cargo fmt
This commit is contained in:
Andrey Zgarbul
parent
d03ec1472b
commit
d67c2c391b
6 changed files with 249 additions and 279 deletions
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@ -3,32 +3,36 @@ use super::{k_cosf, k_sinf, rem_pio2f};
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use core::f64::consts::FRAC_PI_2;
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/* Small multiples of pi/2 rounded to double precision. */
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const C1_PIO2 : f64 = 1.*FRAC_PI_2; /* 0x3FF921FB, 0x54442D18 */
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const C2_PIO2 : f64 = 2.*FRAC_PI_2; /* 0x400921FB, 0x54442D18 */
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const C3_PIO2 : f64 = 3.*FRAC_PI_2; /* 0x4012D97C, 0x7F3321D2 */
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const C4_PIO2 : f64 = 4.*FRAC_PI_2; /* 0x401921FB, 0x54442D18 */
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const C1_PIO2: f64 = 1. * FRAC_PI_2; /* 0x3FF921FB, 0x54442D18 */
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const C2_PIO2: f64 = 2. * FRAC_PI_2; /* 0x400921FB, 0x54442D18 */
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const C3_PIO2: f64 = 3. * FRAC_PI_2; /* 0x4012D97C, 0x7F3321D2 */
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const C4_PIO2: f64 = 4. * FRAC_PI_2; /* 0x401921FB, 0x54442D18 */
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#[inline]
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pub fn cosf(x: f32) -> f32 {
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let x64 = x as f64;
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let x1p120 = f32::from_bits(0x7b800000); // 0x1p120f === 2 ^ 120
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let mut ix = x.to_bits();
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let sign = (ix >> 31) != 0;
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ix &= 0x7fffffff;
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if ix <= 0x3f490fda { /* |x| ~<= pi/4 */
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if ix < 0x39800000 { /* |x| < 2**-12 */
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if ix <= 0x3f490fda {
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/* |x| ~<= pi/4 */
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if ix < 0x39800000 {
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/* |x| < 2**-12 */
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/* raise inexact if x != 0 */
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force_eval!(x + x1p120);
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return 1.;
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}
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return k_cosf(x64);
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}
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if ix <= 0x407b53d1 { /* |x| ~<= 5*pi/4 */
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if ix > 0x4016cbe3 { /* |x| ~> 3*pi/4 */
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return -k_cosf(if sign { x64+C2_PIO2 } else { x64-C2_PIO2 });
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if ix <= 0x407b53d1 {
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/* |x| ~<= 5*pi/4 */
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if ix > 0x4016cbe3 {
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/* |x| ~> 3*pi/4 */
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return -k_cosf(if sign { x64 + C2_PIO2 } else { x64 - C2_PIO2 });
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} else {
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if sign {
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return k_sinf(x64 + C1_PIO2);
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@ -37,9 +41,11 @@ pub fn cosf(x: f32) -> f32 {
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}
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}
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}
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if ix <= 0x40e231d5 { /* |x| ~<= 9*pi/4 */
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if ix > 0x40afeddf { /* |x| ~> 7*pi/4 */
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return k_cosf(if sign { x64+C4_PIO2 } else { x64-C4_PIO2 });
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if ix <= 0x40e231d5 {
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/* |x| ~<= 9*pi/4 */
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if ix > 0x40afeddf {
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/* |x| ~> 7*pi/4 */
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return k_cosf(if sign { x64 + C4_PIO2 } else { x64 - C4_PIO2 });
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} else {
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if sign {
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return k_sinf(-x64 - C3_PIO2);
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@ -51,15 +57,15 @@ pub fn cosf(x: f32) -> f32 {
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/* cos(Inf or NaN) is NaN */
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if ix >= 0x7f800000 {
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return x-x;
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return x - x;
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}
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/* general argument reduction needed */
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let (n, y) = rem_pio2f(x);
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match n&3 {
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0 => { k_cosf( y) },
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1 => { k_sinf(-y) },
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2 => { -k_cosf( y) },
