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https://github.com/pocketpy/pocketpy
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fix linux_aarch64 stdint redefine
This commit is contained in:
parent
7da0afb59f
commit
945f614b98
@ -5,8 +5,6 @@
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extern "C" {
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extern "C" {
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#endif
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#endif
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#define __NEED_float_t
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#define __NEED_double_t
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#ifndef _HUGE_ENUF
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#ifndef _HUGE_ENUF
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#define _HUGE_ENUF 1e+300 // _HUGE_ENUF*_HUGE_ENUF must overflow
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#define _HUGE_ENUF 1e+300 // _HUGE_ENUF*_HUGE_ENUF must overflow
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@ -62,17 +60,6 @@ extern "C" {
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#define predict_true(x) (x)
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#define predict_true(x) (x)
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#define predict_false(x) (x)
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#define predict_false(x) (x)
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typedef signed char int8_t;
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typedef short int16_t;
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typedef int int32_t;
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typedef long long int64_t;
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typedef unsigned char uint8_t;
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typedef unsigned short uint16_t;
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typedef unsigned int uint32_t;
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typedef unsigned long long uint64_t;
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typedef float float_t;
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typedef double double_t;
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int __fpclassify(double);
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int __fpclassify(double);
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int __fpclassifyf(float);
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int __fpclassifyf(float);
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int __fpclassifyl(long double);
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int __fpclassifyl(long double);
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@ -107,7 +94,7 @@ static __inline unsigned long long __DOUBLE_BITS(double __f)
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#define isnormal(x) ( \
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#define isnormal(x) ( \
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sizeof(x) == sizeof(float) ? ((__FLOAT_BITS(x)+0x00800000) & 0x7fffffff) >= 0x01000000 : \
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sizeof(x) == sizeof(float) ? ((__FLOAT_BITS(x)+0x00800000) & 0x7fffffff) >= 0x01000000 : \
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sizeof(x) == sizeof(double) ? ((__DOUBLE_BITS(x)+(1ULL<<52)) & -1ULL>>1) >= 1ULL<<53 : \
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sizeof(x) == sizeof(double) ? ((__DOUBLE_BITS(x)+(1ULL<<52)) & ULLONG_SHIFT1) >= 1ULL<<53 : \
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__fpclassifyl(x) == FP_NORMAL)
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__fpclassifyl(x) == FP_NORMAL)
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#define isfinite(x) ( \
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#define isfinite(x) ( \
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@ -130,20 +117,20 @@ int __signbitl(long double);
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static __inline int __is##rel(type __x, type __y) \
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static __inline int __is##rel(type __x, type __y) \
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{ return !isunordered(__x,__y) && __x op __y; }
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{ return !isunordered(__x,__y) && __x op __y; }
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__ISREL_DEF(lessf, <, float_t)
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__ISREL_DEF(lessf, <, float)
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__ISREL_DEF(less, <, double_t)
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__ISREL_DEF(less, <, double)
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__ISREL_DEF(lessl, <, long double)
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__ISREL_DEF(lessl, <, long double)
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__ISREL_DEF(lessequalf, <=, float_t)
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__ISREL_DEF(lessequalf, <=, float)
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__ISREL_DEF(lessequal, <=, double_t)
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__ISREL_DEF(lessequal, <=, double)
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__ISREL_DEF(lessequall, <=, long double)
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__ISREL_DEF(lessequall, <=, long double)
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__ISREL_DEF(lessgreaterf, !=, float_t)
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__ISREL_DEF(lessgreaterf, !=, float)
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__ISREL_DEF(lessgreater, !=, double_t)
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__ISREL_DEF(lessgreater, !=, double)
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__ISREL_DEF(lessgreaterl, !=, long double)
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__ISREL_DEF(lessgreaterl, !=, long double)
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__ISREL_DEF(greaterf, >, float_t)
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__ISREL_DEF(greaterf, >, float)
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__ISREL_DEF(greater, >, double_t)
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__ISREL_DEF(greater, >, double)
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__ISREL_DEF(greaterl, >, long double)
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__ISREL_DEF(greaterl, >, long double)
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__ISREL_DEF(greaterequalf, >=, float_t)
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__ISREL_DEF(greaterequalf, >=, float)
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__ISREL_DEF(greaterequal, >=, double_t)
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__ISREL_DEF(greaterequal, >=, double)
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__ISREL_DEF(greaterequall, >=, long double)
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__ISREL_DEF(greaterequall, >=, long double)
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#define __tg_pred_2(x, y, p) ( \
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#define __tg_pred_2(x, y, p) ( \
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@ -248,10 +235,10 @@ static inline void fp_force_evall(long double x)
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} \
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} \
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} while(0)
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} while(0)
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typedef union {float _f; uint32_t _i;}asuint_union;
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typedef union {float _f; unsigned int _i;}asuint_union;
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typedef union {uint32_t _i; float _f;}asfloat_union;
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typedef union {unsigned int _i; float _f;}asfloat_union;
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typedef union {double _f; uint64_t _i;}asuint64_union;
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typedef union {double _f; unsigned long long _i;}asuint64_union;
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typedef union {uint64_t _i; double _f;}asdouble_union;
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typedef union {unsigned long long _i; double _f;}asdouble_union;
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#define asuint(f) ((asuint_union){f})._i
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#define asuint(f) ((asuint_union){f})._i
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#define asfloat(i) ((asfloat_union){i})._f
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#define asfloat(i) ((asfloat_union){i})._f
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#define asuint64(f) ((asuint64_union){f})._i
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#define asuint64(f) ((asuint64_union){f})._i
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@ -259,9 +246,9 @@ typedef union {uint64_t _i; double _f;}asdouble_union;
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#define EXTRACT_WORDS(hi,lo,d) \
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#define EXTRACT_WORDS(hi,lo,d) \
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do { \
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do { \
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uint64_t __u = asuint64(d); \
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unsigned long long __u = asuint64(d); \
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(hi) = __u >> 32; \
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(hi) = __u >> 32; \
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(lo) = (uint32_t)__u; \
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(lo) = (unsigned int)__u; \
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} while (0)
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} while (0)
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#define GET_HIGH_WORD(hi,d) \
