Upgrade arm-optimized-routines to 6b594432c8ac46e71686ea21fad30d1c3f79e65a
Test: None
Change-Id: Ib4c9a5f8b339cf2bdef415c25ac8b840ccb12930
diff --git a/Android.bp b/Android.bp
index f22981c..3f3f563 100755
--- a/Android.bp
+++ b/Android.bp
@@ -12,30 +12,7 @@
"-ffp-contract=fast",
],
srcs: [
- "math/cosf.c",
- "math/exp2.c",
- "math/exp2f.c",
- "math/exp2f_data.c",
- "math/exp.c",
- "math/exp_data.c",
- "math/expf.c",
- "math/log2.c",
- "math/log2_data.c",
- "math/log2f.c",
- "math/log2f_data.c",
- "math/log.c",
- "math/log_data.c",
- "math/logf.c",
- "math/logf_data.c",
- "math/math_err.c",
- "math/math_errf.c",
- "math/pow.c",
- "math/pow_log_data.c",
- "math/powf.c",
- "math/powf_log2_data.c",
- "math/sincosf.c",
- "math/sincosf_data.c",
- "math/sinf.c",
+ "math/*.c",
],
// arch-specific settings
@@ -69,10 +46,9 @@
host_supported: true,
cflags: ["-Werror", "-Wno-missing-braces"],
srcs: [
- "math/single/e_rem_pio2.c",
- "test/mathtest.c"
+ "math/test/mathtest.c"
],
- data: ["test/testcases/directed/*.tst"],
+ data: ["math/test/testcases/directed/*.tst"],
local_include_dirs: ["math/include"],
target: {
darwin: {
diff --git a/LICENSE b/LICENSE
index 453ae10..2543b82 100644
--- a/LICENSE
+++ b/LICENSE
@@ -1,6 +1,6 @@
MIT License
-Copyright (c) 1999-2018, Arm Limited.
+Copyright (c) 1999-2019, Arm Limited.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
diff --git a/METADATA b/METADATA
index dd1a535..7c706d5 100644
--- a/METADATA
+++ b/METADATA
@@ -9,11 +9,11 @@
type: GIT
value: "https://github.com/ARM-software/optimized-routines.git"
}
- version: "c7a7debc08741736d4836245b45e555fbf2390ed"
+ version: "6b594432c8ac46e71686ea21fad30d1c3f79e65a"
license_type: NOTICE
last_upgrade_date {
year: 2019
month: 7
- day: 10
+ day: 31
}
}
diff --git a/Makefile b/Makefile
index f5b5d3b..8305684 100644
--- a/Makefile
+++ b/Makefile
@@ -1,6 +1,6 @@
# Makefile - requires GNU make
#
-# Copyright (c) 2018, Arm Limited.
+# Copyright (c) 2018-2019, Arm Limited.
# SPDX-License-Identifier: MIT
srcdir = .
@@ -9,55 +9,38 @@
libdir = $(prefix)/lib
includedir = $(prefix)/include
-MATH_SRCS = $(wildcard $(srcdir)/math/*.[cS])
-MATH_BASE = $(basename $(MATH_SRCS))
-MATH_OBJS = $(MATH_BASE:$(srcdir)/%=build/%.o)
-RTEST_SRCS = $(wildcard $(srcdir)/test/rtest/*.[cS])
-RTEST_BASE = $(basename $(RTEST_SRCS))
-RTEST_OBJS = $(RTEST_BASE:$(srcdir)/%=build/%.o)
-ALL_OBJS = $(MATH_OBJS) \
- $(RTEST_OBJS) \
- build/test/mathtest.o \
- build/test/mathbench.o \
-
-INCLUDES = $(wildcard $(srcdir)/math/include/*.h)
-ALL_INCLUDES = $(INCLUDES:$(srcdir)/math/%=build/%)
-
-ALL_LIBS = \
- build/lib/libmathlib.so \
- build/lib/libmathlib.a \
-
-ALL_TOOLS = \
- build/bin/mathtest \
- build/bin/mathbench \
- build/bin/mathbench_libc \
-
-HOST_TOOLS = \
- build/bin/rtest \
-
-TESTS = $(wildcard $(srcdir)/test/testcases/directed/*.tst)
-RTESTS = $(wildcard $(srcdir)/test/testcases/random/*.tst)
+# Build targets
+ALL_OBJS = $(math-objs) $(string-objs)
+ALL_INCLUDES = $(math-includes) $(string-includes)
+ALL_LIBS = $(math-libs) $(string-libs)
+ALL_TOOLS = $(math-tools) $(string-tools)
+HOST_TOOLS = $(math-host-tools)
# Configure these in config.mk, do not make changes in this file.
HOST_CC = cc
HOST_CFLAGS = -std=c99 -O2
HOST_LDFLAGS =
-HOST_LDLIBS = -lm -lmpfr -lmpc
+HOST_LDLIBS =
EMULATOR =
CFLAGS = -std=c99 -O2
LDFLAGS =
-LDLIBS = -lm
+LDLIBS =
CPPFLAGS =
AR = $(CROSS_COMPILE)ar
RANLIB = $(CROSS_COMPILE)ranlib
INSTALL = install
-CFLAGS_ALL = -I$(srcdir)/math/include $(CPPFLAGS) $(CFLAGS)
+CFLAGS_ALL = -Ibuild/include $(CPPFLAGS) $(CFLAGS)
LDFLAGS_ALL = $(LDFLAGS)
+all:
+
-include config.mk
-all: $(ALL_LIBS) $(ALL_TOOLS) $(ALL_INCLUDES)
+include math/Dir.mk
+include string/Dir.mk
+
+all: all-math all-string
DIRS = $(dir $(ALL_LIBS) $(ALL_TOOLS) $(ALL_OBJS) $(ALL_INCLUDES))
ALL_DIRS = $(sort $(DIRS:%/=%))
@@ -69,11 +52,6 @@
$(ALL_OBJS:%.o=%.os): CFLAGS_ALL += -fPIC
-$(RTEST_OBJS): CC = $(HOST_CC)
-$(RTEST_OBJS): CFLAGS_ALL = $(HOST_CFLAGS)
-
-build/test/mathtest.o: CFLAGS_ALL += -fmath-errno
-
build/%.o: $(srcdir)/%.S
$(CC) $(CFLAGS_ALL) -c -o $@ $<
@@ -86,29 +64,6 @@
build/%.os: $(srcdir)/%.c
$(CC) $(CFLAGS_ALL) -c -o $@ $<
-build/lib/libmathlib.so: $(MATH_OBJS:%.o=%.os)
- $(CC) $(CFLAGS_ALL) $(LDFLAGS_ALL) -shared -o $@ $^
-
-build/lib/libmathlib.a: $(MATH_OBJS)
- rm -f $@
- $(AR) rc $@ $^
- $(RANLIB) $@
-
-build/bin/rtest: $(RTEST_OBJS)
- $(HOST_CC) $(HOST_CFLAGS) $(HOST_LDFLAGS) -o $@ $^ $(HOST_LDLIBS)
-
-build/bin/mathtest: build/test/mathtest.o build/lib/libmathlib.a
- $(CC) $(CFLAGS_ALL) $(LDFLAGS_ALL) -static -o $@ $^ $(LDLIBS)
-
-build/bin/mathbench: build/test/mathbench.o build/lib/libmathlib.a
- $(CC) $(CFLAGS_ALL) $(LDFLAGS_ALL) -static -o $@ $^ $(LDLIBS)
-
-build/bin/mathbench_libc: build/test/mathbench.o
- $(CC) $(CFLAGS_ALL) $(LDFLAGS_ALL) -static -o $@ $^ $(LDLIBS)
-
-build/include/%.h: $(srcdir)/math/include/%.h
- cp $< $@
-
clean:
rm -rf build
@@ -135,12 +90,6 @@
install: install-libs install-headers
-check: $(ALL_TOOLS)
- cat $(TESTS) | $(EMULATOR) build/bin/mathtest
+check: check-math check-string
-rcheck: $(HOST_TOOLS) $(ALL_TOOLS)
- cat $(RTESTS) | build/bin/rtest | $(EMULATOR) build/bin/mathtest
-
-check-all: check rcheck
-
-.PHONY: all clean distclean install install-tools install-libs install-headers check rcheck check-all
+.PHONY: all clean distclean install install-tools install-libs install-headers check
diff --git a/README b/README
index 7c6811b..f0345ba 100644
--- a/README
+++ b/README
@@ -8,16 +8,16 @@
Source code layout:
-auxiliary/ - design tools.
build/ - build directory (created by make).
-math/ - math library source.
+math/ - math subproject sources.
math/include/ - math library public headers.
-math/single/ - code for cpu with only single precision support.
-test/ - test related source.
-test/rtest/ - test generator (requires mpfr and mpc).
-test/testcases/ - test cases.
+math/test/ - math test and benchmark related sources.
+math/tools/ - tools used for designing the algorithms.
+string/ - string routines subproject sources.
+string/include/ - string library public headers.
+string/test/ - string test and benchmark related sources.
-The steps to build the library and run the tests:
+The steps to build the target libraries and run the tests:
cp config.mk.dist config.mk
# edit config.mk if necessary ...
@@ -38,6 +38,3 @@
For cross build, CROSS_COMPILE should be set in config.mk and EMULATOR
should be set for cross testing (e.g. using qemu-user or remote access
to a target machine), see the examples in config.mk.dist.
-
-The script "remez.jl" was used to generate some of the coefficients
-(see comments in the code).
diff --git a/config.mk.dist b/config.mk.dist
index 7cf7393..36f67d8 100644
--- a/config.mk.dist
+++ b/config.mk.dist
@@ -15,15 +15,15 @@
HOST_CFLAGS += -g
CFLAGS += -g
-# Use if the target FPU only supports single precision.
-#CFLAGS += WANT_SINGLEPREC
+# Use if mpfr is available on the target for ulp error checking.
+#LDLIBS += -lmpfr -lgmp
+#CFLAGS += -DUSE_MPFR
# Use with gcc.
CFLAGS += -frounding-math -fexcess-precision=standard -fno-stack-protector
CFLAGS += -ffp-contract=fast -fno-math-errno
# Use with clang.
-#CFLAGS += -DCLANG_EXCEPTIONS
#CFLAGS += -ffp-contract=fast
# Use for cross compilation with gcc.
diff --git a/math/Dir.mk b/math/Dir.mk
new file mode 100644
index 0000000..131f82a
--- /dev/null
+++ b/math/Dir.mk
@@ -0,0 +1,97 @@
+# Makefile fragment - requires GNU make
+#
+# Copyright (c) 2019, Arm Limited.
+# SPDX-License-Identifier: MIT
+
+math-lib-srcs := $(wildcard $(srcdir)/math/*.[cS])
+math-test-srcs := \
+ $(srcdir)/math/test/mathtest.c \
+ $(srcdir)/math/test/mathbench.c \
+ $(srcdir)/math/test/ulp.c \
+
+math-test-host-srcs := $(wildcard $(srcdir)/math/test/rtest/*.[cS])
+math-includes-src := $(wildcard $(srcdir)/math/include/*.h)
+math-includes := $(math-includes-src:$(srcdir)/math/%=build/%)
+
+math-libs := \
+ build/lib/libmathlib.so \
+ build/lib/libmathlib.a \
+
+math-tools := \
+ build/bin/mathtest \
+ build/bin/mathbench \
+ build/bin/mathbench_libc \
+ build/bin/runulp.sh \
+ build/bin/ulp \
+
+math-host-tools := \
+ build/bin/rtest \
+
+math-lib-base := $(basename $(math-lib-srcs))
+math-lib-objs := $(math-lib-base:$(srcdir)/%=build/%.o)
+math-test-base := $(basename $(math-test-srcs))
+math-test-objs := $(math-test-base:$(srcdir)/%=build/%.o)
+math-test-host-base := $(basename $(math-test-host-srcs))
+math-test-host-objs := $(math-test-host-base:$(srcdir)/%=build/%.o)
+
+math-objs := \
+ $(math-lib-objs) \
+ $(math-test-objs) \
+ $(math-test-host-objs) \
+
+all-math: $(math-libs) $(math-tools) $(math-includes)
+
+TESTS = $(wildcard $(srcdir)/math/test/testcases/directed/*.tst)
+RTESTS = $(wildcard $(srcdir)/math/test/testcases/random/*.tst)
+
+$(math-objs) $(math-objs:%.o=%.os): $(math-includes)
+build/math/test/mathtest.o: CFLAGS_ALL += -fmath-errno
+$(math-test-host-objs): CC = $(HOST_CC)
+$(math-test-host-objs): CFLAGS_ALL = $(HOST_CFLAGS)
+
+build/math/test/ulp.o: $(srcdir)/math/test/ulp.h
+
+build/lib/libmathlib.so: $(math-lib-objs:%.o=%.os)
+ $(CC) $(CFLAGS_ALL) $(LDFLAGS_ALL) -shared -o $@ $^
+
+build/lib/libmathlib.a: $(math-lib-objs)
+ rm -f $@
+ $(AR) rc $@ $^
+ $(RANLIB) $@
+
+$(math-host-tools): HOST_LDLIBS += -lm -lmpfr -lmpc
+$(math-tools): LDLIBS += -lm
+
+build/bin/rtest: $(math-test-host-objs)
+ $(HOST_CC) $(HOST_CFLAGS) $(HOST_LDFLAGS) -o $@ $^ $(HOST_LDLIBS)
+
+build/bin/mathtest: build/math/test/mathtest.o build/lib/libmathlib.a
+ $(CC) $(CFLAGS_ALL) $(LDFLAGS_ALL) -static -o $@ $^ $(LDLIBS)
+
+build/bin/mathbench: build/math/test/mathbench.o build/lib/libmathlib.a
+ $(CC) $(CFLAGS_ALL) $(LDFLAGS_ALL) -static -o $@ $^ $(LDLIBS)
+
+build/bin/mathbench_libc: build/math/test/mathbench.o
+ $(CC) $(CFLAGS_ALL) $(LDFLAGS_ALL) -static -o $@ $^ $(LDLIBS)
+
+build/bin/ulp: build/math/test/ulp.o build/lib/libmathlib.a
+ $(CC) $(CFLAGS_ALL) $(LDFLAGS_ALL) -static -o $@ $^ $(LDLIBS)
+
+build/include/%.h: $(srcdir)/math/include/%.h
+ cp $< $@
+
+build/bin/%.sh: $(srcdir)/math/test/%.sh
+ cp $< $@
+
+check-math-test: $(math-tools)
+ cat $(TESTS) | $(EMULATOR) build/bin/mathtest
+
+check-math-rtest: $(math-host-tools) $(math-tools)
+ cat $(RTESTS) | build/bin/rtest | $(EMULATOR) build/bin/mathtest
+
+check-math-ulp: $(math-tools)
+ build/bin/runulp.sh $(EMULATOR)
+
+check-math: check-math-test check-math-rtest check-math-ulp
+
+.PHONY: all-math check-math-test check-math-rtest check-math-ulp check-math
diff --git a/math/cosf.c b/math/cosf.c
index 84a138f..831b39e 100644
--- a/math/cosf.c
+++ b/math/cosf.c
@@ -5,10 +5,6 @@
* SPDX-License-Identifier: MIT
*/
-#if WANT_SINGLEPREC
-#include "single/s_cosf.c"
-#else
-
#include <stdint.h>
#include <math.h>
#include "math_config.h"
@@ -65,5 +61,3 @@
else
return __math_invalidf (y);
}
-
-#endif
diff --git a/math/expf.c b/math/expf.c
index f8238a7..0fe1f7d 100644
--- a/math/expf.c
+++ b/math/expf.c
@@ -5,10 +5,6 @@
* SPDX-License-Identifier: MIT
*/
-#if WANT_SINGLEPREC
-#include "single/e_expf.c"
-#else
-
#include <math.h>
#include <stdint.h>
#include "math_config.h"
@@ -93,4 +89,3 @@
strong_alias (expf, __expf_finite)
hidden_alias (expf, __ieee754_expf)
#endif
-#endif
diff --git a/math/funder.c b/math/funder.c
deleted file mode 100644
index 14fdd2e..0000000
--- a/math/funder.c
+++ /dev/null
@@ -1,3 +0,0 @@
-#if WANT_SINGLEPREC
-#include "single/funder.c"
-#endif
diff --git a/math/logf.c b/math/logf.c
index 9c3657b..ee3120a 100644
--- a/math/logf.c
+++ b/math/logf.c
@@ -5,10 +5,6 @@
* SPDX-License-Identifier: MIT
*/
-#if WANT_SINGLEPREC
-#include "single/e_logf.c"
-#else
-
#include <math.h>
#include <stdint.h>
#include "math_config.h"
@@ -81,4 +77,3 @@
strong_alias (logf, __logf_finite)
hidden_alias (logf, __ieee754_logf)
#endif
-#endif
diff --git a/math/logf_data.c b/math/logf_data.c
index cee9271..53c5f62 100644
--- a/math/logf_data.c
+++ b/math/logf_data.c
@@ -5,8 +5,6 @@
* SPDX-License-Identifier: MIT
*/
-#if !WANT_SINGLEPREC
-
#include "math_config.h"
const struct logf_data __logf_data = {
@@ -33,4 +31,3 @@
-0x1.00ea348b88334p-2, 0x1.5575b0be00b6ap-2, -0x1.ffffef20a4123p-2,
}
};
-#endif
diff --git a/math/powf.c b/math/powf.c
index 1149842..1534a09 100644
--- a/math/powf.c
+++ b/math/powf.c
@@ -5,10 +5,6 @@
* SPDX-License-Identifier: MIT
*/
-#if WANT_SINGLEPREC
-#include "single/e_powf.c"
-#else
-
#include <math.h>
#include <stdint.h>
#include "math_config.h"
@@ -223,4 +219,3 @@
strong_alias (powf, __powf_finite)
hidden_alias (powf, __ieee754_powf)
#endif
-#endif
diff --git a/math/powf_log2_data.c b/math/powf_log2_data.c
index 285d1bd..b9fbdc4 100644
--- a/math/powf_log2_data.c
+++ b/math/powf_log2_data.c
@@ -5,8 +5,6 @@
* SPDX-License-Identifier: MIT
*/
-#if !WANT_SINGLEPREC
-
#include "math_config.h"
const struct powf_log2_data __powf_log2_data = {
@@ -34,4 +32,3 @@
0x1.71547652ab82bp0 * POWF_SCALE,
}
};
-#endif
diff --git a/math/rem_pio2.c b/math/rem_pio2.c
deleted file mode 100644
index 16edd74..0000000
--- a/math/rem_pio2.c
+++ /dev/null
@@ -1 +0,0 @@
-#include "single/e_rem_pio2.c"
diff --git a/math/rredf.c b/math/rredf.c
deleted file mode 100644
index fde20f0..0000000
--- a/math/rredf.c
+++ /dev/null
@@ -1,3 +0,0 @@
-#if WANT_SINGLEPREC
-#include "single/rredf.c"
-#endif
diff --git a/math/sincosf.c b/math/sincosf.c
index fb6a29d..e6cd41e 100644
--- a/math/sincosf.c
+++ b/math/sincosf.c
@@ -5,10 +5,6 @@
* SPDX-License-Identifier: MIT
*/
-#if WANT_SINGLEPREC
-#include "single/s_sincosf.c"
-#else
-
#include <stdint.h>
#include <math.h>
#include "math_config.h"
@@ -81,5 +77,3 @@
#endif
}
}
-
-#endif
diff --git a/math/sincosf_data.c b/math/sincosf_data.c
index 2512f37..5d0b58e 100644
--- a/math/sincosf_data.c
+++ b/math/sincosf_data.c
@@ -5,8 +5,6 @@
* SPDX-License-Identifier: MIT
*/
-#if !WANT_SINGLEPREC
-
#include <stdint.h>
#include <math.h>
#include "math_config.h"
@@ -63,5 +61,3 @@
0x34ddc0db, 0xddc0db62, 0xc0db6295, 0xdb629599,
0x6295993c, 0x95993c43, 0x993c4390, 0x3c439041
};
-
-#endif
diff --git a/math/sinf.c b/math/sinf.c
index f624cde..770b294 100644
--- a/math/sinf.c
+++ b/math/sinf.c
@@ -5,10 +5,6 @@
* SPDX-License-Identifier: MIT
*/
-#if WANT_SINGLEPREC
-#include "single/s_sinf.c"
-#else
-
#include <math.h>
#include "math_config.h"
#include "sincosf.h"
@@ -69,5 +65,3 @@
else
return __math_invalidf (y);
}
-
-#endif
diff --git a/math/single/dunder.c b/math/single/dunder.c
deleted file mode 100644
index faec985..0000000
--- a/math/single/dunder.c
+++ /dev/null
@@ -1,52 +0,0 @@
-/*
- * dunder.c - manually provoke FP exceptions for mathlib
- *
- * Copyright (c) 2009-2018, Arm Limited.
- * SPDX-License-Identifier: MIT
- */
-
-
-#include "math_private.h"
-#include <fenv.h>
-
-__inline double __mathlib_dbl_infnan(double x)
-{
- return x+x;
-}
-
-__inline double __mathlib_dbl_infnan2(double x, double y)
-{
- return x+y;
-}
-
-double __mathlib_dbl_underflow(void)
-{
-#ifdef CLANG_EXCEPTIONS
- feraiseexcept(FE_UNDERFLOW);
-#endif
- return 0x1p-767 * 0x1p-767;
-}
-
-double __mathlib_dbl_overflow(void)
-{
-#ifdef CLANG_EXCEPTIONS
- feraiseexcept(FE_OVERFLOW);
-#endif
- return 0x1p+769 * 0x1p+769;
-}
-
-double __mathlib_dbl_invalid(void)
-{
-#ifdef CLANG_EXCEPTIONS
- feraiseexcept(FE_INVALID);
-#endif
- return 0.0 / 0.0;
-}
-
-double __mathlib_dbl_divzero(void)
-{
-#ifdef CLANG_EXCEPTIONS
- feraiseexcept(FE_DIVBYZERO);
-#endif
- return 1.0 / 0.0;
-}
diff --git a/math/single/e_expf.c b/math/single/e_expf.c
deleted file mode 100644
index 739fe1d..0000000
--- a/math/single/e_expf.c
+++ /dev/null
@@ -1,117 +0,0 @@
-/*
- * e_expf.c - single-precision exp function
- *
- * Copyright (c) 2009-2018, Arm Limited.
- * SPDX-License-Identifier: MIT
- */
-
-/*
- * Algorithm was once taken from Cody & Waite, but has been munged
- * out of all recognition by SGT.
- */
-
-#include <math.h>
-#include <errno.h>
-#include "math_private.h"
-
-float
-expf(float X)
-{
- int N; float XN, g, Rg, Result;
- unsigned ix = fai(X), edgecaseflag = 0;
-
- /*
- * Handle infinities, NaNs and big numbers.
- */
- if (__builtin_expect((ix << 1) - 0x67000000 > 0x85500000 - 0x67000000, 0)) {
- if (!(0x7f800000 & ~ix)) {
- if (ix == 0xff800000)
- return 0.0f;
- else
- return FLOAT_INFNAN(X);/* do the right thing with both kinds of NaN and with +inf */
- } else if ((ix << 1) < 0x67000000) {
- return 1.0f; /* magnitude so small the answer can't be distinguished from 1 */
- } else if ((ix << 1) > 0x85a00000) {
- __set_errno(ERANGE);
- if (ix & 0x80000000) {
- return FLOAT_UNDERFLOW;
- } else {
- return FLOAT_OVERFLOW;
- }
- } else {
- edgecaseflag = 1;
- }
- }
-
- /*
- * Split the input into an integer multiple of log(2)/4, and a
- * fractional part.
- */
- XN = X * (4.0f*1.4426950408889634074f);
-#ifdef __TARGET_FPU_SOFTVFP
- XN = _frnd(XN);
- N = (int)XN;
-#else
- N = (int)(XN + (ix & 0x80000000 ? -0.5f : 0.5f));
- XN = N;
-#endif
- g = (X - XN * 0x1.62ep-3F) - XN * 0x1.0bfbe8p-17F; /* prec-and-a-half representation of log(2)/4 */
-
- /*
- * Now we compute exp(X) in, conceptually, three parts:
- * - a pure power of two which we get from N>>2
- * - exp(g) for g in [-log(2)/8,+log(2)/8], which we compute
- * using a Remez-generated polynomial approximation
- * - exp(k*log(2)/4) (aka 2^(k/4)) for k in [0..3], which we
- * get from a lookup table in precision-and-a-half and
- * multiply by g.
- *
- * We gain a bit of extra precision by the fact that actually
- * our polynomial approximation gives us exp(g)-1, and we add
- * the 1 back on by tweaking the prec-and-a-half multiplication
- * step.
- *
- * Coefficients generated by the command
-
-./auxiliary/remez.jl --variable=g --suffix=f -- '-log(BigFloat(2))/8' '+log(BigFloat(2))/8' 3 0 '(expm1(x))/x'
-
- */
- Rg = g * (
- 9.999999412829185331953781321128516523408059996430919985217971370689774264850229e-01f+g*(4.999999608551332693833317084753864837160947932961832943901913087652889900683833e-01f+g*(1.667292360203016574303631953046104769969440903672618034272397630620346717392378e-01f+g*(4.168230895653321517750133783431970715648192153539929404872173693978116154823859e-02f)))
- );
-
- /*
- * Do the table lookup and combine it with Rg, to get our final
- * answer apart from the exponent.
- */
- {
- static const float twotokover4top[4] = { 0x1p+0F, 0x1.306p+0F, 0x1.6ap+0F, 0x1.ae8p+0F };
- static const float twotokover4bot[4] = { 0x0p+0F, 0x1.fc1464p-13F, 0x1.3cccfep-13F, 0x1.3f32b6p-13F };
- static const float twotokover4all[4] = { 0x1p+0F, 0x1.306fep+0F, 0x1.6a09e6p+0F, 0x1.ae89fap+0F };
- int index = (N & 3);
- Rg = twotokover4top[index] + (twotokover4bot[index] + twotokover4all[index]*Rg);
- N >>= 2;
- }
-
- /*
- * Combine the output exponent and mantissa, and return.
- */
- if (__builtin_expect(edgecaseflag, 0)) {
- Result = fhex(((N/2) << 23) + 0x3f800000);
- Result *= Rg;
- Result *= fhex(((N-N/2) << 23) + 0x3f800000);
- /*
- * Step not mentioned in C&W: set errno reliably.
- */
- if (fai(Result) == 0)
- return MATHERR_EXPF_UFL(Result);
- if (fai(Result) == 0x7f800000)
- return MATHERR_EXPF_OFL(Result);
- return FLOAT_CHECKDENORM(Result);
- } else {
- Result = fhex(N * 8388608.0f + (float)0x3f800000);
- Result *= Rg;
- }
-
- return Result;
-}
diff --git a/math/single/e_logf.c b/math/single/e_logf.c
deleted file mode 100644
index aa29489..0000000
--- a/math/single/e_logf.c
+++ /dev/null
@@ -1,153 +0,0 @@
-/*
- * e_logf.c - single precision log function
- *
- * Copyright (c) 2009-2018, Arm Limited.
- * SPDX-License-Identifier: MIT
- */
-
-/*
- * Algorithm was once taken from Cody & Waite, but has been munged
- * out of all recognition by SGT.
- */
-
-#include <math.h>
-#include <errno.h>
-#include "math_private.h"
-
-float
-logf(float X)
-{
- int N = 0;
- int aindex;
- float a, x, s;
- unsigned ix = fai(X);
-
- if (__builtin_expect((ix - 0x00800000) >= 0x7f800000 - 0x00800000, 0)) {
- if ((ix << 1) > 0xff000000) /* NaN */
- return FLOAT_INFNAN(X);
- if (ix == 0x7f800000) /* +inf */
- return X;
- if (X < 0) { /* anything negative */
- return MATHERR_LOGF_NEG(X);
- }
- if (X == 0) {
- return MATHERR_LOGF_0(X);
- }
- /* That leaves denormals. */
- N = -23;
- X *= 0x1p+23F;
- ix = fai(X);
- }
-
- /*
- * Separate X into three parts:
- * - 2^N for some integer N
- * - a number a of the form (1+k/8) for k=0,...,7
- * - a residual which we compute as s = (x-a)/(x+a), for
- * x=X/2^N.