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_ => { k_sinf( y) },
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match n & 3 {
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0 => k_cosf(y),
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1 => k_sinf(-y),
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2 => -k_cosf(y),
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_ => k_sinf(y),
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}
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}
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@ -1,13 +1,13 @@
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/* |cos(x) - c(x)| < 2**-34.1 (~[-5.37e-11, 5.295e-11]). */
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const C0 : f64 = -0.499999997251031003120; /* -0x1ffffffd0c5e81.0p-54 */
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const C1 : f64 = 0.0416666233237390631894; /* 0x155553e1053a42.0p-57 */
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const C2 : f64 = -0.00138867637746099294692; /* -0x16c087e80f1e27.0p-62 */
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const C3 : f64 = 0.0000243904487962774090654; /* 0x199342e0ee5069.0p-68 */
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const C0: f64 = -0.499999997251031003120; /* -0x1ffffffd0c5e81.0p-54 */
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const C1: f64 = 0.0416666233237390631894; /* 0x155553e1053a42.0p-57 */
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const C2: f64 = -0.00138867637746099294692; /* -0x16c087e80f1e27.0p-62 */
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const C3: f64 = 0.0000243904487962774090654; /* 0x199342e0ee5069.0p-68 */
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#[inline]
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pub(crate) fn k_cosf(x : f64) -> f32 {
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let z = x*x;
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let w = z*z;
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let r = C2+z*C3;
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(((1.0+z*C0) + w*C1) + (w*z)*r) as f32
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pub(crate) fn k_cosf(x: f64) -> f32 {
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let z = x * x;
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let w = z * z;
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let r = C2 + z * C3;
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(((1.0 + z * C0) + w * C1) + (w * z) * r) as f32
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}
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@ -1,14 +1,14 @@
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/* |sin(x)/x - s(x)| < 2**-37.5 (~[-4.89e-12, 4.824e-12]). */
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const S1 : f64 = -0.166666666416265235595; /* -0x15555554cbac77.0p-55 */
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const S2 : f64 = 0.0083333293858894631756; /* 0x111110896efbb2.0p-59 */
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const S3 : f64 = -0.000198393348360966317347; /* -0x1a00f9e2cae774.0p-65 */
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const S4 : f64 = 0.0000027183114939898219064; /* 0x16cd878c3b46a7.0p-71 */
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const S1: f64 = -0.166666666416265235595; /* -0x15555554cbac77.0p-55 */
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const S2: f64 = 0.0083333293858894631756; /* 0x111110896efbb2.0p-59 */
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const S3: f64 = -0.000198393348360966317347; /* -0x1a00f9e2cae774.0p-65 */
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const S4: f64 = 0.0000027183114939898219064; /* 0x16cd878c3b46a7.0p-71 */
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#[inline]
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pub(crate) fn k_sinf(x : f64) -> f32 {
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let z = x*x;
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let w = z*z;
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let r = S3 + z*S4;
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let s = z*x;
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((x + s*(S1 + z*S2)) + s*w*r) as f32
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pub(crate) fn k_sinf(x: f64) -> f32 {
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let z = x * x;
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let w = z * z;
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let r = S3 + z * S4;
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let s = z * x;
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((x + s * (S1 + z * S2)) + s * w * r) as f32
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}
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@ -7,6 +7,7 @@ macro_rules! force_eval {
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}
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mod ceilf;
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mod cosf;
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mod expf;
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mod fabs;
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mod fabsf;
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@ -27,28 +28,22 @@ mod scalbn;
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mod scalbnf;
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mod sqrt;
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mod sqrtf;
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mod cosf;
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mod trunc;
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mod truncf;
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pub use self::{
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ceilf::ceilf, expf::expf, fabs::fabs, fabsf::fabsf, floor::floor, floorf::floorf, fmodf::fmodf,
