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walnux/libs/libm/openlibm/0004-libs-libc-Openlibm-adds-exp10-and-exp10f-function-im.patch
liwenxiang1 8d09eaaee0 libs/libc:Openlibm adds exp10 and exp10f function implementations 
Signed-off-by: liwenxiang1 <liwenxiang1@xiaomi.com>
2024-10-13 02:31:44 +08:00

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From ec638a9e91c7352bb395c5e38b9724cd987dd884 Mon Sep 17 00:00:00 2001
From: liwenxiang1 <liwenxiang1@xiaomi.com>
Date: Thu, 6 Jun 2024 17:51:39 +0800
Subject: [PATCH] libs/libc:Openlibm adds exp10 and exp10f function
implementations
VELAPLATFO-18651
porting the implementation of glibc ieee754
Change-Id: I994083a1a3118655d67960866c31a659e20ecc35
Signed-off-by: liwenxiang1 <liwenxiang1@xiaomi.com>
---
src/Make.files | 2 +-
src/e_exp10.c | 49 +++++++
src/e_exp10f.c | 318 +++++++++++++++++++++++++++++++++++++++++++++
src/math_private.h | 2 +
4 files changed, 370 insertions(+), 1 deletion(-)
create mode 100644 src/e_exp10.c
create mode 100644 src/e_exp10f.c
diff --git a/src/Make.files b/src/Make.files
index 5170403..77e3c55 100644
--- a/src/Make.files
+++ b/src/Make.files
@@ -1,7 +1,7 @@
$(CUR_SRCS) = common.c \
e_acos.c e_acosf.c e_acosh.c e_acoshf.c e_asin.c e_asinf.c \
e_atan2.c e_atan2f.c e_atanh.c e_atanhf.c e_cosh.c e_coshf.c e_exp.c \
- e_expf.c e_fmod.c e_fmodf.c \
+ e_exp10.c e_expf.c e_exp10f.c e_fmod.c e_fmodf.c \
e_hypot.c e_hypotf.c e_j0.c e_j0f.c e_j1.c e_j1f.c \
e_jn.c e_jnf.c e_lgamma.c e_lgamma_r.c e_lgammaf.c e_lgammaf_r.c \
e_log.c e_log10.c e_log10f.c e_log2.c e_log2f.c e_logf.c \
diff --git a/src/e_exp10.c b/src/e_exp10.c
new file mode 100644
index 0000000..bb75ca8
--- /dev/null
+++ b/src/e_exp10.c
@@ -0,0 +1,49 @@
+/* Copyright (C) 2012-2022 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with the GNU C Library; if not, see
+ <https://www.gnu.org/licenses/>. */
+
+#include <math.h>
+#include <math_private.h>
+#include <float.h>
+
+static const double log10_high = 0x2.4d7637p0;
+static const double log10_low = 0x7.6aaa2b05ba95cp-28;
+
+double
+__ieee754_exp10 (double arg)
+{
+ int32_t lx;
+ double arg_high, arg_low;
+ double exp_high, exp_low;
+
+ if (!isfinite (arg))
+ return __ieee754_exp (arg);
+ if (arg < DBL_MIN_10_EXP - DBL_DIG - 10)
+ return DBL_MIN * DBL_MIN;
+ else if (arg > DBL_MAX_10_EXP + 1)
+ return DBL_MAX * DBL_MAX;
+ else if (fabs (arg) < 0x1p-56)
+ return 1.0;
+
+ GET_LOW_WORD (lx, arg);
+ lx &= 0xf8000000;
+ arg_high = arg;
+ SET_LOW_WORD (arg_high, lx);
+ arg_low = arg - arg_high;
+ exp_high = arg_high * log10_high;
+ exp_low = arg_high * log10_low + arg_low * M_LN10;
+ return __ieee754_exp (exp_high) * __ieee754_exp (exp_low);
+}
diff --git a/src/e_exp10f.c b/src/e_exp10f.c
new file mode 100644
index 0000000..6b74b0c
--- /dev/null
+++ b/src/e_exp10f.c
@@ -0,0 +1,318 @@
+/* Single-precision 10^x function.
+ Copyright (C) 2020-2022 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with the GNU C Library; if not, see
+ <https://www.gnu.org/licenses/>. */
+
+#include <math.h>
+#include <float.h>
+#include <stdint.h>
+#include <math_private.h>
+
+/*
+ EXP2F_TABLE_BITS 5
+ EXP2F_POLY_ORDER 3
+
+ Max. ULP error: 0.502 (normal range, nearest rounding).