- *
- * We pick the _nearest_ (N,a) pair, so that (x-a) has magnitude
- * at most 1/16. Hence, we must round things that are just
- * _below_ a power of two up to the next power of two, so this
- * isn't as simple as extracting the raw exponent of the FP
- * number. Instead we must grab the exponent together with the
- * top few bits of the mantissa, and round (in integers) there.
- */
- {
- int rounded = ix + 0x00080000;
- int Nnew = (rounded >> 23) - 127;
- aindex = (rounded >> 20) & 7;
- a = fhex(0x3f800000 + (aindex << 20));
- N += Nnew;
- x = fhex(ix - (Nnew << 23));
- }
-
- if (!N && !aindex) {
- /*
- * Use an alternative strategy for very small |x|, which
- * avoids the 1ULP of relative error introduced in the
- * computation of s. If our nearest (N,a) pair is N=0,a=1,
- * that means we have -1/32 < x-a < 1/16, on which interval
- * the ordinary series for log(1+z) (setting z-x-a) will
- * converge adequately fast; so we can simply find an
- * approximation to log(1+z)/z good on that interval and
- * scale it by z on the way out.
- *
- * Coefficients generated by the command
-
-./auxiliary/remez.jl --variable=z --suffix=f -- '-1/BigFloat(32)' '+1/BigFloat(16)' 3 0 '(log1p(x)-x)/x^2'
-
- */
- float z = x - 1.0f;
- float p = z*z * (
- -4.999999767382730053173434595877399055021398381370452534949864039404089549132551e-01f+z*(3.333416379155995401749506866323446447523793085809161350343357014272193712456391e-01f+z*(-2.501299948811686421962724839011563450757435183422532362736159418564644404218257e-01f+z*(1.903576945606738444146078468935429697455230136403008172485495359631510244557255e-01f)))
- );
-
- return z + p;
- }
-
- /*
- * Now we have N, a and x correct, so that |x-a| <= 1/16.
- * Compute s.
- *
- * (Since |x+a| >= 2, this means that |s| will be at most 1/32.)
- */
- s = (x - a) / (x + a);
-
- /*
- * The point of computing s = (x-a)/(x+a) was that this makes x
- * equal to a * (1+s)/(1-s). So we can now compute log(x) by
- * means of computing log((1+s)/(1-s)) (which has a more
- * efficiently converging series), and adding log(a) which we
- * obtain from a lookup table.
- *
- * So our full answer to log(X) is now formed by adding together
- * N*log(2) + log(a) + log((1+s)/(1-s)).
- *
- * Now log((1+s)/(1-s)) has the exact Taylor series
- *
- * 2s + 2s^3/3 + 2s^5/5 + ...
- *
- * and what we do is to compute all but the first term of that
- * as a polynomial approximation in s^2, then add on the first
- * term - and all the other bits and pieces above - in
- * precision-and-a-half so as to keep the total error down.
- */
- {
- float s2 = s*s;
-
- /*
- * We want a polynomial L(s^2) such that
- *
- * 2s + s^3*L(s^2) = log((1+s)/(1-s))
- *
- * => L(s^2) = (log((1+s)/(1-s)) - 2s) / s^3
- *
- * => L(z) = (log((1+sqrt(z))/(1-sqrt(z))) - 2*sqrt(z)) / sqrt(z)^3
- *
- * The required range of the polynomial is only [0,1/32^2].
- *
- * Our accuracy requirement for the polynomial approximation
- * is that we don't want to introduce any error more than
- * about 2^-23 times the _top_ bit of s. But the value of
- * the polynomial has magnitude about s^3; and since |s| <
- * 2^-5, this gives us |s^3/s| < 2^-10. In other words,
- * our approximation only needs to be accurate to 13 bits or
- * so before its error is lost in the noise when we add it
- * to everything else.
- *
- * Coefficients generated by the command
-
-./auxiliary/remez.jl --variable=s2 --suffix=f -- '0' '1/BigFloat(32^2)' 1 0 '(abs(x) < 1e-20 ? BigFloat(2)/3 + 2*x/5 + 2*x^2/7 + 2*x^3/9 : (log((1+sqrt(x))/(1-sqrt(x)))-2*sqrt(x))/sqrt(x^3))'
-
- */
- float p = s * s2 * (
- 6.666666325680271091157649745099739739798210281016897722498744752867165138320995e-01f+s2*(4.002792299542401431889592846825025487338520940900492146195427243856292349188402e-01f)
- );
-
- static const float log2hi = 0x1.62ep-1F, log2lo = 0x1.0bfbe8p-15F;
- static const float logahi[8] = { 0x0p+0F, 0x1.e26p-4F, 0x1.c8ep-3F, 0x1.46p-2F, 0x1.9f2p-2F, 0x1.f12p-2F, 0x1.1e8p-1F, 0x1.41cp-1F };
- static const float logalo[8] = { 0x0p+0F, 0x1.076e2ap-16F, 0x1.f7c79ap-15F, 0x1.8bc21cp-14F, 0x1.23eccp-14F, 0x1.1ebf5ep-15F, 0x1.7d79c2p-15F, 0x1.8fe846p-13F };
- return (N*log2hi + logahi[aindex]) + (2.0f*s + (N*log2lo + logalo[aindex] + p));
- }
-}
diff --git a/math/single/e_powf.c b/math/single/e_powf.c
deleted file mode 100644
index fa000f6..0000000
--- a/math/single/e_powf.c
+++ /dev/null
@@ -1,658 +0,0 @@
-/*
- * e_powf.c - single-precision power function
- *
- * Copyright (c) 2009-2018, Arm Limited.
- * SPDX-License-Identifier: MIT
- */
-
-#include <math.h>
-#include <errno.h>
-#include "math_private.h"
-
-float
-powf(float x, float y)
-{
- float logh, logl;
- float rlogh, rlogl;
- float sign = 1.0f;
- int expadjust = 0;
- unsigned ix, iy;
-
- ix = fai(x);
- iy = fai(y);
-
- if (__builtin_expect((ix - 0x00800000) >= (0x7f800000 - 0x00800000) ||
- ((iy << 1) + 0x02000000) < 0x40000000, 0)) {
- /*
- * The above test rules out, as quickly as I can see how to,
- * all possible inputs except for a normalised positive x
- * being raised to the power of a normalised (and not
- * excessively small) y. That's the fast-path case: if
- * that's what the user wants, we can skip all of the
- * difficult special-case handling.
- *
- * Now we must identify, as efficiently as we can, cases
- * which will return to the fast path with a little tidying
- * up. These are, in order of likelihood and hence of
- * processing:
- *
- * - a normalised _negative_ x raised to the power of a
- * non-zero finite y. Having identified this case, we
- * must categorise y into one of the three categories
- * 'odd integer', 'even integer' and 'non-integer'; for
- * the last of these we return an error, while for the
- * other two we rejoin the main code path having rendered
- * x positive and stored an appropriate sign to append to
- * the eventual result.
- *
- * - a _denormal_ x raised to the power of a non-zero
- * finite y, in which case we multiply it up by a power
- * of two to renormalise it, store an appropriate
- * adjustment for its base-2 logarithm, and depending on
- * the sign of y either return straight to the main code
- * path or go via the categorisation of y above.
- *
- * - any of the above kinds of x raised to the power of a
- * zero, denormal, nearly-denormal or nearly-infinite y,
- * in which case we must do the checks on x as above but
- * otherwise the algorithm goes through basically
- * unchanged. Denormal and very tiny y values get scaled
- * up to something not in range of accidental underflow
- * when split into prec-and-a-half format; very large y
- * values get scaled down by a factor of two to prevent
- * CLEARBOTTOMHALF's round-up from overflowing them to
- * infinity. (Of course the _output_ will overflow either
- * way - the largest y value that can possibly yield a
- * finite result is well below this range anyway - so
- * this is a safe change.)
- */
- if (__builtin_expect(((iy << 1) + 0x02000000) >= 0x40000000, 1)) { /* normalised and sensible y */
- y_ok_check_x:
-
- if (__builtin_expect((ix - 0x80800000) < (0xff800000 - 0x80800000), 1)) { /* normal but negative x */
- y_ok_x_negative:
-
- x = fabsf(x);
- ix = fai(x);
-
- /*
- * Determine the parity of y, if it's an integer at
- * all.
- */
- {
- int yexp, yunitsbit;
-
- /*
- * Find the exponent of y.
- */
- yexp = (iy >> 23) & 0xFF;
- /*
- * Numbers with an exponent smaller than 0x7F
- * are strictly smaller than 1, and hence must
- * be fractional.
- */
- if (yexp < 0x7F)
- return MATHERR_POWF_NEGFRAC(x,y);
- /*
- * Numbers with an exponent at least 0x97 are by
- * definition even integers.
- */
- if (yexp >= 0x97)
- goto mainpath; /* rejoin main code, giving positive result */
- /*
- * In between, we must check the mantissa.
- *
- * Note that this case includes yexp==0x7f,
- * which means 1 point something. In this case,
- * the 'units bit' we're testing is semantically
- * the lowest bit of the exponent field, not the
- * leading 1 on the mantissa - but fortunately,
- * that bit position will just happen to contain
- * the 1 that we would wish it to, because the
- * exponent describing that particular case just
- * happens to be odd.
- */
- yunitsbit = 0x96 - yexp;
- if (iy & ((1 << yunitsbit)-1))
- return MATHERR_POWF_NEGFRAC(x,y);
- else if (iy & (1 << yunitsbit))
- sign = -1.0f; /* y is odd; result should be negative */
- goto mainpath; /* now we can rejoin the main code */
- }
- } else if (__builtin_expect((ix << 1) != 0 && (ix << 1) < 0x01000000, 0)) { /* denormal x */
- /*
- * Renormalise x.
- */
- x *= 0x1p+27F;
- ix = fai(x);
- /*
- * Set expadjust to compensate for that.
- */
- expadjust = -27;
-
- /* Now we need to handle negative x as above. */
- if (ix & 0x80000000)
- goto y_ok_x_negative;
- else
- goto mainpath;
- } else if ((ix - 0x00800000) < (0x7f800000 - 0x00800000)) {
- /* normal positive x, back here from denormal-y case below */
- goto mainpath;
- }
- } else if (((iy << 1) + 0x02000000) >= 0x02000000) { /* denormal, nearly-denormal or zero y */
- if (y == 0.0F) {
- /*
- * y == 0. Any finite x returns 1 here. (Quiet NaNs
- * do too, but we handle that below since we don't
- * mind doing them more slowly.)
- */
- if ((ix << 1) != 0 && (ix << 1) < 0xFF000000)
- return 1.0f;
- } else {
- /*
- * Denormal or very very small y. In this situation
- * we have to be a bit careful, because when we
- * break up y into precision-and-a-half later on we
- * risk working with denormals and triggering
- * underflow exceptions within this function that
- * aren't related to the smallness of the output. So
- * here we convert all such y values into a standard
- * small-but-not-too-small value which will give the
- * same output.
- *
- * What value should that be? Well, we work in
- * 16*log2(x) below (equivalently, log to the base
- * 2^{1/16}). So the maximum magnitude of that for
- * any finite x is about 2416 (= 16 * (128+23), for
- * log of the smallest denormal x), i.e. certainly
- * less than 2^12. If multiplying that by y gives
- * anything of magnitude less than 2^-32 (and even
- * that's being generous), the final output will be
- * indistinguishable from 1. So any value of y with
- * magnitude less than 2^-(32+12) = 2^-44 is
- * completely indistinguishable from any other such
- * value. Hence we got here in the first place by
- * checking the exponent of y against 64 (i.e. -63,
- * counting the exponent bias), so we might as well
- * normalise all tiny y values to the same threshold
- * of 2^-64.
- */
- iy = 0x1f800000 | (iy & 0x80000000); /* keep the sign; that's important */
- y = fhex(iy);
- }
- goto y_ok_check_x;
- } else if (((iy << 1) + 0x02000000) < 0x01000000) { /* y in top finite exponent bracket */
- y = fhex(fai(y) - 0x00800000); /* scale down by a factor of 2 */
- goto y_ok_check_x;
- }
-
- /*
- * Having dealt with the above cases, we now know that
- * either x is zero, infinite or NaN, or y is infinite or
- * NaN, or both. We can deal with all of those cases without
- * ever rejoining the main code path.
- */
- if ((unsigned)(((ix & 0x7FFFFFFF) - 0x7f800001) < 0x7fc00000 - 0x7f800001) ||
- (unsigned)(((iy & 0x7FFFFFFF) - 0x7f800001) < 0x7fc00000 - 0x7f800001)) {
- /*
- * At least one signalling NaN. Do a token arithmetic
- * operation on the two operands to provoke an exception
- * and return the appropriate QNaN.
- */
- return FLOAT_INFNAN2(x,y);
- } else if (ix==0x3f800000 || (iy << 1)==0) {
- /*
- * C99 says that 1^anything and anything^0 should both
- * return 1, _even for a NaN_. I modify that slightly to
- * apply only to QNaNs (which doesn't violate C99, since
- * C99 doesn't specify anything about SNaNs at all),
- * because I can't bring myself not to throw an
- * exception on an SNaN since its _entire purpose_ is to
- * throw an exception whenever touched.
- */
- return 1.0f;
- } else
- if (((ix & 0x7FFFFFFF) > 0x7f800000) ||
- ((iy & 0x7FFFFFFF) > 0x7f800000)) {
- /*
- * At least one QNaN. Do a token arithmetic operation on
- * the two operands to get the right one to propagate to
- * the output.
- */
- return FLOAT_INFNAN2(x,y);
- } else if (ix == 0x7f800000) {
- /*
- * x = +infinity. Return +infinity for positive y, +0
- * for negative y, and 1 for zero y.
- */
- if (!(iy << 1))
- return MATHERR_POWF_INF0(x,y);
- else if (iy & 0x80000000)
- return 0.0f;
- else
- return INFINITY;
- } else {
- /*
- * Repeat the parity analysis of y above, returning 1
- * (odd), 2 (even) or 0 (fraction).
- */
- int ypar, yexp, yunitsbit;
- yexp = (iy >> 23) & 0xFF;
- if (yexp < 0x7F)
- ypar = 0;
- else if (yexp >= 0x97)
- ypar = 2;
- else {
- yunitsbit = 0x96 - yexp;
- if (iy & ((1 << yunitsbit)-1))
- ypar = 0;
- else if (iy & (1 << yunitsbit))
- ypar = 1;
- else
- ypar = 2;
- }
-
- if (ix == 0xff800000) {
- /*
- * x = -infinity. We return infinity or zero
- * depending on whether y is positive or negative,
- * and the sign is negative iff y is an odd integer.
- * (SGT: I don't like this, but it's what C99
- * mandates.)
- */
- if (!(iy & 0x80000000)) {
- if (ypar == 1)
- return -INFINITY;
- else
- return INFINITY;
- } else {
- if (ypar == 1)
- return -0.0f;
- else
- return +0.0f;
- }
- } else if (ix == 0) {
- /*
- * x = +0. We return +0 for all positive y including
- * infinity; a divide-by-zero-like error for all
- * negative y including infinity; and an 0^0 error
- * for zero y.
- */
- if ((iy << 1) == 0)
- return MATHERR_POWF_00(x,y);
- else if (iy & 0x80000000)
- return MATHERR_POWF_0NEGEVEN(x,y);
- else
- return +0.0f;
- } else if (ix == 0x80000000) {
- /*
- * x = -0. We return errors in almost all cases (the
- * exception being positive integer y, in which case
- * we return a zero of the appropriate sign), but
- * the errors are almost all different. Gah.
- */
- if ((iy << 1) == 0)
- return MATHERR_POWF_00(x,y);
- else if (iy == 0x7f800000)
- return MATHERR_POWF_NEG0FRAC(x,y);
- else if (iy == 0xff800000)
- return MATHERR_POWF_0NEG(x,y);
- else if (iy & 0x80000000)
- return (ypar == 0 ? MATHERR_POWF_0NEG(x,y) :
- ypar == 1 ? MATHERR_POWF_0NEGODD(x,y) :
- /* ypar == 2 ? */ MATHERR_POWF_0NEGEVEN(x,y));
- else
- return (ypar == 0 ? MATHERR_POWF_NEG0FRAC(x,y) :
- ypar == 1 ? -0.0f :
- /* ypar == 2 ? */ +0.0f);
- } else {
- /*
- * Now we know y is an infinity of one sign or the
- * other and x is finite and nonzero. If x == -1 (+1
- * is already ruled out), we return +1; otherwise
- * C99 mandates that we return either +0 or +inf,
- * the former iff exactly one of |x| < 1 and y<0 is
- * true.
- */
- if (ix == 0xbf800000) {
- return +1.0f;
- } else if (!((ix << 1) < 0x7f000000) ^ !(iy & 0x80000000)) {
- return +0.0f;
- }
- else {
- return INFINITY;
- }
- }
- }
- }
-
- mainpath:
-
-#define PHMULTIPLY(rh,rl, xh,xl, yh,yl) do { \
- float tmph, tmpl; \
- tmph = (xh) * (yh); \
- tmpl = (xh) * (yl) + (xl) * ((yh)+(yl)); \
-/* printf("PHMULTIPLY: tmp=%08x+%08x\n", fai(tmph), fai(tmpl)); */ \
- (rh) = CLEARBOTTOMHALF(tmph + tmpl); \
- (rl) = tmpl + (tmph - (rh)); \
-} while (0)
-
-/*
- * Same as the PHMULTIPLY macro above, but bounds the absolute value
- * of rh+rl. In multiplications uncontrolled enough that rh can go
- * infinite, we can get an IVO exception from the subtraction tmph -
- * rh, so we should spot that case in advance and avoid it.
- */
-#define PHMULTIPLY_SATURATE(rh,rl, xh,xl, yh,yl, bound) do { \
- float tmph, tmpl; \
- tmph = (xh) * (yh); \
- if (fabsf(tmph) > (bound)) { \
- (rh) = copysignf((bound),(tmph)); \
- (rl) = 0.0f; \
- } else { \
- tmpl = (xh) * (yl) + (xl) * ((yh)+(yl)); \
- (rh) = CLEARBOTTOMHALF(tmph + tmpl); \
- (rl) = tmpl + (tmph - (rh)); \
- } \
- } while (0)
-
- /*
- * Determine log2 of x to relative prec-and-a-half, as logh +
- * logl.
- *
- * Well, we're actually computing 16*log2(x), so that it's the
- * right size for the subsequently fiddly messing with powers of
- * 2^(1/16) in the exp step at the end.
- */
- if (__builtin_expect((ix - 0x3f7ff000) <= (0x3f801000 - 0x3f7ff000), 0)) {
- /*
- * For x this close to 1, we write x = 1 + t and then
- * compute t - t^2/2 + t^3/3 - t^4/4; and the neat bit is
- * that t itself, being the bottom half of an input
- * mantissa, is in half-precision already, so the output is
- * naturally in canonical prec-and-a-half form.
- */
- float t = x - 1.0;
- float lnh, lnl;
- /*
- * Compute natural log of x in prec-and-a-half.
- */
- lnh = t;
- lnl = - (t * t) * ((1.0f/2.0f) - t * ((1.0f/3.0f) - t * (1.0f/4.0f)));
-
- /*
- * Now we must scale by 16/log(2), still in prec-and-a-half,
- * to turn this from natural log(x) into 16*log2(x).
- */
- PHMULTIPLY(logh, logl, lnh, lnl, 0x1.716p+4F, -0x1.7135a8p-9F);
- } else {
- /*
- * For all other x, we start by normalising to [1,2), and
- * then dividing that further into subintervals. For each
- * subinterval we pick a number a in that interval, compute
- * s = (x-a)/(x+a) in precision-and-a-half, and then find
- * the log base 2 of (1+s)/(1-s), still in precision-and-a-
- * half.
- *
- * Why would we do anything so silly? For two main reasons.
- *
- * Firstly, if s = (x-a)/(x+a), then a bit of algebra tells
- * us that x = a * (1+s)/(1-s); so once we've got
- * log2((1+s)/(1-s)), we need only add on log2(a) and then
- * we've got log2(x). So this lets us treat all our
- * subintervals in essentially the same way, rather than
- * requiring a separate approximation for each one; the only
- * correction factor we need is to store a table of the
- * base-2 logs of all our values of a.
- *
- * Secondly, log2((1+s)/(1-s)) is a nice thing to compute,
- * once we've got s. Switching to natural logarithms for the
- * moment (it's only a scaling factor to sort that out at
- * the end), we write it as the difference of two logs:
- *
- * log((1+s)/(1-s)) = log(1+s) - log(1-s)
- *
- * Now recall that Taylor series expansion gives us
- *
- * log(1+s) = s - s^2/2 + s^3/3 - ...
- *
- * and therefore we also have
- *
- * log(1-s) = -s - s^2/2 - s^3/3 - ...
- *
- * These series are exactly the same except that the odd
- * terms (s, s^3 etc) have flipped signs; so subtracting the
- * latter from the former gives us
- *
- * log(1+s) - log(1-s) = 2s + 2s^3/3 + 2s^5/5 + ...
- *
- * which requires only half as many terms to be computed
- * before the powers of s get too small to see. Then, of
- * course, we have to scale the result by 1/log(2) to
- * convert natural logs into logs base 2.
- *
- * To compute the above series in precision-and-a-half, we
- * first extract a factor of 2s (which we can multiply back
- * in later) so that we're computing 1 + s^2/3 + s^4/5 + ...
- * and then observe that if s starts off small enough to
- * make s^2/3 at most 2^-12, we need only compute the first
- * couple of terms in laborious prec-and-a-half, and can
- * delegate everything after that to a simple polynomial
- * approximation whose error will end up at the bottom of
- * the low word of the result.
- *
- * How many subintervals does that mean we need?
- *
- * To go back to s = (x-a)/(x+a). Let x = a + e, for some
- * positive e. Then |s| = |e| / |2a+e| <= |e/2a|. So suppose
- * we have n subintervals of equal width covering the space
- * from 1 to 2. If a is at the centre of each interval, then
- * we have e at most 1/2n and a can equal any of 1, 1+1/n,
- * 1+2/n, ... 1+(n-1)/n. In that case, clearly the largest
- * value of |e/2a| is given by the largest e (i.e. 1/2n) and
- * the smallest a (i.e. 1); so |s| <= 1/4n. Hence, when we
- * know how big we're prepared to let s be, we simply make
- * sure 1/4n is at most that.
- *
- * And if we want s^2/3 to be at most 2^-12, then that means
- * s^2 is at most 3*2^-12, so that s is at most sqrt(3)*2^-6
- * = 0.02706. To get 1/4n smaller than that, we need to have
- * n>=9.23; so we'll set n=16 (for ease of bit-twiddling),
- * and then s is at most 1/64.
- */
- int n, i;
- float a, ax, sh, sl, lsh, lsl;
-
- /*
- * Let ax be x normalised to a single exponent range.
- * However, the exponent range in question is not a simple
- * one like [1,2). What we do is to round up the top four
- * bits of the mantissa, so that the top 1/32 of each
- * natural exponent range rounds up to the next one and is
- * treated as a displacement from the lowest a in that
- * range.
- *
- * So this piece of bit-twiddling gets us our input exponent
- * and our subinterval index.
- */
- n = (ix + 0x00040000) >> 19;
- i = n & 15;
- n = ((n >> 4) & 0xFF) - 0x7F;
- ax = fhex(ix - (n << 23));
- n += expadjust;
-
- /*
- * Compute the subinterval centre a.
- */
- a = 1.0f + i * (1.0f/16.0f);
-
- /*
- * Compute s = (ax-a)/(ax+a), in precision-and-a-half.
- */
- {
- float u, vh, vl, vapprox, rvapprox;
-
- u = ax - a; /* exact numerator */
- vapprox = ax + a; /* approximate denominator */
- vh = CLEARBOTTOMHALF(vapprox);
- vl = (a - vh) + ax; /* vh+vl is exact denominator */
- rvapprox = 1.0f/vapprox; /* approximate reciprocal of denominator */
-
- sh = CLEARBOTTOMHALF(u * rvapprox);
- sl = ((u - sh*vh) - sh*vl) * rvapprox;
- }
-
- /*
- * Now compute log2(1+s) - log2(1-s). We do this in several
- * steps.
- *
- * By polynomial approximation, we compute
- *
- * log(1+s) - log(1-s)
- * p = ------------------- - 1
- * 2s
- *
- * in single precision only, using a single-precision
- * approximation to s. This polynomial has s^2 as its
- * lowest-order term, so we expect the result to be in
- * [0,2^-12).
- *
- * Then we form a prec-and-a-half number out of 1 and p,
- * which is therefore equal to (log(1+s) - log(1-s))/(2s).
- *
- * Finally, we do two prec-and-a-half multiplications: one
- * by s itself, and one by the constant 32/log(2).
- */
- {
- float s = sh + sl;
- float s2 = s*s;
- /*
- * p is actually a polynomial in s^2, with the first
- * term constrained to zero. In other words, treated on
- * its own terms, we're computing p(s^2) such that p(x)
- * is an approximation to the sum of the series 1/3 +
- * x/5 + x^2/7 + ..., valid on the range [0, 1/40^2].
- */
- float p = s2 * (0.33333332920177422f + s2 * 0.20008275183621479f);
- float th, tl;
-
- PHMULTIPLY(th,tl, 1.0f,p, sh,sl);
- PHMULTIPLY(lsh,lsl, th,tl, 0x1.716p+5F,-0x1.7135a8p-8F);
- }
-
- /*
- * And our final answer for 16*log2(x) is equal to 16n (from
- * the exponent), plus lsh+lsl (the result of the above
- * computation), plus 16*log2(a) which we must look up in a
- * table.
- */
- {
- struct f2 { float h, l; };
- static const struct f2 table[16] = {
- /*
- * When constructing this table, we have to be sure
- * that we produce the same values of a which will
- * be produced by the computation above. Ideally, I
- * would tell Perl to actually do its _arithmetic_
- * in single precision here; but I don't know a way
- * to do that, so instead I just scrupulously
- * convert every intermediate value to and from SP.
- */
- // perl -e 'for ($i=0; $i<16; $i++) { $v = unpack "f", pack "f", 1/16.0; $a = unpack "f", pack "f", $i * $v; $a = unpack "f", pack "f", $a+1.0; $l = 16*log($a)/log(2); $top = unpack "f", pack "f", int($l*256.0+0.5)/256.0; $bot = unpack "f", pack "f", $l - $top; printf "{0f_%08X,0f_%08X}, ", unpack "VV", pack "ff", $top, $bot; } print "\n"' | fold -s -w56 | sed 's/^/ /'
- {0x0p+0F,0x0p+0F}, {0x1.66p+0F,0x1.fb7d64p-11F},
- {0x1.5cp+1F,0x1.a39fbep-15F}, {0x1.fcp+1F,-0x1.f4a37ep-10F},
- {0x1.49cp+2F,-0x1.87b432p-10F}, {0x1.91cp+2F,-0x1.15db84p-12F},
- {0x1.d68p+2F,-0x1.583f9ap-11F}, {0x1.0c2p+3F,-0x1.f5fe54p-10F},
- {0x1.2b8p+3F,0x1.a39fbep-16F}, {0x1.49ap+3F,0x1.e12f34p-11F},
- {0x1.66ap+3F,0x1.1c8f12p-18F}, {0x1.828p+3F,0x1.3ab7cep-14F},
- {0x1.9d6p+3F,-0x1.30158p-12F}, {0x1.b74p+3F,0x1.291eaap-10F},
- {0x1.d06p+3F,-0x1.8125b4p-10F}, {0x1.e88p+3F,0x1.8d66c4p-10F},
- };
- float lah = table[i].h, lal = table[i].l;
- float fn = 16*n;
- logh = CLEARBOTTOMHALF(lsl + lal + lsh + lah + fn);
- logl = lsl - ((((logh - fn) - lah) - lsh) - lal);
- }
- }
-
- /*
- * Now we have 16*log2(x), multiply it by y in prec-and-a-half.