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hypot::hypot, hypotf::hypotf, log10::log10, log10f::log10f, log2::log2, log2f::log2f,
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logf::logf, powf::powf, round::round, roundf::roundf, scalbn::scalbn, scalbnf::scalbnf,
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sqrt::sqrt, sqrtf::sqrtf, trunc::trunc, truncf::truncf, cosf::cosf,
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ceilf::ceilf, cosf::cosf, expf::expf, fabs::fabs, fabsf::fabsf, floor::floor, floorf::floorf,
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fmodf::fmodf, hypot::hypot, hypotf::hypotf, log10::log10, log10f::log10f, log2::log2,
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log2f::log2f, logf::logf, powf::powf, round::round, roundf::roundf, scalbn::scalbn,
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scalbnf::scalbnf, sqrt::sqrt, sqrtf::sqrtf, trunc::trunc, truncf::truncf,
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};
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mod k_cosf;
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mod k_sinf;
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mod rem_pio2f;
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mod rem_pio2_large;
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mod rem_pio2f;
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use self::{
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k_cosf::k_cosf,
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k_sinf::k_sinf,
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rem_pio2f::rem_pio2f,
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rem_pio2_large::rem_pio2_large,
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};
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use self::{k_cosf::k_cosf, k_sinf::k_sinf, rem_pio2_large::rem_pio2_large, rem_pio2f::rem_pio2f};
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fn isnanf(x: f32) -> bool {
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x.to_bits() & 0x7fffffff > 0x7f800000
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@ -1,8 +1,8 @@
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use super::scalbn;
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use super::floor;
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use super::scalbn;
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// initial value for jk
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const INIT_JK : [usize; 4] = [3,4,4,6];
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const INIT_JK: [usize; 4] = [3, 4, 4, 6];
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// Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
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//
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@ -15,140 +15,99 @@ const INIT_JK : [usize; 4] = [3,4,4,6];
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// NB: This table must have at least (e0-3)/24 + jk terms.
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// For quad precision (e0 <= 16360, jk = 6), this is 686.
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#[cfg(target_pointer_width = "32")]
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const IPIO2 : [i32; 66] = [
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0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
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0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
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0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
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0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
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0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
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0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
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0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
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0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
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0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
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0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
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0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
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const IPIO2: [i32; 66] = [
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0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, 0x95993C, 0x439041, 0xFE5163,
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0xABDEBB, 0xC561B7, 0x246E3A, 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
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0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, 0x3991D6, 0x398353, 0x39F49C,
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0x845F8B, 0xBDF928, 0x3B1FF8, 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
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0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, 0xF17B3D, 0x0739F7, 0x8A5292,
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0xEA6BFB, 0x5FB11F, 0x8D5D08, 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
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0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, 0x4D7327, 0x310606, 0x1556CA,
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0x73A8C9, 0x60E27B, 0xC08C6B,
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];
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#[cfg(target_pointer_width = "64")]
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const IPIO2 : [i32; 690] = [
