/src/moddable/xs/tools/fdlibm/e_rem_pio2.c
Line | Count | Source |
1 | | |
2 | | /* |
3 | | * ==================================================== |
4 | | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
5 | | * |
6 | | * Developed at SunSoft, 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 | | * Optimized by Bruce D. Evans. |
13 | | */ |
14 | | |
15 | | /* __ieee754_rem_pio2(x,y) |
16 | | * |
17 | | * return the remainder of x rem pi/2 in y[0]+y[1] |
18 | | * use __kernel_rem_pio2() |
19 | | */ |
20 | | |
21 | | #include "math_private.h" |
22 | | |
23 | | /* |
24 | | * invpio2: 53 bits of 2/pi |
25 | | * pio2_1: first 33 bit of pi/2 |
26 | | * pio2_1t: pi/2 - pio2_1 |
27 | | * pio2_2: second 33 bit of pi/2 |
28 | | * pio2_2t: pi/2 - (pio2_1+pio2_2) |
29 | | * pio2_3: third 33 bit of pi/2 |
30 | | * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) |
31 | | */ |
32 | | |
33 | | static const double |
34 | | zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ |
35 | | two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ |
36 | | invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ |
37 | | pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ |
38 | | pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ |
39 | | pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ |
40 | | pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ |
41 | | pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ |
42 | | pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ |
43 | | |
44 | | #ifdef INLINE_REM_PIO2 |
45 | | static inline |
46 | | #endif |
47 | | int |
48 | | __ieee754_rem_pio2(double x, double *y) |
49 | 176k | { |
50 | 176k | double z,w,t,r,fn; |
51 | 176k | double tx[3],ty[2]; |
52 | 176k | int32_t e0,i,j,nx,n,ix,hx; |
53 | 176k | u_int32_t low; |
54 | | |
55 | 176k | GET_HIGH_WORD(hx,x); /* high word of x */ |
56 | 176k | ix = hx&0x7fffffff; |
57 | | #if 0 /* Must be handled in caller. */ |
58 | | if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ |
59 | | {y[0] = x; y[1] = 0; return 0;} |
60 | | #endif |
61 | 176k | if (ix <= 0x400f6a7a) { /* |x| ~<= 5pi/4 */ |
62 | 160k | if ((ix & 0xfffff) == 0x921fb) /* |x| ~= pi/2 or 2pi/2 */ |
63 | 0 | goto medium; /* cancellation -- use medium case */ |
64 | 160k | if (ix <= 0x4002d97c) { /* |x| ~<= 3pi/4 */ |
65 | 157k | if (hx > 0) { |
66 | 156k | z = x - pio2_1; /* one round good to 85 bits */ |
67 | 156k | y[0] = z - pio2_1t; |
68 | 156k | y[1] = (z-y[0])-pio2_1t; |
69 | 156k | return 1; |
70 | 156k | } else { |
71 | 1.40k | z = x + pio2_1; |
72 | 1.40k | y[0] = z + pio2_1t; |
73 | 1.40k | y[1] = (z-y[0])+pio2_1t; |
74 | 1.40k | return -1; |
75 | 1.40k | } |
76 | 157k | } else { |
77 | 2.64k | if (hx > 0) { |
78 | 869 | z = x - 2*pio2_1; |
