diff options
Diffstat (limited to 'numpy/core/src/npymath')
| -rw-r--r-- | numpy/core/src/npymath/arm64_exports.c | 9 | ||||
| -rw-r--r-- | numpy/core/src/npymath/halffloat.c | 555 | ||||
| -rw-r--r-- | numpy/core/src/npymath/halffloat.cpp | 238 | ||||
| -rw-r--r-- | numpy/core/src/npymath/npy_math_complex.c.src | 458 | ||||
| -rw-r--r-- | numpy/core/src/npymath/npy_math_private.h | 4 |
5 files changed, 690 insertions, 574 deletions
diff --git a/numpy/core/src/npymath/arm64_exports.c b/numpy/core/src/npymath/arm64_exports.c index d65bb4f6d..dfa8054d7 100644 --- a/numpy/core/src/npymath/arm64_exports.c +++ b/numpy/core/src/npymath/arm64_exports.c @@ -1,12 +1,14 @@ #if defined(__arm64__) && defined(__APPLE__) #include <math.h> -/* +/* * Export these for scipy, since the SciPy build for macos arm64 * downloads the macos x86_64 NumPy, and does not error when the * linker fails to use npymathlib.a. Importing numpy will expose * these external functions * See https://github.com/numpy/numpy/issues/22673#issuecomment-1327520055 + * + * This file is actually compiled as part of the main module. */ double npy_asinh(double x) { @@ -20,4 +22,9 @@ double npy_copysign(double y, double x) { double npy_log1p(double x) { return log1p(x); } + +double npy_nextafter(double x, double y) { + return nextafter(x, y); +} + #endif diff --git a/numpy/core/src/npymath/halffloat.c b/numpy/core/src/npymath/halffloat.c deleted file mode 100644 index 51948c736..000000000 --- a/numpy/core/src/npymath/halffloat.c +++ /dev/null @@ -1,555 +0,0 @@ -#define NPY_NO_DEPRECATED_API NPY_API_VERSION - -#include "numpy/halffloat.h" - -/* - * This chooses between 'ties to even' and 'ties away from zero'. - */ -#define NPY_HALF_ROUND_TIES_TO_EVEN 1 -/* - * If these are 1, the conversions try to trigger underflow, - * overflow, and invalid exceptions in the FP system when needed. - */ -#define NPY_HALF_GENERATE_OVERFLOW 1 -#define NPY_HALF_GENERATE_UNDERFLOW 1 -#define NPY_HALF_GENERATE_INVALID 1 - -/* - ******************************************************************** - * HALF-PRECISION ROUTINES * - ******************************************************************** - */ - -float npy_half_to_float(npy_half h) -{ - union { float ret; npy_uint32 retbits; } conv; - conv.retbits = npy_halfbits_to_floatbits(h); - return conv.ret; -} - -double npy_half_to_double(npy_half h) -{ - union { double ret; npy_uint64 retbits; } conv; - conv.retbits = npy_halfbits_to_doublebits(h); - return conv.ret; -} - -npy_half npy_float_to_half(float f) -{ - union { float f; npy_uint32 fbits; } conv; - conv.f = f; - return npy_floatbits_to_halfbits(conv.fbits); -} - -npy_half npy_double_to_half(double d) -{ - union { double d; npy_uint64 dbits; } conv; - conv.d = d; - return npy_doublebits_to_halfbits(conv.dbits); -} - -int npy_half_iszero(npy_half h) -{ - return (h&0x7fff) == 0; -} - -int npy_half_isnan(npy_half h) -{ - return ((h&0x7c00u) == 0x7c00u) && ((h&0x03ffu) != 0x0000u); -} - -int npy_half_isinf(npy_half h) -{ - return ((h&0x7fffu) == 0x7c00u); -} - -int npy_half_isfinite(npy_half h) -{ - return ((h&0x7c00u) != 0x7c00u); -} - -int npy_half_signbit(npy_half h) -{ - return (h&0x8000u) != 0; -} - -npy_half npy_half_spacing(npy_half h) -{ - npy_half ret; - npy_uint16 h_exp = h&0x7c00u; - npy_uint16 h_sig = h&0x03ffu; - if (h_exp == 0x7c00u) { -#if NPY_HALF_GENERATE_INVALID - npy_set_floatstatus_invalid(); -#endif - ret = NPY_HALF_NAN; - } else if (h == 0x7bffu) { -#if NPY_HALF_GENERATE_OVERFLOW - npy_set_floatstatus_overflow(); -#endif - ret = NPY_HALF_PINF; - } else if ((h&0x8000u) && h_sig == 0) { /* Negative boundary case */ - if (h_exp > 0x2c00u) { /* If result is normalized */ - ret = h_exp - 0x2c00u; - } else if(h_exp > 0x0400u) { /* The result is a subnormal, but not the smallest */ - ret = 1 << ((h_exp >> 10) - 2); - } else { - ret = 0x0001u; /* Smallest subnormal half */ - } - } else if (h_exp > 0x2800u) { /* If result is still normalized */ - ret = h_exp - 0x2800u; - } else if (h_exp > 0x0400u) { /* The result is a subnormal, but not the smallest */ - ret = 1 << ((h_exp >> 10) - 1); - } else { - ret = 0x0001u; - } - - return ret; -} - -npy_half npy_half_copysign(npy_half x, npy_half y) -{ - return (x&0x7fffu) | (y&0x8000u); -} - -npy_half npy_half_nextafter(npy_half x, npy_half y) -{ - npy_half ret; - - if (npy_half_isnan(x) || npy_half_isnan(y)) { - ret = NPY_HALF_NAN; - } else if (npy_half_eq_nonan(x, y)) { - ret = x; - } else if (npy_half_iszero(x)) { - ret = (y&0x8000u) + 1; /* Smallest subnormal half */ - } else if (!