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#define GET_HIGH_WORD(hi,d) \
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@ -271,16 +258,16 @@ do { \
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#define GET_LOW_WORD(lo,d) \
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#define GET_LOW_WORD(lo,d) \
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do { \
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do { \
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(lo) = (uint32_t)asuint64(d); \
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(lo) = (unsigned int)asuint64(d); \
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} while (0)
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} while (0)
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#define INSERT_WORDS(d,hi,lo) \
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#define INSERT_WORDS(d,hi,lo) \
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do { \
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do { \
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(d) = asdouble(((uint64_t)(hi)<<32) | (uint32_t)(lo)); \
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(d) = asdouble(((unsigned long long)(hi)<<32) | (unsigned int)(lo)); \
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} while (0)
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} while (0)
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#define SET_HIGH_WORD(d,hi) \
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#define SET_HIGH_WORD(d,hi) \
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INSERT_WORDS(d, hi, (uint32_t)asuint64(d))
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INSERT_WORDS(d, hi, (unsigned int)asuint64(d))
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#define SET_LOW_WORD(d,lo) \
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#define SET_LOW_WORD(d,lo) \
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INSERT_WORDS(d, asuint64(d)>>32, lo)
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INSERT_WORDS(d, asuint64(d)>>32, lo)
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@ -302,15 +289,15 @@ double __cos(double, double);
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double __tan(double, double, int);
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double __tan(double, double, int);
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/* error handling functions */
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/* error handling functions */
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float __math_xflowf(uint32_t, float);
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float __math_xflowf(unsigned int, float);
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float __math_uflowf(uint32_t);
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float __math_uflowf(unsigned int);
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float __math_oflowf(uint32_t);
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float __math_oflowf(unsigned int);
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float __math_divzerof(uint32_t);
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float __math_divzerof(unsigned int);
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float __math_invalidf(float);
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float __math_invalidf(float);
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double __math_xflow(uint32_t, double);
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double __math_xflow(unsigned int, double);
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double __math_uflow(uint32_t);
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double __math_uflow(unsigned int);
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double __math_oflow(uint32_t);
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double __math_oflow(unsigned int);
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double __math_divzero(uint32_t);
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double __math_divzero(unsigned int);
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double __math_invalid(double);
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double __math_invalid(double);
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#if LDBL_MANT_DIG != DBL_MANT_DIG
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#if LDBL_MANT_DIG != DBL_MANT_DIG
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long double __math_invalidl(long double);
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long double __math_invalidl(long double);
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@ -60,7 +60,7 @@ C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
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double __cos(double x, double y)
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double __cos(double x, double y)
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{
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{
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double_t hz,z,r,w;
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double hz,z,r,w;
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z = x*x;
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z = x*x;
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w = z*z;
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w = z*z;
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@ -2,7 +2,7 @@
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int __fpclassify(double x)
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int __fpclassify(double x)
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{
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{
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union {double f; uint64_t i;} u = {x};
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union {double f; unsigned long long i;} u = {x};
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int e = u.i>>52 & 0x7ff;
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int e = u.i>>52 & 0x7ff;
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if (!e) return u.i<<1 ? FP_SUBNORMAL : FP_ZERO;
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if (!e) return u.i<<1 ? FP_SUBNORMAL : FP_ZERO;
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if (e==0x7ff) return u.i<<12 ? FP_NAN : FP_INFINITE;
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if (e==0x7ff) return u.i<<12 ? FP_NAN : FP_INFINITE;
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@ -2,7 +2,7 @@
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int __fpclassifyf(float x)
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int __fpclassifyf(float x)
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{
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{
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union {float f; uint32_t i;} u = {x};
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union {float f; unsigned int i;} u = {x};
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int e = u.i>>23 & 0xff;
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int e = u.i>>23 & 0xff;
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if (!e) return u.i<<1 ? FP_SUBNORMAL : FP_ZERO;
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if (!e) return u.i<<1 ? FP_SUBNORMAL : FP_ZERO;
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if (e==0xff) return u.i<<9 ? FP_NAN : FP_INFINITE;
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if (e==0xff) return u.i<<9 ? FP_NAN : FP_INFINITE;
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@ -1,6 +1,6 @@
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#include "math.h"
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#include "math.h"
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double __math_divzero(uint32_t sign)
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double __math_divzero(unsigned int sign)
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{
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{
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return fp_barrier(sign ? -1.0 : 1.0) / 0.0;
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return fp_barrier(sign ? -1.0 : 1.0) / 0.0;
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}
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}
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@ -1,6 +1,6 @@
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#include "math.h"
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#include "math.h"
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float __math_divzerof(uint32_t sign)
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float __math_divzerof(unsigned int sign)
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{
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{
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return fp_barrierf(sign ? -1.0f : 1.0f) / 0.0f;
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return fp_barrierf(sign ? -1.0f : 1.0f) / 0.0f;
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}
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}
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@ -1,6 +1,6 @@
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#include "math.h"
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#include "math.h"
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double __math_oflow(uint32_t sign)
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double __math_oflow(unsigned int sign)
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{
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{
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return __math_xflow(sign, 0x1p769);
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return __math_xflow(sign, 0x1p769);
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}
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}
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@ -1,6 +1,6 @@
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#include "math.h"
