1 /* origin: FreeBSD /usr/src/lib/msun/src/e_sqrtf.c */ 2 /* 3 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. 4 */ 5 /* 6 * ==================================================== 7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 8 * 9 * Developed at SunPro, a Sun Microsystems, Inc. business. 10 * Permission to use, copy, modify, and distribute this 11 * software is freely granted, provided that this notice 12 * is preserved. 13 * ==================================================== 14 */ 15 16 #include "libm.h" 17 18 static const float tiny = 1.0e-30; 19 20 float sqrtf(float x) 21 { 22 float z; 23 int32_t sign = (int)0x80000000; 24 int32_t ix,s,q,m,t,i; 25 uint32_t r; 26 27 GET_FLOAT_WORD(ix, x); 28 29 /* take care of Inf and NaN */ 30 if ((ix&0x7f800000) == 0x7f800000) 31 return x*x + x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf, sqrt(-inf)=sNaN */ 32 33 /* take care of zero */ 34 if (ix <= 0) { 35 if ((ix&~sign) == 0) 36 return x; /* sqrt(+-0) = +-0 */ 37 if (ix < 0) 38 return (x-x)/(x-x); /* sqrt(-ve) = sNaN */ 39 } 40 /* normalize x */ 41 m = ix>>23; 42 if (m == 0) { /* subnormal x */ 43 for (i = 0; (ix&0x00800000) == 0; i++) 44 ix<<=1; 45 m -= i - 1; 46 } 47 m -= 127; /* unbias exponent */ 48 ix = (ix&0x007fffff)|0x00800000; 49 if (m&1) /* odd m, double x to make it even */ 50 ix += ix; 51 m >>= 1; /* m = [m/2] */ 52 53 /* generate sqrt(x) bit by bit */ 54 ix += ix; 55 q = s = 0; /* q = sqrt(x) */ 56 r = 0x01000000; /* r = moving bit from right to left */ 57 58 while (r != 0) { 59 t = s + r; 60 if (t <= ix) { 61 s = t+r; 62 ix -= t; 63 q += r; 64 } 65 ix += ix; 66 r >>= 1; 67 } 68 69 /* use floating add to find out rounding direction */ 70 if (ix != 0) { 71 z = 1.0f - tiny; /* raise inexact flag */ 72 if (z >= 1.0f) { 73 z = 1.0f + tiny; 74 if (z > 1.0f) 75 q += 2; 76 else 77 q += q & 1; 78 } 79 } 80 ix = (q>>1) + 0x3f000000; 81 SET_FLOAT_WORD(z, ix + ((uint32_t)m << 23)); 82 return z; 83 } 84