(x&0x8000u)) { /* x > 0 */ - if ((npy_int16)x > (npy_int16)y) { /* x > y */ - ret = x-1; - } else { - ret = x+1; - } - } else { - if (!(y&0x8000u) || (x&0x7fffu) > (y&0x7fffu)) { /* x < y */ - ret = x-1; - } else { - ret = x+1; - } - } -#if NPY_HALF_GENERATE_OVERFLOW - if (npy_half_isinf(ret) && npy_half_isfinite(x)) { - npy_set_floatstatus_overflow(); - } -#endif - - return ret; -} - -int npy_half_eq_nonan(npy_half h1, npy_half h2) -{ - return (h1 == h2 || ((h1 | h2) & 0x7fff) == 0); -} - -int npy_half_eq(npy_half h1, npy_half h2) -{ - /* - * The equality cases are as follows: - * - If either value is NaN, never equal. - * - If the values are equal, equal. - * - If the values are both signed zeros, equal. - */ - return (!npy_half_isnan(h1) && !npy_half_isnan(h2)) && - (h1 == h2 || ((h1 | h2) & 0x7fff) == 0); -} - -int npy_half_ne(npy_half h1, npy_half h2) -{ - return !npy_half_eq(h1, h2); -} - -int npy_half_lt_nonan(npy_half h1, npy_half h2) -{ - if (h1&0x8000u) { - if (h2&0x8000u) { - return (h1&0x7fffu) > (h2&0x7fffu); - } else { - /* Signed zeros are equal, have to check for it */ - return (h1 != 0x8000u) || (h2 != 0x0000u); - } - } else { - if (h2&0x8000u) { - return 0; - } else { - return (h1&0x7fffu) < (h2&0x7fffu); - } - } -} - -int npy_half_lt(npy_half h1, npy_half h2) -{ - return (!npy_half_isnan(h1) && !npy_half_isnan(h2)) && npy_half_lt_nonan(h1, h2); -} - -int npy_half_gt(npy_half h1, npy_half h2) -{ - return npy_half_lt(h2, h1); -} - -int npy_half_le_nonan(npy_half h1, npy_half h2) -{ - if (h1&0x8000u) { - if (h2&0x8000u) { - return (h1&0x7fffu) >= (h2&0x7fffu); - } else { - return 1; - } - } else { - if (h2&0x8000u) { - /* Signed zeros are equal, have to check for it */ - return (h1 == 0x0000u) && (h2 == 0x8000u); - } else { - return (h1&0x7fffu) <= (h2&0x7fffu); - } - } -} - -int npy_half_le(npy_half h1, npy_half h2) -{ - return (!npy_half_isnan(h1) && !npy_half_isnan(h2)) && npy_half_le_nonan(h1, h2); -} - -int npy_half_ge(npy_half h1, npy_half h2) -{ - return npy_half_le(h2, h1); -} - -npy_half npy_half_divmod(npy_half h1, npy_half h2, npy_half *modulus) -{ - float fh1 = npy_half_to_float(h1); - float fh2 = npy_half_to_float(h2); - float div, mod; - - div = npy_divmodf(fh1, fh2, &mod); - *modulus = npy_float_to_half(mod); - return npy_float_to_half(div); -} - - - -/* - ******************************************************************** - * BIT-LEVEL CONVERSIONS * - ******************************************************************** - */ - -npy_uint16 npy_floatbits_to_halfbits(npy_uint32 f) -{ - npy_uint32 f_exp, f_sig; - npy_uint16 h_sgn, h_exp, h_sig; - - h_sgn = (npy_uint16) ((f&0x80000000u) >> 16); - f_exp = (f&0x7f800000u); - - /* Exponent overflow/NaN converts to signed inf/NaN */ - if (f_exp >= 0x47800000u) { - if (f_exp == 0x7f800000u) { - /* Inf or NaN */ - f_sig = (f&0x007fffffu); - if (f_sig != 0) { - /* NaN - propagate the flag in the significand... */ - npy_uint16 ret = (npy_uint16) (0x7c00u + (f_sig >> 13)); - /* ...but make sure it stays a NaN */ - if (ret == 0x7c00u) { - ret++; - } - return h_sgn + ret; - } else { - /* signed inf */ - return (npy_uint16) (h_sgn + 0x7c00u); - } - } else { - /* overflow to signed inf */ -#if NPY_HALF_GENERATE_OVERFLOW - npy_set_floatstatus_overflow(); -#endif - return (npy_uint16) (h_sgn + 0x7c00u); - } - } - - /* Exponent underflow converts to a subnormal half or signed zero */ - if (f_exp <= 0x38000000u) { - /* - * Signed zeros, subnormal floats, and floats with small - * exponents all convert to signed zero half-floats. - */ - if (f_exp < 0x33000000u) { -#if NPY_HALF_GENERATE_UNDERFLOW - /* If f != 0, it underflowed to 0 */ - if ((f&0x7fffffff) != 0) { - npy_set_floatstatus_underflow(); - } -#endif - return h_sgn; - } - /* Make the subnormal significand */ - f_exp >>= 23; - f_sig = (0x00800000u + (f&0x007fffffu)); -#if NPY_HALF_GENERATE_UNDERFLOW - /* If it's not exactly represented, it underflowed */ - if ((f_sig&(((npy_uint32)1 << (126 - f_exp)) - 1)) != 0) { - npy_set_floatstatus_underflow(); - } -#endif - /* - * Usually the significand is shifted by 13. For subnormals an - * additional shift needs to occur. This shift is one for the largest - * exponent giving a subnormal `f_exp = 0x38000000 >> 23 = 112`, which - * offsets the new first bit. At most the shift can be 1+10 bits. - */ - f_sig >>= (113 - f_exp); - /* Handle rounding by adding 1 to the bit beyond half precision */ -#if NPY_HALF_ROUND_TIES_TO_EVEN - /* - * If the last bit in the half significand is 0 (already even), and - * the remaining bit pattern is 1000...0, then we do not add one - * to the bit after the half significand. However, the (113 - f_exp) - * shift can lose up to 11 bits, so the || checks them in the original. - * In all other cases, we can just add one. - */ - if (((f_sig&0x00003fffu) != 0x00001000u) || (f&0x000007ffu)) { - f_sig += 0x00001000u; - } -#else - f_sig += 0x00001000u; -#endif - h_sig = (npy_uint16) (f_sig >> 13); - /* - * If the rounding causes a bit to spill into h_exp, it will - * increment h_exp from zero to one and h_sig will be zero. - * This is the correct result. - */ - return (npy_uint16) (h_sgn + h_sig); - } - - /* Regular case with no overflow or underflow */ - h_exp = (npy_uint16) ((f_exp - 0x38000000u) >> 13); - /* Handle rounding by adding 1 to the bit beyond half precision */ - f_sig = (f&0x007fffffu); -#if NPY_HALF_ROUND_TIES_TO_EVEN - /* - * If the last bit in the half significand is 0 (already even), and - * the remaining bit pattern is 1000...0, then we do not add one - * to the bit after the half significand. In all other cases, we do. - */ - if ((f_sig&0x00003fffu) != 0x00001000u) { - f_sig += 0x00001000u; - } -#else - f_sig += 0x00001000u; -#endif - h_sig = (npy_uint16) (f_sig >> 13); - /* - * If the rounding causes a bit to spill into h_exp, it will - * increment h_exp by one and h_sig will be zero. This is the - * correct result. h_exp may increment to 15, at greatest, in - * which case the result overflows to a signed inf. - */ -#if NPY_HALF_GENERATE_OVERFLOW - h_sig += h_exp; - if (h_sig == 0x7c00u) { - npy_set_floatstatus_overflow(); - } - return h_sgn + h_sig; -#else - return h_sgn + h_exp + h_sig; -#endif -} - -npy_uint16 npy_doublebits_to_halfbits(npy_uint64 d) -{ - npy_uint64 d_exp, d_sig; - npy_uint16 h_sgn, h_exp, h_sig; - - h_sgn = (d&0x8000000000000000ULL) >> 48; - d_exp = (d&0x7ff0000000000000ULL); - - /* Exponent overflow/NaN converts to signed inf/NaN */ - if (d_exp >= 0x40f0000000000000ULL) { - if (d_exp == 0x7ff0000000000000ULL) { - /* Inf or NaN */ - d_sig = (d&0x000fffffffffffffULL); - if (d_sig != 0) { - /* NaN - propagate the flag in the significand... */ - npy_uint16 ret = (npy_uint16) (0x7c00u + (d_sig >> 42)); - /* ...but make sure it stays a NaN */ - if (ret == 0x7c00u) { - ret++; - } - return h_sgn + ret; - } else { - /* signed inf */ - return h_sgn + 0x7c00u; - } - } else { - /* overflow to signed inf */ -#if NPY_HALF_GENERATE_OVERFLOW - npy_set_floatstatus_overflow(); -#endif - return h_sgn + 0x7c00u; - } - } - - /* Exponent underflow converts to subnormal half or signed zero */ - if (d_exp <= 0x3f00000000000000ULL) { - /* - * Signed zeros, subnormal floats, and floats with small - * exponents all convert to signed zero half-floats. - */ - if (d_exp < 0x3e60000000000000ULL) { -#if NPY_HALF_GENERATE_UNDERFLOW - /* If d != 0, it underflowed to 0 */ - if ((d&0x7fffffffffffffffULL) != 0) { - npy_set_floatstatus_underflow(); - } -#endif - return h_sgn; - } - /* Make the subnormal significand */ - d_exp >>= 52; - d_sig = (0x0010000000000000ULL + (d&0x000fffffffffffffULL)); -#if NPY_HALF_GENERATE_UNDERFLOW - /* If it's not exactly represented, it underflowed */ - if ((d_sig&(((npy_uint64)1 << (1051 - d_exp)) - 1)) != 0) { - npy_set_floatstatus_underflow(); - } -#endif - /* - * Unlike floats, doubles have enough room to shift left to align - * the subnormal significand leading to no loss of the last bits. - * The smallest possible exponent giving a subnormal is: - * `d_exp = 0x3e60000000000000 >> 52 = 998`. All larger subnormals are - * shifted with respect to it. This adds a shift of 10+1 bits the final - * right shift when comparing it to the one in the normal branch. - */ - assert(d_exp - 998 >= 0); - d_sig <<= (d_exp - 998); - /* Handle rounding by adding 1 to the bit beyond half precision */ -#if NPY_HALF_ROUND_TIES_TO_EVEN - /* - * If the last bit in the half significand is 0 (already even), and - * the remaining bit pattern is 1000...0, then we do not add one - * to the bit after the half significand. In all other cases, we do. - */ - if ((d_sig&0x003fffffffffffffULL) != 0x0010000000000000ULL) { - d_sig += 0x0010000000000000ULL; - } -#else - d_sig += 0x0010000000000000ULL; -#endif - h_sig = (npy_uint16) (d_sig >> 53); - /* - * If