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0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
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0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
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0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
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0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
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0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
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0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
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0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
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0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
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0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
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0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
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0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
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0x47C419, 0xC367CD, 0xDCE809, 0x2A8359, 0xC4768B, 0x961CA6,
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0xDDAF44, 0xD15719, 0x053EA5, 0xFF0705, 0x3F7E33, 0xE832C2,
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0xDE4F98, 0x327DBB, 0xC33D26, 0xEF6B1E, 0x5EF89F, 0x3A1F35,
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0xCAF27F, 0x1D87F1, 0x21907C, 0x7C246A, 0xFA6ED5, 0x772D30,
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0x433B15, 0xC614B5, 0x9D19C3, 0xC2C4AD, 0x414D2C, 0x5D000C,
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0x467D86, 0x2D71E3, 0x9AC69B, 0x006233, 0x7CD2B4, 0x97A7B4,
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0xD55537, 0xF63ED7, 0x1810A3, 0xFC764D, 0x2A9D64, 0xABD770,
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0xF87C63, 0x57B07A, 0xE71517, 0x5649C0, 0xD9D63B, 0x3884A7,
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0xCB2324, 0x778AD6, 0x23545A, 0xB91F00, 0x1B0AF1, 0xDFCE19,
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0xFF319F, 0x6A1E66, 0x615799, 0x47FBAC, 0xD87F7E, 0xB76522,
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0x89E832, 0x60BFE6, 0xCDC4EF, 0x09366C, 0xD43F5D, 0xD7DE16,
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0xDE3B58, 0x929BDE, 0x2822D2, 0xE88628, 0x4D58E2, 0x32CAC6,
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0x16E308, 0xCB7DE0, 0x50C017, 0xA71DF3, 0x5BE018, 0x34132E,
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0x621283, 0x014883, 0x5B8EF5, 0x7FB0AD, 0xF2E91E, 0x434A48,
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0xD36710, 0xD8DDAA, 0x425FAE, 0xCE616A, 0xA4280A, 0xB499D3,
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0xF2A606, 0x7F775C, 0x83C2A3, 0x883C61, 0x78738A, 0x5A8CAF,
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0xBDD76F, 0x63A62D, 0xCBBFF4, 0xEF818D, 0x67C126, 0x45CA55,
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0x36D9CA, 0xD2A828, 0x8D61C2, 0x77C912, 0x142604, 0x9B4612,
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0xC459C4, 0x44C5C8, 0x91B24D, 0xF31700, 0xAD43D4, 0xE54929,
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0x10D5FD, 0xFCBE00, 0xCC941E, 0xEECE70, 0xF53E13, 0x80F1EC,
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0xC3E7B3, 0x28F8C7, 0x940593, 0x3E71C1, 0xB3092E, 0xF3450B,
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0x9C1288, 0x7B20AB, 0x9FB52E, 0xC29247, 0x2F327B, 0x6D550C,
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0x90A772, 0x1FE76B, 0x96CB31, 0x4A1679, 0xE27941, 0x89DFF4,
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0x9794E8, 0x84E6E2, 0x973199, 0x6BED88, 0x365F5F, 0x0EFDBB,
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0xB49A48, 0x6CA467, 0x427271, 0x325D8D, 0xB8159F, 0x09E5BC,
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0x25318D, 0x3974F7, 0x1C0530, 0x010C0D, 0x68084B, 0x58EE2C,
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0x90AA47, 0x02E774, 0x24D6BD, 0xA67DF7, 0x72486E, 0xEF169F,
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0xA6948E, 0xF691B4, 0x5153D1, 0xF20ACF, 0x339820, 0x7E4BF5,
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0x6863B2, 0x5F3EDD, 0x035D40, 0x7F8985, 0x295255, 0xC06437,
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0x10D86D, 0x324832, 0x754C5B, 0xD4714E, 0x6E5445, 0xC1090B,
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0x69F52A, 0xD56614, 0x9D0727, 0x50045D, 0xDB3BB4, 0xC576EA,
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0x17F987, 0x7D6B49, 0xBA271D, 0x296996, 0xACCCC6, 0x5414AD,
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0x6AE290, 0x89D988, 0x50722C, 0xBEA404, 0x940777, 0x7030F3,
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0x27FC00, 0xA871EA, 0x49C266, 0x3DE064, 0x83DD97, 0x973FA3,
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0xFD9443, 0x8C860D, 0xDE4131, 0x9D3992, 0x8C70DD, 0xE7B717,
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0x3BDF08, 0x2B3715, 0xA0805C, 0x93805A, 0x921110, 0xD8E80F,
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0xAF806C, 0x4BFFDB, 0x0F9038, 0x761859, 0x15A562, 0xBBCB61,
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0xB989C7, 0xBD4010, 0x04F2D2, 0x277549, 0xF6B6EB, 0xBB22DB,
|
||||
0xAA140A, 0x2F2689, 0x768364, 0x333B09, 0x1A940E, 0xAA3A51,
|
||||
0xC2A31D, 0xAEEDAF, 0x12265C, 0x4DC26D, 0x9C7A2D, 0x9756C0,
|
||||
0x833F03, 0xF6F009, 0x8C402B, 0x99316D, 0x07B439, 0x15200C,
|
||||
0x5BC3D8, 0xC492F5, 0x4BADC6, 0xA5CA4E, 0xCD37A7, 0x36A9E6,
|
||||
0x9492AB, 0x6842DD, 0xDE6319, 0xEF8C76, 0x528B68, 0x37DBFC,
|
||||
0xABA1AE, 0x3115DF, 0xA1AE00, 0xDAFB0C, 0x664D64, 0xB705ED,
|
||||
