是否有一个C++函数可以准确返回平方根反比的内置 CPU 操作 RSQRTSS 的值?
Is there a C++ function that returns exactly the value of the built-in CPU operation RSQRTSS for inverse square root?
我正在寻找一个返回浮点数的逆 sqrt 的C++函数：通过使用与内置 XMM 操作RSQRTSS(参见 https://www.felixcloutier.com/x86/rsqrtss)完全相同的方法进行rsqrt(x) = 1/sqrt(x)。(即，我想要内置的近似值而不是更精确的1/sqrtf，而且我不在乎速度(很多)。
根据这个问题：
是否有用于双精度平方根反比的快速 C 或 C++ 标准库函数？
。至少没有"双精度的快速方法"可以使用标准的C++库来实现这一点。但是如何缓慢，非标准且具有floats？
RSQRTSS指令可以通过immintrin.h中声明的_mm_rsqrt_ss()内在很容易访问。但我们也可以在软件中模拟指令，就像下面的my_rsqrtf()函数一样。通过简单地观察RSQRTSS的输出，很容易发现其函数值基于一个包含 2个 11个条目的(虚拟)表，每个条目的大小为 12 位。
请注意"虚拟"属性，因为硬件不太可能使用直接的 24 Kbit 表。我对表条目中模式的分析并不建议使用二分表。可以使用更简单的压缩方案 - 就像我在下面的代码中使用的方案 - 基于基值表和偏移表。我的方案只需要一个狭窄的加法器，但将ROM存储减少到13 Kbit，即几乎一半。
以下实施是在使用 Ivy Bridge 架构的英特尔至强处理器 E3-1270 V2 上开发和测试的。各种英特尔架构之间的RSQRTSS实现可能存在一些功能差异，并且不同 x86-84 供应商的架构之间可能存在这种差异。
下面的框架检查my_rsqrtf()仿真是否为所有四种舍入模式、两种 DAZ(非正常值为零)模式和两种 FTZ(齐平为零)模式的RSQRTSS提供按位相同的结果。我们发现函数结果不受任何模式的影响，这与RSQRTSS英特尔在英特尔® 64 和 IA-32 架构软件开发人员手册：
RSQRTSS 指令不受 MXCSR 寄存器中的舍入控制位的影响。当源值为 0.0 时，将返回源值符号的∞。非正态源值被视为 0.0(符号相同)。当源值为负值(−0.0 除外)时，将返回不定浮点。当源值为 SNaN 或 QNaN 时，SNaN 将转换为 QNaN 或返回源 QNaN。
#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <string.h>
#include <math.h>
#include "immintrin.h"
/* SSE reference for RSQRTSS instruction */
float sse_rsqrtf (float a, uint32_t daz, uint32_t ftz, uint32_t rnd)
{
__m128 b, t;
float res;
uint32_t old_mxcsr;
old_mxcsr = _mm_getcsr();
_MM_SET_DENORMALS_ZERO_MODE (daz);
_MM_SET_FLUSH_ZERO_MODE (ftz);
_MM_SET_ROUNDING_MODE (rnd);
b = _mm_set_ss (a);
t = _mm_rsqrt_ss (b);
_mm_store_ss (&res, t);
_mm_setcsr (old_mxcsr);
return res;
}
inline uint32_t float_as_uint32 (float a)
{
uint32_t r;
memcpy (&r, &a, sizeof r);
return r;
}
inline float uint32_as_float (uint32_t a)
{
float r;
memcpy (&r, &a, sizeof r);
return r;
}
#define LOG2_NBR_TAB_ENTRIES (11)
#define NBR_TAB_ENTRIES (1 << LOG2_NBR_TAB_ENTRIES)
#define TAB_ENTRY_BITS (12)
#define BASE_TAB_ENTRY_BITS (9)
/* 128 9-bit entries = 1152 bits */
const uint16_t base_tab[128] = {
0x0ce, 0x0c9, 0x0c3, 0x0be, 0x0b9, 0x0b4, 0x0af, 0x0aa,
0x0a6, 0x0a1, 0x09d, 0x098, 0x094, 0x090, 0x08b, 0x087,
0x083, 0x07f, 0x07c, 0x078, 0x074, 0x070, 0x06d, 0x069,
0x066, 0x062, 0x05f, 0x05c, 0x058, 0x055, 0x052, 0x04f,
0x04c, 0x049, 0x046, 0x043, 0x040, 0x03d, 0x03a, 0x038,
0x035, 0x032, 0x030, 0x02d, 0x02a, 0x028, 0x025, 0x023,
0x021, 0x01e, 0x01c, 0x019, 0x017, 0x015, 0x013, 0x010,
0x00e, 0x00c, 0x00a, 0x008, 0x006, 0x004, 0x002, 0x000,
