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 * Optimized by Bruce D. Evans. 14 */ 15 16 #include <sys/cdefs.h> 17 __FBSDID("$FreeBSD$"); 18 19 /* __ieee754_rem_pio2(x,y) 20 * 21 * return the remainder of x rem pi/2 in y[0]+y[1] 22 * use __kernel_rem_pio2() 23 */ 24 25 #include <float.h> 26 27 #include "math.h" 28 #include "math_private.h" 29 30 /* 31 * invpio2: 53 bits of 2/pi 32 * pio2_1: first 33 bit of pi/2 33 * pio2_1t: pi/2 - pio2_1 34 * pio2_2: second 33 bit of pi/2 35 * pio2_2t: pi/2 - (pio2_1+pio2_2) 36 * pio2_3: third 33 bit of pi/2 37 * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) 38 */ 39 40 static const double 41 zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 42 half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ 43 two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ 44 invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ 45 pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ 46 pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ 47 pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ 48 pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ 49 pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ 50 pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ 51 52 #ifdef INLINE_REM_PIO2 53 extern inline 54 #endif 55 int 56 __ieee754_rem_pio2(double x, double *y) 57 { 58 double z,w,t,r,fn; 59 double tx[3],ty[2]; 60 int32_t e0,i,j,nx,n,ix,hx; 61 u_int32_t low; 62 63 GET_HIGH_WORD(hx,x); /* high word of x */ 64 ix = hx&0x7fffffff; 65 #if 0 /* Must be handled in caller. */ 66 if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ 67 {y[0] = x; y[1] = 0; return 0;} 68 #endif 69 if (ix <= 0x400f6a7a) { /* |x| ~<= 5pi/4 */ 70 if ((ix & 0xfffff) == 0x921fb) /* |x| ~= pi/2 or 2pi/2 */ 71 goto medium; /* cancellation -- use medium case */ 72 if (ix <= 0x4002d97c) { /* |x| ~<= 3pi/4 */ 73 if (hx > 0) { 74 z = x - pio2_1; /* one round good to 85 bits */ 75 y[0] = z - pio2_1t; 76 y[1] = (z-y[0])-pio2_1t; 77 return 1; 78 } else { 79 z = x + pio2_1; 80 y[0] = z + pio2_1t; 81 y[1] = (z-y[0])+pio2_1t; 82 return -1; 83 } 84 } else { 85 if (hx > 0) { 86 z = x - 2*pio2_1; 87 y[0] = z - 2*pio2_1t; 88 y[1] = (z-y[0])-2*pio2_1t; 89 return 2; 90 } else { 91 z = x + 2*pio2_1; 92 y[0] = z + 2*pio2_1t; 93 y[1] = (z-y[0])+2*pio2_1t; 94 return -2; 95 } 96 } 97 } 98 if (ix <= 0x401c463b) { /* |x| ~<= 9pi/4 */ 99 if (ix <= 0x4015fdbc) { /* |x| ~<= 7pi/4 */ 100 if (ix == 0x4012d97c) /* |x| ~= 3pi/2 */ 101 goto medium; 102 if (hx > 0) { 103 z = x - 3*pio2_1; 104 y[0] = z - 3*pio2_1t; 105 y[1] = (z-y[0])-3*pio2_1t; 106 return 3; 107 } else { 108 z = x + 3*pio2_1; 109 y[0] = z + 3*pio2_1t; 110 y[1] = (z-y[0])+3*pio2_1t; 111 return -3; 112 } 113 } else { 114 if (ix == 0x401921fb) /* |x| ~= 4pi/2 */ 115 goto medium; 116 if (hx > 0) { 117 z = x - 4*pio2_1; 118 y[0] = z - 4*pio2_1t; 119 y[1] = (z-y[0])-4*pio2_1t; 120 return 4; 121 } else { 122 z = x + 4*pio2_1; 123 y[0] = z + 4*pio2_1t; 124 y[1] = (z-y[0])+4*pio2_1t; 125 return -4; 126 } 127 } 128 } 129 if(ix<0x413921fb) { /* |x| ~< 2^20*(pi/2), medium size */ 130 medium: 131 /* Use a specialized rint() to get fn. Assume round-to-nearest. */ 132 STRICT_ASSIGN(double,fn,x*invpio2+0x1.8p52); 133 fn = fn-0x1.8p52; 134 #ifdef HAVE_EFFICIENT_IRINT 135 n = irint(fn); 136 #else 137 n = (int32_t)fn; 138 #endif 139 r = x-fn*pio2_1; 140 w = fn*pio2_1t; /* 1st round good to 85 bit */ 141 { 142 u_int32_t high; 143 j = ix>>20; 144 y[0] = r-w; 145 GET_HIGH_WORD(high,y[0]); 146 i = j-((high>>20)&0x7ff); 147 if(i>16) { /* 2nd iteration needed, good to 118 */ 148 t = r; 149 w = fn*pio2_2; 150 r = t-w; 151 w = fn*pio2_2t-((t-r)-w); 152 y[0] = r-w; 153 GET_HIGH_WORD(high,y[0]); 154 i = j-((high>>20)&0x7ff); 155 if(i>49) { /* 3rd iteration need, 151 bits acc */ 156 t = r; /* will cover all possible cases */ 157 w = fn*pio2_3; 158 r = t-w; 159 w = fn*pio2_3t-((t-r)-w); 160 y[0] = r-w; 161 } 162 } 163 } 164 y[1] = (r-y[0])-w; 165 return n; 166 } 167 /* 168 * all other (large) arguments 169 */ 170 if(ix>=0x7ff00000) { /* x is inf or NaN */ 171 y[0]=y[1]=x-x; return 0; 172 } 173 /* set z = scalbn(|x|,ilogb(x)-23) */ 174 GET_LOW_WORD(low,x); 175 SET_LOW_WORD(z,low); 176 e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ 177 SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20))); 178 for(i=0;i<2;i++) { 179 tx[i] = (double)((int32_t)(z)); 180 z = (z-tx[i])*two24; 181 } 182 tx[2] = z; 183 nx = 3; 184 while(tx[nx-1]==zero) nx--; /* skip zero term */ 185 n = __kernel_rem_pio2(tx,ty,e0,nx,1); 186 if(hx<0) {y[0] = -ty[0]; y[1] = -ty[1]; return -n;} 187 y[0] = ty[0]; y[1] = ty[1]; return n; 188 } 189