diff options
Diffstat (limited to 'lib/msun/ld128/e_rem_pio2l.h')
| -rw-r--r-- | lib/msun/ld128/e_rem_pio2l.h | 140 |
1 files changed, 140 insertions, 0 deletions
diff --git a/lib/msun/ld128/e_rem_pio2l.h b/lib/msun/ld128/e_rem_pio2l.h new file mode 100644 index 0000000..5d78c4d --- /dev/null +++ b/lib/msun/ld128/e_rem_pio2l.h @@ -0,0 +1,140 @@ +/* From: @(#)e_rem_pio2.c 1.4 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * Optimized by Bruce D. Evans. + */ + +#include <sys/cdefs.h> +__FBSDID("$FreeBSD$"); + +/* ld128 version of __ieee754_rem_pio2l(x,y) + * + * return the remainder of x rem pi/2 in y[0]+y[1] + * use __kernel_rem_pio2() + */ + +#include <float.h> + +#include "math.h" +#include "math_private.h" +#include "fpmath.h" + +#define BIAS (LDBL_MAX_EXP - 1) + +/* + * XXX need to verify that nonzero integer multiples of pi/2 within the + * range get no closer to a long double than 2**-140, or that + * ilogb(x) + ilogb(min_delta) < 45 - -140. + */ +/* + * invpio2: 113 bits of 2/pi + * pio2_1: first 68 bits of pi/2 + * pio2_1t: pi/2 - pio2_1 + * pio2_2: second 68 bits of pi/2 + * pio2_2t: pi/2 - (pio2_1+pio2_2) + * pio2_3: third 68 bits of pi/2 + * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) + */ + +static const double +zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ +two24 = 1.67772160000000000000e+07; /* 0x41700000, 0x00000000 */ + +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 */ + +static inline __always_inline int +__ieee754_rem_pio2l(long double x, long double *y) +{ + union IEEEl2bits u,u1; + long double z,w,t,r,fn; + double tx[5],ty[3]; + int64_t n; + int e0,ex,i,j,nx; + int16_t expsign; + + u.e = x; + expsign = u.xbits.expsign; + ex = expsign & 0x7fff; + if (ex < BIAS + 45 || ex == BIAS + 45 && + u.bits.manh < 0x921fb54442d1LL) { + /* |x| ~< 2^45*(pi/2), medium size */ + /* Use a specialized rint() to get fn. Assume round-to-nearest. */ + fn = x*invpio2+0x1.8p112; + fn = fn-0x1.8p112; +#ifdef HAVE_EFFICIENT_I64RINT + n = i64rint(fn); +#else + n = fn; +#endif + r = x-fn*pio2_1; + w = fn*pio2_1t; /* 1st round good to 180 bit */ + { + union IEEEl2bits u2; + int ex1; + j = ex; + y[0] = r-w; + u2.e = y[0]; + ex1 = u2.xbits.expsign & 0x7fff; + i = j-ex1; + if(i>51) { /* 2nd iteration needed, good to 248 */ + 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>119) { /* 3rd iteration need, 316 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; + } + } + } + y[1] = (r-y[0])-w; + return n; + } + /* + * all other (large) arguments + */ + if(ex==0x7fff) { /* x is inf or NaN */ + 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<4;i++) { + tx[i] = (double)((int32_t)(z)); + z = (z-tx[i])*two24; + } + tx[4] = z; + nx = 5; + while(tx[nx-1]==zero) nx--; /* skip zero term */ + n = __kernel_rem_pio2(tx,ty,e0,nx,3); + t = (long double)ty[2] + ty[1]; + r = t + ty[0]; + w = ty[0] - (r - t); + if(expsign<0) {y[0] = -r; y[1] = -w; return -n;} + y[0] = r; y[1] = w; return n; +} |
