diff options
Diffstat (limited to 'src/math/__rem_pio2.c')
| -rw-r--r-- | src/math/__rem_pio2.c | 72 |
1 files changed, 34 insertions, 38 deletions
diff --git a/src/math/__rem_pio2.c b/src/math/__rem_pio2.c index 9305be5f..5fafc4a8 100644 --- a/src/math/__rem_pio2.c +++ b/src/math/__rem_pio2.c @@ -29,7 +29,6 @@ * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) */ static const double -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 */ @@ -41,18 +40,19 @@ pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ /* caller must handle the case when reduction is not needed: |x| ~<= pi/4 */ int __rem_pio2(double x, double *y) { - double z,w,t,r,fn; - double tx[3],ty[2]; - int32_t e0,i,j,nx,n,ix,hx; - uint32_t low; + union {double f; uint64_t i;} u = {x}; + double_t z,w,t,r; + double tx[3],ty[2],fn; + uint32_t ix; + int sign, n, ex, ey, i; - GET_HIGH_WORD(hx,x); - ix = hx & 0x7fffffff; + sign = u.i>>63; + ix = u.i>>32 & 0x7fffffff; if (ix <= 0x400f6a7a) { /* |x| ~<= 5pi/4 */ if ((ix & 0xfffff) == 0x921fb) /* |x| ~= pi/2 or 2pi/2 */ goto medium; /* cancellation -- use medium case */ if (ix <= 0x4002d97c) { /* |x| ~<= 3pi/4 */ - if (hx > 0) { + if (!sign) { z = x - pio2_1; /* one round good to 85 bits */ y[0] = z - pio2_1t; y[1] = (z-y[0]) - pio2_1t; @@ -64,7 +64,7 @@ int __rem_pio2(double x, double *y) return -1; } } else { - if (hx > 0) { + if (!sign) { z = x - 2*pio2_1; y[0] = z - 2*pio2_1t; y[1] = (z-y[0]) - 2*pio2_1t; @@ -81,7 +81,7 @@ int __rem_pio2(double x, double *y) if (ix <= 0x4015fdbc) { /* |x| ~<= 7pi/4 */ if (ix == 0x4012d97c) /* |x| ~= 3pi/2 */ goto medium; - if (hx > 0) { + if (!sign) { z = x - 3*pio2_1; y[0] = z - 3*pio2_1t; y[1] = (z-y[0]) - 3*pio2_1t; @@ -95,7 +95,7 @@ int __rem_pio2(double x, double *y) } else { if (ix == 0x401921fb) /* |x| ~= 4pi/2 */ goto medium; - if (hx > 0) { + if (!sign) { z = x - 4*pio2_1; y[0] = z - 4*pio2_1t; y[1] = (z-y[0]) - 4*pio2_1t; @@ -109,32 +109,26 @@ int __rem_pio2(double x, double *y) } } if (ix < 0x413921fb) { /* |x| ~< 2^20*(pi/2), medium size */ - uint32_t high; medium: - /* Use a specialized rint() to get fn. Assume round-to-nearest. */ + /* rint(x/(pi/2)), Assume round-to-nearest. */ fn = x*invpio2 + 0x1.8p52; fn = fn - 0x1.8p52; -// FIXME -#ifdef HAVE_EFFICIENT_IRINT - n = irint(fn); -#else n = (int32_t)fn; -#endif r = x - fn*pio2_1; w = fn*pio2_1t; /* 1st round, good to 85 bits */ - j = ix>>20; y[0] = r - w; - GET_HIGH_WORD(high,y[0]); - i = j - ((high>>20)&0x7ff); - if (i > 16) { /* 2nd round, good to 118 bits */ + u.f = y[0]; + ey = u.i>>52 & 0x7ff; + ex = ix>>20; + if (ex - ey > 16) { /* 2nd round, good to 118 bits */ 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 round, good to 151 bits, covers all cases */ + u.f = y[0]; + ey = u.i>>52 & 0x7ff; + if (ex - ey > 49) { /* 3rd round, good to 151 bits, covers all cases */ t = r; w = fn*pio2_3; r = t - w; @@ -142,7 +136,7 @@ medium: y[0] = r - w; } } - y[1] = (r-y[0]) - w; + y[1] = (r - y[0]) - w; return n; } /* @@ -152,19 +146,21 @@ medium: y[0] = y[1] = x - x; return 0; } - /* set z = scalbn(|x|,ilogb(x)-23) */ - GET_LOW_WORD(low,x); - e0 = (ix>>20) - 1046; /* e0 = ilogb(z)-23; */ - INSERT_WORDS(z, ix - ((int32_t)(e0<<20)), low); - for (i=0; i<2; i++) { - tx[i] = (double)((int32_t)(z)); - z = (z-tx[i])*two24; + /* set z = scalbn(|x|,-ilogb(x)+23) */ + u.f = x; + u.i &= (uint64_t)-1>>12; + u.i |= (uint64_t)(0x3ff + 23)<<52; + z = u.f; + for (i=0; i < 2; i++) { + tx[i] = (double)(int32_t)z; + z = (z-tx[i])*0x1p24; } - tx[2] = z; - nx = 3; - while (tx[nx-1] == 0.0) nx--; /* skip zero term */ - n = __rem_pio2_large(tx,ty,e0,nx,1); - if (hx < 0) { + tx[i] = z; + /* skip zero terms, first term is non-zero */ + while (tx[i] == 0.0) + i--; + n = __rem_pio2_large(tx,ty,(int)(ix>>20)-(0x3ff+23),i+1,1); + if (sign) { y[0] = -ty[0]; y[1] = -ty[1]; return -n; |