- */
- {
- float yh, yl;
- int savedexcepts;
-
- yh = CLEARBOTTOMHALF(y);
- yl = y - yh;
-
- /* This multiplication could become infinite, so to avoid IVO
- * in PHMULTIPLY we bound the output at 4096, which is big
- * enough to allow any non-overflowing case through
- * unmodified. Also, we must mask out the OVF exception, which
- * we won't want left in the FP status word in the case where
- * rlogh becomes huge and _negative_ (since that will be an
- * underflow from the perspective of powf's return value, not
- * an overflow). */
- savedexcepts = __ieee_status(0,0) & (FE_IEEE_OVERFLOW | FE_IEEE_UNDERFLOW);
- PHMULTIPLY_SATURATE(rlogh, rlogl, logh, logl, yh, yl, 4096.0f);
- __ieee_status(FE_IEEE_OVERFLOW | FE_IEEE_UNDERFLOW, savedexcepts);
- }
-
- /*
- * And raise 2 to the power of whatever that gave. Again, this
- * is done in three parts: the fractional part of our input is
- * fed through a polynomial approximation, all but the bottom
- * four bits of the integer part go straight into the exponent,
- * and the bottom four bits of the integer part index into a
- * lookup table of powers of 2^(1/16) in prec-and-a-half.
- */
- {
- float rlog = rlogh + rlogl;
- int i16 = (rlog + (rlog < 0 ? -0.5f : +0.5f));
- float rlogi = i16 >> 4;
-
- float x = rlogl + (rlogh - i16);
-
- static const float powersof2to1over16top[16] = { 0x1p+0F, 0x1.0b4p+0F, 0x1.172p+0F, 0x1.238p+0F, 0x1.306p+0F, 0x1.3dep+0F, 0x1.4bep+0F, 0x1.5aap+0F, 0x1.6ap+0F, 0x1.7ap+0F, 0x1.8acp+0F, 0x1.9c4p+0F, 0x1.ae8p+0F, 0x1.c18p+0F, 0x1.d58p+0F, 0x1.ea4p+0F };
- static const float powersof2to1over16bot[16] = { 0x0p+0F, 0x1.586cfap-12F, 0x1.7078fap-13F, 0x1.e9b9d6p-14F, 0x1.fc1464p-13F, 0x1.4c9824p-13F, 0x1.dad536p-12F, 0x1.07dd48p-12F, 0x1.3cccfep-13F, 0x1.1473ecp-12F, 0x1.ca8456p-13F, 0x1.230548p-13F, 0x1.3f32b6p-13F, 0x1.9bdd86p-12F, 0x1.8dcfbap-16F, 0x1.5f454ap-13F };
- static const float powersof2to1over16all[16] = { 0x1p+0F, 0x1.0b5586p+0F, 0x1.172b84p+0F, 0x1.2387a6p+0F, 0x1.306fep+0F, 0x1.3dea64p+0F, 0x1.4bfdaep+0F, 0x1.5ab07ep+0F, 0x1.6a09e6p+0F, 0x1.7a1148p+0F, 0x1.8ace54p+0F, 0x1.9c4918p+0F, 0x1.ae89fap+0F, 0x1.c199bep+0F, 0x1.d5818ep+0F, 0x1.ea4afap+0F };
- /*
- * Coefficients generated using the command
-
-./auxiliary/remez.jl --suffix=f -- '-1/BigFloat(2)' '+1/BigFloat(2)' 2 0 'expm1(x*log(BigFloat(2))/16)/x'
-
- */
- float p = x * (
- 4.332169876512769231967668743345473181486157887703125512683507537369503902991722e-02f+x*(9.384123108485637159805511308039285411735300871134684682779057580789341719567367e-04f+x*(1.355120515540562256928614563584948866224035897564701496826514330445829352922309e-05f))
- );
- int index = (i16 & 15);
- p = powersof2to1over16top[index] + (powersof2to1over16bot[index] + powersof2to1over16all[index]*p);
-
- if (
- fabsf(rlogi) < 126.0f
- ) {
- return sign * p * fhex((unsigned)((127.0f+rlogi) * 8388608.0f));
- } else if (
- fabsf(rlogi) < 192.0f
- ) {
- int i = rlogi;
- float ret;
-
- ret = sign * p *
- fhex((unsigned)((0x7f+i/2) * 8388608)) *
- fhex((unsigned)((0x7f+i-i/2) * 8388608));
-
- if ((fai(ret) << 1) == 0xFF000000)
- return MATHERR_POWF_OFL(x, y, sign);
- else if ((fai(ret) << 1) == 0)
- return MATHERR_POWF_UFL(x, y, sign);
- else
- return FLOAT_CHECKDENORM(ret);
- } else {
- if (rlogi < 0)
- return MATHERR_POWF_UFL(x, y, sign);
- else
- return MATHERR_POWF_OFL(x, y, sign);
- }
- }
-}
diff --git a/math/single/e_rem_pio2.c b/math/single/e_rem_pio2.c
deleted file mode 100644
index 0cd3a22..0000000
--- a/math/single/e_rem_pio2.c
+++ /dev/null
@@ -1,268 +0,0 @@
-/*
- * e_rem_pio2.c
- *
- * Copyright (c) 1999-2018, Arm Limited.
- * SPDX-License-Identifier: MIT
- */
-
-#include <math.h>
-#include "math_private.h"
-
-int __ieee754_rem_pio2(double x, double *y) {
- int q;
-
- y[1] = 0.0; /* default */
-
- /*
- * Simple cases: all nicked from the fdlibm version for speed.
- */
- {
- static const double invpio2 = 0x1.45f306dc9c883p-1;
- static const double pio2s[] = {
- 0x1.921fb544p+0, /* 1.57079632673412561417e+00 */
- 0x1.0b4611a626331p-34, /* 6.07710050650619224932e-11 */
- 0x1.0b4611a6p-34, /* 6.07710050630396597660e-11 */
- 0x1.3198a2e037073p-69, /* 2.02226624879595063154e-21 */
- 0x1.3198a2ep-69, /* 2.02226624871116645580e-21 */
- 0x1.b839a252049c1p-104, /* 8.47842766036889956997e-32 */
- };
-
- double z,w,t,r,fn;
- int i,j,idx,n,ix,hx;
-
- hx = __HI(x); /* high word of x */
- ix = hx&0x7fffffff;
- if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */
- {y[0] = x; y[1] = 0; return 0;}
- if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */
- if(hx>0) {
- z = x - pio2s[0];
- if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
- y[0] = z - pio2s[1];
-#ifdef bottomhalf
- y[1] = (z-y[0])-pio2s[1];
-#endif
- } else { /* near pi/2, use 33+33+53 bit pi */
- z -= pio2s[2];
- y[0] = z - pio2s[3];
-#ifdef bottomhalf
- y[1] = (z-y[0])-pio2s[3];
-#endif
- }
- return 1;
- } else { /* negative x */
- z = x + pio2s[0];
- if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
- y[0] = z + pio2s[1];
-#ifdef bottomhalf
- y[1] = (z-y[0])+pio2s[1];
-#endif
- } else { /* near pi/2, use 33+33+53 bit pi */
- z += pio2s[2];
- y[0] = z + pio2s[3];
-#ifdef bottomhalf
- y[1] = (z-y[0])+pio2s[3];
-#endif
- }
- return -1;
- }
- }
- if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
- t = fabs(x);
- n = (int) (t*invpio2+0.5);
- fn = (double)n;
- r = t-fn*pio2s[0];
- w = fn*pio2s[1]; /* 1st round good to 85 bit */
- j = ix>>20;
- idx = 1;
- while (1) {
- y[0] = r-w;
- if (idx == 3)
- break;
- i = j-(((__HI(y[0]))>>20)&0x7ff);
- if(i <= 33*idx-17)
- break;
- t = r;
- w = fn*pio2s[2*idx];
- r = t-w;
- w = fn*pio2s[2*idx+1]-((t-r)-w);
- idx++;
- }
-#ifdef bottomhalf
- y[1] = (r-y[0])-w;
-#endif
- if(hx<0) {
- y[0] = -y[0];
-#ifdef bottomhalf
- y[1] = -y[1];
-#endif
- return -n;
- } else {
- return n;
- }
- }
- }
-
- {
- static const unsigned twooverpi[] = {
- /* We start with two zero words, because they take up less
- * space than the array bounds checking and special-case
- * handling that would have to occur in their absence. */
- 0, 0,
- /* 2/pi in hex is 0.a2f9836e... */
- 0xa2f9836e, 0x4e441529, 0xfc2757d1, 0xf534ddc0, 0xdb629599,
- 0x3c439041, 0xfe5163ab, 0xdebbc561, 0xb7246e3a, 0x424dd2e0,
- 0x06492eea, 0x09d1921c, 0xfe1deb1c, 0xb129a73e, 0xe88235f5,
- 0x2ebb4484, 0xe99c7026, 0xb45f7e41, 0x3991d639, 0x835339f4,
- 0x9c845f8b, 0xbdf9283b, 0x1ff897ff, 0xde05980f, 0xef2f118b,
- 0x5a0a6d1f, 0x6d367ecf, 0x27cb09b7, 0x4f463f66, 0x9e5fea2d,
- 0x7527bac7, 0xebe5f17b, 0x3d0739f7, 0x8a5292ea, 0x6bfb5fb1,
- 0x1f8d5d08, 0x56033046,
- };
-
- /*
- * Multiprecision multiplication of this nature is more
- * readily done in integers than in VFP, since we can use
- * UMULL (on CPUs that support it) to multiply 32 by 32 bits
- * at a time whereas the VFP would only be able to do 12x12
- * without losing accuracy.
- *
- * So extract the mantissa of the input number as two 32-bit
- * integers.
- */
- unsigned mant1 = 0x00100000 | (__HI(x) & 0xFFFFF);
- unsigned mant2 = __LO(x);
- /*
- * Now work out which part of our stored value of 2/pi we're
- * supposed to be multiplying by.
- *
- * Let the IEEE exponent field of x be e. With its bias
- * removed, (e-1023) is the index of the set bit in bit 20
- * of 'mant1' (i.e. that set bit has real place value
- * 2^(e-1023)). So the lowest set bit in 'mant1', 52 bits
- * further down, must have place value 2^(e-1075).
- *
- * We begin taking an interest in the value of 2/pi at the
- * bit which multiplies by _that_ to give something with
- * place value at most 2. In other words, the highest bit of
- * 2/pi we're interested in is the one with place value
- * 2/(2^(e-1075)) = 2^(1076-e).
- *
- * The bit at the top of the first zero word of the above
- * array has place value 2^63. Hence, the bit we want to put
- * at the top of the first word we extract from that array
- * is the one at bit index n, where 63-n = 1076-e and hence
- * n=e-1013.
- */
- int topbitindex = ((__HI(x) >> 20) & 0x7FF) - 1013;
- int wordindex = topbitindex >> 5;
- int shiftup = topbitindex & 31;
- int shiftdown = 32 - shiftup;
- unsigned scaled[8];
- int i;
-
- scaled[7] = scaled[6] = 0;
-
- for (i = 6; i-- > 0 ;) {
- /*
- * Extract a word from our representation of 2/pi.
- */
- unsigned word;
- if (shiftup)
- word = (twooverpi[wordindex + i] << shiftup) | (twooverpi[wordindex + i + 1] >> shiftdown);
- else
- word = twooverpi[wordindex + i];
- /*
- * Multiply it by both words of our mantissa. (Should
- * generate UMULLs where available.)
- */
- unsigned long long mult1 = (unsigned long long)word * mant1;
- unsigned long long mult2 = (unsigned long long)word * mant2;
- /*
- * Split those up into 32-bit chunks.
- */
- unsigned bottom1 = (unsigned)mult1, top1 = (unsigned)(mult1 >> 32);
- unsigned bottom2 = (unsigned)mult2, top2 = (unsigned)(mult2 >> 32);
- /*
- * Add those two chunks together.
- */
- unsigned out1, out2, out3;
-
- out3 = bottom2;
- out2 = top2 + bottom1;
- out1 = top1 + (out2 < top2);
- /*
- * And finally add them to our 'scaled' array.
- */
- unsigned s3 = scaled[i+2], s2 = scaled[i+1], s1;
- unsigned carry;
- s3 = out3 + s3; carry = (s3 < out3);
- s2 = out2 + s2 + carry; carry = carry ? (s2 <= out2) : (s2 < out2);
- s1 = out1 + carry;
-
- scaled[i+2] = s3;
- scaled[i+1] = s2;
- scaled[i] = s1;
- }
-
-
- /*
- * The topmost set bit in mant1 is bit 20, and that has
- * place value 2^(e-1023). The topmost bit (bit 31) of the
- * most significant word we extracted from our twooverpi
- * array had place value 2^(1076-e). So the product of those
- * two bits must have place value 2^53; and that bit will
- * have ended up as bit 19 of scaled[0]. Hence, the integer
- * quadrant value we want to output, consisting of the bits
- * with place values 2^1 and 2^0, must be 52 and 53 bits
- * below that, i.e. precisely the topmost two bits of
- * scaled[2].
- *
- * Or, at least, it will be once we add 1/2, to round to the
- * _nearest_ multiple of pi/2 rather than the next one down.
- */
- q = (scaled[2] + (1<<29)) >> 30;
-
- /*
- * Now we construct the output fraction, which is most
- * simply done in the VFP. We just extract four consecutive
- * bit strings from our chunk of binary data, convert them
- * to doubles, equip each with an appropriate FP exponent,
- * add them together, and (don't forget) multiply back up by
- * pi/2. That way we don't have to work out ourselves where
- * the highest fraction bit ended up.
- *
- * Since our displacement from the nearest multiple of pi/2
- * can be positive or negative, the topmost of these four
- * values must be arranged with its 2^-1 bit at the very top
- * of the word, and then treated as a _signed_ integer.
- */
- int i1 = (scaled[2] << 2);
- unsigned i2 = scaled[3];
- unsigned i3 = scaled[4];
- unsigned i4 = scaled[5];
- double f1 = i1, f2 = i2 * (0x1.0p-30), f3 = i3 * (0x1.0p-62), f4 = i4 * (0x1.0p-94);
-
- /*
- * Now f1+f2+f3+f4 is a representation, potentially to
- * twice double precision, of 2^32 times ((2/pi)*x minus
- * some integer). So our remaining job is to multiply
- * back down by (pi/2)*2^-32, and convert back to one
- * single-precision output number.
- */
- double ftop = f1 + (f2 + (f3 + f4));
- ftop = __SET_LO(ftop, 0);
- double fbot = f4 - (((ftop-f1)-f2)-f3);
-
- /* ... and multiply by a prec-and-a-half value of (pi/2)*2^-32. */
- double ret = (ftop * 0x1.921fb54p-32) + (ftop * 0x1.10b4611a62633p-62 + fbot * 0x1.921fb54442d18p-32);
-
- /* Just before we return, take the input sign into account. */
- if (__HI(x) & 0x80000000) {
- q = -q;
- ret = -ret;
- }
- y[0] = ret;
- return q;
- }
-}
diff --git a/math/single/funder.c b/math/single/funder.c
deleted file mode 100644
index ef16f68..0000000
--- a/math/single/funder.c
+++ /dev/null
@@ -1,51 +0,0 @@
-/*
- * funder.c - manually provoke SP exceptions for mathlib
- *
- * Copyright (c) 2009-2018, Arm Limited.
- * SPDX-License-Identifier: MIT
- */
-
-#include <fenv.h>
-#include "math_private.h"
-
-__inline float __mathlib_flt_infnan2(float x, float y)
-{
- return x+y;
-}
-
-__inline float __mathlib_flt_infnan(float x)
-{
- return x+x;
-}
-
-float __mathlib_flt_underflow(void)
-{
-#ifdef CLANG_EXCEPTIONS
- feraiseexcept(FE_UNDERFLOW);
-#endif
- return 0x1p-95F * 0x1p-95F;
-}
-
-float __mathlib_flt_overflow(void)
-{
-#ifdef CLANG_EXCEPTIONS
- feraiseexcept(FE_OVERFLOW);
-#endif
- return 0x1p+97F * 0x1p+97F;
-}
-
-float __mathlib_flt_invalid(void)
-{
-#ifdef CLANG_EXCEPTIONS
- feraiseexcept(FE_INVALID);
-#endif
- return 0.0f / 0.0f;
-}
-
-float __mathlib_flt_divzero(void)
-{
-#ifdef CLANG_EXCEPTIONS
- feraiseexcept(FE_DIVBYZERO);
-#endif
- return 1.0f / 0.0f;
-}
diff --git a/math/single/ieee_status.c b/math/single/ieee_status.c
deleted file mode 100644
index ef846f4..0000000
--- a/math/single/ieee_status.c
+++ /dev/null
@@ -1,38 +0,0 @@
-/*
- * ieee_status.c
- *
- * Copyright (c) 2015-2018, Arm Limited.
- * SPDX-License-Identifier: MIT
- */
-
-#include "math_private.h"
-
-__inline unsigned __ieee_status(unsigned bicmask, unsigned xormask)
-{
-#if defined __aarch64__ && defined __FP_FENV_EXCEPTIONS
- unsigned status_word;
- unsigned ret;
-
-#ifdef __FP_FENV_ROUNDING
-# define MASK (1<<27)|FE_IEEE_FLUSHZERO|FE_IEEE_MASK_ALL_EXCEPT|FE_IEEE_ALL_EXCEPT|FE_IEEE_ROUND_MASK
-#else
-# define MASK (1<<27)|FE_IEEE_FLUSHZERO|FE_IEEE_MASK_ALL_EXCEPT|FE_IEEE_ALL_EXCEPT
-#endif
-
- /* mask out read-only bits */
- bicmask &= MASK;
- xormask &= MASK;
-
- /* modify the status word */
- __asm__ __volatile__ ("mrs %0, fpsr" : "=r" (status_word));
- ret = status_word;
- status_word &= ~bicmask;
- status_word ^= xormask;
- __asm__ __volatile__ ("msr fpsr, %0" : : "r" (status_word));
-
- /* and return what it used to be */
- return ret;
-#else
- return 0;
-#endif
-}
diff --git a/math/single/math_private.h b/math/single/math_private.h
deleted file mode 100644
index eef997d..0000000
--- a/math/single/math_private.h
+++ /dev/null
@@ -1,138 +0,0 @@
-/*
- * math_private.h
- *
- * Copyright (c) 2015-2018, Arm Limited.
- * SPDX-License-Identifier: MIT
- */
-
-/*
- * Header file containing some definitions and other small reusable pieces of
- * code that we need in the libraries.
- */
-
-#ifndef __MATH_PRIVATE_H
-#define __MATH_PRIVATE_H
-
-#include <errno.h>
-#include <stdint.h>
-
-extern int __ieee754_rem_pio2(double, double *);
-extern double __kernel_poly(const double *, int, double);
-
-#define __FP_IEEE
-#define __FP_FENV_EXCEPTIONS
-#define __FP_FENV_ROUNDING
-#define __FP_INEXACT_EXCEPTION
-
-#define __set_errno(val) (errno = (val))
-
-static __inline uint32_t __LO(double x)
-{
- union {double f; uint64_t i;} u = {x};
- return (uint32_t)u.i;
-}
-
-static __inline uint32_t __HI(double x)
-{
- union {double f; uint64_t i;} u = {x};
- return u.i >> 32;
-}
-
-static __inline double __SET_LO(double x, uint32_t lo)
-{
- union {double f; uint64_t i;} u = {x};
- u.i = (u.i >> 32) << 32 | lo;
- return u.f;
-}
-
-static __inline unsigned int fai(float f)
-{
- union {float f; uint32_t i;} u = {f};
- return u.i;
-}
-
-static __inline float fhex(unsigned int n)
-{
- union {uint32_t i; float f;} u = {n};
- return u.f;
-}
-
-#define CLEARBOTTOMHALF(x) fhex((fai(x) + 0x00000800) & 0xFFFFF000)
-
-#define FE_IEEE_OVERFLOW (0x00000004)
-#define FE_IEEE_UNDERFLOW (0x00000008)
-#define FE_IEEE_FLUSHZERO (0x01000000)
-#define FE_IEEE_ROUND_TONEAREST (0x00000000)
-#define FE_IEEE_ROUND_UPWARD (0x00400000)
-#define FE_IEEE_ROUND_DOWNWARD (0x00800000)
-#define FE_IEEE_ROUND_TOWARDZERO (0x00C00000)
-#define FE_IEEE_ROUND_MASK (0x00C00000)
-#define FE_IEEE_MASK_INVALID (0x00000100)
-#define FE_IEEE_MASK_DIVBYZERO (0x00000200)
-#define FE_IEEE_MASK_OVERFLOW (0x00000400)
-#define FE_IEEE_MASK_UNDERFLOW (0x00000800)
-#define FE_IEEE_MASK_INEXACT (0x00001000)
-#define FE_IEEE_MASK_INPUTDENORMAL (0x00008000)
-#define FE_IEEE_MASK_ALL_EXCEPT (0x00009F00)
-#define FE_IEEE_INVALID (0x00000001)
-#define FE_IEEE_DIVBYZERO (0x00000002)
-#define FE_IEEE_INEXACT (0x00000010)
-#define FE_IEEE_INPUTDENORMAL (0x00000080)
-#define FE_IEEE_ALL_EXCEPT (0x0000009F)
-
-extern double __mathlib_dbl_overflow(void);
-extern float __mathlib_flt_overflow(void);
-extern double __mathlib_dbl_underflow(void);
-extern float __mathlib_flt_underflow(void);
-extern double __mathlib_dbl_invalid(void);
-extern float __mathlib_flt_invalid(void);
-extern double __mathlib_dbl_divzero(void);
-extern float __mathlib_flt_divzero(void);
-#define DOUBLE_OVERFLOW ( __mathlib_dbl_overflow() )
-#define FLOAT_OVERFLOW ( __mathlib_flt_overflow() )
-#define DOUBLE_UNDERFLOW ( __mathlib_dbl_underflow() )
-#define FLOAT_UNDERFLOW ( __mathlib_flt_underflow() )
-#define DOUBLE_INVALID ( __mathlib_dbl_invalid() )
-#define FLOAT_INVALID ( __mathlib_flt_invalid() )
-#define DOUBLE_DIVZERO ( __mathlib_dbl_divzero() )
-#define FLOAT_DIVZERO ( __mathlib_flt_divzero() )
-
-extern float __mathlib_flt_infnan(float);
-extern float __mathlib_flt_infnan2(float, float);
-extern double __mathlib_dbl_infnan(double);
-extern double __mathlib_dbl_infnan2(double, double);
-extern unsigned __ieee_status(unsigned, unsigned);
-
-#define FLOAT_INFNAN(x) __mathlib_flt_infnan(x)
-#define FLOAT_INFNAN2(x,y) __mathlib_flt_infnan2(x,y)
-#define DOUBLE_INFNAN(x) __mathlib_dbl_infnan(x)
-#define DOUBLE_INFNAN2(x,y) __mathlib_dbl_infnan2(x,y)
-
-#define MATHERR_POWF_00(x,y) (__set_errno(EDOM), 1.0f)
-#define MATHERR_POWF_INF0(x,y) (__set_errno(EDOM), 1.0f)
-#define MATHERR_POWF_0NEG(x,y) (__set_errno(ERANGE), FLOAT_DIVZERO)
-#define MATHERR_POWF_NEG0FRAC(x,y) (0.0f)
-#define MATHERR_POWF_0NEGODD(x,y) (__set_errno(ERANGE), -FLOAT_DIVZERO)
-#define MATHERR_POWF_0NEGEVEN(x,y) (__set_errno(ERANGE), FLOAT_DIVZERO)
-#define MATHERR_POWF_NEGFRAC(x,y) (__set_errno(EDOM), FLOAT_INVALID)
-#define MATHERR_POWF_ONEINF(x,y) (1.0f)
-#define MATHERR_POWF_OFL(x,y,z) (__set_errno(ERANGE), copysignf(FLOAT_OVERFLOW,z))
-#define MATHERR_POWF_UFL(x,y,z) (__set_errno(ERANGE), copysignf(FLOAT_UNDERFLOW,z))
-
-#define MATHERR_LOGF_0(x) (__set_errno(ERANGE), -FLOAT_DIVZERO)
-#define MATHERR_LOGF_NEG(x) (__set_errno(EDOM), FLOAT_INVALID)
-
-#define MATHERR_SIN_INF(x) (__set_errno(EDOM), DOUBLE_INVALID)
-#define MATHERR_SINF_INF(x) (__set_errno(EDOM), FLOAT_INVALID)
-#define MATHERR_COS_INF(x) (__set_errno(EDOM), DOUBLE_INVALID)
-#define MATHERR_COSF_INF(x) (__set_errno(EDOM), FLOAT_INVALID)
-#define MATHERR_TAN_INF(x) (__set_errno(EDOM), DOUBLE_INVALID)
-#define MATHERR_TANF_INF(x) (__set_errno(EDOM), FLOAT_INVALID)
-
-#define MATHERR_EXPF_UFL(x) (__set_errno(ERANGE), FLOAT_UNDERFLOW)
-#define MATHERR_EXPF_OFL(x) (__set_errno(ERANGE), FLOAT_OVERFLOW)
-
-#define FLOAT_CHECKDENORM(x) ( (fpclassify(x) == FP_SUBNORMAL ? FLOAT_UNDERFLOW : 0), x )
-#define DOUBLE_CHECKDENORM(x) ( (fpclassify(x) == FP_SUBNORMAL ? DOUBLE_UNDERFLOW : 0), x )
-
-#endif /* __MATH_PRIVATE_H */
diff --git a/math/single/poly.c b/math/single/poly.c
deleted file mode 100644
index 4eaf7ff..0000000
--- a/math/single/poly.c
+++ /dev/null
@@ -1,25 +0,0 @@
-/*
- * poly.c
- *
- * Copyright (c) 1998-2018, Arm Limited.
- * SPDX-License-Identifier: MIT
- */
-
-double __kernel_poly(const double *coeffs, int n, double x)
-{
- double result = coeffs[--n];
-
- while ((n & ~0x6) != 0) /* Loop until n even and < 8 */
- result = (result * x) + coeffs[--n];
-
- switch (n)
- {
- case 6: result = (result * x) + coeffs[5];
- result = (result * x) + coeffs[4];
- case 4: result = (result * x) + coeffs[3];
- result = (result * x) + coeffs[2];
- case 2: result = (result * x) + coeffs[1];
- result = (result * x) + coeffs[0];
- }
- return result;
-}
diff --git a/math/single/rredf.c b/math/single/rredf.c
deleted file mode 100644
index a5c3122..0000000
--- a/math/single/rredf.c
+++ /dev/null
@@ -1,239 +0,0 @@
-/*
- * rredf.c - trigonometric range reduction function
- *
- * Copyright (c) 2009-2018, Arm Limited.
- * SPDX-License-Identifier: MIT
- */
-
-/*
- * This code is intended to be used as the second half of a range
- * reducer whose first half is an inline function defined in
- * rredf.h. Each trig function performs range reduction by invoking
- * that, which handles the quickest and most common cases inline
- * before handing off to this function for everything else. Thus a
- * reasonable compromise is struck between speed and space. (I
- * hope.) In particular, this approach avoids a function call
- * overhead in the common case.
- */
-
-#include "math_private.h"
-
-#ifdef __cplusplus
-extern "C" {
-#endif /* __cplusplus */
-
-/*
- * Input values to this function:
- * - x is the original user input value, unchanged by the
- * first-tier reducer in the case where it hands over to us.
- * - q is still the place where the caller expects us to leave the
- * quadrant code.
- * - k is the IEEE bit pattern of x (which it would seem a shame to
- * recompute given that the first-tier reducer already went to
- * the effort of extracting it from the VFP). FIXME: in softfp,
- * on the other hand, it's unconscionably wasteful to replicate
- * this value into a second register and we should change the
- * prototype!
- */
-float __mathlib_rredf2(float x, int *q, unsigned k)
-{
- /*
- * First, weed out infinities and NaNs, and deal with them by
- * returning a negative q.
- */
- if ((k << 1) >= 0xFF000000) {
- *q = -1;
- return x;
- }
- /*
- * We do general range reduction by multiplying by 2/pi, and
- * retaining the bottom two bits of the integer part and an
- * initial chunk of the fraction below that. The integer bits
- * are directly output as *q; the fraction is then multiplied
- * back up by pi/2 before returning it.
- *
- * To get this right, we don't have to multiply by the _whole_
- * of 2/pi right from the most significant bit downwards:
- * instead we can discard any bit of 2/pi with a place value
- * high enough that multiplying it by the LSB of x will yield a
- * place value higher than 2. Thus we can bound the required
- * work by a reasonably small constant regardless of the size of
- * x (unlike, for instance, the IEEE remainder operation).
- *
- * At the other end, however, we must take more care: it isn't
- * adequate just to acquire two integer bits and 24 fraction
- * bits of (2/pi)x, because if a lot of those fraction bits are
- * zero then we will suffer significance loss. So we must keep
- * computing fraction bits as far down as 23 bits below the
- * _highest set fraction bit_.
