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 two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ 43 invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ 44 pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ 45 pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ 46 pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ 47 pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ 48 pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ 49 pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ 50 51 #ifdef INLINE_REM_PIO2 52 static __inline __always_inline 53 #endif 54 int 55 __ieee754_rem_pio2(double x, double *y) 56 { 57 double z,w,t,r,fn; 58 double tx[3],ty[2]; 59 int32_t e0,i,j,nx,n,ix,hx; 60 u_int32_t low; 61 62 GET_HIGH_WORD(hx,x); /* high word of x */ 63 ix = hx&0x7fffffff; 64 #if 0 /* Must be handled in caller. */ 65 if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ 66 {y[0] = x; y[1] = 0; return 0;} 67 #endif 68 if (ix <= 0x400f6a7a) { /* |x| ~<= 5pi/4 */ 69 if ((ix & 0xfffff) == 0x921fb) /* |x| ~= pi/2 or 2pi/2 */ 70 goto medium; /* cancellation -- use medium case */ 71 if (ix <= 0x4002d97c) { /* |x| ~<= 3pi/4 */ 72 if (hx > 0) { 73 z = x - pio2_1; /* one round good to 85 bits */ 74 y[0] = z - pio2_1t; 75 y[1] = (z-y[0])-pio2_1t; 76 return 1; 77 } else { 78 z = x + pio2_1; 79 y[0] = z + pio2_1t; 80 y[1] = (z-y[0])+pio2_1t; 81 return -1; 82 } 83 } else { 84 if (hx > 0) { 85 z = x - 2*pio2_1; 86 y[0] = z - 2*pio2_1t; 87 y[1] = (z-y[0])-2*pio2_1t; 88 return 2; 89 } else { 90 z = x + 2*pio2_1; 91 y[0] = z + 2*pio2_1t; 92 y[1] = (z-y[0])+2*pio2_1t; 93 return -2; 94 } 95 } 96 } 97 if (ix <= 0x401c463b) { /* |x| ~<= 9pi/4 */ 98 if (ix <= 0x4015fdbc) { /* |x| ~<= 7pi/4 */ 99 if (ix == 0x4012d97c) /* |x| ~= 3pi/2 */ 100 goto medium; 101 if (hx > 0) { 102 z = x - 3*pio2_1; 103 y[0] = z - 3*pio2_1t; 104 y[1] = (z-y[0])-3*pio2_1t; 105 return 3; 106 } else { 107 z = x + 3*pio2_1; 108 y[0] = z + 3*pio2_1t; 109 y[1] = (z-y[0])+3*pio2_1t; 110 return -3; 111 } 112 } else { 113 if (ix == 0x401921fb) /* |x| ~= 4pi/2 */ 114 goto medium; 115 if (hx > 0) { 116 z = x - 4*pio2_1; 117 y[0] = z - 4*pio2_1t; 118 y[1] = (z-y[0])-4*pio2_1t; 119 return 4; 120 } else { 121 z = x + 4*pio2_1; 122 y[0] = z + 4*pio2_1t; 123 y[1] = (z-y[0])+4*pio2_1t; 124 return -4; 125 } 126 } 127 } 128 if(ix<0x413921fb) { /* |x| ~< 2^20*(pi/2), medium size */ 129 medium: 130 fn = rnint((double_t)x*invpio2); 131 n = irint(fn); 132 r = x-fn*pio2_1; 133 w = fn*pio2_1t; /* 1st round good to 85 bit */ 134 { 135 u_int32_t high; 136 j = ix>>20; 137 y[0] = r-w; 138 GET_HIGH_WORD(high,y[0]); 139 i = j-((high>>20)&0x7ff); 140 if(i>16) { /* 2nd iteration needed, good to 118 */ 141 t = r; 142 w = fn*pio2_2; 143 r = t-w; 144 w = fn*pio2_2t-((t-r)-w); 145 y[0] = r-w; 146 GET_HIGH_WORD(high,y[0]); 147 i = j-((high>>20)&0x7ff); 148 if(i>49) { /* 3rd iteration need, 151 bits acc */ 149 t = r; /* will cover all possible cases */ 150 w = fn*pio2_3; 151 r = t-w; 152 w = fn*pio2_3t-((t-r)-w); 153 y[0] = r-w; 154 } 155 } 156 } 157 y[1] = (r-y[0])-w; 158 return n; 159 } 160 /* 161 * all other (large) arguments 162 */ 163 if(ix>=0x7ff00000) { /* x is inf or NaN */ 164 y[0]=y[1]=x-x; return 0; 165 } 166 /* set z = scalbn(|x|,ilogb(x)-23) */ 167 GET_LOW_WORD(low,x); 168 e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ 169 INSERT_WORDS(z, ix - ((int32_t)(e0<<20)), low); 170 for(i=0;i<2;i++) { 171 tx[i] = (double)((int32_t)(z)); 172 z = (z-tx[i])*two24; 173 } 174 tx[2] = z; 175 nx = 3; 176 while(tx[nx-1]==zero) nx--; /* skip zero term */ 177 n = __kernel_rem_pio2(tx,ty,e0,nx,1); 178 if(hx<0) {y[0] = -ty[0]; y[1] = -ty[1]; return -n;} 179 y[0] = ty[0]; y[1] = ty[1]; return n; 180 } 181