the rounding causes a bit to spill into h_exp, it will - * increment h_exp from zero to one and h_sig will be zero. - * This is the correct result. - */ - return h_sgn + h_sig; - } - - /* Regular case with no overflow or underflow */ - h_exp = (npy_uint16) ((d_exp - 0x3f00000000000000ULL) >> 42); - /* Handle rounding by adding 1 to the bit beyond half precision */ - d_sig = (d&0x000fffffffffffffULL); -#if NPY_HALF_ROUND_TIES_TO_EVEN - /* - * If the last bit in the half significand is 0 (already even), and - * the remaining bit pattern is 1000...0, then we do not add one - * to the bit after the half significand. In all other cases, we do. - */ - if ((d_sig&0x000007ffffffffffULL) != 0x0000020000000000ULL) { - d_sig += 0x0000020000000000ULL; - } -#else - d_sig += 0x0000020000000000ULL; -#endif - h_sig = (npy_uint16) (d_sig >> 42); - - /* - * If the rounding causes a bit to spill into h_exp, it will - * increment h_exp by one and h_sig will be zero. This is the - * correct result. h_exp may increment to 15, at greatest, in - * which case the result overflows to a signed inf. - */ -#if NPY_HALF_GENERATE_OVERFLOW - h_sig += h_exp; - if (h_sig == 0x7c00u) { - npy_set_floatstatus_overflow(); - } - return h_sgn + h_sig; -#else - return h_sgn + h_exp + h_sig; -#endif -} - -npy_uint32 npy_halfbits_to_floatbits(npy_uint16 h) -{ - npy_uint16 h_exp, h_sig; - npy_uint32 f_sgn, f_exp, f_sig; - - h_exp = (h&0x7c00u); - f_sgn = ((npy_uint32)h&0x8000u) << 16; - switch (h_exp) { - case 0x0000u: /* 0 or subnormal */ - h_sig = (h&0x03ffu); - /* Signed zero */ - if (h_sig == 0) { - return f_sgn; - } - /* Subnormal */ - h_sig <<= 1; - while ((h_sig&0x0400u) == 0) { - h_sig <<= 1; - h_exp++; - } - f_exp = ((npy_uint32)(127 - 15 - h_exp)) << 23; - f_sig = ((npy_uint32)(h_sig&0x03ffu)) << 13; - return f_sgn + f_exp + f_sig; - case 0x7c00u: /* inf or NaN */ - /* All-ones exponent and a copy of the significand */ - return f_sgn + 0x7f800000u + (((npy_uint32)(h&0x03ffu)) << 13); - default: /* normalized */ - /* Just need to adjust the exponent and shift */ - return f_sgn + (((npy_uint32)(h&0x7fffu) + 0x1c000u) << 13); - } -} - -npy_uint64 npy_halfbits_to_doublebits(npy_uint16 h) -{ - npy_uint16 h_exp, h_sig; - npy_uint64 d_sgn, d_exp, d_sig; - - h_exp = (h&0x7c00u); - d_sgn = ((npy_uint64)h&0x8000u) << 48; - switch (h_exp) { - case 0x0000u: /* 0 or subnormal */ - h_sig = (h&0x03ffu); - /* Signed zero */ - if (h_sig == 0) { - return d_sgn; - } - /* Subnormal */ - h_sig <<= 1; - while ((h_sig&0x0400u) == 0) { - h_sig <<= 1; - h_exp++; - } - d_exp = ((npy_uint64)(1023 - 15 - h_exp)) << 52; - d_sig = ((npy_uint64)(h_sig&0x03ffu)) << 42; - return d_sgn + d_exp + d_sig; - case 0x7c00u: /* inf or NaN */ - /* All-ones exponent and a copy of the significand */ - return d_sgn + 0x7ff0000000000000ULL + - (((npy_uint64)(h&0x03ffu)) << 42); - default: /* normalized */ - /* Just need to adjust the exponent and shift */ - return d_sgn + (((npy_uint64)(h&0x7fffu) + 0xfc000u) << 42); - } -} diff --git a/numpy/core/src/npymath/halffloat.cpp b/numpy/core/src/npymath/halffloat.cpp new file mode 100644 index 000000000..aa582c1b9 --- /dev/null +++ b/numpy/core/src/npymath/halffloat.cpp @@ -0,0 +1,238 @@ +#define NPY_NO_DEPRECATED_API NPY_API_VERSION + +/* + * If these are 1, the conversions try to trigger underflow, + * overflow, and invalid exceptions in the FP system when needed. + */ +#define NPY_HALF_GENERATE_OVERFLOW 1 +#define NPY_HALF_GENERATE_INVALID 1 + +#include "numpy/halffloat.h" + +#include "common.hpp" +/* + ******************************************************************** + * HALF-PRECISION ROUTINES * + ******************************************************************** + */ +using namespace np; + +float npy_half_to_float(npy_half h) +{ + return static_cast<float>(Half::FromBits(h)); +} + +double npy_half_to_double(npy_half h) +{ + return static_cast<double>(Half::FromBits(h)); +} + +npy_half npy_float_to_half(float f) +{ + return Half(f).Bits(); +} + +npy_half npy_double_to_half(double d) +{ + return Half(d).Bits(); +} + +int npy_half_iszero(npy_half h) +{ + return (h&0x7fff) == 0; +} + +int npy_half_isnan(npy_half h) +{ + return Half::FromBits(h).IsNaN(); +} + +int npy_half_isinf(npy_half h) +{ + return ((h&0x7fffu) == 0x7c00u); +} + +int npy_half_isfinite(npy_half h) +{ + return ((h&0x7c00u) != 0x7c00u); +} + +int npy_half_signbit(npy_half h) +{ + return (h&0x8000u) != 0; +} + +npy_half