e_rem_pio2.cpp (4782B)
1 /* @(#)e_rem_pio2.c 1.4 95/01/18 */ 2 /* 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 6 * Developed at SunSoft, a Sun Microsystems, Inc. business. 7 * Permission to use, copy, modify, and distribute this 8 * software is freely granted, provided that this notice 9 * is preserved. 10 * ==================================================== 11 * 12 * Optimized by Bruce D. Evans. 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 <float.h> 25 26 #include "math_private.h" 27 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 38 static const double 39 zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 40 two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ 41 invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ 42 pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ 43 pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ 44 pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ 45 pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ 46 pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ 47 pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ 48 49 #ifdef INLINE_REM_PIO2 50 static inline 51 #endif 52 int 53 __ieee754_rem_pio2(double x, double *y) 54 { 55 double z,w,t,r,fn; 56 double tx[3],ty[2]; 57 int32_t e0,i,j,nx,n,ix,hx; 58 u_int32_t low; 59 60 GET_HIGH_WORD(hx,x); /* high word of x */ 61 ix = hx&0x7fffffff; 62 #if 0 /* Must be handled in caller. */ 63 if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ 64 {y[0] = x; y[1] = 0; return 0;} 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 */ 72 y[0] = z - pio2_1t; 73 y[1] = (z-y[0])-pio2_1t; 74 return 1; 75 } else { 76 z = x + pio2_1; 77 y[0] = z + pio2_1t; 78 y[1] = (z-y[0])+pio2_1t; 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; 92 } 93 } 94 } 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 } 110 } else { 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 */ 127 medium: 128 fn = rnint((double_t)x*invpio2); 129 n = irint(fn); 130 r = x-fn*pio2_1; 131 w = fn*pio2_1t; /* 1st round good to 85 bit */ 132 { 133 u_int32_t high; 134 j = ix>>20; 135 y[0] = r-w; 136 GET_HIGH_WORD(high,y[0]); 137 i = j-((high>>20)&0x7ff); 138 if(i>16) { /* 2nd iteration needed, good to 118 */ 139 t = r; 140 w = fn*pio2_2; 141 r = t-w; 142 w = fn*pio2_2t-((t-r)-w); 143 y[0] = r-w; 144 GET_HIGH_WORD(high,y[0]); 145 i = j-((high>>20)&0x7ff); 146 if(i>49) { /* 3rd iteration need, 151 bits acc */ 147 t = r; /* will cover all possible cases */ 148 w = fn*pio2_3; 149 r = t-w; 150 w = fn*pio2_3t-((t-r)-w); 151 y[0] = r-w; 152 } 153 } 154 } 155 y[1] = (r-y[0])-w; 156 return n; 157 } 158 /* 159 * all other (large) arguments 160 */ 161 if(ix>=0x7ff00000) { /* x is inf or NaN */ 162 y[0]=y[1]=x-x; return 0; 163 } 164 /* set z = scalbn(|x|,ilogb(x)-23) */ 165 GET_LOW_WORD(low,x); 166 e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ 167 INSERT_WORDS(z, ix - ((int32_t)(e0<<20)), low); 168 for(i=0;i<2;i++) { 169 tx[i] = (double)((int32_t)(z)); 170 z = (z-tx[i])*two24; 171 } 172 tx[2] = z; 173 nx = 3; 174 while(tx[nx-1]==zero) nx--; /* skip zero term */ 175 n = __kernel_rem_pio2(tx,ty,e0,nx,1); 176 if(hx<0) {y[0] = -ty[0]; y[1] = -ty[1]; return -n;} 177 y[0] = ty[0]; y[1] = ty[1]; return n; 178 }