+ Max. relative error: 2^-33.240 (before rounding to float).
+ Wrong count: 169839.
+ Non-nearest ULP error: 1 (rounded ULP error).
+
+ Detailed error analysis (for EXP2F_TABLE_BITS=3 thus N=32):
+
+ - We first compute z = RN(InvLn10N * x) where
+
+ InvLn10N = N*log(10)/log(2) * (1 + theta1) with |theta1| < 2^-54.150
+
+ since z is rounded to nearest:
+
+ z = InvLn10N * x * (1 + theta2) with |theta2| < 2^-53
+
+ thus z = N*log(10)/log(2) * x * (1 + theta3) with |theta3| < 2^-52.463
+
+ - Since |x| < 38 in the main branch, we deduce:
+
+ z = N*log(10)/log(2) * x + theta4 with |theta4| < 2^-40.483
+
+ - We then write z = k + r where k is an integer and |r| <= 0.5 (exact)
+
+ - We thus have
+
+ x = z*log(2)/(N*log(10)) - theta4*log(2)/(N*log(10))
+ = z*log(2)/(N*log(10)) + theta5 with |theta5| < 2^-47.215
+
+ 10^x = 2^(k/N) * 2^(r/N) * 10^theta5
+ = 2^(k/N) * 2^(r/N) * (1 + theta6) with |theta6| < 2^-46.011
+
+ - Then 2^(k/N) is approximated by table lookup, the maximal relative error
+ is for (k%N) = 5, with
+
+ s = 2^(i/N) * (1 + theta7) with |theta7| < 2^-53.249
+
+ - 2^(r/N) is approximated by a degree-3 polynomial, where the maximal
+ mathematical relative error is 2^-33.243.
+
+ - For C[0] * r + C[1], assuming no FMA is used, since |r| <= 0.5 and
+ |C[0]| < 1.694e-6, |C[0] * r| < 8.47e-7, and the absolute error on
+ C[0] * r is bounded by 1/2*ulp(8.47e-7) = 2^-74. Then we add C[1] with
+ |C[1]| < 0.000235, thus the absolute error on C[0] * r + C[1] is bounded
+ by 2^-65.994 (z is bounded by 0.000236).
+
+ - For r2 = r * r, since |r| <= 0.5, we have |r2| <= 0.25 and the absolute
+ error is bounded by 1/4*ulp(0.25) = 2^-56 (the factor 1/4 is because |r2|
+ cannot exceed 1/4, and on the left of 1/4 the distance between two
+ consecutive numbers is 1/4*ulp(1/4)).
+
+ - For y = C[2] * r + 1, assuming no FMA is used, since |r| <= 0.5 and
+ |C[2]| < 0.0217, the absolute error on C[2] * r is bounded by 2^-60,
+ and thus the absolute error on C[2] * r + 1 is bounded by 1/2*ulp(1)+2^60
+ < 2^-52.988, and |y| < 1.01085 (the error bound is better if a FMA is
+ used).
+
+ - for z * r2 + y: the absolute error on z is bounded by 2^-65.994, with
+ |z| < 0.000236, and the absolute error on r2 is bounded by 2^-56, with
+ r2 < 0.25, thus |z*r2| < 0.000059, and the absolute error on z * r2
+ (including the rounding error) is bounded by:
+
+ 2^-65.994 * 0.25 + 0.000236 * 2^-56 + 1/2*ulp(0.000059) < 2^-66.429.
+
+ Now we add y, with |y| < 1.01085, and error on y bounded by 2^-52.988,
+ thus the absolute error is bounded by:
+
+ 2^-66.429 + 2^-52.988 + 1/2*ulp(1.01085) < 2^-51.993
+
+ - Now we convert the error on y into relative error. Recall that y
+ approximates 2^(r/N), for |r| <= 0.5 and N=32. Thus 2^(-0.5/32) <= y,
+ and the relative error on y is bounded by
+
+ 2^-51.993/2^(-0.5/32) < 2^-51.977
+
+ - Taking into account the mathematical relative error of 2^-33.243 we have:
+
+ y = 2^(r/N) * (1 + theta8) with |theta8| < 2^-33.242
+
+ - Since we had s = 2^(k/N) * (1 + theta7) with |theta7| < 2^-53.249,
+ after y = y * s we get y = 2^(k/N) * 2^(r/N) * (1 + theta9)
+ with |theta9| < 2^-33.241
+
+ - Finally, taking into account the error theta6 due to the rounding error on
+ InvLn10N, and when multiplying InvLn10N * x, we get:
+
+ y = 10^x * (1 + theta10) with |theta10| < 2^-33.240
+
+ - Converting into binary64 ulps, since y < 2^53*ulp(y), the error is at most
+ 2^19.76 ulp(y)
+
+ - If the result is a binary32 value in the normal range (i.e., >= 2^-126),
+ then the error is at most 2^-9.24 ulps, i.e., less than 0.00166 (in the
+ subnormal range, the error in ulps might be larger).
