浮点标准 IEEE754 精要 - 版本历史

Comcat：/* 精度限制 */

2019-11-28T02:22:58Z

‎精度限制

Comcat：/* 类型互转通用函数 */

2019-11-28T02:16:16Z

‎类型互转通用函数

Comcat：/* 精度限制 */

2019-11-27T23:57:18Z

‎精度限制

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2019-11-27T23:56:37Z

‎精度限制

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2019-11-27T23:55:10Z

‎精度限制

Comcat：/* 半精度浮点 */

2019-11-27T23:54:34Z

‎半精度浮点

Comcat：/* 半精度浮点 */

2019-11-27T23:38:11Z

‎半精度浮点

Comcat：/* 类型互转通用函数 */

2019-11-27T12:18:21Z

‎类型互转通用函数

Comcat：/* 类型互转通用函数 */

2019-11-27T12:16:12Z

‎类型互转通用函数

Comcat：/* 类型互转通用函数 */

2019-11-27T12:13:38Z

‎类型互转通用函数

@@ 第112行： / 第112行： @@
 '''Precision limitations on decimal values in [1, 2048]:'''
-* Decimals between 1 and 2: fixed interval 2^−10 (1+2^−10 is the next largest float after 1)
+* Decimals between 1 and 2: fixed interval 2^−10 (1+2^−10 is the next largest float after 1) ≈ 0.001
-* Decimals between 2 and 4: fixed interval 2^−9
+* Decimals between 2 and 4: fixed interval 2^−9 ≈ 0.002
-* Decimals between 4 and 8: fixed interval 2^−8
+* Decimals between 4 and 8: fixed interval 2^−8 ≈ 0.004
-* Decimals between 8 and 16: fixed interval 2^−7
+* Decimals between 8 and 16: fixed interval 2^−7 ≈ 0.008
-* Decimals between 16 and 32: fixed interval 2^−6
+* Decimals between 16 and 32: fixed interval 2^−6 ≈ 0.016
-* Decimals between 32 and 64: fixed interval 2^−5
+* Decimals between 32 and 64: fixed interval 2^−5 ≈ 0.031
-* Decimals between 64 and 128: fixed interval 2^−4
+* Decimals between 64 and 128: fixed interval 2^−4 = 0.0625
-* Decimals between 128 and 256: fixed interval 2^−3
+* Decimals between 128 and 256: fixed interval 2^−3 = 0.125
-* Decimals between 256 and 512: fixed interval 2^−2
+* Decimals between 256 and 512: fixed interval 2^−2 = 0.25
-* Decimals between 512 and 1024: fixed interval 2^−1
+* Decimals between 512 and 1024: fixed interval 2^−1 = 0.5
-* Decimals between 1024 and 2048: fixed interval 2^0
+* Decimals between 1024 and 2048: fixed interval 2^0 = 1

@@ 第205行： / 第205行： @@
 <source lang=bash>
 Testing the float16, supported by gcc...
 sizeof(fp16): 2
 f1 = 0.2321
+---------------------------------------------------
-Testing the float16 function...
+Testing the general function of float16...
-Convert fp32=1.245 to fp16, HEX: 3CFB
+Convert fp32=13.245 to fp16, HEX: 4A9F
-fp16 to float: 1.245
+fp16 to float: 13.242
 </source>

@@ 第132行： / 第132行： @@
 * Integers between 8192 and 16384 round to a multiple of 8
 * Integers between 16384 and 32768 round to a multiple of 16
-* Integers between 32768 and 65519 round to a multiple of 32[9]
+* Integers between 32768 and 65519 round to a multiple of 32
 * Integers above 65519 are rounded to "infinity" if using round-to-even, or above 65535 if using round-to-zero, or above 65504 if using round-to-infinity.

