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@ -132,76 +132,110 @@ static union {
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/* Get two 32 bit ints from a double. */
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#define EXTRACT_WORDS_L(ix0,ix1,d) \
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do { \
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ieee_double_shape_type_little ew_u; \
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ew_u.value = (d); \
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(ix0) = ew_u.parts.msw; \
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(ix1) = ew_u.parts.lsw; \
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#define EXTRACT_WORDS_L(ix0,ix1,d) \
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do { \
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ieee_double_shape_type_little ew_u; \
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ew_u.value = (d); \
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(ix0) = ew_u.parts.msw; \
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(ix1) = ew_u.parts.lsw; \
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} while (0)
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/* Set a double from two 32 bit ints. */
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#define INSERT_WORDS_L(d,ix0,ix1) \
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do { \
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ieee_double_shape_type_little iw_u; \
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iw_u.parts.msw = (ix0); \
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iw_u.parts.lsw = (ix1); \
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(d) = iw_u.value; \
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#define INSERT_WORDS_L(d,ix0,ix1) \
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do { \
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ieee_double_shape_type_little iw_u; \
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iw_u.parts.msw = (ix0); \
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iw_u.parts.lsw = (ix1); \
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(d) = iw_u.value; \
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} while (0)
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/* Get two 32 bit ints from a double. */
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#define EXTRACT_WORDS_B(ix0,ix1,d) \
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do { \
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ieee_double_shape_type_big ew_u; \
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ew_u.value = (d); \
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(ix0) = ew_u.parts.msw; \
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(ix1) = ew_u.parts.lsw; \
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#define EXTRACT_WORDS_B(ix0,ix1,d) \
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do { \
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ieee_double_shape_type_big ew_u; \
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ew_u.value = (d); \
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(ix0) = ew_u.parts.msw; \
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(ix1) = ew_u.parts.lsw; \
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} while (0)
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/* Set a double from two 32 bit ints. */
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#define INSERT_WORDS_B(d,ix0,ix1) \
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do { \
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ieee_double_shape_type_big iw_u; \
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iw_u.parts.msw = (ix0); \
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iw_u.parts.lsw = (ix1); \
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(d) = iw_u.value; \
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#define INSERT_WORDS_B(d,ix0,ix1) \
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do { \
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ieee_double_shape_type_big iw_u; \
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iw_u.parts.msw = (ix0); \
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iw_u.parts.lsw = (ix1); \
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(d) = iw_u.value; \
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} while (0)
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/* Get the more significant 32 bit int from a double. */
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#define GET_HIGH_WORD_L(i,d) \
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do { \
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ieee_double_shape_type_little gh_u; \
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gh_u.value = (d); \
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(i) = gh_u.parts.msw; \
