ipiq: Add simple IPI latency measure sysctls (2)
[dragonfly.git] / lib / libm / src / e_rem_pio2.c
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1
2/* @(#)e_rem_pio2.c 1.4 95/01/18 */
6ff43c94 3/* $FreeBSD: head/lib/msun/src/e_rem_pio2.c 239195 2012-08-11 15:47:22Z dim $ */
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4/*
5 * ====================================================
6 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
7 *
1a3b704c 8 * Developed at SunSoft, a Sun Microsystems, Inc. business.
b34b60bc 9 * Permission to use, copy, modify, and distribute this
6ff43c94 10 * software is freely granted, provided that this notice
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11 * is preserved.
12 * ====================================================
13 *
1a3b704c 14 * Optimized by Bruce D. Evans.
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15 */
16
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17/* __ieee754_rem_pio2(x,y)
18 *
19 * return the remainder of x rem pi/2 in y[0]+y[1]
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20 * use __kernel_rem_pio2()
21 */
22
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23#include <float.h>
24
25#include "math.h"
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26#include "math_private.h"
27
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28/*
29 * invpio2: 53 bits of 2/pi
30 * pio2_1: first 33 bit of pi/2
31 * pio2_1t: pi/2 - pio2_1
32 * pio2_2: second 33 bit of pi/2
33 * pio2_2t: pi/2 - (pio2_1+pio2_2)
34 * pio2_3: third 33 bit of pi/2
35 * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
36 */
37
38static const double
39zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
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40two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
41invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
42pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
43pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
44pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
45pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
46pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
47pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
48
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49#ifdef INLINE_REM_PIO2
50static __inline __always_inline
51#endif
52int
53__ieee754_rem_pio2(double x, double *y)
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54{
55 double z,w,t,r,fn;
1a3b704c 56 double tx[3],ty[2];
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57 int32_t e0,i,j,nx,n,ix,hx;
58 u_int32_t low;
59
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60 GET_HIGH_WORD(hx,x); /* high word of x */
61 ix = hx&0x7fffffff;
1a3b704c 62#if 0 /* Must be handled in caller. */
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63 if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */
64 {y[0] = x; y[1] = 0; return 0;}
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65#endif
66 if (ix <= 0x400f6a7a) { /* |x| ~<= 5pi/4 */
67 if ((ix & 0xfffff) == 0x921fb) /* |x| ~= pi/2 or 2pi/2 */
68 goto medium; /* cancellation -- use medium case */
69 if (ix <= 0x4002d97c) { /* |x| ~<= 3pi/4 */
70 if (hx > 0) {
71 z = x - pio2_1; /* one round good to 85 bits */
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72 y[0] = z - pio2_1t;
73 y[1] = (z-y[0])-pio2_1t;
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74 return 1;
75 } else {
76 z = x + pio2_1;
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77 y[0] = z + pio2_1t;
78 y[1] = (z-y[0])+pio2_1t;
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79 return -1;
80 }
81 } else {
82 if (hx > 0) {
83 z = x - 2*pio2_1;
84 y[0] = z - 2*pio2_1t;
85 y[1] = (z-y[0])-2*pio2_1t;
86 return 2;
87 } else {
88 z = x + 2*pio2_1;
89 y[0] = z + 2*pio2_1t;
90 y[1] = (z-y[0])+2*pio2_1t;
91 return -2;
b34b60bc 92 }
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93 }
94 }
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95 if (ix <= 0x401c463b) { /* |x| ~<= 9pi/4 */
96 if (ix <= 0x4015fdbc) { /* |x| ~<= 7pi/4 */
97 if (ix == 0x4012d97c) /* |x| ~= 3pi/2 */
98 goto medium;
99 if (hx > 0) {
100 z = x - 3*pio2_1;
101 y[0] = z - 3*pio2_1t;
102 y[1] = (z-y[0])-3*pio2_1t;
103 return 3;
104 } else {
105 z = x + 3*pio2_1;
106 y[0] = z + 3*pio2_1t;
107 y[1] = (z-y[0])+3*pio2_1t;
108 return -3;
109 }
b34b60bc 110 } else {
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111 if (ix == 0x401921fb) /* |x| ~= 4pi/2 */
112 goto medium;
113 if (hx > 0) {
114 z = x - 4*pio2_1;
115 y[0] = z - 4*pio2_1t;
116 y[1] = (z-y[0])-4*pio2_1t;
117 return 4;
118 } else {
119 z = x + 4*pio2_1;
120 y[0] = z + 4*pio2_1t;
121 y[1] = (z-y[0])+4*pio2_1t;
122 return -4;
123 }
124 }
125 }
126 if(ix<0x413921fb) { /* |x| ~< 2^20*(pi/2), medium size */
127medium:
128 /* Use a specialized rint() to get fn. Assume round-to-nearest. */
129 STRICT_ASSIGN(double,fn,x*invpio2+0x1.8p52);
130 fn = fn-0x1.8p52;
131#ifdef HAVE_EFFICIENT_IRINT
132 n = irint(fn);
133#else
134 n = (int32_t)fn;
135#endif
136 r = x-fn*pio2_1;
137 w = fn*pio2_1t; /* 1st round good to 85 bit */
138 {
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139 u_int32_t high;
140 j = ix>>20;
6ff43c94 141 y[0] = r-w;
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142 GET_HIGH_WORD(high,y[0]);
143 i = j-((high>>20)&0x7ff);
144 if(i>16) { /* 2nd iteration needed, good to 118 */
145 t = r;
6ff43c94 146 w = fn*pio2_2;
b34b60bc 147 r = t-w;
6ff43c94 148 w = fn*pio2_2t-((t-r)-w);
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149 y[0] = r-w;
150 GET_HIGH_WORD(high,y[0]);
151 i = j-((high>>20)&0x7ff);
152 if(i>49) { /* 3rd iteration need, 151 bits acc */
153 t = r; /* will cover all possible cases */
6ff43c94 154 w = fn*pio2_3;
b34b60bc 155 r = t-w;
6ff43c94 156 w = fn*pio2_3t-((t-r)-w);
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157 y[0] = r-w;
158 }
159 }
160 }
161 y[1] = (r-y[0])-w;
1a3b704c 162 return n;
b34b60bc 163 }
6ff43c94 164 /*
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165 * all other (large) arguments
166 */
167 if(ix>=0x7ff00000) { /* x is inf or NaN */
168 y[0]=y[1]=x-x; return 0;
169 }
170 /* set z = scalbn(|x|,ilogb(x)-23) */
171 GET_LOW_WORD(low,x);
b34b60bc 172 e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */
1a3b704c 173 INSERT_WORDS(z, ix - ((int32_t)(e0<<20)), low);
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174 for(i=0;i<2;i++) {
175 tx[i] = (double)((int32_t)(z));
176 z = (z-tx[i])*two24;
177 }
178 tx[2] = z;
179 nx = 3;
180 while(tx[nx-1]==zero) nx--; /* skip zero term */
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181 n = __kernel_rem_pio2(tx,ty,e0,nx,1);
182 if(hx<0) {y[0] = -ty[0]; y[1] = -ty[1]; return -n;}
183 y[0] = ty[0]; y[1] = ty[1]; return n;
b34b60bc 184}