0x1f8, 0x1f0, 0x1e9, 0x1e1, 0x1da, 0x1d3, 0x1cc, 0x1c5,
0x1bf, 0x1b8, 0x1b2, 0x1ab, 0x1a5, 0x19f, 0x199, 0x194,
0x18e, 0x188, 0x183, 0x17e, 0x178, 0x173, 0x16e, 0x169,
0x164, 0x15f, 0x15a, 0x156, 0x151, 0x14d, 0x148, 0x144,
0x13f, 0x13b, 0x137, 0x133, 0x12f, 0x12b, 0x127, 0x123,
0x11f, 0x11b, 0x118, 0x114, 0x110, 0x10d, 0x109, 0x106,
0x102, 0x0ff, 0x0fc, 0x0f8, 0x0f5, 0x0f2, 0x0ef, 0x0eb,
0x0e8, 0x0e5, 0x0e2, 0x0df, 0x0dc, 0x0d9, 0x0d7, 0x0d4,
};
/* 2048 6-bit entries = 12288 bits */
const uint8_t ofs_tab[2048] = {
0x2f, 0x2c, 0x2a, 0x27, 0x24, 0x21, 0x1e, 0x1c, 0x19, 0x16, 0x13, 0x10, 0x0e, 0x0b, 0x08, 0x05,
0x2b, 0x28, 0x25, 0x22, 0x1f, 0x1d, 0x1a, 0x17, 0x15, 0x12, 0x0f, 0x0c, 0x0a, 0x07, 0x04, 0x02,
0x2f, 0x2c, 0x29, 0x27, 0x24, 0x21, 0x1f, 0x1c, 0x19, 0x17, 0x14, 0x11, 0x0f, 0x0c, 0x09, 0x07,
0x2c, 0x29, 0x27, 0x24, 0x22, 0x1f, 0x1c, 0x1a, 0x17, 0x15, 0x12, 0x0f, 0x0d, 0x0a, 0x08, 0x05,
0x2a, 0x28, 0x25, 0x23, 0x20, 0x1e, 0x1b, 0x18, 0x16, 0x13, 0x11, 0x0e, 0x0c, 0x09, 0x07, 0x04,
0x2a, 0x27, 0x24, 0x22, 0x1f, 0x1d, 0x1a, 0x18, 0x15, 0x13, 0x10, 0x0e, 0x0b, 0x09, 0x07, 0x04,
0x2a, 0x27, 0x25, 0x22, 0x20, 0x1d, 0x1b, 0x18, 0x16, 0x13, 0x11, 0x0f, 0x0c, 0x0a, 0x07, 0x05,
0x2a, 0x28, 0x26, 0x23, 0x21, 0x1e, 0x1c, 0x1a, 0x17, 0x15, 0x12, 0x10, 0x0e, 0x0b, 0x09, 0x07,
0x24, 0x22, 0x1f, 0x1d, 0x1b, 0x18, 0x16, 0x14, 0x11, 0x0f, 0x0d, 0x0a, 0x08, 0x06, 0x03, 0x01,
0x27, 0x24, 0x22, 0x20, 0x1d, 0x1b, 0x19, 0x16, 0x14, 0x12, 0x10, 0x0d, 0x0b, 0x09, 0x06, 0x04,
0x22, 0x20, 0x1d, 0x1b, 0x19, 0x17, 0x14, 0x12, 0x10, 0x0e, 0x0b, 0x09, 0x07, 0x05, 0x02, 0x00,
0x26, 0x24, 0x21, 0x1f, 0x1d, 0x1b, 0x19, 0x16, 0x14, 0x12, 0x10, 0x0e, 0x0b, 0x09, 0x07, 0x05,
0x23, 0x20, 0x1e, 0x1c, 0x1a, 0x18, 0x16, 0x13, 0x11, 0x0f, 0x0d, 0x0b, 0x09, 0x06, 0x04, 0x02,
0x20, 0x1e, 0x1c, 0x1a, 0x17, 0x15, 0x13, 0x11, 0x0f, 0x0d, 0x0b, 0x09, 0x06, 0x04, 0x02, 0x00,
0x26, 0x24, 0x22, 0x20, 0x1e, 0x1c, 0x19, 0x17, 0x15, 0x13, 0x11, 0x0f, 0x0d, 0x0b, 0x09, 0x07,
0x25, 0x23, 0x21, 0x1f, 0x1d, 0x1a, 0x18, 0x16, 0x14, 0x12, 0x10, 0x0e, 0x0c, 0x0a, 0x08, 0x06,
0x24, 0x22, 0x20, 0x1e, 0x1c, 0x1a, 0x18, 0x16, 0x14, 0x12, 0x10, 0x0e, 0x0c, 0x0a, 0x08, 0x06,
0x24, 0x22, 0x20, 0x1e, 0x1c, 0x1a, 0x18, 0x16, 0x14, 0x12, 0x10, 0x0e, 0x0c, 0x0a, 0x08, 0x06,
0x1d, 0x1b, 0x19, 0x17, 0x15, 0x13, 0x11, 0x0f, 0x0d, 0x0b, 0x09, 0x07, 0x05, 0x03, 0x01, 0x00,
0x1e, 0x1c, 0x1a, 0x18, 0x16, 0x14, 0x12, 0x10, 0x0e, 0x0c, 0x0b, 0x09, 0x07, 0x05, 0x03, 0x01,
0x1f, 0x1d, 0x1c, 0x1a, 0x18, 0x16, 0x14, 0x12, 0x10, 0x0e, 0x0d, 0x0b, 0x09, 0x07, 0x05, 0x03,
