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