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#define GET_HIGH_WORD_L(i,d) \
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do { \
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ieee_double_shape_type_little gh_u; \
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gh_u.value = (d); \
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(i) = gh_u.parts.msw; \
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} while (0)
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/* Get the more significant 32 bit int from a double. */
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#define GET_HIGH_WORD_B(i,d) \
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do { \
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ieee_double_shape_type_big gh_u; \
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gh_u.value = (d); \
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(i) = gh_u.parts.msw; \
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#define GET_HIGH_WORD_B(i,d) \
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do { \
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ieee_double_shape_type_big gh_u; \
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gh_u.value = (d); \
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(i) = gh_u.parts.msw; \
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} while (0)
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/* Set the more significant 32 bits of a double from an int. */
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#define SET_HIGH_WORD_L(d,v) \
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do { \
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ieee_double_shape_type_little sh_u; \
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sh_u.value = (d); \
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sh_u.parts.msw = (v); \
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(d) = sh_u.value; \
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#define SET_HIGH_WORD_L(d,v) \
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do { \
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ieee_double_shape_type_little sh_u; \
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sh_u.value = (d); \
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sh_u.parts.msw = (v); \
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(d) = sh_u.value; \
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} while (0)
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/* Set the more significant 32 bits of a double from an int. */
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#define SET_HIGH_WORD_B(d,v) \
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do { \
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ieee_double_shape_type_big sh_u; \
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sh_u.value = (d); \
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sh_u.parts.msw = (v); \
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(d) = sh_u.value; \
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#define SET_HIGH_WORD_B(d,v) \
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do { \
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ieee_double_shape_type_big sh_u; \
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sh_u.value = (d); \
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sh_u.parts.msw = (v); \
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(d) = sh_u.value; \
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} while (0)
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/* Set the less significant 32 bits of a double from an int. */
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#define SET_LOW_WORD_L(d,v) \
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do { \
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ieee_double_shape_type_little sh_u; \
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sh_u.value = (d); \
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sh_u.parts.lsw = (v); \
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(d) = sh_u.value; \
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} while (0)
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/* Set the more significant 32 bits of a double from an int. */
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#define SET_LOW_WORD_B(d,v) \
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do { \
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ieee_double_shape_type_big sh_u; \
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sh_u.value = (d); \
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sh_u.parts.lsw = (v); \
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(d) = sh_u.value; \
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} while (0)
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/* Get the less significant 32 bit int from a double. */