0x21, 0x20, 0x1e, 0x1c, 0x1a, 0x18, 0x16, 0x15, 0x13, 0x11, 0x0f, 0x0d, 0x0b, 0x0a, 0x08, 0x06,
0x1c, 0x1a, 0x19, 0x17, 0x15, 0x13, 0x11, 0x10, 0x0e, 0x0c, 0x0a, 0x08, 0x07, 0x05, 0x03, 0x01,
0x1f, 0x1e, 0x1c, 0x1a, 0x18, 0x16, 0x15, 0x13, 0x11, 0x0f, 0x0e, 0x0c, 0x0a, 0x08, 0x07, 0x05,
0x1b, 0x19, 0x18, 0x16, 0x14, 0x12, 0x11, 0x0f, 0x0d, 0x0b, 0x0a, 0x08, 0x06, 0x04, 0x03, 0x01,
0x1f, 0x1e, 0x1c, 0x1a, 0x18, 0x17, 0x15, 0x13, 0x12, 0x10, 0x0e, 0x0c, 0x0b, 0x09, 0x07, 0x06,
0x1c, 0x1a, 0x19, 0x17, 0x15, 0x13, 0x12, 0x10, 0x0e, 0x0d, 0x0b, 0x09, 0x08, 0x06, 0x04, 0x03,
0x19, 0x17, 0x16, 0x14, 0x12, 0x11, 0x0f, 0x0d, 0x0c, 0x0a, 0x08, 0x07, 0x05, 0x03, 0x02, 0x00,
0x1f, 0x1d, 0x1b, 0x1a, 0x18, 0x16, 0x15, 0x13, 0x11, 0x10, 0x0e, 0x0d, 0x0b, 0x09, 0x08, 0x06,
0x1d, 0x1b, 0x19, 0x18, 0x16, 0x14, 0x13, 0x11, 0x10, 0x0e, 0x0c, 0x0b, 0x09, 0x08, 0x06, 0x04,
0x1b, 0x19, 0x18, 0x16, 0x15, 0x13, 0x11, 0x10, 0x0e, 0x0d, 0x0b, 0x0a, 0x08, 0x06, 0x05, 0x03,
0x1a, 0x18, 0x17, 0x15, 0x13, 0x12, 0x10, 0x0f, 0x0d, 0x0c, 0x0a, 0x09, 0x07, 0x06, 0x04, 0x02,
0x19, 0x17, 0x16, 0x14, 0x13, 0x11, 0x10, 0x0e, 0x0d, 0x0b, 0x0a, 0x08, 0x07, 0x05, 0x03, 0x02,
0x18, 0x17, 0x15, 0x14, 0x12, 0x11, 0x0f, 0x0e, 0x0c, 0x0b, 0x09, 0x08, 0x06, 0x05, 0x03, 0x02,
0x18, 0x17, 0x15, 0x14, 0x12, 0x11, 0x0f, 0x0e, 0x0d, 0x0b, 0x0a, 0x08, 0x07, 0x05, 0x04, 0x02,
0x19, 0x17, 0x16, 0x14, 0x13, 0x11, 0x10, 0x0e, 0x0d, 0x0c, 0x0a, 0x09, 0x07, 0x06, 0x04, 0x03,
0x19, 0x18, 0x16, 0x15, 0x14, 0x12, 0x11, 0x0f, 0x0e, 0x0c, 0x0b, 0x0a, 0x08, 0x07, 0x05, 0x04,
0x1a, 0x19, 0x18, 0x16, 0x15, 0x13, 0x12, 0x10, 0x0f, 0x0e, 0x0c, 0x0b, 0x09, 0x08, 0x07, 0x05,
0x1c, 0x1a, 0x19, 0x18, 0x16, 0x15, 0x13, 0x12, 0x11, 0x0f, 0x0e, 0x0c, 0x0b, 0x0a, 0x08, 0x07,
0x15, 0x14, 0x13, 0x11, 0x10, 0x0f, 0x0d, 0x0c, 0x0a, 0x09, 0x08, 0x06, 0x05, 0x04, 0x02, 0x01,
0x17, 0x16, 0x15, 0x13, 0x12, 0x11, 0x0f, 0x0e, 0x0d, 0x0b, 0x0a, 0x08, 0x07, 0x06, 0x04, 0x03,
0x1a, 0x18, 0x17, 0x16, 0x14, 0x13, 0x12, 0x10, 0x0f, 0x0e, 0x0c, 0x0b, 0x0a, 0x08, 0x07, 0x06,
0x14, 0x13, 0x12, 0x10, 0x0f, 0x0e, 0x0c, 0x0b, 0x0a, 0x08, 0x07, 0x06, 0x05, 0x03, 0x02, 0x01,
0x17, 0x16, 0x15, 0x13, 0x12, 0x11, 0x0f, 0x0e, 0x0d, 0x0c, 0x0a, 0x09, 0x08, 0x06, 0x05, 0x04,
0x1b, 0x19, 0x18, 0x17, 0x15, 0x14, 0x13, 0x12, 0x10, 0x0f, 0x0e, 0x0c, 0x0b, 0x0a, 0x09, 0x07,
0x16, 0x15, 0x13, 0x12, 0x11, 0x10, 0x0e, 0x0d, 0x0c, 0x0b, 0x09, 0x08, 0x07, 0x06, 0x04, 0x03,
