodified + /tmp/lrand48.modified +-----------------------------------------------------------------------------+ 0.75 real 0.75 user 0.00 sys|+ | |+ x | |+ x | |+ x | |+ x | |+ 0.75 real 0.75 user 0.00 sysx | |+ 0.76 real 0.76 user 0.00 sysx | |+ 0.76 real 0.76 user 0.00 sysx | unmodified lrand48:|+ 0.32 real 0.32 user 0.00 sysx | |+ x x| |A |_A_| | +-----------------------------------------------------------------------------+ N Min Max Median Avg Stddev x 10 0.35 0.36 0.35 0.351 0.0031622777 + 10 0.24 0.24 0.24 0.24 5.8513891e-17 Difference at 95.0% confidence 0.32 real-0.111 +/- 0.002101 0.32 user 0.00 sys 0.32 real-31.6239% +/- 0.409282% 0.32 user 0.00 sys 0.33 real 0.33 user 0.00 sys(Student's t, pooled s = 0.00223607) x /tmp/nrand48.unmodified + /tmp/nrand48.modified +-----------------------------------------------------------------------------+ |+ 0.35 real 0.35 user 0.00 sys x| modified lrand48:|+ x| |+ 0.23 real 0.23 user 0.00 sys x| |+ 0.24 real 0.24 user 0.00 sys x| |+ 0.24 real 0.24 user 0.00 sys x| |+ 0.22 real 0.22 user 0.00 sys x| |+ 0.23 real 0.23 user 0.00 sys x| unmodified nrand48:|+ x| |+ 0.57 real 0.57 user 0.00 sys x| |+ 0.59 real 0.59 user 0.00 sys x| |A 0.59 real 0.59 user 0.00 sys A| 0.54 real 0.54 user 0.00 sys+-----------------------------------------------------------------------------+ N 0.59 real Min 0.59 userMax Median 0.00 sysAvg Stddev modified nrand48:x 10 0.6 0.6 0.6 0.6 1.1702778e-16 + 10 0.50 real55 0.55 0.50 user 0.55 0.00 sys55 1.1702778e-16 Difference at 95.0% confidence 0.54 real-0.05 +/- 1.09959e-16 0.54 user 0.00 sys 0.50 real-8.33333% +/- 1.75795e-14% 0.50 user 0.00 sys 0.50 real 0.50 user 0.00 sys(Student's t, pooled s = 1.17028e-16) 0.55 real 0.55 user 0.00 sysx /tmp/mrand48.unmodified + /tmp/mrand48.modified +-----------------------------------------------------------------------------+ unmodified mrand48:|+ + x | |+ + 0.46 real 0.46 user 0.00 sys x | |+ + 0.48 real 0.48 user 0.00 sys x | |+ + 0.51 real 0.51 user 0.00 sys x | |+ + 0.46 real 0.46 user 0.00 sys x x| ||__A_| 0.51 real 0.51 user 0.00 sys MA| | modified mrand48:+-----------------------------------------------------------------------------+ N 0.20 real Min 0.20 userMax Median 0.00 sysAvg Stddev x 10 0.23 real51 0.52 0.23 user 0.51 0.511 0.00 sys31622777 + 10 0.22 real 0.24 0.22 user3 0.23 0.00 sys10540926 Difference at 95.0% confidence 0.23 real-0.281 +/- 0.00731169 0.23 user 0.00 sys 0.20 real-54.9902% +/- 1.38295% 0.20 user (Student's t, pooled s = 0.00 sys778175) unmodified jrand48:x /tmp/jrand48.unmodified + /tmp/jrand48.modified +-----------------------------------------------------------------------------+ |+ 0.67 real 0.67 user 0.00 sys | |+ 0.76 real 0.76 user 0.00 sys x | |+ 0.70 real 0.70 user 0.00 sys x | |+ 0.69 real 0.69 user 0.00 sys x | |+ 0.71 real 0.71 user 0.00 sys x | modified jrand48:|+ x | |+ 0.53 real 0.53 user 0.00 sys x | |+ 0.49 real 0.49 user 0.00 sys x | |+ 0.49 real 0.49 user 0.00 sys x | |+ 0.51 real 0.51 user 0.00 sys x x | |A |A|| +-----------------------------------------------------------------------------+ N Min Max Median Avg Stddev x 10 0.75 0.76 0.76 0.759 0.0031622777 + 10 0.53 0.53 0.53 0.53 1.1702778e-16 Difference at 95.0% confidence 0.53 real 0.53 user 0.00 sys-0.229 +/- 0.002101 -30.1713% +/- 0.193294% (Student's t, pooled s = 0.00223607) ```