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