1 /* @(#)e_rem_pio2.c 5.1 93/09/24 */ 2 /* 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 6 * Developed at SunPro, 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 13 #if defined(LIBM_SCCS) && !defined(lint) 14 static char rcsid[] = "$NetBSD: e_rem_pio2.c,v 1.8 1995/05/10 20:46:02 jtc Exp $"; 15 #endif 16 17 /* __ieee754_rem_pio2(x,y) 18 * 19 * return the remainder of x rem pi/2 in y[0]+y[1] 20 * use __kernel_rem_pio2() 21 */ 22 23 #include "math.h" 24 #include "math_private.h" 25 26 static const int32_t npio2_hw[] = { 27 0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C, 28 0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C, 29 0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A, 30 0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C, 31 0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB, 32 0x404858EB, 0x404921FB, 33 }; 34 35 /* 36 * invpio2: 53 bits of 2/pi 37 * pio2_1: first 33 bit of pi/2 38 * pio2_1t: pi/2 - pio2_1 39 * pio2_2: second 33 bit of pi/2 40 * pio2_2t: pi/2 - (pio2_1+pio2_2) 41 * pio2_3: third 33 bit of pi/2 42 * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) 43 */ 44 45 static const double 46 zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 47 half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ 48 two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ 49 invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ 50 pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ 51 pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ 52 pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ 53 pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ 54 pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ 55 pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ 56 57 int32_t 58 __ieee754_rem_pio2(double x, double *y) 59 { 60 double z,w,t,r,fn; 61 double tx[3]; 62 int32_t e0,i,j,nx,n,ix,hx; 63 u_int32_t low; 64 65 GET_HIGH_WORD(hx,x); /* high word of x */ 66 ix = hx&0x7fffffff; 67 if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ 68 {y[0] = x; y[1] = 0; return 0;} 69 if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */ 70 if(hx>0) { 71 z = x - pio2_1; 72 if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ 73 y[0] = z - pio2_1t; 74 y[1] = (z-y[0])-pio2_1t; 75 } else { /* near pi/2, use 33+33+53 bit pi */ 76 z -= pio2_2; 77 y[0] = z - pio2_2t; 78 y[1] = (z-y[0])-pio2_2t; 79 } 80 return 1; 81 } else { /* negative x */ 82 z = x + pio2_1; 83 if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ 84 y[0] = z + pio2_1t; 85 y[1] = (z-y[0])+pio2_1t; 86 } else { /* near pi/2, use 33+33+53 bit pi */ 87 z += pio2_2; 88 y[0] = z + pio2_2t; 89 y[1] = (z-y[0])+pio2_2t; 90 } 91 return -1; 92 } 93 } 94 if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */ 95 t = fabs(x); 96 n = (int32_t) (t*invpio2+half); 97 fn = (double)n; 98 r = t-fn*pio2_1; 99 w = fn*pio2_1t; /* 1st round good to 85 bit */ 100 if(n<32&&ix!=npio2_hw[n-1]) { 101 y[0] = r-w; /* quick check no cancellation */ 102 } else { 103 u_int32_t high; 104 j = ix>>20; 105 y[0] = r-w; 106 GET_HIGH_WORD(high,y[0]); 107 i = j-((high>>20)&0x7ff); 108 if(i>16) { /* 2nd iteration needed, good to 118 */ 109 t = r; 110 w = fn*pio2_2; 111 r = t-w; 112 w = fn*pio2_2t-((t-r)-w); 113 y[0] = r-w; 114 GET_HIGH_WORD(high,y[0]); 115 i = j-((high>>20)&0x7ff); 116 if(i>49) { /* 3rd iteration need, 151 bits acc */ 117 t = r; /* will cover all possible cases */ 118 w = fn*pio2_3; 119 r = t-w; 120 w = fn*pio2_3t-((t-r)-w); 121 y[0] = r-w; 122 } 123 } 124 } 125 y[1] = (r-y[0])-w; 126 if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} 127 else return n; 128 } 129 /* 130 * all other (large) arguments 131 */ 132 if(ix>=0x7ff00000) { /* x is inf or NaN */ 133 y[0]=y[1]=x-x; return 0; 134 } 135 /* set z = scalbn(|x|,ilogb(x)-23) */ 136 GET_LOW_WORD(low,x); 137 SET_LOW_WORD(z,low); 138 e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ 139 SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20))); 140 for(i=0;i<2;i++) { 141 tx[i] = (double)((int32_t)(z)); 142 z = (z-tx[i])*two24; 143 } 144 tx[2] = z; 145 nx = 3; 146 while(tx[nx-1]==zero) nx--; /* skip zero term */ 147 n = __kernel_rem_pio2(tx,y,e0,nx,2); 148 if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} 149 return n; 150 } 151