| /* @(#)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 (__builtin_expect (ha > 0x5f300000, 0)) /* a>2**500 */ |
| { |
| if (ha >= 0x7ff00000) /* Inf or NaN */ |
| { |
| u_int32_t low; |
| w = a + b; /* for sNaN */ |
| 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)); |
| return t1 * w; |
| } |
| else |
| return w; |
| } |
| strong_alias (__ieee754_hypot, __hypot_finite) |
