diff options
Diffstat (limited to 'newlib/libm')
| -rw-r--r-- | newlib/libm/common/Makefile.am | 5 | ||||
| -rw-r--r-- | newlib/libm/common/Makefile.in | 34 | ||||
| -rw-r--r-- | newlib/libm/common/cosf.c | 88 | ||||
| -rw-r--r-- | newlib/libm/common/math_config.h | 84 | ||||
| -rw-r--r-- | newlib/libm/common/sincosf.c | 104 | ||||
| -rw-r--r-- | newlib/libm/common/sincosf.h | 172 | ||||
| -rw-r--r-- | newlib/libm/common/sincosf_data.c | 87 | ||||
| -rw-r--r-- | newlib/libm/common/sinf.c | 92 | ||||
| -rw-r--r-- | newlib/libm/math/sf_cos.c | 2 | ||||
| -rw-r--r-- | newlib/libm/math/sf_sin.c | 2 | ||||
| -rw-r--r-- | newlib/libm/math/wf_sincos.c | 3 |
11 files changed, 667 insertions, 6 deletions
diff --git a/newlib/libm/common/Makefile.am b/newlib/libm/common/Makefile.am index 3e2620c7e..97b24315b 100644 --- a/newlib/libm/common/Makefile.am +++ b/newlib/libm/common/Makefile.am @@ -25,7 +25,7 @@ fsrc = sf_finite.c sf_copysign.c sf_modf.c sf_scalbn.c \ sf_scalbln.c sf_trunc.c \ sf_exp.c sf_exp2.c sf_exp2_data.c sf_log.c sf_log_data.c \ sf_log2.c sf_log2_data.c sf_pow_log2_data.c sf_pow.c \ - math_errf.c + sinf.c cosf.c sincosf.c sincosf_data.c math_errf.c lsrc = atanl.c cosl.c sinl.c tanl.c tanhl.c frexpl.c modfl.c ceill.c fabsl.c \ floorl.c log1pl.c expm1l.c acosl.c asinl.c atan2l.c coshl.c sinhl.c \ @@ -38,6 +38,7 @@ lsrc = atanl.c cosl.c sinl.c tanl.c tanhl.c frexpl.c modfl.c ceill.c fabsl.c \ sl_finite.c libcommon_la_LDFLAGS = -Xcompiler -nostdlib +lib_a_CFLAGS = -fbuiltin -fno-math-errno if USE_LIBTOOL noinst_LTLIBRARIES = libcommon.la @@ -52,7 +53,7 @@ lib_a_SOURCES = $(src) $(fsrc) if HAVE_LONG_DOUBLE lib_a_SOURCES += $(lsrc) endif # HAVE_LONG_DOUBLE -lib_a_CFLAGS = $(AM_CFLAGS) +lib_a_CFLAGS += $(AM_CFLAGS) noinst_DATA = endif # USE_LIBTOOL diff --git a/newlib/libm/common/Makefile.in b/newlib/libm/common/Makefile.in index 6a0ba73d2..c944ac790 100644 --- a/newlib/libm/common/Makefile.in +++ b/newlib/libm/common/Makefile.in @@ -55,6 +55,7 @@ build_triplet = @build@ host_triplet = @host@ @HAVE_LONG_DOUBLE_TRUE@@USE_LIBTOOL_TRUE@am__append_1 = $(lsrc) @HAVE_LONG_DOUBLE_TRUE@@USE_LIBTOOL_FALSE@am__append_2 = $(lsrc) +@USE_LIBTOOL_FALSE@am__append_3 = $(AM_CFLAGS) DIST_COMMON = $(srcdir)/../../Makefile.shared $(srcdir)/Makefile.in \ $(srcdir)/Makefile.am subdir = common @@ -114,6 +115,8 @@ am__objects_2 = lib_a-sf_finite.$(OBJEXT) lib_a-sf_copysign.$(OBJEXT) \ lib_a-sf_log.$(OBJEXT) lib_a-sf_log_data.$(OBJEXT) \ lib_a-sf_log2.$(OBJEXT) lib_a-sf_log2_data.$(OBJEXT) \ lib_a-sf_pow_log2_data.$(OBJEXT) lib_a-sf_pow.$(OBJEXT) \ + lib_a-sinf.$(OBJEXT) lib_a-cosf.$(OBJEXT) \ + lib_a-sincosf.$(OBJEXT) lib_a-sincosf_data.$(OBJEXT) \ lib_a-math_errf.$(OBJEXT) am__objects_3 = lib_a-atanl.$(OBJEXT) lib_a-cosl.$(OBJEXT) \ lib_a-sinl.$(OBJEXT) lib_a-tanl.$(OBJEXT) \ @@ -169,7 +172,8 @@ am__objects_6 = sf_finite.lo sf_copysign.lo sf_modf.lo sf_scalbn.lo \ sf_nearbyint.lo sf_remquo.lo sf_round.lo sf_scalbln.lo \ sf_trunc.lo sf_exp.lo sf_exp2.lo sf_exp2_data.lo sf_log.lo \ sf_log_data.lo sf_log2.lo sf_log2_data.lo sf_pow_log2_data.lo \ - sf_pow.lo math_errf.lo + sf_pow.lo sinf.lo cosf.lo sincosf.lo sincosf_data.lo \ + math_errf.lo am__objects_7 = atanl.lo cosl.lo sinl.lo tanl.lo tanhl.lo frexpl.lo \ modfl.lo ceill.lo fabsl.lo floorl.lo log1pl.lo expm1l.lo \ acosl.lo asinl.lo atan2l.lo coshl.lo sinhl.lo expl.lo \ @@ -361,7 +365,7 @@ fsrc = sf_finite.c sf_copysign.c sf_modf.c