diff options
| -rw-r--r-- | src/math/logf.c | 110 | ||||
| -rw-r--r-- | src/math/logf_data.c | 33 | ||||
| -rw-r--r-- | src/math/logf_data.h | 20 |
3 files changed, 109 insertions, 54 deletions
diff --git a/src/math/logf.c b/src/math/logf.c index 52230a1b..7ee5d7fe 100644 --- a/src/math/logf.c +++ b/src/math/logf.c @@ -1,69 +1,71 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/e_logf.c */ /* - * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. - */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * Single-precision log 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. - * ==================================================== + * Copyright (c) 2017-2018, Arm Limited. + * SPDX-License-Identifier: MIT */ #include <math.h> #include <stdint.h> +#include "libm.h" +#include "logf_data.h" + +/* +LOGF_TABLE_BITS = 4 +LOGF_POLY_ORDER = 4 + +ULP error: 0.818 (nearest rounding.) +Relative error: 1.957 * 2^-26 (before rounding.) +*/ -static const float -ln2_hi = 6.9313812256e-01, /* 0x3f317180 */ -ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */ -/* |(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 T __logf_data.tab +#define A __logf_data.poly +#define Ln2 __logf_data.ln2 +#define N (1 << LOGF_TABLE_BITS) +#define OFF 0x3f330000 float logf(float x) { - union {float f; uint32_t i;} u = {x}; - float_t hfsq,f,s,z,R,w,t1,t2,dk; - uint32_t ix; - int k; + double_t z, r, r2, y, y0, invc, logc; + uint32_t ix, iz, 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) /* log(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; + } + + /* 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 - LOGF_TABLE_BITS)) % N; + k = (int32_t)tmp >> 23; /* arithmetic shift */ + iz = ix - (tmp & 0x1ff << 23); + invc = T[i].invc; + logc = T[i].logc; + z = (double_t)asfloat(iz); - /* 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; + /* log(x) = log1p(z/c-1) + log(c) + k*Ln2 */ + r = z * invc - 1; + y0 = logc + (double_t)k * Ln2; - 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; - dk = k; - return s*(hfsq+R) + dk*ln2_lo - hfsq + f + dk*ln2_hi; + /* Pipelined polynomial evaluation to approximate log1p(r). */ + r2 = r * r; + y = A[1] * r + A[2]; + y = A[0] * r2 + y; + y = y * r2 + (y0 + r); + return eval_as_float(y); } diff --git a/src/math/logf_data.c b/src/math/logf_data.c new file mode 100644 index 00000000..857221f7 --- /dev/null +++ b/src/math/logf_data.c @@ -0,0 +1,33 @@ +/* + * Data definition for logf. + * + * Copyright (c) 2017-2018, Arm Limited. + * SPDX-License-Identifier: MIT + */ + +#include "logf_data.h" + +const struct logf_data __logf_data = { + .tab = { + { 0x1.661ec79f8f3bep+0, -0x1.57bf7808caadep-2 }, + { 0x1.571ed4aaf883dp+0, -0x1.2bef0a7c06ddbp-2 }, + { 0x1.49539f0f010bp+0, -0x1.01eae7f513a67p-2 }, + { 0x1.3c995b0b80385p+0, -0x1.b31d8a68224e9p-3 }, + { 0x1.30d190c8864a5p+0, -0x1.6574f0ac07758p-3 }, + { 0x1.25e227b0b8eap+0, -0x1.1aa2bc79c81p-3 }, + { 0x1.1bb4a4a1a343fp+0, -0x1.a4e76ce8c0e5ep-4 }, + { 0x1.12358f08ae5bap+0, -0x1.1973c5a611cccp-4 }, + { 0x1.0953f419900a7p+0, -0x1.252f438e10c1ep-5 }, + { 0x1p+0, 0x0p+0 }, + { 0x1.e608cfd9a47acp-1, 0x1.aa5aa5df25984p-5 }, + { 0x1.ca4b31f026aap-1, 0x1.c5e53aa362eb4p-4 }, + { 0x1.b2036576afce6p-1, 0x1.526e57720db08p-3 }, + { 0x1.9c2d163a1aa2dp-1, 0x1.bc2860d22477p-3 }, + { 0x1.886e6037841edp-1, 0x1.1058bc8a07ee1p-2 }, + { 0x1.767dcf5534862p-1, 0x1.4043057b6ee09p-2 }, + }, + .ln2 = 0x1.62e42fefa39efp-1, + .poly = { + -0x1.00ea348b88334p-2, 0x1.5575b0be00b6ap-2, -0x1.ffffef20a4123p-2, + } +}; diff --git a/src/math/logf_data.h b/src/math/logf_data.h new file mode 100644 index 00000000..00cff6f8 --- /dev/null +++ b/src/math/logf_data.h @@ -0,0 +1,20 @@ +/* + * Copyright (c) 2017-2018, Arm Limited. + * SPDX-License-Identifier: MIT + */ +#ifndef _LOGF_DATA_H +#define _LOGF_DATA_H + +#include <features.h> + +#define LOGF_TABLE_BITS 4 +#define LOGF_POLY_ORDER 4 +extern hidden const struct logf_data { + struct { + double invc, logc; + } tab[1 << LOGF_TABLE_BITS]; + double ln2; + double poly[LOGF_POLY_ORDER - 1]; /* First order coefficient is 1. */ +} __logf_data; + +#endif |