79 | 869 | y[0] = z - 2*pio2_1t; |
80 | 869 | y[1] = (z-y[0])-2*pio2_1t; |
81 | 869 | return 2; |
82 | 1.77k | } else { |
83 | 1.77k | z = x + 2*pio2_1; |
84 | 1.77k | y[0] = z + 2*pio2_1t; |
85 | 1.77k | y[1] = (z-y[0])+2*pio2_1t; |
86 | 1.77k | return -2; |
87 | 1.77k | } |
88 | 2.64k | } |
89 | 160k | } |
90 | 16.4k | if (ix <= 0x401c463b) { /* |x| ~<= 9pi/4 */ |
91 | 2.89k | if (ix <= 0x4015fdbc) { /* |x| ~<= 7pi/4 */ |
92 | 1.79k | if (ix == 0x4012d97c) /* |x| ~= 3pi/2 */ |
93 | 0 | goto medium; |
94 | 1.79k | if (hx > 0) { |
95 | 898 | z = x - 3*pio2_1; |
96 | 898 | y[0] = z - 3*pio2_1t; |
97 | 898 | y[1] = (z-y[0])-3*pio2_1t; |
98 | 898 | return 3; |
99 | 898 | } else { |
100 | 898 | z = x + 3*pio2_1; |
101 | 898 | y[0] = z + 3*pio2_1t; |
102 | 898 | y[1] = (z-y[0])+3*pio2_1t; |
103 | 898 | return -3; |
104 | 898 | } |
105 | 1.79k | } else { |
106 | 1.10k | if (ix == 0x401921fb) /* |x| ~= 4pi/2 */ |
107 | 0 | goto medium; |
108 | 1.10k | if (hx > 0) { |
109 | 652 | z = x - 4*pio2_1; |
110 | 652 | y[0] = z - 4*pio2_1t; |
111 | 652 | y[1] = (z-y[0])-4*pio2_1t; |
112 | 652 | return 4; |
113 | 652 | } else { |
114 | 448 | z = x + 4*pio2_1; |
115 | 448 | y[0] = z + 4*pio2_1t; |
116 | 448 | y[1] = (z-y[0])+4*pio2_1t; |
117 | 448 | return -4; |
118 | 448 | } |
119 | 1.10k | } |
120 | 2.89k | } |
121 | 13.5k | if(ix<0x413921fb) { /* |x| ~< 2^20*(pi/2), medium size */ |
122 | 8.91k | medium: |
123 | 8.91k | fn = rnint((double_t)x*invpio2); |
124 | 8.91k | n = irint(fn); |
125 | 8.91k | r = x-fn*pio2_1; |
126 | 8.91k | w = fn*pio2_1t; /* 1st round good to 85 bit */ |
127 | 8.91k | { |
128 | 8.91k | u_int32_t high; |
129 | 8.91k | j = ix>>20; |
130 | 8.91k | y[0] = r-w; |
131 | 8.91k | GET_HIGH_WORD(high,y[0]); |
132 | 8.91k | i = j-((high>>20)&0x7ff); |
133 | 8.91k | if(i>16) { /* 2nd iteration needed, good to 118 */ |
134 | 1.49k | t = r; |
135 | 1.49k | w = fn*pio2_2; |
136 | 1.49k | r = t-w; |
137 | 1.49k | w = fn*pio2_2t-((t-r)-w); |
138 | 1.49k | y[0] = r-w; |
139 | 1.49k | GET_HIGH_WORD(high,y[0]); |
140 | 1.49k | i = j-((high>>20)&0x7ff); |
141 | 1.49k | if(i>49) { /* 3rd iteration need, 151 bits acc */ |
142 | 0 | t = r; /* will cover all possible cases */ |
143 | 0 | w = fn*pio2_3; |
144 | 0 | r = t-w; |
145 | 0 | w = fn*pio2_3t-((t-r)-w); |
146 | 0 | y[0] = r-w; |
147 | 0 | } |
148 | 1.49k | } |
149 | 8.91k | } |
150 | 8.91k | y[1] = (r-y[0])-w; |
151 | 8.91k | return n; |
152 | 8.91k | } |
153 | | /* |
154 | | * all other (large) arguments |
155 | | */ |
156 | 4.63k | if(ix>=0x7ff00000) { /* x is inf or NaN */ |
157 | 0 | y[0]=y[1]=x-x; return 0; |
158 | 0 | } |
159 | | /* set z = scalbn(|x|,ilogb(x)-23) */ |
160 | 4.63k | GET_LOW_WORD(low,x); |
161 | 4.63k | e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ |
162 | 4.63k | INSERT_WORDS(z, ix - ((int32_t)((u_int32_t)e0<<20)), low); |
163 | 13.9k | for(i=0;i<2;i++) { |
164 | 9.26k | tx[i] = (double)((int32_t)(z)); |
165 | 9.26k | z = (z-tx[i])*two24; |
166 | 9.26k | } |
167 | 4.63k | tx[2] = z; |
168 | 4.63k | nx = 3; |
169 | 9.64k | while(tx[nx-1]==zero) nx--; /* skip zero term */ |
170 | 4.63k | n = __kernel_rem_pio2(tx,ty,e0,nx,1); |
171 | 4.63k | if(hx<0) {y[0] = -ty[0]; y[1] = -ty[1]; return -n;} |
172 | 2.37k | y[0] = ty[0]; y[1] = ty[1]; return n; |
173 | 4.63k | } Unexecuted instantiation: __ieee754_rem_pio2 s_cos.c:__ieee754_rem_pio2 Line | Count | Source | 49 | 166k | { | 50 | 166k | double z,w,t,r,fn; | 51 | 166k | double tx[3],ty[2]; | 52 | 166k | int32_t e0,i,j,nx,n,ix,hx; | 53 | 166k | u_int32_t low; | 54 | | | 55 | 166k | GET_HIGH_WORD(hx,x); /* high word of x */ | 56 | 166k | ix = hx&0x7fffffff; | 57 | | #if 0 /* Must be handled in caller. */ | 58 | | if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ | 59 | | {y[0] = x; y[1] = 0; return 0;} | 60 | | #endif | 61 | 166k | if (ix <= 0x400f6a7a) { /* |x| ~<= 5pi/4 */ | 62 | 156k | if ((ix & 0xfffff) == 0x921fb) /* |x| ~= pi/2 or 2pi/2 */ | 63 | 0 | goto medium; /* cancellation -- use medium case */ | 64 | 156k | if (ix <= 0x4002d97c) { /* |x| ~<= 3pi/4 */ | 65 | 155k | if (hx > 0) { | 66 | 155k | z = x - pio2_1; /* one round good to 85 bits */ | 67 | 155k | y[0] = z - pio2_1t; | 68 | 155k | y[1] = (z-y[0])-pio2_1t; | 69 | 155k | return 1; | 70 | 155k | } else { | 71 | 760 | z = x + pio2_1; | 72 | 760 | y[0] = z + pio2_1t; | 73 | 760 | y[1] = (z-y[0])+pio2_1t; | 74 | 760 | return -1; | 75 | 760 | } | 76 | 155k | } else { | 77 | 1.13k | if (hx > 0) { | 78 | 640 | z = x - 2*pio2_1; | 79 | 640 | y[0] = z - 2*pio2_1t; | 80 | 640 | y[1] = (z-y[0])-2*pio2_1t; | 81 | 640 | return 2; | 82 | 640 | } else { | 83 | 491 | z = x + 2*pio2_1; | 84 | 491 | y[0] = z + 2*pio2_1t; | 85 | 491 | y[1] = (z-y[0])+2*pio2_1t; | 86 | 491 | return -2; | 87 | 491 | } | 88 | 1.13k | } | 89 | 156k | } | 90 | 9.71k | if (ix <= 0x401c463b) { /* |x| ~<= 9pi/4 */ | 91 | 2.01k | if (ix <= 0x4015fdbc) { /* |x| ~<= 7pi/4 */ | 92 | 1.18k | if (ix == 0x4012d97c) /* |x| ~= 3pi/2 */ | 93 | 0 | goto medium; | 94 | 1.18k | if (hx > 0) { | 95 | 652 | z = x - 3*pio2_1; | 96 | 652 | y[0] = z - 3*pio2_1t; | 97 | 652 | y[1] = (z-y[0])-3*pio2_1t; | 98 | 652 | return 3; | 99 | 652 | } else { | 100 | 534 | z = x + 3*pio2_1; | 101 | 534 | y[0] = z + 3*pio2_1t; | 102 | 534 | y[1] = (z-y[0])+3*pio2_1t; | 103 | 534 | return -3; | 104 | 534 | } | 105 | 1.18k | } else { | 106 | 831 | if (ix == 0x401921fb) /* |x| ~= 4pi/2 */ | 107 | 0 | goto medium; | 108 | 831 | if (hx > 0) { | 109 | 459 | z = x - 4*pio2_1; | 110 | 459 | y[0] = z - 