File: | src/lib/libm/src/e_rem_pio2.c |
Warning: | line 133, column 2 Assigned value is garbage or undefined |
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1 | /* @(#)e_rem_pio2.c 5.1 93/09/24 */ | |||
2 | /* | |||
3 | * ==================================================== | |||
4 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. | |||
5 | * | |||
6 | * Developed at SunPro, a Sun Microsystems, Inc. business. | |||
7 | * Permission to use, copy, modify, and distribute this | |||
8 | * software is freely granted, provided that this notice | |||
9 | * is preserved. | |||
10 | * ==================================================== | |||
11 | */ | |||
12 | ||||
13 | /* __ieee754_rem_pio2(x,y) | |||
14 | * | |||
15 | * return the remainder of x rem pi/2 in y[0]+y[1] | |||
16 | * use __kernel_rem_pio2() | |||
17 | */ | |||
18 | ||||
19 | #include "math.h" | |||
20 | #include "math_private.h" | |||
21 | ||||
22 | static const int32_t npio2_hw[] = { | |||
23 | 0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C, | |||
24 | 0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C, | |||
25 | 0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A, | |||
26 | 0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C, | |||
27 | 0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB, | |||
28 | 0x404858EB, 0x404921FB, | |||
29 | }; | |||
30 | ||||
31 | /* | |||
32 | * invpio2: 53 bits of 2/pi | |||
33 | * pio2_1: first 33 bit of pi/2 | |||
34 | * pio2_1t: pi/2 - pio2_1 | |||
35 | * pio2_2: second 33 bit of pi/2 | |||
36 | * pio2_2t: pi/2 - (pio2_1+pio2_2) | |||
37 | * pio2_3: third 33 bit of pi/2 | |||
38 | * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) | |||
39 | */ | |||
40 | ||||
41 | static const double | |||
42 | zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ | |||
43 | half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ | |||
44 | two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ | |||
45 | invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ | |||
46 | pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ | |||
47 | pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ | |||
48 | pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ | |||
49 | pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ | |||
50 | pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ | |||
51 | pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ | |||
52 | ||||
53 | int32_t | |||
54 | __ieee754_rem_pio2(double x, double *y) | |||
55 | { | |||
56 | double z,w,t,r,fn; | |||
| ||||
57 | double tx[3]; | |||
58 | int32_t e0,i,j,nx,n,ix,hx; | |||
59 | u_int32_t low; | |||
60 | ||||
61 | GET_HIGH_WORD(hx,x)do { ieee_double_shape_type gh_u; gh_u.value = (x); (hx) = gh_u .parts.msw; } while (0); /* high word of x */ | |||
62 | ix = hx&0x7fffffff; | |||
63 | if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ | |||
64 | {y[0] = x; y[1] = 0; return 0;} | |||
65 | if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */ | |||
66 | if(hx>0) { | |||
67 | z = x - pio2_1; | |||
68 | if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ | |||
69 | y[0] = z - pio2_1t; | |||
70 | y[1] = (z-y[0])-pio2_1t; | |||
71 | } else { /* near pi/2, use 33+33+53 bit pi */ | |||
72 | z -= pio2_2; | |||
73 | y[0] = z - pio2_2t; | |||
74 | y[1] = (z-y[0])-pio2_2t; | |||
75 | } | |||
76 | return 1; | |||
77 | } else { /* negative x */ | |||
78 | z = x + pio2_1; | |||
79 | if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ | |||
80 | y[0] = z + pio2_1t; | |||
81 | y[1] = (z-y[0])+pio2_1t; | |||
82 | } else { /* near pi/2, use 33+33+53 bit pi */ | |||
83 | z += pio2_2; | |||
84 | y[0] = z + pio2_2t; | |||
85 | y[1] = (z-y[0])+pio2_2t; | |||
86 | } | |||
87 | return -1; | |||
88 | } | |||
89 | } | |||
90 | if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */ | |||
91 | t = fabs(x); | |||
92 | n = (int32_t) (t*invpio2+half); | |||
93 | fn = (double)n; | |||
94 | r = t-fn*pio2_1; | |||
95 | w = fn*pio2_1t; /* 1st round good to 85 bit */ | |||
96 | if(n<32&&ix!=npio2_hw[n-1]) { | |||
97 | y[0] = r-w; /* quick check no cancellation */ | |||
98 | } else { | |||
99 | u_int32_t high; | |||
100 | j = ix>>20; | |||
101 | y[0] = r-w; | |||
102 | GET_HIGH_WORD(high,y[0])do { ieee_double_shape_type gh_u; gh_u.value = (y[0]); (high) = gh_u.parts.msw; } while (0); | |||
103 | i = j-((high>>20)&0x7ff); | |||
104 | if(i>16) { /* 2nd iteration needed, good to 118 */ | |||
105 | t = r; | |||
106 | w = fn*pio2_2; | |||
107 | r = t-w; | |||
108 | w = fn*pio2_2t-((t-r)-w); | |||
109 | y[0] = r-w; | |||
110 | GET_HIGH_WORD(high,y[0])do { ieee_double_shape_type gh_u; gh_u.value = (y[0]); (high) = gh_u.parts.msw; } while (0); | |||
111 | i = j-((high>>20)&0x7ff); | |||
112 | if(i>49) { /* 3rd iteration need, 151 bits acc */ | |||
113 | t = r; /* will cover all possible cases */ | |||
114 | w = fn*pio2_3; | |||
115 | r = t-w; | |||
116 | w = fn*pio2_3t-((t-r)-w); | |||
117 | y[0] = r-w; | |||
118 | } | |||
119 | } | |||
120 | } | |||
121 | y[1] = (r-y[0])-w; | |||
122 | if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} | |||
123 | else return n; | |||
124 | } | |||
125 | /* | |||
126 | * all other (large) arguments | |||
127 | */ | |||
128 | if(ix>=0x7ff00000) { /* x is inf or NaN */ | |||
129 | y[0]=y[1]=x-x; return 0; | |||
130 | } | |||
131 | /* set z = scalbn(|x|,ilogb(x)-23) */ | |||
132 | GET_LOW_WORD(low,x)do { ieee_double_shape_type gl_u; gl_u.value = (x); (low) = gl_u .parts.lsw; } while (0); | |||
133 | SET_LOW_WORD(z,low)do { ieee_double_shape_type sl_u; sl_u.value = (z); sl_u.parts .lsw = (low); (z) = sl_u.value; } while (0); | |||
| ||||
134 | e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ | |||
135 | SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20)))do { ieee_double_shape_type sh_u; sh_u.value = (z); sh_u.parts .msw = (ix - ((int32_t)(e0<<20))); (z) = sh_u.value; } while (0); | |||
136 | for(i=0;i<2;i++) { | |||
137 | tx[i] = (double)((int32_t)(z)); | |||
138 | z = (z-tx[i])*two24; | |||
139 | } | |||
140 | tx[2] = z; | |||
141 | nx = 3; | |||
142 | while(tx[nx-1]==zero) nx--; /* skip zero term */ | |||
143 | n = __kernel_rem_pio2(tx,y,e0,nx,2); | |||
144 | if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} | |||
145 | return n; | |||
146 | } |