npy_half_spacing(npy_half h) +{ + npy_half ret; + npy_uint16 h_exp = h&0x7c00u; + npy_uint16 h_sig = h&0x03ffu; + if (h_exp == 0x7c00u) { +#if NPY_HALF_GENERATE_INVALID + npy_set_floatstatus_invalid(); +#endif + ret = NPY_HALF_NAN; + } else if (h == 0x7bffu) { +#if NPY_HALF_GENERATE_OVERFLOW + npy_set_floatstatus_overflow(); +#endif + ret = NPY_HALF_PINF; + } else if ((h&0x8000u) && h_sig == 0) { /* Negative boundary case */ + if (h_exp > 0x2c00u) { /* If result is normalized */ + ret = h_exp - 0x2c00u; + } else if(h_exp > 0x0400u) { /* The result is a subnormal, but not the smallest */ + ret = 1 << ((h_exp >> 10) - 2); + } else { + ret = 0x0001u; /* Smallest subnormal half */ + } + } else if (h_exp > 0x2800u) { /* If result is still normalized */ + ret = h_exp - 0x2800u; + } else if (h_exp > 0x0400u) { /* The result is a subnormal, but not the smallest */ + ret = 1 << ((h_exp >> 10) - 1); + } else { + ret = 0x0001u; + } + + return ret; +} + +npy_half npy_half_copysign(npy_half x, npy_half y) +{ + return (x&0x7fffu) | (y&0x8000u); +} + +npy_half npy_half_nextafter(npy_half x, npy_half y) +{ + npy_half ret; + + if (npy_half_isnan(x) || npy_half_isnan(y)) { + ret = NPY_HALF_NAN; + } else if (npy_half_eq_nonan(x, y)) { + ret = x; + } else if (npy_half_iszero(x)) { + ret = (y&0x8000u) + 1; /* Smallest subnormal half */ + } else if (!(x&0x8000u)) { /* x > 0 */ + if ((npy_int16)x > (npy_int16)y) { /* x > y */ + ret = x-1; + } else { + ret = x+1; + } + } else { + if (!(y&0x8000u) || (x&0x7fffu) > (y&0x7fffu)) { /* x < y */ + ret = x-1; + } else { + ret = x+1; + } + } +#if NPY_HALF_GENERATE_OVERFLOW + if (npy_half_isinf(ret) && npy_half_isfinite(x)) { + npy_set_floatstatus_overflow(); + } +#endif + + return ret; +} + +int npy_half_eq_nonan(npy_half h1, npy_half h2) +{ + return Half::FromBits(h1).Equal(Half::FromBits(h2)); +} + +int npy_half_eq(npy_half h1, npy_half h2) +{ + return Half::FromBits(h1) == Half::FromBits(h2); +} + +int npy_half_ne(npy_half h1, npy_half h2) +{ + return Half::FromBits(h1) != Half::FromBits(h2); +} + +int npy_half_lt_nonan(npy_half h1, npy_half h2) +{ + return Half::FromBits(h1).Less(Half::FromBits(h2)); +} + +int npy_half_lt(npy_half h1, npy_half h2) +{ + return Half::FromBits(h1) < Half::FromBits(h2); +} + +int npy_half_gt(npy_half h1, npy_half h2) +{ + return npy_half_lt(h2, h1); +} + +int npy_half_le_nonan(npy_half h1, npy_half h2) +{ + return Half::FromBits(h1).LessEqual(Half::FromBits(h2)); +} + +int npy_half_le(npy_half h1, npy_half h2) +{ + return Half::FromBits(h1) <= Half::FromBits(h2); +} + +int npy_half_ge(npy_half h1, npy_half h2) +{ + return npy_half_le(h2, h1); +} + +npy_half npy_half_divmod(npy_half h1, npy_half h2, npy_half *modulus) +{ + float fh1 = npy_half_to_float(h1); + float fh2 = npy_half_to_float(h2); + float div, mod; + + div = npy_divmodf(fh1, fh2, &mod); + *modulus = npy_float_to_half(mod); + return npy_float_to_half(div); +} + + +/* + ******************************************************************** + * BIT-LEVEL CONVERSIONS * + ******************************************************************** + */ + +npy_uint16 npy_floatbits_to_halfbits(npy_uint32 f) +{ + if constexpr (Half::kNativeConversion<float>) { + return BitCast<uint16_t>(Half(BitCast<float>(f))); + } + else { + return half_private::FromFloatBits(f); + } +} + +npy_uint16 npy_doublebits_to_halfbits(npy_uint64 d) +{ + if constexpr (Half::kNativeConversion<double>) { + return BitCast<uint16_t>(Half(BitCast<double>(d))); + } + else { + return half_private::FromDoubleBits(d); + } +} + +npy_uint32 npy_halfbits_to_floatbits(npy_uint16 h) +{ + if constexpr (Half::kNativeConversion<float>) { + return BitCast<uint32_t>(static_cast<float>(Half::FromBits(h))); + } + else { + return half_private::ToFloatBits(h); + } +} + +npy_uint64 npy_halfbits_to_doublebits(npy_uint16 h) +{ + if constexpr (Half::kNativeConversion<double>) { + return BitCast<uint64_t>(static_cast<double>(Half::FromBits(h))); + } + else { + return half_private::ToDoubleBits(h); + } +} + diff --git a/numpy/core/src/npymath/npy_math_complex.c.src b/numpy/core/src/npymath/npy_math_complex.c.src index eff7f8e13..eb9d810b7 100644 --- a/numpy/core/src/npymath/npy_math_complex.c.src +++ b/numpy/core/src/npymath/npy_math_complex.c.src @@ -535,6 +535,443 @@ npy_cpow@c@ (@ctype@ a, @ctype@ b) #endif } + +#ifndef HAVE_CCOS@C@ +@ctype@ +npy_ccos@c@(@ctype@ z) +{ + /* ccos(z) = ccosh(I * z) */ + return