2c76a4cb41
GitOrigin-RevId: c757e9bd77b16ca2e03c89bf8bc9ecb28e0c06ad
292 lines
13 KiB
Diff
292 lines
13 KiB
Diff
--- a/Source/Intel/math.h 2023-10-20 09:43:42.640416006 -0400
|
|
+++ b/Source/Intel/math.h 2023-10-20 09:47:59.743127003 -0400
|
|
@@ -1,5 +1,5 @@
|
|
/*
|
|
- * Copyright (c) 2002 Apple Computer, Inc. All rights reserved.
|
|
+ * Copyright (c) 2002-2015 Apple Inc. All rights reserved.
|
|
*
|
|
* @APPLE_LICENSE_HEADER_START@
|
|
*
|
|
@@ -27,14 +27,17 @@
|
|
* Contains: typedefs, prototypes, and macros germane to C99 floating point.*
|
|
* *
|
|
*******************************************************************************/
|
|
+#ifndef __MATH_H__
|
|
+#define __MATH_H__
|
|
+
|
|
#ifndef __MATH__
|
|
#define __MATH__
|
|
+#endif
|
|
|
|
-#include <sys/cdefs.h> /* For definition of __DARWIN_UNIX03 et al */
|
|
+#include <sys/cdefs.h>
|
|
+#include <Availability.h>
|
|
|
|
-#ifdef __cplusplus
|
|
-extern "C" {
|
|
-#endif
|
|
+__BEGIN_DECLS
|
|
|
|
/******************************************************************************
|
|
* Floating point data types *
|
|
@@ -87,14 +90,26 @@
|
|
#define FP_SUBNORMAL 5
|
|
#define FP_SUPERNORMAL 6 /* meaningful only on PowerPC */
|
|
|
|
-/* fma() *function call* is more costly than equivalent (in-line) multiply and add operations */
|
|
-/* For single and double precision, the cost isn't too bad, because we can fall back on higher */
|
|
-/* precision hardware, with the necessary range to handle infinite precision products. However, */
|
|
-/* expect the long double fma to be at least an order of magnitude slower than a simple multiply */
|
|
-/* and an add. */
|
|
-#undef FP_FAST_FMA
|
|
-#undef FP_FAST_FMAF
|
|
-#undef FP_FAST_FMAL
|
|
+#if defined __arm64__ || defined __ARM_VFPV4__
|
|
+/* On these architectures, fma(), fmaf( ), and fmal( ) are generally about as
|
|
+ fast as (or faster than) separate multiply and add of the same operands. */
|
|
+# define FP_FAST_FMA 1
|
|
+# define FP_FAST_FMAF 1
|
|
+# define FP_FAST_FMAL 1
|
|
+#elif (defined __i386__ || defined __x86_64__) && (defined __FMA__)
|
|
+/* When targeting the FMA ISA extension, fma() and fmaf( ) are generally
|
|
+ about as fast as (or faster than) separate multiply and add of the same
|
|
+ operands, but fmal( ) may be more costly. */
|
|
+# define FP_FAST_FMA 1
|
|
+# define FP_FAST_FMAF 1
|
|
+# undef FP_FAST_FMAL
|
|
+#else
|
|
+/* On these architectures, fma( ), fmaf( ), and fmal( ) function calls are
|
|
+ significantly more costly than separate multiply and add operations. */
|
|
+# undef FP_FAST_FMA
|
|
+# undef FP_FAST_FMAF
|
|
+# undef FP_FAST_FMAL
|
|
+#endif
|
|
|
|
/* The values returned by `ilogb' for 0 and NaN respectively. */
|
|
#define FP_ILOGB0 (-2147483647 - 1)
|
|
@@ -191,6 +206,23 @@
|
|
static __inline__ int __inline_isnormalf( float __x ) { float fabsf = __builtin_fabsf(__x); if( __x != __x ) return 0; return fabsf < __builtin_inff() && fabsf >= __FLT_MIN__; }
|
|
static __inline__ int __inline_isnormald( double __x ) { double fabsf = __builtin_fabs(__x); if( __x != __x ) return 0; return fabsf < __builtin_inf() && fabsf >= __DBL_MIN__; }
|
|
static __inline__ int __inline_isnormal( long double __x ) { long double fabsf = __builtin_fabsl(__x); if( __x != __x ) return 0; return fabsf < __builtin_infl() && fabsf >= __LDBL_MIN__; }
|
|
+
|
|
+#if defined __i386__ || defined __x86_64__
|
|
+__header_always_inline int __inline_signbitl(long double __x) {
|
|
+ union {
|
|
+ long double __ld;
|
|
+ struct{ unsigned long long __m; unsigned short __sexp; } __p;
|
|
+ } __u;
|
|
+ __u.__ld = __x;
|
|
+ return (int)(__u.__p.__sexp >> 15);
|
|
+}
|
|
+#else
|
|
+__header_always_inline int __inline_signbitl(long double __x) {
|
|
+ union { long double __f; unsigned long long __u;} __u;
|
|
+ __u.__f = __x;
|
|
