e_rem_pio2l.h revision 176465
1 2/* @(#)e_rem_pio2.c 1.4 95/01/18 */ 3/* 4 * ==================================================== 5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6 * 7 * Developed at SunSoft, a Sun Microsystems, Inc. business. 8 * Permission to use, copy, modify, and distribute this 9 * software is freely granted, provided that this notice 10 * is preserved. 11 * ==================================================== 12 * 13 */ 14 15#include <sys/cdefs.h> 16__FBSDID("$FreeBSD: head/lib/msun/src/e_rem_pio2.c 176465 2008-02-22 15:55:14Z bde $"); 17 18/* __ieee754_rem_pio2(x,y) 19 * 20 * return the remainder of x rem pi/2 in y[0]+y[1] 21 * use __kernel_rem_pio2() 22 */ 23 24#include <float.h> 25 26#include "math.h" 27#include "math_private.h" 28 29static const int32_t npio2_hw[] = { 300x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C, 310x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C, 320x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A, 330x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C, 340x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB, 350x404858EB, 0x404921FB, 36}; 37 38/* 39 * invpio2: 53 bits of 2/pi 40 * pio2_1: first 33 bit of pi/2 41 * pio2_1t: pi/2 - pio2_1 42 * pio2_2: second 33 bit of pi/2 43 * pio2_2t: pi/2 - (pio2_1+pio2_2) 44 * pio2_3: third 33 bit of pi/2 45 * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) 46 */ 47 48static const double 49zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 50half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ 51two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ 52invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ 53pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ 54pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ 55pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ 56pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ 57pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ 58pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ 59 60#ifdef INLINE_REM_PIO2 61extern inline 62#endif 63int 64__ieee754_rem_pio2(double x, double *y) 65{ 66 double z,w,t,r,fn; 67 double tx[3]; 68 int32_t e0,i,j,nx,n,ix,hx; 69 u_int32_t low; 70 71 GET_HIGH_WORD(hx,x); /* high word of x */ 72 ix = hx&0x7fffffff; 73#if 0 /* Must be handled in caller. */ 74 if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ 75 {y[0] = x; y[1] = 0; return 0;} 76#endif 77 if (ix <= 0x400f6a7a) { /* |x| ~<= 5pi/4 */ 78 if ((ix & 0xfffff) == 0x921fb) /* |x| ~= pi/2 or 2pi/2 */ 79 goto medium; /* cancellation -- use medium case */ 80 if (ix <= 0x4002d97c) { /* |x| ~<= 3pi/4 */ 81 if (hx > 0) { 82 z = x - pio2_1; /* one round good to 85 bits */ 83 y[0] = z - pio2_1t; 84 y[1] = (z-y[0])-pio2_1t; 85 return 1; 86 } else { 87 z = x + pio2_1; 88 y[0] = z + pio2_1t; 89 y[1] = (z-y[0])+pio2_1t; 90 return -1; 91 } 92 } else { 93 if (hx > 0) { 94 z = x - 2*pio2_1; 95 y[0] = z - 2*pio2_1t; 96 y[1] = (z-y[0])-2*pio2_1t; 97 return 2; 98 } else { 99 z = x + 2*pio2_1; 100 y[0] = z + 2*pio2_1t; 101 y[1] = (z-y[0])+2*pio2_1t; 102 return -2; 103 } 104 } 105 } 106 if (ix <= 0x401c463b) { /* |x| ~<= 9pi/4 */ 107 if (ix <= 0x4015fdbc) { /* |x| ~<= 7pi/4 */ 108 if (ix == 0x4012d97c) /* |x| ~= 3pi/2 */ 109 goto medium; 110 if (hx > 0) { 111 z = x - 3*pio2_1; 112 y[0] = z - 3*pio2_1t; 113 y[1] = (z-y[0])-3*pio2_1t; 114 return 3; 115 } else { 116 z = x + 3*pio2_1; 117 y[0] = z + 3*pio2_1t; 118 y[1] = (z-y[0])+3*pio2_1t; 119 return -3; 120 } 121 } else { 122 if (ix == 0x401921fb) /* |x| ~= 4pi/2 */ 123 goto medium; 124 if (hx > 0) { 125 z = x - 4*pio2_1; 126 y[0] = z - 4*pio2_1t; 127 y[1] = (z-y[0])-4*pio2_1t; 128 return 4; 129 } else { 130 z = x + 4*pio2_1; 131 y[0] = z + 4*pio2_1t; 132 y[1] = (z-y[0])+4*pio2_1t; 133 return -4; 134 } 135 } 136 } 137 if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */ 138medium: 139 t = fabs(x); 140#ifdef HAVE_EFFICIENT_IRINT 141 /* Use a specialized rint() to get fn. Assume round-to-nearest. */ 142 STRICT_ASSIGN(double,fn,t*invpio2+0x1.8p52); 143 fn = fn-0x1.8p52; 144 n = irint(fn); 145#else 146 n = (int32_t) (t*invpio2+half); 147 fn = (double)n; 148#endif 149 r = t-fn*pio2_1; 150 w = fn*pio2_1t; /* 1st round good to 85 bit */ 151 if(n<32&&ix!=npio2_hw[n-1]) { 152 y[0] = r-w; /* quick check no cancellation */ 153 } else { 154 u_int32_t high; 155 j = ix>>20; 156 y[0] = r-w; 157 GET_HIGH_WORD(high,y[0]); 158 i = j-((high>>20)&0x7ff); 159 if(i>16) { /* 2nd iteration needed, good to 118 */ 160 t = r; 161 w = fn*pio2_2; 162 r = t-w; 163 w = fn*pio2_2t-((t-r)-w); 164 y[0] = r-w; 165 GET_HIGH_WORD(high,y[0]); 166 i = j-((high>>20)&0x7ff); 167 if(i>49) { /* 3rd iteration need, 151 bits acc */ 168 t = r; /* will cover all possible cases */ 169 w = fn*pio2_3; 170 r = t-w; 171 w = fn*pio2_3t-((t-r)-w); 172 y[0] = r-w; 173 } 174 } 175 } 176 y[1] = (r-y[0])-w; 177 if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} 178 else return n; 179 } 180 /* 181 * all other (large) arguments 182 */ 183 if(ix>=0x7ff00000) { /* x is inf or NaN */ 184 y[0]=y[1]=x-x; return 0; 185 } 186 /* set z = scalbn(|x|,ilogb(x)-23) */ 187 GET_LOW_WORD(low,x); 188 SET_LOW_WORD(z,low); 189 e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ 190 SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20))); 191 for(i=0;i<2;i++) { 192 tx[i] = (double)((int32_t)(z)); 193 z = (z-tx[i])*two24; 194 } 195 tx[2] = z; 196 nx = 3; 197 while(tx[nx-1]==zero) nx--; /* skip zero term */ 198 n = __kernel_rem_pio2(tx,y,e0,nx,2); 199 if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} 200 return n; 201} 202