- *
- * The immediate question, therefore, is what the bound on this
- * end of the job will be. In other words: what is the smallest
- * difference between an integer multiple of pi/2 and a
- * representable IEEE single precision number larger than the
- * maximum size handled by rredf.h?
- *
- * The most difficult cases for each exponent can readily be
- * found by Tim Peters's modular minimisation algorithm, and are
- * tabulated in mathlib/tests/directed/rredf.tst. The single
- * worst case is the IEEE single-precision number 0x6F79BE45,
- * whose numerical value is in the region of 7.7*10^28; when
- * reduced mod pi/2, it attains the value 0x30DDEEA9, or about
- * 0.00000000161. The highest set bit of this value is the one
- * with place value 2^-30; so its lowest is 2^-53. Hence, to be
- * sure of having enough fraction bits to output at full single
- * precision, we must be prepared to collect up to 53 bits of
- * fraction in addition to our two bits of integer part.
- *
- * To begin with, this means we must store the value of 2/pi to
- * a precision of 128+53 = 181 bits. That's six 32-bit words.
- * (Hardly a chore, unlike the equivalent problem in double
- * precision!)
- */
- {
- static const unsigned twooverpi[] = {
- /* We start with a zero word, because that takes up less
- * space than the array bounds checking and special-case
- * handling that would have to occur in its absence. */
- 0,
- /* 2/pi in hex is 0.a2f9836e... */
- 0xa2f9836e, 0x4e441529, 0xfc2757d1,
- 0xf534ddc0, 0xdb629599, 0x3c439041,
- /* Again, to avoid array bounds overrun, we store a spare
- * word at the end. And it would be a shame to fill it
- * with zeroes when we could use more bits of 2/pi... */
- 0xfe5163ab
- };
-
- /*
- * Multiprecision multiplication of this nature is more
- * readily done in integers than in VFP, since we can use
- * UMULL (on CPUs that support it) to multiply 32 by 32 bits
- * at a time whereas the VFP would only be able to do 12x12
- * without losing accuracy.
- *
- * So extract the mantissa of the input number as a 32-bit
- * integer.
- */
- unsigned mantissa = 0x80000000 | (k << 8);
-
- /*
- * Now work out which part of our stored value of 2/pi we're
- * supposed to be multiplying by.
- *
- * Let the IEEE exponent field of x be e. With its bias
- * removed, (e-127) is the index of the set bit at the top
- * of 'mantissa' (i.e. that set bit has real place value
- * 2^(e-127)). So the lowest set bit in 'mantissa', 23 bits
- * further down, must have place value 2^(e-150).
- *
- * We begin taking an interest in the value of 2/pi at the
- * bit which multiplies by _that_ to give something with
- * place value at most 2. In other words, the highest bit of
- * 2/pi we're interested in is the one with place value
- * 2/(2^(e-150)) = 2^(151-e).
- *
- * The bit at the top of the first (zero) word of the above
- * array has place value 2^31. Hence, the bit we want to put
- * at the top of the first word we extract from that array
- * is the one at bit index n, where 31-n = 151-e and hence
- * n=e-120.
- */
- int topbitindex = ((k >> 23) & 0xFF) - 120;
- int wordindex = topbitindex >> 5;
- int shiftup = topbitindex & 31;
- int shiftdown = 32 - shiftup;
- unsigned word1, word2, word3;
- if (shiftup) {
- word1 = (twooverpi[wordindex] << shiftup) | (twooverpi[wordindex+1] >> shiftdown);
- word2 = (twooverpi[wordindex+1] << shiftup) | (twooverpi[wordindex+2] >> shiftdown);
- word3 = (twooverpi[wordindex+2] << shiftup) | (twooverpi[wordindex+3] >> shiftdown);
- } else {
- word1 = twooverpi[wordindex];
- word2 = twooverpi[wordindex+1];
- word3 = twooverpi[wordindex+2];
- }
-
- /*
- * Do the multiplications, and add them together.
- */
- unsigned long long mult1 = (unsigned long long)word1 * mantissa;
- unsigned long long mult2 = (unsigned long long)word2 * mantissa;
- unsigned long long mult3 = (unsigned long long)word3 * mantissa;
-
- unsigned /* bottom3 = (unsigned)mult3, */ top3 = (unsigned)(mult3 >> 32);
- unsigned bottom2 = (unsigned)mult2, top2 = (unsigned)(mult2 >> 32);
- unsigned bottom1 = (unsigned)mult1, top1 = (unsigned)(mult1 >> 32);
-
- unsigned out3, out2, out1, carry;
-
- out3 = top3 + bottom2; carry = (out3 < top3);
- out2 = top2 + bottom1 + carry; carry = carry ? (out2 <= top2) : (out2 < top2);
- out1 = top1 + carry;
-
- /*
- * The two words we multiplied to get mult1 had their top
- * bits at (respectively) place values 2^(151-e) and
- * 2^(e-127). The value of those two bits multiplied
- * together will have ended up in bit 62 (the
- * topmost-but-one bit) of mult1, i.e. bit 30 of out1.
- * Hence, that bit has place value 2^(151-e+e-127) = 2^24.
- * So the integer value that we want to output as q,
- * consisting of the bits with place values 2^1 and 2^0,
- * must be 23 and 24 bits below that, i.e. in bits 7 and 6
- * of out1.
- *
- * Or, at least, it will be once we add 1/2, to round to the
- * _nearest_ multiple of pi/2 rather than the next one down.
- */
- *q = (out1 + (1<<5)) >> 6;
-
- /*
- * Now we construct the output fraction, which is most
- * simply done in the VFP. We just extract three consecutive
- * bit strings from our chunk of binary data, convert them
- * to integers, equip each with an appropriate FP exponent,
- * add them together, and (don't forget) multiply back up by
- * pi/2. That way we don't have to work out ourselves where
- * the highest fraction bit ended up.
- *
- * Since our displacement from the nearest multiple of pi/2
- * can be positive or negative, the topmost of these three
- * values must be arranged with its 2^-1 bit at the very top
- * of the word, and then treated as a _signed_ integer.
- */
- {
- int i1 = (out1 << 26) | ((out2 >> 19) << 13);
- unsigned i2 = out2 << 13;
- unsigned i3 = out3;
- float f1 = i1, f2 = i2 * (1.0f/524288.0f), f3 = i3 * (1.0f/524288.0f/524288.0f);
-
- /*
- * Now f1+f2+f3 is a representation, potentially to
- * twice double precision, of 2^32 times ((2/pi)*x minus
- * some integer). So our remaining job is to multiply
- * back down by (pi/2)*2^-32, and convert back to one
- * single-precision output number.
- */
-
- /* Normalise to a prec-and-a-half representation... */
- float ftop = CLEARBOTTOMHALF(f1+f2+f3), fbot = f3-((ftop-f1)-f2);
-
- /* ... and multiply by a prec-and-a-half value of (pi/2)*2^-32. */
- float ret = (ftop * 0x1.92p-32F) + (ftop * 0x1.fb5444p-44F + fbot * 0x1.921fb6p-32F);
-
- /* Just before we return, take the input sign into account. */
- if (k & 0x80000000) {
- *q = 0x10000000 - *q;
- ret = -ret;
- }
- return ret;
- }
- }
-}
-
-#ifdef __cplusplus
-} /* end of extern "C" */
-#endif /* __cplusplus */
-
-/* end of rredf.c */
diff --git a/math/single/rredf.h b/math/single/rredf.h
deleted file mode 100644
index 41d3a0c..0000000
--- a/math/single/rredf.h
+++ /dev/null
@@ -1,146 +0,0 @@
-/*
- * rredf.h - trigonometric range reduction function written new for RVCT 4.1
- *
- * Copyright (c) 2009-2018, Arm Limited.
- * SPDX-License-Identifier: MIT
- */
-
-/*
- * This header file defines an inline function which all three of
- * the single-precision trig functions (sinf, cosf, tanf) should use
- * to perform range reduction. The inline function handles the
- * quickest and most common cases inline, before handing off to an
- * out-of-line function defined in rredf.c for everything else. Thus
- * a reasonable compromise is struck between speed and space. (I
- * hope.) In particular, this approach avoids a function call
- * overhead in the common case.
- */
-
-#ifndef _included_rredf_h
-#define _included_rredf_h
-
-#include "math_private.h"
-
-#ifdef __cplusplus
-extern "C" {
-#endif /* __cplusplus */
-
-extern float __mathlib_rredf2(float x, int *q, unsigned k);
-
-/*
- * Semantics of the function:
- * - x is the single-precision input value provided by the user
- * - the return value is in the range [-pi/4,pi/4], and is equal
- * (within reasonable accuracy bounds) to x minus n*pi/2 for some
- * integer n. (FIXME: perhaps some slippage on the output
- * interval is acceptable, requiring more range from the
- * following polynomial approximations but permitting more
- * approximate rred decisions?)
- * - *q is set to a positive value whose low two bits match those
- * of n. Alternatively, it comes back as -1 indicating that the
- * input value was trivial in some way (infinity, NaN, or so
- * small that we can safely return sin(x)=tan(x)=x,cos(x)=1).
- */
-static __inline float __mathlib_rredf(float x, int *q)
-{
- /*
- * First, extract the bit pattern of x as an integer, so that we
- * can repeatedly compare things to it without multiple
- * overheads in retrieving comparison results from the VFP.
- */
- unsigned k = fai(x);
-
- /*
- * Deal immediately with the simplest possible case, in which x
- * is already within the interval [-pi/4,pi/4]. This also
- * identifies the subcase of ludicrously small x.
- */
- if ((k << 1) < (0x3f490fdb << 1)) {
- if ((k << 1) < (0x39800000 << 1))
- *q = -1;
- else
- *q = 0;
- return x;
- }
-
- /*
- * The next plan is to multiply x by 2/pi and convert to an
- * integer, which gives us n; then we subtract n*pi/2 from x to
- * get our output value.
- *
- * By representing pi/2 in that final step by a prec-and-a-half
- * approximation, we can arrange good accuracy for n strictly
- * less than 2^13 (so that an FP representation of n has twelve
- * zero bits at the bottom). So our threshold for this strategy
- * is 2^13 * pi/2 - pi/4, otherwise known as 8191.75 * pi/2 or
- * 4095.875*pi. (Or, for those perverse people interested in
- * actual numbers rather than multiples of pi/2, about 12867.5.)
- */
- if (__builtin_expect((k & 0x7fffffff) < 0x46490e49, 1)) {
- float nf = 0.636619772367581343f * x;
- /*
- * The difference between that single-precision constant and
- * the real 2/pi is about 2.568e-8. Hence the product nf has a
- * potential error of 2.568e-8|x| even before rounding; since
- * |x| < 4096 pi, that gives us an error bound of about
- * 0.0003305.
- *
- * nf is then rounded to single precision, with a max error of
- * 1/2 ULP, and since nf goes up to just under 8192, half a
- * ULP could be as big as 2^-12 ~= 0.0002441.
- *
- * So by the time we convert nf to an integer, it could be off
- * by that much, causing the wrong integer to be selected, and
- * causing us to return a value a little bit outside the
- * theoretical [-pi/4,+pi/4] output interval.
- *
- * How much outside? Well, we subtract nf*pi/2 from x, so the
- * error bounds above have be be multiplied by pi/2. And if
- * both of the above sources of error suffer their worst cases
- * at once, then the very largest value we could return is
- * obtained by adding that lot to the interval bound pi/4 to
- * get
- *
- * pi/4 + ((2/pi - 0f_3f22f983)*4096*pi + 2^-12) * pi/2
- *
- * which comes to 0f_3f494b02. (Compare 0f_3f490fdb = pi/4.)
- *
- * So callers of this range reducer should be prepared to
- * handle numbers up to that large.
- */
-#ifdef __TARGET_FPU_SOFTVFP
- nf = _frnd(nf);
-#else
- if (k & 0x80000000)
- nf = (nf - 8388608.0f) + 8388608.0f;
- else
- nf = (nf + 8388608.0f) - 8388608.0f; /* round to _nearest_ integer. FIXME: use some sort of frnd in softfp */
-#endif
- *q = 3 & (int)nf;
-#if 0
- /*
- * FIXME: now I need a bunch of special cases to avoid
- * having to do the full four-word reduction every time.
- * Also, adjust the comment at the top of this section!
- */
- if (__builtin_expect((k & 0x7fffffff) < 0x46490e49, 1))
- return ((x - nf * 0x1.92p+0F) - nf * 0x1.fb4p-12F) - nf * 0x1.4442d2p-24F;
- else
-#endif
- return ((x - nf * 0x1.92p+0F) - nf * 0x1.fb4p-12F) - nf * 0x1.444p-24F - nf * 0x1.68c234p-39F;
- }
-
- /*
- * That's enough to do in-line; if we're still playing, hand off
- * to the out-of-line main range reducer.
- */
- return __mathlib_rredf2(x, q, k);
-}
-
-#ifdef __cplusplus
-} /* end of extern "C" */
-#endif /* __cplusplus */
-
-#endif /* included */
-
-/* end of rredf.h */
diff --git a/math/single/s_cosf.c b/math/single/s_cosf.c
deleted file mode 100644
index 0e40b52..0000000
--- a/math/single/s_cosf.c
+++ /dev/null
@@ -1,11 +0,0 @@
-/*
- * s_cosf.c - single precision cosine function
- *
- * Copyright (c) 2009-2018, Arm Limited.
- * SPDX-License-Identifier: MIT
- */
-
-#define COSINE
-#include "s_sincosf.c"
-
-/* end of s_cosf.c */
diff --git a/math/single/s_sincosf.c b/math/single/s_sincosf.c
deleted file mode 100644
index 38a8511..0000000
--- a/math/single/s_sincosf.c
+++ /dev/null
@@ -1,109 +0,0 @@
-/*
- * s_sincosf.c - single precision sine and cosine functions
- *
- * Copyright (c) 2009-2018, Arm Limited.
- * SPDX-License-Identifier: MIT
- */
-
-/*
- * Source: my own head, and Remez-generated polynomial approximations.
- */
-
-#include <fenv.h>
-#include <math.h>
-#include <errno.h>
-#include "rredf.h"
-#include "math_private.h"
-
-#ifdef __cplusplus
-extern "C" {
-#endif /* __cplusplus */
-
-#ifndef COSINE
-#define FUNCNAME sinf
-#define SOFTFP_FUNCNAME __softfp_sinf
-#define DO_SIN (!(q & 1))
-#define NEGATE_SIN ((q & 2))
-#define NEGATE_COS ((q & 2))
-#define TRIVIAL_RESULT(x) FLOAT_CHECKDENORM(x)
-#define ERR_INF MATHERR_SINF_INF
-#else
-#define FUNCNAME cosf
-#define SOFTFP_FUNCNAME __softfp_cosf
-#define DO_SIN (q & 1)
-#define NEGATE_SIN (!(q & 2))
-#define NEGATE_COS ((q & 2))
-#define TRIVIAL_RESULT(x) 1.0f
-#define ERR_INF MATHERR_COSF_INF
-#endif
-
-float FUNCNAME(float x)
-{
- int q;
-
- /*
- * Range-reduce x to the range [-pi/4,pi/4].
- */
- {
- /*
- * I enclose the call to __mathlib_rredf in braces so that
- * the address-taken-ness of qq does not propagate
- * throughout the rest of the function, for what that might
- * be worth.
- */
- int qq;
- x = __mathlib_rredf(x, &qq);
- q = qq;
- }
- if (__builtin_expect(q < 0, 0)) { /* this signals tiny, inf, or NaN */
- unsigned k = fai(x) << 1;
- if (k < 0xFF000000) /* tiny */
- return TRIVIAL_RESULT(x);
- else if (k == 0xFF000000) /* inf */
- return ERR_INF(x);
- else /* NaN */
- return FLOAT_INFNAN(x);
- }
-
- /*
- * Depending on the quadrant we were in, we may have to compute
- * a sine-like function (f(0)=0) or a cosine-like one (f(0)=1),
- * and we may have to negate it.
- */
- if (DO_SIN) {
- float x2 = x*x;
- /*
- * Coefficients generated by the command
-
-./auxiliary/remez.jl --variable=x2 --suffix=f -- '0' 'atan(BigFloat(1))^2' 2 0 'x==0 ? -1/BigFloat(6) : (x->(sin(x)-x)/x^3)(sqrt(x))' 'sqrt(x^3)'
-
- */
- x += x * (x2 * (
- -1.666665066929417292436220415142244613956015227491999719404711781344783392564922e-01f+x2*(8.331978663157089651408875887703995477889496917296385733254577121461421466427772e-03f+x2*(-1.949563623766929906511886482584265500187314705496861877317774185883215997931494e-04f))
- ));
- if (NEGATE_SIN)
- x = -x;
- return x;
- } else {
- float x2 = x*x;
- /*
- * Coefficients generated by the command
-
-./auxiliary/remez.jl --variable=x2 --suffix=f -- '0' 'atan(BigFloat(1))^2' 2 0 'x==0 ? -1/BigFloat(6) : (x->(cos(x)-1)/x^2)(sqrt(x))' 'x'
-
- */
- x = 1.0f + x2*(
- -4.999989478137016757327030935768632852012781143541026304540837816323349768666875e-01f+x2*(4.165629457842617238353362092016541041535652603456375154392942188742496860024377e-02f+x2*(-1.35978231111049428748566568960423202948250988565693107969571193763372093404347e-03f))
- );
- if (NEGATE_COS)
- x = -x;
- return x;
- }
-}
-
-
-#ifdef __cplusplus
-} /* end of extern "C" */
-#endif /* __cplusplus */
-
-/* end of sincosf.c */
diff --git a/math/single/s_sinf.c b/math/single/s_sinf.c
deleted file mode 100644
index ab0f628..0000000
--- a/math/single/s_sinf.c
+++ /dev/null
@@ -1,11 +0,0 @@
-/*
- * s_sinf.c - single precision sine function
- *
- * Copyright (c) 2009-2018, Arm Limited.
- * SPDX-License-Identifier: MIT
- */
-
-#define SINE
-#include "s_sincosf.c"
-
-/* end of s_sinf.c */
diff --git a/math/single/s_tanf.c b/math/single/s_tanf.c
deleted file mode 100644
index 0e13d95..0000000
--- a/math/single/s_tanf.c
+++ /dev/null
@@ -1,77 +0,0 @@
-/*
- * s_tanf.c - single precision tangent function
- *
- * Copyright (c) 2009-2018, Arm Limited.
- * SPDX-License-Identifier: MIT
- */
-
-/*
- * Source: my own head, and Remez-generated polynomial approximations.
- */
-
-#include <math.h>
-#include "math_private.h"
-#include <errno.h>
-#include <fenv.h>
-#include "rredf.h"
-
-#ifdef __cplusplus
-extern "C" {
-#endif /* __cplusplus */
-
-float tanf(float x)
-{
- int q;
-
- /*
- * Range-reduce x to the range [-pi/4,pi/4].
- */
- {
- /*
- * I enclose the call to __mathlib_rredf in braces so that
- * the address-taken-ness of qq does not propagate
- * throughout the rest of the function, for what that might
- * be worth.
- */
- int qq;
- x = __mathlib_rredf(x, &qq);
- q = qq;
- }
- if (__builtin_expect(q < 0, 0)) { /* this signals tiny, inf, or NaN */
- unsigned k = fai(x) << 1;
- if (k < 0xFF000000) /* tiny */
- return FLOAT_CHECKDENORM(x);
- else if (k == 0xFF000000) /* inf */
- return MATHERR_TANF_INF(x);
- else /* NaN */
- return FLOAT_INFNAN(x);
- }
-
- /*
- * We use a direct polynomial approximation for tan(x) on
- * [-pi/4,pi/4], and then take the negative reciprocal of the
- * result if we're in an interval surrounding an odd rather than
- * even multiple of pi/2.
- *
- * Coefficients generated by the command
-
-./auxiliary/remez.jl --variable=x2 --suffix=f -- '0' '(pi/BigFloat(4))^2' 5 0 'x==0 ? 1/BigFloat(3) : (tan(sqrt(x))-sqrt(x))/sqrt(x^3)' 'sqrt(x^3)'
-
- */
- {
- float x2 = x*x;
- x += x * (x2 * (
- 3.333294809182307633621540045249152105330074691488121206914336806061620616979305e-01f+x2*(1.334274588580033216191949445078951865160600494428914956688702429547258497367525e-01f+x2*(5.315177279765676178198868818834880279286012428084733419724267810723468887753723e-02f+x2*(2.520300881849204519070372772571624013984546591252791443673871814078418474596388e-02f+x2*(2.051177187082974766686645514206648277055233230110624602600687812103764075834307e-03f+x2*(9.943421494628597182458186353995299429948224864648292162238582752158235742046109e-03f)))))
- ));
- if (q & 1)
- x = -1.0f/x;
-
- return x;
- }
-}
-
-#ifdef __cplusplus
-} /* end of extern "C" */
-#endif /* __cplusplus */
-
-/* end of s_tanf.c */
diff --git a/math/tanf.c b/math/tanf.c
deleted file mode 100644
index d3799f5..0000000
--- a/math/tanf.c
+++ /dev/null
@@ -1,3 +0,0 @@
-#if WANT_SINGLEPREC
-#include "single/s_tanf.c"
-#endif
diff --git a/test/mathbench.c b/math/test/mathbench.c
similarity index 100%
rename from test/mathbench.c
rename to math/test/mathbench.c
diff --git a/test/mathtest.c b/math/test/mathtest.c
similarity index 99%
rename from test/mathtest.c
rename to math/test/mathtest.c
index f535452..6ea3953 100644
--- a/test/mathtest.c
+++ b/math/test/mathtest.c
@@ -40,8 +40,6 @@
_Pragma(STR(import IMPORT_SYMBOL))
#endif
-EXTERN_C int __ieee754_rem_pio2(double, double *);
-
int dmsd, dlsd;
int quiet = 0;
@@ -1094,7 +1092,6 @@
case m_islessgreaterf: intres = islessgreater(s_arg1.f, s_arg2.f); break;
case m_isunorderedf: intres = isunordered(s_arg1.f, s_arg2.f); break;
- case m_rred: intres = 3 & __ieee754_rem_pio2(d_arg1.f, d_res.da); break;
default:
printf("unhandled macro: %s\n",t.func->name);
return test_fail;
diff --git a/test/rtest/dotest.c b/math/test/rtest/dotest.c
similarity index 100%
rename from test/rtest/dotest.c
rename to math/test/rtest/dotest.c
diff --git a/test/rtest/intern.h b/math/test/rtest/intern.h
similarity index 100%
rename from test/rtest/intern.h
rename to math/test/rtest/intern.h
diff --git a/test/rtest/main.c b/math/test/rtest/main.c
similarity index 100%
rename from test/rtest/main.c
rename to math/test/rtest/main.c
diff --git a/test/rtest/random.c b/math/test/rtest/random.c
similarity index 100%
rename from test/rtest/random.c
rename to math/test/rtest/random.c
diff --git a/test/rtest/random.h b/math/test/rtest/random.h
similarity index 100%
rename from test/rtest/random.h
rename to math/test/rtest/random.h
diff --git a/test/rtest/semi.c b/math/test/rtest/semi.c
similarity index 100%
rename from test/rtest/semi.c
rename to math/test/rtest/semi.c
diff --git a/test/rtest/semi.h b/math/test/rtest/semi.h
similarity index 100%
rename from test/rtest/semi.h
rename to math/test/rtest/semi.h
diff --git a/test/rtest/types.h b/math/test/rtest/types.h
similarity index 100%
rename from test/rtest/types.h
rename to math/test/rtest/types.h
diff --git a/test/rtest/wrappers.c b/math/test/rtest/wrappers.c
similarity index 100%
rename from test/rtest/wrappers.c
rename to math/test/rtest/wrappers.c
diff --git a/test/rtest/wrappers.h b/math/test/rtest/wrappers.h
similarity index 100%
rename from test/rtest/wrappers.h
rename to math/test/rtest/wrappers.h
diff --git a/math/test/runulp.sh b/math/test/runulp.sh
new file mode 100755
index 0000000..d7d79a4
--- /dev/null
+++ b/math/test/runulp.sh
@@ -0,0 +1,85 @@
+#!/bin/bash
+
+# ULP error check script.
+#
+# Copyright (c) 2019, Arm Limited.
+# SPDX-License-Identifier: MIT
+
+#set -x
+set -eu
+
+# cd to bin directory.
+cd "${0%/*}"
+
+rmodes='n u d z'
+#rmodes=n
+flags='-q'
+emu="$@"
+
+t() {
+ [ $r = "n" ] && Lt=$L || Lt=$Ldir
+ $emu ./ulp -r $r -e $Lt $flags "$@"
+}
+
+Ldir=0.5
+for r in $rmodes
+do
+L=0.01
+t exp 0 0xffff000000000000 10000
+t exp 0x1p-6 0x1p6 40000
+t exp -0x1p-6 -0x1p6 40000
+t exp 633.3 733.3 10000
+t exp -633.3 -777.3 10000
+
+L=0.01
+t exp2 0 0xffff000000000000 10000
+t exp2 0x1p-6 0x1p6 40000
+t exp2 -0x1p-6 -0x1p6 40000
+t exp2 633.3 733.3 10000
+t exp2 -633.3 -777.3 10000
+
+L=0.05
+t pow 0.5 2.0 x 0 inf 20000
+t pow -0.5 -2.0 x 0 inf 20000
+t pow 0.5 2.0 x -0 -inf 20000
+t pow -0.5 -2.0 x -0 -inf 20000
+t pow 0.5 2.0 x 0x1p-10 0x1p10 40000
+t pow 0.5 2.0 x -0x1p-10 -0x1p10 40000
+t pow 0 inf x 0.5 2.0 80000
+t pow 0 inf x -0.5 -2.0 80000
+t pow 0x1.fp-1 0x1.08p0 x 0x1p8 0x1p17 80000
+t pow 0x1.fp-1 0x1.08p0 x -0x1p8 -0x1p17 80000
+t pow 0 0x1p-1000 x 0 1.0 50000
+t pow 0x1p1000 inf x 0 1.0 50000
+t pow 0x1.ffffffffffff0p-1 0x1.0000000000008p0 x 0x1p60 0x1p68 50000
+t pow 0x1.ffffffffff000p-1 0x1p0 x 0x1p50 0x1p52 50000
+t pow -0x1.ffffffffff000p-1 -0x1p0 x 0x1p50 0x1p52 50000
+
+L=0.01
+t expf 0 0xffff0000 10000
+t expf 0x1p-14 0x1p8 50000
+t expf -0x1p-14 -0x1p8 50000
+
+L=0.01
+t exp2f 0 0xffff0000 10000
+t exp2f 0x1p-14 0x1p8 50000
+t exp2f -0x1p-14 -0x1p8 50000
+
+L=0.06
+t sinf 0 0xffff0000 10000
+t sinf 0x1p-14 0x1p54 50000
+t sinf -0x1p-14 -0x1p54 50000
+
+L=0.06
+t cosf 0 0xffff0000 10000
+t cosf 0x1p-14 0x1p54 50000
+t cosf -0x1p-14 -0x1p54 50000
+
+L=0.4
+t powf 0x1p-1 0x1p1 x 0x1p-7 0x1p7 50000
+t powf 0x1p-1 0x1p1 x -0x1p-7 -0x1p7 50000
+t powf 0x1p-70 0x1p70 x 0x1p-1 0x1p1 50000
+t powf 0x1p-70 0x1p70 x -0x1p-1 -0x1p1 50000
+t powf 0x1.ep-1 0x1.1p0 x 0x1p8 0x1p14 50000
+t powf 0x1.ep-1 0x1.1p0 x -0x1p8 -0x1p14 50000
+done
diff --git a/test/testcases/directed/cosf.tst b/math/test/testcases/directed/cosf.tst
similarity index 100%
rename from test/testcases/directed/cosf.tst
rename to math/test/testcases/directed/cosf.tst
diff --git a/test/testcases/directed/exp.tst b/math/test/testcases/directed/exp.tst
similarity index 100%
rename from test/testcases/directed/exp.tst
rename to math/test/testcases/directed/exp.tst
diff --git a/test/testcases/directed/exp2.tst b/math/test/testcases/directed/exp2.tst
similarity index 100%
rename from test/testcases/directed/exp2.tst
rename to math/test/testcases/directed/exp2.tst
diff --git a/test/testcases/directed/exp2f.tst b/math/test/testcases/directed/exp2f.tst
similarity index 100%
rename from test/testcases/directed/exp2f.tst
rename to math/test/testcases/directed/exp2f.tst
diff --git a/test/testcases/directed/expf.tst b/math/test/testcases/directed/expf.tst
similarity index 100%
rename from test/testcases/directed/expf.tst
rename to math/test/testcases/directed/expf.tst
diff --git a/test/testcases/directed/log.tst b/math/test/testcases/directed/log.tst
similarity index 100%
rename from test/testcases/directed/log.tst
rename to math/test/testcases/directed/log.tst
diff --git a/test/testcases/directed/log2.tst b/math/test/testcases/directed/log2.tst
similarity index 100%
rename from test/testcases/directed/log2.tst
rename to math/test/testcases/directed/log2.tst
diff --git a/test/testcases/directed/log2f.tst b/math/test/testcases/directed/log2f.tst
similarity index 100%
rename from test/testcases/directed/log2f.tst
rename to math/test/testcases/directed/log2f.tst
diff --git a/test/testcases/directed/logf.tst b/math/test/testcases/directed/logf.tst
similarity index 100%
rename from test/testcases/directed/logf.tst
rename to math/test/testcases/directed/logf.tst
diff --git a/test/testcases/directed/pow.tst b/math/test/testcases/directed/pow.tst
similarity index 100%
rename from test/testcases/directed/pow.tst
rename to math/test/testcases/directed/pow.tst
diff --git a/test/testcases/directed/powf.tst b/math/test/testcases/directed/powf.tst
similarity index 100%
rename from test/testcases/directed/powf.tst
rename to math/test/testcases/directed/powf.tst
diff --git a/test/testcases/directed/sincosf.tst b/math/test/testcases/directed/sincosf.tst
similarity index 100%
rename from test/testcases/directed/sincosf.tst
rename to math/test/testcases/directed/sincosf.tst
diff --git a/test/testcases/directed/sinf.tst b/math/test/testcases/directed/sinf.tst
similarity index 100%
rename from test/testcases/directed/sinf.tst
rename to math/test/testcases/directed/sinf.tst
diff --git a/test/testcases/random/double.tst b/math/test/testcases/random/double.tst
similarity index 92%
rename from test/testcases/random/double.tst
rename to math/test/testcases/random/double.tst
index 4306259..c37e837 100644
--- a/test/testcases/random/double.tst
+++ b/math/test/testcases/random/double.tst
@@ -3,7 +3,6 @@
!! Copyright (c) 1999-2018, Arm Limited.