0x1a, 0x19, 0x17, 0x16, 0x15, 0x14, 0x12, 0x11, 0x10, 0x0f, 0x0d, 0x0c, 0x0b, 0x0a, 0x08, 0x07,
0x16, 0x15, 0x13, 0x12, 0x11, 0x10, 0x0e, 0x0d, 0x0c, 0x0b, 0x0a, 0x08, 0x07, 0x06, 0x05, 0x03,
0x12, 0x11, 0x10, 0x0f, 0x0d, 0x0c, 0x0b, 0x0a, 0x08, 0x07, 0x06, 0x05, 0x04, 0x02, 0x01, 0x00,
0x17, 0x16, 0x14, 0x13, 0x12, 0x11, 0x10, 0x0e, 0x0d, 0x0c, 0x0b, 0x0a, 0x08, 0x07, 0x06, 0x05,
0x14, 0x12, 0x11, 0x10, 0x0f, 0x0e, 0x0d, 0x0b, 0x0a, 0x09, 0x08, 0x07, 0x05, 0x04, 0x03, 0x02,
0x19, 0x18, 0x16, 0x15, 0x14, 0x13, 0x12, 0x11, 0x0f, 0x0e, 0x0d, 0x0c, 0x0b, 0x0a, 0x08, 0x07,
0x16, 0x15, 0x14, 0x13, 0x11, 0x10, 0x0f, 0x0e, 0x0d, 0x0c, 0x0b, 0x09, 0x08, 0x07, 0x06, 0x05,
0x14, 0x13, 0x11, 0x10, 0x0f, 0x0e, 0x0d, 0x0c, 0x0b, 0x09, 0x08, 0x07, 0x06, 0x05, 0x04, 0x03,
0x11, 0x10, 0x0f, 0x0e, 0x0d, 0x0c, 0x0b, 0x0a, 0x08, 0x07, 0x06, 0x05, 0x04, 0x03, 0x02, 0x01,
0x18, 0x16, 0x15, 0x14, 0x13, 0x12, 0x11, 0x10, 0x0f, 0x0e, 0x0c, 0x0b, 0x0a, 0x09, 0x08, 0x07,
0x16, 0x15, 0x14, 0x12, 0x11, 0x10, 0x0f, 0x0e, 0x0d, 0x0c, 0x0b, 0x0a, 0x09, 0x08, 0x06, 0x05,
0x14, 0x13, 0x12, 0x11, 0x10, 0x0f, 0x0e, 0x0d, 0x0c, 0x0b, 0x09, 0x08, 0x07, 0x06, 0x05, 0x04,
0x13, 0x12, 0x11, 0x10, 0x0f, 0x0e, 0x0d, 0x0b, 0x0a, 0x09, 0x08, 0x07, 0x06, 0x05, 0x04, 0x03,
0x12, 0x11, 0x10, 0x0f, 0x0e, 0x0d, 0x0c, 0x0a, 0x09, 0x08, 0x07, 0x06, 0x05, 0x04, 0x03, 0x02,
0x11, 0x10, 0x0f, 0x0e, 0x0d, 0x0c, 0x0b, 0x0a, 0x09, 0x08, 0x07, 0x06, 0x04, 0x03, 0x02, 0x01,
0x10, 0x0f, 0x0e, 0x0d, 0x0c, 0x0b, 0x0a, 0x09, 0x08, 0x07, 0x06, 0x05, 0x04, 0x03, 0x02, 0x01,
0x10, 0x0f, 0x0e, 0x0d, 0x0c, 0x0b, 0x0a, 0x09, 0x08, 0x07, 0x06, 0x05, 0x04, 0x03, 0x02, 0x01,
0x10, 0x0f, 0x0e, 0x0d, 0x0c, 0x0b, 0x0a, 0x09, 0x08, 0x07, 0x06, 0x05, 0x04, 0x03, 0x02, 0x01,
0x3e, 0x3a, 0x36, 0x32, 0x2e, 0x2a, 0x26, 0x22, 0x1e, 0x1a, 0x16, 0x12, 0x0e, 0x0b, 0x07, 0x03,
0x3f, 0x3b, 0x37, 0x33, 0x2f, 0x2b, 0x27, 0x24, 0x20, 0x1c, 0x18, 0x14, 0x10, 0x0c, 0x09, 0x05,
0x39, 0x35, 0x31, 0x2e, 0x2a, 0x26, 0x22, 0x1e, 0x1b, 0x17, 0x13, 0x0f, 0x0c, 0x08, 0x04, 0x00,
0x3d, 0x39, 0x35, 0x31, 0x2e, 0x2a, 0x26, 0x23, 0x1f, 0x1b, 0x18, 0x14, 0x10, 0x0d, 0x09, 0x05,
0x3a, 0x36, 0x32, 0x2f, 0x2b, 0x27, 0x24, 0x20, 0x1d, 0x19, 0x15, 0x12, 0x0e, 0x0b, 0x07, 0x03,
0x38, 0x34, 0x31, 0x2d, 0x2a, 0x26, 0x22, 0x1f, 0x1b, 0x18, 0x14, 0x11, 0x0d, 0x0a, 0x06, 0x03,
0x37, 0x34, 0x30, 0x2d, 0x29, 0x26, 0x22, 0x1f, 0x1b, 0x18, 0x15, 0x11, 0x0e, 0x0a, 0x07, 0x03,
0x38, 0x35, 0x31, 0x2e, 0x2a, 0x27, 0x24, 0x20, 0x1d, 0x19, 0x16, 0x13, 0x0f, 0x0c, 0x09, 0x05,
