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Diffstat (limited to 'src/math/__rem_pio2l.c')
| -rw-r--r-- | src/math/__rem_pio2l.c | 131 |
1 files changed, 131 insertions, 0 deletions
diff --git a/src/math/__rem_pio2l.c b/src/math/__rem_pio2l.c new file mode 100644 index 00000000..10af404c --- /dev/null +++ b/src/math/__rem_pio2l.c @@ -0,0 +1,131 @@ +/* origin: FreeBSD /usr/src/lib/msun/ld80/e_rem_pio2.c */ +/* + * ==================================================== + * 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 "libm.h" +#if LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 +/* ld80 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) + +/* + * invpio2: 64 bits of 2/pi + * pio2_1: first 39 bits of pi/2 + * pio2_1t: pi/2 - pio2_1 + * pio2_2: second 39 bits of pi/2 + * pio2_2t: pi/2 - (pio2_1+pio2_2) + * pio2_3: third 39 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 */ +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 */ + +int __rem_pio2l(long double x, long double *y) +{ + union IEEEl2bits u,u1; + 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; + + /* |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 + r = x-fn*pio2_1; + w = fn*pio2_1t; /* 1st round good to 102 bit */ + j = ex; + 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 */ + 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 */ + 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<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 = __rem_pio2_large(tx,ty,e0,nx,2); + r = (long double)ty[0] + ty[1]; + w = ty[1] - (r - ty[0]); + if (expsign < 0) { + y[0] = -r; + y[1] = -w; + return -n; + } + y[0] = r; + y[1] = w; + return n; +} +#endif |