diff options
Diffstat (limited to 'src/math/log2f.c')
| -rw-r--r-- | src/math/log2f.c | 114 |
1 files changed, 56 insertions, 58 deletions
diff --git a/src/math/log2f.c b/src/math/log2f.c index b3e305fe..c368f88f 100644 --- a/src/math/log2f.c +++ b/src/math/log2f.c @@ -1,74 +1,72 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/e_log2f.c */ /* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * Single-precision log2 function. * - * 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. - * ==================================================== - */ -/* - * See comments in log2.c. + * Copyright (c) 2017-2018, Arm Limited. + * SPDX-License-Identifier: MIT */ #include <math.h> #include <stdint.h> +#include "libm.h" +#include "log2f_data.h" + +/* +LOG2F_TABLE_BITS = 4 +LOG2F_POLY_ORDER = 4 + +ULP error: 0.752 (nearest rounding.) +Relative error: 1.9 * 2^-26 (before rounding.) +*/ -static const float -ivln2hi = 1.4428710938e+00, /* 0x3fb8b000 */ -ivln2lo = -1.7605285393e-04, /* 0xb9389ad4 */ -/* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */ -Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */ -Lg2 = 0xccce13.0p-25, /* 0.40000972152 */ -Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */ -Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */ +#define N (1 << LOG2F_TABLE_BITS) +#define T __log2f_data.tab +#define A __log2f_data.poly +#define OFF 0x3f330000 float log2f(float x) { - union {float f; uint32_t i;} u = {x}; - float_t hfsq,f,s,z,R,w,t1,t2,hi,lo; - uint32_t ix; - int k; + double_t z, r, r2, p, y, y0, invc, logc; + uint32_t ix, iz, top, tmp; + int k, i; - ix = u.i; - k = 0; - if (ix < 0x00800000 || ix>>31) { /* x < 2**-126 */ - if (ix<<1 == 0) - return -1/(x*x); /* log(+-0)=-inf */ - if (ix>>31) - return (x-x)/0.0f; /* log(-#) = NaN */ - /* subnormal number, scale up x */ - k -= 25; - x *= 0x1p25f; - u.f = x; - ix = u.i; - } else if (ix >= 0x7f800000) { - return x; - } else if (ix == 0x3f800000) + ix = asuint(x); + /* Fix sign of zero with downward rounding when x==1. */ + if (WANT_ROUNDING && predict_false(ix == 0x3f800000)) return 0; + if (predict_false(ix - 0x00800000 >= 0x7f800000 - 0x00800000)) { + /* x < 0x1p-126 or inf or nan. */ + if (ix * 2 == 0) + return __math_divzerof(1); + if (ix == 0x7f800000) /* log2(inf) == inf. */ + return x; + if ((ix & 0x80000000) || ix * 2 >= 0xff000000) + return __math_invalidf(x); + /* x is subnormal, normalize it. */ + ix = asuint(x * 0x1p23f); + ix -= 23 << 23; + } - /* reduce x into [sqrt(2)/2, sqrt(2)] */ - ix += 0x3f800000 - 0x3f3504f3; - k += (int)(ix>>23) - 0x7f; - ix = (ix&0x007fffff) + 0x3f3504f3; - u.i = ix; - x = u.f; + /* x = 2^k z; where z is in range [OFF,2*OFF] and exact. + The range is split into N subintervals. + The ith subinterval contains z and c is near its center. */ + tmp = ix - OFF; + i = (tmp >> (23 - LOG2F_TABLE_BITS)) % N; + top = tmp & 0xff800000; + iz = ix - top; + k = (int32_t)tmp >> 23; /* arithmetic shift */ + invc = T[i].invc; + logc = T[i].logc; + z = (double_t)asfloat(iz); - f = x - 1.0f; - s = f/(2.0f + f); - z = s*s; - w = z*z; - t1= w*(Lg2+w*Lg4); - t2= z*(Lg1+w*Lg3); - R = t2 + t1; - hfsq = 0.5f*f*f; + /* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */ + r = z * invc - 1; + y0 = logc + (double_t)k; - hi = f - hfsq; - u.f = hi; - u.i &= 0xfffff000; - hi = u.f; - lo = f - hi - hfsq + s*(hfsq+R); - return (lo+hi)*ivln2lo + lo*ivln2hi + hi*ivln2hi + k; + /* Pipelined polynomial evaluation to approximate log1p(r)/ln2. */ + r2 = r * r; + y = A[1] * r + A[2]; + y = A[0] * r2 + y; + p = A[3] * r + y0; + y = y * r2 + p; + return eval_as_float(y); } |