0x32, 0x2e, 0x2b, 0x28, 0x24, 0x21, 0x1e, 0x1a, 0x17, 0x14, 0x11, 0x0d, 0x0a, 0x07, 0x03, 0x00,
0x35, 0x31, 0x2e, 0x2b, 0x28, 0x24, 0x21, 0x1e, 0x1b, 0x17, 0x14, 0x11, 0x0e, 0x0a, 0x07, 0x04,
0x31, 0x2e, 0x2a, 0x27, 0x24, 0x21, 0x1e, 0x1a, 0x17, 0x14, 0x11, 0x0e, 0x0b, 0x07, 0x04, 0x01,
0x36, 0x33, 0x30, 0x2c, 0x29, 0x26, 0x23, 0x20, 0x1d, 0x1a, 0x17, 0x13, 0x10, 0x0d, 0x0a, 0x07,
0x34, 0x31, 0x2e, 0x2b, 0x28, 0x25, 0x21, 0x1e, 0x1b, 0x18, 0x15, 0x12, 0x0f, 0x0c, 0x09, 0x06,
0x33, 0x30, 0x2d, 0x2a, 0x27, 0x24, 0x21, 0x1e, 0x1b, 0x18, 0x15, 0x12, 0x0f, 0x0c, 0x09, 0x06,
0x33, 0x30, 0x2d, 0x2a, 0x27, 0x24, 0x21, 0x1e, 0x1b, 0x18, 0x15, 0x13, 0x10, 0x0d, 0x0a, 0x07,
0x2c, 0x29, 0x26, 0x23, 0x20, 0x1d, 0x1a, 0x18, 0x15, 0x12, 0x0f, 0x0c, 0x09, 0x06, 0x03, 0x01,
0x2e, 0x2b, 0x28, 0x25, 0x22, 0x1f, 0x1d, 0x1a, 0x17, 0x14, 0x11, 0x0e, 0x0c, 0x09, 0x06, 0x03,
0x30, 0x2e, 0x2b, 0x28, 0x25, 0x22, 0x20, 0x1d, 0x1a, 0x17, 0x14, 0x12, 0x0f, 0x0c, 0x09, 0x07,
0x2c, 0x29, 0x26, 0x24, 0x21, 0x1e, 0x1b, 0x19, 0x16, 0x13, 0x10, 0x0e, 0x0b, 0x08, 0x06, 0x03,
0x28, 0x25, 0x23, 0x20, 0x1d, 0x1b, 0x18, 0x15, 0x13, 0x10, 0x0d, 0x0b, 0x08, 0x05, 0x03, 0x00,
0x2d, 0x2b, 0x28, 0x25, 0x23, 0x20, 0x1d, 0x1b, 0x18, 0x15, 0x13, 0x10, 0x0e, 0x0b, 0x08, 0x06,
0x2b, 0x28, 0x26, 0x23, 0x21, 0x1e, 0x1b, 0x19, 0x16, 0x14, 0x11, 0x0f, 0x0c, 0x09, 0x07, 0x04,
0x2a, 0x27, 0x25, 0x22, 0x1f, 0x1d, 0x1a, 0x18, 0x15, 0x13, 0x10, 0x0e, 0x0b, 0x09, 0x06, 0x03,
0x29, 0x26, 0x24, 0x21, 0x1f, 0x1c, 0x1a, 0x17, 0x15, 0x12, 0x10, 0x0d, 0x0b, 0x08, 0x06, 0x03,
0x29, 0x26, 0x24, 0x21, 0x1f, 0x1d, 0x1a, 0x18, 0x15, 0x13, 0x10, 0x0e, 0x0b, 0x09, 0x06, 0x04,
0x2a, 0x27, 0x25, 0x22, 0x20, 0x1d, 0x1b, 0x19, 0x16, 0x14, 0x11, 0x0f, 0x0d, 0x0a, 0x08, 0x05,
0x2b, 0x29, 0x26, 0x24, 0x21, 0x1f, 0x1d, 0x1a, 0x18, 0x15, 0x13, 0x11, 0x0e, 0x0c, 0x0a, 0x07,
0x25, 0x23, 0x20, 0x1e, 0x1b, 0x19, 0x17, 0x14, 0x12, 0x10, 0x0d, 0x0b, 0x09, 0x06, 0x04, 0x02,
0x27, 0x25, 0x23, 0x20, 0x1e, 0x1c, 0x1a, 0x17, 0x15, 0x13, 0x10, 0x0e, 0x0c, 0x09, 0x07, 0x05,
0x23, 0x20, 0x1e, 0x1c, 0x1a, 0x17, 0x15, 0x13, 0x10, 0x0e, 0x0c, 0x0a, 0x07, 0x05, 0x03, 0x01,
0x26, 0x24, 0x22, 0x20, 0x1d, 0x1b, 0x19, 0x17, 0x15, 0x12, 0x10, 0x0e, 0x0c, 0x09, 0x07, 0x05,
0x23, 0x21, 0x1e, 0x1c, 0x1a, 0x18, 0x16, 0x13, 0x11, 0x0f, 0x0d, 0x0b, 0x08, 0x06, 0x04, 0x02,
0x28, 0x25, 0x23, 0x21, 0x1f, 0x1d, 0x1b, 0x18, 0x16, 0x14, 0x12, 0x10, 0x0e, 0x0c, 0x09, 0x07,
0x25, 0x23, 0x21, 0x1f, 0x1d, 0x1a, 0x18, 0x16, 0x14, 0x12, 0x10, 0x0e, 0x0c, 0x09, 0x07, 0x05,