0x306529, 0xBF5657, 0x3AFF47, 0xB9F96A, 0xF3BE75, 0xDF9328,
|
||||
0x3080AB, 0xF68C66, 0x15CB04, 0x0622FA, 0x1DE4D9, 0xA4B33D,
|
||||
0x8F1B57, 0x09CD36, 0xE9424E, 0xA4BE13, 0xB52333, 0x1AAAF0,
|
||||
0xA8654F, 0xA5C1D2, 0x0F3F0B, 0xCD785B, 0x76F923, 0x048B7B,
|
||||
0x721789, 0x53A6C6, 0xE26E6F, 0x00EBEF, 0x584A9B, 0xB7DAC4,
|
||||
0xBA66AA, 0xCFCF76, 0x1D02D1, 0x2DF1B1, 0xC1998C, 0x77ADC3,
|
||||
0xDA4886, 0xA05DF7, 0xF480C6, 0x2FF0AC, 0x9AECDD, 0xBC5C3F,
|
||||
0x6DDED0, 0x1FC790, 0xB6DB2A, 0x3A25A3, 0x9AAF00, 0x9353AD,
|
||||
0x0457B6, 0xB42D29, 0x7E804B, 0xA707DA, 0x0EAA76, 0xA1597B,
|
||||
0x2A1216, 0x2DB7DC, 0xFDE5FA, 0xFEDB89, 0xFDBE89, 0x6C76E4,
|
||||
0xFCA906, 0x70803E, 0x156E85, 0xFF87FD, 0x073E28, 0x336761,
|
||||
0x86182A, 0xEABD4D, 0xAFE7B3, 0x6E6D8F, 0x396795, 0x5BBF31,
|
||||
0x48D784, 0x16DF30, 0x432DC7, 0x356125, 0xCE70C9, 0xB8CB30,
|
||||
0xFD6CBF, 0xA200A4, 0xE46C05, 0xA0DD5A, 0x476F21, 0xD21262,
|
||||
0x845CB9, 0x496170, 0xE0566B, 0x015299, 0x375550, 0xB7D51E,
|
||||
0xC4F133, 0x5F6E13, 0xE4305D, 0xA92E85, 0xC3B21D, 0x3632A1,
|
||||
0xA4B708, 0xD4B1EA, 0x21F716, 0xE4698F, 0x77FF27, 0x80030C,
|
||||
0x2D408D, 0xA0CD4F, 0x99A520, 0xD3A2B3, 0x0A5D2F, 0x42F9B4,
|
||||
0xCBDA11, 0xD0BE7D, 0xC1DB9B, 0xBD17AB, 0x81A2CA, 0x5C6A08,
|
||||
0x17552E, 0x550027, 0xF0147F, 0x8607E1, 0x640B14, 0x8D4196,
|
||||
0xDEBE87, 0x2AFDDA, 0xB6256B, 0x34897B, 0xFEF305, 0x9EBFB9,
|
||||
0x4F6A68, 0xA82A4A, 0x5AC44F, 0xBCF82D, 0x985AD7, 0x95C7F4,
|
||||
0x8D4D0D, 0xA63A20, 0x5F57A4, 0xB13F14, 0x953880, 0x0120CC,
|
||||
0x86DD71, 0xB6DEC9, 0xF560BF, 0x11654D, 0x6B0701, 0xACB08C,
|
||||
0xD0C0B2, 0x485551, 0x0EFB1E, 0xC37295, 0x3B06A3, 0x3540C0,
|
||||
0x7BDC06, 0xCC45E0, 0xFA294E, 0xC8CAD6, 0x41F3E8, 0xDE647C,
|
||||
0xD8649B, 0x31BED9, 0xC397A4, 0xD45877, 0xC5E369, 0x13DAF0,
|
||||
0x3C3ABA, 0x461846, 0x5F7555, 0xF5BDD2, 0xC6926E, 0x5D2EAC,
|
||||
0xED440E, 0x423E1C, 0x87C461, 0xE9FD29, 0xF3D6E7, 0xCA7C22,
|
||||
0x35916F, 0xC5E008, 0x8DD7FF, 0xE26A6E, 0xC6FDB0, 0xC10893,
|
||||
0x745D7C, 0xB2AD6B, 0x9D6ECD, 0x7B723E, 0x6A11C6, 0xA9CFF7,
|
||||
0xDF7329, 0xBAC9B5, 0x5100B7, 0x0DB2E2, 0x24BA74, 0x607DE5,
|
||||
0x8AD874, 0x2C150D, 0x0C1881, 0x94667E, 0x162901, 0x767A9F,
|
||||
0xBEFDFD, 0xEF4556, 0x367ED9, 0x13D9EC, 0xB9BA8B, 0xFC97C4,
|
||||
0x27A831, 0xC36EF1, 0x36C594, 0x56A8D8, 0xB5A8B4, 0x0ECCCF,
|
||||
0x2D8912, 0x34576F, 0x89562C, 0xE3CE99, 0xB920D6, 0xAA5E6B,
|
||||
0x9C2A3E, 0xCC5F11, 0x4A0BFD, 0xFBF4E1, 0x6D3B8E, 0x2C86E2,
|
||||
0x84D4E9, 0xA9B4FC, 0xD1EEEF, 0xC9352E, 0x61392F, 0x442138,
|
||||
0xC8D91B, 0x0AFC81, 0x6A4AFB, 0xD81C2F, 0x84B453, 0x8C994E,
|
||||
0xCC2254, 0xDC552A, 0xD6C6C0, 0x96190B, 0xB8701A, 0x649569,
|
||||
0x605A26, 0xEE523F, 0x0F117F, 0x11B5F4, 0xF5CBFC, 0x2DBC34,
|
||||
0xEEBC34, 0xCC5DE8, 0x605EDD, 0x9B8E67, 0xEF3392, 0xB817C9,
|
||||
0x9B5861, 0xBC57E1, 0xC68351, 0x103ED8, 0x4871DD, 0xDD1C2D,
|
||||
0xA118AF, 0x462C21, 0xD7F359, 0x987AD9, 0xC0549E, 0xFA864F,
|
||||
0xFC0656, 0xAE79E5, 0x362289, 0x22AD38, 0xDC9367, 0xAAE855,
|
||||
0x382682, 0x9BE7CA, 0xA40D51, 0xB13399, 0x0ED7A9, 0x480569,
|
||||
0xF0B265, 0xA7887F, 0x974C88, 0x36D1F9, 0xB39221, 0x4A827B,
|
||||
0x21CF98, 0xDC9F40, 0x5547DC, 0x3A74E1, 0x42EB67, 0xDF9DFE,
|
||||
0x5FD45E, 0xA4677B, 0x7AACBA, 0xA2F655, 0x23882B, 0x55BA41,
|
||||
0x086E59, 0x862A21, 0x834739, 0xE6E389, 0xD49EE5, 0x40FB49,
|
||||
0xE956FF, 0xCA0F1C, 0x8A59C5, 0x2BFA94, 0xC5C1D3, 0xCFC50F,
|
||||
0xAE5ADB, 0x86C547, 0x624385, 0x3B8621, 0x94792C, 0x876110,
|
||||
0x7B4C2A, 0x1A2C80, 0x12BF43, 0x902688, 0x893C78, 0xE4C4A8,
|
||||
0x7BDBE5, 0xC23AC4, 0xEAF426, 0x8A67F7, 0xBF920D, 0x2BA365,
|
||||
0xB1933D, 0x0B7CBD, 0xDC51A4, 0x63DD27, 0xDDE169, 0x19949A,
|
||||
0x9529A8, 0x28CE68, 0xB4ED09, 0x209F44, 0xCA984E, 0x638270,
|
||||
0x237C7E, 0x32B90F, 0x8EF5A7, 0xE75614, 0x08F121, 0x2A9DB5,
|
||||
0x4D7E6F, 0x5119A5, 0xABF9B5, 0xD6DF82, 0x61DD96, 0x023616,
|
||||
0x9F3AC4, 0xA1A283, 0x6DED72, 0x7A8D39, 0xA9B882, 0x5C326B,
|
||||
const IPIO2: [i32; 690] = [
|
||||
0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, 0x95993C, 0x439041, 0xFE5163,
|
||||
0xABDEBB, 0xC561B7, 0x246E3A, 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
|
||||
0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, 0x3991D6, 0x398353, 0x39F49C,
|
||||
0x845F8B, 0xBDF928, 0x3B1FF8, 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
|
||||
0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, 0xF17B3D, 0x0739F7, 0x8A5292,
|
||||
0xEA6BFB, 0x5FB11F, 0x8D5D08, 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
|
||||
0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, 0x4D7327, 0x310606, 0x1556CA,
|
||||
0x73A8C9, 0x60E27B, 0xC08C6B, 0x47C419, 0xC367CD, 0xDCE809, 0x2A8359, 0xC4768B, 0x961CA6,
|
||||
0xDDAF44, 0xD15719, 0x053EA5, 0xFF0705, 0x3F7E33, 0xE832C2, 0xDE4F98, 0x327DBB, 0xC33D26,
|
||||
0xEF6B1E, 0x5EF89F, 0x3A1F35, 0xCAF27F, 0x1D87F1, 0x21907C, 0x7C246A, 0xFA6ED5, 0x772D30,
|
||||
0x433B15, 0xC614B5, 0x9D19C3, 0xC2C4AD, 0x414D2C, 0x5D000C, 0x467D86, 0x2D71E3, 0x9AC69B,
|
||||
0x006233, 0x7CD2B4, 0x97A7B4, 0xD55537, 0xF63ED7, 0x1810A3, 0xFC764D, 0x2A9D64, 0xABD770,
|
||||
0xF87C63, 0x57B07A, 0xE71517, 0x5649C0, 0xD9D63B, 0x3884A7, 0xCB2324, 0x778AD6, 0x23545A,
|
||||
0xB91F00, 0x1B0AF1, 0xDFCE19, 0xFF319F, 0x6A1E66, 0x615799, 0x47FBAC, 0xD87F7E, 0xB76522,
|
||||
0x89E832, 0x60BFE6, 0xCDC4EF, 0x09366C, 0xD43F5D, 0xD7DE16, 0xDE3B58, 0x929BDE, 0x2822D2,
|
||||
0xE88628, 0x4D58E2, 0x32CAC6, 0x16E308, 0xCB7DE0, 0x50C017, 0xA71DF3, 0x5BE018, 0x34132E,
|
||||
0x621283, 0x014883, 0x5B8EF5, 0x7FB0AD, 0xF2E91E, 0x434A48, 0xD36710, 0xD8DDAA, 0x425FAE,
|
||||
0xCE616A, 0xA4280A, 0xB499D3, 0xF2A606, 0x7F775C, 0x83C2A3, 0x883C61, 0x78738A, 0x5A8CAF,
|
||||
0xBDD76F, 0x63A62D, 0xCBBFF4, 0xEF818D, 0x67C126, 0x45CA55, 0x36D9CA, 0xD2A828, 0x8D61C2,
|
||||
0x77C912, 0x142604, 0x9B4612, 0xC459C4, 0x44C5C8, 0x91B24D, 0xF31700, 0xAD43D4, 0xE54929,
|
||||