npy_ccosh@c@(npy_cpack@c@(-npy_cimag@c@(z), npy_creal@c@(z))); +} +#endif + +#ifndef HAVE_CSIN@C@ +@ctype@ +npy_csin@c@(@ctype@ z) +{ + /* csin(z) = -I * csinh(I * z) */ + z = npy_csinh@c@(npy_cpack@c@(-npy_cimag@c@(z), npy_creal@c@(z))); + return npy_cpack@c@(npy_cimag@c@(z), -npy_creal@c@(z)); +} +#endif + +#ifndef HAVE_CTAN@C@ +@ctype@ +npy_ctan@c@(@ctype@ z) +{ + /* ctan(z) = -I * ctanh(I * z) */ + z = npy_ctanh@c@(npy_cpack@c@(-npy_cimag@c@(z), npy_creal@c@(z))); + return (npy_cpack@c@(npy_cimag@c@(z), -npy_creal@c@(z))); +} +#endif + +#ifndef HAVE_CCOSH@C@ +/* + * Taken from the msun library in FreeBSD, rev 226599. + * + * Hyperbolic cosine of a complex argument z = x + i y. + * + * cosh(z) = cosh(x+iy) + * = cosh(x) cos(y) + i sinh(x) sin(y). + * + * Exceptional values are noted in the comments within the source code. + * These values and the return value were taken from n1124.pdf. + * + * CCOSH_BIG is chosen such that + * spacing(0.5 * exp(CCOSH_BIG)) > 0.5*exp(-CCOSH_BIG) + * although the exact value assigned to CCOSH_BIG is not so important + */ +@ctype@ +npy_ccosh@c@(@ctype@ z) +{ +#if @precision@ == 1 + const npy_float CCOSH_BIG = 9.0f; + const npy_float CCOSH_HUGE = 1.70141183e+38f; +#endif +#if @precision@ == 2 + const npy_double CCOSH_BIG = 22.0; + const npy_double CCOSH_HUGE = 8.9884656743115795e+307; +#endif +#if @precision@ >= 3 +#if NPY_SIZEOF_LONGDOUBLE == NPY_SIZEOF_DOUBLE + const npy_longdouble CCOSH_BIG = 22.0L; + const npy_longdouble CCOSH_HUGE = 8.9884656743115795e+307L; +#else + const npy_longdouble CCOSH_BIG = 24.0L; + const npy_longdouble CCOSH_HUGE = 5.94865747678615882543e+4931L; +#endif +#endif + + @type@ x, y, h, absx; + npy_int xfinite, yfinite; + + x = npy_creal@c@(z); + y = npy_cimag@c@(z); + + xfinite = npy_isfinite(x); + yfinite = npy_isfinite(y); + + /* Handle the nearly-non-exceptional cases where x and y are finite. */ + if (xfinite && yfinite) { + if (y == 0) { + return npy_cpack@c@(npy_cosh@c@(x), x * y); + } + absx = npy_fabs@c@(x); + if (absx < CCOSH_BIG) { + /* small x: normal case */ + return npy_cpack@c@(npy_cosh@c@(x) * npy_cos@c@(y), + npy_sinh@c@(x) * npy_sin@c@(y)); + } + + /* |x| >= 22, so cosh(x) ~= exp(|x|) */ + if (absx < SCALED_CEXP_LOWER@C@) { + /* x < 710: exp(|x|) won't overflow */ + h = npy_exp@c@(absx) * 0.5@c@; + return npy_cpack@c@(h * npy_cos@c@(y), + npy_copysign@c@(h, x) * npy_sin@c@(y)); + } + else if (absx < SCALED_CEXP_UPPER@C@) { + /* x < 1455: scale to avoid overflow */ + z = _npy_scaled_cexp@c@(absx, y, -1); + return npy_cpack@c@(npy_creal@c@(z), + npy_cimag@c@(z) * npy_copysign@c@(1, x)); + } + else { + /* x >= 1455: the result always overflows */ + h = CCOSH_HUGE * x; + return npy_cpack@c@(h * h * npy_cos@c@(y), h * npy_sin@c@(y)); + } + } + + /* + * cosh(+-0 +- I Inf) = dNaN + I sign(d(+-0, dNaN))0. + * The sign of 0 in the result is unspecified. Choice = normally + * the same as dNaN. Raise the invalid floating-point exception. + * + * cosh(+-0 +- I NaN) = d(NaN) + I sign(d(+-0, NaN))0. + * The sign of 0 in the result is unspecified. Choice = normally + * the same as d(NaN). + */ + if (x == 0 && !yfinite) { + return npy_cpack@c@(y - y, npy_copysign@c@(0, x * (y - y))); + } + + /* + * cosh(+-Inf +- I 0) = +Inf + I (+-)(+-)0. + * + * cosh(NaN +- I 0) = d(NaN) + I sign(d(NaN, +-0))0. + * The sign of 0 in the result is unspecified. + */ + if (y == 0 && !xfinite) { + return npy_cpack@c@(x * x, npy_copysign@c@(0, x) * y); + } + + /* + * cosh(x +- I Inf) = dNaN + I dNaN. + * Raise the invalid floating-point exception for finite nonzero x. + * + * cosh(x + I NaN) = d(NaN) + I d(NaN). + * Optionally raises the invalid floating-point exception for finite + * nonzero x. Choice = don't raise (except for signaling NaNs). + */ + if (xfinite && !yfinite) { + return npy_cpack@c@(y - y, x * (y - y)); + } + + /* + * cosh(+-Inf + I NaN) = +Inf + I d(NaN). + * + * cosh(+-Inf +- I Inf) = +Inf + I dNaN. + * The sign of Inf in the result is unspecified. Choice = always +. + * Raise the invalid floating-point exception. + * + * cosh(+-Inf + I y) = +Inf cos(y) +- I Inf sin(y) + */ + if (npy_isinf(x)) { + if (!yfinite) { + return npy_cpack@c@(x * x, x * (y - y)); + } + return npy_cpack@c@((x * x) * npy_cos@c@(y), x * npy_sin@c@(y)); + } + + /* + * cosh(NaN + I NaN) = d(NaN) + I d(NaN). + * + * cosh(NaN +- I Inf) = d(NaN) + I d(NaN). + * Optionally raises the invalid floating-point exception. + * Choice = raise. + * + * cosh(NaN + I y) = d(NaN) + I