+ return (int)(__u.__u >> 63);
|
|
+}
|
|
+#endif
|
|
|
|
#else
|
|
|
|
@@ -509,7 +541,112 @@
|
|
extern long double __infl( void );
|
|
extern float __nan( void ); /* 10.3 (and later) must retain in ABI for backward compatability */
|
|
|
|
-#if !defined(_ANSI_SOURCE)
|
|
+
|
|
+/******************************************************************************
|
|
+ * Apple extensions to the C standard *
|
|
+ ******************************************************************************/
|
|
+
|
|
+/* Because these functions are not specified by any relevant standard, they
|
|
+ are prefixed with __, which places them in the implementor's namespace, so
|
|
+ they should not conflict with any developer or third-party code. If they
|
|
+ are added to a relevant standard in the future, un-prefixed names may be
|
|
+ added to the library and they may be moved out of this section of the
|
|
+ header.
|
|
+
|
|
+ Because these functions are non-standard, they may not be available on non-
|
|
+ Apple platforms. */
|
|
+
|
|
+/* __exp10(x) returns 10**x. Edge cases match those of exp( ) and exp2( ). */
|
|
+extern float __exp10f(float) __OSX_AVAILABLE_STARTING(__MAC_10_9, __IPHONE_7_0);
|
|
+extern double __exp10(double) __OSX_AVAILABLE_STARTING(__MAC_10_9, __IPHONE_7_0);
|
|
+
|
|
+/* __sincos(x,sinp,cosp) computes the sine and cosine of x with a single
|
|
+ function call, storing the sine in the memory pointed to by sinp, and
|
|
+ the cosine in the memory pointed to by cosp. Edge cases match those of
|
|
+ separate calls to sin( ) and cos( ). */
|
|
+__header_always_inline void __sincosf(float __x, float *__sinp, float *__cosp);
|
|
+__header_always_inline void __sincos(double __x, double *__sinp, double *__cosp);
|
|
+
|
|
+/* __sinpi(x) returns the sine of pi times x; __cospi(x) and __tanpi(x) return
|
|
+ the cosine and tangent, respectively. These functions can produce a more
|
|
+ accurate answer than expressions of the form sin(M_PI * x) because they
|
|
+ avoid any loss of precision that results from rounding the result of the
|
|
+ multiplication M_PI * x. They may also be significantly more efficient in
|
|
+ some cases because the argument reduction for these functions is easier
|
|
+ to compute. Consult the man pages for edge case details. */
|
|
+extern float __cospif(float) __OSX_AVAILABLE_STARTING(__MAC_10_9, __IPHONE_7_0);
|
|
+extern double __cospi(double) __OSX_AVAILABLE_STARTING(__MAC_10_9, __IPHONE_7_0);
|
|
+extern float __sinpif(float) __OSX_AVAILABLE_STARTING(__MAC_10_9, __IPHONE_7_0);
|
|
+extern double __sinpi(double) __OSX_AVAILABLE_STARTING(__MAC_10_9, __IPHONE_7_0);
|
|
+extern float __tanpif(float) __OSX_AVAILABLE_STARTING(__MAC_10_9, __IPHONE_7_0);
|
|
+extern double __tanpi(double) __OSX_AVAILABLE_STARTING(__MAC_10_9, __IPHONE_7_0);
|
|
+
|
|
+#if (defined __MAC_OS_X_VERSION_MIN_REQUIRED && __MAC_OS_X_VERSION_MIN_REQUIRED < 1090) || \
|
|
+ (defined __IPHONE_OS_VERSION_MIN_REQUIRED && __IPHONE_OS_VERSION_MIN_REQUIRED < 70000)
|
|
+/* __sincos and __sincosf were introduced in OSX 10.9 and iOS 7.0. When
|
|
+ targeting an older system, we simply split them up into discrete calls
|
|
+ to sin( ) and cos( ). */
|
|
+__header_always_inline void __sincosf(float __x, float *__sinp, float *__cosp) {
|
|
+ *__sinp = sinf(__x);
|
|
+ *__cosp = cosf(__x);
|
|
+}
|
|
+
|
|
+__header_always_inline void __sincos(double __x, double *__sinp, double *__cosp) {
|
|
+ *__sinp = sin(__x);
|
|
+ *__cosp = cos(__x);
|
|
+}
|
|
+#else
|
|
+/* __sincospi(x,sinp,cosp) computes the sine and cosine of pi times x with a
|
|
+ single function call, storing the sine in the memory pointed to by sinp,
|
|
+ and the cosine in the memory pointed to by cosp. Edge cases match those
|
|
+ of separate calls to __sinpi( ) and __cospi( ), and are documented in the
|
|
+ man pages.
