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/* __ieee754_rem_pio2(x,y) 14 * 15 * return the remainder of x rem pi/2 in y[0]+y[1] 16 * use __kernel_rem_pio2() 17 */ 18 19#include "math.h" 20#include "math_private.h" 21 22static const int32_t npio2_hw[] = { 230x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C, 240x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C, 250x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A, 260x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C, 270x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB, 280x404858EB, 0x404921FB, 29}; 30 31/* 32 * invpio2: 53 bits of 2/pi 33 * pio2_1: first 33 bit of pi/2 34 * pio2_1t: pi/2 - pio2_1 35 * pio2_2: second 33 bit of pi/2 36 * pio2_2t: pi/2 - (pio2_1+pio2_2) 37 * pio2_3: third 33 bit of pi/2 38 * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) 39 */ 40 41static const double 42zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 43half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ 44two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ 45invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ 46pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ 47pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ 48pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ 49pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ 50pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ 51pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ 52 53int32_t 54__ieee754_rem_pio2(double x, double *y) 55{ 56 double z,w,t,r,fn; 57 double tx[3]; 58 int32_t e0,i,j,nx,n,ix,hx; 59 u_int32_t low; 60 61 GET_HIGH_WORD(hx,x); /* high word of x */ 62 ix = hx&0x7fffffff; 63 if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ 64 {y[0] = x; y[1] = 0; return 0;} 65 if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */ 66 if(hx>0) { 67 z = x - pio2_1; 68 if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ 69 y[0] = z - pio2_1t; 70 y[1] = (z-y[0])-pio2_1t; 71 } else { /* near pi/2, use 33+33+53 bit pi */ 72 z -= pio2_2; 73 y[0] = z - pio2_2t; 74 y[1] = (z-y[0])-pio2_2t; 75 } 76 return 1; 77 } else { /* negative x */ 78 z = x + pio2_1; 79 if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ 80 y[0] = z + pio2_1t; 81 y[1] = (z-y[0])+pio2_1t; 82 } else { /* near pi/2, use 33+33+53 bit pi */ 83 z += pio2_2; 84 y[0] = z + pio2_2t; 85 y[1] = (z-y[0])+pio2_2t; 86 } 87 return -1; 88 } 89 } 90 if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */ 91 t = fabs(x); 92 n = (int32_t) (t*invpio2+half); 93 fn = (double)n; 94 r = t-fn*pio2_1; 95 w = fn*pio2_1t; /* 1st round good to 85 bit */ 96 if(n<32&&ix!=npio2_hw[n-1]) { 97 y[0] = r-w; /* quick check no cancellation */ 98 } else { 99 u_int32_t high; 100 j = ix>>20; 101 y[0] = r-w; 102 GET_HIGH_WORD(high,y[0]); 103 i = j-((high>>20)&0x7ff); 104 if(i>16) { /* 2nd iteration needed, good to 118 */ 105 t = r; 106 w = fn*pio2_2; 107 r = t-w; 108 w = fn*pio2_2t-((t-r)-w); 109 y[0] = r-w; 110 GET_HIGH_WORD(high,y[0]); 111 i = j-((high>>20)&0x7ff); 112 if(i>49) { /* 3rd iteration need, 151 bits acc */ 113 t = r; /* will cover all possible cases */ 114 w = fn*pio2_3; 115 r = t-w; 116 w = fn*pio2_3t-((t-r)-w); 117 y[0] = r-w; 118 } 119 } 120 } 121 y[1] = (r-y[0])-w; 122 if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} 123 else return n; 124 } 125 /* 126 * all other (large) arguments 127 */ 128 if(ix>=0x7ff00000) { /* x is inf or NaN */ 129 y[0]=y[1]=x-x; return 0; 130 } 131 /* set z = scalbn(|x|,ilogb(x)-23) */ 132 GET_LOW_WORD(low,x); 133 SET_LOW_WORD(z,low); 134 e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ 135 SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20))); 136 for(i=0;i<2;i++) { 137 tx[i] = (double)((int32_t)(z)); 138 z = (z-tx[i])*two24; 139 } 140 tx[2] = z; 141 nx = 3; 142 while(tx[nx-1]==zero) nx--; /* skip zero term */ 143 n = __kernel_rem_pio2(tx,y,e0,nx,2); 144 if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} 145 return n; 146} 147