@@ 第93行： / 第93行： @@
 '''Precision limitations on decimal values in [0, 1]:'''
-* Decimals between 2−24 (minimum positive subnormal) and 2−14 (maximum subnormal): fixed interval 2−24
+* Decimals between 2^−24 (minimum positive subnormal) and 2^−14 (maximum subnormal): fixed interval 2^−24
-* Decimals between 2−14 (minimum positive normal) and 2−13: fixed interval 2−24
+* Decimals between 2^−14 (minimum positive normal) and 2^−13: fixed interval 2^−24
-* Decimals between 2−13 and 2−12: fixed interval 2−23
+* Decimals between 2^−13 and 2^−12: fixed interval 2^−23
-* Decimals between 2−12 and 2−11: fixed interval 2−22
+* Decimals between 2^−12 and 2^−11: fixed interval 2^−22
-* Decimals between 2−11 and 2−10: fixed interval 2−21
+* Decimals between 2^−11 and 2^−10: fixed interval 2^−21
-* Decimals between 2−10 and 2−9: fixed interval 2−20
+* Decimals between 2^−10 and 2^−9: fixed interval 2^−20
-* Decimals between 2−9 and 2−8: fixed interval 2−19
+* Decimals between 2^−9 and 2^−8: fixed interval 2^−19
-* Decimals between 2−8 and 2−7: fixed interval 2−18
+* Decimals between 2^−8 and 2^−7: fixed interval 2^−18
-* Decimals between 2−7 and 2−6: fixed interval 2−17
+* Decimals between 2^−7 and 2^−6: fixed interval 2^−17
-* Decimals between 2−6 and 2−5: fixed interval 2−16
+* Decimals between 2^−6 and 2^−5: fixed interval 2^−16
-* Decimals between 2−5 and 2−4: fixed interval 2−15
+* Decimals between 2^−5 and 2^−4: fixed interval 2^−15
-* Decimals between 2−4 and 2−3: fixed interval 2−14
+* Decimals between 2^−4 and 2^−3: fixed interval 2^−14
-* Decimals between 2−3 and 2−2: fixed interval 2−13
+* Decimals between 2^−3 and 2^−2: fixed interval 2^−13
-* Decimals between 2−2 and 2−1: fixed interval 2−12
+* Decimals between 2^−2 and 2^−1: fixed interval 2^−12
-* Decimals between 2−1 and 2−0: fixed interval 2−11
+* Decimals between 2^−1 and 2^−0: fixed interval 2^−11
 '''Precision limitations on decimal values in [1, 2048]:'''
-* Decimals between 1 and 2: fixed interval 2−10 (1+2−10 is the next largest float after 1)
+* Decimals between 1 and 2: fixed interval 2^−10 (1+2^−10 is the next largest float after 1)
-* Decimals between 2 and 4: fixed interval 2−9
+* Decimals between 2 and 4: fixed interval 2^−9
-* Decimals between 4 and 8: fixed interval 2−8
+* Decimals between 4 and 8: fixed interval 2^−8
-* Decimals between 8 and 16: fixed interval 2−7
+* Decimals between 8 and 16: fixed interval 2^−7
-* Decimals between 16 and 32: fixed interval 2−6
+* Decimals between 16 and 32: fixed interval 2^−6
-* Decimals between 32 and 64: fixed interval 2−5
+* Decimals between 32 and 64: fixed interval 2^−5
-* Decimals between 64 and 128: fixed interval 2−4
+* Decimals between 64 and 128: fixed interval 2^−4
-* Decimals between 128 and 256: fixed interval 2−3
+* Decimals between 128 and 256: fixed interval 2^−3
-* Decimals between 256 and 512: fixed interval 2−2
+* Decimals between 256 and 512: fixed interval 2^−2
-* Decimals between 512 and 1024: fixed interval 2−1
+* Decimals between 512 and 1024: fixed interval 2^−1
-* Decimals between 1024 and 2048: fixed interval 20
+* Decimals between 1024 and 2048: fixed interval 2^0