4*pio2_1t; | 111 | 459 | y[1] = (z-y[0])-4*pio2_1t; | 112 | 459 | return 4; | 113 | 459 | } else { | 114 | 372 | z = x + 4*pio2_1; | 115 | 372 | y[0] = z + 4*pio2_1t; | 116 | 372 | y[1] = (z-y[0])+4*pio2_1t; | 117 | 372 | return -4; | 118 | 372 | } | 119 | 831 | } | 120 | 2.01k | } | 121 | 7.69k | if(ix<0x413921fb) { /* |x| ~< 2^20*(pi/2), medium size */ | 122 | 6.65k | medium: | 123 | 6.65k | fn = rnint((double_t)x*invpio2); | 124 | 6.65k | n = irint(fn); | 125 | 6.65k | r = x-fn*pio2_1; | 126 | 6.65k | w = fn*pio2_1t; /* 1st round good to 85 bit */ | 127 | 6.65k | { | 128 | 6.65k | u_int32_t high; | 129 | 6.65k | j = ix>>20; | 130 | 6.65k | y[0] = r-w; | 131 | 6.65k | GET_HIGH_WORD(high,y[0]); | 132 | 6.65k | i = j-((high>>20)&0x7ff); | 133 | 6.65k | if(i>16) { /* 2nd iteration needed, good to 118 */ | 134 | 228 | t = r; | 135 | 228 | w = fn*pio2_2; | 136 | 228 | r = t-w; | 137 | 228 | w = fn*pio2_2t-((t-r)-w); | 138 | 228 | y[0] = r-w; | 139 | 228 | GET_HIGH_WORD(high,y[0]); | 140 | 228 | i = j-((high>>20)&0x7ff); | 141 | 228 | if(i>49) { /* 3rd iteration need, 151 bits acc */ | 142 | 0 | t = r; /* will cover all possible cases */ | 143 | 0 | w = fn*pio2_3; | 144 | 0 | r = t-w; | 145 | 0 | w = fn*pio2_3t-((t-r)-w); | 146 | 0 | y[0] = r-w; | 147 | 0 | } | 148 | 228 | } | 149 | 6.65k | } | 150 | 6.65k | y[1] = (r-y[0])-w; | 151 | 6.65k | return n; | 152 | 6.65k | } | 153 | | /* | 154 | | * all other (large) arguments | 155 | | */ | 156 | 1.04k | if(ix>=0x7ff00000) { /* x is inf or NaN */ | 157 | 0 | y[0]=y[1]=x-x; return 0; | 158 | 0 | } | 159 | | /* set z = scalbn(|x|,ilogb(x)-23) */ | 160 | 1.04k | GET_LOW_WORD(low,x); | 161 | 1.04k | e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ | 162 | 1.04k | INSERT_WORDS(z, ix - ((int32_t)((u_int32_t)e0<<20)), low); | 163 | 3.12k | for(i=0;i<2;i++) { | 164 | 2.08k | tx[i] = (double)((int32_t)(z)); | 165 | 2.08k | z = (z-tx[i])*two24; | 166 | 2.08k | } | 167 | 1.04k | tx[2] = z; | 168 | 1.04k | nx = 3; | 169 | 1.97k | while(tx[nx-1]==zero) nx--; /* skip zero term */ | 170 | 1.04k | n = __kernel_rem_pio2(tx,ty,e0,nx,1); | 171 | 1.04k | if(hx<0) {y[0] = -ty[0]; y[1] = -ty[1]; return -n;} | 172 | 885 | y[0] = ty[0]; y[1] = ty[1]; return n; | 173 | 1.04k | } |
s_sin.c:__ieee754_rem_pio2 Line | Count | Source | 49 | 5.26k | { | 50 | 5.26k | double z,w,t,r,fn; | 51 | 5.26k | double tx[3],ty[2]; | 52 | 5.26k | int32_t e0,i,j,nx,n,ix,hx; | 53 | 5.26k | u_int32_t low; | 54 | | | 55 | 5.26k | GET_HIGH_WORD(hx,x); /* high word of x */ | 56 | 5.26k | ix = hx&0x7fffffff; | 57 | | #if 0 /* Must be handled in caller. */ | 58 | | if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ | 59 | | {y[0] = x; y[1] = 0; return 0;} | 60 | | #endif | 61 | 5.26k | if (ix <= 0x400f6a7a) { /* |x| ~<= 