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#define GET_LOW_WORD_L(i,d) \
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do { \
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ieee_double_shape_type_little gl_u; \
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gl_u.value = (d); \
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(i) = gl_u.parts.lsw; \
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} while (0)
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/* Get the less significant 32 bit int from a double. */
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#define GET_LOW_WORD_B(i,d) \
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do { \
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ieee_double_shape_type_big gl_u; \
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gl_u.value = (d); \
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(i) = gl_u.parts.lsw; \
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} while (0)
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/*
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@ -262,6 +296,22 @@ typedef union
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SET_HIGH_WORD_B(d,v); \
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} while (0)
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#define GET_LOW_WORD(d,v) \
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do { \
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if (is_little_endian()) \
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GET_LOW_WORD_L(d,v); \
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else \
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GET_LOW_WORD_B(d,v); \
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} while (0)
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#define SET_LOW_WORD(d,v) \
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do { \
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if (is_little_endian()) \
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SET_LOW_WORD_L(d,v); \
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else \
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SET_LOW_WORD_B(d,v); \
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} while (0)
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#define __HI(x) (is_little_endian() ? __HIL(x) : __HIB(x))
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#define __LO(x) (is_little_endian() ? __LOL(x) : __LOB(x))
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@ -314,12 +364,219 @@ TWO52[2]={
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-4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */
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};
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#ifdef __STDC__
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static const double
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#else
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static double
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#endif
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atanhi[] = {
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4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
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7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
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9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
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1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
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};
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#ifdef __STDC__
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static const double
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#else
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static double
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#endif
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atanlo[] = {
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2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
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3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
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1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
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6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
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};
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#ifdef __STDC__
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static const double
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#else
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static double
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#endif
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aT[] = {
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3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