|
|
+
|
|
+ These functions were introduced in OSX 10.9 and iOS 7.0. Because they are
|
|
+ implemented as header inlines, weak-linking does not function as normal,
|
|
+ and they are simply hidden when targeting earlier OS versions. */
|
|
+__header_always_inline void __sincospif(float __x, float *__sinp, float *__cosp);
|
|
+__header_always_inline void __sincospi(double __x, double *__sinp, double *__cosp);
|
|
+
|
|
+/* Implementation details of __sincos and __sincospi allowing them to return
|
|
+ two results while allowing the compiler to optimize away unnecessary load-
|
|
+ store traffic. Although these interfaces are exposed in the math.h header
|
|
+ to allow compilers to generate better code, users should call __sincos[f]
|
|
+ and __sincospi[f] instead and allow the compiler to emit these calls. */
|
|
+struct __float2 { float __sinval; float __cosval; };
|
|
+struct __double2 { double __sinval; double __cosval; };
|
|
+
|
|
+extern struct __float2 __sincosf_stret(float);
|
|
+extern struct __double2 __sincos_stret(double);
|
|
+extern struct __float2 __sincospif_stret(float);
|
|
+extern struct __double2 __sincospi_stret(double);
|
|
+
|
|
+__header_always_inline void __sincosf(float __x, float *__sinp, float *__cosp) {
|
|
+ const struct __float2 __stret = __sincosf_stret(__x);
|
|
+ *__sinp = __stret.__sinval; *__cosp = __stret.__cosval;
|
|
+}
|
|
+
|
|
+__header_always_inline void __sincos(double __x, double *__sinp, double *__cosp) {
|
|
+ const struct __double2 __stret = __sincos_stret(__x);
|
|
+ *__sinp = __stret.__sinval; *__cosp = __stret.__cosval;
|
|
+}
|
|
+
|
|
+__header_always_inline void __sincospif(float __x, float *__sinp, float *__cosp) {
|
|
+ const struct __float2 __stret = __sincospif_stret(__x);
|
|
+ *__sinp = __stret.__sinval; *__cosp = __stret.__cosval;
|
|
+}
|
|
+
|
|
+__header_always_inline void __sincospi(double __x, double *__sinp, double *__cosp) {
|
|
+ const struct __double2 __stret = __sincospi_stret(__x);
|
|
+ *__sinp = __stret.__sinval; *__cosp = __stret.__cosval;
|
|
+}
|
|
+#endif
|
|
+
|
|
+/******************************************************************************
|
|
+ * POSIX/UNIX extensions to the C standard *
|
|
+ ******************************************************************************/
|
|
+
|
|
+#if __DARWIN_C_LEVEL >= 199506L
|
|
extern double j0 ( double );
|
|
|
|
extern double j1 ( double );
|
|
@@ -543,14 +680,32 @@
|
|
extern int signgam; /* required for unix 2003 */
|
|
|
|
|
|
-#endif /* !defined(_ANSI_SOURCE) */
|
|
+#endif /* __DARWIN_C_LEVEL >= 199506L */
|
|
|
|
-#if !defined(__NOEXTENSIONS__) && (!defined(_POSIX_C_SOURCE) || defined(_DARWIN_C_SOURCE))
|
|
-#define __WANT_EXTENSIONS__
|
|
-#endif
|
|
+/* Long-double versions of M_E, etc for convenience on Intel where long-
|
|
