[SYCL] Add support for MSVC internal math functions in device library

libdevice/cmath_wrapper.cpp

@@ -17,12 +17,20 @@ float logf(float x) { return __devicelib_logf(x); }
 
 DEVICE_EXTERN_C
 float expf(float x) { return __devicelib_expf(x); }
-
+// On Windows, the math.h includes wrapper definition for functions:
+// frexpf, ldexpf, hypotf, so we can't provide these 3 functions in
+// device libraries which may lead to multiple definition error.
+// The "hypotf" on Windows will call an internal function "_hypotf"
+// and frexpf, ldexpf will call corresponding double version:
+// frexp and ldexp. frexpf and ldexpf can only be used on platforms
+// with fp64 support currently.
+#ifndef _WIN32
 DEVICE_EXTERN_C
 float frexpf(float x, int *exp) { return __devicelib_frexpf(x, exp); }
 
 DEVICE_EXTERN_C
 float ldexpf(float x, int exp) { return __devicelib_ldexpf(x, exp); }
+#endif
 
 DEVICE_EXTERN_C
 float log10f(float x) { return __devicelib_log10f(x); }
@@ -54,8 +62,13 @@ float sqrtf(float x) { return __devicelib_sqrtf(x); }
 DEVICE_EXTERN_C
 float cbrtf(float x) { return __devicelib_cbrtf(x); }
 
+#ifndef _WIN32
 DEVICE_EXTERN_C
 float hypotf(float x, float y) { return __devicelib_hypotf(x, y); }
+#else
+DEVICE_EXTERN_C
+float _hypotf(float x, float y) { return __devicelib_hypotf(x, y); }
+#endif
 
 DEVICE_EXTERN_C
 float erff(float x) { return __devicelib_erff(x); }
@@ -128,3 +141,230 @@ float asinhf(float x) { return __devicelib_asinhf(x); }
 