0x23, 0x21, 0x1f, 0x1d, 0x1b, 0x19, 0x16, 0x14, 0x12, 0x10, 0x0e, 0x0c, 0x0a, 0x08, 0x06, 0x04,
0x22, 0x1f, 0x1d, 0x1b, 0x19, 0x17, 0x15, 0x13, 0x11, 0x0f, 0x0d, 0x0b, 0x09, 0x07, 0x05, 0x03,
0x21, 0x1f, 0x1c, 0x1a, 0x18, 0x16, 0x14, 0x12, 0x10, 0x0e, 0x0c, 0x0a, 0x08, 0x06, 0x04, 0x02,
0x20, 0x1e, 0x1c, 0x1a, 0x18, 0x16, 0x14, 0x12, 0x10, 0x0e, 0x0c, 0x0a, 0x08, 0x06, 0x04, 0x02,
0x20, 0x1e, 0x1c, 0x1a, 0x18, 0x16, 0x14, 0x12, 0x10, 0x0e, 0x0c, 0x0a, 0x08, 0x06, 0x04, 0x02,
0x20, 0x1f, 0x1d, 0x1b, 0x19, 0x17, 0x15, 0x13, 0x11, 0x0f, 0x0d, 0x0b, 0x09, 0x07, 0x05, 0x03,
0x21, 0x1f, 0x1e, 0x1c, 0x1a, 0x18, 0x16, 0x14, 0x12, 0x10, 0x0e, 0x0c, 0x0a, 0x08, 0x07, 0x05,
0x23, 0x21, 0x1f, 0x1d, 0x1b, 0x19, 0x17, 0x15, 0x14, 0x12, 0x10, 0x0e, 0x0c, 0x0a, 0x08, 0x06,
0x1c, 0x1b, 0x19, 0x17, 0x15, 0x13, 0x11, 0x0f, 0x0e, 0x0c, 0x0a, 0x08, 0x06, 0x04, 0x02, 0x01,
0x1f, 0x1d, 0x1b, 0x19, 0x17, 0x15, 0x14, 0x12, 0x10, 0x0e, 0x0c, 0x0a, 0x09, 0x07, 0x05, 0x03,
0x21, 0x1f, 0x1e, 0x1c, 0x1a, 0x18, 0x16, 0x15, 0x13, 0x11, 0x0f, 0x0d, 0x0c, 0x0a, 0x08, 0x06,
0x1c, 0x1b, 0x19, 0x17, 0x15, 0x13, 0x12, 0x10, 0x0e, 0x0c, 0x0a, 0x09, 0x07, 0x05, 0x03, 0x02,
0x20, 0x1e, 0x1c, 0x1a, 0x19, 0x17, 0x15, 0x13, 0x12, 0x10, 0x0e, 0x0c, 0x0b, 0x09, 0x07, 0x05,
0x1c, 0x1a, 0x18, 0x16, 0x15, 0x13, 0x11, 0x0f, 0x0e, 0x0c, 0x0a, 0x08, 0x07, 0x05, 0x03, 0x01,
0x20, 0x1e, 0x1c, 0x1b, 0x19, 0x17, 0x15, 0x14, 0x12, 0x10, 0x0f, 0x0d, 0x0b, 0x09, 0x08, 0x06,
0x1c, 0x1b, 0x19, 0x17, 0x15, 0x14, 0x12, 0x10, 0x0f, 0x0d, 0x0b, 0x0a, 0x08, 0x06, 0x05, 0x03,
0x19, 0x17, 0x16, 0x14, 0x12, 0x11, 0x0f, 0x0d, 0x0c, 0x0a, 0x08, 0x07, 0x05, 0x03, 0x02, 0x00,
0x1e, 0x1d, 0x1b, 0x19, 0x18, 0x16, 0x14, 0x13, 0x11, 0x10, 0x0e, 0x0c, 0x0b, 0x09, 0x07, 0x06,
0x1c, 0x1a, 0x19, 0x17, 0x16, 0x14, 0x12, 0x11, 0x0f, 0x0d, 0x0c, 0x0a, 0x08, 0x07, 0x05, 0x04,
0x1a, 0x18, 0x17, 0x15, 0x14, 0x12, 0x10, 0x0f, 0x0d, 0x0b, 0x0a, 0x08, 0x07, 0x05, 0x03, 0x02,
0x18, 0x17, 0x15, 0x13, 0x12, 0x10, 0x0f, 0x0d, 0x0c, 0x0a, 0x08, 0x07, 0x05, 0x04, 0x02, 0x00,
0x1f, 0x1d, 0x1c, 0x1a, 0x19, 0x17, 0x15, 0x14, 0x12, 0x11, 0x0f, 0x0e, 0x0c, 0x0a, 0x09, 0x07,
0x1e, 0x1c, 0x1b, 0x19, 0x18, 0x16, 0x14, 0x13, 0x11, 0x10, 0x0e, 0x0d, 0x0b, 0x0a, 0x08, 0x07,
0x1d, 0x1c, 0x1a, 0x18, 0x17, 0x15, 0x14, 0x12, 0x11, 0x0f, 0x0e, 0x0c, 0x0b, 0x09, 0x08, 0x06,
0x1d, 0x1b, 0x1a, 0x18, 0x17, 0x15, 0x13, 0x12, 0x10, 0x0f, 0x0d, 0x0c, 0x0a, 0x09, 0x07, 0x06,
