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Diffstat (limited to 'REORG.TODO/sysdeps/ieee754/dbl-64/e_hypot.c')
| -rw-r--r-- | REORG.TODO/sysdeps/ieee754/dbl-64/e_hypot.c | 161 |
1 files changed, 161 insertions, 0 deletions
diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_hypot.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_hypot.c new file mode 100644 index 0000000000..76eb408348 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_hypot.c @@ -0,0 +1,161 @@ +/* @(#)e_hypot.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_hypot(x,y) + * + * Method : + * If (assume round-to-nearest) z=x*x+y*y + * has error less than sqrt(2)/2 ulp, than + * sqrt(z) has error less than 1 ulp (exercise). + * + * So, compute sqrt(x*x+y*y) with some care as + * follows to get the error below 1 ulp: + * + * Assume x>y>0; + * (if possible, set rounding to round-to-nearest) + * 1. if x > 2y use + * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y + * where x1 = x with lower 32 bits cleared, x2 = x-x1; else + * 2. if x <= 2y use + * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y)) + * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, + * y1= y with lower 32 bits chopped, y2 = y-y1. + * + * NOTE: scaling may be necessary if some argument is too + * large or too tiny + * + * Special cases: + * hypot(x,y) is INF if x or y is +INF or -INF; else + * hypot(x,y) is NAN if x or y is NAN. + * + * Accuracy: + * hypot(x,y) returns sqrt(x^2+y^2) with error less + * than 1 ulps (units in the last place) + */ + +#include <math.h> +#include <math_private.h> + +double +__ieee754_hypot (double x, double y) +{ + double a, b, t1, t2, y1, y2, w; + int32_t j, k, ha, hb; + + GET_HIGH_WORD (ha, x); + ha &= 0x7fffffff; + GET_HIGH_WORD (hb, y); + hb &= 0x7fffffff; + if (hb > ha) + { + a = y; b = x; j = ha; ha = hb; hb = j; + } + else + { + a = x; b = y; + } + SET_HIGH_WORD (a, ha); /* a <- |a| */ + SET_HIGH_WORD (b, hb); /* b <- |b| */ + if ((ha - hb) > 0x3c00000) + { + return a + b; + } /* x/y > 2**60 */ + k = 0; + if (__glibc_unlikely (ha > 0x5f300000)) /* a>2**500 */ + { + if (ha >= 0x7ff00000) /* Inf or NaN */ + { + u_int32_t low; + w = a + b; /* for sNaN */ + if (issignaling (a) || issignaling (b)) + return w; + GET_LOW_WORD (low, a); + if (((ha & 0xfffff) | low) == 0) + w = a; + GET_LOW_WORD (low, b); + if (((hb ^ 0x7ff00000) | low) == 0) + w = b; + return w; + } + /* scale a and b by 2**-600 */ + ha -= 0x25800000; hb -= 0x25800000; k += 600; + SET_HIGH_WORD (a, ha); + SET_HIGH_WORD (b, hb); + } + if (__builtin_expect (hb < 0x23d00000, 0)) /* b < 2**-450 */ + { + if (hb <= 0x000fffff) /* subnormal b or 0 */ + { + u_int32_t low; + GET_LOW_WORD (low, b); + if ((hb | low) == 0) + return a; + t1 = 0; + SET_HIGH_WORD (t1, 0x7fd00000); /* t1=2^1022 */ + b *= t1; + a *= t1; + k -= 1022; + GET_HIGH_WORD (ha, a); + GET_HIGH_WORD (hb, b); + if (hb > ha) + { + t1 = a; + a = b; + b = t1; + j = ha; + ha = hb; + hb = j; + } + } + else /* scale a and b by 2^600 */ + { + ha += 0x25800000; /* a *= 2^600 */ + hb += 0x25800000; /* b *= 2^600 */ + k -= 600; + SET_HIGH_WORD (a, ha); + SET_HIGH_WORD (b, hb); + } + } + /* medium size a and b */ + w = a - b; + if (w > b) + { + t1 = 0; + SET_HIGH_WORD (t1, ha); + t2 = a - t1; + w = __ieee754_sqrt (t1 * t1 - (b * (-b) - t2 * (a + t1))); + } + else + { + a = a + a; + y1 = 0; + SET_HIGH_WORD (y1, hb); + y2 = b - y1; + t1 = 0; + SET_HIGH_WORD (t1, ha + 0x00100000); + t2 = a - t1; + w = __ieee754_sqrt (t1 * y1 - (w * (-w) - (t1 * y2 + t2 * b))); + } + if (k != 0) + { + u_int32_t high; + t1 = 1.0; + GET_HIGH_WORD (high, t1); + SET_HIGH_WORD (t1, high + (k << 20)); + w *= t1; + math_check_force_underflow_nonneg (w); + return w; + } + else + return w; +} +strong_alias (__ieee754_hypot, __hypot_finite) |