 DEVICE_EXTERN_C
 float atanhf(float x) { return __devicelib_atanhf(x); }
+
+#if defined(_WIN32)
+#include <math.h>
+union _Fval { // pun floating type as integer array
+  unsigned short _Sh[8];
+  float _Val;
+};
+
+union _Dconst {            // pun float types as integer array
+  unsigned short _Word[2]; // TRANSITION, ABI: Twice as large as necessary.
+  float _Float;
+};
+
+#define _F0 1 // little-endian
+#define _F1 0
+
+// IEEE 754 float properties
+#define FHUGE_EXP (int)(_FMAX * 900L / 1000)
+
+#define NBITS (16 + _FOFF)
+#define FSIGN(x) (((_Fval *)(char *)&(x))->_Sh[_F0] & _FSIGN)
+
+#define INIT(w0)                                                               \
+  { 0, w0 }
+
+#define _FXbig (float)((NBITS + 1) * 347L / 1000)
+DEVICE_EXTERN_C
+short _FDtest(float *px) { // categorize *px
+  _Fval *ps = (_Fval *)(char *)px;
+  short ret = 0;
+  if ((ps->_Sh[_F0] & _FMASK) == _FMAX << _FOFF)
+    ret = (short)((ps->_Sh[_F0] & _FFRAC) != 0 || ps->_Sh[_F1] != 0 ? _NANCODE
+                                                                    : _INFCODE);
+  else if ((ps->_Sh[_F0] & ~_FSIGN) != 0 || ps->_Sh[_F1] != 0)
+    ret = (ps->_Sh[_F0] & _FMASK) == 0 ? _DENORM : _FINITE;
+
+  return ret;
+}
+
+DEVICE_EXTERN_C
+short _FDnorm(_Fval *ps) { // normalize float fraction
+  short xchar;
+  unsigned short sign = (unsigned short)(ps->_Sh[_F0] & _FSIGN);
+
+  xchar = 1;
+  if ((ps->_Sh[_F0] &= _FFRAC) != 0 || ps->_Sh[_F1]) { // nonzero, scale
+    if (ps->_Sh[_F0] == 0) {
+      ps->_Sh[_F0] = ps->_Sh[_F1];
+      ps->_Sh[_F1] = 0;
+      xchar -= 16;
+    }
+
+    for (; ps->_Sh[_F0] < 1 << _FOFF; --xchar) { // shift left by 1
+      ps->_Sh[_F0] = (unsigned short)(ps->_Sh[_F0] << 1 | ps->_Sh[_F1] >> 15);
+      ps->_Sh[_F1] <<= 1;
+    }
+    for (; 1 << (_FOFF + 1) <= ps->_Sh[_F0]; ++xchar) { // shift right by 1
+      ps->_Sh[_F1] = (unsigned short)(ps->_Sh[_F1] >> 1 | ps->_Sh[_F0] << 15);
+      ps->_Sh[_F0] >>= 1;
+    }
+    ps->_Sh[_F0] &= _FFRAC;
+  }
+  ps->_Sh[_F0] |= sign;
+  return xchar;
+}
+
+DEVICE_EXTERN_C
+short _FDscale(float *px, long lexp) { // scale *px by 2^xexp with checking
+  _Dconst _FInf = {INIT(_FMAX << _FOFF)};
+  _Fval *ps = (_Fval *)(char *)px;
+  short xchar = (short)((ps->_Sh[_F0] & _FMASK) >> _FOFF);
+
+  if (xchar == _FMAX)
+    return (short)((ps->_Sh[_F0] & _FFRAC) != 0 || ps->_Sh[_F1] != 0
+                       ? _NANCODE
+                       : _INFCODE);
+  if (xchar == 0 && 0 < (xchar = _FDnorm(ps)))
+    return 0;
+
+  short ret = 0;
+  if (0 < lexp && _FMAX - xchar <= lexp) { // overflow, return +/-INF
+    *px = ps->_Sh[_F0] & _FSIGN ? -_FInf._Float : _FInf._Float;
+    ret = _INFCODE;
+  } else if (-xchar < lexp) { // finite result, repack
+    ps->_Sh[_F0] =
+        (unsigned short)(ps->_Sh[_F0] & ~_FMASK | (lexp + xchar) << _FOFF);
+    ret = _FINITE;
+  } else { // denormalized, scale
+    unsigned short sign = (unsigned short)(ps->_Sh[_F0] & _FSIGN);
+
+    ps->_Sh[_F0] = (unsigned short)(1 << _FOFF | ps->_Sh[_F0] & _FFRAC);
+    lexp += xchar - 1;
+    if (lexp < -(16 + 1 + _FOFF) || 0 <= lexp) { // underflow, return +/-0
+      ps->_Sh[_F0] = sign;
+      ps->_Sh[_F1] = 0;
+      ret = 0;
+    } else { // nonzero, align fraction
+      ret = _FINITE;
+      short xexp = (short)lexp;
+      unsigned short psx = 0;
+
+      if (xexp <= -16) { // scale by words
