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("$FreeBSD$"); 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 "math.h" 25 #include "math_private.h" 26 27 static const int32_t npio2_hw[] = { 28 0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C, 29 0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C, 30 0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A, 31 0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C, 32 0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB, 33 0x404858EB, 0x404921FB, 34 }; 35 36 /* 37 * invpio2: 53 bits of 2/pi 38 * pio2_1: first 33 bit of pi/2 39 * pio2_1t: pi/2 - pio2_1 40 * pio2_2: second 33 bit of pi/2 41 * pio2_2t: pi/2 - (pio2_1+pio2_2) 42 * pio2_3: third 33 bit of pi/2 43 * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) 44 */ 45 46 static const double 47 zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 48 half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ 49 two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ 50 invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ 51 pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ 52 pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ 53 pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ 54 pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ 55 pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ 56 pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ 57 58 #ifdef INLINE_REM_PIO2 59 extern inline 60 #endif 61 int 62 __ieee754_rem_pio2(double x, double *y) 63 { 64 double z,w,t,r,fn; 65 double tx[3]; 66 int32_t e0,i,j,nx,n,ix,hx; 67 u_int32_t low; 68 69 GET_HIGH_WORD(hx,x); /* high word of x */ 70 ix = hx&0x7fffffff; 71 #if 0 /* Must be handled in caller. */ 72 if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ 73 {y[0] = x; y[1] = 0; return 0;} 74 #endif 75 if (ix <= 0x400f6a7a) { /* |x| ~<= 5pi/4 */ 76 if ((ix & 0xfffff) == 0x921fb) /* |x| ~= pi/2 or 2pi/2 */ 77 goto medium; /* cancellation -- use medium case */ 78 if (ix <= 0x4002d97c) { /* |x| ~<= 3pi/4 */ 79 if (hx > 0) { 80 z = x - pio2_1; /* one round good to 85 bits */ 81 y[0] = z - pio2_1t; 82 y[1] = (z-y[0])-pio2_1t; 83 return 1; 84 } else { 85 z = x + pio2_1; 86 y[0] = z + pio2_1t; 87 y[1] = (z-y[0])+pio2_1t; 88 return -1; 89 } 90 } else { 91 if (hx > 0) { 92 z = x - 2*pio2_1; 93 y[0] = z - 2*pio2_1t; 94 y[1] = (z-y[0])-2*pio2_1t; 95 return 2; 96 } else { 97 z = x + 2*pio2_1; 98 y[0] = z + 2*pio2_1t; 99 y[1] = (z-y[0])+2*pio2_1t; 100 return -2; 101 } 102 } 103 } 104 if (ix <= 0x401c463b) { /* |x| ~<= 9pi/4 */ 105 if (ix <= 0x4015fdbc) { /* |x| ~<= 7pi/4 */ 106 if (ix == 0x4012d97c) /* |x| ~= 3pi/2 */ 107 goto medium; 108 if (hx > 0) { 109 z = x - 3*pio2_1; 110 y[0] = z - 3*pio2_1t; 111 y[1] = (z-y[0])-3*pio2_1t; 112 return 3; 113 } else { 114 z = x + 3*pio2_1; 115 y[0] = z + 3*pio2_1t; 116 y[1] = (z-y[0])+3*pio2_1t; 117 return -3; 118 } 119 } else { 120 if (ix == 0x401921fb) /* |x| ~= 4pi/2 */ 121 goto medium; 122 if (hx > 0) { 123 z = x - 4*pio2_1; 124 y[0] = z - 4*pio2_1t; 125 y[1] = (z-y[0])-4*pio2_1t; 126 return 4; 127 } else { 128 z = x + 4*pio2_1; 129 y[0] = z + 4*pio2_1t; 130 y[1] = (z-y[0])+4*pio2_1t; 131 return -4; 132 } 133 } 134 } 135 if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */ 136 medium: 137 t = fabs(x); 138 n = (int32_t) (t*invpio2+half); 139 fn = (double)n; 140 r = t-fn*pio2_1; 141 w = fn*pio2_1t; /* 1st round good to 85 bit */ 142 if(n<32&&ix!=npio2_hw[n-1]) { 143 y[0] = r-w; /* quick check no cancellation */ 144 } else { 145 u_int32_t high; 146 j = ix>>20; 147 y[0] = r-w; 148 GET_HIGH_WORD(high,y[0]); 149 i = j-((high>>20)&0x7ff); 150 if(i>16) { /* 2nd iteration needed, good to 118 */ 151 t = r; 152 w = fn*pio2_2; 153 r = t-w; 154 w = fn*pio2_2t-((t-r)-w); 155 y[0] = r-w; 156 GET_HIGH_WORD(high,y[0]); 157 i = j-((high>>20)&0x7ff); 158 if(i>49) { /* 3rd iteration need, 151 bits acc */ 159 t = r; /* will cover all possible cases */ 160 w = fn*pio2_3; 161 r = t-w; 162 w = fn*pio2_3t-((t-r)-w); 163 y[0] = r-w; 164 } 165 } 166 } 167 y[1] = (r-y[0])-w; 168 if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} 169 else return n; 170 } 171 /* 172 * all other (large) arguments 173 */ 174 if(ix>=0x7ff00000) { /* x is inf or NaN */ 175 y[0]=y[1]=x-x; return 0; 176 } 177 /* set z = scalbn(|x|,ilogb(x)-23) */ 178 GET_LOW_WORD(low,x); 179 SET_LOW_WORD(z,low); 180 e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ 181 SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20))); 182 for(i=0;i<2;i++) { 183 tx[i] = (double)((int32_t)(z)); 184 z = (z-tx[i])*two24; 185 } 186 tx[2] = z; 187 nx = 3; 188 while(tx[nx-1]==zero) nx--; /* skip zero term */ 189 n = __kernel_rem_pio2(tx,y,e0,nx,2); 190 if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} 191 return n; 192 } 193