Page 287 - ARM 64 Bit Assembly Language

276 Chapter 8

47 -1/3! = AAAAAAAA as an S(-2,32)
48 1/5! = 44444445 as an S(-6,32)
49 -1/7! = 97F97F97 as an S(-12,32)
50 1/9! = 5C778E96 as an S(-18,32)
51 -1/11! = 9466EA60 as an S(-25,32)
52 1/13! = 5849184F as an S(-32,32)
53 -1/15! = 94603063 as an S(-40,32)
54 1/17! = 654B1DC1 as an S(-48,32)
55
56 Combining the two tables of power and coefficient formats, we
57 can now determine how much shift we need after each step in
58 order to do all sums in S(2,61) format:
59
60 power powerfmt coef coeffmt resultfmt right shift
61 x S(1,30) * 1 (skip the multiply) 1 -> S(2,61)
62 x^3 S(3,28) * -1/3! S(-2,32) = S(2,61) 0 -> S(2,61)
63 x^5 S(5,26) * 1/5! S(-6,32) = S(0,63) 2 -> S(2,61)
64 x^7 S(7,24) * -1/7! S(-12,32) = S(-4,64) 6 -> S(2,61)
65 x^9 S(9,22) * 1/9! S(-18,32) = S(-8,64) 10-> S(2,61)
66 x^11 S(11,20) * -1/11! S(-25,32) = S(-13,64) 15-> S(2,61)
67 x^13 S(13,18) * 1/13! S(-32,32) = S(-18,64) 20-> S(2,61)
68 x^15 S(15,16) * -1/15! S(-40,32) = S(-24,64) 26-> S(2,61)
69 x^17 S(17,14) * 1/17! S(-48,32) = S(-30,64) 32-> S(2,61)
70 Note: the last row has a shift of 32, which indicates that
71 it can contribute no more than 1/2 bit of precision
72 to the 32-bit result.
73 */
74
75 // We will define a few constants that may be useful
76 .data
77 .global pi
78 pi: .word 0x3243F6A8 // pi as an S(3,28)
79 .equ PI_LO,0xF6A8
80 .equ PI_HI,0x3243
81 pi_2: .word 0x1921FB54 // pi/2 as an S(3,28)
82 .equ PI_2_LO,0xFB54
83 .equ PI_2_HI,0x1921
84 pi_x2: .word 0x6487ED51 // 2*pi as an S(3,28)
85 .equ PI_X2_LO,0xED51
86 .equ PI_X2_HI,0x6487
87
88 // This is the table of coefficients and shifts for sinq to use
89 .align 3 // align to double word boundary
90 sintab: .word 0xAAAAAAAA, 0 // -1/3! as an S(-2,32)
91 .word 0x44444445, 2 // 1/5! as an S(-6,32)
92 .word 0x97F97F97, 6 // -1/7! as an S(-12,32)
93 .word 0x5C778E96, 10 // 1/9! as an S(-18,32)
94 .word 0x9466EA60, 15 // -1/11! as an S(-25,32)
95 .word 0x5849184F, 20 // 1/13! as an S(-32,32)