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#include "math.h"
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float __math_oflowf(uint32_t sign)
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float __math_oflowf(unsigned int sign)
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{
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{
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return __math_xflowf(sign, 0x1p97f);
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return __math_xflowf(sign, 0x1p97f);
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}
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}
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@ -1,6 +1,6 @@
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#include "math.h"
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#include "math.h"
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double __math_uflow(uint32_t sign)
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double __math_uflow(unsigned int sign)
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{
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{
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return __math_xflow(sign, 0x1p-767);
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return __math_xflow(sign, 0x1p-767);
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}
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}
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@ -1,6 +1,6 @@
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#include "math.h"
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#include "math.h"
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float __math_uflowf(uint32_t sign)
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float __math_uflowf(unsigned int sign)
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{
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{
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return __math_xflowf(sign, 0x1p-95f);
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return __math_xflowf(sign, 0x1p-95f);
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}
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}
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@ -1,6 +1,6 @@
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#include "math.h"
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#include "math.h"
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double __math_xflow(uint32_t sign, double y)
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double __math_xflow(unsigned int sign, double y)
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{
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{
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return eval_as_double(fp_barrier(sign ? -y : y) * y);
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return eval_as_double(fp_barrier(sign ? -y : y) * y);
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}
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}
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@ -1,6 +1,6 @@
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#include "math.h"
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#include "math.h"
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float __math_xflowf(uint32_t sign, float y)
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float __math_xflowf(unsigned int sign, float y)
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{
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{
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return eval_as_float(fp_barrierf(sign ? -y : y) * y);
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return eval_as_float(fp_barrierf(sign ? -y : y) * y);
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}
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}
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@ -48,10 +48,10 @@ pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
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/* caller must handle the case when reduction is not needed: |x| ~<= pi/4 */
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/* caller must handle the case when reduction is not needed: |x| ~<= pi/4 */
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int __rem_pio2(double x, double *y)
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int __rem_pio2(double x, double *y)
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{
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{
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union {double f; uint64_t i;} u = {x};
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union {double f; unsigned long long i;} u = {x};
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double_t z,w,t,r,fn;
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double z,w,t,r,fn;
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double tx[3],ty[2];
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double tx[3],ty[2];
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uint32_t ix;
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unsigned int ix;
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int sign, n, ex, ey, i;
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int sign, n, ex, ey, i;
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sign = u.i>>63;
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sign = u.i>>63;
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@ -119,8 +119,8 @@ int __rem_pio2(double x, double *y)
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if (ix < 0x413921fb) { /* |x| ~< 2^20*(pi/2), medium size */
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if (ix < 0x413921fb) { /* |x| ~< 2^20*(pi/2), medium size */
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medium:
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medium:
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/* rint(x/(pi/2)) */
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/* rint(x/(pi/2)) */
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fn = (double_t)x*invpio2 + toint - toint;
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fn = (double)x*invpio2 + toint - toint;
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n = (int32_t)fn;
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n = (int)fn;
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r = x - fn*pio2_1;
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r = x - fn*pio2_1;
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w = fn*pio2_1t; /* 1st round, good to 85 bits */
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w = fn*pio2_1t; /* 1st round, good to 85 bits */
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/* Matters with directed rounding. */
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/* Matters with directed rounding. */
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@ -167,11 +167,11 @@ medium:
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}
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}
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/* set z = scalbn(|x|,-ilogb(x)+23) */
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/* set z = scalbn(|x|,-ilogb(x)+23) */
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u.f = x;
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u.f = x;
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u.i &= (uint64_t)-1>>12;
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u.i &= (unsigned long long)-1>>12;
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u.i |= (uint64_t)(0x3ff + 23)<<52;
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u.i |= (unsigned long long)(0x3ff + 23)<<52;
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z = u.f;
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z = u.f;
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for (i=0; i < 2; i++) {
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for (i=0; i < 2; i++) {
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tx[i] = (double)(int32_t)z;
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tx[i] = (double)(int)z;
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z = (z-tx[i])*0x1p24;
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z = (z-tx[i])*0x1p24;
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}
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}
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tx[i] = z;
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tx[i] = z;
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@ -138,7 +138,7 @@ static const int init_jk[] = {3,4,4,6}; /* initial value for jk */
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* NB: This table must have at least (e0-3)/24 + jk terms.
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* NB: This table must have at least (e0-3)/24 + jk terms.
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* For quad precision (e0 <= 16360, jk = 6), this is 686.
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* For quad precision (e0 <= 16360, jk = 6), this is 686.
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*/
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*/
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static const int32_t ipio2[] = {
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static const int ipio2[] = {
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0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
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0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
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0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
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0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
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0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
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0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
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@ -272,7 +272,7 @@ static const double PIo2[] = {