5pi/4 */ | 62 | 2.25k | if ((ix & 0xfffff) == 0x921fb) /* |x| ~= pi/2 or 2pi/2 */ | 63 | 0 | goto medium; /* cancellation -- use medium case */ | 64 | 2.25k | if (ix <= 0x4002d97c) { /* |x| ~<= 3pi/4 */ | 65 | 846 | if (hx > 0) { | 66 | 425 | z = x - pio2_1; /* one round good to 85 bits */ | 67 | 425 | y[0] = z - pio2_1t; | 68 | 425 | y[1] = (z-y[0])-pio2_1t; | 69 | 425 | return 1; | 70 | 425 | } else { | 71 | 421 | z = x + pio2_1; | 72 | 421 | y[0] = z + pio2_1t; | 73 | 421 | y[1] = (z-y[0])+pio2_1t; | 74 | 421 | return -1; | 75 | 421 | } | 76 | 1.41k | } else { | 77 | 1.41k | if (hx > 0) { | 78 | 205 | z = x - 2*pio2_1; | 79 | 205 | y[0] = z - 2*pio2_1t; | 80 | 205 | y[1] = (z-y[0])-2*pio2_1t; | 81 | 205 | return 2; | 82 | 1.20k | } else { | 83 | 1.20k | z = x + 2*pio2_1; | 84 | 1.20k | y[0] = z + 2*pio2_1t; | 85 | 1.20k | y[1] = (z-y[0])+2*pio2_1t; | 86 | 1.20k | return -2; | 87 | 1.20k | } | 88 | 1.41k | } | 89 | 2.25k | } | 90 | 3.00k | if (ix <= 0x401c463b) { /* |x| ~<= 9pi/4 */ | 91 | 636 | if (ix <= 0x4015fdbc) { /* |x| ~<= 7pi/4 */ | 92 | 482 | if (ix == 0x4012d97c) /* |x| ~= 3pi/2 */ | 93 | 0 | goto medium; | 94 | 482 | if (hx > 0) { | 95 | 197 | z = x - 3*pio2_1; | 96 | 197 | y[0] = z - 3*pio2_1t; | 97 | 197 | y[1] = (z-y[0])-3*pio2_1t; | 98 | 197 | return 3; | 99 | 285 | } else { | 100 | 285 | z = x + 3*pio2_1; | 101 | 285 | y[0] = z + 3*pio2_1t; | 102 | 285 | y[1] = (z-y[0])+3*pio2_1t; | 103 | 285 | return -3; | 104 | 285 | } | 105 | 482 | } else { | 106 | 154 | if (ix == 0x401921fb) /* |x| ~= 4pi/2 */ | 107 | 0 | goto medium; | 108 | 154 | if (hx > 0) { | 109 | 146 | z = x - 4*pio2_1; | 110 | 146 | y[0] = z - 4*pio2_1t; | 111 | 146 | y[1] = (z-y[0])-4*pio2_1t; | 112 | 146 | return 4; | 113 | 146 | } else { | 114 | 8 | z = x + 4*pio2_1; | 115 | 8 | y[0] = z + 4*pio2_1t; | 116 | 8 | y[1] = (z-y[0])+4*pio2_1t; | 117 | 8 | return -4; | 118 | 8 | } | 119 | 154 | } | 120 | 636 | } | 121 | 2.36k | if(ix<0x413921fb) { /* |x| ~< 2^20*(pi/2), medium size */ | 122 | 1.62k | medium: | 123 | 1.62k | fn = rnint((double_t)x*invpio2); | 124 | 1.62k | n = irint(fn); | 125 | 1.62k | r = x-fn*pio2_1; | 126 | 1.62k | w = fn*pio2_1t; /* 1st round good to 85 bit */ | 127 | 1.62k | { | 128 | 1.62k | u_int32_t high; | 129 | 1.62k | j = ix>>20; | 130 | 1.62k | y[0] = r-w; | 131 | 1.62k | GET_HIGH_WORD(high,y[0]); | 132 | 1.62k | i = j-((high>>20)&0x7ff); | 133 | 1.62k | if(i>16) { /* 2nd iteration needed, good to 118 */ | 134 | 986 | t = r; | 135 | 986 | w = fn*pio2_2; | 136 | 986 | r = t-w; | 137 | 986 | w = fn*pio2_2t-((t-r)-w); | 138 | 986 | y[0] = r-w; | 139 | 986 | GET_HIGH_WORD(high,y[0]); | 140 | 986 | i = j-((high>>20)&0x7ff); | 141 | 986 | if(i>49) { /* 3rd iteration need, 151 bits acc */ | 142 | 0 | t = r; /* will cover all possible cases */ | 143 | 0 | w = fn*pio2_3; | 144 | 0 | r = t-w; | 145 | 0 | w = fn*pio2_3t-((t-r)-w); | 146 | 0 | y[0] = r-w; | 147 | 0 | } | 148 | 986 | } | 149 | 1.62k | } | 150 | 1.62k | y[1] = (r-y[0])-w; | 151 | 1.62k | return n; | 152 | 1.62k | } | 153 | | /* | 154 | | * all other (large) arguments | 155 | | */ | 156 | 741 | if(ix>=0x7ff00000) { /* x is inf or NaN */ | 157 | 0 | y[0]=y[1]=x-x; return 0; | 158 | 0 | } | 159 | | /* set z = scalbn(|x|,ilogb(x)-23) */ | 160 | 741 | GET_LOW_WORD(low,x); | 161 | 741 | e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ | 162 | 741 | INSERT_WORDS(z, ix - ((int32_t)((u_int32_t)e0<<20)), low); | 163 | 2.22k | for(i=0;i<2;i++) { | 164 | 1.48k | tx[i] = (double)((int32_t)(z)); | 165 | 1.48k | z = (z-tx[i])*two24; | 166 | 1.48k | } | 167 | 741 | tx[2] = z; | 168 | 741 | nx = 3; | 169 | 2.07k | while(tx[nx-1]==zero) nx--; /* skip zero term */ | 170 | 741 | n = __kernel_rem_pio2(tx,ty,e0,nx,1); | 171 | 741 | if(hx<0) {y[0] = -ty[0]; y[1] = -ty[1]; return -n;} | 172 | 665 | y[0] = ty[0]; y[1] = ty[1]; return n; | 173 | 741 | } |
s_tan.c:__ieee754_rem_pio2 Line | Count | Source | 49 | 5.08k | { | 50 | 5.08k | double z,w,t,r,fn; | 51 | 5.08k | double tx[3],ty[2]; | 52 | 5.08k | int32_t e0,i,j,nx,n,ix,hx; | 53 | 5.08k | u_int32_t low; | 54 | | | 55 | 5.08k | GET_HIGH_WORD(hx,x); /* high word of x */ | 56 | 5.08k | ix = hx&0x7fffffff; | 57 | | #if 0 /* Must be handled in caller. */ | 58 | | if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ | 59 | | {y[0] = x; y[1] = 0; return 0;} | 60 | | #endif | 61 | 5.08k | if (ix <= 0x400f6a7a) { /* |x| ~<= 5pi/4 */ | 62 | 1.36k | if ((ix & 0xfffff) == 0x921fb) /* |x| ~= pi/2 or 2pi/2 */ | 63 | 0 | goto medium; /* cancellation -- use medium case */ | 64 | 1.36k | if (ix <= 0x4002d97c) { /* |x| ~<= 3pi/4 */ | 65 | 1.26k | if (hx > 0) { | 66 | 1.04k | z = x - pio2_1; /* one round good to 85 bits */ | 67 | 1.04k | y[0] = z - pio2_1t; | 68 | 1.04k | y[1] = (z-y[0])-pio2_1t; | 69 | 1.04k | return 1; | 70 | 1.04k | } else { | 71 | 225 | z = x + pio2_1; | 72 | 225 | y[0] = z + pio2_1t; | 73 | 225 | y[1] = (z-y[0])+pio2_1t; | 74 | 225 | return -1; | 75 | 225 | } | 76 | 1.26k | } else { | 77 | 98 | if (hx > 0) { | 78 | 24 | z = x - 2*pio2_1; | 79 | 24 | y[0] = z - 2*pio2_1t; | 80 | 24 | y[1] = (z-y[0])-2*pio2_1t; | 81 | 24 | return 2; | 82 | 74 | } else { | 83 | 74 | z = x + 2*pio2_1; | 84 | 74 | y[0] = z + 2*pio2_1t; | 85 | 74 | y[1] = (z-y[0])+2*pio2_1t; | 86 | 74 | return -2; | 87 | 74 | } | 88 | 98 | } | 89 | 1.36k | } | 90 | 3.72k | if (ix <= 0x401c463b) { /* |x| ~<= 9pi/4 */ | 91 | 243 | if (ix <= 0x4015fdbc) { /* |x| ~<= 7pi/4 */ | 92 | 128 | if (ix == 0x4012d97c) /* |x| ~= 3pi/2 */ | 93 | 0 | goto medium; | 