diff options
Diffstat (limited to 'sysdeps/ieee754/dbl-64/e_rem_pio2.c')
| -rw-r--r-- | sysdeps/ieee754/dbl-64/e_rem_pio2.c | 215 |
1 files changed, 121 insertions, 94 deletions
diff --git a/sysdeps/ieee754/dbl-64/e_rem_pio2.c b/sysdeps/ieee754/dbl-64/e_rem_pio2.c index 4478be0b07..2f55ca294b 100644 --- a/sysdeps/ieee754/dbl-64/e_rem_pio2.c +++ b/sysdeps/ieee754/dbl-64/e_rem_pio2.c @@ -57,110 +57,137 @@ static const int32_t npio2_hw[] = { */ static const double -zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ -half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ -two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ -invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ -pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ -pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ -pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ -pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ -pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ -pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ + zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ + half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ + two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ + invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ + pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ + pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ + pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ + pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ + pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ + pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ int32_t -__ieee754_rem_pio2(double x, double *y) +__ieee754_rem_pio2 (double x, double *y) { - double z,w,t,r,fn; - double tx[3]; - int32_t e0,i,j,nx,n,ix,hx; - u_int32_t low; + double z, w, t, r, fn; + double tx[3]; + int32_t e0, i, j, nx, n, ix, hx; + u_int32_t low; - GET_HIGH_WORD(hx,x); /* high word of x */ - ix = hx&0x7fffffff; - if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ - {y[0] = x; y[1] = 0; return 0;} - if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */ - if(hx>0) { - z = x - pio2_1; - if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ - y[0] = z - pio2_1t; - y[1] = (z-y[0])-pio2_1t; - } else { /* near pi/2, use 33+33+53 bit pi */ - z -= pio2_2; - y[0] = z - pio2_2t; - y[1] = (z-y[0])-pio2_2t; - } - return 1; - } else { /* negative x */ - z = x + pio2_1; - if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ - y[0] = z + pio2_1t; - y[1] = (z-y[0])+pio2_1t; - } else { /* near pi/2, use 33+33+53 bit pi */ - z += pio2_2; - y[0] = z + pio2_2t; - y[1] = (z-y[0])+pio2_2t; - } - return -1; + GET_HIGH_WORD (hx, x); /* high word of x */ + ix = hx & 0x7fffffff; + if (ix <= 0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ + { + y[0] = x; y[1] = 0; return 0; + } + if (ix < 0x4002d97c) /* |x| < 3pi/4, special case with n=+-1 */ + { + if (hx > 0) + { + z = x - pio2_1; + if (ix != 0x3ff921fb) /* 33+53 bit pi is good enough */ + { + y[0] = z - pio2_1t; + y[1] = (z - y[0]) - pio2_1t; + } + else /* near pi/2, use 33+33+53 bit pi */ + { + z -= pio2_2; + y[0] = z - pio2_2t; + y[1] = (z - y[0]) - pio2_2t; } + return 1; } - if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */ - t = fabs(x); - n = (int32_t) (t*invpio2+half); - fn = (double)n; - r = t-fn*pio2_1; - w = fn*pio2_1t; /* 1st round good to 85 bit */ - if(n<32&&ix!=npio2_hw[n-1]) { - y[0] = r-w; /* quick check no cancellation */ - } else { - u_int32_t high; - j = ix>>20; - y[0] = r-w; - GET_HIGH_WORD(high,y[0]); - i = j-((high>>20)&0x7ff); - if(i>16) { /* 2nd iteration needed, good to 118 */ - t = r; - w = fn*pio2_2; - r = t-w; - w = fn*pio2_2t-((t-r)-w); - y[0] = r-w; - GET_HIGH_WORD(high,y[0]); - i = j-((high>>20)&0x7ff); - if(i>49) { /* 3rd iteration need, 151 bits acc */ - t = r; /* will cover all possible cases */ - w = fn*pio2_3; - r = t-w; - w = fn*pio2_3t-((t-r)-w); - y[0] = r-w; - } - } + else /* negative x */ + { + z = x + pio2_1; + if (ix != 0x3ff921fb) /* 33+53 bit pi is good enough */ + { + y[0] = z + pio2_1t; + y[1] = (z - y[0]) + pio2_1t; + } + else /* near pi/2, use 33+33+53 bit pi */ + { + z += pio2_2; + y[0] = z + pio2_2t; + y[1] = (z - y[0]) + pio2_2t; } - y[1] = (r-y[0])-w; - if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} - else return n; + return -1; } - /* - * all other (large) arguments - */ - if(ix>=0x7ff00000) { /* x is inf or NaN */ - y[0]=y[1]=x-x; return 0; + } + if (ix <= 0x413921fb) /* |x| ~<= 2^19*(pi/2), medium size */ + { + t = fabs (x); + n = (int32_t) (t * invpio2 + half); + fn = (double) n; + r = t - fn * pio2_1; + w = fn * pio2_1t; /* 1st round good to 85 bit */ + if (n < 32 && ix != npio2_hw[n - 1]) + { + y[0] = r - w; /* quick check no cancellation */ } - /* set z = scalbn(|x|,ilogb(x)-23) */ - GET_LOW_WORD(low,x); - SET_LOW_WORD(z,low); - e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ - SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20))); - for(i=0;i<2;i++) { - tx[i] = (double)((int32_t)(z)); - z = (z-tx[i])*two24; + else + { + u_int32_t high; + j = ix >> 20; + y[0] = r - w; + GET_HIGH_WORD (high, y[0]); + i = j - ((high >> 20) & 0x7ff); + if (i > 16) /* 2nd iteration needed, good to 118 */ + { + t = r; + w = fn * pio2_2; + r = t - w; + w = fn * pio2_2t - ((t - r) - w); + y[0] = r - w; + GET_HIGH_WORD (high, y[0]); + i = j - ((high >> 20) & 0x7ff); + if (i > 49) /* 3rd iteration need, 151 bits acc */ + { + t = r; /* will cover all possible cases */ + w = fn * pio2_3; + r = t - w; + w = fn * pio2_3t - ((t - r) - w); + y[0] = r - w; + } + } } - tx[2] = z; - nx = 3; - while(tx[nx-1]==zero) nx--; /* skip zero term */ - n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi); - if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} + y[1] = (r - y[0]) - w; + if (hx < 0) + { + y[0] = -y[0]; y[1] = -y[1]; return -n; + } + else return n; + } + /* + * all other (large) arguments + */ + if (ix >= 0x7ff00000) /* x is inf or NaN */ + { + y[0] = y[1] = x - x; return 0; + } + /* set z = scalbn(|x|,ilogb(x)-23) */ + GET_LOW_WORD (low, x); + SET_LOW_WORD (z, low); + e0 = (ix >> 20) - 1046; /* e0 = ilogb(z)-23; */ + SET_HIGH_WORD (z, ix - ((int32_t) (e0 << 20))); + for (i = 0; i < 2; i++) + { + tx[i] = (double) ((int32_t) (z)); + z = (z - tx[i]) * two24; + } + tx[2] = z; + nx = 3; + while (tx[nx - 1] == zero) + nx--; /* skip zero term */ + n = __kernel_rem_pio2 (tx, y, e0, nx, 2, two_over_pi); + if (hx < 0) + { + y[0] = -y[0]; y[1] = -y[1]; return -n; + } + return n; } - #endif |