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-1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
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1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
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-1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
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9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
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-7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
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6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
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-5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
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4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
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-3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
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1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
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};
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#ifdef __STDC__
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static const double
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#else
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static double
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#endif
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zero = 0.0,
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pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
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pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
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pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
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pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
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#ifdef __STDC__
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static const double
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#else
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static double
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#endif
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bp[] = {1.0, 1.5,},
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dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
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dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
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two = 2.0,
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two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */
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two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
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twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */
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/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
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L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
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L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
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L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
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L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
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L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
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L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
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P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
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P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
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P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
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P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
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P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
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lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
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lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
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lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
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ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
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cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
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cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
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cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
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ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
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ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
|
|
|
|
|
ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
|
|
|
|
|
|
|
|
|
|
static double freebsd_sqrt(double x);
|
|
|
|
|
static double freebsd_floor(double x);
|
|
|
|
|
static double freebsd_ceil(double x);
|
|
|
|
|
static double freebsd_fabs(double x);
|
|
|
|
|
static double freebsd_rint(double x);
|
|
|
|
|
static int freebsd_isnan(double x);
|
|
|
|
|
static double freebsd_atan(double x);
|
|
|
|
|
static double freebsd_atan2(double y, double x);
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
static double freebsd_atan(double x)
|
|
|
|
|
{
|
|
|
|
|
double w,s1,s2,z;
|
|
|
|
|
int32_t ix,hx,id;
|
|
|
|
|
|
|
|
|
|
GET_HIGH_WORD(hx,x);
|
|
|
|
|
ix = hx&0x7fffffff;
|
|
|
|
|
if(ix>=0x44100000) { /* if |x| >= 2^66 */
|
|
|
|
|
u_int32_t low;
|
|
|
|
|
GET_LOW_WORD(low,x);
|
|
|
|
|
if(ix>0x7ff00000||
|
|
|
|
|
(ix==0x7ff00000&&(low!=0)))
|
|
|
|
|
return x+x; /* NaN */
|
|
|
|
|
if(hx>0) return atanhi[3]+*(volatile double *)&atanlo[3];
|
|
|
|
|
else return -atanhi[3]-*(volatile double *)&atanlo[3];
|
|
|
|
|
} if (ix < 0x3fdc0000) { /* |x| < 0.4375 */
|
|
|
|
|
if (ix < 0x3e400000) { /* |x| < 2^-27 */
|
|
|
|
|
if(huge+x>one) return x; /* raise inexact */
|
|
|
|
|
}
|
|
|
|
|
id = -1;
|
|
|
|
|
} else {
|
|
|
|
|
x = freebsd_fabs(x);
|
|
|
|
|
if (ix < 0x3ff30000) { /* |x| < 1.1875 */
|
|
|
|
|
if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */
|
|
|
|
|
id = 0; x = (2.0*x-one)/(2.0+x);
|
|
|
|
|
} else { /* 11/16<=|x|< 19/16 */
|
|
|
|
|
id = 1; x = (x-one)/(x+one);
|
|
|
|
|
}
|
|
|
|
|
} else {
|
|
|
|
|
if (ix < 0x40038000) { /* |x| < 2.4375 */
|
|
|
|
|
id = 2; x = (x-1.5)/(one+1.5*x);
|
|
|
|
|
} else { /* 2.4375 <= |x| < 2^66 */
|
|
|
|
|
id = 3; x = -1.0/x;
|
|
|
|
|
}
|
|
|
|
|
}}
|
|
|
|
|
/* end of argument reduction */
|
|
|
|
|
z = x*x;
|
|
|
|
|
w = z*z;
|
|
|
|
|
/* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
|
|
|
|
|
s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
|
|
|
|
|
s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
|
|
|
|
|
if (id<0) return x - x*(s1+s2);
|
|
|
|
|
else {
|
|
|
|
|
z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
|
|
|
|
|
return (hx<0)? -z:z;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
static double freebsd_atan2(double y, double x)
|
|
|
|
|
{
|
|
|
|
|
double z;
|
|
|
|
|
int32_t k,m,hx,hy,ix,iy;
|
|
|
|
|
u_int32_t lx,ly;
|
|
|
|
|
|
|
|
|
|
EXTRACT_WORDS(hx,lx,x);
|
|
|
|
|
ix = hx&0x7fffffff;
|
|
|
|
|
EXTRACT_WORDS(hy,ly,y);
|
|
|
|
|
iy = hy&0x7fffffff;
|
|
|
|
|
if(((ix|((lx|-lx)>>31))>0x7ff00000)||
|
|
|
|
|
((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */
|
|
|
|
|
return x+y;
|
|
|
|
|
if(hx==0x3ff00000&&lx==0) return freebsd_atan(y); /* x=1.0 */
|
|
|
|
|
m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
|
|
|
|
|
|
|
|
|
|
/* when y = 0 */
|
|
|
|
|
if((iy|ly)==0) {
|
|
|
|
|
switch(m) {
|
|
|
|
|
case 0:
|
|
|
|
|
case 1: return y; /* atan(+-0,+anything)=+-0 */
|
|
|
|
|
case 2: return pi+tiny;/* atan(+0,-anything) = pi */
|
|
|
|
|
case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
/* when x = 0 */
|
|
|
|
|
if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
|
|
|
|
|
|
|
|
|
|
/* when x is INF */
|
|
|
|
|
if(ix==0x7ff00000) {
|
|
|
|
|
if(iy==0x7ff00000) {
|
|
|
|
|
switch(m) {
|
|
|
|
|
case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
|
|
|
|
|
case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
|
|
|
|
|
case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
|
|
|
|
|
case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
|
|
|
|
|
}
|
|
|
|
|
} else {
|
|
|
|
|
switch(m) {
|
|
|
|
|
case 0: return zero ; /* atan(+...,+INF) */
|
|
|
|
|
case 1: return -zero ; /* atan(-...,+INF) */
|
|
|
|
|
case 2: return pi+tiny ; /* atan(+...,-INF) */
|
|
|
|
|
case 3: return -pi-tiny ; /* atan(-...,-INF) */
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
/* when y is INF */
|
|
|
|
|
if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
|
|
|
|
|
|
|
|
|
|
/* compute y/x */
|
|
|
|
|
k = (iy-ix)>>20;
|
|
|
|
|
if(k > 60) { /* |y/x| > 2**60 */
|
|
|
|
|
z=pi_o_2+0.5*pi_lo;
|
|
|
|
|
m&=1;
|
|
|
|
|
}
|
|
|
|
|
else if(hx<0&&k<-60) z=0.0; /* 0 > |y|/x > -2**-60 */
|
|
|
|
|
else z=freebsd_atan(fabs(y/x)); /* safe to do y/x */
|
|
|
|
|
switch (m) {
|
|
|
|
|
case 0: return z ; /* atan(+,+) */
|
|
|
|
|
case 1: return -z ; /* atan(-,+) */
|
|
|
|
|
case 2: return pi-(z-pi_lo);/* atan(+,-) */
|
|
|
|
|
default: /* case 3 */
|
|
|
|
|
return (z-pi_lo)-pi;/* atan(-,-) */
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
static double freebsd_sqrt(double x) /* wrapper sqrt */
|
|
|
|
|
{
|
|
|
|
|
