| /* 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; |
| } |