diff options
Diffstat (limited to 'src/math/sqrtf.c')
| -rw-r--r-- | src/math/sqrtf.c | 140 |
1 files changed, 70 insertions, 70 deletions
diff --git a/src/math/sqrtf.c b/src/math/sqrtf.c index d6ace38a..740d81cb 100644 --- a/src/math/sqrtf.c +++ b/src/math/sqrtf.c @@ -1,83 +1,83 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/e_sqrtf.c */ -/* - * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. - */ -/* - * ==================================================== - * 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. - * ==================================================== - */ - +#include <stdint.h> +#include <math.h> #include "libm.h" +#include "sqrt_data.h" -static const float tiny = 1.0e-30; +#define FENV_SUPPORT 1 -float sqrtf(float x) +static inline uint32_t mul32(uint32_t a, uint32_t b) { - float z; - int32_t sign = (int)0x80000000; - int32_t ix,s,q,m,t,i; - uint32_t r; + return (uint64_t)a*b >> 32; +} - GET_FLOAT_WORD(ix, x); +/* see sqrt.c for more detailed comments. */ - /* take care of Inf and NaN */ - if ((ix&0x7f800000) == 0x7f800000) - return x*x + x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf, sqrt(-inf)=sNaN */ +float sqrtf(float x) +{ + uint32_t ix, m, m1, m0, even, ey; - /* take care of zero */ - if (ix <= 0) { - if ((ix&~sign) == 0) - return x; /* sqrt(+-0) = +-0 */ - if (ix < 0) - return (x-x)/(x-x); /* sqrt(-ve) = sNaN */ - } - /* normalize x */ - m = ix>>23; - if (m == 0) { /* subnormal x */ - for (i = 0; (ix&0x00800000) == 0; i++) - ix<<=1; - m -= i - 1; + ix = asuint(x); + if (predict_false(ix - 0x00800000 >= 0x7f800000 - 0x00800000)) { + /* x < 0x1p-126 or inf or nan. */ + if (ix * 2 == 0) + return x; + if (ix == 0x7f800000) + return x; + if (ix > 0x7f800000) + return __math_invalidf(x); + /* x is subnormal, normalize it. */ + ix = asuint(x * 0x1p23f); + ix -= 23 << 23; } - m -= 127; /* unbias exponent */ - ix = (ix&0x007fffff)|0x00800000; - if (m&1) /* odd m, double x to make it even */ - ix += ix; - m >>= 1; /* m = [m/2] */ - /* generate sqrt(x) bit by bit */ - ix += ix; - q = s = 0; /* q = sqrt(x) */ - r = 0x01000000; /* r = moving bit from right to left */ + /* x = 4^e m; with int e and m in [1, 4). */ + even = ix & 0x00800000; + m1 = (ix << 8) | 0x80000000; + m0 = (ix << 7) & 0x7fffffff; + m = even ? m0 : m1; - while (r != 0) { - t = s + r; - if (t <= ix) { - s = t+r; - ix -= t; - q += r; - } - ix += ix; - r >>= 1; - } + /* 2^e is the exponent part of the return value. */ + ey = ix >> 1; + ey += 0x3f800000 >> 1; + ey &= 0x7f800000; + + /* compute r ~ 1/sqrt(m), s ~ sqrt(m) with 2 goldschmidt iterations. */ + static const uint32_t three = 0xc0000000; + uint32_t r, s, d, u, i; + i = (ix >> 17) % 128; + r = (uint32_t)__rsqrt_tab[i] << 16; + /* |r*sqrt(m) - 1| < 0x1p-8 */ + s = mul32(m, r); + /* |s/sqrt(m) - 1| < 0x1p-8 */ + d = mul32(s, r); + u = three - d; + r = mul32(r, u) << 1; + /* |r*sqrt(m) - 1| < 0x1.7bp-16 */ + s = mul32(s, u) << 1; + /* |s/sqrt(m) - 1| < 0x1.7bp-16 */ + d = mul32(s, r); + u = three - d; + s = mul32(s, u); + /* -0x1.03p-28 < s/sqrt(m) - 1 < 0x1.fp-31 */ + s = (s - 1)>>6; + /* s < sqrt(m) < s + 0x1.08p-23 */ - /* use floating add to find out rounding direction */ - if (ix != 0) { - z = 1.0f - tiny; /* raise inexact flag */ - if (z >= 1.0f) { - z = 1.0f + tiny; - if (z > 1.0f) - q += 2; - else - q += q & 1; - } + /* compute nearest rounded result. */ + uint32_t d0, d1, d2; + float y, t; + d0 = (m << 16) - s*s; + d1 = s - d0; + d2 = d1 + s + 1; + s += d1 >> 31; + s &= 0x007fffff; + s |= ey; + y = asfloat(s); + if (FENV_SUPPORT) { + /* handle rounding and inexact exception. */ + uint32_t tiny = predict_false(d2==0) ? 0 : 0x01000000; + tiny |= (d1^d2) & 0x80000000; + t = asfloat(tiny); + y = eval_as_float(y + t); } - ix = (q>>1) + 0x3f000000; - SET_FLOAT_WORD(z, ix + ((uint32_t)m << 23)); - return z; + return y; } |