diff options
Diffstat (limited to 'src/math/__rem_pio2l.c')
| -rw-r--r-- | src/math/__rem_pio2l.c | 117 |
1 files changed, 64 insertions, 53 deletions
diff --git a/src/math/__rem_pio2l.c b/src/math/__rem_pio2l.c index f0cb99ac..8b15b7b2 100644 --- a/src/math/__rem_pio2l.c +++ b/src/math/__rem_pio2l.c @@ -13,15 +13,22 @@ * Optimized by Bruce D. Evans. */ #include "libm.h" -#if LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 -/* ld80 version of __rem_pio2(x,y) +#if (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 +/* ld80 and ld128 version of __rem_pio2(x,y) * * return the remainder of x rem pi/2 in y[0]+y[1] * use __rem_pio2_large() for large x */ -#define BIAS (LDBL_MAX_EXP - 1) - +#if LDBL_MANT_DIG == 64 +/* u ~< 0x1p25*pi/2 */ +#define SMALL(u) (((u.i.se & 0x7fffU)<<16 | u.i.m>>48) < ((0x3fff + 25)<<16 | 0x921f>>1 | 0x8000)) +#define TOINT 0x1.8p63 +#define QUOBITS(x) ((uint32_t)(int32_t)x & 0x7fffffff) +#define ROUND1 22 +#define ROUND2 61 +#define NX 3 +#define NY 2 /* * invpio2: 64 bits of 2/pi * pio2_1: first 39 bits of pi/2 @@ -32,60 +39,61 @@ * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) */ static const double -two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ pio2_1 = 1.57079632679597125389e+00, /* 0x3FF921FB, 0x54444000 */ pio2_2 = -1.07463465549783099519e-12, /* -0x12e7b967674000.0p-92 */ pio2_3 = 6.36831716351370313614e-25; /* 0x18a2e037074000.0p-133 */ - static const long double invpio2 = 6.36619772367581343076e-01L, /* 0xa2f9836e4e44152a.0p-64 */ pio2_1t = -1.07463465549719416346e-12L, /* -0x973dcb3b399d747f.0p-103 */ pio2_2t = 6.36831716351095013979e-25L, /* 0xc51701b839a25205.0p-144 */ pio2_3t = -2.75299651904407171810e-37L; /* -0xbb5bf6c7ddd660ce.0p-185 */ +#elif LDBL_MANT_DIG == 113 +/* u ~< 0x1p45*pi/2 */ +#define SMALL(u) (((u.i.se & 0x7fffU)<<16 | u.i.top) < ((0x3fff + 45)<<16 | 0x921f)) +#define TOINT 0x1.8p112 +#define QUOBITS(x) ((uint32_t)(int64_t)x & 0x7fffffff) +#define ROUND1 51 +#define ROUND2 119 +#define NX 5 +#define NY 3 +static const long double +invpio2 = 6.3661977236758134307553505349005747e-01L, /* 0x145f306dc9c882a53f84eafa3ea6a.0p-113 */ +pio2_1 = 1.5707963267948966192292994253909555e+00L, /* 0x1921fb54442d18469800000000000.0p-112 */ +pio2_1t = 2.0222662487959507323996846200947577e-21L, /* 0x13198a2e03707344a4093822299f3.0p-181 */ +pio2_2 = 2.0222662487959507323994779168837751e-21L, /* 0x13198a2e03707344a400000000000.0p-181 */ +pio2_2t = 2.0670321098263988236496903051604844e-43L, /* 0x127044533e63a0105df531d89cd91.0p-254 */ +pio2_3 = 2.0670321098263988236499468110329591e-43L, /* 0x127044533e63a0105e00000000000.0p-254 */ +pio2_3t = -2.5650587247459238361625433492959285e-65L; /* -0x159c4ec64ddaeb5f78671cbfb2210.0p-327 */ +#endif int __rem_pio2l(long double x, long double *y) { - union IEEEl2bits u,u1; + union ldshape u,uz; long double z,w,t,r,fn; - double tx[3],ty[2]; - int e0,ex,i,j,nx,n; - int16_t expsign; - - u.e = x; - expsign = u.xbits.expsign; - ex = expsign & 0x7fff; - if (ex < BIAS + 25 || (ex == BIAS + 25 && u.bits.manh < 0xc90fdaa2)) { - union IEEEl2bits u2; - int ex1; + double tx[NX],ty[NY]; + int ex,ey,n,i; - /* |x| ~< 2^25*(pi/2), medium size */ - /* Use a specialized rint() to get fn. Assume round-to-nearest. */ - fn = x*invpio2 + 0x1.8p63; - fn = fn - 0x1.8p63; -// FIXME -//#ifdef HAVE_EFFICIENT_IRINT -// n = irint(fn); -//#else - n = fn; -//#endif + u.f = x; + ex = u.i.se & 0x7fff; + if (SMALL(u)) { + /* rint(x/(pi/2)), Assume round-to-nearest. */ + fn = x*invpio2 + TOINT - TOINT; + n = QUOBITS(fn); r = x-fn*pio2_1; - w = fn*pio2_1t; /* 1st round good to 102 bit */ - j = ex; + w = fn*pio2_1t; /* 1st round good to 102/180 bits (ld80/ld128) */ y[0] = r-w; - u2.e = y[0]; - ex1 = u2.xbits.expsign & 0x7fff; - i = j-ex1; - if (i > 22) { /* 2nd iteration needed, good to 141 */ + u.f = y[0]; + ey = u.i.se & 0x7fff; + if (ex - ey > ROUND1) { /* 2nd iteration needed, good to 141/248 (ld80/ld128) */ t = r; w = fn*pio2_2; r = t-w; w = fn*pio2_2t-((t-r)-w); y[0] = r-w; - u2.e = y[0]; - ex1 = u2.xbits.expsign & 0x7fff; - i = j-ex1; - if (i > 61) { /* 3rd iteration need, 180 bits acc */ - t = r; /* will cover all possible cases */ + u.f = y[0]; + ey = u.i.se & 0x7fff; + if (ex - ey > ROUND2) { /* 3rd iteration, good to 180/316 bits */ + t = r; /* will cover all possible cases (not verified for ld128) */ w = fn*pio2_3; r = t-w; w = fn*pio2_3t-((t-r)-w); @@ -102,23 +110,26 @@ int __rem_pio2l(long double x, long double *y) y[0] = y[1] = x - x; return 0; } - /* set z = scalbn(|x|,ilogb(x)-23) */ - u1.e = x; - e0 = ex - BIAS - 23; /* e0 = ilogb(|x|)-23; */ - u1.xbits.expsign = ex - e0; - z = u1.e; - for (i=0; i<2; i++) { + /* set z = scalbn(|x|,-ilogb(x)+23) */ + uz.f = x; + uz.i.se = 0x3fff + 23; + z = uz.f; + for (i=0; i < NX - 1; i++) { tx[i] = (double)(int32_t)z; - z = (z-tx[i])*two24; + 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,2); - r = (long double)ty[0] + ty[1]; - w = ty[1] - (r - ty[0]); - if (expsign < 0) { + tx[i] = z; + while (tx[i] == 0) + i--; + n = __rem_pio2_large(tx, ty, ex-0x3fff-23, i+1, NY); + w = ty[1]; + if (NY == 3) + w += ty[2]; + r = ty[0] + w; + /* TODO: for ld128 this does not follow the recommendation of the + comments of __rem_pio2_large which seem wrong if |ty[0]| > |ty[1]+ty[2]| */ + w -= r - ty[0]; + if (u.i.se >> 15) { y[0] = -r; y[1] = -w; return -n; |