+
+ Note that this bound is tight, since for x=-0x25.54ac0p0 the final value of
+ y (before conversion to float) differs from 879853 ulps from the correctly
+ rounded value, and 879853 ~ 2^19.7469. */
+
+/* math_narrow_eval reduces its floating-point argument to the range
+ and precision of its semantic type. (The original evaluation may
+ still occur with excess range and precision, so the result may be
+ affected by double rounding.) */
+
+#define TOINT_INTRINSICS 0
+#define WANT_ERRNO_UFLOW 0
+#define FLT_EVAL_METHOD 0
+/* Shared between expf, exp2f, exp10f, and powf. */
+#define EXP2F_TABLE_BITS 5
+#define EXP2F_POLY_ORDER 3
+#define N (1 << EXP2F_TABLE_BITS)
+#define InvLn10N (0x3.5269e12f346e2p0 * N) /* log(10)/log(2) to nearest */
+
+#if (__GNUC__ >= 3) || __has_builtin (__builtin_expect)
+# define __glibc_unlikely(cond) __builtin_expect ((cond), 0)
+# define __glibc_likely(cond) __builtin_expect ((cond), 1)
+#else
+# define __glibc_unlikely(cond) (cond)
+# define __glibc_likely(cond) (cond)
+#endif
+
+#if FLT_EVAL_METHOD == 0
+# define math_narrow_eval(x) (x)
+#else
+# if FLT_EVAL_METHOD == 1
+# define excess_precision(type) __builtin_types_compatible_p (type, float)
+# else
+# define excess_precision(type) (__builtin_types_compatible_p (type, float) \
+ || __builtin_types_compatible_p (type, \
+ double))
+# endif
+# define math_narrow_eval(x) \
+ ({ \
+ __typeof (x) math_narrow_eval_tmp = (x); \
+ if (excess_precision (__typeof (math_narrow_eval_tmp))) \
+ __asm__ ("" : "+m" (math_narrow_eval_tmp)); \
+ math_narrow_eval_tmp; \
+ })
+#endif
+
+const struct exp2f_data
+{
+ uint64_t tab[1 << EXP2F_TABLE_BITS];
+ double shift_scaled;
+ double poly[EXP2F_POLY_ORDER];
+ double shift;
+ double invln2_scaled;
+ double poly_scaled[EXP2F_POLY_ORDER];
+} __exp2f_data;
+
+const struct exp2f_data __exp2f_data = {
+ /* tab[i] = uint(2^(i/N)) - (i << 52-BITS)
+ used for computing 2^(k/N) for an int |k| < 150 N as
+ double(tab[k%N] + (k << 52-BITS)) */
+ .tab = {
+0x3ff0000000000000, 0x3fefd9b0d3158574, 0x3fefb5586cf9890f, 0x3fef9301d0125b51,
+0x3fef72b83c7d517b, 0x3fef54873168b9aa, 0x3fef387a6e756238, 0x3fef1e9df51fdee1,
+0x3fef06fe0a31b715, 0x3feef1a7373aa9cb, 0x3feedea64c123422, 0x3feece086061892d,
+0x3feebfdad5362a27, 0x3feeb42b569d4f82, 0x3feeab07dd485429, 0x3feea47eb03a5585,
+0x3feea09e667f3bcd, 0x3fee9f75e8ec5f74, 0x3feea11473eb0187, 0x3feea589994cce13,
+0x3feeace5422aa0db, 0x3feeb737b0cdc5e5, 0x3feec49182a3f090, 0x3feed503b23e255d,
+0x3feee89f995ad3ad, 0x3feeff76f2fb5e47, 0x3fef199bdd85529c, 0x3fef3720dcef9069,
+0x3fef5818dcfba487, 0x3fef7c97337b9b5f, 0x3fefa4afa2a490da, 0x3fefd0765b6e4540,
+ },
+ .shift_scaled = 0x1.8p+52 / N,
+ .poly = { 0x1.c6af84b912394p-5, 0x1.ebfce50fac4f3p-3, 0x1.62e42ff0c52d6p-1 },
+ .shift = 0x1.8p+52,
+ .invln2_scaled = 0x1.71547652b82fep+0 * N,
+ .poly_scaled = {
+0x1.c6af84b912394p-5/N/N/N, 0x1.ebfce50fac4f3p-3/N/N, 0x1.62e42ff0c52d6p-1/N
+ },
+};
+
+#define T __exp2f_data.tab
+#define C __exp2f_data.poly_scaled