sf_scalbn.c \ sf_scalbln.c sf_trunc.c \ sf_exp.c sf_exp2.c sf_exp2_data.c sf_log.c sf_log_data.c \ sf_log2.c sf_log2_data.c sf_pow_log2_data.c sf_pow.c \ - math_errf.c + sinf.c cosf.c sincosf.c sincosf_data.c math_errf.c lsrc = atanl.c cosl.c sinl.c tanl.c tanhl.c frexpl.c modfl.c ceill.c fabsl.c \ floorl.c log1pl.c expm1l.c acosl.c asinl.c atan2l.c coshl.c sinhl.c \ @@ -374,6 +378,7 @@ lsrc = atanl.c cosl.c sinl.c tanl.c tanhl.c frexpl.c modfl.c ceill.c fabsl.c \ sl_finite.c libcommon_la_LDFLAGS = -Xcompiler -nostdlib +lib_a_CFLAGS = -fbuiltin -fno-math-errno $(am__append_3) @USE_LIBTOOL_TRUE@noinst_LTLIBRARIES = libcommon.la @USE_LIBTOOL_TRUE@libcommon_la_SOURCES = $(src) $(fsrc) \ @USE_LIBTOOL_TRUE@ $(am__append_1) @@ -381,7 +386,6 @@ libcommon_la_LDFLAGS = -Xcompiler -nostdlib @USE_LIBTOOL_TRUE@noinst_DATA = objectlist.awk.in @USE_LIBTOOL_FALSE@noinst_LIBRARIES = lib.a @USE_LIBTOOL_FALSE@lib_a_SOURCES = $(src) $(fsrc) $(am__append_2) -@USE_LIBTOOL_FALSE@lib_a_CFLAGS = $(AM_CFLAGS) # # documentation rules @@ -944,6 +948,30 @@ lib_a-sf_pow.o: sf_pow.c lib_a-sf_pow.obj: sf_pow.c $(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_pow.obj `if test -f 'sf_pow.c'; then $(CYGPATH_W) 'sf_pow.c'; else $(CYGPATH_W) '$(srcdir)/sf_pow.c'; fi` +lib_a-sinf.o: sinf.c + $(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sinf.o `test -f 'sinf.c' || echo '$(srcdir)/'`sinf.c + +lib_a-sinf.obj: sinf.c + $(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sinf.obj `if test -f 'sinf.c'; then $(CYGPATH_W) 'sinf.c'; else $(CYGPATH_W) '$(srcdir)/sinf.c'; fi` + +lib_a-cosf.o: cosf.c + $(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-cosf.o `test -f 'cosf.c' || echo '$(srcdir)/'`cosf.c + +lib_a-cosf.obj: cosf.c + $(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-cosf.obj `if test -f 'cosf.c'; then $(CYGPATH_W) 'cosf.c'; else $(CYGPATH_W) '$(srcdir)/cosf.c'; fi` + +lib_a-sincosf.o: sincosf.c + $(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sincosf.o `test -f 'sincosf.c' || echo '$(srcdir)/'`sincosf.c + +lib_a-sincosf.obj: sincosf.c + $(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sincosf.obj `if test -f 'sincosf.c'; then $(CYGPATH_W) 'sincosf.c'; else $(CYGPATH_W) '$(srcdir)/sincosf.c'; fi` + +lib_a-sincosf_data.o: sincosf_data.c + $(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sincosf_data.o `test -f 'sincosf_data.c' || echo '$(srcdir)/'`sincosf_data.c + +lib_a-sincosf_data.obj: sincosf_data.c + $(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sincosf_data.obj `if test -f 'sincosf_data.c'; then $(CYGPATH_W) 'sincosf_data.c'; else $(CYGPATH_W) '$(srcdir)/sincosf_data.c'; fi` + lib_a-math_errf.o: math_errf.c $(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-math_errf.o `test -f 'math_errf.c' || echo '$(srcdir)/'`math_errf.c diff --git a/newlib/libm/common/cosf.c b/newlib/libm/common/cosf.c new file mode 100644 index 000000000..aac0a9aee --- /dev/null +++ b/newlib/libm/common/cosf.c @@ -0,0 +1,88 @@ +/* Single-precision cos function. + Copyright (c) 2018 Arm Ltd. All rights reserved. + + Redistribution and use in source and binary forms, with or without + modification, are permitted provided that the following conditions + are met: + 1. Redistributions of source code must retain the above copyright + notice, this list of conditions and the following disclaimer. + 2. Redistributions in binary form must reproduce the above copyright + notice, this list of conditions and the following disclaimer in the + documentation and/or other materials provided with the distribution. + 3. The name of the company may not be used to endorse or promote + products derived from this software without specific prior written + permission. + + THIS SOFTWARE IS PROVIDED BY ARM LTD ``AS IS AND ANY EXPRESS OR IMPLIED + WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF + MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + IN NO EVENT SHALL ARM LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, + SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED + TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR + PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF + LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING + NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS + SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ + +#include "fdlibm.h" +#if !__OBSOLETE_MATH + +#include <stdint.h> +#include <math.h> +#include "math_config.h" +#include "sincosf.h" + +/* Fast cosf implementation. Worst-case ULP is 0.56072, maximum relative + error is 0.5303p-23. A single-step signed range reduction is used for + small values. Large inputs have their range reduced using fast integer + arithmetic. +*/ +float +cosf (float y) +{ + double x = y; + double s; + int n; + sincos_t *p = &sincosf_table[0]; + + if (abstop12 (y) < abstop12 (pio4)) + { + double x2 = x * x; + + if (unlikely (abstop12 (y) < abstop12 (0x1p-12f))) + return 1.0f; + + return sinf_poly (x, x2, p, 1); + } + else if (likely (abstop12 (y) < abstop12 (120.0f))) + { + x = reduce_fast (x, p, &n); + + /* Setup the signs for sin and cos. */ + s = p->sign[n & 3]; + + if (n & 2) + p = &sincosf_table[1]; + + return sinf_poly (x * s, x * x, p, n ^ 1); + } + else if (abstop12 (y) < abstop12 (INFINITY)) + { + uint32_t xi = asuint (y); + int sign = xi >> 31; + + x = reduce_large (xi, &n); + + /* Setup signs for sin and cos - include original sign. */ + s = p->sign[(n + sign) & 3]; + + if ((n + sign) & 2) + p = &sincosf_table[1]; + + return sinf_poly (x * s, x * x, p, n ^ 1); + } + else + return __math_invalidf (y); +} + +#endif diff --git a/newlib/libm/common/math_config.h b/newlib/libm/common/math_config.h index c5667844a..6d87376ab 100644 --- a/newlib/libm/common/math_config.h +++ b/newlib/libm/common/math_config.h @@ -1,5 +1,5 @@ /* Configuration for math routines. - Copyright (c) 2017 ARM Ltd. All rights reserved. + Copyright (c) 2017-2018 Arm Ltd. All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions @@ -43,6 +43,44 @@ # define WANT_ERRNO_UFLOW (WANT_ROUNDING && WANT_ERRNO) #endif +/* Compiler can inline round as a single instruction. */ +#ifndef HAVE_FAST_ROUND +# if __aarch64__ +# define HAVE_FAST_ROUND 1 +# else +# define HAVE_FAST_ROUND 0 +# endif +#endif + +/* Compiler can inline lround, but not (long)round(x). */ +#ifndef HAVE_FAST_LROUND +# if __aarch64__ && (100*__GNUC__ + __GNUC_MINOR__) >= 408 && __NO_MATH_ERRNO__ +# define HAVE_FAST_LROUND 1 +# else +# define HAVE_FAST_LROUND 0 +# endif +#endif + +#if HAVE_FAST_ROUND +# define TOINT_INTRINSICS 1 + +static inline double_t +roundtoint (double_t x) +{ + return round (x); +} + +static inline uint64_t +converttoint (double_t x) +{ +# if HAVE_FAST_LROUND + return lround (x); +# else + return (long) round (x); +# endif +} +#endif + #ifndef TOINT_INTRINSICS # define TOINT_INTRINSICS 0 #endif @@ -109,12 +147,56 @@ issignalingf_inline (float x) return 2 * (ix ^ 0x00400000) > 2u * 0x7fc00000; } +/* Force the evaluation of a floating-point expression for its side-effect. */ +#if __aarch64__ && __GNUC__ +static inline void +force_eval_float (float x) +{ + __asm__ __volatile__ ("" : "+w" (x)); +} +static inline void +force_eval_double (double x) +{ + __asm__ __volatile__ ("" : "+w" (x)); +} +#else +static inline void +force_eval_float (float x) +{ + volatile float y = x; +} +static inline void +force_eval_double (double x) +{ + volatile double y = x; +} +#endif + +/* Evaluate an expression as the specified type, normally a type + cast should be enough, but compilers implement non-standard + excess-precision handling, so when FLT_EVAL_METHOD != 0 then + these functions may need to be customized. */ +static inline float +eval_as_float (float x) +{ + return x; +} +static inline double +eval_as_double (double x) +{ + return x; +} + #ifdef __GNUC__ # define HIDDEN __attribute__ ((__visibility__ ("hidden"))) # define NOINLINE __attribute__ ((noinline)) +# define likely(x) __builtin_expect (!!(x), 1) +# define unlikely(x) __builtin_expect (x, 0) #else # define HIDDEN # define NOINLINE +# define likely(x) (x) +# define unlikely(x) (x) #endif HIDDEN float __math_oflowf (unsigned long); diff --git a/newlib/libm/common/sincosf.c b/newlib/libm/common/sincosf.c new file mode 100644 index 000000000..85f12642f --- /dev/null +++ b/newlib/libm/common/sincosf.c @@ -0,0 +1,104 @@ +/* Single-precision sincos function. + Copyright (c) 2018 Arm Ltd. All rights reserved. + + Redistribution and use in source and binary forms, with or without + modification, are permitted provided that the following conditions + are met: + 1. Redistributions of source code must retain the above copyright + notice, this list of conditions and the following disclaimer. + 2. Redistributions in binary form must reproduce the above copyright + notice, this list of conditions and the following disclaimer in the + documentation and/or other materials provided with the distribution. + 3. The name of the company may not be used to endorse or promote + products derived from this software without specific prior written + permission. + + THIS SOFTWARE IS PROVIDED BY ARM LTD ``AS IS AND ANY EXPRESS OR IMPLIED + WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF + MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + IN NO EVENT SHALL ARM LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, + SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED + TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR + PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF + LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING + NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS + SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ + +#include "fdlibm.h" +#if !__OBSOLETE_MATH + +#include <stdint.h> +#include <math.h> +#include "math_config.h" +#include "sincosf.h" + +/* Fast sincosf implementation. Worst-case ULP is 0.56072, maximum relative + error is 0.5303p-23. A single-step signed range reduction is used for + small values. Large inputs have their range reduced using fast integer + arithmetic. +*/ +void +sincosf (float y, float *sinp, float *cosp) +{ + double x = y; + double s; + int n; + sincos_t *p = &sincosf_table[0]; + + if (abstop12 (y) < abstop12 (pio4)) + { + double x2 = x * x; + + if (unlikely (abstop12 (y) < abstop12 (0x1p-12f))) + { + if (unlikely (abstop12 (y) < abstop12 (0x1p-126f))) + /* Force underflow for tiny y. */ + force_eval_float (x2); + *sinp = y; + *cosp = 1.0f; + return; + } + + sincosf_poly (x, x2, p, 0, sinp, cosp); + } + else if (abstop12 (y) < abstop12 (120.0f)) + { + x = reduce_fast (x, p, &n); + + /* Setup the signs for sin and cos. */ + s = p->sign[n & 3]; + + if (n & 2) + p = &sincosf_table[1]; + + sincosf_poly (x * s, x * x, p, n, sinp, cosp); + } + else if (likely (abstop12 (y) < abstop12 (INFINITY))) + { + uint32_t xi = asuint (y); + int sign = xi >> 31; + + x = reduce_large (xi, &n); + + /* Setup signs for sin and cos - include original sign. */ + s = p->sign[(n + sign) & 3]; + + if ((n + sign) & 2) + p = &sincosf_table[1]; + + sincosf_poly (x * s, x * x, p, n, sinp, cosp); + } + else + { + /* Return NaN if Inf or NaN for both sin and cos. */ + *sinp = *cosp = y - y; +#if WANT_ERRNO + /* Needed to set errno for +-Inf, the add is a hack to work + around a gcc register allocation issue: just passing y + affects code generation in the fast path. */ + __math_invalidf (y + y); +#endif + } +} + +#endif diff --git a/newlib/libm/common/sincosf.h b/newlib/libm/common/sincosf.h new file mode 100644 index 000000000..2f3b2f83b --- /dev/null +++ b/newlib/libm/common/sincosf.h @@ -0,0 +1,172 @@ +/* Header for single-precision sin/cos/sincos functions. + Copyright (c) 2018 Arm Ltd. All rights reserved. + + Redistribution and use in source and binary forms, with or without + modification, are permitted provided that the following conditions + are met: + 1. Redistributions of source code must retain the above copyright + notice, this list of conditions and the following disclaimer. + 2. Redistributions in binary form must reproduce the above copyright + notice, this list of conditions and the following disclaimer in the + documentation and/or other materials provided with the distribution. + 3. The name of the company may not be used to endorse or promote + products derived from this software without specific prior written + permission. + + THIS SOFTWARE IS PROVIDED BY ARM LTD ``AS IS AND ANY EXPRESS OR IMPLIED + WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF + MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + IN NO EVENT SHALL ARM LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, + SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED + TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR + PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF + LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING + NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS + SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ + +#include <stdint.h> +#include <math.h> +#include "math_config.h" + +/* PI * 2^-64. */ +static const double pi64 = 0x1.921FB54442D18p-62; +/* PI / 4. */ +static const double pio4 = 0x1.921FB54442D18p-1; + +typedef const struct +{ + double sign[4]; + double hpi_inv, hpi, c0, c1, c2, c3, c4, s1, s2, s3; +} sincos_t; + +extern sincos_t sincosf_table[2] HIDDEN; + +extern const uint32_t inv_pio4[] HIDDEN; + +/* abstop12 assumes floating point reinterpret is fast by default. + If floating point comparisons are faster, define PREFER_FLOAT_COMPARISON. */ +#if PREFER_FLOAT_COMPARISON +static inline float +abstop12 (float x) +{ + return fabsf (x); +} +#else +static inline uint32_t +abstop12 (float