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int __rem_pio2_large(double *x, double *y, int e0, int nx, int prec)
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int __rem_pio2_large(double *x, double *y, int e0, int nx, int prec)
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{
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{
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int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
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int jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
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double z,fw,f[20],fq[20],q[20];
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double z,fw,f[20],fq[20],q[20];
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|
||||||
/* initialize jk*/
|
/* initialize jk*/
|
||||||
@ -300,15 +300,15 @@ int __rem_pio2_large(double *x, double *y, int e0, int nx, int prec)
|
|||||||
recompute:
|
recompute:
|
||||||
/* distill q[] into iq[] reversingly */
|
/* distill q[] into iq[] reversingly */
|
||||||
for (i=0,j=jz,z=q[jz]; j>0; i++,j--) {
|
for (i=0,j=jz,z=q[jz]; j>0; i++,j--) {
|
||||||
fw = (double)(int32_t)(0x1p-24*z);
|
fw = (double)(int)(0x1p-24*z);
|
||||||
iq[i] = (int32_t)(z - 0x1p24*fw);
|
iq[i] = (int)(z - 0x1p24*fw);
|
||||||
z = q[j-1]+fw;
|
z = q[j-1]+fw;
|
||||||
}
|
}
|
||||||
|
|
||||||
/* compute n */
|
/* compute n */
|
||||||
z = scalbn(z,q0); /* actual value of z */
|
z = scalbn(z,q0); /* actual value of z */
|
||||||
z -= 8.0*floor(z*0.125); /* trim off integer >= 8 */
|
z -= 8.0*floor(z*0.125); /* trim off integer >= 8 */
|
||||||
n = (int32_t)z;
|
n = (int)z;
|
||||||
z -= (double)n;
|
z -= (double)n;
|
||||||
ih = 0;
|
ih = 0;
|
||||||
if (q0 > 0) { /* need iq[jz-1] to determine n */
|
if (q0 > 0) { /* need iq[jz-1] to determine n */
|
||||||
@ -375,13 +375,13 @@ recompute:
|
|||||||
} else { /* break z into 24-bit if necessary */
|
} else { /* break z into 24-bit if necessary */
|
||||||
z = scalbn(z,-q0);
|
z = scalbn(z,-q0);
|
||||||
if (z >= 0x1p24) {
|
if (z >= 0x1p24) {
|
||||||
fw = (double)(int32_t)(0x1p-24*z);
|
fw = (double)(int)(0x1p-24*z);
|
||||||
iq[jz] = (int32_t)(z - 0x1p24*fw);
|
iq[jz] = (int)(z - 0x1p24*fw);
|
||||||
jz += 1;
|
jz += 1;
|
||||||
q0 += 24;
|
q0 += 24;
|
||||||
iq[jz] = (int32_t)fw;
|
iq[jz] = (int)fw;
|
||||||
} else
|
} else
|
||||||
iq[jz] = (int32_t)z;
|
iq[jz] = (int)z;
|
||||||
}
|
}
|
||||||
|
|
||||||
/* convert integer "bit" chunk to floating-point value */
|
/* convert integer "bit" chunk to floating-point value */
|
||||||
@ -411,7 +411,7 @@ recompute:
|
|||||||
fw = 0.0;
|
fw = 0.0;
|
||||||
for (i=jz; i>=0; i--)
|
for (i=jz; i>=0; i--)
|
||||||
fw += fq[i];
|
fw += fq[i];
|
||||||
// TODO: drop excess precision here once double_t is used
|
// TODO: drop excess precision here once double is used
|
||||||
fw = (double)fw;
|
fw = (double)fw;
|
||||||
y[0] = ih==0 ? fw : -fw;
|
y[0] = ih==0 ? fw : -fw;
|
||||||
fw = fq[0]-fw;
|
fw = fq[0]-fw;
|
||||||
|
@ -5,7 +5,7 @@ int __signbit(double x)
|
|||||||
{
|
{
|
||||||
union {
|
union {
|
||||||
double d;
|
double d;
|
||||||
uint64_t i;
|
unsigned long long i;
|
||||||
} y = { x };
|
} y = { x };
|
||||||
return y.i>>63;
|
return y.i>>63;
|
||||||
}
|
}
|
||||||
|
@ -5,7 +5,7 @@ int __signbitf(float x)
|
|||||||
{
|
{
|
||||||
union {
|
union {
|
||||||
float f;
|
float f;
|
||||||
uint32_t i;
|
unsigned int i;
|
||||||
} y = { x };
|
} y = { x };
|
||||||
return y.i>>31;
|
return y.i>>31;
|
||||||
}
|
}
|
||||||
|
@ -51,7 +51,7 @@ S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
|
|||||||
|
|
||||||
double __sin(double x, double y, int iy)
|
double __sin(double x, double y, int iy)
|
||||||
{
|
{
|
||||||
double_t z,r,v,w;
|
double z,r,v,w;
|
||||||
|
|
||||||
z = x*x;
|
z = x*x;
|
||||||
w = z*z;
|
w = z*z;
|
||||||
|
@ -65,9 +65,9 @@ pio4lo = 3.06161699786838301793e-17; /* 3C81A626, 33145C07 */
|
|||||||
|
|
||||||
double __tan(double x, double y, int odd)
|
double __tan(double x, double y, int odd)
|
||||||
{
|
{
|
||||||
double_t z, r, v, w, s, a;
|
double z, r, v, w, s, a;
|
||||||
double w0, a0;
|
double w0, a0;
|
||||||
uint32_t hx;
|
unsigned int hx;
|
||||||
int big, sign;
|
int big, sign;
|
||||||
|
|
||||||
GET_HIGH_WORD(hx,x);
|
GET_HIGH_WORD(hx,x);
|
||||||
|
@ -51,7 +51,7 @@ qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
|
|||||||
|
|
||||||
static double R(double z)
|
static double R(double z)
|
||||||
{
|
{
|
||||||
double_t p, q;
|
double p, q;
|
||||||
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
|
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
|
||||||
q = 1.0+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
|
q = 1.0+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
|
||||||
return p/q;
|
return p/q;
|
||||||
@ -60,13 +60,13 @@ static double R(double z)
|
|||||||
double acos(double x)
|
double acos(double x)
|
||||||
{
|
{
|
||||||
double z,w,s,c,df;
|
double z,w,s,c,df;
|
||||||
uint32_t hx,ix;
|
unsigned int hx,ix;
|
||||||
|
|
||||||
GET_HIGH_WORD(hx, x);
|
GET_HIGH_WORD(hx, x);
|
||||||
ix = hx & 0x7fffffff;
|
ix = hx & 0x7fffffff;
|
||||||
/* |x| >= 1 or nan */
|
/* |x| >= 1 or nan */
|
||||||
if (ix >= 0x3ff00000) {
|
if (ix >= 0x3ff00000) {
|
||||||
uint32_t lx;
|
unsigned int lx;
|
||||||
|
|
||||||
GET_LOW_WORD(lx,x);
|
GET_LOW_WORD(lx,x);
|
||||||
if ((ix-0x3ff00000 | lx) == 0) {
|
if ((ix-0x3ff00000 | lx) == 0) {
|
||||||
|
@ -58,7 +58,7 @@ qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
|
|||||||
|
|
||||||
static double R(double z)
|
static double R(double z)
|
||||||
{
|
{
|
||||||
double_t p, q;
|
double p, q;
|
||||||
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
|
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
|
||||||
q = 1.0+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
|
q = 1.0+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
|
||||||
return p/q;
|
return p/q;
|
||||||
@ -67,13 +67,13 @@ static double R(double z)
|
|||||||
double asin(double x)
|
double asin(double x)
|
||||||
{
|
{
|
||||||
double z,r,s;
|
double z,r,s;
|
||||||
uint32_t hx,ix;
|
unsigned int hx,ix;
|
||||||
|
|
||||||
GET_HIGH_WORD(hx, x);
|
GET_HIGH_WORD(hx, x);
|
||||||
ix = hx & 0x7fffffff;
|
ix = hx & 0x7fffffff;
|
||||||
/* |x| >= 1 or nan */
|
/* |x| >= 1 or nan */
|
||||||
if (ix >= 0x3ff00000) {
|
if (ix >= 0x3ff00000) {
|
||||||
uint32_t lx;
|
unsigned int lx;
|
||||||
GET_LOW_WORD(lx, x);
|
GET_LOW_WORD(lx, x);
|
||||||
if ((ix-0x3ff00000 | lx) == 0)
|
if ((ix-0x3ff00000 | lx) == 0)
|
||||||
/* asin(1) = +-pi/2 with inexact */
|
/* asin(1) = +-pi/2 with inexact */
|
||||||
|
@ -62,8 +62,8 @@ static const double aT[] = {
|
|||||||
|
|
||||||
double atan(double x)
|
double atan(double x)
|
||||||
{
|
{
|
||||||
double_t w,s1,s2,z;
|
double w,s1,s2,z;
|
||||||
uint32_t ix,sign;
|
unsigned int ix,sign;
|
||||||
int id;
|
int id;
|
||||||
|
|
||||||
GET_HIGH_WORD(ix, x);
|
GET_HIGH_WORD(ix, x);
|
||||||
|
@ -46,7 +46,7 @@ pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
|
|||||||
double atan2(double y, double x)
|
double atan2(double y, double x)
|
||||||
{
|
{
|
||||||
double z;
|
double z;
|
||||||
uint32_t m,lx,ly,ix,iy;
|
unsigned int m,lx,ly,ix,iy;
|
||||||
|
|
||||||
if (isnan(x) || isnan(y))
|
if (isnan(x) || isnan(y))
|
||||||
return x+y;
|
return x+y;
|
||||||
|
@ -17,7 +17,7 @@
|
|||||||
|
|
||||||
#include <math.h>
|
#include <math.h>
|
||||||
|
|
||||||
static const uint32_t
|
static const unsigned int
|
||||||
B1 = 715094163, /* B1 = (1023-1023/3-0.03306235651)*2**20 */
|
B1 = 715094163, /* B1 = (1023-1023/3-0.03306235651)*2**20 */
|
||||||
B2 = 696219795; /* B2 = (1023-1023/3-54/3-0.03306235651)*2**20 */
|
B2 = 696219795; /* B2 = (1023-1023/3-54/3-0.03306235651)*2**20 */
|
||||||
|
|
||||||
@ -31,9 +31,9 @@ P4 = 0.145996192886612446982; /* 0x3fc2b000, 0xd4e4edd7 */
|
|||||||
|
|
||||||
double cbrt(double x)
|
double cbrt(double x)
|
||||||
{
|
{
|
||||||
union {double f; uint64_t i;} u = {x};
|
union {double f; unsigned long long i;} u = {x};
|
||||||
double_t r,s,t,w;
|
double r,s,t,w;
|
||||||
uint32_t hx = u.i>>32 & 0x7fffffff;
|
unsigned int hx = u.i>>32 & 0x7fffffff;
|
||||||
|
|
||||||
if (hx >= 0x7ff00000) /* cbrt(NaN,INF) is itself */
|
if (hx >= 0x7ff00000) /* cbrt(NaN,INF) is itself */
|
||||||
return x+x;
|
return x+x;
|
||||||
@ -62,7 +62,7 @@ double cbrt(double x)
|
|||||||
} else
|
} else
|
||||||
hx = hx/3 + B1;
|
hx = hx/3 + B1;
|
||||||
u.i &= 1ULL<<63;
|
u.i &= 1ULL<<63;
|
||||||
u.i |= (uint64_t)hx << 32;
|
u.i |= (unsigned long long)hx << 32;
|
||||||
t = u.f;
|
t = u.f;
|
||||||
|
|
||||||
/*
|
/*
|
||||||
|
@ -5,13 +5,13 @@
|
|||||||
#elif FLT_EVAL_METHOD==2
|
#elif FLT_EVAL_METHOD==2
|
||||||
#define EPS LDBL_EPSILON
|
#define EPS LDBL_EPSILON
|
||||||
#endif
|
#endif
|
||||||
static const double_t toint = 1/EPS;
|
static const double toint = 1/EPS;
|
||||||
|
|
||||||
double ceil(double x)
|
double ceil(double x)
|
||||||
{
|
{
|
||||||
union {double f; uint64_t i;} u = {x};
|
union {double f; unsigned long long i;} u = {x};
|
||||||
int e = u.i >> 52 & 0x7ff;
|
int e = u.i >> 52 & 0x7ff;
|
||||||
double_t y;
|
double y;
|
||||||
|
|
||||||
if (e >= 0x3ff+52 || x == 0)
|
if (e >= 0x3ff+52 || x == 0)
|
||||||
return x;
|
return x;
|
||||||
|
@ -45,7 +45,7 @@
|
|||||||
double cos(double x)
|
double cos(double x)
|
||||||
{
|
{
|
||||||
double y[2];
|
double y[2];
|
||||||
uint32_t ix;
|
unsigned int ix;
|
||||||
unsigned n;
|
unsigned n;
|
||||||
|
|
||||||
GET_HIGH_WORD(ix, x);
|
GET_HIGH_WORD(ix, x);
|
||||||
|
@ -23,12 +23,12 @@
|
|||||||
is scale*(1+TMP) without intermediate rounding. The bit representation of
|
is scale*(1+TMP) without intermediate rounding. The bit representation of
|
||||||
scale is in SBITS, however it has a computed exponent that may have
|
scale is in SBITS, however it has a computed exponent that may have
|
||||||
overflown into the sign bit so that needs to be adjusted before using it as
|
overflown into the sign bit so that needs to be adjusted before using it as
|
||||||
a double. (int32_t)KI is the k used in the argument reduction and exponent
|