!! SPDX-License-Identifier: MIT
-test rred 10000
test exp 10000
test exp2 10000
test log 10000
diff --git a/test/testcases/random/float.tst b/math/test/testcases/random/float.tst
similarity index 100%
rename from test/testcases/random/float.tst
rename to math/test/testcases/random/float.tst
diff --git a/test/traces/exp.txt b/math/test/traces/exp.txt
similarity index 100%
rename from test/traces/exp.txt
rename to math/test/traces/exp.txt
diff --git a/test/traces/sincosf.txt b/math/test/traces/sincosf.txt
similarity index 100%
rename from test/traces/sincosf.txt
rename to math/test/traces/sincosf.txt
diff --git a/math/test/ulp.c b/math/test/ulp.c
new file mode 100644
index 0000000..8de6e5b
--- /dev/null
+++ b/math/test/ulp.c
@@ -0,0 +1,714 @@
+/*
+ * ULP error checking tool for math functions.
+ *
+ * Copyright (c) 2019, Arm Limited.
+ * SPDX-License-Identifier: MIT
+ */
+
+#include <ctype.h>
+#include <fenv.h>
+#include <float.h>
+#include <math.h>
+#include <stdint.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+
+/* Don't depend on mpfr by default. */
+#ifndef USE_MPFR
+# define USE_MPFR 0
+#endif
+#if USE_MPFR
+# include <mpfr.h>
+#endif
+
+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
+asuint (float f)
+{
+ union
+ {
+ float f;
+ uint32_t i;
+ } u = {f};
+ return u.i;
+}
+
+static inline float
+asfloat (uint32_t i)
+{
+ union
+ {
+ uint32_t i;
+ float f;
+ } u = {i};
+ return u.f;
+}
+
+static uint64_t seed = 0x0123456789abcdef;
+static uint64_t
+rand64 (void)
+{
+ seed = 6364136223846793005ull * seed + 1;
+ return seed ^ (seed >> 32);
+}
+
+/* Uniform random in [0,n]. */
+static uint64_t
+randn (uint64_t n)
+{
+ uint64_t r, m;
+
+ if (n == 0)
+ return 0;
+ n++;
+ if (n == 0)
+ return rand64 ();
+ for (;;)
+ {
+ r = rand64 ();
+ m = r % n;
+ if (r - m <= -n)
+ return m;
+ }
+}
+
+struct gen
+{
+ uint64_t start;
+ uint64_t len;
+ uint64_t start2;
+ uint64_t len2;
+ uint64_t off;
+ uint64_t step;
+ uint64_t cnt;
+};
+
+struct args_f1
+{
+ float x;
+};
+
+struct args_f2
+{
+ float x;
+ float x2;
+};
+
+struct args_d1
+{
+ double x;
+};
+
+struct args_d2
+{
+ double x;
+ double x2;
+};
+
+/* result = y + tail*2^ulpexp. */
+struct ret_f
+{
+ float y;
+ double tail;
+ int ulpexp;
+ int ex;
+ int ex_may;
+};
+
+struct ret_d
+{
+ double y;
+ double tail;
+ int ulpexp;
+ int ex;
+ int ex_may;
+};
+
+static inline uint64_t
+next1 (struct gen *g)
+{
+ /* For single argument use randomized incremental steps,
+ that produce dense sampling without collisions and allow
+ testing all inputs in a range. */
+ uint64_t r = g->start + g->off;
+ g->off += g->step + randn (g->step / 2);
+ if (g->off > g->len)
+ g->off -= g->len; /* hack. */
+ return r;
+}
+
+static inline uint64_t
+next2 (uint64_t *x2, struct gen *g)
+{
+ /* For two arguments use uniform random sampling. */
+ uint64_t r = g->start + randn (g->len);
+ *x2 = g->start2 + randn (g->len2);
+ return r;
+}
+
+static struct args_f1
+next_f1 (void *g)
+{
+ return (struct args_f1){asfloat (next1 (g))};
+}
+
+static struct args_f2
+next_f2 (void *g)
+{
+ uint64_t x2;
+ uint64_t x = next2 (&x2, g);
+ return (struct args_f2){asfloat (x), asfloat (x2)};
+}
+
+static struct args_d1
+next_d1 (void *g)
+{
+ return (struct args_d1){asdouble (next1 (g))};
+}
+
+static struct args_d2
+next_d2 (void *g)
+{
+ uint64_t x2;
+ uint64_t x = next2 (&x2, g);
+ return (struct args_d2){asdouble (x), asdouble (x2)};
+}
+
+struct conf
+{
+ int r;
+ int rc;
+ int quiet;
+ int mpfr;
+ int fenv;
+ unsigned long long n;
+ double softlim;
+ double errlim;
+};
+
+struct fun
+{
+ const char *name;
+ int arity;
+ int singleprec;
+ union
+ {
+ float (*f1) (float);
+ float (*f2) (float, float);
+ double (*d1) (double);
+ double (*d2) (double, double);
+ } fun;
+ union
+ {
+ double (*f1) (double);
+ double (*f2) (double, double);
+ long double (*d1) (long double);
+ long double (*d2) (long double, long double);
+ } fun_long;
+#if USE_MPFR
+ union
+ {
+ int (*f1) (mpfr_t, const mpfr_t, mpfr_rnd_t);
+ int (*f2) (mpfr_t, const mpfr_t, const mpfr_t, mpfr_rnd_t);
+ int (*d1) (mpfr_t, const mpfr_t, mpfr_rnd_t);
+ int (*d2) (mpfr_t, const mpfr_t, const mpfr_t, mpfr_rnd_t);
+ } fun_mpfr;
+#endif
+};
+
+static const struct fun fun[] = {
+#if USE_MPFR
+# define F(x, x_long, x_mpfr, a, s, t) \
+ {#x, a, s, {.t = x}, {.t = x_long}, {.t = x_mpfr}},
+#else
+# define F(x, x_long, x_mpfr, a, s, t) \
+ {#x, a, s, {.t = x}, {.t = x_long}},
+#endif
+#define F1(x) F (x##f, x, mpfr_##x, 1, 1, f1)
+#define F2(x) F (x##f, x, mpfr_##x, 2, 1, f2)
+#define D1(x) F (x, x##l, mpfr_##x, 1, 0, d1)
+#define D2(x) F (x, x##l, mpfr_##x, 2, 0, d2)
+ F1 (sin)
+ F1 (cos)
+ F1 (exp)
+ F1 (exp2)
+ F1 (log)
+ F1 (log2)
+ F2 (pow)
+ D1 (exp)
+ D1 (exp2)
+ D1 (log)
+ D1 (log2)
+ D2 (pow)
+ {0}};
+
+/* Boilerplate for generic calls. */
+
+static inline int
+ulpscale_f (float x)
+{
+ int e = asuint (x) >> 23 & 0xff;
+ if (!e)
+ e++;
+ return e - 0x7f - 23;
+}
+static inline int
+ulpscale_d (double x)
+{
+ int e = asuint64 (x) >> 52 & 0x7ff;
+ if (!e)
+ e++;
+ return e - 0x3ff - 52;
+}
+static inline float
+call_f1 (const struct fun *f, struct args_f1 a)
+{
+ return f->fun.f1 (a.x);
+}
+static inline float
+call_f2 (const struct fun *f, struct args_f2 a)
+{
+ return f->fun.f2 (a.x, a.x2);
+}
+
+static inline double
+call_d1 (const struct fun *f, struct args_d1 a)
+{
+ return f->fun.d1 (a.x);
+}
+static inline double
+call_d2 (const struct fun *f, struct args_d2 a)
+{
+ return f->fun.d2 (a.x, a.x2);
+}
+static inline double
+call_long_f1 (const struct fun *f, struct args_f1 a)
+{
+ return f->fun_long.f1 (a.x);
+}
+static inline double
+call_long_f2 (const struct fun *f, struct args_f2 a)
+{
+ return f->fun_long.f2 (a.x, a.x2);
+}
+static inline long double
+call_long_d1 (const struct fun *f, struct args_d1 a)
+{
+ return f->fun_long.d1 (a.x);
+}
+static inline long double
+call_long_d2 (const struct fun *f, struct args_d2 a)
+{
+ return f->fun_long.d2 (a.x, a.x2);
+}
+static inline void
+printcall_f1 (const struct fun *f, struct args_f1 a)
+{
+ printf ("%s(%a)", f->name, a.x);
+}
+static inline void
+printcall_f2 (const struct fun *f, struct args_f2 a)
+{
+ printf ("%s(%a, %a)", f->name, a.x, a.x2);
+}
+static inline void
+printcall_d1 (const struct fun *f, struct args_d1 a)
+{
+ printf ("%s(%a)", f->name, a.x);
+}
+static inline void
+printcall_d2 (const struct fun *f, struct args_d2 a)
+{
+ printf ("%s(%a, %a)", f->name, a.x, a.x2);
+}
+static inline void
+printgen_f1 (const struct fun *f, struct gen *gen)
+{
+ printf ("%s in [%a;%a]", f->name, asfloat (gen->start),
+ asfloat (gen->start + gen->len));
+}
+static inline void
+printgen_f2 (const struct fun *f, struct gen *gen)
+{
+ printf ("%s in [%a;%a] x [%a;%a]", f->name, asfloat (gen->start),
+ asfloat (gen->start + gen->len), asfloat (gen->start2),
+ asfloat (gen->start2 + gen->len2));
+}
+static inline void
+printgen_d1 (const struct fun *f, struct gen *gen)
+{
+ printf ("%s in [%a;%a]", f->name, asdouble (gen->start),
+ asdouble (gen->start + gen->len));
+}
+static inline void
+printgen_d2 (const struct fun *f, struct gen *gen)
+{
+ printf ("%s in [%a;%a] x [%a;%a]", f->name, asdouble (gen->start),
+ asdouble (gen->start + gen->len), asdouble (gen->start2),
+ asdouble (gen->start2 + gen->len2));
+}
+
+#define reduce_f1(a, f, op) (f (a.x))
+#define reduce_f2(a, f, op) (f (a.x) op f (a.x2))
+#define reduce_d1(a, f, op) (f (a.x))
+#define reduce_d2(a, f, op) (f (a.x) op f (a.x2))
+
+#ifndef IEEE_754_2008_SNAN
+# define IEEE_754_2008_SNAN 1
+#endif
+static inline int
+issignaling_f (float x)
+{
+ uint32_t ix = asuint (x);
+ if (!IEEE_754_2008_SNAN)
+ return (ix & 0x7fc00000) == 0x7fc00000;
+ return 2 * (ix ^ 0x00400000) > 2u * 0x7fc00000;
+}
+static inline int
+issignaling_d (double x)
+{
+ uint64_t ix = asuint64 (x);
+ if (!IEEE_754_2008_SNAN)
+ return (ix & 0x7ff8000000000000) == 0x7ff8000000000000;
+ return 2 * (ix ^ 0x0008000000000000) > 2 * 0x7ff8000000000000ULL;
+}
+
+#if USE_MPFR
+static mpfr_rnd_t
+rmap (int r)
+{
+ switch (r)
+ {
+ case FE_TONEAREST:
+ return MPFR_RNDN;
+ case FE_TOWARDZERO:
+ return MPFR_RNDZ;
+ case FE_UPWARD:
+ return MPFR_RNDU;
+ case FE_DOWNWARD:
+ return MPFR_RNDD;
+ }
+ return -1;
+}
+
+#define prec_mpfr_f 50
+#define prec_mpfr_d 80
+#define prec_f 24
+#define prec_d 53
+#define emin_f -148
+#define emin_d -1073
+#define emax_f 128
+#define emax_d 1024
+static inline int
+call_mpfr_f1 (mpfr_t y, const struct fun *f, struct args_f1 a, mpfr_rnd_t r)
+{
+ MPFR_DECL_INIT (x, prec_f);
+ mpfr_set_flt (x, a.x, MPFR_RNDN);
+ return f->fun_mpfr.f1 (y, x, r);
+}
+static inline int
+call_mpfr_f2 (mpfr_t y, const struct fun *f, struct args_f2 a, mpfr_rnd_t r)
+{
+ MPFR_DECL_INIT (x, prec_f);
+ MPFR_DECL_INIT (x2, prec_f);
+ mpfr_set_flt (x, a.x, MPFR_RNDN);
+ mpfr_set_flt (x2, a.x2, MPFR_RNDN);
+ return f->fun_mpfr.f2 (y, x, x2, r);
+}
+static inline int
+call_mpfr_d1 (mpfr_t y, const struct fun *f, struct args_d1 a, mpfr_rnd_t r)
+{
+ MPFR_DECL_INIT (x, prec_d);
+ mpfr_set_d (x, a.x, MPFR_RNDN);
+ return f->fun_mpfr.d1 (y, x, r);
+}
+static inline int
+call_mpfr_d2 (mpfr_t y, const struct fun *f, struct args_d2 a, mpfr_rnd_t r)
+{
+ MPFR_DECL_INIT (x, prec_d);
+ MPFR_DECL_INIT (x2, prec_d);
+ mpfr_set_d (x, a.x, MPFR_RNDN);
+ mpfr_set_d (x2, a.x2, MPFR_RNDN);
+ return f->fun_mpfr.d2 (y, x, x2, r);
+}
+#endif
+
+#define float_f float
+#define double_f double
+#define copysign_f copysignf
+#define nextafter_f nextafterf
+#define fabs_f fabsf
+#define asuint_f asuint
+#define asfloat_f asfloat
+#define scalbn_f scalbnf
+#define lscalbn_f scalbn
+#define halfinf_f 0x1p127f
+#define min_normal_f 0x1p-126f
+
+#define float_d double
+#define double_d long double
+#define copysign_d copysign
+#define nextafter_d nextafter
+#define fabs_d fabs
+#define asuint_d asuint64
+#define asfloat_d asdouble
+#define scalbn_d scalbn
+#define lscalbn_d scalbnl
+#define halfinf_d 0x1p1023
+#define min_normal_d 0x1p-1022
+
+#define NEW_RT
+#define RT(x) x##_f
+#define T(x) x##_f1
+#include "ulp.h"
+#undef T
+#define T(x) x##_f2
+#include "ulp.h"
+#undef T
+#undef RT
+
+#define NEW_RT
+#define RT(x) x##_d
+#define T(x) x##_d1
+#include "ulp.h"
+#undef T
+#define T(x) x##_d2
+#include "ulp.h"
+#undef T
+#undef RT
+
+static void
+usage (void)
+{
+ puts ("./ulp [-q] [-m] [-f] [-r nudz] [-l soft-ulplimit] [-e ulplimit] func "
+ "lo [hi [x lo2 hi2] [count]]");
+ puts ("Compares func against a higher precision implementation in [lo; hi].");
+ puts ("-q: quiet.");
+ puts ("-m: use mpfr even if faster method is available.");
+ puts ("-f: disable fenv testing (rounding modes and exceptions).");
+ puts ("Supported func:");
+ for (const struct fun *f = fun; f->name; f++)
+ printf ("\t%s\n", f->name);
+ exit (1);
+}
+
+static void
+cmp (const struct fun *f, struct gen *gen, const struct conf *conf)
+{
+ if (f->arity == 1 && f->singleprec)
+ cmp_f1 (f, gen, conf);
+ else if (f->arity == 2 && f->singleprec)
+ cmp_f2 (f, gen, conf);
+ else if (f->arity == 1 && !f->singleprec)
+ cmp_d1 (f, gen, conf);
+ else if (f->arity == 2 && !f->singleprec)
+ cmp_d2 (f, gen, conf);
+ else
+ usage ();
+}
+
+static uint64_t
+getnum (const char *s, int singleprec)
+{
+ // int i;
+ uint64_t sign = 0;
+ // char buf[12];
+
+ if (s[0] == '+')
+ s++;
+ else if (s[0] == '-')
+ {
+ sign = singleprec ? 1ULL << 31 : 1ULL << 63;
+ s++;
+ }
+ /* 0xXXXX is treated as bit representation, '-' flips the sign bit. */
+ if (s[0] == '0' && tolower (s[1]) == 'x' && strchr (s, 'p') == 0)
+ return sign ^ strtoull (s, 0, 0);
+ // /* SNaN, QNaN, NaN, Inf. */
+ // for (i=0; s[i] && i < sizeof buf; i++)
+ // buf[i] = tolower(s[i]);
+ // buf[i] = 0;
+ // if (strcmp(buf, "snan") == 0)
+ // return sign | (singleprec ? 0x7fa00000 : 0x7ff4000000000000);
+ // if (strcmp(buf, "qnan") == 0 || strcmp(buf, "nan") == 0)
+ // return sign | (singleprec ? 0x7fc00000 : 0x7ff8000000000000);
+ // if (strcmp(buf, "inf") == 0 || strcmp(buf, "infinity") == 0)
+ // return sign | (singleprec ? 0x7f800000 : 0x7ff0000000000000);
+ /* Otherwise assume it's a floating-point literal. */
+ return sign
+ | (singleprec ? asuint (strtof (s, 0)) : asuint64 (strtod (s, 0)));
+}
+
+static void
+parsegen (struct gen *g, int argc, char *argv[], const struct fun *f)
+{
+ int singleprec = f->singleprec;
+ int arity = f->arity;
+ uint64_t a, b, a2, b2, n;
+ if (argc < 1)
+ usage ();
+ b = a = getnum (argv[0], singleprec);
+ n = 0;
+ if (argc > 1 && strcmp (argv[1], "x") == 0)
+ {
+ argc -= 2;
+ argv += 2;
+ }
+ else if (argc > 1)
+ {
+ b = getnum (argv[1], singleprec);
+ if (argc > 2 && strcmp (argv[2], "x") == 0)
+ {
+ argc -= 3;
+ argv += 3;
+ }
+ }
+ b2 = a2 = getnum (argv[0], singleprec);
+ if (argc > 1)
+ b2 = getnum (argv[1], singleprec);
+ if (argc > 2)
+ n = strtoull (argv[2], 0, 0);
+ if (argc > 3)
+ usage ();
+ //printf("ab %lx %lx ab2 %lx %lx n %lu\n", a, b, a2, b2, n);
+ if (arity == 1)
+ {
+ g->start = a;
+ g->len = b - a;
+ if (n - 1 > b - a)
+ n = b - a + 1;
+ g->off = 0;
+ g->step = n ? (g->len + 1) / n : 1;
+ g->start2 = g->len2 = 0;
+ g->cnt = n;
+ }
+ else if (arity == 2)
+ {
+ g->start = a;
+ g->len = b - a;
+ g->off = g->step = 0;
+ g->start2 = a2;
+ g->len2 = b2 - a2;
+ g->cnt = n;
+ }
+ else
+ usage ();
+}
+
+int
+main (int argc, char *argv[])
+{
+ const struct fun *f;
+ struct gen gen;
+ struct conf conf;
+ conf.rc = 'n';
+ conf.quiet = 0;
+ conf.mpfr = 0;
+ conf.fenv = 1;
+ conf.softlim = 0;
+ conf.errlim = INFINITY;
+ for (;;)
+ {
+ argc--;
+ argv++;
+ if (argc < 1)
+ usage ();
+ if (argv[0][0] != '-')
+ break;
+ switch (argv[0][1])
+ {
+ case 'e':
+ argc--;
+ argv++;
+ if (argc < 1)
+ usage ();
+ conf.errlim = strtod (argv[0], 0);
+ break;
+ case 'f':
+ conf.fenv = 0;
+ break;
+ case 'l':
+ argc--;
+ argv++;
+ if (argc < 1)
+ usage ();
+ conf.softlim = strtod (argv[0], 0);
+ break;
+ case 'm':
+ conf.mpfr = 1;
+ break;
+ case 'q':
+ conf.quiet = 1;
+ break;
+ case 'r':
+ conf.rc = argv[0][2];
+ if (!conf.rc)
+ {
+ argc--;
+ argv++;
+ if (argc < 1)
+ usage ();
+ conf.rc = argv[0][0];
+ }
+ break;
+ default:
+ usage ();
+ }
+ }
+ switch (conf.rc)
+ {
+ case 'n':
+ conf.r = FE_TONEAREST;
+ break;
+ case 'u':
+ conf.r = FE_UPWARD;
+ break;
+ case 'd':
+ conf.r = FE_DOWNWARD;
+ break;
+ case 'z':
+ conf.r = FE_TOWARDZERO;
+ break;
+ default:
+ usage ();
+ }
+ for (f = fun; f->name; f++)
+ if (strcmp (argv[0], f->name) == 0)
+ break;
+ if (!f->name)
+ usage ();
+ if (!f->singleprec && LDBL_MANT_DIG == DBL_MANT_DIG)
+ conf.mpfr = 1; /* Use mpfr if long double has no extra precision. */
+ if (!USE_MPFR && conf.mpfr)
+ {
+ puts ("mpfr is not available.");
+ return 1;
+ }
+ argc--;
+ argv++;
+ parsegen (&gen, argc, argv, f);
+ conf.n = gen.cnt;
+ cmp (f, &gen, &conf);
+}
diff --git a/math/test/ulp.h b/math/test/ulp.h
new file mode 100644
index 0000000..07b0cb6
--- /dev/null
+++ b/math/test/ulp.h
@@ -0,0 +1,338 @@
+/*
+ * Generic functions for ULP error estimation.
+ *
+ * Copyright (c) 2019, Arm Limited.
+ * SPDX-License-Identifier: MIT
+ */
+
+/* For each different math function type,
+ T(x) should add a different suffix to x.