x) +{ + return (asuint (x) >> 20) & 0x7ff; +} +#endif + +/* Compute the sine and cosine of inputs X and X2 (X squared), using the + polynomial P and store the results in SINP and COSP. N is the quadrant, + if odd the cosine and sine polynomials are swapped. */ +static inline void +sincosf_poly (double x, double x2, sincos_t *p, int n, float *sinp, float *cosp) +{ + double x3, x4, x5, x6, s, c, c1, c2, s1; + + x4 = x2 * x2; + x3 = x2 * x; + c2 = p->c3 + x2 * p->c4; + s1 = p->s2 + x2 * p->s3; + + /* Swap sin/cos result based on quadrant. */ + float *tmp = (n & 1 ? cosp : sinp); + cosp = (n & 1 ? sinp : cosp); + sinp = tmp; + + c1 = p->c0 + x2 * p->c1; + x5 = x3 * x2; + x6 = x4 * x2; + + s = x + x3 * p->s1; + c = c1 + x4 * p->c2; + + *sinp = s + x5 * s1; + *cosp = c + x6 * c2; +} + +/* Return the sine of inputs X and X2 (X squared) using the polynomial P. + N is the quadrant, and if odd the cosine polynomial is used. */ +static inline float +sinf_poly (double x, double x2, sincos_t *p, int n) +{ + double x3, x4, x6, x7, s, c, c1, c2, s1; + + if ((n & 1) == 0) + { + x3 = x * x2; + s1 = p->s2 + x2 * p->s3; + + x7 = x3 * x2; + s = x + x3 * p->s1; + + return s + x7 * s1; + } + else + { + x4 = x2 * x2; + c2 = p->c3 + x2 * p->c4; + c1 = p->c0 + x2 * p->c1; + + x6 = x4 * x2; + c = c1 + x4 * p->c2; + + return c + x6 * c2; + } +} + +/* Fast range reduction using single multiply-subtract. Return the modulo of + X as a value between -PI/4 and PI/4 and store the quadrant in NP. + The values for PI/2 and 2/PI are accessed via P. Since PI/2 as a double + is accurate to 55 bits and the worst-case cancellation happens at 6 * PI/4, + only 2 multiplies are required and the result is accurate for |X| <= 120.0. + Use round/lround if inlined, otherwise convert to int. To avoid inaccuracies + introduced by truncating negative values, compute the quadrant * 2^24. */ +static inline double +reduce_fast (double x, sincos_t *p, int *np) +{ + double r; +#if TOINT_INTRINSICS + r = x * p->hpi_inv; + *np = converttoint (r); + return x - roundtoint (r) * p->hpi; +#else + r = x * p->hpi_inv; + int n = ((int)r + 0x800000) >> 24; + *np = n; + return x - n * p->hpi; +#endif +} + +/* Reduce the range of XI to a multiple of PI/4 using fast integer arithmetic. + XI is a reinterpreted float and must be >= 2.0f (the sign bit is ignored). + Return the modulo between -PI/4 and PI/4 and store the quadrant in NP. + Reduction uses a table of 4/PI with 192 bits of precision. A 32x96->128 bit + multiply computes the exact 2.62-bit fixed-point modulo. Since the result + can have at most 29 leading zeros after the binary point, the double + precision result is accurate to 33 bits. */ +static inline double +reduce_large (uint32_t xi, int *np) +{ + const uint32_t *arr = &inv_pio4[(xi >> 26) & 15]; + int shift = (xi >> 23) & 7; + uint64_t n, res0, res1, res2; + + xi = (xi & 0xffffff) | 0x800000; + xi <<= shift; + + res0 = xi * arr[0]; + res1 = (uint64_t)xi * arr[4]; + res2 = (uint64_t)xi * arr[8]; + res0 = (res2 >> 32) | (res0 << 32); + res0 += res1; + + n = (res0 + (1ULL << 61)) >> 62; + res0 -= n << 62; + double x = (int64_t)res0; + *np = n; + return x * pi64; +} diff --git a/newlib/libm/common/sincosf_data.c b/newlib/libm/common/sincosf_data.c new file mode 100644 index 000000000..069ee7bf6 --- /dev/null +++ b/newlib/libm/common/sincosf_data.c @@ -0,0 +1,87 @@ +/* Data definitions for sinf, cosf and sincosf. + Copyright (c) 2018 Arm Ltd. All rights reserved. + + Redistribution and use in source and binary forms, with or without + modification, are permitted provided that the following conditions + are met: + 1. Redistributions of source code must retain the above copyright + notice, this list of conditions and the following disclaimer. + 2. Redistributions in binary form must reproduce the above copyright + notice, this list of conditions and the following disclaimer in the + documentation and/or other materials provided with the distribution. + 3. The name of the company may not be used to endorse or promote + products derived from this software without specific prior written + permission. + + THIS SOFTWARE IS PROVIDED BY ARM LTD ``AS IS AND ANY EXPRESS OR IMPLIED + WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF + MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + IN NO EVENT SHALL ARM LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, + SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED + TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR + PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF + LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING + NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS + SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ + +#include "fdlibm.h" +#if !__OBSOLETE_MATH + +#include <stdint.h> +#include <math.h> +#include "math_config.h" +#include "sincosf.h" + +/* The constants and polynomials for sine and cosine. The 2nd entry + computes -cos (x) rather than cos (x) to get negation for free. */ +sincos_t sincosf_table[2] = +{ + { + { 1.0, -1.0, -1.0, 1.0 }, +#if TOINT_INTRINSICS + 0x1.45F306DC9C883p-1, +#else + 0x1.45F306DC9C883p+23, +#endif + 0x1.921FB54442D18p0, + 0x1p0, + -0x1.ffffffd0c621cp-2, + 0x1.55553e1068f19p-5, + -0x1.6c087e89a359dp-10, + 0x1.99343027bf8c3p-16, + -0x1.555545995a603p-3, + 0x1.1107605230bc4p-7, + -0x1.994eb3774cf24p-13 + }, + { + { 1.0, -1.0, -1.0, 1.0 }, +#if TOINT_INTRINSICS + 0x1.45F306DC9C883p-1, +#else + 0x1.45F306DC9C883p+23, +#endif + 0x1.921FB54442D18p0, + -0x1p0, + 0x1.ffffffd0c621cp-2, + -0x1.55553e1068f19p-5, + 0x1.6c087e89a359dp-10, + -0x1.99343027bf8c3p-16, + -0x1.555545995a603p-3, + 0x1.1107605230bc4p-7, + -0x1.994eb3774cf24p-13 + } +}; + +/* Table with 4/PI to 192 bit precision. To avoid unaligned accesses + only 8 new bits are added per entry, making the table 4 times larger. */ +const uint32_t inv_pio4[24] = +{ + 0xa2, 0xa2f9, 0xa2f983, 0xa2f9836e, + 0xf9836e4e, 0x836e4e44, 0x6e4e4415, 0x4e441529, + 0x441529fc, 0x1529fc27, 0x29fc2757, 0xfc2757d1, + 0x2757d1f5, 0x57d1f534, 0xd1f534dd, 0xf534ddc0, + 0x34ddc0db, 0xddc0db62, 0xc0db6295, 0xdb629599, + 0x6295993c, 0x95993c43, 0x993c4390, 0x3c439041 +}; + +#endif diff --git a/newlib/libm/common/sinf.c b/newlib/libm/common/sinf.c new file mode 100644 index 000000000..c1baf4237 --- /dev/null +++ b/newlib/libm/common/sinf.c @@ -0,0 +1,92 @@ +/* Single-precision sin function. + Copyright (c) 2018 Arm Ltd. All rights reserved. + + Redistribution and use in source and binary forms, with or without + modification, are permitted provided that the following conditions + are met: + 1. Redistributions of source code must retain the above copyright + notice, this list of conditions and the following disclaimer. + 2. Redistributions in binary form must reproduce the above copyright + notice, this list of conditions and the