94 | 128 | if (hx > 0) { | 95 | 49 | z = x - 3*pio2_1; | 96 | 49 | y[0] = z - 3*pio2_1t; | 97 | 49 | y[1] = (z-y[0])-3*pio2_1t; | 98 | 49 | return 3; | 99 | 79 | } else { | 100 | 79 | z = x + 3*pio2_1; | 101 | 79 | y[0] = z + 3*pio2_1t; | 102 | 79 | y[1] = (z-y[0])+3*pio2_1t; | 103 | 79 | return -3; | 104 | 79 | } | 105 | 128 | } else { | 106 | 115 | if (ix == 0x401921fb) /* |x| ~= 4pi/2 */ | 107 | 0 | goto medium; | 108 | 115 | if (hx > 0) { | 109 | 47 | z = x - 4*pio2_1; | 110 | 47 | y[0] = z - 4*pio2_1t; | 111 | 47 | y[1] = (z-y[0])-4*pio2_1t; | 112 | 47 | return 4; | 113 | 68 | } else { | 114 | 68 | z = x + 4*pio2_1; | 115 | 68 | y[0] = z + 4*pio2_1t; | 116 | 68 | y[1] = (z-y[0])+4*pio2_1t; | 117 | 68 | return -4; | 118 | 68 | } | 119 | 115 | } | 120 | 243 | } | 121 | 3.48k | if(ix<0x413921fb) { /* |x| ~< 2^20*(pi/2), medium size */ | 122 | 628 | medium: | 123 | 628 | fn = rnint((double_t)x*invpio2); | 124 | 628 | n = irint(fn); | 125 | 628 | r = x-fn*pio2_1; | 126 | 628 | w = fn*pio2_1t; /* 1st round good to 85 bit */ | 127 | 628 | { | 128 | 628 | u_int32_t high; | 129 | 628 | j = ix>>20; | 130 | 628 | y[0] = r-w; | 131 | 628 | GET_HIGH_WORD(high,y[0]); | 132 | 628 | i = j-((high>>20)&0x7ff); | 133 | 628 | if(i>16) { /* 2nd iteration needed, good to 118 */ | 134 | 282 | t = r; | 135 | 282 | w = fn*pio2_2; | 136 | 282 | r = t-w; | 137 | 282 | w = fn*pio2_2t-((t-r)-w); | 138 | 282 | y[0] = r-w; | 139 | 282 | GET_HIGH_WORD(high,y[0]); | 140 | 282 | i = j-((high>>20)&0x7ff); | 141 | 282 | if(i>49) { /* 3rd iteration need, 151 bits acc */ | 142 | 0 | t = r; /* will cover all possible cases */ | 143 | 0 | w = fn*pio2_3; | 144 | 0 | r = t-w; | 145 | 0 | w = fn*pio2_3t-((t-r)-w); | 146 | 0 | y[0] = r-w; | 147 | 0 | } | 148 | 282 | } | 149 | 628 | } | 150 | 628 | y[1] = (r-y[0])-w; | 151 | 628 | return n; | 152 | 628 | } | 153 | | /* | 154 | | * all other (large) arguments | 155 | | */ | 156 | 2.85k | if(ix>=0x7ff00000) { /* x is inf or NaN */ | 157 | 0 | y[0]=y[1]=x-x; return 0; | 158 | 0 | } | 159 | | /* set z = scalbn(|x|,ilogb(x)-23) */ | 160 | 2.85k | GET_LOW_WORD(low,x); | 161 | 2.85k | e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ | 162 | 2.85k | INSERT_WORDS(z, ix - ((int32_t)((u_int32_t)e0<<20)), low); | 163 | 8.55k | for(i=0;i<2;i++) { | 164 | 5.70k | tx[i] = (double)((int32_t)(z)); | 165 | 5.70k | z = (z-tx[i])*two24; | 166 | 5.70k | } | 167 | 2.85k | tx[2] = z; | 168 | 2.85k | nx = 3; | 169 | 5.59k | while(tx[nx-1]==zero) nx--; /* skip zero term */ | 170 | 2.85k | n = __kernel_rem_pio2(tx,ty,e0,nx,1); | 171 | 2.85k | if(hx<0) {y[0] = -ty[0]; y[1] = -ty[1]; return -n;} | 172 | 823 | y[0] = ty[0]; y[1] = ty[1]; return n; | 173 | 2.85k | } |
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