orca/milepost/ext/angle_headers/CL/cl_half.h

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2022-08-19 18:55:00 +00:00
/*******************************************************************************
* Copyright (c) 2019-2020 The Khronos Group Inc.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
******************************************************************************/
/**
* This is a header-only utility library that provides OpenCL host code with
* routines for converting to/from cl_half values.
*
* Example usage:
*
* #include <CL/cl_half.h>
* ...
* cl_half h = cl_half_from_float(0.5f, CL_HALF_RTE);
* cl_float f = cl_half_to_float(h);
*/
#ifndef OPENCL_CL_HALF_H
#define OPENCL_CL_HALF_H
#include <CL/cl_platform.h>
#include <stdint.h>
#ifdef __cplusplus
extern "C" {
#endif
/**
* Rounding mode used when converting to cl_half.
*/
typedef enum
{
CL_HALF_RTE, // round to nearest even
CL_HALF_RTZ, // round towards zero
CL_HALF_RTP, // round towards positive infinity
CL_HALF_RTN, // round towards negative infinity
} cl_half_rounding_mode;
/* Private utility macros. */
#define CL_HALF_EXP_MASK 0x7C00
#define CL_HALF_MAX_FINITE_MAG 0x7BFF
/*
* Utility to deal with values that overflow when converting to half precision.
*/
static inline cl_half cl_half_handle_overflow(cl_half_rounding_mode rounding_mode,
uint16_t sign)
{
if (rounding_mode == CL_HALF_RTZ)
{
// Round overflow towards zero -> largest finite number (preserving sign)
return (sign << 15) | CL_HALF_MAX_FINITE_MAG;
}
else if (rounding_mode == CL_HALF_RTP && sign)
{
// Round negative overflow towards positive infinity -> most negative finite number
return (1 << 15) | CL_HALF_MAX_FINITE_MAG;
}
else if (rounding_mode == CL_HALF_RTN && !sign)
{
// Round positive overflow towards negative infinity -> largest finite number
return CL_HALF_MAX_FINITE_MAG;
}
// Overflow to infinity
return (sign << 15) | CL_HALF_EXP_MASK;
}
/*
* Utility to deal with values that underflow when converting to half precision.
*/
static inline cl_half cl_half_handle_underflow(cl_half_rounding_mode rounding_mode,
uint16_t sign)
{
if (rounding_mode == CL_HALF_RTP && !sign)
{
// Round underflow towards positive infinity -> smallest positive value
return (sign << 15) | 1;
}
else if (rounding_mode == CL_HALF_RTN && sign)
{
// Round underflow towards negative infinity -> largest negative value
return (sign << 15) | 1;
}
// Flush to zero
return (sign << 15);
}
/**
* Convert a cl_float to a cl_half.