@ -777,6 +1034,271 @@ freebsd_fmaxf(float x, float y)
|
|
|
|
|
return (x > y ? x : y);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
static double
|
|
|
|
|
freebsd_copysign(double x, double y)
|
|
|
|
|
{
|
|
|
|
|
u_int32_t hx,hy;
|
|
|
|
|
GET_HIGH_WORD(hx,x);
|
|
|
|
|
GET_HIGH_WORD(hy,y);
|
|
|
|
|
SET_HIGH_WORD(x,(hx&0x7fffffff)|(hy&0x80000000));
|
|
|
|
|
return x;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
static double
|
|
|
|
|
freebsd_scalbn(double x, int n)
|
|
|
|
|
{
|
|
|
|
|
int32_t k,hx,lx;
|
|
|
|
|
EXTRACT_WORDS(hx,lx,x);
|
|
|
|
|
k = (hx&0x7ff00000)>>20; /* extract exponent */
|
|
|
|
|
if (k==0) { /* 0 or subnormal x */
|
|
|
|
|
if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */
|
|
|
|
|
x *= two54;
|
|
|
|
|
GET_HIGH_WORD(hx,x);
|
|
|
|
|
k = ((hx&0x7ff00000)>>20) - 54;
|
|
|
|
|
if (n< -50000) return tiny*x; /*underflow*/
|
|
|
|
|
}
|
|
|
|
|
if (k==0x7ff) return x+x; /* NaN or Inf */
|
|
|
|
|
k = k+n;
|
|
|
|
|
if (k > 0x7fe) return huge*freebsd_copysign(huge,x); /* overflow */
|
|
|
|
|
if (k > 0) /* normal result */
|
|
|
|
|
{SET_HIGH_WORD(x,(hx&0x800fffff)|(k<<20)); return x;}
|
|
|
|
|
if (k <= -54) {
|
|
|
|
|
if (n > 50000) /* in case integer overflow in n+k */
|
|
|
|
|
return huge*freebsd_copysign(huge,x); /*overflow*/
|
|
|
|
|
else return tiny*freebsd_copysign(tiny,x); /*underflow*/
|
|
|
|
|
}
|
|
|
|
|
k += 54; /* subnormal result */
|
|
|
|
|
SET_HIGH_WORD(x,(hx&0x800fffff)|(k<<20));
|
|
|
|
|
return x*twom54;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
static double
|
|
|
|
|
freebsd_pow(double x, double y)
|
|
|
|
|
{
|
|
|
|
|
double z,ax,z_h,z_l,p_h,p_l;
|
|
|
|
|
double y1,t1,t2,r,s,t,u,v,w;
|
|
|
|
|
int32_t i,j,k,yisint,n;
|
|
|
|
|
int32_t hx,hy,ix,iy;
|
|
|
|
|
u_int32_t lx,ly;
|
|
|
|
|
|
|
|
|
|
EXTRACT_WORDS(hx,lx,x);
|
|
|
|
|
EXTRACT_WORDS(hy,ly,y);
|
|
|
|
|
ix = hx&0x7fffffff; iy = hy&0x7fffffff;
|
|
|
|
|
|
|
|
|
|
/* y==zero: x**0 = 1 */
|
|
|
|
|
if((iy|ly)==0) return one;
|
|
|
|
|
|
|
|
|
|
/* x==1: 1**y = 1, even if y is NaN */
|
|
|
|
|
if (hx==0x3ff00000 && lx == 0) return one;
|
|
|
|
|
|
|
|
|
|
/* y!=zero: result is NaN if either arg is NaN */
|
|
|
|
|
if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) ||
|
|
|
|
|
iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0)))
|
|
|
|
|
return (x+0.0)+(y+0.0);
|
|
|
|
|
|
|
|
|
|
/* determine if y is an odd int when x < 0
|
|
|
|
|
* yisint = 0 ... y is not an integer
|
|
|
|
|
* yisint = 1 ... y is an odd int
|
|
|
|
|
* yisint = 2 ... y is an even int
|
|
|
|
|
*/
|
|
|
|
|
yisint = 0;
|
|
|
|
|
if(hx<0) {
|
|
|
|
|
if(iy>=0x43400000) yisint = 2; /* even integer y */
|
|
|
|
|
else if(iy>=0x3ff00000) {
|
|
|
|
|
k = (iy>>20)-0x3ff; /* exponent */
|
|
|
|
|
if(k>20) {
|
|
|
|
|
j = ly>>(52-k);
|
|
|
|
|
if((j<<(52-k))==ly) yisint = 2-(j&1);
|
|
|
|
|
} else if(ly==0) {
|
|
|
|
|
j = iy>>(20-k);
|
|
|
|
|
if((j<<(20-k))==iy) yisint = 2-(j&1);
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
/* special value of y */
|
|
|
|
|
if(ly==0) {
|
|
|
|
|
if (iy==0x7ff00000) { /* y is +-inf */
|
|
|
|
|
if(((ix-0x3ff00000)|lx)==0)
|
|
|
|
|
return one; /* (-1)**+-inf is NaN */
|
|
|
|
|
else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */
|
|
|
|
|
return (hy>=0)? y: zero;
|
|
|
|
|
else /* (|x|<1)**-,+inf = inf,0 */
|
|
|
|
|
return (hy<0)?-y: zero;
|
|
|
|
|
}
|
|
|
|
|
if(iy==0x3ff00000) { /* y is +-1 */
|
|
|
|
|
if(hy<0) return one/x; else return x;
|
|
|
|
|
}
|
|
|
|
|
if(hy==0x40000000) return x*x; /* y is 2 */
|
|
|
|
|
if(hy==0x40080000) return x*x*x; /* y is 3 */
|
|
|
|
|
if(hy==0x40100000) { /* y is 4 */
|
|
|
|
|
u = x*x;
|
|
|
|
|
return u*u;
|
|
|
|
|
}
|
|
|
|
|
if(hy==0x3fe00000) { /* y is 0.5 */
|
|
|
|
|
if(hx>=0) /* x >= +0 */
|
|
|
|
|
return sqrt(x);
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
ax = fabs(x);
|
|
|
|
|
/* special value of x */
|
|
|
|
|
if(lx==0) {
|
|
|
|
|
if(ix==0x7ff00000||ix==0||ix==0x3ff00000){
|
|
|
|
|
z = ax; /*x is +-0,+-inf,+-1*/
|
|
|
|
|
if(hy<0) z = one/z; /* z = (1/|x|) */
|
|
|
|
|
if(hx<0) {
|
|
|
|
|
if(((ix-0x3ff00000)|yisint)==0) {
|
|
|
|
|
z = (z-z)/(z-z); /* (-1)**non-int is NaN */
|
|
|
|
|
} else if(yisint==1)
|
|
|
|
|
z = -z; /* (x<0)**odd = -(|x|**odd) */
|
|
|
|
|
}
|
|
|
|
|
return z;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
/* CYGNUS LOCAL + fdlibm-5.3 fix: This used to be
|
|
|
|
|
n = (hx>>31)+1;
|
|
|
|
|
but ANSI C says a right shift of a signed negative quantity is
|
|
|
|
|
implementation defined. */
|
|
|
|
|
n = ((u_int32_t)hx>>31)-1;
|
|
|
|
|
|
|
|
|
|
/* (x<0)**(non-int) is NaN */
|
|
|
|
|
if((n|yisint)==0) return (x-x)/(x-x);
|
|
|
|
|
|
|
|
|
|
s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
|
|
|
|
|
if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */
|
|
|
|
|
|
|
|
|
|
/* |y| is huge */
|
|
|
|
|
if(iy>0x41e00000) { /* if |y| > 2**31 */
|
|
|
|
|
if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */
|
|
|
|
|
if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
|
|
|
|
|
if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
|
|
|
|
|
}
|
|
|
|
|
/* over/underflow if x is not close to one */
|
|
|
|
|
if(ix<0x3fefffff) return (hy<0)? s*huge*huge:s*tiny*tiny;
|
|
|
|
|
if(ix>0x3ff00000) return (hy>0)? s*huge*huge:s*tiny*tiny;
|
|
|
|
|
/* now |1-x| is tiny <= 2**-20, suffice to compute
|
|
|
|
|
log(x) by x-x^2/2+x^3/3-x^4/4 */
|
|
|
|
|
t = ax-one; /* t has 20 trailing zeros */
|
|
|
|
|
w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));
|
|
|
|
|
u = ivln2_h*t; /* ivln2_h has 21 sig. bits */
|
|
|
|
|
v = t*ivln2_l-w*ivln2;
|
|
|
|
|
t1 = u+v;
|
|
|
|
|
SET_LOW_WORD(t1,0);
|
|
|
|
|
t2 = v-(t1-u);
|
|
|
|
|
} else {
|
|
|
|
|
double ss,s2,s_h,s_l,t_h,t_l;
|
|
|
|
|
n = 0;
|
|
|
|
|
/* take care subnormal number */
|
|
|
|
|
if(ix<0x00100000)
|
|
|
|
|
{ax *= two53; n -= 53; GET_HIGH_WORD(ix,ax); }
|
|
|
|
|
n += ((ix)>>20)-0x3ff;
|
|
|
|
|
j = ix&0x000fffff;
|
|
|
|
|
/* determine interval */
|
|
|
|
|
ix = j|0x3ff00000; /* normalize ix */
|
|
|
|
|
if(j<=0x3988E) k=0; /* |x|<sqrt(3/2) */
|
|
|
|
|
else if(j<0xBB67A) k=1; /* |x|<sqrt(3) */
|
|
|
|
|
else {k=0;n+=1;ix -= 0x00100000;}
|
|
|
|
|
SET_HIGH_WORD(ax,ix);
|
|
|
|
|
|
|
|
|
|
/* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
|
|
|
|
|
u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
|
|
|
|
|
v = one/(ax+bp[k]);
|
|
|
|
|
ss = u*v;
|
|
|
|
|
s_h = ss;
|
|
|
|
|
SET_LOW_WORD(s_h,0);
|
|
|
|
|
/* t_h=ax+bp[k] High */
|
|
|
|
|
t_h = zero;
|
|
|
|
|
SET_HIGH_WORD(t_h,((ix>>1)|0x20000000)+0x00080000+(k<<18));
|
|
|
|
|
t_l = ax - (t_h-bp[k]);
|
|
|
|
|
s_l = v*((u-s_h*t_h)-s_h*t_l);
|
|
|
|
|
/* compute log(ax) */
|
|
|
|
|
s2 = ss*ss;
|
|
|
|
|
r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
|
|
|
|
|
r += s_l*(s_h+ss);
|
|
|
|
|
s2 = s_h*s_h;
|
|
|
|
|
t_h = 3.0+s2+r;
|
|
|
|
|
SET_LOW_WORD(t_h,0);
|
|
|
|
|
t_l = r-((t_h-3.0)-s2);
|
|
|
|
|
/* u+v = ss*(1+...) */
|
|
|
|
|
u = s_h*t_h;
|
|
|
|
|
v = s_l*t_h+t_l*ss;
|
|
|
|
|
/* 2/(3log2)*(ss+...) */
|
|
|
|
|
p_h = u+v;
|
|
|
|
|
SET_LOW_WORD(p_h,0);
|
|
|
|
|
p_l = v-(p_h-u);
|
|
|
|
|
z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
|
|
|
|
|
z_l = cp_l*p_h+p_l*cp+dp_l[k];
|
|
|
|
|
/* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
|
|
|
|
|
t = (double)n;
|
|
|
|
|
t1 = (((z_h+z_l)+dp_h[k])+t);
|
|
|
|
|
SET_LOW_WORD(t1,0);
|
|
|
|
|
t2 = z_l-(((t1-t)-dp_h[k])-z_h);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
/* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
|
|
|
|
|
y1 = y;
|
|
|
|
|
SET_LOW_WORD(y1,0);
|
|
|
|
|
p_l = (y-y1)*t1+y*t2;
|
|
|
|
|
p_h = y1*t1;
|
|
|
|
|
z = p_l+p_h;
|
|
|
|
|
EXTRACT_WORDS(j,i,z);
|
|
|
|
|
if (j>=0x40900000) { /* z >= 1024 */
|
|
|
|
|
if(((j-0x40900000)|i)!=0) /* if z > 1024 */
|
|
|
|
|
return s*huge*huge; /* overflow */
|
|
|
|
|
else {
|
|
|
|
|
if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */
|
|
|
|
|
}
|
|
|
|
|
} else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */
|
|
|
|
|
if(((j-0xc090cc00)|i)!=0) /* z < -1075 */
|
|
|
|
|
return s*tiny*tiny; /* underflow */
|
|
|
|
|
else {
|
|
|
|
|
if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
/*
|
|
|
|
|
* compute 2**(p_h+p_l)
|
|
|
|
|
*/
|
|
|
|
|
i = j&0x7fffffff;
|
|
|
|
|
k = (i>>20)-0x3ff;
|
|
|
|
|
n = 0;
|
|
|
|
|
if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */
|
|
|
|
|
n = j+(0x00100000>>(k+1));
|
|
|
|
|
k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */
|
|
|
|
|
t = zero;
|
|
|
|
|
SET_HIGH_WORD(t,n&~(0x000fffff>>k));
|
|
|
|
|
n = ((n&0x000fffff)|0x00100000)>>(20-k);
|
|
|
|
|
if(j<0) n = -n;
|
|
|
|
|
p_h -= t;
|
|
|
|
|
}
|
|
|
|
|
t = p_l+p_h;
|
|
|
|
|
SET_LOW_WORD(t,0);
|
|
|
|
|
u = t*lg2_h;
|
|
|
|
|
v = (p_l-(t-p_h))*lg2+t*lg2_l;
|
|
|
|
|
z = u+v;
|
|
|
|
|
w = v-(z-u);
|
|
|
|
|
t = z*z;
|
|
|
|
|
t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
|
|
|
|
|
r = (z*t1)/(t1-two)-(w+z*w);
|
|
|
|
|
z = one-(r-z);
|
|
|
|
|
GET_HIGH_WORD(j,z);
|
|
|
|
|
j += (n<<20);
|
|
|
|
|
if((j>>20)<=0) z = freebsd_scalbn(z,n); /* subnormal output */
|
|
|
|
|
else SET_HIGH_WORD(z,j);
|
|
|
|
|
return s*z;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
double atan(double x)
|
|
|
|
|
{
|
|
|
|
|
return freebsd_atan(x);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
double atan2(double y, double x)
|
|
|
|
|
{
|
|
|
|
|
return freebsd_atan2(y, x);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
double sqrt(double x)
|
|
|
|
|
{
|
|
|
|
|
return freebsd_sqrt(x);
|
|
|
|
|
@ -863,3 +1385,14 @@ fmaxf(float x, float y)
|
|
|
|
|
return freebsd_fmaxf(x, y);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
double
|
|
|
|
|
pow(double x, double y)
|
|
|
|
|
{
|
|
|
|
|
return freebsd_pow(x, y);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
double
|
|
|
|
|
scalbn(double x, int n)
|
|
|
|
|
{
|
|
|
|
|
return freebsd_scalbn(x, n);
|
|
|
|
|
}
|
|
|
|
|
|