Page 327 - ARM 64 Bit Assembly Language

316 Chapter 9

18 .word 0x13A86D09, 0x3DE61246 // 1.605904383682161e-10
19 .word 0xE733B81F, 0xBD6AE7F3 // -7.647163731819816e-13
20 .word 0x7030AD4A, 0x3CE952C7 // 2.811457254345521e-15
21 .word 0x46814157, 0xBC62F49B // -8.220635246624329e-18
22 .equ TERMS,((. - ctab)/8)
23 // ---------------------------------------------------------------
24 .text
25 .align 2
26 // double sin_a_d(double x)
27 // sin_a_f_d implements the sine function using IEEE
28 // double precision floating point. It computes sine
29 // by summing the first ten terms of the Taylor series.
30 .global sin_a_d
31 sin_a_d:// d0 contains x
32 ldr x0,=ctab // load pointer to coefficient table
33 // initialize variables
34 fmul d1,d0,d0 // d1 <- x^2
35 fmov d3,d0 // d3 <- x
36 mov x3,#TERMS // load loop counter
37 // loop over table
38 loop: fmul d3,d1,d3 // d4 <- x^(2n+1)
39 ldr d4,[x0],#8 // load coefficient and increment pointer
40 subs x3,x3,#1 // decrement and test loop counter
41 fmadd d0,d3,d4,d0 // d0 += next term
42 bne loop // loop nine times
43 ret

Listing 9.2 shows a double precision floating point implementation of the sine function, us-
ing the ARM FP/NEON instruction set. Again, there is a table of constants, each of which
is the reciprocal of one of the factorial divisors in the Taylor series for sine. The subroutine
calculates the powers of x one-by-one, and multiplies each power by the next constant in
the table, summing the results as it goes. Note that the table of constants is longer than the
fixed point version of the code, because there are more bits of precision in a double precision
floating point number than there are in the fixed point representation that was used previ-
ously.

9.8.1 Performance comparison

Table 9.2 shows the performance of different implementations of the sine function, with
and without compiler optimization. The Single Precision C and Double Precision C imple-
mentations are the standard implementations provided by GCC. The comparison tests were
performed by timing each of the four cases on the same set of 100,000,000 random numbers,
with and without compiler optimization.