*/
static inline cl_half cl_half_from_float(cl_float f, cl_half_rounding_mode rounding_mode)
{
// Type-punning to get direct access to underlying bits
union
{
cl_float f;
uint32_t i;
} f32;
f32.f = f;
// Extract sign bit
uint16_t sign = f32.i >> 31;
// Extract FP32 exponent and mantissa
uint32_t f_exp = (f32.i >> (CL_FLT_MANT_DIG - 1)) & 0xFF;
uint32_t f_mant = f32.i & ((1 << (CL_FLT_MANT_DIG - 1)) - 1);
// Remove FP32 exponent bias
int32_t exp = f_exp - CL_FLT_MAX_EXP + 1;
// Add FP16 exponent bias
uint16_t h_exp = (uint16_t)(exp + CL_HALF_MAX_EXP - 1);
// Position of the bit that will become the FP16 mantissa LSB
uint32_t lsb_pos = CL_FLT_MANT_DIG - CL_HALF_MANT_DIG;
// Check for NaN / infinity
if (f_exp == 0xFF)
{
if (f_mant)
{
// NaN -> propagate mantissa and silence it
uint16_t h_mant = (uint16_t)(f_mant >> lsb_pos);
h_mant |= 0x200;
return (sign << 15) | CL_HALF_EXP_MASK | h_mant;
}
else
{
// Infinity -> zero mantissa
return (sign << 15) | CL_HALF_EXP_MASK;
}
}
// Check for zero
if (!f_exp && !f_mant)
{
return (sign << 15);
}
// Check for overflow
if (exp >= CL_HALF_MAX_EXP)
{
return cl_half_handle_overflow(rounding_mode, sign);
}
// Check for underflow
if (exp < (CL_HALF_MIN_EXP - CL_HALF_MANT_DIG - 1))
{
return cl_half_handle_underflow(rounding_mode, sign);
}
// Check for value that will become denormal
if (exp < -14)
{
// Denormal -> include the implicit 1 from the FP32 mantissa
h_exp = 0;
f_mant |= 1 << (CL_FLT_MANT_DIG - 1);
// Mantissa shift amount depends on exponent
lsb_pos = -exp + (CL_FLT_MANT_DIG - 25);
}
// Generate FP16 mantissa by shifting FP32 mantissa
uint16_t h_mant = (uint16_t)(f_mant >> lsb_pos);
// Check whether we need to round
uint32_t halfway = 1 << (lsb_pos - 1);
uint32_t mask = (halfway << 1) - 1;
switch (rounding_mode)
{
case CL_HALF_RTE:
if ((f_mant & mask) > halfway)
{
// More than halfway -> round up
h_mant += 1;
}
else if ((f_mant & mask) == halfway)
{
// Exactly halfway -> round to nearest even
if (h_mant & 0x1)
h_mant += 1;
}
break;
case CL_HALF_RTZ:
// Mantissa has already been truncated -> do nothing
break;
case CL_HALF_RTP:
if ((f_mant & mask) && !sign)
{
// Round positive numbers up
h_mant += 1;
}
break;
case CL_HALF_RTN:
if ((f_mant & mask) && sign)
{
// Round negative numbers down
h_mant += 1;
}
break;
}
// Check for mantissa overflow
if (h_mant & 0x400)
{
h_exp += 1;
h_mant = 0;
}
return (sign << 15) | (h_exp << 10) | h_mant;
}
/**
* Convert a cl_double to a cl_half.
*/
static inline cl_half cl_half_from_double(cl_double d, cl_half_rounding_mode rounding_mode)
{
// Type-punning to get direct access to underlying bits
union
{
cl_double d;
uint64_t i;
} f64;
f64.d = d;
// Extract sign bit
uint16_t sign = f64.i >> 63;
// Extract FP64 exponent and mantissa
uint64_t d_exp = (f64.i >> (CL_DBL_MANT_DIG - 1)) & 0x7FF;
uint64_t d_mant = f64.i & (((uint64_t)1 << (CL_DBL_MANT_DIG - 1)) - 1);
// Remove FP64 exponent bias
int64_t exp = d_exp - CL_DBL_MAX_EXP + 1;
// Add FP16 exponent bias
uint16_t h_exp = (uint16_t)(exp + CL_HALF_MAX_EXP - 1);
// Position of the bit that will become the FP16 mantissa LSB
uint32_t lsb_pos = CL_DBL_MANT_DIG - CL_HALF_MANT_DIG;