0x1c, 0x1b, 0x19, 0x18, 0x16, 0x15, 0x13, 0x12, 0x10, 0x0f, 0x0d, 0x0c, 0x0b, 0x09, 0x08, 0x06,
0x1d, 0x1b, 0x1a, 0x18, 0x17, 0x15, 0x14, 0x12, 0x11, 0x0f, 0x0e, 0x0c, 0x0b, 0x09, 0x08, 0x06,
0x1d, 0x1c, 0x1a, 0x19, 0x17, 0x16, 0x14, 0x13, 0x11, 0x10, 0x0e, 0x0d, 0x0b, 0x0a, 0x09, 0x07,
0x16, 0x14, 0x13, 0x11, 0x10, 0x0e, 0x0d, 0x0c, 0x0a, 0x09, 0x07, 0x06, 0x04, 0x03, 0x02, 0x00,
0x17, 0x15, 0x14, 0x12, 0x11, 0x10, 0x0e, 0x0d, 0x0b, 0x0a, 0x08, 0x07, 0x06, 0x04, 0x03, 0x01,
};
#define IEEE_BINARY32_EXPO_BIAS (127)
#define IEEE_BINARY32_MANT_BITS (23)
#define IEEE_BINARY32_EXPO_BITS (8)
#define IEEE_BINARY32_EXPO_MASK (0x7f800000)
#define IEEE_BINARY32_NAN_INDEF (0xffc00000)
#define IEEE_BINARY32_POS_INF (0x7f800000)
#define IEEE_BINARY32_POS_ZERO (0x00000000)
#define IEEE_BINARY32_MIN_NORM (0x00800000)
#define IEEE_BINARY32_SIGN_BIT (0x80000000)
/* Emulate the RSQRTSS instruction in software */
float my_rsqrtf (float x)
{
float r;
uint32_t arg, res, idx, expo, mant;
arg = float_as_uint32 (x);
/* zeros and subnormals */
if ((arg & ~IEEE_BINARY32_SIGN_BIT) < IEEE_BINARY32_MIN_NORM) {
res = IEEE_BINARY32_POS_INF | (arg & IEEE_BINARY32_SIGN_BIT);
r = uint32_as_float (res);
}
/* NaNs */
else if ((arg & ~IEEE_BINARY32_SIGN_BIT) > IEEE_BINARY32_POS_INF) {
r = x + x; // convert SNaN to QNaN
}
/* negative arguments */
else if (arg & IEEE_BINARY32_SIGN_BIT) {
res = IEEE_BINARY32_NAN_INDEF;
r = uint32_as_float (res);
}
/* positive infinity */
else if (arg == IEEE_BINARY32_POS_INF) {
res = IEEE_BINARY32_POS_ZERO;
r = uint32_as_float (res);
}
/* positive normals */
else {
/* extract exponent lsb and leading mantissa bits for table index */
expo = (arg & IEEE_BINARY32_EXPO_MASK) >> IEEE_BINARY32_MANT_BITS;
idx = (arg >> (IEEE_BINARY32_MANT_BITS - LOG2_NBR_TAB_ENTRIES + 1))
& (NBR_TAB_ENTRIES - 1);
/* compute exponent and mantissa of reciprocal square root */
expo = (3 * IEEE_BINARY32_EXPO_BIAS + ~expo) >> 1;
mant = (((base_tab [idx >> 4] << (TAB_ENTRY_BITS - BASE_TAB_ENTRY_BITS)) + ofs_tab [idx])
<< (IEEE_BINARY32_MANT_BITS - TAB_ENTRY_BITS));
/* combine exponent and mantissa bits to compute final result */
res = (expo << IEEE_BINARY32_MANT_BITS) | mant;
r = uint32_as_float (res);
}
return r;
}
#define NBR_RND_MODES (4)
#define NBR_DAZ_MODES (2)
#define NBR_FTZ_MODES (2)
int main (void)
{
const uint32_t rnd_mode [NBR_RND_MODES] =
{
_MM_ROUND_NEAREST,
_MM_ROUND_TOWARD_ZERO,
_MM_ROUND_DOWN,
_MM_ROUND_UP
};
const uint32_t ftz_mode [NBR_FTZ_MODES] =
{
_MM_FLUSH_ZERO_OFF,
_MM_FLUSH_ZERO_ON
