Elliott Hughes | a0ee078 | 2013-01-30 19:06:37 -0800 | [diff] [blame] | 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 | * Optimized by Bruce D. Evans. |
| 14 | */ |
| 15 | |
| 16 | #include <sys/cdefs.h> |
| 17 | __FBSDID("$FreeBSD$"); |
| 18 | |
| 19 | /* __ieee754_rem_pio2(x,y) |
| 20 | * |
| 21 | * return the remainder of x rem pi/2 in y[0]+y[1] |
| 22 | * use __kernel_rem_pio2() |
| 23 | */ |
| 24 | |
| 25 | #include <float.h> |
| 26 | |
| 27 | #include "math.h" |
| 28 | #include "math_private.h" |
| 29 | |
| 30 | /* |
| 31 | * invpio2: 53 bits of 2/pi |
| 32 | * pio2_1: first 33 bit of pi/2 |
| 33 | * pio2_1t: pi/2 - pio2_1 |
| 34 | * pio2_2: second 33 bit of pi/2 |
| 35 | * pio2_2t: pi/2 - (pio2_1+pio2_2) |
| 36 | * pio2_3: third 33 bit of pi/2 |
| 37 | * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) |
| 38 | */ |
| 39 | |
| 40 | static const double |
| 41 | zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ |
| 42 | two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ |
| 43 | invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ |
| 44 | pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ |
| 45 | pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ |
| 46 | pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ |
| 47 | pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ |
| 48 | pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ |
| 49 | pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ |
| 50 | |
| 51 | #ifdef INLINE_REM_PIO2 |
| 52 | static __inline __always_inline |
| 53 | #endif |
| 54 | int |
| 55 | __ieee754_rem_pio2(double x, double *y) |
| 56 | { |
| 57 | double z,w,t,r,fn; |
| 58 | double tx[3],ty[2]; |
| 59 | int32_t e0,i,j,nx,n,ix,hx; |
| 60 | u_int32_t low; |
| 61 | |
| 62 | GET_HIGH_WORD(hx,x); /* high word of x */ |
| 63 | ix = hx&0x7fffffff; |
| 64 | #if 0 /* Must be handled in caller. */ |
| 65 | if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ |
| 66 | {y[0] = x; y[1] = 0; return 0;} |
| 67 | #endif |
| 68 | if (ix <= 0x400f6a7a) { /* |x| ~<= 5pi/4 */ |
| 69 | if ((ix & 0xfffff) == 0x921fb) /* |x| ~= pi/2 or 2pi/2 */ |
| 70 | goto medium; /* cancellation -- use medium case */ |
| 71 | if (ix <= 0x4002d97c) { /* |x| ~<= 3pi/4 */ |
| 72 | if (hx > 0) { |
| 73 | z = x - pio2_1; /* one round good to 85 bits */ |
| 74 | y[0] = z - pio2_1t; |
| 75 | y[1] = (z-y[0])-pio2_1t; |
| 76 | return 1; |
| 77 | } else { |
| 78 | z = x + pio2_1; |
| 79 | y[0] = z + pio2_1t; |
| 80 | y[1] = (z-y[0])+pio2_1t; |
| 81 | return -1; |
| 82 | } |
| 83 | } else { |
| 84 | if (hx > 0) { |
| 85 | z = x - 2*pio2_1; |
| 86 | y[0] = z - 2*pio2_1t; |
| 87 | y[1] = (z-y[0])-2*pio2_1t; |
| 88 | return 2; |
| 89 | } else { |
| 90 | z = x + 2*pio2_1; |
| 91 | y[0] = z + 2*pio2_1t; |
| 92 | y[1] = (z-y[0])+2*pio2_1t; |
| 93 | return -2; |