a double. (int)KI is the k used in the argument reduction and exponent
|
||||||
adjustment of scale, positive k here means the result may overflow and
|
adjustment of scale, positive k here means the result may overflow and
|
||||||
negative k means the result may underflow. */
|
negative k means the result may underflow. */
|
||||||
static inline double specialcase(double_t tmp, uint64_t sbits, uint64_t ki)
|
static inline double specialcase(double tmp, unsigned long long sbits, unsigned long long ki)
|
||||||
{
|
{
|
||||||
double_t scale, y;
|
double scale, y;
|
||||||
|
|
||||||
if ((ki & 0x80000000) == 0) {
|
if ((ki & 0x80000000) == 0) {
|
||||||
/* k > 0, the exponent of scale might have overflowed by <= 460. */
|
/* k > 0, the exponent of scale might have overflowed by <= 460. */
|
||||||
@ -46,7 +46,7 @@ static inline double specialcase(double_t tmp, uint64_t sbits, uint64_t ki)
|
|||||||
range to avoid double rounding that can cause 0.5+E/2 ulp error where
|
range to avoid double rounding that can cause 0.5+E/2 ulp error where
|
||||||
E is the worst-case ulp error outside the subnormal range. So this
|
E is the worst-case ulp error outside the subnormal range. So this
|
||||||
is only useful if the goal is better than 1 ulp worst-case error. */
|
is only useful if the goal is better than 1 ulp worst-case error. */
|
||||||
double_t hi, lo;
|
double hi, lo;
|
||||||
lo = scale - y + scale * tmp;
|
lo = scale - y + scale * tmp;
|
||||||
hi = 1.0 + y;
|
hi = 1.0 + y;
|
||||||
lo = 1.0 - hi + y + lo;
|
lo = 1.0 - hi + y + lo;
|
||||||
@ -62,16 +62,16 @@ static inline double specialcase(double_t tmp, uint64_t sbits, uint64_t ki)
|
|||||||
}
|
}
|
||||||
|
|
||||||
/* Top 12 bits of a double (sign and exponent bits). */
|
/* Top 12 bits of a double (sign and exponent bits). */
|
||||||
static inline uint32_t top12(double x)
|
static inline unsigned int top12(double x)
|
||||||
{
|
{
|
||||||
return asuint64(x) >> 52;
|
return asuint64(x) >> 52;
|
||||||
}
|
}
|
||||||
|
|
||||||
double exp(double x)
|
double exp(double x)
|
||||||
{
|
{
|
||||||
uint32_t abstop;
|
unsigned int abstop;
|
||||||
uint64_t ki, idx, top, sbits;
|
unsigned long long ki, idx, top, sbits;
|
||||||
double_t kd, z, r, r2, scale, tail, tmp;
|
double kd, z, r, r2, scale, tail, tmp;
|
||||||
|
|
||||||
abstop = top12(x) & 0x7ff;
|
abstop = top12(x) & 0x7ff;
|
||||||
if (predict_false(abstop - top12(0x1p-54) >= top12(512.0) - top12(0x1p-54))) {
|
if (predict_false(abstop - top12(0x1p-54) >= top12(512.0) - top12(0x1p-54))) {
|
||||||
@ -103,7 +103,7 @@ double exp(double x)
|
|||||||
/* z - kd is in [-0.5-2^-16, 0.5] in all rounding modes. */
|
/* z - kd is in [-0.5-2^-16, 0.5] in all rounding modes. */
|
||||||
kd = eval_as_double(z + Shift);
|
kd = eval_as_double(z + Shift);
|
||||||
ki = asuint64(kd) >> 16;
|
ki = asuint64(kd) >> 16;
|
||||||
kd = (double_t)(int32_t)ki;
|
kd = (double)(int)ki;
|
||||||
#else
|
#else
|
||||||
/* z - kd is in [-1, 1] in non-nearest rounding modes. */
|
/* z - kd is in [-1, 1] in non-nearest rounding modes. */
|
||||||
kd = eval_as_double(z + Shift);
|
kd = eval_as_double(z + Shift);
|
||||||
|
@ -19,7 +19,7 @@ extern const struct exp_data {
|
|||||||
double poly[4]; /* Last four coefficients. */
|
double poly[4]; /* Last four coefficients. */
|
||||||
double exp2_shift;
|
double exp2_shift;
|
||||||
double exp2_poly[EXP2_POLY_ORDER];
|
double exp2_poly[EXP2_POLY_ORDER];
|
||||||
uint64_t tab[2*(1 << EXP_TABLE_BITS)];
|
unsigned long long tab[2*(1 << EXP_TABLE_BITS)];
|
||||||
} __exp_data;
|
} __exp_data;
|
||||||
|
|
||||||
#endif
|
#endif
|
||||||
|
@ -2,7 +2,7 @@
|
|||||||
|
|
||||||
double fabs(double x)
|
double fabs(double x)
|
||||||
{
|
{
|
||||||
union {double f; uint64_t i;} u = {x};
|
union {double f; unsigned long long i;} u = {x};
|
||||||
u.i &= ULLONG_NSHIFT/2;
|
u.i &= ULLONG_NSHIFT/2;
|
||||||
return u.f;
|
return u.f;
|
||||||
}
|
}
|
||||||
|
@ -3,8 +3,8 @@
|
|||||||
int factorial(int n)
|
int factorial(int n)
|
||||||
{
|
{
|
||||||
if (n < 0) return (int)__math_invalid(-1.0f);
|
if (n < 0) return (int)__math_invalid(-1.0f);
|
||||||
int32_t r = 1;
|
int r = 1;
|
||||||
for (int32_t i = 2; i <= n; i++)
|
for (int i = 2; i <= n; i++)
|
||||||
{
|
{
|
||||||
r = r * i;
|
r = r * i;
|
||||||
}
|
}
|
||||||
|
@ -5,13 +5,13 @@
|
|||||||
#elif FLT_EVAL_METHOD==2
|
#elif FLT_EVAL_METHOD==2
|
||||||
#define EPS LDBL_EPSILON
|
#define EPS LDBL_EPSILON
|
||||||
#endif
|
#endif
|
||||||
static const double_t toint = 1/EPS;
|
static const double toint = 1/EPS;
|
||||||
|
|
||||||
double floor(double x)
|
double floor(double x)
|
||||||
{
|
{
|
||||||
union {double f; uint64_t i;} u = {x};
|
union {double f; unsigned long long i;} u = {x};
|
||||||
int e = u.i >> 52 & 0x7ff;
|
int e = u.i >> 52 & 0x7ff;
|
||||||
double_t y;
|
double y;
|
||||||
|
|
||||||
if (e >= 0x3ff+52 || x == 0)
|
if (e >= 0x3ff+52 || x == 0)
|
||||||
return x;
|
return x;
|
||||||
|
@ -2,15 +2,15 @@
|
|||||||
|
|
||||||
double fmod(double x, double y)
|
double fmod(double x, double y)
|
||||||
{
|
{
|
||||||
union {double f; uint64_t i;} ux = {x}, uy = {y};
|
union {double f; unsigned long long i;} ux = {x}, uy = {y};
|
||||||
int ex = ux.i>>52 & 0x7ff;
|
int ex = ux.i>>52 & 0x7ff;
|
||||||
int ey = uy.i>>52 & 0x7ff;
|
int ey = uy.i>>52 & 0x7ff;
|
||||||
int sx = ux.i>>63;
|
int sx = ux.i>>63;
|
||||||
uint64_t i;
|
unsigned long long i;
|
||||||
|
|
||||||
/* in the followings uxi should be ux.i, but then gcc wrongly adds */
|
/* in the followings uxi should be ux.i, but then gcc wrongly adds */
|
||||||
/* float load/store to inner loops ruining performance and code size */
|
/* float load/store to inner loops ruining performance and code size */
|
||||||
uint64_t uxi = ux.i;
|
unsigned long long uxi = ux.i;
|
||||||
|
|
||||||
if (uy.i<<1 == 0 || isnan(y) || ex == 0x7ff)
|
if (uy.i<<1 == 0 || isnan(y) || ex == 0x7ff)
|
||||||
return (x*y)/(x*y);
|
return (x*y)/(x*y);
|
||||||
@ -57,11 +57,11 @@ double fmod(double x, double y)
|
|||||||
/* scale result */
|
/* scale result */
|
||||||
if (ex > 0) {
|
if (ex > 0) {
|
||||||
uxi -= 1ULL << 52;
|
uxi -= 1ULL << 52;
|
||||||
uxi |= (uint64_t)ex << 52;
|
uxi |= (unsigned long long)ex << 52;
|
||||||
} else {
|
} else {
|
||||||
uxi >>= -ex + 1;
|
uxi >>= -ex + 1;
|
||||||
}
|
}
|
||||||
uxi |= (uint64_t)sx << 63;
|
uxi |= (unsigned long long)sx << 63;
|
||||||
ux.i = uxi;
|
ux.i = uxi;
|
||||||
return ux.f;
|
return ux.f;
|
||||||
}
|
}
|
||||||
|
@ -6,7 +6,7 @@ int gcd(int a, int b)
|
|||||||
if (b < 0) b = -b;
|
if (b < 0) b = -b;
|
||||||
while (b != 0)
|
while (b != 0)
|
||||||
{
|
{
|
||||||
int32_t t = b;
|
int t = b;
|
||||||
b = a % b;
|
b = a % b;
|
||||||
a = t;
|
a = t;
|
||||||
}
|
}
|
||||||
|
@ -18,16 +18,16 @@
|
|||||||
#define OFF 0x3fe6000000000000
|
#define OFF 0x3fe6000000000000
|
||||||
|
|
||||||
/* Top 16 bits of a double. */
|
/* Top 16 bits of a double. */
|
||||||
static inline uint32_t top16(double x)
|
static inline unsigned int top16(double x)
|
||||||
{
|
{
|
||||||
return asuint64(x) >> 48;
|
return asuint64(x) >> 48;
|
||||||
}
|
}
|
||||||
|
|
||||||
double log(double x)
|
double log(double x)
|
||||||
{
|
{
|
||||||
double_t w, z, r, r2, r3, y, invc, logc, kd, hi, lo;
|
double w, z, r, r2, r3, y, invc, logc, kd, hi, lo;
|
||||||
uint64_t ix, iz, tmp;
|
unsigned long long ix, iz, tmp;
|
||||||
uint32_t top;
|
unsigned int top;
|
||||||
int k, i;
|
int k, i;
|
||||||
|
|
||||||
ix = asuint64(x);
|
ix = asuint64(x);
|
||||||
@ -48,8 +48,8 @@ double log(double x)
|
|||||||
r3 * (B[7] + r * B[8] + r2 * B[9] + r3 * B[10])));
|
r3 * (B[7] + r * B[8] + r2 * B[9] + r3 * B[10])));
|
||||||
/* Worst-case error is around 0.507 ULP. */
|
/* Worst-case error is around 0.507 ULP. */
|
||||||
w = r * 0x1p27;
|
w = r * 0x1p27;
|
||||||
double_t rhi = r + w - w;
|
double rhi = r + w - w;
|
||||||
double_t rlo = r - rhi;
|
double rlo = r - rhi;
|
||||||
w = rhi * rhi * B[0]; /* B[0] == -0.5. */
|
w = rhi * rhi * B[0]; /* B[0] == -0.5. */
|
||||||
hi = r + w;
|
hi = r + w;
|
||||||
lo = r - hi + w;
|
lo = r - hi + w;
|
||||||
@ -76,7 +76,7 @@ double log(double x)
|
|||||||
The ith subinterval contains z and c is near its center. */
|
The ith subinterval contains z and c is near its center. */
|
||||||
tmp = ix - OFF;
|
tmp = ix - OFF;
|
||||||
i = (tmp >> (52 - LOG_TABLE_BITS)) % N;
|
i = (tmp >> (52 - LOG_TABLE_BITS)) % N;
|
||||||
k = (int64_t)tmp >> 52; /* arithmetic shift */
|
k = (long long)tmp >> 52; /* arithmetic shift */
|
||||||
iz = ix - (tmp & 0xfffULL << 52);
|
iz = ix - (tmp & 0xfffULL << 52);
|
||||||
invc = T[i].invc;
|
invc = T[i].invc;
|
||||||
logc = T[i].logc;
|
logc = T[i].logc;
|
||||||
@ -91,7 +91,7 @@ double log(double x)
|
|||||||
/* rounding error: 0x1p-55/N + 0x1p-66. */
|
/* rounding error: 0x1p-55/N + 0x1p-66. */
|
||||||
r = (z - T2[i].chi - T2[i].clo) * invc;
|
r = (z - T2[i].chi - T2[i].clo) * invc;
|
||||||
#endif
|
#endif
|
||||||
kd = (double_t)k;
|
kd = (double)k;
|
||||||
|
|
||||||
/* hi + lo = r + log(c) + k*Ln2. */
|
/* hi + lo = r + log(c) + k*Ln2. */
|
||||||
w = kd * Ln2hi + logc;
|
w = kd * Ln2hi + logc;
|
||||||
|
@ -34,9 +34,9 @@ Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
|
|||||||
|
|
||||||
double log10(double x)
|
double log10(double x)
|
||||||
{
|
{
|
||||||
union {double f; uint64_t i;} u = {x};
|
union {double f; unsigned long long i;} u = {x};
|
||||||
double_t hfsq,f,s,z,R,w,t1,t2,dk,y,hi,lo,val_hi,val_lo;
|
double hfsq,f,s,z,R,w,t1,t2,dk,y,hi,lo,val_hi,val_lo;
|
||||||
uint32_t hx;
|
unsigned int hx;
|
||||||
int k;
|
int k;
|
||||||
|
|
||||||
hx = u.i>>32;
|
hx = u.i>>32;
|
||||||
@ -60,7 +60,7 @@ double log10(double x)
|
|||||||
hx += 0x3ff00000 - 0x3fe6a09e;
|
hx += 0x3ff00000 - 0x3fe6a09e;
|
||||||
k += (int)(hx>>20) - 0x3ff;
|
k += (int)(hx>>20) - 0x3ff;
|
||||||
hx = (hx&0x000fffff) + 0x3fe6a09e;
|
hx = (hx&0x000fffff) + 0x3fe6a09e;
|
||||||
u.i = (uint64_t)hx<<32 | (u.i&0xffffffff);
|
u.i = (unsigned long long)hx<<32 | (u.i&0xffffffff);
|
||||||
x = u.f;
|
x = u.f;
|
||||||
|
|
||||||
f = x - 1.0;
|
f = x - 1.0;
|
||||||
@ -76,7 +76,7 @@ double log10(double x)
|
|||||||
/* hi+lo = f - hfsq + s*(hfsq+R) ~ log(1+f) */
|
/* hi+lo = f - hfsq + s*(hfsq+R) ~ log(1+f) */
