ieee 754: start section

Author: cirosantilli

README.adoc

@@ -12063,7 +12063,7 @@ Particularly important numerical analysis instruction, that is used in particula
 * Dot product
 * Matrix multiplication
 
-FMA is so important that IEEE 754 specifies it with single precision drop compared to a separate add and multiply!
+FMA is so important that <<ieee-754>> specifies it with single precision drop compared to a separate add and multiply!
 
 Micro-op fun: http://stackoverflow.com/questions/28630864/how-is-fma-implemented
 
@@ -12990,6 +12990,19 @@ Old floating point unit that you should likely not use anymore, prefer instead t
 ** link:userland/arch/x86_64/fsqrt.S[] FSQRT: square root
 ** link:userland/arch/x86_64/fxch.S[] FXCH: swap ST0 and another register
 
+The ST0-ST7 x87 FPU registers are actually 80-bits wide, this can be seen from GDB with:
+
+....
+i r st0 st1
+....
+
+By counting the number of hex digits, we have 20 digits instead of 16!
+
+Instructions such as FLDL convert standard <<ieee-754>> 64-bit values from memory into this custom 80-bit format.
+
+* https://stackoverflow.com/questions/3206101/extended-80-bit-double-floating-point-in-x87-not-sse2-we-dont-miss-it
+* https://en.wikipedia.org/wiki/Extended_precision#x86_extended_precision_format
+
 ==== x86 x87 FPU vs SIMD
 
 http://stackoverflow.com/questions/1844669/benefits-of-x87-over-sse
@@ -14177,6 +14190,18 @@ http://infocenter.arm.com/help/topic/com.arm.doc.ddi0438i/DDI0438I_cortex_a15_r4
 
 2013.
 
+== IEEE 754
+
+https://en.wikipedia.org/wiki/IEEE_754
+
+Examples:
+
+* link:userland/arch/x86_64/ieee754.S[]
+* link:lkmc/float.h[]
+* https://stackoverflow.com/questions/8341395/what-is-a-subnormal-floating-point-number/53203428#53203428
+* https://stackoverflow.com/questions/18118408/what-is-difference-between-quiet-nan-and-signaling-nan/55648118#55648118
+* https://stackoverflow.com/questions/2618059/in-java-what-does-nan-mean/55673220#55673220
+
 == Baremetal
 
 Getting started at: <<baremetal-setup>>

lkmc/float.h

@@ -0,0 +1,20 @@
+#ifndef LKMC_FLOAT_H
+#define LKMC_FLOAT_H
+
+/* https://github.com/cirosantilli/linux-kernel-module-cheat#ieee-754 */
+
+#define LKMC_FLOAT_64_SIGN_BITS 1
+#define LKMC_FLOAT_64_EXP_BITS 11
+#define LKMC_FLOAT_64_MANTISSA_BITS 52
+#define LKMC_FLOAT_64_EXP_BIAS ((1 << (LKMC_FLOAT_64_EXP_BITS - 1)) - 1)
+#define LKMC_FLOAT_64_EXP_INFINITY_BIASED ((1 << LKMC_FLOAT_64_EXP_BITS) - 1)
+#define LKMC_FLOAT_64_EXP_INFINITY (LKMC_FLOAT_64_EXP_INFINITY_BIASED - LKMC_FLOAT_64_EXP_BIAS)
+#define LKMC_FLOAT_64(sign, exp, mantissa) ((((sign << LKMC_FLOAT_64_EXP_BITS) | exp + LKMC_FLOAT_64_EXP_BIAS) << LKMC_FLOAT_64_MANTISSA_BITS) | mantissa)
+#define LKMC_FLOAT_64_PLUS_INFINITY LKMC_FLOAT_64(0x0, LKMC_FLOAT_64_EXP_INFINITY, 0x0)
+#define LKMC_FLOAT_64_MINUS_INFINITY LKMC_FLOAT_64(0x1, LKMC_FLOAT_64_EXP_INFINITY, 0x0)
+#define LKMC_FLOAT_64_QNAN(x) LKMC_FLOAT_64(0x0, LKMC_FLOAT_64_EXP_INFINITY, (x) | (1 << (LKMC_FLOAT_64_MANTISSA_BITS - 1)))
+#define LKMC_FLOAT_64_QNAN_DEFAULT LKMC_FLOAT_64_QNAN(1 << (LKMC_FLOAT_64_MANTISSA_BITS - 2))
+#define LKMC_FLOAT_64_SNAN(x) LKMC_FLOAT_64(0x0, LKMC_FLOAT_64_EXP_INFINITY, x)
+#define LKMC_FLOAT_64_SNAN_DEFAULT LKMC_FLOAT_64_SNAN(1 << (LKMC_FLOAT_64_MANTISSA_BITS - 2))
+
+#endif

userland/arch/x86_64/ieee754.S

@@ -0,0 +1,59 @@
+/* https://github.com/cirosantilli/linux-kernel-module-cheat#ieee-754 */
+
+#include <lkmc.h>
+#include <lkmc/float.h>
+
+.data
+    double_1_5: .quad LKMC_FLOAT_64(0x0, 0x0, 0x8000000000000)
+    double_2_5: .quad LKMC_FLOAT_64(0x0, 0x1, 0x4000000000000)
+    double_4_0: .quad LKMC_FLOAT_64(0x0, 0x2, 0x0000000000000)
+    double_minus_4_0: .quad LKMC_FLOAT_64(0x1, 0x2, 0x10000000000000)
+    double_plus_infinity: .quad LKMC_FLOAT_64_PLUS_INFINITY
+    double_nan: .quad LKMC_FLOAT_64_QNAN_DEFAULT
+    double_ref_1_5: .double 1.5
+    double_ref_2_5: .double 2.5
+    double_ref_4_0: .double 4.0
+    double_ref_minus_4_0: .double -4.0
+    double_ref_plus_infinity: .double inf
+    double_ref_nan: .double nan
+LKMC_PROLOGUE
+    /* Check that our macros are correct. */
+    LKMC_ASSERT_EQ(double_1_5, double_ref_1_5)
+    LKMC_ASSERT_EQ(double_2_5, double_ref_2_5)
+    LKMC_ASSERT_EQ(double_4_0, double_ref_4_0)
+    LKMC_ASSERT_EQ(double_minus_4_0, double_ref_minus_4_0)
+    LKMC_ASSERT_EQ(double_plus_infinity, double_ref_plus_infinity)
+    /* TODO: GAS nan is a different NaN: 0x7FFFFFFF */
+    /*LKMC_ASSERT_EQ(double_nan, double_ref_nan)*/
+
+    /* x87 80-bit FPU: https://github.com/cirosantilli/linux-kernel-module-cheat#x86-x87-fpu-instructions */
+
+        /* 1.5 + 2.5 == 4.0. */
+        fldl double_1_5
+        fldl double_2_5
+        faddp %st, %st(1)
+        fldl double_4_0
+        fcomip %st(1)
+        LKMC_ASSERT(je)
+
+        /* 4.0 + -4.0 == 0.0. */
+        fldl double_minus_4_0
+        faddp %st, %st(1)
+        fldz
+        fcomip %st(1)
+        LKMC_ASSERT(je)
+
+        /* 0.0 + inf == inf */
+        fldl double_plus_infinity
+        faddp %st, %st(1)
+        fldl double_plus_infinity
+        fcomip %st(1)
+        LKMC_ASSERT(je)
+
+        /*  inf + nan == nan */
+        fldl double_nan
+        faddp %st, %st(1)
+        fldl double_nan
+        fcomip %st(1)
+        LKMC_ASSERT(je)
+LKMC_EPILOGUE