d(NaN). + * Optionally raises the invalid floating-point exception for finite + * nonzero y. Choice = don't raise (except for signaling NaNs). + */ + return npy_cpack@c@((x * x) * (y - y), (x + x) * (y - y)); +} +#undef CCOSH_BIG +#undef CCOSH_HUGE +#endif + +#ifndef HAVE_CSINH@C@ +/* + * Taken from the msun library in FreeBSD, rev 226599. + * + * Hyperbolic sine of a complex argument z = x + i y. + * + * sinh(z) = sinh(x+iy) + * = sinh(x) cos(y) + i cosh(x) sin(y). + * + * Exceptional values are noted in the comments within the source code. + * These values and the return value were taken from n1124.pdf. + */ +@ctype@ +npy_csinh@c@(@ctype@ z) +{ +#if @precision@ == 1 + const npy_float CSINH_BIG = 9.0f; + const npy_float CSINH_HUGE = 1.70141183e+38f; +#endif +#if @precision@ == 2 + const npy_double CSINH_BIG = 22.0; + const npy_double CSINH_HUGE = 8.9884656743115795e+307; +#endif +#if @precision@ >= 3 +#if NPY_SIZEOF_LONGDOUBLE == NPY_SIZEOF_DOUBLE + const npy_longdouble CSINH_BIG = 22.0L; + const npy_longdouble CSINH_HUGE = 8.9884656743115795e+307L; +#else + const npy_longdouble CSINH_BIG = 24.0L; + const npy_longdouble CSINH_HUGE = 5.94865747678615882543e+4931L; +#endif +#endif + + @type@ x, y, h, absx; + npy_int xfinite, yfinite; + + x = npy_creal@c@(z); + y = npy_cimag@c@(z); + + xfinite = npy_isfinite(x); + yfinite = npy_isfinite(y); + + /* Handle the nearly-non-exceptional cases where x and y are finite. */ + if (xfinite && yfinite) { + if (y == 0) { + return npy_cpack@c@(npy_sinh@c@(x), y); + } + absx = npy_fabs@c@(x); + if (absx < CSINH_BIG) { + /* small x: normal case */ + return npy_cpack@c@(npy_sinh@c@(x) * npy_cos@c@(y), + npy_cosh@c@(x) * npy_sin@c@(y)); + } + + /* |x| >= 22, so cosh(x) ~= exp(|x|) */ + if (absx < SCALED_CEXP_LOWER@C@) { + /* x < 710: exp(|x|) won't overflow */ + h = npy_exp@c@(npy_fabs@c@(x)) * 0.5@c@; + return npy_cpack@c@(npy_copysign@c@(h, x) * npy_cos@c@(y), + h * npy_sin@c@(y)); + } + else if (x < SCALED_CEXP_UPPER@C@) { + /* x < 1455: scale to avoid overflow */ + z = _npy_scaled_cexp@c@(absx, y, -1); + return npy_cpack@c@(npy_creal@c@(z) * npy_copysign@c@(1, x), + npy_cimag@c@(z)); + } + else { + /* x >= 1455: the result always overflows */ + h = CSINH_HUGE * x; + return npy_cpack@c@(h * npy_cos@c@(y), h * h * npy_sin@c@(y)); + } + } + + /* + * sinh(+-0 +- I Inf) = sign(d(+-0, dNaN))0 + I dNaN. + * The sign of 0 in the result is unspecified. Choice = normally + * the same as dNaN. Raise the invalid floating-point exception. + * + * sinh(+-0 +- I NaN) = sign(d(+-0, NaN))0 + I d(NaN). + * The sign of 0 in the result is unspecified. Choice = normally + * the same as d(NaN). + */ + if (x == 0 && !yfinite) { + return npy_cpack@c@(npy_copysign@c@(0, x * (y - y)), y - y); + } + + /* + * sinh(+-Inf +- I 0) = +-Inf + I +-0. + * + * sinh(NaN +- I 0) = d(NaN) + I +-0. + */ + if (y == 0 && !xfinite) { + if (npy_isnan(x)) { + return z; + } + return npy_cpack@c@(x, npy_copysign@c@(0, y)); + } + + /* + * sinh(x +- I Inf) = dNaN + I dNaN. + * Raise the invalid floating-point exception for finite nonzero x. + * + * sinh(x + I NaN) = d(NaN) + I d(NaN). + * Optionally raises the invalid floating-point exception for finite + * nonzero x. Choice = don't raise (except for signaling NaNs). + */ + if (xfinite && !yfinite) { + return npy_cpack@c@(y - y, x * (y - y)); + } + + /* + * sinh(+-Inf + I NaN) = +-Inf + I d(NaN). + * The sign of Inf in the result is unspecified. Choice = normally + * the same as d(NaN). + * + * sinh(+-Inf +- I Inf) = +Inf + I dNaN. + * The sign of Inf in the result is unspecified. Choice = always +. + * Raise the invalid floating-point exception. + * + * sinh(+-Inf + I y) = +-Inf cos(y) + I Inf sin(y) + */ + if (!xfinite && !npy_isnan(x)) { + if (!yfinite) { + return npy_cpack@c@(x * x, x * (y - y)); + } + return npy_cpack@c@(x * npy_cos@c@(y), + NPY_INFINITY@C@ * npy_sin@c@(y)); + } + + /* + * sinh(NaN + I NaN) = d(NaN) + I d(NaN). + * + * sinh(NaN +- I Inf) = d(NaN) + I d(NaN). + * Optionally raises the invalid floating-point exception. + * Choice = raise. + * + * sinh(NaN + I y) = d(NaN) + I d(NaN). + * Optionally raises the invalid floating-point exception for finite + * nonzero y. Choice = don't raise (except for signaling NaNs). + */ + return npy_cpack@c@((x * x) * (y - y), (x + x) * (y - y)); +} +#undef CSINH_BIG +#undef CSINH_HUGE +#endif + +#ifndef HAVE_CTANH@C@ +/* + * Taken from the msun library in FreeBSD, rev 