|
||||||
hi = f - hfsq;
|
hi = f - hfsq;
|
||||||
u.f = hi;
|
u.f = hi;
|
||||||
u.i &= (uint64_t)-1<<32;
|
u.i &= (unsigned long long)-1<<32;
|
||||||
hi = u.f;
|
hi = u.f;
|
||||||
lo = f - hi - hfsq + s*(hfsq+R);
|
lo = f - hi - hfsq + s*(hfsq+R);
|
||||||
|
|
||||||
|
@ -18,16 +18,16 @@
|
|||||||
#define OFF 0x3fe6000000000000
|
#define OFF 0x3fe6000000000000
|
||||||
|
|
||||||
/* Top 16 bits of a double. */
|
/* Top 16 bits of a double. */
|
||||||
static inline uint32_t top16(double x)
|
static inline unsigned int top16(double x)
|
||||||
{
|
{
|
||||||
return asuint64(x) >> 48;
|
return asuint64(x) >> 48;
|
||||||
}
|
}
|
||||||
|
|
||||||
double log2(double x)
|
double log2(double x)
|
||||||
{
|
{
|
||||||
double_t z, r, r2, r4, y, invc, logc, kd, hi, lo, t1, t2, t3, p;
|
double z, r, r2, r4, y, invc, logc, kd, hi, lo, t1, t2, t3, p;
|
||||||
uint64_t ix, iz, tmp;
|
unsigned long long ix, iz, tmp;
|
||||||
uint32_t top;
|
unsigned int top;
|
||||||
int k, i;
|
int k, i;
|
||||||
|
|
||||||
ix = asuint64(x);
|
ix = asuint64(x);
|
||||||
@ -44,7 +44,7 @@ double log2(double x)
|
|||||||
hi = r * InvLn2hi;
|
hi = r * InvLn2hi;
|
||||||
lo = r * InvLn2lo + __builtin_fma(r, InvLn2hi, -hi);
|
lo = r * InvLn2lo + __builtin_fma(r, InvLn2hi, -hi);
|
||||||
#else
|
#else
|
||||||
double_t rhi, rlo;
|
double rhi, rlo;
|
||||||
rhi = asdouble(asuint64(r) & ULLONG_NSHIFT << 32);
|
rhi = asdouble(asuint64(r) & ULLONG_NSHIFT << 32);
|
||||||
rlo = r - rhi;
|
rlo = r - rhi;
|
||||||
hi = rhi * InvLn2hi;
|
hi = rhi * InvLn2hi;
|
||||||
@ -79,12 +79,12 @@ double log2(double x)
|
|||||||
The ith subinterval contains z and c is near its center. */
|
The ith subinterval contains z and c is near its center. */
|
||||||
tmp = ix - OFF;
|
tmp = ix - OFF;
|
||||||
i = (tmp >> (52 - LOG2_TABLE_BITS)) % N;
|
i = (tmp >> (52 - LOG2_TABLE_BITS)) % N;
|
||||||
k = (int64_t)tmp >> 52; /* arithmetic shift */
|
k = (long long)tmp >> 52; /* arithmetic shift */
|
||||||
iz = ix - (tmp & 0xfffULL << 52);
|
iz = ix - (tmp & 0xfffULL << 52);
|
||||||
invc = T[i].invc;
|
invc = T[i].invc;
|
||||||
logc = T[i].logc;
|
logc = T[i].logc;
|
||||||
z = asdouble(iz);
|
z = asdouble(iz);
|
||||||
kd = (double_t)k;
|
kd = (double)k;
|
||||||
|
|
||||||
/* log2(x) = log2(z/c) + log2(c) + k. */
|
/* log2(x) = log2(z/c) + log2(c) + k. */
|
||||||
/* r ~= z/c - 1, |r| < 1/(2*N). */
|
/* r ~= z/c - 1, |r| < 1/(2*N). */
|
||||||
@ -94,7 +94,7 @@ double log2(double x)
|
|||||||
t1 = r * InvLn2hi;
|
t1 = r * InvLn2hi;
|
||||||
t2 = r * InvLn2lo + __builtin_fma(r, InvLn2hi, -t1);
|
t2 = r * InvLn2lo + __builtin_fma(r, InvLn2hi, -t1);
|
||||||
#else
|
#else
|
||||||
double_t rhi, rlo;
|
double rhi, rlo;
|
||||||
/* rounding error: 0x1p-55/N + 0x1p-65. */
|
/* rounding error: 0x1p-55/N + 0x1p-65. */
|
||||||
r = (z - T2[i].chi - T2[i].clo) * invc;
|
r = (z - T2[i].chi - T2[i].clo) * invc;
|
||||||
rhi = asdouble(asuint64(r) & ULLONG_NSHIFT << 32);
|
rhi = asdouble(asuint64(r) & ULLONG_NSHIFT << 32);
|
||||||
|
@ -2,8 +2,8 @@
|
|||||||
|
|
||||||
double modf(double x, double *iptr)
|
double modf(double x, double *iptr)
|
||||||
{
|
{
|
||||||
union {double f; uint64_t i;} u = {x};
|
union {double f; unsigned long long i;} u = {x};
|
||||||
uint64_t mask;
|
unsigned long long mask;
|
||||||
int e = (int)(u.i>>52 & 0x7ff) - 0x3ff;
|
int e = (int)(u.i>>52 & 0x7ff) - 0x3ff;
|
||||||
|
|
||||||
/* no fractional part */
|
/* no fractional part */
|
||||||
|
@ -23,7 +23,7 @@ ulperr_exp: 0.509 ULP (ULP error of exp, 0.511 ULP without fma)
|
|||||||
#define OFF 0x3fe6955500000000
|
#define OFF 0x3fe6955500000000
|
||||||
|
|
||||||
/* Top 12 bits of a double (sign and exponent bits). */
|
/* Top 12 bits of a double (sign and exponent bits). */
|
||||||
static inline uint32_t top12(double x)
|
static inline unsigned int top12(double x)
|
||||||
{
|
{
|
||||||
return asuint64(x) >> 52;
|
return asuint64(x) >> 52;
|
||||||
}
|
}
|
||||||
@ -31,11 +31,11 @@ static inline uint32_t top12(double x)
|
|||||||
/* Compute y+TAIL = log(x) where the rounded result is y and TAIL has about
|
/* Compute y+TAIL = log(x) where the rounded result is y and TAIL has about
|
||||||
additional 15 bits precision. IX is the bit representation of x, but
|
additional 15 bits precision. IX is the bit representation of x, but
|
||||||
normalized in the subnormal range using the sign bit for the exponent. */
|
normalized in the subnormal range using the sign bit for the exponent. */
|
||||||
static inline double_t log_inline(uint64_t ix, double_t *tail)
|
static inline double log_inline(unsigned long long ix, double *tail)
|
||||||
{
|
{
|
||||||
/* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
|
/* double for better performance on targets with FLT_EVAL_METHOD==2. */
|
||||||
double_t z, r, y, invc, logc, logctail, kd, hi, t1, t2, lo, lo1, lo2, p;
|
double z, r, y, invc, logc, logctail, kd, hi, t1, t2, lo, lo1, lo2, p;
|
||||||
uint64_t iz, tmp;
|
unsigned long long iz, tmp;
|
||||||
int k, i;
|
int k, i;
|
||||||
|
|
||||||
/* x = 2^k z; where z is in range [OFF,2*OFF) and exact.
|
/* x = 2^k z; where z is in range [OFF,2*OFF) and exact.
|
||||||
@ -43,10 +43,10 @@ static inline double_t log_inline(uint64_t ix, double_t *tail)
|
|||||||
The ith subinterval contains z and c is near its center. */
|
The ith subinterval contains z and c is near its center. */
|
||||||
tmp = ix - OFF;
|
tmp = ix - OFF;
|
||||||
i = (tmp >> (52 - POW_LOG_TABLE_BITS)) % N;
|
i = (tmp >> (52 - POW_LOG_TABLE_BITS)) % N;
|
||||||
k = (int64_t)tmp >> 52; /* arithmetic shift */
|
k = (long long)tmp >> 52; /* arithmetic shift */
|
||||||
iz = ix - (tmp & 0xfffULL << 52);
|
iz = ix - (tmp & 0xfffULL << 52);
|
||||||
z = asdouble(iz);
|
z = asdouble(iz);
|
||||||
kd = (double_t)k;
|
kd = (double)k;
|
||||||
|
|
||||||
/* log(x) = k*Ln2 + log(c) + log1p(z/c-1). */
|
/* log(x) = k*Ln2 + log(c) + log1p(z/c-1). */
|
||||||
invc = T[i].invc;
|
invc = T[i].invc;
|
||||||
@ -59,10 +59,10 @@ static inline double_t log_inline(uint64_t ix, double_t *tail)
|
|||||||
r = __builtin_fma(z, invc, -1.0);
|
r = __builtin_fma(z, invc, -1.0);
|
||||||
#else
|
#else
|
||||||
/* Split z such that rhi, rlo and rhi*rhi are exact and |rlo| <= |r|. */
|
/* Split z such that rhi, rlo and rhi*rhi are exact and |rlo| <= |r|. */
|
||||||
double_t zhi = asdouble((iz + (1ULL << 31)) & (ULLONG_NSHIFT << 32));
|
double zhi = asdouble((iz + (1ULL << 31)) & (ULLONG_NSHIFT << 32));
|
||||||
double_t zlo = z - zhi;
|
double zlo = z - zhi;
|
||||||
double_t rhi = zhi * invc - 1.0;
|
double rhi = zhi * invc - 1.0;
|
||||||
double_t rlo = zlo * invc;
|
double rlo = zlo * invc;
|
||||||
r = rhi + rlo;
|
r = rhi + rlo;
|
||||||
#endif
|
#endif
|
||||||
|
|
||||||
@ -73,7 +73,7 @@ static inline double_t log_inline(uint64_t ix, double_t *tail)
|
|||||||
lo2 = t1 - t2 + r;
|
lo2 = t1 - t2 + r;
|
||||||
|
|
||||||
/* Evaluation is optimized assuming superscalar pipelined execution. */
|
/* Evaluation is optimized assuming superscalar pipelined execution. */
|
||||||
double_t ar, ar2, ar3, lo3, lo4;
|
double ar, ar2, ar3, lo3, lo4;
|
||||||
ar = A[0] * r; /* A[0] = -0.5. */
|
ar = A[0] * r; /* A[0] = -0.5. */
|
||||||
ar2 = r * ar;
|
ar2 = r * ar;
|
||||||
ar3 = r * ar2;
|
ar3 = r * ar2;
|
||||||
@ -83,8 +83,8 @@ static inline double_t log_inline(uint64_t ix, double_t *tail)
|
|||||||
lo3 = __builtin_fma(ar, r, -ar2);
|
lo3 = __builtin_fma(ar, r, -ar2);
|
||||||
lo4 = t2 - hi + ar2;
|
lo4 = t2 - hi + ar2;
|
||||||
#else
|
#else
|
||||||
double_t arhi = A[0] * rhi;
|
double arhi = A[0] * rhi;
|
||||||
double_t arhi2 = rhi * arhi;
|
double arhi2 = rhi * arhi;
|
||||||
hi = t2 + arhi2;
|
hi = t2 + arhi2;
|
||||||
lo3 = rlo * (ar + arhi);
|
lo3 = rlo * (ar + arhi);
|
||||||
lo4 = t2 - hi + arhi2;
|
lo4 = t2 - hi + arhi2;
|
||||||
@ -116,12 +116,12 @@ static inline double_t log_inline(uint64_t ix, double_t *tail)
|
|||||||
is scale*(1+TMP) without intermediate rounding. The bit representation of
|
is scale*(1+TMP) without intermediate rounding. The bit representation of
|
||||||
scale is in SBITS, however it has a computed exponent that may have
|
scale is in SBITS, however it has a computed exponent that may have
|
||||||
overflown into the sign bit so that needs to be adjusted before using it as
|
overflown into the sign bit so that needs to be adjusted before using it as
|
||||||
a double. (int32_t)KI is the k used in the argument reduction and exponent
|
a double. (int)KI is the k used in the argument reduction and exponent
|
||||||
adjustment of scale, positive k here means the result may overflow and
|
adjustment of scale, positive k here means the result may overflow and
|
||||||
negative k means the result may underflow. */
|
negative k means the result may underflow. */
|
||||||
static inline double specialcase(double_t tmp, uint64_t sbits, uint64_t ki)
|
static inline double specialcase(double tmp, unsigned long long sbits, unsigned long long ki)
|
||||||
{
|
{
|
||||||
double_t scale, y;
|
double scale, y;
|
||||||
|
|
||||||
if ((ki & 0x80000000) == 0) {
|
if ((ki & 0x80000000) == 0) {
|
||||||
/* k > 0, the exponent of scale might have overflowed by <= 460. */
|
/* k > 0, the exponent of scale might have overflowed by <= 460. */
|
||||||
@ -140,7 +140,7 @@ static inline double specialcase(double_t tmp, uint64_t sbits, uint64_t ki)
|
|||||||
range to avoid double rounding that can cause 0.5+E/2 ulp error where
|
range to avoid double rounding that can cause 0.5+E/2 ulp error where
|
||||||
E is the worst-case ulp error outside the subnormal range. So this
|
E is the worst-case ulp error outside the subnormal range. So this
|
||||||
is only useful if the goal is better than 1 ulp worst-case error. */
|
is only useful if the goal is better than 1 ulp worst-case error. */
|
||||||
double_t hi, lo, one = 1.0;
|
double hi, lo, one = 1.0;
|
||||||
if (y < 0.0)
|
if (y < 0.0)
|
||||||
one = -1.0;
|
one = -1.0;
|
||||||
lo = scale - y + scale * tmp;
|
lo = scale - y + scale * tmp;
|
||||||
@ -161,12 +161,12 @@ static inline double specialcase(double_t tmp, uint64_t sbits, uint64_t ki)
|
|||||||
|
|
||||||
/* Computes sign*exp(x+xtail) where |xtail| < 2^-8/N and |xtail| <= |x|.
