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Diffstat (limited to 'src/math/__rem_pio2.c')
| -rw-r--r-- | src/math/__rem_pio2.c | 176 |
1 files changed, 176 insertions, 0 deletions
diff --git a/src/math/__rem_pio2.c b/src/math/__rem_pio2.c new file mode 100644 index 00000000..a7d779e0 --- /dev/null +++ b/src/math/__rem_pio2.c @@ -0,0 +1,176 @@ +/* origin: FreeBSD /usr/src/lib/msun/src/e_rem_pio2.c */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * 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. + */ +/* __rem_pio2(x,y) + * + * return the remainder of x rem pi/2 in y[0]+y[1] + * use __rem_pio2_large() for large x + */ + +#include "libm.h" + +/* + * invpio2: 53 bits of 2/pi + * pio2_1: first 33 bit of pi/2 + * pio2_1t: pi/2 - pio2_1 + * pio2_2: second 33 bit of pi/2 + * pio2_2t: pi/2 - (pio2_1+pio2_2) + * pio2_3: third 33 bit 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 */ +invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ +pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ +pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ +pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ +pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ +pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ +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; + + GET_HIGH_WORD(hx,x); + ix = hx & 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) { + z = x - pio2_1; /* one round good to 85 bits */ + y[0] = z - pio2_1t; + y[1] = (z-y[0]) - pio2_1t; + return 1; + } else { + z = x + pio2_1; + y[0] = z + pio2_1t; + y[1] = (z-y[0]) + pio2_1t; + return -1; + } + } else { + if (hx > 0) { + z = x - 2*pio2_1; + y[0] = z - 2*pio2_1t; + y[1] = (z-y[0]) - 2*pio2_1t; + return 2; + } else { + z = x + 2*pio2_1; + y[0] = z + 2*pio2_1t; + y[1] = (z-y[0]) + 2*pio2_1t; + return -2; + } + } + } + if (ix <= 0x401c463b) { /* |x| ~<= 9pi/4 */ + if (ix <= 0x4015fdbc) { /* |x| ~<= 7pi/4 */ + if (ix == 0x4012d97c) /* |x| ~= 3pi/2 */ + goto medium; + if (hx > 0) { + z = x - 3*pio2_1; + y[0] = z - 3*pio2_1t; + y[1] = (z-y[0]) - 3*pio2_1t; + return 3; + } else { + z = x + 3*pio2_1; + y[0] = z + 3*pio2_1t; + y[1] = (z-y[0]) + 3*pio2_1t; + return -3; + } + } else { + if (ix == 0x401921fb) /* |x| ~= 4pi/2 */ + goto medium; + if (hx > 0) { + z = x - 4*pio2_1; + y[0] = z - 4*pio2_1t; + y[1] = (z-y[0]) - 4*pio2_1t; + return 4; + } else { + z = x + 4*pio2_1; + y[0] = z + 4*pio2_1t; + y[1] = (z-y[0]) + 4*pio2_1t; + return -4; + } + } + } + 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. */ + STRICT_ASSIGN(double, 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 */ + 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 */ + t = r; + 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 (ix >= 0x7ff00000) { /* x is inf or NaN */ + 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; + } + tx[2] = z; + nx = 3; + while (tx[nx-1] == zero) nx--; /* skip zero term */ + n = __rem_pio2_large(tx,ty,e0,nx,1); + if (hx < 0) { + y[0] = -ty[0]; + y[1] = -ty[1]; + return -n; + } + y[0] = ty[0]; + y[1] = ty[1]; + return n; +} |