following disclaimer in the + documentation and/or other materials provided with the distribution. + 3. The name of the company may not be used to endorse or promote + products derived from this software without specific prior written + permission. + + THIS SOFTWARE IS PROVIDED BY ARM LTD ``AS IS AND ANY EXPRESS OR IMPLIED + WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF + MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + IN NO EVENT SHALL ARM LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, + SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED + TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR + PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF + LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING + NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS + SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ + +#include "fdlibm.h" +#if !__OBSOLETE_MATH + +#include <math.h> +#include "math_config.h" +#include "sincosf.h" + +/* Fast sinf implementation. Worst-case ULP is 0.56072, maximum relative + error is 0.5303p-23. A single-step signed range reduction is used for + small values. Large inputs have their range reduced using fast integer + arithmetic. +*/ +float +sinf (float y) +{ + double x = y; + double s; + int n; + sincos_t *p = &sincosf_table[0]; + + if (abstop12 (y) < abstop12 (pio4)) + { + s = x * x; + + if (unlikely (abstop12 (y) < abstop12 (0x1p-12f))) + { + if (unlikely (abstop12 (y) < abstop12 (0x1p-126f))) + /* Force underflow for tiny y. */ + force_eval_float (s); + return y; + } + + return sinf_poly (x, s, p, 0); + } + else if (likely (abstop12 (y) < abstop12 (120.0f))) + { + x = reduce_fast (x, p, &n); + + /* Setup the signs for sin and cos. */ + s = p->sign[n & 3]; + + if (n & 2) + p = &sincosf_table[1]; + + return sinf_poly (x * s, x * x, p, n); + } + else if (abstop12 (y) < abstop12 (INFINITY)) + { + uint32_t xi = asuint (y); + int sign = xi >> 31; + + x = reduce_large (xi, &n); + + /* Setup signs for sin and cos - include original sign. */ + s = p->sign[(n + sign) & 3]; + + if ((n + sign) & 2) + p = &sincosf_table[1]; + + return sinf_poly (x * s, x * x, p, n); + } + else + return __math_invalidf (y); +} + +#endif diff --git a/newlib/libm/math/sf_cos.c b/newlib/libm/math/sf_cos.c index 4c0a9a535..8cb0eb008 100644 --- a/newlib/libm/math/sf_cos.c +++ b/newlib/libm/math/sf_cos.c @@ -14,6 +14,7 @@ */ #include "fdlibm.h" +#if __OBSOLETE_MATH #ifdef __STDC__ static const float one=1.0; @@ -66,3 +67,4 @@ static float one=1.0; } #endif /* defined(_DOUBLE_IS_32BITS) */ +#endif /* __OBSOLETE_MATH */ diff --git a/newlib/libm/math/sf_sin.c b/newlib/libm/math/sf_sin.c index da81845d9..c3ec6e2e4 100644 --- a/newlib/libm/math/sf_sin.c +++ b/newlib/libm/math/sf_sin.c @@ -14,6 +14,7 @@ */ #include "fdlibm.h" +#if __OBSOLETE_MATH #ifdef __STDC__ float sinf(float x) @@ -60,3 +61,4 @@ } #endif /* defined(_DOUBLE_IS_32BITS) */ +#endif /* __OBSOLETE_MATH */ diff --git a/newlib/libm/math/wf_sincos.c b/newlib/libm/math/wf_sincos.c index 477c60401..69eb922c9 100644 --- a/newlib/libm/math/wf_sincos.c +++ b/newlib/libm/math/wf_sincos.c @@ -1,6 +1,8 @@ /* sincos -- currently no more efficient than two separate calls to sin and cos. */ #include "fdlibm.h" +#if __OBSOLETE_MATH + #include <errno.h> #ifdef __STDC__ @@ -31,3 +33,4 @@ *cosx = cosf((float) x); } #endif /* defined(_DOUBLE_IS_32BITS) */ +#endif /* __OBSOLETE_MATH */ |