|
/* Computes sign*exp(x+xtail) where |xtail| < 2^-8/N and |xtail| <= |x|.
|
||||||
The sign_bias argument is SIGN_BIAS or 0 and sets the sign to -1 or 1. */
|
The sign_bias argument is SIGN_BIAS or 0 and sets the sign to -1 or 1. */
|
||||||
static inline double exp_inline(double_t x, double_t xtail, uint32_t sign_bias)
|
static inline double exp_inline(double x, double xtail, unsigned int sign_bias)
|
||||||
{
|
{
|
||||||
uint32_t abstop;
|
unsigned int abstop;
|
||||||
uint64_t ki, idx, top, sbits;
|
unsigned long long ki, idx, top, sbits;
|
||||||
/* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
|
/* double for better performance on targets with FLT_EVAL_METHOD==2. */
|
||||||
double_t kd, z, r, r2, scale, tail, tmp;
|
double kd, z, r, r2, scale, tail, tmp;
|
||||||
|
|
||||||
abstop = top12(x) & 0x7ff;
|
abstop = top12(x) & 0x7ff;
|
||||||
if (predict_false(abstop - top12(0x1p-54) >=
|
if (predict_false(abstop - top12(0x1p-54) >=
|
||||||
@ -174,7 +174,7 @@ static inline double exp_inline(double_t x, double_t xtail, uint32_t sign_bias)
|
|||||||
if (abstop - top12(0x1p-54) >= 0x80000000) {
|
if (abstop - top12(0x1p-54) >= 0x80000000) {
|
||||||
/* Avoid spurious underflow for tiny x. */
|
/* Avoid spurious underflow for tiny x. */
|
||||||
/* Note: 0 is common input. */
|
/* Note: 0 is common input. */
|
||||||
double_t one = WANT_ROUNDING ? 1.0 + x : 1.0;
|
double one = WANT_ROUNDING ? 1.0 + x : 1.0;
|
||||||
return sign_bias ? -one : one;
|
return sign_bias ? -one : one;
|
||||||
}
|
}
|
||||||
if (abstop >= top12(1024.0)) {
|
if (abstop >= top12(1024.0)) {
|
||||||
@ -198,7 +198,7 @@ static inline double exp_inline(double_t x, double_t xtail, uint32_t sign_bias)
|
|||||||
/* z - kd is in [-0.5-2^-16, 0.5] in all rounding modes. */
|
/* z - kd is in [-0.5-2^-16, 0.5] in all rounding modes. */
|
||||||
kd = eval_as_double(z + Shift);
|
kd = eval_as_double(z + Shift);
|
||||||
ki = asuint64(kd) >> 16;
|
ki = asuint64(kd) >> 16;
|
||||||
kd = (double_t)(int32_t)ki;
|
kd = (double)(int)ki;
|
||||||
#else
|
#else
|
||||||
/* z - kd is in [-1, 1] in non-nearest rounding modes. */
|
/* z - kd is in [-1, 1] in non-nearest rounding modes. */
|
||||||
kd = eval_as_double(z + Shift);
|
kd = eval_as_double(z + Shift);
|
||||||
@ -230,7 +230,7 @@ static inline double exp_inline(double_t x, double_t xtail, uint32_t sign_bias)
|
|||||||
|
|
||||||
/* Returns 0 if not int, 1 if odd int, 2 if even int. The argument is
|
/* Returns 0 if not int, 1 if odd int, 2 if even int. The argument is
|
||||||
the bit representation of a non-zero finite floating-point value. */
|
the bit representation of a non-zero finite floating-point value. */
|
||||||
static inline int checkint(uint64_t iy)
|
static inline int checkint(unsigned long long iy)
|
||||||
{
|
{
|
||||||
int e = iy >> 52 & 0x7ff;
|
int e = iy >> 52 & 0x7ff;
|
||||||
if (e < 0x3ff)
|
if (e < 0x3ff)
|
||||||
@ -245,16 +245,16 @@ static inline int checkint(uint64_t iy)
|
|||||||
}
|
}
|
||||||
|
|
||||||
/* Returns 1 if input is the bit representation of 0, infinity or nan. */
|
/* Returns 1 if input is the bit representation of 0, infinity or nan. */
|
||||||
static inline int zeroinfnan(uint64_t i)
|
static inline int zeroinfnan(unsigned long long i)
|
||||||
{
|
{
|
||||||
return 2 * i - 1 >= 2 * asuint64(INFINITY) - 1;
|
return 2 * i - 1 >= 2 * asuint64(INFINITY) - 1;
|
||||||
}
|
}
|
||||||
|
|
||||||
double pow(double x, double y)
|
double pow(double x, double y)
|
||||||
{
|
{
|
||||||
uint32_t sign_bias = 0;
|
unsigned int sign_bias = 0;
|
||||||
uint64_t ix, iy;
|
unsigned long long ix, iy;
|
||||||
uint32_t topx, topy;
|
unsigned int topx, topy;
|
||||||
|
|
||||||
ix = asuint64(x);
|
ix = asuint64(x);
|
||||||
iy = asuint64(y);
|
iy = asuint64(y);
|
||||||
@ -281,7 +281,7 @@ double pow(double x, double y)
|
|||||||
return y * y;
|
return y * y;
|
||||||
}
|
}
|
||||||
if (predict_false(zeroinfnan(ix))) {
|
if (predict_false(zeroinfnan(ix))) {
|
||||||
double_t x2 = x * x;
|
double x2 = x * x;
|
||||||
if (ix >> 63 && checkint(iy) == 1)
|
if (ix >> 63 && checkint(iy) == 1)
|
||||||
x2 = -x2;
|
x2 = -x2;
|
||||||
/* Without the barrier some versions of clang hoist the 1/x2 and
|
/* Without the barrier some versions of clang hoist the 1/x2 and
|
||||||
@ -323,17 +323,17 @@ double pow(double x, double y)
|
|||||||
}
|
}
|
||||||
}
|
}
|
||||||
|
|
||||||
double_t lo;
|
double lo;
|
||||||
double_t hi = log_inline(ix, &lo);
|
double hi = log_inline(ix, &lo);
|
||||||
double_t ehi, elo;
|
double ehi, elo;
|
||||||
#if __FP_FAST_FMA
|
#if __FP_FAST_FMA
|
||||||
ehi = y * hi;
|
ehi = y * hi;
|
||||||
elo = y * lo + __builtin_fma(y, hi, -ehi);
|
elo = y * lo + __builtin_fma(y, hi, -ehi);
|
||||||
#else
|
#else
|
||||||
double_t yhi = asdouble(iy & ULLONG_NSHIFT << 27);
|
double yhi = asdouble(iy & ULLONG_NSHIFT << 27);
|
||||||
double_t ylo = y - yhi;
|
double ylo = y - yhi;
|
||||||
double_t lhi = asdouble(asuint64(hi) & ULLONG_NSHIFT << 27);
|
double lhi = asdouble(asuint64(hi) & ULLONG_NSHIFT << 27);
|
||||||
double_t llo = hi - lhi + lo;
|
double llo = hi - lhi + lo;
|
||||||
ehi = yhi * lhi;
|
ehi = yhi * lhi;
|
||||||
elo = ylo * lhi + y * llo; /* |elo| < |ehi| * 2^-25. */
|
elo = ylo * lhi + y * llo; /* |elo| < |ehi| * 2^-25. */
|
||||||
#endif
|
#endif
|
||||||
|
@ -2,8 +2,8 @@
|
|||||||
|
|
||||||
double scalbn(double x, int n)
|
double scalbn(double x, int n)
|
||||||
{
|
{
|
||||||
union {double f; uint64_t i;} u;
|
union {double f; unsigned long long i;} u;
|
||||||
double_t y = x;
|
double y = x;
|
||||||
|
|
||||||
if (n > 1023) {
|
if (n > 1023) {
|
||||||
y *= 0x1p1023;
|
y *= 0x1p1023;
|
||||||
@ -26,7 +26,7 @@ double scalbn(double x, int n)
|
|||||||
n = -1022;
|
n = -1022;
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