0x10D5FD, 0xFCBE00, 0xCC941E, 0xEECE70, 0xF53E13, 0x80F1EC, 0xC3E7B3, 0x28F8C7, 0x940593,
|
||||
0x3E71C1, 0xB3092E, 0xF3450B, 0x9C1288, 0x7B20AB, 0x9FB52E, 0xC29247, 0x2F327B, 0x6D550C,
|
||||
0x90A772, 0x1FE76B, 0x96CB31, 0x4A1679, 0xE27941, 0x89DFF4, 0x9794E8, 0x84E6E2, 0x973199,
|
||||
0x6BED88, 0x365F5F, 0x0EFDBB, 0xB49A48, 0x6CA467, 0x427271, 0x325D8D, 0xB8159F, 0x09E5BC,
|
||||
0x25318D, 0x3974F7, 0x1C0530, 0x010C0D, 0x68084B, 0x58EE2C, 0x90AA47, 0x02E774, 0x24D6BD,
|
||||
0xA67DF7, 0x72486E, 0xEF169F, 0xA6948E, 0xF691B4, 0x5153D1, 0xF20ACF, 0x339820, 0x7E4BF5,
|
||||
0x6863B2, 0x5F3EDD, 0x035D40, 0x7F8985, 0x295255, 0xC06437, 0x10D86D, 0x324832, 0x754C5B,
|
||||
0xD4714E, 0x6E5445, 0xC1090B, 0x69F52A, 0xD56614, 0x9D0727, 0x50045D, 0xDB3BB4, 0xC576EA,
|
||||
0x17F987, 0x7D6B49, 0xBA271D, 0x296996, 0xACCCC6, 0x5414AD, 0x6AE290, 0x89D988, 0x50722C,
|
||||
0xBEA404, 0x940777, 0x7030F3, 0x27FC00, 0xA871EA, 0x49C266, 0x3DE064, 0x83DD97, 0x973FA3,
|
||||
0xFD9443, 0x8C860D, 0xDE4131, 0x9D3992, 0x8C70DD, 0xE7B717, 0x3BDF08, 0x2B3715, 0xA0805C,
|
||||
0x93805A, 0x921110, 0xD8E80F, 0xAF806C, 0x4BFFDB, 0x0F9038, 0x761859, 0x15A562, 0xBBCB61,
|
||||
0xB989C7, 0xBD4010, 0x04F2D2, 0x277549, 0xF6B6EB, 0xBB22DB, 0xAA140A, 0x2F2689, 0x768364,
|
||||
0x333B09, 0x1A940E, 0xAA3A51, 0xC2A31D, 0xAEEDAF, 0x12265C, 0x4DC26D, 0x9C7A2D, 0x9756C0,
|
||||
0x833F03, 0xF6F009, 0x8C402B, 0x99316D, 0x07B439, 0x15200C, 0x5BC3D8, 0xC492F5, 0x4BADC6,
|
||||
0xA5CA4E, 0xCD37A7, 0x36A9E6, 0x9492AB, 0x6842DD, 0xDE6319, 0xEF8C76, 0x528B68, 0x37DBFC,
|
||||
0xABA1AE, 0x3115DF, 0xA1AE00, 0xDAFB0C, 0x664D64, 0xB705ED, 0x306529, 0xBF5657, 0x3AFF47,
|
||||
0xB9F96A, 0xF3BE75, 0xDF9328, 0x3080AB, 0xF68C66, 0x15CB04, 0x0622FA, 0x1DE4D9, 0xA4B33D,
|
||||
0x8F1B57, 0x09CD36, 0xE9424E, 0xA4BE13, 0xB52333, 0x1AAAF0, 0xA8654F, 0xA5C1D2, 0x0F3F0B,
|
||||
0xCD785B, 0x76F923, 0x048B7B, 0x721789, 0x53A6C6, 0xE26E6F, 0x00EBEF, 0x584A9B, 0xB7DAC4,
|
||||
0xBA66AA, 0xCFCF76, 0x1D02D1, 0x2DF1B1, 0xC1998C, 0x77ADC3, 0xDA4886, 0xA05DF7, 0xF480C6,
|
||||
0x2FF0AC, 0x9AECDD, 0xBC5C3F, 0x6DDED0, 0x1FC790, 0xB6DB2A, 0x3A25A3, 0x9AAF00, 0x9353AD,
|
||||
0x0457B6, 0xB42D29, 0x7E804B, 0xA707DA, 0x0EAA76, 0xA1597B, 0x2A1216, 0x2DB7DC, 0xFDE5FA,
|
||||
0xFEDB89, 0xFDBE89, 0x6C76E4, 0xFCA906, 0x70803E, 0x156E85, 0xFF87FD, 0x073E28, 0x336761,
|
||||
0x86182A, 0xEABD4D, 0xAFE7B3, 0x6E6D8F, 0x396795, 0x5BBF31, 0x48D784, 0x16DF30, 0x432DC7,
|
||||
0x356125, 0xCE70C9, 0xB8CB30, 0xFD6CBF, 0xA200A4, 0xE46C05, 0xA0DD5A, 0x476F21, 0xD21262,
|
||||
0x845CB9, 0x496170, 0xE0566B, 0x015299, 0x375550, 0xB7D51E, 0xC4F133, 0x5F6E13, 0xE4305D,
|
||||
0xA92E85, 0xC3B21D, 0x3632A1, 0xA4B708, 0xD4B1EA, 0x21F716, 0xE4698F, 0x77FF27, 0x80030C,
|
||||
0x2D408D, 0xA0CD4F, 0x99A520, 0xD3A2B3, 0x0A5D2F, 0x42F9B4, 0xCBDA11, 0xD0BE7D, 0xC1DB9B,
|
||||
0xBD17AB, 0x81A2CA, 0x5C6A08, 0x17552E, 0x550027, 0xF0147F, 0x8607E1, 0x640B14, 0x8D4196,
|
||||
0xDEBE87, 0x2AFDDA, 0xB6256B, 0x34897B, 0xFEF305, 0x9EBFB9, 0x4F6A68, 0xA82A4A, 0x5AC44F,
|
||||
0xBCF82D, 0x985AD7, 0x95C7F4, 0x8D4D0D, 0xA63A20, 0x5F57A4, 0xB13F14, 0x953880, 0x0120CC,
|
||||
0x86DD71, 0xB6DEC9, 0xF560BF, 0x11654D, 0x6B0701, 0xACB08C, 0xD0C0B2, 0x485551, 0x0EFB1E,
|
||||
0xC37295, 0x3B06A3, 0x3540C0, 0x7BDC06, 0xCC45E0, 0xFA294E, 0xC8CAD6, 0x41F3E8, 0xDE647C,
|
||||
0xD8649B, 0x31BED9, 0xC397A4, 0xD45877, 0xC5E369, 0x13DAF0, 0x3C3ABA, 0x461846, 0x5F7555,
|
||||
0xF5BDD2, 0xC6926E, 0x5D2EAC, 0xED440E, 0x423E1C, 0x87C461, 0xE9FD29, 0xF3D6E7, 0xCA7C22,
|
||||
0x35916F, 0xC5E008, 0x8DD7FF, 0xE26A6E, 0xC6FDB0, 0xC10893, 0x745D7C, 0xB2AD6B, 0x9D6ECD,
|
||||
0x7B723E, 0x6A11C6, 0xA9CFF7, 0xDF7329, 0xBAC9B5, 0x5100B7, 0x0DB2E2, 0x24BA74, 0x607DE5,
|
||||
0x8AD874, 0x2C150D, 0x0C1881, 0x94667E, 0x162901, 0x767A9F, 0xBEFDFD, 0xEF4556, 0x367ED9,
|
||||
0x13D9EC, 0xB9BA8B, 0xFC97C4, 0x27A831, 0xC36EF1, 0x36C594, 0x56A8D8, 0xB5A8B4, 0x0ECCCF,
|
||||
0x2D8912, 0x34576F, 0x89562C, 0xE3CE99, 0xB920D6, 0xAA5E6B, 0x9C2A3E, 0xCC5F11, 0x4A0BFD,
|
||||
0xFBF4E1, 0x6D3B8E, 0x2C86E2, 0x84D4E9, 0xA9B4FC, 0xD1EEEF, 0xC9352E, 0x61392F, 0x442138,
|
||||
0xC8D91B, 0x0AFC81, 0x6A4AFB, 0xD81C2F, 0x84B453, 0x8C994E, 0xCC2254, 0xDC552A, 0xD6C6C0,
|
||||
0x96190B, 0xB8701A, 0x649569, 0x605A26, 0xEE523F, 0x0F117F, 0x11B5F4, 0xF5CBFC, 0x2DBC34,
|
||||
0xEEBC34, 0xCC5DE8, 0x605EDD, 0x9B8E67, 0xEF3392, 0xB817C9, 0x9B5861, 0xBC57E1, 0xC68351,
|
||||
0x103ED8, 0x4871DD, 0xDD1C2D, 0xA118AF, 0x462C21, 0xD7F359, 0x987AD9, 0xC0549E, 0xFA864F,
|
||||
0xFC0656, 0xAE79E5, 0x362289, 0x22AD38, 0xDC9367, 0xAAE855, 0x382682, 0x9BE7CA, 0xA40D51,
|
||||
0xB13399, 0x0ED7A9, 0x480569, 0xF0B265, 0xA7887F, 0x974C88, 0x36D1F9, 0xB39221, 0x4A827B,
|
||||
0x21CF98, 0xDC9F40, 0x5547DC, 0x3A74E1, 0x42EB67, 0xDF9DFE, 0x5FD45E, 0xA4677B, 0x7AACBA,
|
||||
0xA2F655, 0x23882B, 0x55BA41, 0x086E59, 0x862A21, 0x834739, 0xE6E389, 0xD49EE5, 0x40FB49,
|
||||
0xE956FF, 0xCA0F1C, 0x8A59C5, 0x2BFA94, 0xC5C1D3, 0xCFC50F, 0xAE5ADB, 0x86C547, 0x624385,
|
||||
0x3B8621, 0x94792C, 0x876110, 0x7B4C2A, 0x1A2C80, 0x12BF43, 0x902688, 0x893C78, 0xE4C4A8,
|
||||
0x7BDBE5, 0xC23AC4, 0xEAF426, 0x8A67F7, 0xBF920D, 0x2BA365, 0xB1933D, 0x0B7CBD, 0xDC51A4,
|
||||
0x63DD27, 0xDDE169, 0x19949A, 0x9529A8, 0x28CE68, 0xB4ED09, 0x209F44, 0xCA984E, 0x638270,
|
||||
0x237C7E, 0x32B90F, 0x8EF5A7, 0xE75614, 0x08F121, 0x2A9DB5, 0x4D7E6F, 0x5119A5, 0xABF9B5,
|
||||
0xD6DF82, 0x61DD96, 0x023616, 0x9F3AC4, 0xA1A283, 0x6DED72, 0x7A8D39, 0xA9B882, 0x5C326B,
|
||||
0x5B2746, 0xED3400, 0x7700D2, 0x55F4FC, 0x4D5901, 0x8071E0,
|
||||
];
|
||||
|
||||
const PIO2 : [f64; 8] = [
|
||||
const PIO2: [f64; 8] = [
|
||||
1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */
|
||||
7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */
|
||||
5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */
|
||||
|
|
@ -251,92 +210,91 @@ const PIO2 : [f64; 8] = [
|
|||
/// more accurately, = 0 mod 8 ). Thus the number of operations are
|
||||
/// independent of the exponent of the input.