226600. + * + * Hyperbolic tangent of a complex argument z = x + i y. + * + * The algorithm is from: + * + * W. Kahan. Branch Cuts for Complex Elementary Functions or Much + * Ado About Nothing's Sign Bit. In The State of the Art in + * Numerical Analysis, pp. 165 ff. Iserles and Powell, eds., 1987. + * + * Method: + * + * Let t = tan(x) + * beta = 1/cos^2(y) + * s = sinh(x) + * rho = cosh(x) + * + * We have: + * + * tanh(z) = sinh(z) / cosh(z) + * + * sinh(x) cos(y) + i cosh(x) sin(y) + * = --------------------------------- + * cosh(x) cos(y) + i sinh(x) sin(y) + * + * cosh(x) sinh(x) / cos^2(y) + i tan(y) + * = ------------------------------------- + * 1 + sinh^2(x) / cos^2(y) + * + * beta rho s + i t + * = ---------------- + * 1 + beta s^2 + * + * Modifications: + * + * I omitted the original algorithm's handling of overflow in tan(x) after + * verifying with nearpi.c that this can't happen in IEEE single or double + * precision. I also handle large x differently. + */ + +#define TANH_HUGE 22.0 +#define TANHF_HUGE 11.0F +#define TANHL_HUGE 42.0L + +@ctype@ +npy_ctanh@c@(@ctype@ z) +{ + @type@ x, y; + @type@ t, beta, s, rho, denom; + + x = npy_creal@c@(z); + y = npy_cimag@c@(z); + + /* + * ctanh(NaN + i 0) = NaN + i 0 + * + * ctanh(NaN + i y) = NaN + i NaN for y != 0 + * + * The imaginary part has the sign of x*sin(2*y), but there's no + * special effort to get this right. + * + * ctanh(+-Inf +- i Inf) = +-1 +- 0 + * + * ctanh(+-Inf + i y) = +-1 + 0 sin(2y) for y finite + * + * The imaginary part of the sign is unspecified. This special + * case is only needed to avoid a spurious invalid exception when + * y is infinite. + */ + if (!npy_isfinite(x)) { + if (npy_isnan(x)) { + return npy_cpack@c@(x, (y == 0 ? y : x * y)); + } + return npy_cpack@c@(npy_copysign@c@(1,x), + npy_copysign@c@(0, + npy_isinf(y) ? + y : npy_sin@c@(y) * npy_cos@c@(y))); + } + + /* + * ctanh(x + i NAN) = NaN + i NaN + * ctanh(x +- i Inf) = NaN + i NaN + */ + if (!npy_isfinite(y)) { + return (npy_cpack@c@(y - y, y - y)); + } + + /* + * ctanh(+-huge + i +-y) ~= +-1 +- i 2sin(2y)/exp(2x), using the + * approximation sinh^2(huge) ~= exp(2*huge) / 4. + * We use a modified formula to avoid spurious overflow. + */ + if (npy_fabs@c@(x) >= TANH@C@_HUGE) { + @type@ exp_mx = npy_exp@c@(-npy_fabs@c@(x)); + return npy_cpack@c@(npy_copysign@c@(1, x), + 4 * npy_sin@c@(y) * npy_cos@c@(y) * + exp_mx * exp_mx); + } + + /* Kahan's algorithm */ + t = npy_tan@c@(y); + beta = 1 + t * t; /* = 1 / cos^2(y) */ + s = npy_sinh@c@(x); + rho = npy_sqrt@c@(1 + s * s); /* = cosh(x) */ + denom = 1 + beta * s * s; + return (npy_cpack@c@((beta * rho * s) / denom, t / denom)); +} +#undef TANH_HUGE +#undef TANHF_HUGE +#undef TANHL_HUGE +#endif + #if !defined (HAVE_CACOS@C@) || !defined (HAVE_CASINH@C@) /* * Complex inverse trig functions taken from the msum library in FreeBSD @@ -1327,8 +1764,10 @@ npy_@kind@@c@(@ctype@ z) /**end repeat1**/ /**begin repeat1 - * #kind = cexp,clog,csqrt,cacos,casin,catan,cacosh,casinh,catanh# - * #KIND = CEXP,CLOG,CSQRT,CACOS,CASIN,CATAN,CACOSH,CASINH,CATANH# + * #kind = cexp,clog,csqrt,ccos,csin,ctan,ccosh,csinh,ctanh, + * cacos,casin,catan,cacosh,casinh,catanh# + * #KIND = CEXP,CLOG,CSQRT,CCOS,CSIN,CTAN,CCOSH,CSINH,CTANH, + * CACOS,CASIN,CATAN,CACOSH,CASINH,CATANH# */ #ifdef HAVE_@KIND@@C@ @ctype@ @@ -1343,20 +1782,5 @@ npy_@kind@@c@(@ctype@ z) #endif /**end repeat1**/ -/* Mandatory complex functions */ - -/**begin repeat1 - * #kind = csin,csinh,ccos,ccosh,ctan,ctanh# - */ -@ctype@ -npy_@kind@@c@(@ctype@ z) -{ - __@ctype@_to_c99_cast z1; - __@ctype@_to_c99_cast ret; - z1.npy_z = z; - ret.c99_z = @kind@@c@(z1.c99_z); - return ret.npy_z; -} -/**end repeat1**/ /**end repeat**/ diff --git a/numpy/core/src/npymath/npy_math_private.h b/numpy/core/src/npymath/npy_math_private.h index a474b3de3..20c94f98a 100644 --- a/numpy/core/src/npymath/npy_math_private.h +++ b/numpy/core/src/npymath/npy_math_private.h @@ -21,6 +21,7 @@ #include <Python.h> #ifdef __cplusplus #include <cmath> +#include <complex> using std::isgreater; using std::isless; #else @@ -494,8 +495,9 @@ do { \ * Microsoft C defines _MSC_VER * Intel compiler does not use MSVC complex types, but defines _MSC_VER by * default. + * since c++17 msvc is no longer support them. */ -#if defined(_MSC_VER) && !defined(__INTEL_COMPILER) +#if !defined(__cplusplus) && defined(_MSC_VER) && !defined(__INTEL_COMPILER) typedef union { npy_cdouble npy_z; _Dcomplex c99_z; |