| 94 | } |
| 95 | } |
| 96 | } |
| 97 | if (ix <= 0x401c463b) { /* |x| ~<= 9pi/4 */ |
| 98 | if (ix <= 0x4015fdbc) { /* |x| ~<= 7pi/4 */ |
| 99 | if (ix == 0x4012d97c) /* |x| ~= 3pi/2 */ |
| 100 | goto medium; |
| 101 | if (hx > 0) { |
| 102 | z = x - 3*pio2_1; |
| 103 | y[0] = z - 3*pio2_1t; |
| 104 | y[1] = (z-y[0])-3*pio2_1t; |
| 105 | return 3; |
| 106 | } else { |
| 107 | z = x + 3*pio2_1; |
| 108 | y[0] = z + 3*pio2_1t; |
| 109 | y[1] = (z-y[0])+3*pio2_1t; |
| 110 | return -3; |
| 111 | } |
| 112 | } else { |
| 113 | if (ix == 0x401921fb) /* |x| ~= 4pi/2 */ |
| 114 | goto medium; |
| 115 | if (hx > 0) { |
| 116 | z = x - 4*pio2_1; |
| 117 | y[0] = z - 4*pio2_1t; |
| 118 | y[1] = (z-y[0])-4*pio2_1t; |
| 119 | return 4; |
| 120 | } else { |
| 121 | z = x + 4*pio2_1; |
| 122 | y[0] = z + 4*pio2_1t; |
| 123 | y[1] = (z-y[0])+4*pio2_1t; |
| 124 | return -4; |
| 125 | } |
| 126 | } |
| 127 | } |
| 128 | if(ix<0x413921fb) { /* |x| ~< 2^20*(pi/2), medium size */ |
| 129 | medium: |
| 130 | /* Use a specialized rint() to get fn. Assume round-to-nearest. */ |
| 131 | STRICT_ASSIGN(double,fn,x*invpio2+0x1.8p52); |
| 132 | fn = fn-0x1.8p52; |
| 133 | #ifdef HAVE_EFFICIENT_IRINT |
| 134 | n = irint(fn); |
| 135 | #else |
| 136 | n = (int32_t)fn; |
| 137 | #endif |
| 138 | r = x-fn*pio2_1; |
| 139 | w = fn*pio2_1t; /* 1st round good to 85 bit */ |
| 140 | { |
| 141 | u_int32_t high; |
| 142 | j = ix>>20; |
| 143 | y[0] = r-w; |
| 144 | GET_HIGH_WORD(high,y[0]); |
| 145 | i = j-((high>>20)&0x7ff); |
| 146 | if(i>16) { /* 2nd iteration needed, good to 118 */ |
| 147 | t = r; |
| 148 | w = fn*pio2_2; |
| 149 | r = t-w; |
| 150 | w = fn*pio2_2t-((t-r)-w); |
| 151 | y[0] = r-w; |
| 152 | GET_HIGH_WORD(high,y[0]); |
| 153 | i = j-((high>>20)&0x7ff); |
| 154 | if(i>49) { /* 3rd iteration need, 151 bits acc */ |
| 155 | t = r; /* will cover all possible cases */ |
| 156 | w = fn*pio2_3; |
| 157 | r = t-w; |
| 158 | w = fn*pio2_3t-((t-r)-w); |
| 159 | y[0] = r-w; |
| 160 | } |
| 161 | } |
| 162 | } |
| 163 | y[1] = (r-y[0])-w; |
| 164 | return n; |
| 165 | } |
| 166 | /* |
| 167 | * all other (large) arguments |
| 168 | */ |
| 169 | if(ix>=0x7ff00000) { /* x is inf or NaN */ |
| 170 | y[0]=y[1]=x-x; return 0; |
| 171 | } |
| 172 | /* set z = scalbn(|x|,ilogb(x)-23) */ |
| 173 | GET_LOW_WORD(low,x); |
| 174 | e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ |
| 175 | INSERT_WORDS(z, ix - ((int32_t)(e0<<20)), low); |
| 176 | for(i=0;i<2;i++) { |
| 177 | tx[i] = (double)((int32_t)(z)); |
| 178 | z = (z-tx[i])*two24; |
| 179 | } |
| 180 | tx[2] = z; |
| 181 | nx = 3; |
| 182 | while(tx[nx-1]==zero) nx--; /* skip zero term */ |
| 183 | n = __kernel_rem_pio2(tx,ty,e0,nx,1); |
| 184 | if(hx<0) {y[0] = -ty[0]; y[1] = -ty[1]; return -n;} |
| 185 | y[0] = ty[0]; y[1] = ty[1]; return n; |
| 186 | } |