|
||||
#[inline]
|
||||
pub(crate) fn rem_pio2_large(x : &[f64], y : &mut [f64], e0 : i32, prec : usize) -> i32 {
|
||||
let x1p24 = f64::from_bits(0x4170000000000000); // 0x1p24 === 2 ^ 24
|
||||
pub(crate) fn rem_pio2_large(x: &[f64], y: &mut [f64], e0: i32, prec: usize) -> i32 {
|
||||
let x1p24 = f64::from_bits(0x4170000000000000); // 0x1p24 === 2 ^ 24
|
||||
let x1p_24 = f64::from_bits(0x3e70000000000000); // 0x1p_24 === 2 ^ (-24)
|
||||
|
||||
|
||||
#[cfg(target_pointer_width = "64")]
|
||||
assert!(e0 <= 16360);
|
||||
|
||||
|
||||
let nx = x.len();
|
||||
|
||||
let mut fw : f64;
|
||||
let mut n : i32;
|
||||
let mut ih : i32;
|
||||
let mut z : f64;
|
||||
let mut f : [f64;20] = [0.;20];
|
||||
let mut fq : [f64;20] = [0.;20];
|
||||
let mut q : [f64;20] = [0.;20];
|
||||
let mut iq : [i32;20] = [0;20];
|
||||
|
||||
|
||||
let mut fw: f64;
|
||||
let mut n: i32;
|
||||
let mut ih: i32;
|
||||
let mut z: f64;
|
||||
let mut f: [f64; 20] = [0.; 20];
|
||||
let mut fq: [f64; 20] = [0.; 20];
|
||||
let mut q: [f64; 20] = [0.; 20];
|
||||
let mut iq: [i32; 20] = [0; 20];
|
||||
|
||||
/* initialize jk*/
|
||||
let jk = INIT_JK[prec];
|
||||
let jp = jk;
|
||||
|
||||
/* determine jx,jv,q0, note that 3>q0 */
|
||||
let jx = nx-1;
|
||||
let mut jv = (e0-3)/24;
|
||||
let jx = nx - 1;
|
||||
let mut jv = (e0 - 3) / 24;
|
||||
if jv < 0 {
|
||||
jv=0;
|
||||
jv = 0;
|
||||
}
|
||||
let mut q0 = e0-24*(jv+1);
|
||||
let mut q0 = e0 - 24 * (jv + 1);
|
||||
let jv = jv as usize;
|
||||
|
||||
/* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
|
||||
let mut j = (jv-jx) as i32;
|
||||
let m = jx+jk;
|
||||
let mut j = (jv - jx) as i32;
|
||||
let m = jx + jk;
|
||||
for i in 0..=m {
|
||||
f[i] = if j<0 {
|
||||
0.
