Moving get_buffer

float16.cr

@@ -0,0 +1,191 @@
+print_result  0.0
+print_result -0.0
+print_result  1.5
+print_result -1.5
+print_result  (1_f32 / 0_f32).as(Float32)
+print_result -(1_f32 / 0_f32).as(Float32)
+print_result  (0_f32 / 0_f32).as(Float32)
+print_result -(0_f32 / 0_f32).as(Float32)
+print_result  65504.0
+print_result  10_000.0
+print_result -10_000.0
+print_result 153.0
+print_result -3992.0
+# print_result 0.15625
+# print_result  10.539187
+# print_result -10.539187
+
+def print_result(value : Float32)
+	final_value, status = f32_to_f16 value
+	puts "#{get_summary value}"
+	puts "#{get_summary final_value} => status: #{status}"
+end
+
+def binary_8(v)
+	sprintf "%08b", v & 0xFF
+end
+
+def binary_16(v)
+	sprintf "%08b %08b", (v >> 8) & 0xFF, v & 0xFF
+end
+
+def binary_24(v)
+    sprintf "%08b %08b %08b", (v >> 16) & 0xFF, (v >> 8) & 0xFF, v & 0xFF
+end
+
+def binary_32(v)
+    sprintf "%08b %08b %08b %08b", (v >> 24) & 0xFF, (v >> 16) & 0xFF, (v >> 8) & 0xFF, v & 0xFF
+end
+
+def binary_mantisse_f32(v)
+	binary_24(v)[1..] # mantisse only is 23-bit, remove the first represented bit
+end
+
+def binary_mantisse_f16(v)
+	binary_16(v)[6..] # mantisse only is 10-bit, remove the first represented bits
+end
+
+
+def get_buffer(value : UInt16)
+	[ ((value >> 8) & 0xFF).to_u8, (value & 0xFF).to_u8 ]
+end
+
+def get_summary(value : Float32)
+	buffer = get_buffer value
+
+	# 0 or 1
+	sign = (buffer[0].to_u32 >> 7) 
+	# 8-bit value
+	exp  = ((buffer[0].to_u32 & 0x7F) << 1) | (buffer[1].to_u32 >> 7)
+	# 23-bit value
+	man  = (buffer[1].to_u32 << 16) | (buffer[2].to_u32 << 8) | buffer[3].to_u32
+
+	str_value = "%15.6f" % value
+	str_sign  = binary_8(sign)[-1]
+	str_exp   = "%10s" % binary_8(exp)
+	str_man   = "%28s" % binary_mantisse_f32(man)
+
+	"32-bit: #{str_value} => #{str_sign} #{str_exp} #{str_man}"
+end
+
+# Float16 in a UInt16 value
+def get_summary(value : UInt16)
+	buffer = get_buffer value
+
+	# 1-bit value
+	sign = (buffer[0].to_u32 >> 7) 
+	# 5-bit value
+	exp  = (buffer[0].to_u32 & 0x7F) >> 2
+	# 23-bit value
+	man  = ((buffer[0].to_u32 & 0x03) << 8) | buffer[1].to_u32
+
+	str_value = "%15d" % value
+	str_sign  = binary_8(sign)[-1]       #  1-bit value
+	str_exp   = "%10s" % binary_8(exp)[3..7]      #  5-bit value
+	str_man   = "%28s" % binary_mantisse_f16(man) # 10-bit value
+
+	"16-bit: #{str_value} => #{str_sign} #{str_exp} #{str_man}"
+end
+
+def get_buffer(value : Float32)
+	# TODO: is there a simpler way to perform binary operations over a float?
+	# Extract IEEE754 components
+	io = IO::Memory.new
+	io.write_bytes(value, IO::ByteFormat::NetworkEndian)
+	io.rewind
+	v = io.gets(4)
+
+	if v.nil?
+		raise "cannot perform f32 to f16 on value #{value}"
+	end
+
+	v.to_slice
+end
+
+enum ConversionInfo
+	OK
+	NotANumber
+	Overflow
+	Underflow
+	FullUnderflow
+	Infinite
+	NegativeInfinite
+end
+
+def f32_to_f16(value : Float32) 
+
+	buffer = get_buffer value
+
+	# 0 or 1
+	sign = (buffer[0].to_u32 >> 7) 
+	# 8-bit value
+	exp  = ((buffer[0].to_u32 & 0x7F) << 1) | (buffer[1].to_u32 >> 7)
+	# 23-bit value
+	man  = ((buffer[1].to_u32 & 0x7F) << 16) | (buffer[2].to_u32 << 8) | buffer[3].to_u32
+
+	# Check for all exponent bits being set, which is Infinity or NaN
+	if exp == 0xFF
+		# Set mantissa MSB for NaN (and also keep shifted mantissa bits)
+		nan_bit = man == 0 ? 0 : 0x0200
+		final_value = (((sign << 15) | 0x7C00 | nan_bit | man) & 0xFFFF).to_u16
+		conversion_info = if nan_bit != 0
+			ConversionInfo::NotANumber
+		elsif sign == 0
+			ConversionInfo::Infinite
+		else
+			ConversionInfo::NegativeInfinite
+		end
+		return final_value, conversion_info
+	end
+
+	# The number is normalized, start assembling half precision version
+	half_sign = sign << 15
+
+	# Unbias the exponent, then bias for half precision
+	half_exp = (exp.to_i64 - 127 + 15).to_i16
+
+	# Check for exponent overflow, return +infinity
+	if half_exp >= 0x1F
+		final_value = (half_sign | 0x7C00).to_u16
+		return final_value, ConversionInfo::Overflow
+	end
+
+	# Check for underflow
+	if half_exp <= 0
+		# Check mantissa for what we can do
+		if 14 - half_exp > 24
+			# No rounding possibility, so this is a full underflow, return signed zero
+			return half_sign.to_u16, ConversionInfo::FullUnderflow
+		end
+
+		# Don't forget about hidden leading mantissa bit when assembling mantissa
+		man = man | 0x0080_0000
+		half_man = man >> (14 - half_exp)
+
+		# Check for rounding (see comment above functions)
+		round_bit = 1 << (13 - half_exp)
+		if (man & round_bit) != 0 && (man & (3 * round_bit - 1)) != 0
+			half_man += 1
+		end
+
+		# No exponent for subnormals
+		final_value = (half_sign | half_man).to_u16
+
+		return final_value, ConversionInfo::Underflow
+	end
+
+	# Rebias the exponent
+	half_exp = (half_exp) << 10
+	half_man = (man >> 13) & 0x03FF
+	# Check for rounding (see comment above functions)
+	round_bit = 0x0000_1000u32
+	final_value = if (man & round_bit) != 0 && (man & (3 * round_bit - 1)) != 0
+		# Round it
+		((half_sign | half_exp | half_man) + 1).to_u16
+	else
+		v = (half_sign | half_exp | half_man)
+		(half_sign | half_exp | half_man).to_u16
+	end
+
+	return final_value, ConversionInfo::OK
+end