};
const uint32_t daz_mode [NBR_DAZ_MODES] =
{
_MM_DENORMALS_ZERO_OFF,
_MM_DENORMALS_ZERO_ON
};
uint32_t iarg, ires, iref;
float arg, res, ref;
double relerr, maxrelerr;
for (int rnd = 0; rnd < NBR_RND_MODES; rnd++) {
printf ("rnd=%dn", rnd);
for (int ftz = 0; ftz < NBR_FTZ_MODES; ftz++) {
printf (" ftz=%dn", ftz);
for (int daz = 0; daz < NBR_DAZ_MODES; daz++) {
printf (" daz=%dn", daz); fflush(stdout);
maxrelerr = 0;
iarg = 0;
do {
arg = uint32_as_float (iarg);
ref = sse_rsqrtf (arg, daz_mode[daz], ftz_mode[ftz], rnd_mode[rnd]);
res = my_rsqrtf (arg);
if ((arg >= 1.17549435e-38f) && (arg < 3.40282347e+38f)) { /* normals only */
relerr = fabs ((ref - sqrt(1.0/(double)arg)) / sqrt(1.0/(double)arg));
if (relerr > maxrelerr) maxrelerr = relerr;
}
iref = float_as_uint32 (ref);
ires = float_as_uint32 (res);
if (ires != iref) {
printf ("!!!! rnd=%d ftz=%d daz=%d arg=%08x res=%08x ref=%08xn",
rnd, ftz, daz, iarg, ires, iref);
return EXIT_FAILURE;
}
iarg++;
} while (iarg);
printf (" maxrelerr = %15.8en", maxrelerr);
}
}
}
printf ("RSQRTSS emulation test passedn");
return EXIT_SUCCESS;
}
标准库中没有执行此操作的函数，但编译器可能会优化表达式1 / sqrt(value)使其发出 RSQRTSS 指令。例如，使用编译器标志-ffast-math -march=native，GCC 将发出该指令，请参阅：https://godbolt.org/z/cL6seG
对于它的价值，我最终在 C++ 内以普通汇编形式实现它，正如 Andrieux @François所建议的那样(更准确地说，我使用了 ASMJIT)。
这效果很好，尽管它有失去可移植性的缺点(虽然比普通的asm少)。但这在某种程度上是我的问题固有的，因为我想使用一个非常具体的 x86 函数。
这是我的代码：
typedef float(*JITFunc)();
JITFunc func;
asmjit::JitRuntime jit_runtime;
asmjit::CodeHolder code;
code.init(jit_runtime.getCodeInfo());
asmjit::X86Compiler cc(&code);
cc.addFunc(asmjit::FuncSignature0<float>());
float value = 2.71; // Some example value.
asmjit::X86Xmm x = cc.newXmm();
setXmmVar(cc, x, value);
cc.rsqrtss(x, x); // THE asm function.
cc.ret(x);
cc.endFunc();
cc.finalize();
jit_runtime.add(&func, &code);
return func(); // Or something to that effect. func() is the result, anyway.
相关文章：
- 内置函数可查看CPP中的成员变量
- 是否有内置方法可以强制转换为不同的基础类型，但保留常量限定符?
- 按字母顺序对字符串中的字母进行排序，而无需使用内置的 sort(）
- 将字符串转换为浮点数或整数，而无需使用内置函数(如 atoi 或 atof）
- 如何从 c++ 中类中内置的数组继承
- 如何捕获 C++ 内置异常对象
- macOS 是内置在 clang 编译器中还是内置于 xcode ide 中?
- 将编译器开关添加到 Eclipse CDT 内置编译器设置生成?
- gcc Atomic在gcc 4.1.1中内置了奇怪的行为
- 是否有用于元素部分移位的 simd 指令/内在/内置指令?
- 何时包含内置类型和运算符的标头?
- 基本类型与内置类型有什么区别C++
- 指内置类型的文字
- GLUT 问题：重新声明 c++ 内置类型'wchar_t'时出错
- 像自定义类一样构造的指针(内置类型）如何工作?
- 内置类型与用户定义的类型 C++
- 将内置类型变量传递给只有一个类类型参数的"+"运算符函数时自动类型转换的构造函数
- C++内置类型的基于类型的调度
- 是否有一个C++函数可以准确返回平方根反比的内置 CPU 操作 RSQRTSS 的值?
- CPU 内置 OpenGL 函数