+        psx = ps->_Sh[_F1] | (psx != 0 ? 1 : 0);
+        ps->_Sh[_F1] = ps->_Sh[_F0];
+        ps->_Sh[_F0] = 0;
+        xexp += 16;
+      }
+      if ((xexp = (short)-xexp) != 0) { // scale by bits
+        psx = (ps->_Sh[_F1] << (16 - xexp)) | (psx != 0 ? 1 : 0);
+        ps->_Sh[_F1] = (unsigned short)(ps->_Sh[_F1] >> xexp |
+                                        ps->_Sh[_F0] << (16 - xexp));
+        ps->_Sh[_F0] >>= xexp;
+      }
+
+      ps->_Sh[_F0] |= sign;
+      if ((0x8000 < psx || 0x8000 == psx && (ps->_Sh[_F1] & 0x0001) != 0) &&
+          (++ps->_Sh[_F1] & 0xffff) == 0)
+        ++ps->_Sh[_F0]; // round up
+      else if (ps->_Sh[_F0] == sign && ps->_Sh[_F1] == 0)
+        ret = 0;
+    }
+  }
+
+  return ret;
+}
+
+DEVICE_EXTERN_C
+short _FExp(float *px, float y,
+            short eoff) { // compute y * e^(*px), (*px) finite, |y| not huge
+  static const float hugexp = FHUGE_EXP;
+  _Dconst _FInf = {INIT(_FMAX << _FOFF)};
+  static const float p[] = {1.0F, 60.09114349F};
+  static const float q[] = {12.01517514F, 120.18228722F};
+  static const float c1 = (22713.0F / 32768.0F);
+  static const float c2 = 1.4286068203094172321214581765680755e-6F;
+  static const float invln2 = 1.4426950408889634073599246810018921F;
+  short ret = 0;
+  if (*px < -hugexp || y == 0.0F) { // certain underflow
+    *px = 0.0F;
+  } else if (hugexp < *px) { // certain overflow
+    *px = _FInf._Float;
+    ret = _INFCODE;
+  } else { // xexp won't overflow
+    float g = *px * invln2;
+    short xexp = (short)(g + (g < 0.0F ? -0.5F : +0.5F));
+
+    g = xexp;
+    g = (float)((*px - g * c1) - g * c2);
+    if (-__FLT_EPSILON__ < g && g < __FLT_EPSILON__) {
+      *px = y;
+    } else { // g * g worth computing
+      const float z = g * g;
+      const float w = q[0] * z + q[1];
+
+      g *= z + p[1];
+      *px = (w + g) / (w - g) * 2.0F * y;
+      --xexp;
+    }
+    ret = _FDscale(px, (long)xexp + eoff);
+  }
+  return ret;
+}
+
+DEVICE_EXTERN_C
+float _FCosh(float x, float y) { // compute y * cosh(x), |y| <= 1
+  switch (_FDtest(&x)) {         // test for special codes
+  case _NANCODE:
+  case _INFCODE:
+    return x;
+  case 0:
+    return y;
+  default: // finite
+    if (y == 0.0F)
+      return y;
+
+    if (x < 0.0F)
+      x = -x;
+
+    if (x < _FXbig) { // worth adding in exp(-x)
+      _FExp(&x, 1.0F, -1);
+      return y * (x + 0.25F / x);
+    }
+    _FExp(&x, y, -1);
+    return x;
+  }
+}
+
+DEVICE_EXTERN_C
+float _FSinh(float x, float y) { // compute y * sinh(x), |y| <= 1
+  _Dconst _FRteps = {INIT((_FBIAS - NBITS / 2) << _FOFF)};
+  static const float p[] = {0.00020400F, 0.00832983F, 0.16666737F, 0.99999998F};
+  short neg;
+
+  switch (_FDtest(&x)) { // test for special codes
+  case _NANCODE:
+    return x;
+  case _INFCODE:
+    return y != 0.0F ? x : FSIGN(x) ? -y : y;
+  case 0:
+    return x * y;
+  default: // finite
+    if (y == 0.0F)
+      return x < 0.0F ? -y : y;
+
+    if (x < 0.0F) {
+      x = -x;
+      neg = 1;
+    } else
+      neg = 0;
+
+    if (x < _FRteps._Float) {
+      x *= y; // x tiny
+    } else if (x < 1.0F) {
+      float w = x * x;
+
+      x += ((p[0] * w + p[1]) * w + p[2]) * w * x;
+      x *= y;
+    } else if (x < _FXbig) { // worth adding in exp(-x)
+      _FExp(&x, 1.0F, -1);
+      x = y * (x - 0.25F / x);
+    } else
+      _FExp(&x, y, -1);
+
+    return neg ? -x : x;
+  }
+}
+#endif