Marc-B-Reynolds

----------------------------------------------------------------------------
starting: vrecpe_f32 on [3f800000, 40000000]
// min/max ulp   -45502 44978
// abs max ulp   45502.375051
// correctly:    0.002611% (219)
// faithfully:   0.005555% (466)
//   2 ulp:      0.005436% (456)
//   3 ulp:      0.005460% (458)
//   4 ulp:      0.005329% (447)
//   5 ulp:      0.005531% (464)

Marc-B-Reynolds

click for range breakdown

checking on [3f800000,40000000] [1.000000e+00,2.000000e+00]

func	e	max ULP	CR	FR	2 ULP	> 2 ULP	CR%	FR%	2 ULP%	> 2 ULP%
vrsqrte_f32	--	4947968	103	225	216	8388065	0.001228	0.002682	0.002575	99.993515
FRSR_Mon0	--	564177	3	8	6	8388592	0.000036	0.000095	0.000072	99.999797
FRSR_Deg0	--	403258	0	0	0	8388609	0.000000	0.000000	0.000000	100.000000
FRSR_Mon1	--	14751	230	464	466	8387449	0.002742	0.005531	0.005555	99.986172

Marc-B-Reynolds

// Public Domain under http://unlicense.org, see link for details.

#include <stdint.h>
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <string.h>

#include "xmmintrin.h"
#include "wmmintrin.h"

Marc-B-Reynolds

// SEE: https://marc-b-reynolds.github.io/math/2019/03/12/FpDiv.html

#include <stdint.h>
#include <stdio.h>
#include <string.h>
#include <math.h>

#define RANDOMIZE

#define TEST_LEN UINT64_C(0x0000000100000000)

Marc-B-Reynolds

#include <stdint.h>
#include <stdio.h>
#include <string.h>
#include <math.h>

#define RANDOMIZE

#define TEST_LEN 0x7fffffff

#define VARIANT_FMA

Marc-B-Reynolds

00 : mean=0.000000,variance=0.000000,std-dev=0.000000, count=67108863 on [0.000000,0.000000]
01 : mean=6.511208,variance=3.084904,std-dev=1.756390, count=67108863 on [2.000000,31.000000]
02 : mean=6.254943,variance=3.523351,std-dev=1.877059, count=67108863 on [2.000000,30.000000]
03 : mean=6.142395,variance=3.876341,std-dev=1.968843, count=67108863 on [2.000000,31.000000]
04 : mean=6.083418,variance=4.125431,std-dev=2.031116, count=67108863 on [2.000000,31.000000]
05 : mean=6.046452,variance=4.320036,std-dev=2.078470, count=67108863 on [2.000000,31.000000]
06 : mean=6.018018,variance=4.485348,std-dev=2.117864, count=67108863 on [2.000000,31.000000]
07 : mean=5.996642,variance=4.607561,std-dev=2.146523, count=67108863 on [2.000000,33.000000]
08 : mean=5.986188,variance=4.664854,std-dev=2.159827, count=67108863 on [2.000000,32.000000]
09 : mean=5.987023,variance=4.672484,std-dev=2.161593, count=67108863 on [2.000000,33.000000]

Marc-B-Reynolds

// 1) "Tables of linear congruential generators of different sizes and good lattice structure" (1999), Pierre L'Ecuyer
// 2) Pre-print version of (3)  (https://arxiv.org/abs/2001.05304)
// 3) "Computationally easy, spectrally good multipliers for congruential pseudorandom number generators" (2021), Guy L. Steele Jr. & Sebastiano Vigna (https://onlinelibrary.wiley.com/doi/epdf/10.1002/spe.3030)

// inline comment number is bit width of constant

const uint32_t lcg_mul_k_table_32[] =
{
  // (3) Table 4 LCGs
  0x0000d9f5, // 16      

Marc-B-Reynolds

// Public Domain under http://unlicense.org, see link for details.

#include <stdint.h>
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <string.h>

#include "xmmintrin.h"
#include "wmmintrin.h"

Marc-B-Reynolds

{% if page.mathjax3 %} 

<script>
window.MathJax = {
  options: {
    menuOptions: {
      settings: {
        zoom: "None",
        zscale: "150%"
      }

Marc-B-Reynolds

/* -*- mode: c; -*- */

// create primary range approximations of sin(pi x) and cos(pi x) for x on [-1/4,1/4]
// both for single and double precision

R = [0;1/4];
T = floating;
E = relative;
B = [|24...|];