u.i = (uint64_t)(0x3ff+n)<<52;
|
u.i = (unsigned long long)(0x3ff+n)<<52;
|
||||||
x = y * u.f;
|
x = y * u.f;
|
||||||
return x;
|
return x;
|
||||||
}
|
}
|
||||||
|
@ -45,7 +45,7 @@
|
|||||||
double sin(double x)
|
double sin(double x)
|
||||||
{
|
{
|
||||||
double y[2];
|
double y[2];
|
||||||
uint32_t ix;
|
unsigned int ix;
|
||||||
unsigned n;
|
unsigned n;
|
||||||
|
|
||||||
/* High word of x. */
|
/* High word of x. */
|
||||||
|
@ -4,24 +4,24 @@
|
|||||||
#define FENV_SUPPORT 1
|
#define FENV_SUPPORT 1
|
||||||
|
|
||||||
/* returns a*b*2^-32 - e, with error 0 <= e < 1. */
|
/* returns a*b*2^-32 - e, with error 0 <= e < 1. */
|
||||||
static inline uint32_t mul32(uint32_t a, uint32_t b)
|
static inline unsigned int mul32(unsigned int a, unsigned int b)
|
||||||
{
|
{
|
||||||
return (uint64_t)a*b >> 32;
|
return (unsigned long long)a*b >> 32;
|
||||||
}
|
}
|
||||||
|
|
||||||
/* returns a*b*2^-64 - e, with error 0 <= e < 3. */
|
/* returns a*b*2^-64 - e, with error 0 <= e < 3. */
|
||||||
static inline uint64_t mul64(uint64_t a, uint64_t b)
|
static inline unsigned long long mul64(unsigned long long a, unsigned long long b)
|
||||||
{
|
{
|
||||||
uint64_t ahi = a>>32;
|
unsigned long long ahi = a>>32;
|
||||||
uint64_t alo = a&0xffffffff;
|
unsigned long long alo = a&0xffffffff;
|
||||||
uint64_t bhi = b>>32;
|
unsigned long long bhi = b>>32;
|
||||||
uint64_t blo = b&0xffffffff;
|
unsigned long long blo = b&0xffffffff;
|
||||||
return ahi*bhi + (ahi*blo >> 32) + (alo*bhi >> 32);
|
return ahi*bhi + (ahi*blo >> 32) + (alo*bhi >> 32);
|
||||||
}
|
}
|
||||||
|
|
||||||
double sqrt(double x)
|
double sqrt(double x)
|
||||||
{
|
{
|
||||||
uint64_t ix, top, m;
|
unsigned long long ix, top, m;
|
||||||
|
|
||||||
/* special case handling. */
|
/* special case handling. */
|
||||||
ix = asuint64(x);
|
ix = asuint64(x);
|
||||||
@ -103,11 +103,11 @@ double sqrt(double x)
|
|||||||
and after switching to 64 bit
|
and after switching to 64 bit
|
||||||
m: 2.62 r: 0.64, s: 2.62, d: 2.62, u: 2.62, three: 2.62 */
|
m: 2.62 r: 0.64, s: 2.62, d: 2.62, u: 2.62, three: 2.62 */
|
||||||
|
|
||||||
static const uint64_t three = 0xc0000000;
|
static const unsigned long long three = 0xc0000000;
|
||||||
uint64_t r, s, d, u, i;
|
unsigned long long r, s, d, u, i;
|
||||||
|
|
||||||
i = (ix >> 46) % 128;
|
i = (ix >> 46) % 128;
|
||||||
r = (uint32_t)__rsqrt_tab[i] << 16;
|
r = (unsigned int)__rsqrt_tab[i] << 16;
|
||||||
/* |r sqrt(m) - 1| < 0x1.fdp-9 */
|
/* |r sqrt(m) - 1| < 0x1.fdp-9 */
|
||||||
s = mul32(m>>32, r);
|
s = mul32(m>>32, r);
|
||||||
/* |s/sqrt(m) - 1| < 0x1.fdp-9 */
|
/* |s/sqrt(m) - 1| < 0x1.fdp-9 */
|
||||||
@ -134,7 +134,7 @@ double sqrt(double x)
|
|||||||
compute nearest rounded result:
|
compute nearest rounded result:
|
||||||
the nearest result to 52 bits is either s or s+0x1p-52,
|
the nearest result to 52 bits is either s or s+0x1p-52,
|
||||||
we can decide by comparing (2^52 s + 0.5)^2 to 2^104 m. */
|
we can decide by comparing (2^52 s + 0.5)^2 to 2^104 m. */
|
||||||
uint64_t d0, d1, d2;
|
unsigned long long d0, d1, d2;
|
||||||
double y, t;
|
double y, t;
|
||||||
d0 = (m << 42) - s*s;
|
d0 = (m << 42) - s*s;
|
||||||
d1 = s - d0;
|
d1 = s - d0;
|
||||||
@ -147,7 +147,7 @@ double sqrt(double x)
|
|||||||
/* handle rounding modes and inexact exception:
|
/* handle rounding modes and inexact exception:
|
||||||
only (s+1)^2 == 2^42 m case is exact otherwise
|
only (s+1)^2 == 2^42 m case is exact otherwise
|
||||||
add a tiny value to cause the fenv effects. */
|
add a tiny value to cause the fenv effects. */
|
||||||
uint64_t tiny = predict_false(d2==0) ? 0 : 0x0010000000000000;
|
unsigned long long tiny = predict_false(d2==0) ? 0 : 0x0010000000000000;
|
||||||
tiny |= (d1^d2) & 0x8000000000000000;
|
tiny |= (d1^d2) & 0x8000000000000000;
|
||||||
t = asdouble(tiny);
|
t = asdouble(tiny);
|
||||||
y = eval_as_double(y + t);
|
y = eval_as_double(y + t);
|
||||||
|
@ -1,5 +1,5 @@
|
|||||||
#include "sqrt_data.h"
|
#include "sqrt_data.h"
|
||||||
const uint16_t __rsqrt_tab[128] = {
|
const unsigned short __rsqrt_tab[128] = {
|
||||||
0xb451,0xb2f0,0xb196,0xb044,0xaef9,0xadb6,0xac79,0xab43,
|
0xb451,0xb2f0,0xb196,0xb044,0xaef9,0xadb6,0xac79,0xab43,
|
||||||
0xaa14,0xa8eb,0xa7c8,0xa6aa,0xa592,0xa480,0xa373,0xa26b,
|
0xaa14,0xa8eb,0xa7c8,0xa6aa,0xa592,0xa480,0xa373,0xa26b,
|
||||||
0xa168,0xa06a,0x9f70,0x9e7b,0x9d8a,0x9c9d,0x9bb5,0x9ad1,
|
0xa168,0xa06a,0x9f70,0x9e7b,0x9d8a,0x9c9d,0x9bb5,0x9ad1,
|
||||||
|
@ -7,6 +7,6 @@
|
|||||||
if x in [2,4): i = (int)(32*x-64);
|
if x in [2,4): i = (int)(32*x-64);
|
||||||
__rsqrt_tab[i]*2^-16 is estimating 1/sqrt(x) with small relative error:
|
__rsqrt_tab[i]*2^-16 is estimating 1/sqrt(x) with small relative error:
|
||||||
|__rsqrt_tab[i]*0x1p-16*sqrt(x) - 1| < -0x1.fdp-9 < 2^-8 */
|
|__rsqrt_tab[i]*0x1p-16*sqrt(x) - 1| < -0x1.fdp-9 < 2^-8 */
|
||||||
extern const uint16_t __rsqrt_tab[128];
|
extern const unsigned short __rsqrt_tab[128];
|
||||||
|
|
||||||
#endif
|
#endif
|
||||||
|
@ -44,7 +44,7 @@
|
|||||||
double tan(double x)
|
double tan(double x)
|
||||||
{
|
{
|
||||||
double y[2];
|
double y[2];
|
||||||
uint32_t ix;
|
unsigned int ix;
|
||||||
unsigned n;
|
unsigned n;
|
||||||
|
|
||||||
GET_HIGH_WORD(ix, x);
|
GET_HIGH_WORD(ix, x);
|
||||||
|
@ -2,9 +2,9 @@
|
|||||||
|
|
||||||
double trunc(double x)
|
double trunc(double x)
|
||||||
{
|
{
|
||||||
union {double f; uint64_t i;} u = {x};
|
union {double f; unsigned long long i;} u = {x};
|
||||||
int e = (int)(u.i >> 52 & 0x7ff) - 0x3ff + 12;
|
int e = (int)(u.i >> 52 & 0x7ff) - 0x3ff + 12;
|
||||||
uint64_t m;
|
unsigned long long m;
|
||||||
|
|
||||||
if (e >= 52 + 12)
|
if (e >= 52 + 12)
|
||||||
return x;
|
return x;
|
||||||
|
Loading…
x
Reference in New Issue
Block a user