+ RT(x) should add a return type specific suffix to x. */
+
+#ifdef NEW_RT
+#undef NEW_RT
+
+# if USE_MPFR
+static int RT(ulpscale_mpfr) (mpfr_t x, int t)
+{
+ /* TODO: pow of 2 cases. */
+ if (mpfr_regular_p (x))
+ {
+ mpfr_exp_t e = mpfr_get_exp (x) - RT(prec);
+ if (e < RT(emin))
+ e = RT(emin) - 1;
+ if (e > RT(emax) - RT(prec))
+ e = RT(emax) - RT(prec);
+ return e;
+ }
+ if (mpfr_zero_p (x))
+ return RT(emin) - 1;
+ if (mpfr_inf_p (x))
+ return RT(emax) - RT(prec);
+ /* NaN. */
+ return 0;
+}
+# endif
+
+/* Difference between exact result and closest real number that
+ gets rounded to got, i.e. error before rounding, for a correctly
+ rounded result the difference is 0. */
+static double RT(ulperr) (RT(float) got, const struct RT(ret) * p, int r)
+{
+ RT(float) want = p->y;
+ RT(float) d;
+ double e;
+
+ if (RT(asuint) (got) == RT(asuint) (want))
+ return 0.0;
+ if (signbit (got) != signbit (want))
+ /* May have false positives with NaN. */
+ //return isnan(got) && isnan(want) ? 0 : INFINITY;
+ return INFINITY;
+ if (!isfinite (want) || !isfinite (got))
+ {
+ if (isnan (got) != isnan (want))
+ return INFINITY;
+ if (isnan (want))
+ return 0;
+ if (isinf (got))
+ {
+ got = RT(copysign) (RT(halfinf), got);
+ want *= 0.5f;
+ }
+ if (isinf (want))
+ {
+ want = RT(copysign) (RT(halfinf), want);
+ got *= 0.5f;
+ }
+ }
+ if (r == FE_TONEAREST)
+ {
+ // TODO: incorrect when got vs want cross a powof2 boundary
+ /* error = got > want
+ ? got - want - tail ulp - 0.5 ulp
+ : got - want - tail ulp + 0.5 ulp; */
+ d = got - want;
+ e = d > 0 ? -p->tail - 0.5 : -p->tail + 0.5;
+ }
+ else
+ {
+ if ((r == FE_DOWNWARD && got < want) || (r == FE_UPWARD && got > want)
+ || (r == FE_TOWARDZERO && fabs (got) < fabs (want)))
+ got = RT(nextafter) (got, want);
+ d = got - want;
+ e = -p->tail;
+ }
+ return RT(scalbn) (d, -p->ulpexp) + e;
+}
+
+static int RT(isok) (RT(float) ygot, int exgot, RT(float) ywant, int exwant,
+ int exmay)
+{
+ return RT(asuint) (ygot) == RT(asuint) (ywant)
+ && ((exgot ^ exwant) & ~exmay) == 0;
+}
+
+static int RT(isok_nofenv) (RT(float) ygot, RT(float) ywant)
+{
+ return RT(asuint) (ygot) == RT(asuint) (ywant);
+}
+#endif
+
+static inline void T(call_fenv) (const struct fun *f, struct T(args) a, int r,
+ RT(float) * y, int *ex)
+{
+ if (r != FE_TONEAREST)
+ fesetround (r);
+ feclearexcept (FE_ALL_EXCEPT);
+ *y = T(call) (f, a);
+ *ex = fetestexcept (FE_ALL_EXCEPT);
+ if (r != FE_TONEAREST)
+ fesetround (FE_TONEAREST);
+}
+
+static inline void T(call_nofenv) (const struct fun *f, struct T(args) a,
+ int r, RT(float) * y, int *ex)
+{
+ *y = T(call) (f, a);
+ *ex = 0;
+}
+
+static inline int T(call_long_fenv) (const struct fun *f, struct T(args) a,
+ int r, struct RT(ret) * p,
+ RT(float) ygot, int exgot)
+{
+ if (r != FE_TONEAREST)
+ fesetround (r);
+ feclearexcept (FE_ALL_EXCEPT);
+ RT(double) yl = T(call_long) (f, a);
+ p->y = (RT(float)) yl;
+ volatile RT(float) vy = p->y; // TODO: barrier
+ (void) vy;
+ p->ex = fetestexcept (FE_ALL_EXCEPT);
+ if (r != FE_TONEAREST)
+ fesetround (FE_TONEAREST);
+ p->ex_may = FE_INEXACT;
+ if (RT(isok) (ygot, exgot, p->y, p->ex, p->ex_may))
+ return 1;
+ p->ulpexp = RT(ulpscale) (p->y);
+ if (isinf (p->y))
+ p->tail = RT(lscalbn) (yl - (RT(double)) 2 * RT(halfinf), -p->ulpexp);
+ else
+ p->tail = RT(lscalbn) (yl - p->y, -p->ulpexp);
+ if (RT(fabs) (p->y) < RT(min_normal))
+ {
+ /* TODO: subnormal result is treated as undeflow even if it's
+ exact since call_long may not raise inexact correctly. */
+ if (p->y != 0 || (p->ex & FE_INEXACT))
+ p->ex |= FE_UNDERFLOW | FE_INEXACT;
+ }
+ return 0;
+}
+static inline int T(call_long_nofenv) (const struct fun *f, struct T(args) a,
+ int r, struct RT(ret) * p,
+ RT(float) ygot, int exgot)
+{
+ RT(double) yl = T(call_long) (f, a);
+ p->y = (RT(float)) yl;
+ if (RT(isok_nofenv) (ygot, p->y))
+ return 1;
+ p->ulpexp = RT(ulpscale) (p->y);
+ if (isinf (p->y))
+ p->tail = RT(lscalbn) (yl - (RT(double)) 2 * RT(halfinf), -p->ulpexp);
+ else
+ p->tail = RT(lscalbn) (yl - p->y, -p->ulpexp);
+ return 0;
+}
+
+/* There are nan input args and all quiet. */
+static inline int T(qnanpropagation) (struct T(args) a)
+{
+ return T(reduce) (a, isnan, ||) && !T(reduce) (a, RT(issignaling), ||);
+}
+static inline RT(float) T(sum) (struct T(args) a)
+{
+ return T(reduce) (a, , +);
+}
+
+/* returns 1 if the got result is ok. */
+static inline int T(call_mpfr_fix) (const struct fun *f, struct T(args) a,
+ int r_fenv, struct RT(ret) * p,
+ RT(float) ygot, int exgot)
+{
+#if USE_MPFR
+ int t, t2;
+ mpfr_rnd_t r = rmap (r_fenv);
+ MPFR_DECL_INIT(my, RT(prec_mpfr));
+ MPFR_DECL_INIT(mr, RT(prec));
+ MPFR_DECL_INIT(me, RT(prec_mpfr));
+ mpfr_clear_flags ();
+ t = T(call_mpfr) (my, f, a, r);
+ /* Double rounding. */
+ t2 = mpfr_set (mr, my, r);
+ if (t2)
+ t = t2;
+ mpfr_set_emin (RT(emin));
+ mpfr_set_emax (RT(emax));
+ t = mpfr_check_range (mr, t, r);
+ t = mpfr_subnormalize (mr, t, r);
+ mpfr_set_emax (MPFR_EMAX_DEFAULT);
+ mpfr_set_emin (MPFR_EMIN_DEFAULT);
+ p->y = mpfr_get_d (mr, r);
+ p->ex = t ? FE_INEXACT : 0;
+ p->ex_may = FE_INEXACT;
+ if (mpfr_underflow_p () && (p->ex & FE_INEXACT))
+ /* TODO: handle before and after rounding uflow cases. */
+ p->ex |= FE_UNDERFLOW;
+ if (mpfr_overflow_p ())
+ p->ex |= FE_OVERFLOW | FE_INEXACT;
+ if (mpfr_divby0_p ())
+ p->ex |= FE_DIVBYZERO;
+ //if (mpfr_erangeflag_p ())
+ // p->ex |= FE_INVALID;
+ if (!mpfr_nanflag_p () && RT(isok) (ygot, exgot, p->y, p->ex, p->ex_may))
+ return 1;
+ if (mpfr_nanflag_p () && !T(qnanpropagation) (a))
+ p->ex |= FE_INVALID;
+ p->ulpexp = RT(ulpscale_mpfr) (my, t);
+ if (!isfinite (p->y))
+ {
+ p->tail = 0;
+ if (isnan (p->y))
+ {
+ /* If an input was nan keep its sign. */
+ p->y = T(sum) (a);
+ if (!isnan (p->y))
+ p->y = (p->y - p->y) / (p->y - p->y);
+ return RT(isok) (ygot, exgot, p->y, p->ex, p->ex_may);
+ }
+ mpfr_set_si_2exp (mr, signbit (p->y) ? -1 : 1, 1024, MPFR_RNDN);
+ if (mpfr_cmpabs (my, mr) >= 0)
+ return RT(isok) (ygot, exgot, p->y, p->ex, p->ex_may);
+ }
+ mpfr_sub (me, my, mr, MPFR_RNDN);
+ mpfr_mul_2si (me, me, -p->ulpexp, MPFR_RNDN);
+ p->tail = mpfr_get_d (me, MPFR_RNDN);
+ return 0;
+#else
+ abort ();
+#endif
+}
+
+static void T(cmp) (const struct fun *f, struct gen *gen,
+ const struct conf *conf)
+{
+ double maxerr = 0;
+ uint64_t cnt = 0;
+ uint64_t cnt1 = 0;
+ uint64_t cnt2 = 0;
+ uint64_t cntfail = 0;
+ int r = conf->r;
+ int use_mpfr = conf->mpfr;
+ int fenv = conf->fenv;
+ for (;;)
+ {
+ struct RT(ret) want;
+ struct T(args) a = T(next) (gen);
+ int exgot;
+ RT(float) ygot;
+ if (fenv)
+ T(call_fenv) (f, a, r, &ygot, &exgot);
+ else
+ T(call_nofenv) (f, a, r, &ygot, &exgot);
+ cnt++;
+ int ok = use_mpfr
+ ? T(call_mpfr_fix) (f, a, r, &want, ygot, exgot)
+ : (fenv ? T(call_long_fenv) (f, a, r, &want, ygot, exgot)
+ : T(call_long_nofenv) (f, a, r, &want, ygot, exgot));
+ if (!ok)
+ {
+ int print = 0;
+ int fail = 0;
+ double err = RT(ulperr) (ygot, &want, r);
+ double abserr = fabs (err);
+ // TODO: count errors below accuracy limit.
+ if (abserr > 0)
+ cnt1++;
+ if (abserr > 1)
+ cnt2++;
+ if (abserr > conf->errlim)
+ {
+ print = fail = 1;
+ cntfail++;
+ }
+ if (abserr > maxerr)
+ {
+ maxerr = abserr;
+ if (!conf->quiet && abserr > conf->softlim)
+ print = 1;
+ }
+ if (print)
+ {
+ T(printcall) (f, a);
+ // TODO: inf ulp handling
+ printf (" got %a want %a %+g ulp err %g\n", ygot, want.y,
+ want.tail, err);
+ }
+ int diff = fenv ? exgot ^ want.ex : 0;
+ if (fenv && (diff & ~want.ex_may))
+ {
+ if (!fail)
+ {
+ fail = 1;
+ cntfail++;
+ }
+ T(printcall) (f, a);
+ printf (" is %a %+g ulp, got except 0x%0x", want.y, want.tail,
+ exgot);
+ if (diff & exgot)
+ printf (" wrongly set: 0x%x", diff & exgot);
+ if (diff & ~exgot)
+ printf (" wrongly clear: 0x%x", diff & ~exgot);
+ putchar ('\n');
+ }
+ }
+ if (cnt >= conf->n)
+ break;
+ if (!conf->quiet && cnt % 0x100000 == 0)
+ printf ("progress: %6.3f%% cnt %llu cnt1 %llu cnt2 %llu cntfail %llu "
+ "maxerr %g\n",
+ 100.0 * cnt / conf->n, (unsigned long long) cnt,
+ (unsigned long long) cnt1, (unsigned long long) cnt2,
+ (unsigned long long) cntfail, maxerr);
+ }
+ double cc = cnt;
+ if (cntfail)
+ printf ("FAIL ");
+ else
+ printf ("PASS ");
+ T(printgen) (f, gen);
+ printf (" round %c errlim %g maxerr %g %s cnt %llu cnt1 %llu %g%% cnt2 %llu "
+ "%g%% cntfail %llu %g%%\n",
+ conf->rc, conf->errlim,
+ maxerr, conf->r == FE_TONEAREST ? "+0.5" : "+1.0",
+ (unsigned long long) cnt,
+ (unsigned long long) cnt1, 100.0 * cnt1 / cc,
+ (unsigned long long) cnt2, 100.0 * cnt2 / cc,
+ (unsigned long long) cntfail, 100.0 * cntfail / cc);
+}
diff --git a/math/tools/cos.sollya b/math/tools/cos.sollya
new file mode 100644
index 0000000..bd72d6b
--- /dev/null
+++ b/math/tools/cos.sollya
@@ -0,0 +1,31 @@
+// polynomial for approximating cos(x)
+//
+// Copyright (c) 2019, Arm Limited.
+// SPDX-License-Identifier: MIT
+
+deg = 8; // polynomial degree
+a = -pi/4; // interval
+b = pi/4;
+
+// find even polynomial with minimal abs error compared to cos(x)
+
+f = cos(x);
+
+// return p that minimizes |f(x) - poly(x) - x^d*p(x)|
+approx = proc(poly,d) {
+ return remez(f(x)-poly(x), deg-d, [a;b], x^d, 1e-10);
+};
+
+// first coeff is fixed, iteratively find optimal double prec coeffs
+poly = 1;
+for i from 1 to deg/2 do {
+ p = roundcoefficients(approx(poly,2*i), [|D ...|]);
+ poly = poly + x^(2*i)*coeff(p,0);
+};
+
+display = hexadecimal;
+print("rel error:", accurateinfnorm(1-poly(x)/f(x), [a;b], 30));
+print("abs error:", accurateinfnorm(f(x)-poly(x), [a;b], 30));
+print("in [",a,b,"]");
+print("coeffs:");
+for i from 0 to deg do coeff(poly,i);
diff --git a/math/tools/exp.sollya b/math/tools/exp.sollya
new file mode 100644
index 0000000..b7a462c
--- /dev/null
+++ b/math/tools/exp.sollya
@@ -0,0 +1,35 @@
+// polynomial for approximating e^x
+//
+// Copyright (c) 2019, Arm Limited.
+// SPDX-License-Identifier: MIT
+
+deg = 5; // poly degree
+N = 128; // table entries
+b = log(2)/(2*N); // interval
+b = b + b*0x1p-16; // increase interval for non-nearest rounding (TOINT_NARROW)
+a = -b;
+
+// find polynomial with minimal abs error
+
+// return p that minimizes |exp(x) - poly(x) - x^d*p(x)|
+approx = proc(poly,d) {
+ return remez(exp(x)-poly(x), deg-d, [a;b], x^d, 1e-10);
+};
+
+// first 2 coeffs are fixed, iteratively find optimal double prec coeffs
+poly = 1 + x;
+for i from 2 to deg do {
+ p = roundcoefficients(approx(poly,i), [|D ...|]);
+ poly = poly + x^i*coeff(p,0);
+};
+
+display = hexadecimal;
+print("rel error:", accurateinfnorm(1-poly(x)/exp(x), [a;b], 30));
+print("abs error:", accurateinfnorm(exp(x)-poly(x), [a;b], 30));
+print("in [",a,b,"]");
+// double interval error for non-nearest rounding
+print("rel2 error:", accurateinfnorm(1-poly(x)/exp(x), [2*a;2*b], 30));
+print("abs2 error:", accurateinfnorm(exp(x)-poly(x), [2*a;2*b], 30));
+print("in [",2*a,2*b,"]");
+print("coeffs:");
+for i from 0 to deg do coeff(poly,i);
diff --git a/math/tools/exp2.sollya b/math/tools/exp2.sollya
new file mode 100644
index 0000000..e760769
--- /dev/null
+++ b/math/tools/exp2.sollya
@@ -0,0 +1,48 @@
+// polynomial for approximating 2^x
+//
+// Copyright (c) 2019, Arm Limited.
+// SPDX-License-Identifier: MIT
+
+// exp2f parameters
+deg = 3; // poly degree
+N = 32; // table entries
+b = 1/(2*N); // interval
+a = -b;
+
+//// exp2 parameters
+//deg = 5; // poly degree
+//N = 128; // table entries
+//b = 1/(2*N); // interval
+//a = -b;
+
+// find polynomial with minimal relative error
+
+f = 2^x;
+
+// return p that minimizes |f(x) - poly(x) - x^d*p(x)|/|f(x)|
+approx = proc(poly,d) {
+ return remez(1 - poly(x)/f(x), deg-d, [a;b], x^d/f(x), 1e-10);
+};
+// return p that minimizes |f(x) - poly(x) - x^d*p(x)|
+approx_abs = proc(poly,d) {
+ return remez(f(x) - poly(x), deg-d, [a;b], x^d, 1e-10);
+};
+
+// first coeff is fixed, iteratively find optimal double prec coeffs
+poly = 1;
+for i from 1 to deg do {
+ p = roundcoefficients(approx(poly,i), [|D ...|]);
+// p = roundcoefficients(approx_abs(poly,i), [|D ...|]);
+ poly = poly + x^i*coeff(p,0);
+};
+
+display = hexadecimal;
+print("rel error:", accurateinfnorm(1-poly(x)/2^x, [a;b], 30));
+print("abs error:", accurateinfnorm(2^x-poly(x), [a;b], 30));
+print("in [",a,b,"]");
+// double interval error for non-nearest rounding:
+print("rel2 error:", accurateinfnorm(1-poly(x)/2^x, [2*a;2*b], 30));
+print("abs2 error:", accurateinfnorm(2^x-poly(x), [2*a;2*b], 30));
+print("in [",2*a,2*b,"]");
+print("coeffs:");
+for i from 0 to deg do coeff(poly,i);
diff --git a/math/tools/log.sollya b/math/tools/log.sollya
new file mode 100644
index 0000000..6df4db4
--- /dev/null
+++ b/math/tools/log.sollya
@@ -0,0 +1,35 @@
+// polynomial for approximating log(1+x)
+//
+// Copyright (c) 2019, Arm Limited.
+// SPDX-License-Identifier: MIT
+
+deg = 12; // poly degree
+// |log(1+x)| > 0x1p-4 outside the interval
+a = -0x1p-4;
+b = 0x1.09p-4;
+
+// find log(1+x)/x polynomial with minimal relative error
+// (minimal relative error polynomial for log(1+x) is the same * x)
+deg = deg-1; // because of /x
+
+// f = log(1+x)/x; using taylor series
+f = 0;
+for i from 0 to 60 do { f = f + (-x)^i/(i+1); };
+
+// return p that minimizes |f(x) - poly(x) - x^d*p(x)|/|f(x)|
+approx = proc(poly,d) {
+ return remez(1 - poly(x)/f(x), deg-d, [a;b], x^d/f(x), 1e-10);
+};
+
+// first coeff is fixed, iteratively find optimal double prec coeffs
+poly = 1;
+for i from 1 to deg do {
+ p = roundcoefficients(approx(poly,i), [|D ...|]);
+ poly = poly + x^i*coeff(p,0);
+};
+
+display = hexadecimal;
+print("rel error:", accurateinfnorm(1-poly(x)/f(x), [a;b], 30));
+print("in [",a,b,"]");
+print("coeffs:");
+for i from 0 to deg do coeff(poly,i);
diff --git a/math/tools/log2.sollya b/math/tools/log2.sollya
new file mode 100644
index 0000000..4a364c0
--- /dev/null
+++ b/math/tools/log2.sollya
@@ -0,0 +1,42 @@
+// polynomial for approximating log2(1+x)
+//
+// Copyright (c) 2019, Arm Limited.
+// SPDX-License-Identifier: MIT
+
+deg = 11; // poly degree
+// |log2(1+x)| > 0x1p-4 outside the interval
+a = -0x1.5b51p-5;
+b = 0x1.6ab2p-5;
+
+ln2 = evaluate(log(2),0);
+invln2hi = double(1/ln2 + 0x1p21) - 0x1p21; // round away last 21 bits
+invln2lo = double(1/ln2 - invln2hi);
+
+// find log2(1+x)/x polynomial with minimal relative error
+// (minimal relative error polynomial for log2(1+x) is the same * x)
+deg = deg-1; // because of /x
+
+// f = log(1+x)/x; using taylor series
+f = 0;
+for i from 0 to 60 do { f = f + (-x)^i/(i+1); };
+f = f/ln2;
+
+// return p that minimizes |f(x) - poly(x) - x^d*p(x)|/|f(x)|
+approx = proc(poly,d) {
+ return remez(1 - poly(x)/f(x), deg-d, [a;b], x^d/f(x), 1e-10);
+};
+
+// first coeff is fixed, iteratively find optimal double prec coeffs
+poly = invln2hi + invln2lo;
+for i from 1 to deg do {
+ p = roundcoefficients(approx(poly,i), [|D ...|]);
+ poly = poly + x^i*coeff(p,0);
+};
+
+display = hexadecimal;
+print("invln2hi:", invln2hi);
+print("invln2lo:", invln2lo);
+print("rel error:", accurateinfnorm(1-poly(x)/f(x), [a;b], 30));
+print("in [",a,b,"]");
+print("coeffs:");
+for i from 0 to deg do coeff(poly,i);
diff --git a/math/tools/log2_abs.sollya b/math/tools/log2_abs.sollya
new file mode 100644
index 0000000..82c4dac
--- /dev/null
+++ b/math/tools/log2_abs.sollya
@@ -0,0 +1,41 @@
+// polynomial for approximating log2(1+x)
+//
+// Copyright (c) 2019, Arm Limited.
+// SPDX-License-Identifier: MIT
+
+deg = 7; // poly degree
+// interval ~= 1/(2*N), where N is the table entries
+a= -0x1.f45p-8;
+b= 0x1.f45p-8;
+
+ln2 = evaluate(log(2),0);
+invln2hi = double(1/ln2 + 0x1p21) - 0x1p21; // round away last 21 bits
+invln2lo = double(1/ln2 - invln2hi);
+
+// find log2(1+x) polynomial with minimal absolute error
+f = log(1+x)/ln2;
+
+// return p that minimizes |f(x) - poly(x) - x^d*p(x)|
+approx = proc(poly,d) {
+ return remez(f(x) - poly(x), deg-d, [a;b], x^d, 1e-10);
+};
+
+// first coeff is fixed, iteratively find optimal double prec coeffs
+poly = x*(invln2lo + invln2hi);
+for i from 2 to deg do {
+ p = roundcoefficients(approx(poly,i), [|D ...|]);
+ poly = poly + x^i*coeff(p,0);
+};
+
+display = hexadecimal;
+print("invln2hi:", invln2hi);
+print("invln2lo:", invln2lo);
+print("abs error:", accurateinfnorm(f(x)-poly(x), [a;b], 30));
+//// relative error computation fails if f(0)==0
+//// g = f(x)/x = log2(1+x)/x; using taylor series
+//g = 0;
+//for i from 0 to 60 do { g = g + (-x)^i/(i+1)/ln2; };
+//print("rel error:", accurateinfnorm(1-(poly(x)/x)/g(x), [a;b], 30));
+print("in [",a,b,"]");
+print("coeffs:");
+for i from 0 to deg do coeff(poly,i);
diff --git a/math/tools/log_abs.sollya b/math/tools/log_abs.sollya
new file mode 100644
index 0000000..a2ac190
--- /dev/null
+++ b/math/tools/log_abs.sollya
@@ -0,0 +1,35 @@
+// polynomial for approximating log(1+x)
+//
+// Copyright (c) 2019, Arm Limited.
+// SPDX-License-Identifier: MIT
+
+deg = 6; // poly degree
+// interval ~= 1/(2*N), where N is the table entries
+a = -0x1.fp-9;
+b = 0x1.fp-9;
+
+// find log(1+x) polynomial with minimal absolute error
+f = log(1+x);
+
+// return p that minimizes |f(x) - poly(x) - x^d*p(x)|
+approx = proc(poly,d) {
+ return remez(f(x) - poly(x), deg-d, [a;b], x^d, 1e-10);
+};
+
+// first coeff is fixed, iteratively find optimal double prec coeffs
+poly = x;
+for i from 2 to deg do {
+ p = roundcoefficients(approx(poly,i), [|D ...|]);
+ poly = poly + x^i*coeff(p,0);
+};
+
+display = hexadecimal;
+print("abs error:", accurateinfnorm(f(x)-poly(x), [a;b], 30));
+// relative error computation fails if f(0)==0
+// g = f(x)/x = log(1+x)/x; using taylor series
+g = 0;
+for i from 0 to 60 do { g = g + (-x)^i/(i+1); };
+print("rel error:", accurateinfnorm(1-poly(x)/x/g(x), [a;b], 30));
+print("in [",a,b,"]");
+print("coeffs:");
+for i from 0 to deg do coeff(poly,i);
diff --git a/math/tools/plot.py b/math/tools/plot.py
new file mode 100755
index 0000000..09c8ec6
--- /dev/null
+++ b/math/tools/plot.py
@@ -0,0 +1,56 @@
+#!/usr/bin/python
+
+# ULP error plot tool.
+#
+# Copyright (c) 2019, Arm Limited.
+# SPDX-License-Identifier: MIT
+
+import numpy as np
+import matplotlib.pyplot as plt
+import sys
+import re
+
+# example usage:
+# build/bin/ulp -e .0001 log 0.5 2.0 2345678 | math/tools/plot.py
+
+def fhex(s):
+ return float.fromhex(s)
+
+def parse(f):
+ xs = []
+ ys = []
+ es = []
+ # Has to match the format used in ulp.c
+ r = re.compile(r'[^ (]+\(([^ )]*)\) got [^ ]+ want ([^ ]+) [^ ]+ ulp err ([^ ]+)')
+ for line in f:
+ m = r.match(line)
+ if m:
+ x = fhex(m.group(1))
+ y = fhex(m.group(2))
+ e = float(m.group(3))
+ xs.append(x)
+ ys.append(y)
+ es.append(e)
+ elif line.startswith('PASS') or line.startswith('FAIL'):
+ # Print the summary line
+ print(line)
+ return xs, ys, es
+
+def plot(xs, ys, es):
+ if len(xs) < 2:
+ print('not enough samples')
+ return
+ a = min(xs)
+ b = max(xs)
+ fig, (ax0,ax1) = plt.subplots(nrows=2)
+ es = map(abs, es) # ignore the sign
+ emax = max(es)
+ ax0.text(a+(b-a)*0.7, emax*0.8, '%s\n%g'%(emax.hex(),emax))
+ ax0.plot(xs,es,'rx')
+ ax0.grid()
+ ax1.plot(xs,ys,'rx')
+ ax1.grid()
+ plt.show()
+
+xs, ys, es = parse(sys.stdin)
+plot(xs, ys, es)
diff --git a/auxiliary/remez.jl b/math/tools/remez.jl
similarity index 100%
rename from auxiliary/remez.jl
rename to math/tools/remez.jl
diff --git a/math/tools/sin.sollya b/math/tools/sin.sollya
new file mode 100644
index 0000000..a6e8511
--- /dev/null
+++ b/math/tools/sin.sollya
@@ -0,0 +1,37 @@
+// polynomial for approximating sin(x)
+//
+// Copyright (c) 2019, Arm Limited.
+// SPDX-License-Identifier: MIT
+
+deg = 7; // polynomial degree
+a = -pi/4; // interval
+b = pi/4;
+
+// find even polynomial with minimal abs error compared to sin(x)/x
+
+// account for /x
+deg = deg-1;
+
+// f = sin(x)/x;
+f = 1;
+c = 1;
+for i from 1 to 60 do { c = 2*i*(2*i + 1)*c; f = f + (-1)^i*x^(2*i)/c; };
+
+// return p that minimizes |f(x) - poly(x) - x^d*p(x)|
+approx = proc(poly,d) {
+ return remez(f(x)-poly(x), deg-d, [a;b], x^d, 1e-10);
+};
+
+// first coeff is fixed, iteratively find optimal double prec coeffs
+poly = 1;
+for i from 1 to deg/2 do {
+ p = roundcoefficients(approx(poly,2*i), [|D ...|]);
+ poly = poly + x^(2*i)*coeff(p,0);
+};
+
+display = hexadecimal;
+print("rel error:", accurateinfnorm(1-poly(x)/f(x), [a;b], 30));
+print("abs error:", accurateinfnorm(sin(x)-x*poly(x), [a;b], 30));
+print("in [",a,b,"]");
+print("coeffs:");
+for i from 0 to deg do coeff(poly,i);
diff --git a/string/Dir.mk b/string/Dir.mk
new file mode 100644
index 0000000..e179642
--- /dev/null
+++ b/string/Dir.mk
@@ -0,0 +1,51 @@
+# Makefile fragment - requires GNU make
+#
+# Copyright (c) 2019, Arm Limited.
+# SPDX-License-Identifier: MIT
+
+string-lib-srcs := $(wildcard $(srcdir)/string/*.[cS])
+string-includes-src := $(wildcard $(srcdir)/string/include/*.h)
+string-includes := $(string-includes-src:$(srcdir)/string/%=build/%)
+string-test-srcs := $(wildcard $(srcdir)/string/test/*.c)
+
+string-libs := \
+ build/lib/libstringlib.so \
+ build/lib/libstringlib.a \
+
+string-tools := \
+ build/bin/test/memcpy \
+
+string-lib-base := $(basename $(string-lib-srcs))
+string-lib-objs := $(string-lib-base:$(srcdir)/%=build/%.o)
+string-test-base := $(basename $(string-test-srcs))
+string-test-objs := $(string-test-base:$(srcdir)/%=build/%.o)
+
+string-objs := \
+ $(string-lib-objs) \
+ $(string-test-objs) \
+
+all-string: $(string-libs) $(string-tools) $(string-includes)
+
+$(string-objs) $(string-objs:%.o=%.os): $(string-includes)
+
+build/lib/libstringlib.so: $(string-lib-objs:%.o=%.os)
+ $(CC) $(CFLAGS_ALL) $(LDFLAGS_ALL) -shared -o $@ $^
+
+build/lib/libstringlib.a: $(string-lib-objs)
+ rm -f $@
+ $(AR) rc $@ $^
+ $(RANLIB) $@
+
+build/bin/test/%: build/string/test/%.o build/lib/libstringlib.a
+ $(CC) $(CFLAGS_ALL) $(LDFLAGS_ALL) -static -o $@ $^ $(LDLIBS)
+
+build/include/%.h: $(srcdir)/string/include/%.h
+ cp $< $@
+
+build/bin/%.sh: $(srcdir)/string/test/%.sh
+ cp $< $@
+
+check-string: $(string-tools)
+ $(EMULATOR) build/bin/test/memcpy
+
+.PHONY: all-string check-string
diff --git a/string/asmdefs.h b/string/asmdefs.h
new file mode 100644
index 0000000..7a5bf6b
--- /dev/null
+++ b/string/asmdefs.h
@@ -0,0 +1,17 @@
+/*
+ * Macros for asm code.
+ *
+ * Copyright (c) 2019, Arm Limited.
+ * SPDX-License-Identifier: MIT
+ */
+
+#define ENTRY(name) \
+ .global name; \
+ .type name,%function; \
+ .align 4; \
+ name: \
+ .cfi_startproc;
+
+#define END(name) \
+ .cfi_endproc; \
+ .size name, .-name;
diff --git a/string/include/stringlib.h b/string/include/stringlib.h
new file mode 100644
index 0000000..753d06a
--- /dev/null
+++ b/string/include/stringlib.h
@@ -0,0 +1,17 @@
+/*
+ * Public API.
+ *
+ * Copyright (c) 2019, Arm Limited.
+ * SPDX-License-Identifier: MIT
+ */
+
+#include <stddef.h>
+
+/* restrict is not needed, but kept for documenting the interface contract. */
+#ifndef __restrict
+# define __restrict
+#endif
+
+#if __aarch64__
+void *__memcpy_bytewise (void *__restrict, const void *__restrict, size_t);
+#endif
diff --git a/string/memcpy_bytewise.S b/string/memcpy_bytewise.S
new file mode 100644
index 0000000..7ee3474
--- /dev/null
+++ b/string/memcpy_bytewise.S
@@ -0,0 +1,23 @@
+/*
+ * Trivial AArch64 memcpy.
+ *
+ * Copyright (c) 2019, Arm Limited.
+ * SPDX-License-Identifier: MIT
+ */
+
+#if __aarch64__
+#include "asmdefs.h"
+
+ENTRY (__memcpy_bytewise)
+ cbz x2, 2f
+ mov x3, 0
+1:
+ ldrb w4, [x1, x3]
+ strb w4, [x0, x3]
+ add x3, x3, 1
+ cmp x3, x2
+ bne 1b
+2:
+ ret
+END (__memcpy_bytewise)
+#endif
diff --git a/string/test/memcpy.c b/string/test/memcpy.c
new file mode 100644
index 0000000..1dccac7
--- /dev/null
+++ b/string/test/memcpy.c
@@ -0,0 +1,94 @@
+/*
+ * memcpy test.
