9 Implementation Notes 9.2 Database Cache Performance 9.4 Auxiliary Store

9.3 Floating Point Performance

Note. This section contains data that is so antiquated that we’re not sure it has much relevance to modern hardware configurations. It is included for the sake of completeness and as a historical curiosity .

Table 2: Floating Point Benchmarks

	With 80387		No 80387
	Repetitions	Average	Repetitions	Average
	2,000k	Time	200k	Time
Operation	(seconds)	( $\mu$ sec)	(seconds)	( $\mu$ sec)
Add	25.9	13.0	34.3	172
Subtract	25.9	13.0	35.3	177
Multiply	28.4	14.2	44.3	222
Divide	33.6	16.8	50.9	255
Inner product ¹	40.3	20.2	61.9	310
Scalar multiply ²	30.2	15.1	45.0	225
Loop overhead		1.3		1.3

¹ sum += a[cursor[i]]*y[cursor[j]]
² a[cursor[i]] *= scalar

A variety of floating point operations were monitored under MS DOS version 3.30 on a 16 Mhz IBM PS/2 Model 70 with a 16 Mhz 80387 coprocessor and a 27 msec, 60 Mbyte fixed disk drive. The 32 bit operations available on the 80386 were not used. Table 2 catalogs the time requirements of the simple arithmetical operations, inner product accumulation, and multiplying a vector by a scalar. All benchmarks were performed using double precision real numbers. The test contains a loop that was restarted after every 500 operations, e.g. 200k repetitions also includes the overhead of starting and stopping a loop 400 times. With this testing scheme, all loop counters and array indices were maintained in the registers.

The measurements in Table 3 provide a similar analysis of math functions in the Microsoft C Version 5.1 math library. These benchmarks were conducted with a single loop whose counter was a long integer.

Table 3: Math Library Benchmarks

	With 80387		No 80387
	Repetitions	Average	Repetitions	Average
	300k	Time	10k	Time
Operation	(seconds)	( $\mu$ sec)	(seconds)	( $\mu$ sec)
acos	36.2	121	30.5	3,050
asin	35.1	117	29.9	2,990
atan	26.0	87	23.0	2,300
cos	37.7	126	25.3	2,530
sin	37.0	123	24.7	2,470
tan	31.7	106	19.2	1,920
log	25.4	85	18.5	1,850
sqrt	16.5	55	5.7	570
pow	51.4	171	38.6	3,860
j0 ¹	235.1	784	60.7	6,070
j6	662.0²	2,207	176.3	17,603
y0 ³	510.0²	1,700	146.4	14,640
Loop overhead		3		3

¹ Bessel function of the first kind, order 0.
² Extrapolated from 30,000 repetitions.
³ Bessel function of the second kind, order 0.

Differences in loop overheads found in Table 2 and Table 3 are accounted for by the differences in the loop counter implementation described above. The 3 $\mu$sec overhead reflects the time required to increment a long integer and monitor the termination condition (which also involved a long integer comparison). The 1.3 $\mu$sec overhead reflects the time required to increment a register and monitor the termination condition (which involved a register comparison).