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Diffstat (limited to 'lib/mlibc/options/ansi/musl-generic-math/sqrt.c')
| -rw-r--r-- | lib/mlibc/options/ansi/musl-generic-math/sqrt.c | 185 |
1 files changed, 0 insertions, 185 deletions
diff --git a/lib/mlibc/options/ansi/musl-generic-math/sqrt.c b/lib/mlibc/options/ansi/musl-generic-math/sqrt.c deleted file mode 100644 index b277567..0000000 --- a/lib/mlibc/options/ansi/musl-generic-math/sqrt.c +++ /dev/null @@ -1,185 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/e_sqrt.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. - * ==================================================== - */ -/* sqrt(x) - * Return correctly rounded sqrt. - * ------------------------------------------ - * | Use the hardware sqrt if you have one | - * ------------------------------------------ - * Method: - * Bit by bit method using integer arithmetic. (Slow, but portable) - * 1. Normalization - * Scale x to y in [1,4) with even powers of 2: - * find an integer k such that 1 <= (y=x*2^(2k)) < 4, then - * sqrt(x) = 2^k * sqrt(y) - * 2. Bit by bit computation - * Let q = sqrt(y) truncated to i bit after binary point (q = 1), - * i 0 - * i+1 2 - * s = 2*q , and y = 2 * ( y - q ). (1) - * i i i i - * - * To compute q from q , one checks whether - * i+1 i - * - * -(i+1) 2 - * (q + 2 ) <= y. (2) - * i - * -(i+1) - * If (2) is false, then q = q ; otherwise q = q + 2 . - * i+1 i i+1 i - * - * With some algebric manipulation, it is not difficult to see - * that (2) is equivalent to - * -(i+1) - * s + 2 <= y (3) - * i i - * - * The advantage of (3) is that s and y can be computed by - * i i - * the following recurrence formula: - * if (3) is false - * - * s = s , y = y ; (4) - * i+1 i i+1 i - * - * otherwise, - * -i -(i+1) - * s = s + 2 , y = y - s - 2 (5) - * i+1 i i+1 i i - * - * One may easily use induction to prove (4) and (5). - * Note. Since the left hand side of (3) contain only i+2 bits, - * it does not necessary to do a full (53-bit) comparison - * in (3). - * 3. Final rounding - * After generating the 53 bits result, we compute one more bit. - * Together with the remainder, we can decide whether the - * result is exact, bigger than 1/2ulp, or less than 1/2ulp - * (it will never equal to 1/2ulp). - * The rounding mode can be detected by checking whether - * huge + tiny is equal to huge, and whether huge - tiny is - * equal to huge for some floating point number "huge" and "tiny". - * - * Special cases: - * sqrt(+-0) = +-0 ... exact - * sqrt(inf) = inf - * sqrt(-ve) = NaN ... with invalid signal - * sqrt(NaN) = NaN ... with invalid signal for signaling NaN - */ - -#include "libm.h" - -static const double tiny = 1.0e-300; - -double sqrt(double x) -{ - double z; - int32_t sign = (int)0x80000000; - int32_t ix0,s0,q,m,t,i; - uint32_t r,t1,s1,ix1,q1; - - EXTRACT_WORDS(ix0, ix1, x); - - /* take care of Inf and NaN */ - if ((ix0&0x7ff00000) == 0x7ff00000) { - return x*x + x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf, sqrt(-inf)=sNaN */ - } - /* take care of zero */ - if (ix0 <= 0) { - if (((ix0&~sign)|ix1) == 0) - return x; /* sqrt(+-0) = +-0 */ - if (ix0 < 0) - return (x-x)/(x-x); /* sqrt(-ve) = sNaN */ - } - /* normalize x */ - m = ix0>>20; - if (m == 0) { /* subnormal x */ - while (ix0 == 0) { - m -= 21; - ix0 |= (ix1>>11); - ix1 <<= 21; - } - for (i=0; (ix0&0x00100000) == 0; i++) - ix0<<=1; - m -= i - 1; - ix0 |= ix1>>(32-i); - ix1 <<= i; - } - m -= 1023; /* unbias exponent */ - ix0 = (ix0&0x000fffff)|0x00100000; - if (m & 1) { /* odd m, double x to make it even */ - ix0 += ix0 + ((ix1&sign)>>31); - ix1 += ix1; - } - m >>= 1; /* m = [m/2] */ - - /* generate sqrt(x) bit by bit */ - ix0 += ix0 + ((ix1&sign)>>31); - ix1 += ix1; - q = q1 = s0 = s1 = 0; /* [q,q1] = sqrt(x) */ - r = 0x00200000; /* r = moving bit from right to left */ - - while (r != 0) { - t = s0 + r; - if (t <= ix0) { - s0 = t + r; - ix0 -= t; - q += r; - } - ix0 += ix0 + ((ix1&sign)>>31); - ix1 += ix1; - r >>= 1; - } - - r = sign; - while (r != 0) { - t1 = s1 + r; - t = s0; - if (t < ix0 || (t == ix0 && t1 <= ix1)) { - s1 = t1 + r; - if ((t1&sign) == sign && (s1&sign) == 0) - s0++; - ix0 -= t; - if (ix1 < t1) - ix0--; - ix1 -= t1; - q1 += r; - } - ix0 += ix0 + ((ix1&sign)>>31); - ix1 += ix1; - r >>= 1; - } - - /* use floating add to find out rounding direction */ - if ((ix0|ix1) != 0) { - z = 1.0 - tiny; /* raise inexact flag */ - if (z >= 1.0) { - z = 1.0 + tiny; - if (q1 == (uint32_t)0xffffffff) { - q1 = 0; - q++; - } else if (z > 1.0) { - if (q1 == (uint32_t)0xfffffffe) - q++; - q1 += 2; - } else - q1 += q1 & 1; - } - } - ix0 = (q>>1) + 0x3fe00000; - ix1 = q1>>1; - if (q&1) - ix1 |= sign; - ix0 += m << 20; - INSERT_WORDS(z, ix0, ix1); - return z; -} |