+ *
+ * Copyright (c) 2019, Arm Limited.
+ * SPDX-License-Identifier: MIT
+ */
+
+#include <stdint.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include "stringlib.h"
+
+static const struct fun
+{
+ const char *name;
+ void *(*fun)(void *, const void *, size_t);
+} funtab[] = {
+#define F(x) {#x, x},
+F(memcpy)
+#if __aarch64__
+F(__memcpy_bytewise)
+#endif
+#undef F
+ {0, 0}
+};
+
+static int test_status;
+#define ERR(...) (test_status=1, printf(__VA_ARGS__))
+
+#define A 32
+#define LEN 250000
+static unsigned char dbuf[LEN+2*A];
+static unsigned char sbuf[LEN+2*A];
+static unsigned char wbuf[LEN+2*A];
+
+static void *alignup(void *p)
+{
+ return (void*)(((uintptr_t)p + A-1) & -A);
+}
+
+static void test(const struct fun *fun, int dalign, int salign, int len)
+{
+ unsigned char *src = alignup(sbuf);
+ unsigned char *dst = alignup(dbuf);
+ unsigned char *want = wbuf;
+ unsigned char *s = src + salign;
+ unsigned char *d = dst + dalign;
+ unsigned char *w = want + dalign;
+ void *p;
+ int i;
+
+ if (len > LEN || dalign >= A || salign >= A)
+ abort();
+ for (i = 0; i < len+A; i++) {
+ src[i] = '?';
+ want[i] = dst[i] = '*';
+ }
+ for (i = 0; i < len; i++)
+ s[i] = w[i] = 'a' + i%23;
+
+ p = fun->fun(d, s, len);
+ if (p != d)
+ ERR("%s(%p,..) returned %p\n", fun->name, d, p);
+ for (i = 0; i < len+A; i++) {
+ if (dst[i] != want[i]) {
+ ERR("%s(align %d, align %d, %d) failed\n", fun->name, dalign, salign, len);
+ ERR("got : %.*s\n", dalign+len+1, dst);
+ ERR("want: %.*s\n", dalign+len+1, want);
+ break;
+ }
+ }
+}
+
+int main()
+{
+ int r = 0;
+ for (int i=0; funtab[i].name; i++) {
+ test_status = 0;
+ for (int d = 0; d < A; d++)
+ for (int s = 0; s < A; s++) {
+ int n;
+ for (n = 0; n < 100; n++)
+ test(funtab+i, d, s, n);
+ for (; n < LEN; n *= 2)
+ test(funtab+i, d, s, n);
+ }
+ if (test_status) {
+ r = -1;
+ ERR("FAIL %s\n", funtab[i].name);
+ }
+ }
+ return r;
+}
diff --git a/test/testcases/directed/rred.tst b/test/testcases/directed/rred.tst
deleted file mode 100644
index 41e4e70..0000000
--- a/test/testcases/directed/rred.tst
+++ /dev/null
@@ -1,96 +0,0 @@
-; rred.tst
-;
-; Copyright (c) 1999-2018, Arm Limited.
-; SPDX-License-Identifier: MIT
-
-func=rred op1=40000000.00000000 result=3fdb7812.aeef4b9e.e59 res2=00000001 errno=0
-func=rred op1=400fffff.ffffffff result=bfe6cbe3.f9990e95.a79 res2=00000003 errno=0
-func=rred op1=40100000.00000000 result=bfe6cbe3.f9990e91.a79 res2=00000003 errno=0
-func=rred op1=4012d97c.7f3321d2 result=bcaa7939.4c9e8a0a.515 res2=00000003 errno=0
-func=rred op1=401c90fd.aa22168c result=bfe6cbe3.f9990e92.c1f res2=00000001 errno=0
-func=rred op1=401f6a7a.2955385f result=3cc4f828.2013467b.b36 res2=00000001 errno=0
-func=rred op1=40200000.00000000 result=3fc2b0ba.d558f434.f82 res2=00000001 errno=0
-func=rred op1=4025fdbb.e9bba775 result=bcbee2c2.d963a10c.099 res2=00000003 errno=0
-func=rred op1=402c463a.beccb2bc result=3cd6128a.83448c3c.217 res2=00000001 errno=0
-func=rred op1=402c90fd.aa22168c result=3fc2b0ba.d558f42c.251 res2=00000001 errno=0
-func=rred op1=40300000.00000000 result=3fd2b0ba.d558f434.f82 res2=00000002 errno=0
-func=rred op1=4031475c.c9eedf00 result=bce6111d.218effa2.5d5 res2=00000003 errno=0
-func=rred op1=403dd85a.7410f58d result=3cc61565.46afa56f.a9d res2=00000003 errno=0
-func=rred op1=403fb53d.14aa9c2f result=3fd2b0ba.d558f429.f05 res2=00000000 errno=0
-func=rred op1=4046c6cb.c45dc8de result=3c26d61b.58c99c42.f13 res2=00000001 errno=0
-func=rred op1=4049eb0b.2ee64e81 result=bcb19abb.2567f738.bf7 res2=00000001 errno=0
-func=rred op1=404fb53d.14aa9c2a result=3fe2b0ba.d558f2e9.f05 res2=00000000 errno=0
-func=rred op1=404fb53d.14aa9c34 result=3fe2b0ba.d558f569.f05 res2=00000000 errno=0
-func=rred op1=4051abe4.b73fefb5 result=bcd1a34b.6fa942d3.588 res2=00000001 errno=0
-func=rred op1=405f05f2.3c0427aa result=3cc1b746.c796f33c.131 res2=00000003 errno=0
-func=rred op1=405fb53d.14aa9c20 result=bfd9c501.fbacf2b9.592 res2=00000001 errno=0
-func=rred op1=405fb53d.14aa9c34 result=bfd9c501.fbacdeb9.592 res2=00000001 errno=0
-func=rred op1=406ae65f.0030f844 result=3cc1c2b1.d543580a.349 res2=00000001 errno=0
-func=rred op1=406e0a9e.6ab97de7 result=bcc1899a.90e56003.8d3 res2=00000001 errno=0
-func=rred op1=406fb53d.14aa9c20 result=3fe87ef4.acdb6777.340 res2=00000001 errno=0
-func=rred op1=406fb53d.14aa9c34 result=3fe87ef4.acdb7b77.340 res2=00000001 errno=0
-func=rred op1=4078d695.62476091 result=3cc1d987.f09c21a6.778 res2=00000001 errno=0
-func=rred op1=407bfad4.cccfe634 result=bcda5f88.6ddaa73a.860 res2=00000001 errno=0
-func=rred op1=407fb53d.14aa9c30 result=bfa460d4.ed16b422.511 res2=00000003 errno=0
-func=rred op1=407fe781.0b53247a result=bfa460d4.ed18ba33.f74 res2=00000001 errno=0
-func=rred op1=40821cfd.a23b2280 result=3cc1f05e.0bf4eb42.ba7 res2=00000001 errno=0
-func=rred op1=408b7099.e6806f3c result=bcc139ad.312e9e60.a2f res2=00000003 errno=0
-func=rred op1=408fb53d.14aa9c30 result=bfb460d4.ed16b422.511 res2=00000002 errno=0
-func=rred op1=408fe781.0b53247a result=bfb460d4.ed18ba33.f74 res2=00000002 errno=0
-func=rred op1=409471e4.b34c75af result=3cc24bb6.795811b3.c63 res2=00000001 errno=0
-func=rred op1=40991bb2.d56f1c0d result=bcc0de54.c3cb77ef.972 res2=00000003 errno=0
-func=rred op1=409ff412.08fd45ee result=bfc460d4.ed2d0bb8.60c res2=00000002 errno=0
-func=rred op1=409ff412.08fd4733 result=bfc460d4.ed046bb8.60c res2=00000002 errno=0
-func=rred op1=40ab4e0b.2cec917e result=3cc35dbf.c1818506.e98 res2=00000001 errno=0
-func=rred op1=40ada2f2.3dfde4ad result=bcbf9896.f7440938.e7b res2=00000003 errno=0
-func=rred op1=40affa5a.87d256f9 result=bfd460d4.ed2d147a.959 res2=00000002 errno=0
-func=rred op1=40affa5a.87d257d2 result=bfd460d4.ed11f47a.959 res2=00000002 errno=0
-func=rred op1=40b90a6b.78a52d2e result=3cc4cb21.770e1ecb.189 res2=00000001 errno=0
-func=rred op1=40bfe691.f24548fd result=bcbb5071.d69e3bec.5a7 res2=00000003 errno=0
-func=rred op1=40bffd7e.c73cdcf3 result=bfe460d4.ed7e88db.aff res2=00000002 errno=0
-func=rred op1=40bffd7e.c73ce20a result=bfe460d4.ecdba8db.aff res2=00000002 errno=0
-func=rred op1=40c5a4fb.ea3a16b6 result=bcb875ae.6b850863.fc5 res2=00000003 errno=0
-func=rred op1=40c7e89b.9e817b06 result=3cc7a5e4.e2275253.76c res2=00000001 errno=0
-func=rred op1=40cfff10.e6f21c1e result=3fd30499.988aa830.25d res2=00000001 errno=0
-func=rred op1=40cfff10.e6f2264d result=3fd30499.9da22830.25d res2=00000001 errno=0
-func=rred op1=40d635e3.d74befca result=bcaa1541.7e407485.076 res2=00000003 errno=0
-func=rred op1=40d757b3.b16fa1f2 result=3ccd5b6b.b859b964.331 res2=00000001 errno=0
-func=rred op1=40dfff10.e6f2264d result=3fe30499.9da22830.25d res2=00000002 errno=0
-func=rred op1=40dfffd9.f6ccbe3f result=3fe30499.988a73cf.0b7 res2=00000000 errno=0
-func=rred op1=40e5ed6f.e0c30340 result=bccefafe.cb152585.3e2 res2=00000001 errno=0
-func=rred op1=40e67e57.cdd4dc54 result=3ca396f5.3352c400.db0 res2=00000003 errno=0
-func=rred op1=40efffd9.f6cca9e0 result=bfd87587.17a4e524.ec7 res2=00000001 errno=0
-func=rred op1=40efffd9.f6ccd29e result=bfd87586.c628e524.ec7 res2=00000001 errno=0
-func=rred op1=40f65a1d.d290660f result=bcb049c6.e4971284.99e res2=00000001 errno=0
-func=rred op1=40f6a291.c9195299 result=3ccbbbd8.a59e4d43.27f res2=00000003 errno=0
-func=rred op1=40ffffd9.f6cca9e0 result=bfe87587.17a4e524.ec7 res2=00000002 errno=0
-func=rred op1=40ffffd9.f6ccd29e result=bfe87586.c628e524.ec7 res2=00000002 errno=0
-func=rred op1=4100dec1.da5fa53f result=3cbd626f.ccfc2601.489 res2=00000001 errno=0
-func=rred op1=410bf9b3.c6059d24 result=bcb6c813.2f84c308.c64 res2=00000001 errno=0
-func=rred op1=410fffd9.f6ccca78 result=3fa58e8f.b9e8fe6b.441 res2=00000003 errno=0
-func=rred op1=410ffff3.18c7fe24 result=3fa58e87.93ddb859.9df res2=00000001 errno=0
-func=rred op1=41139c6f.d67805a7 result=bc8988ef.e18ff83f.598 res2=00000003 errno=0
-func=rred op1=41193c05.c9ed3cbc result=3cb065d7.3720c4f8.efd res2=00000001 errno=0
-func=rred op1=411fff9b.21d874d7 result=3fb58e8e.fc452d97.637 res2=00000000 errno=0
-func=rred op1=411fffff.a9c5a846 result=3fb58e87.93d81550.cae res2=00000000 errno=0
-func=rred op1=41223d98.d86bd573 result=3ccbc9e0.cee3267d.52f res2=00000001 errno=0
-func=rred op1=412a9adc.c7f96cf0 result=bcbd2a4f.27e8c118.9ca res2=00000003 errno=0
-func=rred op1=412fff9b.21d874d7 result=3fc58e8e.fc452d97.637 res2=00000000 errno=0
-func=rred op1=412fffff.a9c5a846 result=3fc58e87.93d81550.cae res2=00000000 errno=0
-func=rred op1=41344bdb.557e1dc1 result=bcd2ae9d.61bc91ca.8a4 res2=00000001 errno=0
-func=rred op1=413fffff.a9c31c60 result=3fd58de4.9a581550.cae res2=00000000 errno=0
-func=rred op1=413fffff.a9c8342c result=3fd58f2a.8d581550.cae res2=00000000 errno=0
-func=rred op1=414ffffc.8587170a result=3fe58ebd.e6f97e12.ffa res2=00000000 errno=0
-func=rred op1=414fffff.a9c31c60 result=3fe58de4.9a581550.cae res2=00000000 errno=0
-func=rred op1=415ffffa.f366e59a result=bfcc9ae3.c1cfd521.646 res2=00000001 errno=0
-func=rred op1=415fffff.a9c31c60 result=bfcca0b5.cf60be3b.dda res2=00000001 errno=0
-func=rred op1=416ffffb.57eea140 result=bfdc9b47.17f13de3.992 res2=00000000 errno=0
-func=rred op1=416fffff.a9c31c60 result=bfdca0b5.cf60be3b.dda res2=00000002 errno=0
-func=rred op1=417fffff.dbde54a8 result=3fe551c4.1816e793.952 res2=00000001 errno=0
-func=rred op1=417fffff.dc2fd169 result=3fe5f4bd.9a16e793.952 res2=00000001 errno=0
-func=rred op1=418fffff.c2f2ac7f result=bfcb1c87.2d275aa1.21c res2=00000001 errno=0
-func=rred op1=418fffff.f5004ffc result=bfce81b9.e5acfda9.f4d res2=00000001 errno=0
-func=rred op1=419fffff.c2eae9c2 result=bfdb98b2.fd275aa1.21c res2=00000002 errno=0
-func=rred op1=419fffff.f5004ffc result=bfde81b9.e5acfda9.f4d res2=00000002 errno=0
-func=rred op1=41afffff.c2e7cf10 result=3fe67998.8b60ff8f.6b7 res2=00000003 errno=0
-func=rred op1=41afffff.fb48ced1 result=3fe3c23c.c1caa825.7df res2=00000001 errno=0
diff --git a/test/testcases/directed/rred2.tst b/test/testcases/directed/rred2.tst
deleted file mode 100644
index 558c18e..0000000
--- a/test/testcases/directed/rred2.tst
+++ /dev/null
@@ -1,516 +0,0 @@
-; rred2.tst
-;
-; Copyright (c) 1999-2018, Arm Limited.
-; SPDX-License-Identifier: MIT
-
-func=rred op1=4139eb71.48f354d6 result=3c8d0afa.32c646ca.18a res2=00000001 errno=0
-func=rred op1=414344ba.16f4f99a result=3cc23686.da4d2965.916 res2=00000003 errno=0
-func=rred op1=414a4327.087660e3 result=bccb599f.84bc5cab.fb1 res2=00000003 errno=0
-func=rred op1=41569815.aff42738 result=3cc5d7e6.20a5f23e.d47 res2=00000001 errno=0
-func=rred op1=415d3ecc.e1f28274 result=bcad49a4.1d0b3b67.209 res2=00000003 errno=0
-func=rred op1=416841c3.7c73be07 result=3ccd1aa4.ad5783f1.5aa res2=00000001 errno=0
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-func=rred op1=4b476e1e.e2edd343 result=bca97f34.292862a0.82d res2=00000003 errno=0
-func=rred op1=4b50539b.48d14c55 result=bc635481.dbfbe4fb.940 res2=00000003 errno=0
-func=rred op1=4b598cb2.f78611bc result=3cb7af47.fc88c528.ece res2=00000003 errno=0
-func=rred op1=4b63e0dd.15df8fcc result=bcba19d8.380841c8.5f7 res2=00000001 errno=0
-func=rred op1=4b6d19f4.c4945533 result=3cb679ff.dec906d9.33a res2=00000001 errno=0
-func=rred op1=4b76b6c8.06b2d0c4 result=3cb544b7.c1094889.7a6 res2=00000003 errno=0
-func=rred op1=4b7a4409.d3c1143b result=bcbc8468.7387be67.d1f res2=00000001 errno=0
-func=rred op1=4b854bd2.8e493048 result=bcbeeef8.af073b07.447 res2=00000001 errno=0
-func=rred op1=4b8baeff.4c2ab4b7 result=3cb06f97.4a0a4f4a.956 res2=00000003 errno=0
-func=rred op1=4b96014d.4a7e0086 result=3ca734ed.a616ac17.60d res2=00000003 errno=0
-func=rred op1=4b9af984.8ff5e479 result=bcc44c9c.ce8296c2.873 res2=00000001 errno=0
-func=rred op1=4ba0ae58.a6ebb474 result=3ccb11f3.2a8ef38f.52a res2=00000001 errno=0
-func=rred op1=4bab5441.ee104c98 result=bc9ee82c.23c23bbf.8e6 res2=00000003 errno=0
-func=rred op1=4bb8aac7.9c47268f result=3caef5c5.3a4c3a4e.fa7 res2=00000001 errno=0
-func=rred op1=4bbdfdbc.3fd972a1 result=bcc73187.60742c73.85d res2=00000003 errno=0
-func=rred op1=4bc47f31.728c3972 result=bcb72e21.1ad1accf.aad res2=00000001 errno=0
-func=rred op1=4bcf7fd8.17cb39b5 result=3cb73bba.315bab5f.16e res2=00000001 errno=0
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-func=rred op1=4be84a40.a64ab4ca result=3c9f54f4.d812303a.ef0 res2=00000001 errno=0
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-func=rred op1=4c00826c.5dd702ce result=3ccb33f1.e2e7eff5.e0d res2=00000003 errno=0
-func=rred op1=4c03ecf4.9b990c61 result=bc9da1d2.06d25e4d.6c7 res2=00000003 errno=0
-func=rred op1=4c10090a.775f3363 result=3ca0840b.d4a90114.38d res2=00000001 errno=0
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-func=rred op1=4c21faff.897c1fe2 result=bc9a3b8c.6452ba72.673 res2=00000003 errno=0
-func=rred op1=4c2e201f.dca17a47 result=3ccc0d83.4b87d8ec.a22 res2=00000003 errno=0
-func=rred op1=4c39068a.3c1d4354 result=3cba7934.903d538b.d7e res2=00000003 errno=0
-func=rred op1=4c3af87f.4e3a2fd3 result=bcb3aca9.4b3e0bd5.cd6 res2=00000001 errno=0
-func=rred op1=4c4772b9.f4e99e1a result=bcd3bc13.5638b21c.299 res2=00000001 errno=0
-func=rred op1=4c4e7e44.a78ac18c result=3c4ed415.f54c8cb8.572 res2=00000003 errno=0
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-func=rred op1=4c5bc267.71d40270 result=3cca9808.a632a018.903 res2=00000001 errno=0
-func=rred op1=4c66deb3.7da81129 result=3c671f10.77f9698a.416 res2=00000001 errno=0
-func=rred op1=4c6fdc33.4266211a result=bcc9df10.2272d4cc.3e3 res2=00000001 errno=0
-func=rred op1=4c762fbc.303a6162 result=3ccb1358.fe07d24b.719 res2=00000001 errno=0
-func=rred op1=4c7f2d3b.f4f87153 result=bcc963bf.ca9da299.5cd res2=00000001 errno=0
-func=rred op1=4c82b76f.41ffe114 result=3ccb8ea9.55dd047e.52f res2=00000001 errno=0
-func=rred op1=4c8b05f7.b950413e result=bcc8aac7.46ddd74d.0ac res2=00000003 errno=0
-func=rred op1=4c90fb48.cae2a0ed result=3ccc854a.058768e4.15a res2=00000001 errno=0
-func=rred op1=4c9cc21e.306d8165 result=bcc6bd85.e7890e81.855 res2=00000003 errno=0
-func=rred op1=4ca3ecfe.2445590b result=3ccf692c.14869615.5dd res2=00000001 errno=0
-func=rred op1=4ca9d068.d70ac947 result=bcc3d9a3.d889e150.3d2 res2=00000003 errno=0
-func=rred op1=4cb565d8.d0f6b51a result=3cd29878.1942783b.f71 res2=00000001 errno=0
-func=rred op1=4cbff71f.543c1d9b result=bcb46eb9.f7c3eaad.43d res2=00000003 errno=0
-func=rred op1=4cc3cb58.3f0f66ff result=bca97368.f4e18efe.5c0 res2=00000003 errno=0
-func=rred op1=4ccb6ae9.68f21762 result=3c8582b4.01abf6e7.ec9 res2=00000003 errno=0
-func=rred op1=4cd55505.de5bbc14 result=3cc0c236.3ac105ca.aa6 res2=00000003 errno=0
-func=rred op1=4cd9e13b.c9a5c24d result=bccacb94.34fc4e6c.dad res2=00000001 errno=0
-func=rred op1=4ce85ff7.a3a6e9bb result=3cc3728c.baf684a7.a7f res2=00000001 errno=0
-func=rred op1=4cee75db.2e3d4509 result=bcb16265.74411267.634 res2=00000003 errno=0
-func=rred op1=4cf30ab6.2c0ffab6 result=3cc622e3.3b2c0384.a58 res2=00000003 errno=0
-func=rred op1=4cf615a7.f15b285d result=bca80370.e7ac295a.d04 res2=00000001 errno=0
-func=rred op1=4d01e58e.52ea1a07 result=bc7405e7.30019397.1d4 res2=00000001 errno=0
-func=rred op1=4d0f9b03.076325b8 result=3cb44255.8eabddae.7ac res2=00000001 errno=0
-func=rred op1=4d13fd9b.2222a132 result=bcb943cf.5aac4294.421 res2=00000003 errno=0
-func=rred op1=4d1d82f6.382a9e8d result=3ccfa3de.c901e5bf.2a0 res2=00000001 errno=0
-func=rred op1=4d29cc4f.14c2e375 result=3cae81b7.8556f191.66f res2=00000001 errno=0
-func=rred op1=4d2be45b.e3fb6aa0 result=bcbe4549.26aca77a.096 res2=00000003 errno=0
-func=rred op1=4d35d8ee.b3d67ebe result=3ca47ec3.ed5627c5.d85 res2=00000001 errno=0
-func=rred op1=4d3fd7bc.44e7cf57 result=bcc4241e.5f56b8a2.cc0 res2=00000003 errno=0
-func=rred op1=4d42d338.1bc408cd result=3cd6d22e.0c56a2a7.35d res2=00000001 errno=0
-func=rred op1=4d4cd205.acd55966 result=bca38d0a.72acff68.623 res2=00000001 errno=0
-func=rred op1=4d556219.cf69875b result=bcd19445.e1abf3aa.10f res2=00000003 errno=0
-func=rred op1=4d59557a.3055ec12 result=3ca5707d.67ff5023.4e7 res2=00000003 errno=0
-func=rred op1=4d679734.72163568 result=3cc9dae3.4755fbce.abf res2=00000003 errno=0
-func=rred op1=4d6b13bf.ee95a2bc result=bca1a997.7d5aaead.75e res2=00000001 errno=0
-func=rred op1=4d7a349d.0f75c767 result=3ca93763.52a3f199.271 res2=00000003 errno=0
-func=rred op1=4d7bf2e2.cdb57e11 result=bcc7f770.5203ab13.bfa res2=00000001 errno=0
-func=rred op1=4d836fad.13d05eb8 result=3cc10617.88a8a477.f10 res2=00000001 errno=0
-func=rred op1=4d844ecf.f2f03a0d result=bcba7e63.3c080604.30d res2=00000003 errno=0
-func=rred op1=4d907cc6.858d980b result=3cb06297.93f69a42.6c1 res2=00000003 errno=0
-func=rred op1=4d9741b6.813300ba result=bc746ffe.964146b0.9c5 res2=00000001 errno=0
-func=rred op1=4da265cb.3c3ee90c result=bcc24d17.720cb8e2.fac res2=00000001 errno=0
-func=rred op1=4dac1da1.c6271868 result=3cbf7e2f.3e892019.ce7 res2=00000003 errno=0
-func=rred op1=4db4d3c0.deb8f4e3 result=bcc39417.5b70cd4e.048 res2=00000003 errno=0
-func=rred op1=4db9afac.23ad0c91 result=3cbcf02f.6bc0f743.bae res2=00000001 errno=0
-func=rred op1=4dc03a4e.0fa93aa0 result=bcc4db17.44d4e1b9.0e5 res2=00000001 errno=0
-func=rred op1=4dce491e.f2bcc6d4 result=3cb5462f.f3687cc1.804 res2=00000003 errno=0
-func=rred op1=4dd3be02.486e1dad result=bcc9f716.ea653365.356 res2=00000001 errno=0
-func=rred op1=4ddac56a.b9f7e3c7 result=3ca61c61.508fb2d2.644 res2=00000003 errno=0
-func=rred op1=4de33322.fd48b212 result=3c6ac62b.a4e6c21c.7f8 res2=00000003 errno=0
-func=rred op1=4deed3fe.3de2326f result=bcb399cd.391a109f.b85 res2=00000003 errno=0
-func=rred op1=4df53a6c.bf3dd966 result=bcc404e5.e7adaba8.2a5 res2=00000003 errno=0
-func=rred op1=4dfcccb4.7bed0b1b result=3c8414a0.bbad1195.5fa res2=00000001 errno=0
-func=rred op1=4e022f7e.1c4e1e68 result=3cc68779.ff234dda.d64 res2=00000003 errno=0
-func=rred op1=4e0dd059.5ce79ec5 result=bcc25883.2d5f3f86.626 res2=00000003 errno=0
-func=rred op1=4e12b150.8ccb683d result=3cc833dc.b971b9fc.9e4 res2=00000003 errno=0
-func=rred op1=4e1d4e86.ec6a54f0 result=bcbfabde.2bd33aa7.6cd res2=00000001 errno=0
-func=rred op1=4e27bf02.845c39ac result=3ccd3904.e85cfe61.f62 res2=00000003 errno=0
-func=rred op1=4e2840d4.f4d98381 result=bcb8fa53.42998a20.4cf res2=00000001 errno=0
-func=rred op1=4e357912.c0d275df result=3cd1f547.e8cb5774.8b0 res2=00000003 errno=0
-func=rred op1=4e3a86c4.b863474e result=bc9396ca.1bb1e22b.b53 res2=00000001 errno=0
-func=rred op1=4e46dcf3.dad5fcb0 result=3cb5e079.1dfa4991.923 res2=00000001 errno=0
-func=rred op1=4e4e3095.95f091ec result=bcc4bba1.9cd615de.a3b res2=00000003 errno=0
-func=rred op1=4e58b1dc.499ca1ff result=3ca82a28.2042b0f7.6f3 res2=00000003 errno=0
-func=rred op1=4e5c5bad.2729ec9d result=bcc9a154.23c28e69.910 res2=00000001 errno=0
-func=rred op1=4e62fa9f.52e722d3 result=3c824d78.12433b2e.e82 res2=00000001 errno=0
-func=rred op1=4e64cf87.c1adc822 result=bcce8706.aaaf06f4.7e5 res2=00000003 errno=0
-func=rred op1=4e701f00.d78c633d result=bcb14d1b.19697ac5.d83 res2=00000001 errno=0
-func=rred op1=4e75d63d.ce41e269 result=3cba73d7.228b185d.4c3 res2=00000003 errno=0
-func=rred op1=4e818cd0.1539c308 result=bca9737a.29b157f4.3c4 res2=00000003 errno=0
-func=rred op1=4e84686e.9094829e result=3cbf0735.271be729.064 res2=00000001 errno=0
-func=rred op1=4e9a5338.1fd6a48c result=bcc3169b.9f4501f7.2d3 res2=00000001 errno=0
-func=rred op1=4e9bc107.5d840457 result=3c964eeb.f5aa3cd3.27f res2=00000003 errno=0
-func=rred op1=4ea5f004.1a8833ca result=bccfd058.b41dadf1.4b6 res2=00000003 errno=0
-func=rred op1=4ea75dd3.58359395 result=3cb7e133.0fadca63.b21 res2=00000003 errno=0
-func=rred op1=4eb3be6a.17e0fb69 result=bcdca1e9.6ee782f2.c3d res2=00000003 errno=0
-func=rred op1=4ebdf2a1.602b3cb8 result=3ca32a5d.c1a321b2.139 res2=00000003 errno=0
-func=rred op1=4ec12aea.b2bcd6bd result=bcafbc96.91bf8e36.650 res2=00000001 errno=0
-func=rred op1=4ecfc256.005588ce result=3ce6ae8d.33939848.90e res2=00000001 errno=0
-func=rred op1=4ed675f9.08206d8a result=3cbcbf8c.a274b28b.1d6 res2=00000001 errno=0
-func=rred op1=4ed8a793.0ac7a5eb result=bcb62767.b0edfd5d.5b3 res2=00000001 errno=0
-func=rred op1=4ee2b7a4.dc1b05f3 result=3cc7f4f5.320bea1e.987 res2=00000003 errno=0
-func=rred op1=4eec65e7.36cd0d82 result=bcc15cd0.408534f0.d65 res2=00000001 errno=0
-func=rred op1=4ef1f147.c76bee58 result=bcaf1e85.7ece905f.320 res2=00000003 errno=0
-func=rred op1=4ef5af9b.f37155ef result=3c8cd8d8.11decc13.d49 res2=00000001 errno=0
-func=rred op1=4f00754c.3bc0c65a result=3cce8d1a.23929f4c.5aa res2=00000003 errno=0
-func=rred op1=4f0ea83f.d7274d1b result=bca0b219.75df2a55.47b res2=00000001 errno=0
-func=rred op1=4f11334a.01965a59 result=3cbdfbae.c856ae39.835 res2=00000001 errno=0
-func=rred op1=4f1a2bed.e54c5185 result=bc722d6b.677e225a.eb6 res2=00000003 errno=0
-func=rred op1=4f27edc4.ec5ed3ba result=3caa932a.a4ef07c8.772 res2=00000003 errno=0
-func=rred op1=4f2c6a16.de39cf50 result=bcb1d4f0.2c570c7a.f67 res2=00000001 errno=0
-func=rred op1=4f307334.680a6573 result=bcc879ba.d592ce6d.144 res2=00000003 errno=0
-func=rred op1=4f3f6855.70b34201 result=3cd98672.bd40eb1a.c5b res2=00000001 errno=0
-func=rred op1=4f431168.2dbdddb1 result=3ca17c74.f12ff69b.017 res2=00000003 errno=0
-func=rred op1=413d10a4.f0adcc4f result=3fe87fe6.30304a38.943 res2=00000000 error=0
-func=rred op1=413dba61.a2c03b33 result=3fe0b7a6.a6a685cf.8d6 res2=00000003 error=0
-func=rred op1=c13a34ec.768d711d result=3fe5b7b8.a1db2f4c.b12 res2=00000003 error=0
-func=rred op1=c13cb161.35c98a0f result=3fd67e4f.059466c9.c6f res2=00000001 error=0
-func=rred op1=c13c38d1.7027b607 result=bfdd0737.0b906a40.52b res2=00000002 error=0
-func=rred op1=c13ef602.452f3f79 result=3fe36561.56e3f603.3f7 res2=00000001 error=0
-func=rred op1=c13d6289.355ffec1 result=3fd89d90.7d0bce31.6f3 res2=00000001 error=0
-func=rred op1=413a0a72.b8d35b21 result=3fca0190.f80f3eb6.40a res2=00000002 error=0
-func=rred op1=413cb6dc.3281c1d3 result=bfb5dc53.6f66760b.40a res2=00000000 error=0
-func=rred op1=c13b2097.5e434fcb result=bfe4dc84.b351e6a4.9f6 res2=00000000 error=0
-func=rred op1=c139f416.e781b5a7 result=bfd7826d.074f358e.b0d res2=00000002 error=0
diff --git a/test/testcases/directed/rred3.tst b/test/testcases/directed/rred3.tst
deleted file mode 100644
index 8967eb2..0000000
--- a/test/testcases/directed/rred3.tst
+++ /dev/null
@@ -1,505 +0,0 @@
-; rred3.tst
-;
-; Copyright (c) 1999-2018, Arm Limited.