+#define SHIFT __exp2f_data.shift
+
+static inline uint32_t
+asuint (float f)
+{
+ union
+ {
+ float f;
+ uint32_t i;
+ } u = {f};
+ return u.i;
+}
+
+static inline uint64_t
+asuint64 (double f)
+{
+ union
+ {
+ double f;
+ uint64_t i;
+ } u = {f};
+ return u.i;
+}
+
+static inline double
+asdouble (uint64_t i)
+{
+ union
+ {
+ uint64_t i;
+ double f;
+ } u = {i};
+ return u.f;
+}
+
+static inline uint32_t
+top13 (float x)
+{
+ return asuint (x) >> 19;
+}
+
+__attribute__((noinline)) static float
+xflowf (uint32_t sign, float y)
+{
+ y = (sign ? -y : y) * y;
+ return y;
+}
+
+float
+__math_oflowf (uint32_t sign)
+{
+ return xflowf (sign, 0x1p97f);
+}
+
+float
+__math_uflowf (uint32_t sign)
+{
+ return xflowf (sign, 0x1p-95f);
+}
+
+float
+__ieee754_exp10f (float x)
+{
+ uint32_t abstop;
+ uint64_t ki, t;
+ double kd, xd, z, r, r2, y, s;
+
+ xd = (double) x;
+ abstop = top13 (x) & 0xfff; /* Ignore sign. */
+ if (__glibc_unlikely (abstop >= top13 (38.0f)))
+ {
+ /* |x| >= 38 or x is nan. */
+ if (asuint (x) == asuint (-INFINITY))
+ return 0.0f;
+ if (abstop >= top13 (INFINITY))
+ return x + x;
+ /* 0x26.8826ap0 is the largest value such that 10^x < 2^128. */
+ if (x > 0x26.8826ap0f)
+ return __math_oflowf (0);
+ /* -0x2d.278d4p0 is the smallest value such that 10^x > 2^-150. */
+ if (x < -0x2d.278d4p0f)
+ return __math_uflowf (0);
+#if WANT_ERRNO_UFLOW
+ if (x < -0x2c.da7cfp0)
+ return __math_may_uflowf (0);
+#endif
+ /* the smallest value such that 10^x >= 2^-126 (normal range)
+ is x = -0x25.ee060p0 */
+ /* we go through here for 2014929 values out of 2060451840
+ (not counting NaN and infinities, i.e., about 0.1% */
+ }
+
+ /* x*N*Ln10/Ln2 = k + r with r in [-1/2, 1/2] and int k. */
+ z = InvLn10N * xd;
+ /* |xd| < 38 thus |z| < 1216 */
+#if TOINT_INTRINSICS
+ kd = roundtoint (z);
+ ki = converttoint (z);
+#else
+# define SHIFT __exp2f_data.shift
+ kd = math_narrow_eval ((double) (z + SHIFT)); /* Needs to be double. */
+ ki = asuint64 (kd);
+ kd -= SHIFT;
+#endif
+ r = z - kd;
+
+ /* 10^x = 10^(k/N) * 10^(r/N) ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
+ t = T[ki % N];
+ t += ki << (52 - EXP2F_TABLE_BITS);
+ s = asdouble (t);
+ z = C[0] * r + C[1];
+ r2 = r * r;
+ y = C[2] * r + 1;
+ y = z * r2 + y;
+ y = y * s;
+ return (float) y;
+}
diff --git a/src/math_private.h b/src/math_private.h
index f2e0943..ce1ba8b 100644
--- a/src/math_private.h
+++ b/src/math_private.h
@@ -293,6 +293,7 @@ irint(double x)
#define __ieee754_asin asin
#define __ieee754_atan2 atan2
#define __ieee754_exp exp
+#define __ieee754_exp10 exp10
#define __ieee754_cosh cosh
#define __ieee754_fmod fmod
#define __ieee754_pow pow
@@ -316,6 +317,7 @@ irint(double x)
#define __ieee754_asinf asinf
#define __ieee754_atan2f atan2f
#define __ieee754_expf expf
+#define __ieee754_exp10f exp10f
#define __ieee754_coshf coshf
#define __ieee754_fmodf fmodf
#define __ieee754_powf powf
--
2.34.1
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