+ double is not the same as double. Define __MATH_LONG_DOUBLE_CONSTANTS
|
|
+ to make these constants available. */
|
|
+#if defined __MATH_LONG_DOUBLE_CONSTANTS
|
|
+#define M_El 0xa.df85458a2bb4a9bp-2L
|
|
+#define M_LOG2El 0xb.8aa3b295c17f0bcp-3L
|
|
+#define M_LOG10El 0xd.e5bd8a937287195p-5L
|
|
+#define M_LN2l 0xb.17217f7d1cf79acp-4L
|
|
+#define M_LN10l 0x9.35d8dddaaa8ac17p-2L
|
|
+#define M_PIl 0xc.90fdaa22168c235p-2L
|
|
+#define M_PI_2l 0xc.90fdaa22168c235p-3L
|
|
+#define M_PI_4l 0xc.90fdaa22168c235p-4L
|
|
+#define M_1_PIl 0xa.2f9836e4e44152ap-5L
|
|
+#define M_2_PIl 0xa.2f9836e4e44152ap-4L
|
|
+#define M_2_SQRTPIl 0x9.06eba8214db688dp-3L
|
|
+#define M_SQRT2l 0xb.504f333f9de6484p-3L
|
|
+#define M_SQRT1_2l 0xb.504f333f9de6484p-4L
|
|
+#endif /* defined __MATH_LONG_DOUBLE_CONSTANTS */
|
|
|
|
-#ifdef __WANT_EXTENSIONS__
|
|
+/******************************************************************************
|
|
+ * Legacy BSD extensions to the C standard *
|
|
+ ******************************************************************************/
|
|
|
|
+#if __DARWIN_C_LEVEL >= __DARWIN_C_FULL
|
|
#define FP_SNAN FP_NAN
|
|
#define FP_QNAN FP_NAN
|
|
|
|
@@ -560,11 +715,6 @@
|
|
/* Legacy API: please use C99 lround() instead. */
|
|
extern long int roundtol ( double );
|
|
|
|
-/*
|
|
- * XOPEN/SVID
|
|
- */
|
|
-#if !defined(_ANSI_SOURCE) && (!defined(_POSIX_C_SOURCE) || defined(_DARWIN_C_SOURCE))
|
|
-#if (!defined(_XOPEN_SOURCE) || defined(_DARWIN_C_SOURCE))
|
|
#if !defined(__cplusplus)
|
|
/* used by matherr below */
|
|
struct exception {
|
|
@@ -592,19 +742,12 @@
|
|
#define TLOSS 5
|
|
#define PLOSS 6
|
|
|
|
-#endif /* (!_XOPEN_SOURCE || _DARWIN_C_SOURCE) */
|
|
-#endif /* !_ANSI_SOURCE && (!_POSIX_C_SOURCE || _DARWIN_C_SOURCE) */
|
|
-
|
|
-#if !defined( __STRICT_ANSI__) && !defined(_ANSI_SOURCE) && (!defined(_POSIX_C_SOURCE) || defined(_DARWIN_C_SOURCE))
|
|
-
|
|
/* Legacy API: please use C99 isfinite() instead. */
|
|
extern int finite ( double );
|
|
|
|
/* Legacy API: please use C99 tgamma() instead. */
|
|
extern double gamma ( double );
|
|
|
|
-#if (!defined(_XOPEN_SOURCE) || defined(_DARWIN_C_SOURCE))
|
|
-
|
|
#if !defined(__cplusplus)
|
|
extern int matherr ( struct exception * );
|
|
#endif
|
|
@@ -633,14 +776,8 @@
|
|
extern double lgamma_r ( double, int * ) AVAILABLE_MAC_OS_X_VERSION_10_6_AND_LATER;
|
|
extern long double lgammal_r ( long double, int * ) AVAILABLE_MAC_OS_X_VERSION_10_6_AND_LATER;
|
|
#endif /* _REENTRANT */
|
|
-
|
|
-#endif /* (!_XOPEN_SOURCE || _DARWIN_C_SOURCE) */
|
|
-#endif /* !_ANSI_SOURCE && (!_POSIX_C_SOURCE || _DARWIN_C_SOURCE) */
|
|
-
|
|
-#endif /* __WANT_EXTENSIONS__ */
|
|
|
|
-#ifdef __cplusplus
|
|
-}
|
|
-#endif
|
|
+#endif /* __DARWIN_C_LEVEL >= __DARWIN_C_FULL */
|
|
|
|
-#endif /* __MATH__ */
|
|
+__END_DECLS
|
|
+#endif /* __MATH_H__ */
|