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/* @(#)e_rem_pio2.c 5.1 93/09/24 */ |
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/* |
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* ==================================================== |
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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* |
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* Developed at SunPro, a Sun Microsystems, Inc. business. |
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* Permission to use, copy, modify, and distribute this |
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* software is freely granted, provided that this notice |
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* is preserved. |
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* ==================================================== |
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*/ |
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/* __ieee754_rem_pio2(x,y) |
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* |
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* return the remainder of x rem pi/2 in y[0]+y[1] |
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* use __kernel_rem_pio2() |
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*/ |
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#include "math.h" |
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#include "math_private.h" |
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static const int32_t npio2_hw[] = { |
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0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C, |
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0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C, |
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0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A, |
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0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C, |
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0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB, |
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0x404858EB, 0x404921FB, |
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}; |
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/* |
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* invpio2: 53 bits of 2/pi |
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* pio2_1: first 33 bit of pi/2 |
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* pio2_1t: pi/2 - pio2_1 |
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* pio2_2: second 33 bit of pi/2 |
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* pio2_2t: pi/2 - (pio2_1+pio2_2) |
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* pio2_3: third 33 bit of pi/2 |
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* pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) |
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*/ |
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static const double |
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zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ |
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half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ |
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two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ |
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invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ |
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pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ |
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pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ |
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pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ |
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pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ |
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pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ |
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pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ |
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int32_t |
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__ieee754_rem_pio2(double x, double *y) |
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{ |
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double z,w,t,r,fn; |
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double tx[3]; |
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int32_t e0,i,j,nx,n,ix,hx; |
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u_int32_t low; |
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GET_HIGH_WORD(hx,x); /* high word of x */ |
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ix = hx&0x7fffffff; |
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if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ |
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{y[0] = x; y[1] = 0; return 0;} |
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if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */ |
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if(hx>0) { |
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z = x - pio2_1; |
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if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ |
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y[0] = z - pio2_1t; |
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y[1] = (z-y[0])-pio2_1t; |
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} else { /* near pi/2, use 33+33+53 bit pi */ |
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z -= pio2_2; |
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y[0] = z - pio2_2t; |
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y[1] = (z-y[0])-pio2_2t; |
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} |
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return 1; |
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} else { /* negative x */ |
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z = x + pio2_1; |
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if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ |
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y[0] = z + pio2_1t; |
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y[1] = (z-y[0])+pio2_1t; |
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} else { /* near pi/2, use 33+33+53 bit pi */ |
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z += pio2_2; |
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y[0] = z + pio2_2t; |
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y[1] = (z-y[0])+pio2_2t; |
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} |
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return -1; |
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} |
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} |
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if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */ |
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t = fabs(x); |
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n = (int32_t) (t*invpio2+half); |
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fn = (double)n; |
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r = t-fn*pio2_1; |
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w = fn*pio2_1t; /* 1st round good to 85 bit */ |
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if(n<32&&ix!=npio2_hw[n-1]) { |
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y[0] = r-w; /* quick check no cancellation */ |
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} else { |
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u_int32_t high; |
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j = ix>>20; |
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y[0] = r-w; |
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GET_HIGH_WORD(high,y[0]); |
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i = j-((high>>20)&0x7ff); |
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if(i>16) { /* 2nd iteration needed, good to 118 */ |
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t = r; |
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w = fn*pio2_2; |
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r = t-w; |
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w = fn*pio2_2t-((t-r)-w); |
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y[0] = r-w; |
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GET_HIGH_WORD(high,y[0]); |
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i = j-((high>>20)&0x7ff); |
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if(i>49) { /* 3rd iteration need, 151 bits acc */ |
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t = r; /* will cover all possible cases */ |
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w = fn*pio2_3; |
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r = t-w; |
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w = fn*pio2_3t-((t-r)-w); |
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y[0] = r-w; |
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} |
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} |
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} |
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y[1] = (r-y[0])-w; |
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if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} |
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else return n; |
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} |
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/* |
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* all other (large) arguments |
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*/ |
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if(ix>=0x7ff00000) { /* x is inf or NaN */ |
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y[0]=y[1]=x-x; return 0; |
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} |
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/* set z = scalbn(|x|,ilogb(x)-23) */ |
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GET_LOW_WORD(low,x); |
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SET_LOW_WORD(z,low); |
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e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ |
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SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20))); |
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for(i=0;i<2;i++) { |
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tx[i] = (double)((int32_t)(z)); |
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z = (z-tx[i])*two24; |
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} |
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tx[2] = z; |
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nx = 3; |
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while(tx[nx-1]==zero) nx--; /* skip zero term */ |
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n = __kernel_rem_pio2(tx,y,e0,nx,2); |
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if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} |
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return n; |
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} |