-; SPDX-License-Identifier: MIT
-
-func=rred op1=4f454f91.26ab5b7c result=bccabf68.428292b8.71a res2=00000003 errno=0
-func=rred op1=4f569eab.0985179b result=bc561ece.c9c577fd.3e9 res2=00000003 errno=0
-func=rred op1=4f5b7b07.c8260da4 result=3cd61dee.99d944a9.b99 res2=00000001 errno=0
-func=rred op1=4f64d809.9ba17aa6 result=3cb123f9.b608e0bb.0c7 res2=00000001 errno=0
-func=rred op1=4f68654c.7768b490 result=bcb285e6.a2a5383a.e06 res2=00000003 errno=0
-func=rred op1=4f71868a.855f3127 result=bcdf60e1.eb2be0c7.29c res2=00000001 errno=0
-func=rred op1=4f7f440e.697237f9 result=3cc9b5f6.910d5118.92b res2=00000003 errno=0
-func=rred op1=4f808557.ebaaea77 result=3caf8419.92d91276.712 res2=00000001 errno=0
-func=rred op1=4f8cb7fe.275f44bf result=bcb549c0.7bdde73a.883 res2=00000003 errno=0
-func=rred op1=4f939201.7a980109 result=3ca9fc65.e067b477.218 res2=00000001 errno=0
-func=rred op1=4f99ab54.98722e2d result=bcb80d9a.5516963a.300 res2=00000003 errno=0
-func=rred op1=4fa51856.420e8c52 result=3c9dd9fc.f709f0f1.047 res2=00000001 errno=0
-func=rred op1=4fa824ff.d0fba2e4 result=bcbd954e.0787f439.7fb res2=00000003 errno=0
-func=rred op1=4fb0a57e.3ee1734d result=bce19716.baece8b3.584 res2=00000001 errno=0
-func=rred op1=4fbfa481.6315d27b result=3cb6637d.b94774b4.c35 res2=00000003 errno=0
-func=rred op1=4fc0956b.15462ee2 result=bcad509f.1805f781.fae res2=00000001 errno=0
-func=rred op1=4fcb2196.364d750b result=3c512bbb.e07f2de1.317 res2=00000003 errno=0
-func=rred op1=4fd2d6e0.abaa5d9a result=3cae635a.d60dea60.0e0 res2=00000001 errno=0
-func=rred op1=4fd8e020.9fe94653 result=bcc5fc77.520479a1.7c3 res2=00000003 errno=0
-func=rred op1=4fe1b625.e078463e result=bcac3de3.59fe04a3.e7d res2=00000003 errno=0
-func=rred op1=4fec4251.017f8c67 result=3cc6ca84.208a6fc8.0a8 res2=00000003 errno=0
-func=rred op1=4ff24683.461151ec result=3cb04469.290ee80e.1a1 res2=00000001 errno=0
-func=rred op1=4ffa9138.d0b4695d result=bcc52e6a.837e837a.ede res2=00000001 errno=0
-func=rred op1=5001fe54.9344cc15 result=bca7f2f4.61de392b.9b7 res2=00000003 errno=0
-func=rred op1=500b69c4.e919fae2 result=3cc8669d.bd965c15.272 res2=00000003 errno=0
-func=rred op1=50168ff5.64c92090 result=bc9eba2c.e33d4476.056 res2=00000003 errno=0
-func=rred op1=501fb337.07d1c986 result=3cb8da47.194e7efe.b2d res2=00000001 errno=0
-func=rred op1=50246b3c.556d393e result=3cccb18c.b5b6278d.738 res2=00000003 errno=0
-func=rred op1=502d464f.45a95c5d result=bccbca39.fe45e1ba.5c2 res2=00000003 errno=0
-func=rred op1=5030ebf8.0b96d86c result=bcb70ba1.aa6df358.841 res2=00000001 errno=0
-func=rred op1=50357d98.dd1b2ce7 result=3cc50301.7ce6d66f.f22 res2=00000001 errno=0
-func=rred op1=5043bdf6.b82ffc7e result=bccae2e7.46d59be7.44b res2=00000001 errno=0
-func=rred op1=504df394.e2e6991d result=3cce8032.2496b333.a24 res2=00000003 errno=0
-func=rred op1=505254f7.61e36a75 result=bcd8f744.78a1c79f.e46 res2=00000003 errno=0
-func=rred op1=505f5c94.39332b26 result=3cdc948f.5662deec.41f res2=00000001 errno=0
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-func=rred op1=5bccbdec.c7d9fcb6 result=bcccd8ef.52bd874b.f5e res2=00000003 errno=0
-func=rred op1=5bd7e279.2019b6a4 result=3cc60277.2f2991b1.5f9 res2=00000001 errno=0
-func=rred op1=5bd9d3da.96669f78 result=bcb3be89.7efd5cd7.e38 res2=00000003 errno=0
-func=rred op1=5be85ed1.7dacf0d9 result=3ccc1410.66ff0354.168 res2=00000003 errno=0
-func=rred op1=5be95782.38d36543 result=bc9e6d5c.3d49e649.d6d res2=00000001 errno=0
-func=rred op1=5bf2e28b.9339bd65 result=3c921f6d.8161a6cb.e08 res2=00000003 errno=0
-func=rred op1=5bffcc78.de6d0d21 result=bcc17a9b.ced127fe.677 res2=00000001 errno=0
-func=rred op1=5c061d06.e6069154 result=bca55da5.7c9912e3.e69 res2=00000001 errno=0
-func=rred op1=5c0c15a5.2e0cfefd result=3cd356c2.7f966f54.e2c res2=00000003 errno=0
-func=rred op1=5c11837a.189cf088 result=bcd66a3e.2e907f34.605 res2=00000001 errno=0
-func=rred op1=5c1df10f.063d060f result=3c9dc26b.0c547567.b4e res2=00000001 errno=0
-func=rred op1=5c2095c5.2c84ecff result=bcc0063c.1d72ce2a.ece res2=00000003 errno=0
-func=rred op1=5c2869cd.4cbb61ba result=3cb99008.4476c425.cdb res2=00000001 errno=0
-func=rred op1=5c31bc28.5fdf5532 result=3c90c98b.1f76c507.9cc res2=00000003 errno=0
-func=rred op1=5c37436a.1960f987 result=bcb12b42.b4bb61a1.ff5 res2=00000001 errno=0
-func=rred op1=5c43ec97.a2f2f343 result=bcd4510c.caa1a693.6cc res2=00000003 errno=0
-func=rred op1=5c4a9a3c.8fceffcb result=3ca92e50.af32278b.6b2 res2=00000001 errno=0
-func=rred op1=5c536791.9b165854 result=3ccfdb9c.70434e08.a88 res2=00000003 errno=0
-func=rred op1=5c58eed3.5497fca9 result=bcb5bf5d.11ddaf7e.492 res2=00000003 errno=0
-func=rred op1=5c60e673.c243d3a1 result=bcaab52f.044499f4.f58 res2=00000001 errno=0
-func=rred op1=5c69c487.f2337e3a result=3c8b779c.eaa3c069.0fe res2=00000001 errno=0
-func=rred op1=5c75c058.290969b6 result=3cc28104.ee21010e.2dc res2=00000001 errno=0
-func=rred op1=5c7dc8b7.bb5d92be result=bcb7463b.66f021e7.d39 res2=00000003 errno=0
-func=rred op1=5c87c270.0d9e73f8 result=3cc5eff8.8b75791b.4fb res2=00000003 errno=0
-func=rred op1=5c8bc69f.d6c8887c result=bcb06854.2c4731cd.8f9 res2=00000001 errno=0
-func=rred op1=5c98c37b.ffe8f919 result=3ccccddf.c61e6935.93b res2=00000003 errno=0
-func=rred op1=5c9ac593.e47e035b result=bc85642d.b7aa8cc8.3d0 res2=00000001 errno=0
-func=rred op1=5ca3d3eb.eecbe13c result=3ca61e91.7cb91d37.00a res2=00000001 errno=0
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-func=rred op1=5cb0db9d.ed1812bd result=bcb5c15f.9a31d4ff.9ed res2=00000003 errno=0
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-func=rred op1=5cc8c8e6.ea7ed98b result=3ccba635.dbe76484.c0c res2=00000001 errno=0
-func=rred op1=5ccfba8e.e030fbaa result=bca4a9c9.f29bfc59.796 res2=00000001 errno=0
-func=rred op1=5cd4d242.6bcb7624 result=3ca79359.06d63e14.87e res2=00000003 errno=0
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-func=rred op1=5cef3b63.a1b13136 result=3cc1ae82.c520ae8f.65e res2=00000001 errno=0
-func=rred op1=5cfa06d3.06be53ad result=3ccd782f.488bcd99.a9d res2=00000003 errno=0
-func=rred op1=5cff7af9.40f11670 result=bc97da39.6bda6e50.9bd res2=00000001 errno=0
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-func=rred op1=5d0f9ac4.1091090d result=bcd6276d.8959a33e.832 res2=00000001 errno=0
-func=rred op1=5d179c3a.f0b4d0d4 result=bcb1e3ab.10e3d2bc.74e res2=00000003 errno=0
-func=rred op1=5d1cd0cb.8ba7ae5d result=3cbd4306.fcc8a96c.9ae res2=00000003 errno=0
-func=rred op1=5d23acdb.c896ae06 result=bcbdd0c7.c6d109e4.c2d res2=00000001 errno=0
-func=rred op1=5d28e16c.63898b8f result=3cd01f27.1521fb9b.572 res2=00000001 errno=0
-func=rred op1=5d31b52c.34879c9f result=bccad580.9955bc1a.af5 res2=00000001 errno=0
-func=rred op1=5d3ec87b.1fb6bfc4 result=3cdbc563.660b0287.912 res2=00000001 errno=0
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-func=rred op1=5d4f21ba.3053eb1a result=3caf594f.d184a1b7.aa4 res2=00000001 errno=0
-func=rred op1=5d51888c.ac3906f4 result=bca05b23.06303ae9.8d6 res2=00000001 errno=0
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-func=rred op1=5d75eaaf.d74748b1 result=bcc471eb.c7bc49a3.f0c res2=00000001 errno=0
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-func=rred op1=5d8b820c.cdd52299 result=bca5cefb.f19f8b57.4f7 res2=00000001 errno=0
-func=rred op1=5d94543b.277ff3e8 result=bccdfc73.85b03b34.280 res2=00000003 errno=0
-func=rred op1=5d9e4dbb.491c0f8d result=3cc8889a.9a40eac6.65e res2=00000001 errno=0
-func=rred op1=5da157ef.3a1528a5 result=3cb05aef.28215fb9.b10 res2=00000001 errno=0
-func=rred op1=5da5ba12.65236a62 result=bcc888ce.784fc5f6.425 res2=00000001 errno=0
-func=rred op1=5db20ada.d8e6e3e2 result=3cd9e583.dd990815.df5 res2=00000001 errno=0
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-func=rred op1=5dcebf7f.d196dc53 result=bcd72c19.130683d6.a54 res2=00000001 errno=0
-func=rred op1=5dd80bb7.85d6027c result=bcbb44a7.ab949073.d10 res2=00000001 errno=0
-func=rred op1=5dddd3b1.ee87bab3 result=3cb05880.bf6f197b.5c5 res2=00000001 errno=0
-func=rred op1=5de1cdd6.2b9cb975 result=3ccdfad4.953961b5.44d res2=00000001 errno=0
-func=rred op1=5defe852.61f02860 result=bc95e545.5c01b9e8.025 res2=00000001 errno=0
-func=rred op1=5df9e564.807aa7c1 result=3cb05204.fd93b37f.cfe res2=00000001 errno=0
-func=rred op1=5dfbfa04.f3e3156e result=bcce0150.5714c7b0.d15 res2=00000003 errno=0
-func=rred op1=5e01eb4f.e7fe9da9 result=3cc30ead.a913eabc.d02 res2=00000001 errno=0
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-func=rred op1=5e13f133.7d36193c result=bcbb5e96.b3022862.02e res2=00000001 errno=0
-func=rred op1=5e1de26e.ccb8accd result=3ccde761.4fa72fc2.9f7 res2=00000001 errno=0
-func=rred op1=5e21f2ae.571716b6 result=bcc8a1ee.0781f125.029 res2=00000001 errno=0
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-func=rred op1=5e30f36b.c4079573 result=bcd74399.b1c1d586.827 res2=00000001 errno=0
-func=rred op1=5e3ee1b1.5fc82e10 result=3ced3837.24c721f3.5f6 res2=00000001 errno=0
-func=rred op1=5e407779.b20c1158 result=bd0240b0.7732a570.d90 res2=00000003 errno=0
-func=rred op1=5e4f6501.e0dc2b38 result=3ccd4bc7.2315a02d.747 res2=00000001 errno=0
-func=rred op1=5e51b106.168d1822 result=3cad9a07.1c4f9915.c89 res2=00000001 errno=0
-func=rred op1=5e52b048.a99c9965 result=bc9c6107.3767b574.780 res2=00000001 errno=0
-func=rred op1=5e6b88cb.b4e32576 result=3c638ffe.4e7e3a15.09c res2=00000003 errno=0
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-func=rred op1=5e769ce8.e5b81ecc result=3cbe3687.0ec38ae6.70e res2=00000001 errno=0
-func=rred op1=5e779c2b.78c7a00f result=bcccaf47.30a1ae5c.cc2 res2=00000001 errno=0
-func=rred op1=5e8912da.4d4da221 result=3cbf6f86.f3ab6e87.c18 res2=00000003 errno=0
-func=rred op1=5e8dfebd.1c78a8cb result=bcba8b87.600be002.7f1 res2=00000001 errno=0
-func=rred op1=5e936ba0.13df9a6e result=3cc05443.6c49a914.891 res2=00000001 errno=0
-func=rred op1=5e95e191.7b751dc3 result=bcb95287.7b23fc61.2e7 res2=00000003 errno=0
-func=rred op1=5ea77a35.e4615ff2 result=3cc2c643.36197057.2a4 res2=00000001 errno=0
-func=rred op1=5eaf9761.8564eafa result=bcb1fc88.1db4a699.4ad res2=00000003 errno=0
-func=rred op1=5eb98180.cca242b4 result=3cc7aa42.c9b8fedc.6cb res2=00000001 errno=0
-func=rred op1=5ebd9016.9d240838 result=bca06911.eceb131d.8bd res2=00000003 errno=0
-func=rred op1=5ecc8c71.290396d7 result=3ca6b6ea.b011610c.87b res2=00000003 errno=0
-func=rred op1=5ece93bc.11447999 result=bcc616cc.98ef6b60.adc res2=00000001 errno=0
-func=rred op1=5ed5286b.81ba94c9 result=3cbeeb73.a686ea9b.4da res2=00000003 errno=0
-func=rred op1=5ed62c10.f5db062a result=bcb89d9a.e3609cac.51c res2=00000001 errno=0
-func=rred op1=5ee27a0e.22368523 result=bcc48356.6825d7e4.eec res2=00000003 errno=0
diff --git a/test/testcases/directed/rred4.tst b/test/testcases/directed/rred4.tst
deleted file mode 100644
index 1b84f45..0000000
--- a/test/testcases/directed/rred4.tst
+++ /dev/null
@@ -1,504 +0,0 @@
-; rred4.tst
-;
-; Copyright (c) 1999-2018, Arm Limited.
-; SPDX-License-Identifier: MIT
-
-func=rred op1=5ee8da6e.555f15d0 result=3ccad12f.2b4c25d3.eaa res2=00000001 errno=0
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-func=rred op1=5f1e5090.43ed71be result=3c966ae3.892121b9.b5c res2=00000001 errno=0
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-func=rred op1=5f634654.c6040e3d result=3cc13820.4e72adae.01c res2=00000001 errno=0
-func=rred op1=5f660507.de0cf1d1 result=bc830f98.96d0b804.4b7 res2=00000003 errno=0
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-func=rred op1=5f900004.52080ab1 result=3cc477cd.8b4150c3.cd7 res2=00000001 errno=0
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-func=rred op1=5fa30286.180a7e41 result=3cb5e002.7fb1e983.4f7 res2=00000001 errno=0
-func=rred op1=5fae5ce0.6a12139c result=bcd1b4ff.5da76cce.858 res2=00000001 errno=0
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-func=rred op1=5fc54467.6c8c54ed result=bcd71f64.424c99a5.9d5 res2=00000001 errno=0
-func=rred op1=5fca99be.328f0328 result=3cb0ac0c.8829f2d3.27e res2=00000001 errno=0
-func=rred op1=5fd42376.c24b6997 result=bc93f61c.29ab0224.dd4 res2=00000001 errno=0
-func=rred op1=5fda396d.f9ceb4b6 result=3cd755d3.2f69cfcc.8d8 res2=00000003 errno=0
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-func=rred op1=6cb3517f.5a800dea result=3c8adfed.2e2a2216.8c7 res2=00000001 errno=0
-func=rred op1=6cbe288a.a8f52fd5 result=bcaf2480.86ff7a7e.69a res2=00000001 errno=0
-func=rred op1=6cc47fca.fbb528e0 result=bcc1403f.16625f60.9d9 res2=00000001 errno=0
-func=rred op1=6cccfa3f.07c014df result=3ca427f1.e29f9990.e95 res2=00000003 errno=0
-func=rred op1=6cd2ba59.89e5806f result=3ccb5438.07b22c29.124 res2=00000001 errno=0
-func=rred op1=6cdd9164.d85aa25a result=bcb51087.95afadb5.f4f res2=00000001 errno=0
-func=rred op1=6ce7da4c.48d2caa7 result=3cd2b418.7c80fc78.c37 res2=00000003 errno=0
-func=rred op1=6ce87172.196d5822 result=bc9e8243.fa6a72aa.bac res2=00000001 errno=0
-func=rred op1=6cf5e178.b9f6b306 result=3cb33f5c.2f8f856b.ddc res2=00000001 errno=0
-func=rred op1=6cfb016b.78e3fd3e result=bcc8e0d0.14fcfc0b.4c4 res2=00000003 errno=0
-func=rred op1=6d072975.69b20594 result=3c8ff1d1.92d260b4.032 res2=00000003 errno=0
-func=rred op1=6d09b96e.c928aab0 result=bcd040b0.89cbcc5a.fd8 res2=00000001 errno=0
-func=rred op1=6d168577.11d45c4d result=3cc53e79.48bcab77.1df res2=00000001 errno=0
-func=rred op1=6d17cd73.c18faedb result=bcba8409.c8102694.3a6 res2=00000003 errno=0
-func=rred op1=6d215f18.0f45842f result=3ca7f55d.2e1dc887.026 res2=00000001 errno=0
-func=rred op1=6d2d97d1.1bfc3040 result=bcc884ec.aee30088.fa3 res2=00000001 errno=0
-func=rred op1=6d33f247.908cf03e result=3cd83d24.ee806487.fe4 res2=00000003 errno=0
-func=rred op1=6d3a60a3.42d71aea result=bcc08878.4a2e685b.f96 res2=00000001 errno=0
-func=rred op1=6d48c50c.5644903f result=bc71f1f0.18a7003e.f92 res2=00000001 errno=0
-func=rred op1=6d4e8f69.b0b111a4 result=3cadb393.8fbd80ac.240 res2=00000001 errno=0
-func=rred op1=6d551212.32c50a37 result=3cc765cd.ad589085.0a9 res2=00000001 errno=0
-func=rred op1=6d5c7806.79c41647 result=bcc9a40b.b06d708c.e9c res2=00000003 errno=0
-func=rred op1=6d612131.ea184bd6 result=bcb35645.ce088065.d05 res2=00000003 errno=0
-func=rred op1=6d66eb8f.4484cd3b result=3cc646ae.abce2081.1b0 res2=00000003 errno=0
-func=rred op1=6d703473.61386a54 result=3ca4ba9b.836a008c.a77 res2=00000001 errno=0
-func=rred op1=6d79b1ca.df2471c1 result=bccd0168.b50cc098.b87 res2=00000001 errno=0
-func=rred op1=6d80aad2.a5a85b15 result=bcbc4f3d.da5c0085.4ce res2=00000003 errno=0
-func=rred op1=6d884ead.11d49f7e result=3cbf17e9.451f00d2.fb3 res2=00000003 errno=0
-func=rred op1=6d944190.398684e9 result=3cc9e942.644480af.d15 res2=00000001 errno=0
-func=rred op1=6d9cd229.2e92aad4 result=bcb98692.6f990037.9e9 res2=00000001 errno=0
-func=rred op1=6da27631.6f976fff result=bc932fdb.b0bbfeab.dc6 res2=00000003 errno=0
-func=rred op1=6da6834e.47e58a94 result=3cafdd49.2e7601c3.60b res2=00000001 errno=0
-func=rred op1=6db9aabb.bb3c1ab4 result=bcc18f40.23fb7fc6.c66 res2=00000003 errno=0
-func=rred op1=6dbdb7d8.938a3549 result=3c995ada.fb74062f.08b res2=00000003 errno=0
-func=rred op1=6dc0e27a.b5ec27ef result=3cc7e5f6.e2d88152.888 res2=00000003 errno=0
-func=rred op1=6dc81705.0190d2a4 result=bc8a09b8.cc07ee51.601 res2=00000001 errno=0
-func=rred op1=6dd1ac56.12c1cbf7 result=3cbc9c12.14f503f9.34b res2=00000003 errno=0
-func=rred op1=6dde81b3.f05fd951 result=bcc4d077.3d7c7d90.f26 res2=00000001 errno=0
-func=rred op1=6de21143.c12c9dfb result=bca3874a.9905f2bd.081 res2=00000003 errno=0
-func=rred op1=6de7b217.532600a0 result=3ccafb76.88348514.1eb res2=00000003 errno=0
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-func=rred op1=6dfdea4f.6abf9e4b result=3cc137d1.3bb18bb5.9aa res2=00000001 errno=0
-func=rred op1=6e022a7f.2cc7527c result=bcda8297.aa1e39b2.bf6 res2=00000001 errno=0
-func=rred op1=6e0e038a.d65a52cc result=3c7e37b7.8592d857.d3b res2=00000003 errno=0
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-func=rred op1=6e1af40c.805ade37 result=3cd4f1e7.3348d4e1.260 res2=00000001 errno=0
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-func=rred op1=6e2c8869.6127f2c2 result=bcc7347f.97822a09.244 res2=00000001 errno=0
-func=rred op1=6e374038.db5cee1e result=3cd052f4.78a006d2.4b3 res2=00000001 errno=0
-func=rred op1=6e3d45fa.1bc122c7 result=bcc36d88.a6cfcefe.29c res2=00000001 errno=0
-func=rred op1=6e4320ff.23450bc2 result=3cd2366f.f0f93457.c87 res2=00000001 errno=0
-func=rred op1=6e49e451.1e427070 result=bcbb862c.7b888cdb.643 res2=00000003 errno=0
-func=rred op1=6e54730b.44b7cceb result=bca8d4a1.717e415e.f49 res2=00000003 errno=0
-func=rred op1=6e5bf3ed.fa4e619e result=3c858c58.50525be3.7c8 res2=00000003 errno=0
-func=rred op1=6e657ad9.b2bdc582 result=3cc074a1.47ce91ea.21a res2=00000003 errno=0
-func=rred op1=6e6aec1f.8c486907 result=bcca2d66.f683671d.2c6 res2=00000001 errno=0
-func=rred op1=6e78b763.d6861390 result=3cc3262c.51d8dd66.913 res2=00000001 errno=0
-func=rred op1=6e7f3078.1e16afac result=bcb0c000.535f5ee9.a5e res2=00000003 errno=0
diff --git a/test/testcases/directed/rred5.tst b/test/testcases/directed/rred5.tst
deleted file mode 100644
index d123472..0000000
--- a/test/testcases/directed/rred5.tst
+++ /dev/null
@@ -1,563 +0,0 @@
-; rred5.tst
-;
-; Copyright (c) 1999-2018, Arm Limited.
-; SPDX-License-Identifier: MIT
-
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-func=rred op1=6f3e6564.f8e3bf31 result=3cb9c950.0b3c8016.9ac res2=00000001 errno=0
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-func=rred op1=6f5db4d5.0442dee5 result=3cc15431.ae95c3cc.8bc res2=00000001 errno=0
-func=rred op1=6f6110ae.4243f569 result=bcdb455b.a32019bc.66d res2=00000001 errno=0
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