// Check for NaN / infinity
if (d_exp == 0x7FF)
{
if (d_mant)
{
// NaN -> propagate mantissa and silence it
uint16_t h_mant = (uint16_t)(d_mant >> lsb_pos);
h_mant |= 0x200;
return (sign << 15) | CL_HALF_EXP_MASK | h_mant;
}
else
{
// Infinity -> zero mantissa
return (sign << 15) | CL_HALF_EXP_MASK;
}
}
// Check for zero
if (!d_exp && !d_mant)
{
return (sign << 15);
}
// Check for overflow
if (exp >= CL_HALF_MAX_EXP)
{
return cl_half_handle_overflow(rounding_mode, sign);
}
// Check for underflow
if (exp < (CL_HALF_MIN_EXP - CL_HALF_MANT_DIG - 1))
{
return cl_half_handle_underflow(rounding_mode, sign);
}
// Check for value that will become denormal
if (exp < -14)
{
// Include the implicit 1 from the FP64 mantissa
h_exp = 0;
d_mant |= (uint64_t)1 << (CL_DBL_MANT_DIG - 1);
// Mantissa shift amount depends on exponent
lsb_pos = (uint32_t)(-exp + (CL_DBL_MANT_DIG - 25));
}
// Generate FP16 mantissa by shifting FP64 mantissa
uint16_t h_mant = (uint16_t)(d_mant >> lsb_pos);
// Check whether we need to round
uint64_t halfway = (uint64_t)1 << (lsb_pos - 1);
uint64_t mask = (halfway << 1) - 1;
switch (rounding_mode)
{
case CL_HALF_RTE:
if ((d_mant & mask) > halfway)
{
// More than halfway -> round up
h_mant += 1;
}
else if ((d_mant & mask) == halfway)
{
// Exactly halfway -> round to nearest even
if (h_mant & 0x1)
h_mant += 1;
}
break;
case CL_HALF_RTZ:
// Mantissa has already been truncated -> do nothing
break;
case CL_HALF_RTP:
if ((d_mant & mask) && !sign)
{
// Round positive numbers up
h_mant += 1;
}
break;
case CL_HALF_RTN:
if ((d_mant & mask) && sign)
{
// Round negative numbers down
h_mant += 1;
}
break;
}
// Check for mantissa overflow
if (h_mant & 0x400)
{
h_exp += 1;
h_mant = 0;
}
return (sign << 15) | (h_exp << 10) | h_mant;
}
/**
* Convert a cl_half to a cl_float.
*/
static inline cl_float cl_half_to_float(cl_half h)
{
// Type-punning to get direct access to underlying bits
union
{
cl_float f;
uint32_t i;
} f32;
// Extract sign bit
uint16_t sign = h >> 15;
// Extract FP16 exponent and mantissa
uint16_t h_exp = (h >> (CL_HALF_MANT_DIG - 1)) & 0x1F;
uint16_t h_mant = h & 0x3FF;
// Remove FP16 exponent bias
int32_t exp = h_exp - CL_HALF_MAX_EXP + 1;
// Add FP32 exponent bias
uint32_t f_exp = exp + CL_FLT_MAX_EXP - 1;
// Check for NaN / infinity
if (h_exp == 0x1F)
{
if (h_mant)
{
// NaN -> propagate mantissa and silence it
uint32_t f_mant = h_mant << (CL_FLT_MANT_DIG - CL_HALF_MANT_DIG);
f_mant |= 0x400000;
f32.i = (sign << 31) | 0x7F800000 | f_mant;
return f32.f;
}
else
{
// Infinity -> zero mantissa
f32.i = (sign << 31) | 0x7F800000;
return f32.f;
}
}
// Check for zero / denormal
if (h_exp == 0)
{
if (h_mant == 0)
{
// Zero -> zero exponent
f_exp = 0;
}
else
{
// Denormal -> normalize it
// - Shift mantissa to make most-significant 1 implicit
// - Adjust exponent accordingly
uint32_t shift = 0;
while ((h_mant & 0x400) == 0)
{
h_mant <<= 1;
shift++;
}
h_mant &= 0x3FF;
f_exp -= shift - 1;
}
}
f32.i = (sign << 31) | (f_exp << 23) | (h_mant << 13);
return f32.f;
}
#undef CL_HALF_EXP_MASK
#undef CL_HALF_MAX_FINITE_MAG
#ifdef __cplusplus
}
#endif
#endif /* OPENCL_CL_HALF_H */