@@ 第91行： / 第91行： @@
 === 精度限制 ===
-Precision limitations on decimal values in [0, 1][edit]
+'''Precision limitations on decimal values in [0, 1]:'''
 Decimals between 2−24 (minimum positive subnormal) and 2−14 (maximum subnormal): fixed interval 2−24
-Decimals between 2−14 (minimum positive normal) and 2−13: fixed interval 2−24
+* Decimals between 2−24 (minimum positive subnormal) and 2−14 (maximum subnormal): fixed interval 2−24
-Decimals between 2−13 and 2−12: fixed interval 2−23
+* Decimals between 2−14 (minimum positive normal) and 2−13: fixed interval 2−24
-Decimals between 2−12 and 2−11: fixed interval 2−22
+* Decimals between 2−13 and 2−12: fixed interval 2−23
-Decimals between 2−11 and 2−10: fixed interval 2−21
+* Decimals between 2−12 and 2−11: fixed interval 2−22
-Decimals between 2−10 and 2−9: fixed interval 2−20
+* Decimals between 2−11 and 2−10: fixed interval 2−21
-Decimals between 2−9 and 2−8: fixed interval 2−19
+* Decimals between 2−10 and 2−9: fixed interval 2−20
-Decimals between 2−8 and 2−7: fixed interval 2−18
+* Decimals between 2−9 and 2−8: fixed interval 2−19
-Decimals between 2−7 and 2−6: fixed interval 2−17
+* Decimals between 2−8 and 2−7: fixed interval 2−18
-Decimals between 2−6 and 2−5: fixed interval 2−16
+* Decimals between 2−7 and 2−6: fixed interval 2−17
-Decimals between 2−5 and 2−4: fixed interval 2−15
+* Decimals between 2−6 and 2−5: fixed interval 2−16
-Decimals between 2−4 and 2−3: fixed interval 2−14
+* Decimals between 2−5 and 2−4: fixed interval 2−15
-Decimals between 2−3 and 2−2: fixed interval 2−13
+* Decimals between 2−4 and 2−3: fixed interval 2−14
-Decimals between 2−2 and 2−1: fixed interval 2−12
+* Decimals between 2−3 and 2−2: fixed interval 2−13
-Decimals between 2−1 and 2−0: fixed interval 2−11
+* Decimals between 2−2 and 2−1: fixed interval 2−12
 '''Precision limitations on decimal values in [1, 2048]:'''

@@ 第64行： / 第64行： @@
-例子
+=== 例子 ===
 <pre>
@@ 第86行： / 第86行： @@
 11111 0000000000 = 0xfc00 = -infinity
 </pre>
 <br>

@@ 第67行： / 第67行： @@
 <pre>
-00000 0000000001 = 2^-14 x (0 + 1/1024)  ≈ 0.000000059605 (smallest positive subnormal number)
+00000 0000000001 = 0x0001 = 2^-14 x (0 + 1/1024)  ≈ 0.000000059605 (smallest positive subnormal number)
-00000 1111111111 = 2^-14 x (0 + 1023/1024) ≈ 0.000060976 (largest subnormal number)
+00000 1111111111 = 0x03ff = 2^-14 x (0 + 1023/1024) ≈ 0.000060976 (largest subnormal number)
-00001 0000000000 = 2^-14 x (1 + 0/1024) ≈ 0.000061035  (smallest positive normal number)
+00001 0000000000 = 0x0400 = 2^-14 x (1 + 0/1024) ≈ 0.000061035  (smallest positive normal number)
-11110 1111111111 = 2^15 x (1 + 1023/1024) = 65504 (largest normal number)
+11110 1111111111 = 0x7bff = 2^15 x (1 + 1023/1024) = 65504 (largest normal number)
-01110 1111111111 = 2^-1 x (1 + 1023/1024) ≈ 0.99951 (largest number less than one)
+01110 1111111111 = 0x3bff = 2^-1 x (1 + 1023/1024) ≈ 0.99951 (largest number less than one)
-01111 0000000000 = 2^0 x (1 + 0/1024) = 1
+01111 0000000000 = 0x3c00 = 2^0 x (1 + 0/1024) = 1
 01111 0000000001 = 0x3c01 = 2^0 x (1 + 1/1024) ≈ 1.001

@@ 第152行： / 第152行： @@
 	delay(5000);
+}
 </source>

@@ 第107行： / 第107行： @@
 <source lang=cpp>
-float myFloat = 1.24;
+#include  "ieeehalfprecision.c"
-uint16_t myfp16;
-float2halfp(&myfp16, &myFloat, 1);     // it accepts a series of floats, so use 1 to input 1 float
-// an example to revert the half float back
+void test_fp16()
 float myfp32;
-halfp2float(&myfp32, &myfp16, 1);
+	float myFloat = 1.245;
 </source>

@@ 第102行： / 第102行： @@
 === 类型互转通用函数 ===
-与 float / double 类型互相转换的跨平台通用函数
+与 float / double 类型互相转换的跨平台通用函数：
 import the file "[[ieeehalfprecision.c]]" into your project and use it like this :