e_rem_pio2l.h revision 176385
1 2/* @(#)e_rem_pio2.c 1.4 95/01/18 */ 3/* 4 * ==================================================== 5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6 * 7 * Developed at SunSoft, a Sun Microsystems, Inc. business. 8 * Permission to use, copy, modify, and distribute this 9 * software is freely granted, provided that this notice 10 * is preserved. 11 * ==================================================== 12 * 13 */ 14 15#include <sys/cdefs.h> 16__FBSDID("$FreeBSD: head/lib/msun/src/e_rem_pio2.c 176385 2008-02-18 14:02:12Z bde $"); 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 "math.h" 25#include "math_private.h" 26 27static const int32_t npio2_hw[] = { 280x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C, 290x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C, 300x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A, 310x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C, 320x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB, 330x404858EB, 0x404921FB, 34}; 35 36/* 37 * invpio2: 53 bits of 2/pi 38 * pio2_1: first 33 bit of pi/2 39 * pio2_1t: pi/2 - pio2_1 40 * pio2_2: second 33 bit of pi/2 41 * pio2_2t: pi/2 - (pio2_1+pio2_2) 42 * pio2_3: third 33 bit of pi/2 43 * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) 44 */ 45 46static const double 47zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 48half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ 49two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ 50invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ 51pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ 52pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ 53pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ 54pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ 55pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ 56pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ 57 58#ifdef INLINE_REM_PIO2 59extern inline 60#endif 61int 62__ieee754_rem_pio2(double x, double *y) 63{ 64 double z,w,t,r,fn; 65 double tx[3]; 66 int32_t e0,i,j,nx,n,ix,hx; 67 u_int32_t low; 68 69 GET_HIGH_WORD(hx,x); /* high word of x */ 70 ix = hx&0x7fffffff; 71 if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ 72 {y[0] = x; y[1] = 0; return 0;} 73 if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */ 74 if(hx>0) { 75 z = x - pio2_1; 76 if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ 77 y[0] = z - pio2_1t; 78 y[1] = (z-y[0])-pio2_1t; 79 } else { /* near pi/2, use 33+33+53 bit pi */ 80 z -= pio2_2; 81 y[0] = z - pio2_2t; 82 y[1] = (z-y[0])-pio2_2t; 83 } 84 return 1; 85 } else { /* negative x */ 86 z = x + pio2_1; 87 if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ 88 y[0] = z + pio2_1t; 89 y[1] = (z-y[0])+pio2_1t; 90 } else { /* near pi/2, use 33+33+53 bit pi */ 91 z += pio2_2; 92 y[0] = z + pio2_2t; 93 y[1] = (z-y[0])+pio2_2t; 94 } 95 return -1; 96 } 97 } 98 if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */ 99 t = fabs(x); 100 n = (int32_t) (t*invpio2+half); 101 fn = (double)n; 102 r = t-fn*pio2_1; 103 w = fn*pio2_1t; /* 1st round good to 85 bit */ 104 if(n<32&&ix!=npio2_hw[n-1]) { 105 y[0] = r-w; /* quick check no cancellation */ 106 } else { 107 u_int32_t high; 108 j = ix>>20; 109 y[0] = r-w; 110 GET_HIGH_WORD(high,y[0]); 111 i = j-((high>>20)&0x7ff); 112 if(i>16) { /* 2nd iteration needed, good to 118 */ 113 t = r; 114 w = fn*pio2_2; 115 r = t-w; 116 w = fn*pio2_2t-((t-r)-w); 117 y[0] = r-w; 118 GET_HIGH_WORD(high,y[0]); 119 i = j-((high>>20)&0x7ff); 120 if(i>49) { /* 3rd iteration need, 151 bits acc */ 121 t = r; /* will cover all possible cases */ 122 w = fn*pio2_3; 123 r = t-w; 124 w = fn*pio2_3t-((t-r)-w); 125 y[0] = r-w; 126 } 127 } 128 } 129 y[1] = (r-y[0])-w; 130 if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} 131 else return n; 132 } 133 /* 134 * all other (large) arguments 135 */ 136 if(ix>=0x7ff00000) { /* x is inf or NaN */ 137 y[0]=y[1]=x-x; return 0; 138 } 139 /* set z = scalbn(|x|,ilogb(x)-23) */ 140 GET_LOW_WORD(low,x); 141 SET_LOW_WORD(z,low); 142 e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ 143 SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20))); 144 for(i=0;i<2;i++) { 145 tx[i] = (double)((int32_t)(z)); 146 z = (z-tx[i])*two24; 147 } 148 tx[2] = z; 149 nx = 3; 150 while(tx[nx-1]==zero) nx--; /* skip zero term */ 151 n = __kernel_rem_pio2(tx,y,e0,nx,2); 152 if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} 153 return n; 154} 155