|
||||
} else {
|
||||
IPIO2[j as usize] as f64
|
||||
};
|
||||
f[i] = if j < 0 { 0. } else { IPIO2[j as usize] as f64 };
|
||||
j += 1
|
||||
}
|
||||
|
||||
|
||||
/* compute q[0],q[1],...q[jk] */
|
||||
for i in 0..=jk {
|
||||
fw = 0f64;
|
||||
for j in 0..=jx {
|
||||
fw += x[j]*f[jx+i-j];
|
||||
fw += x[j] * f[jx + i - j];
|
||||
}
|
||||
q[i] = fw;
|
||||
}
|
||||
|
||||
|
||||
let mut jz = jk;
|
||||
|
||||
|
||||
'recompute: loop {
|
||||
/* distill q[] into iq[] reversingly */
|
||||
let mut i = 0i32;
|
||||
z = q[jz];
|
||||
for j in (1..=jz).rev() {
|
||||
fw = (x1p_24*z) as i32 as f64;
|
||||
iq[i as usize] = (z - x1p24*fw) as i32;
|
||||
z = q[j-1]+fw;
|
||||
fw = (x1p_24 * z) as i32 as f64;
|
||||
iq[i as usize] = (z - x1p24 * fw) as i32;
|
||||
z = q[j - 1] + fw;
|
||||
i += 1;
|
||||
}
|
||||
|
||||
|
||||
/* compute n */
|
||||
z = scalbn(z, q0); /* actual value of z */
|
||||
z -= 8.0*floor(z*0.125); /* trim off integer >= 8 */
|
||||
n = z as i32;
|
||||
z = scalbn(z, q0); /* actual value of z */
|
||||
z -= 8.0 * floor(z * 0.125); /* trim off integer >= 8 */
|
||||
n = z as i32;
|
||||
z -= n as f64;
|
||||
ih = 0;
|
||||
if q0 > 0 { /* need iq[jz-1] to determine n */
|
||||
i = iq[jz-1] >> (24-q0);
|
||||
if q0 > 0 {
|
||||
/* need iq[jz-1] to determine n */
|
||||
i = iq[jz - 1] >> (24 - q0);
|
||||
n += i;
|
||||
iq[jz-1] -= i << (24-q0);
|
||||
ih = iq[jz-1] >> (23-q0);
|
||||
iq[jz - 1] -= i << (24 - q0);
|
||||
ih = iq[jz - 1] >> (23 - q0);
|
||||
} else if q0 == 0 {
|
||||
ih = iq[jz-1]>>23;
|
||||
ih = iq[jz - 1] >> 23;
|
||||
} else if z >= 0.5 {
|
||||
ih = 2;
|
||||
}
|
||||
|
||||
if ih > 0 { /* q > 0.5 */
|
||||
|
||||
if ih > 0 {
|
||||
/* q > 0.5 */
|
||||
n += 1;
|
||||
let mut carry = 0i32;
|
||||
for i in 0..jz { /* compute 1-q */
|
||||
for i in 0..jz {
|
||||
/* compute 1-q */
|
||||
let j = iq[i];
|
||||
if carry == 0 {
|
||||
if j != 0 {
|
||||
|
|
@ -347,10 +305,15 @@ pub(crate) fn rem_pio2_large(x : &[f64], y : &mut [f64], e0 : i32, prec : usize)
|
|||
iq[i] = 0xffffff - j;
|
||||
}
|
||||
}
|
||||
if q0 > 0 { /* rare case: chance is 1 in 12 */
|
||||
if q0 > 0 {
|
||||
/* rare case: chance is 1 in 12 */
|
||||
match q0 {
|
||||
1 => { iq[jz-1] &= 0x7fffff; },
|
||||
2 => { iq[jz-1] &= 0x3fffff; },
|
||||
1 => {
|
||||
iq[jz - 1] &= 0x7fffff;
|
||||
}
|
||||
2 => {
|
||||
iq[jz - 1] &= 0x3fffff;
|
||||
}
|
||||
_ => {}
|
||||
}
|
||||
}
|
||||
|
|
@ -361,24 +324,26 @@ pub(crate) fn rem_pio2_large(x : &[f64], y : &mut [f64], e0 : i32, prec : usize)
|
|||
}
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
/* check if recomputation is needed */
|
||||
if z == 0. {
|
||||
let mut j = 0;
|
||||
for i in (jk..=jz-1).rev() {
|
||||
for i in (jk..=jz - 1).rev() {
|
||||
j |= iq[i];
|
||||
}
|
||||
if j == 0 { /* need recomputation */
|
||||
if j == 0 {
|
||||
/* need recomputation */
|
||||
let mut k = 1;
|
||||
while iq[jk-k]==0 {
|
||||
k += 1; /* k = no. of terms needed */
|
||||
while iq[jk - k] == 0 {
|
||||
k += 1; /* k = no. of terms needed */
|
||||
}
|
||||
|
||||
for i in (jz+1)..=(jz+k) { /* add q[jz+1] to q[jz+k] */
|
||||
f[jx+i] = IPIO2[jv+i] as f64;
|
||||
|
||||
for i in (jz + 1)..=(jz + k) {
|
||||
/* add q[jz+1] to q[jz+k] */
|
||||
f[jx + i] = IPIO2[jv + i] as f64;
|
||||
fw = 0f64;
|
||||
for j in 0..=jx {
|
||||
fw += x[j]*f[jx+i-j];
|
||||
fw += x[j] * f[jx + i - j];
|
||||
}
|
||||
q[i] = fw;
|
||||
}
|
||||
|
|
@ -389,7 +354,7 @@ pub(crate) fn rem_pio2_large(x : &[f64], y : &mut [f64], e0 : i32, prec : usize)
|
|||
|
||||
break;
|
||||
}
|
||||
|
||||
|
||||
/* chop off zero terms */
|
||||
if z == 0. {
|
||||
jz -= 1;
|
||||
|
|
@ -398,11 +363,12 @@ pub(crate) fn rem_pio2_large(x : &[f64], y : &mut [f64], e0 : i32, prec : usize)
|
|||
jz -= 1;
|
||||
q0 -= 24;
|
||||
}
|
||||
} else { /* break z into 24-bit if necessary */
|
||||
} else {
|
||||
/* break z into 24-bit if necessary */
|
||||
z = scalbn(z, -q0);
|
||||
if z >= x1p24 {
|
||||
fw = (x1p_24*z) as i32 as f64;
|
||||
iq[jz] = (z - x1p24*fw) as i32;
|
||||
fw = (x1p_24 * z) as i32 as f64;
|
||||
iq[jz] = (z - x1p24 * fw) as i32;
|
||||
jz += 1;
|
||||
q0 += 24;
|
||||
iq[jz] = fw as i32;
|
||||
|
|
@ -410,25 +376,25 @@ pub(crate) fn rem_pio2_large(x : &[f64], y : &mut [f64], e0 : i32, prec : usize)
|
|||
iq[jz] = z as i32;
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
/* convert integer "bit" chunk to floating-point value */
|
||||
fw = scalbn(1., q0);
|
||||
for i in (0..=jz).rev() {
|
||||
q[i] = fw*(iq[i] as f64);
|
||||
q[i] = fw * (iq[i] as f64);
|
||||
fw *= x1p_24;
|
||||
}
|
||||
|
||||
|
||||
/* compute PIo2[0,...,jp]*q[jz,...,0] */
|
||||
for i in (0..=jz).rev() {
|
||||
fw = 0f64;
|
||||
let mut k = 0;
|
||||
while (k <= jp) && (k <= jz-i) {
|
||||
fw += PIO2[k]*q[i+k];
|
||||
while (k <= jp) && (k <= jz - i) {
|
||||
fw += PIO2[k] * q[i + k];
|
||||
k += 1;
|
||||
}
|
||||
fq[jz-i] = fw;
|
||||
fq[jz - i] = fw;
|
||||
}
|
||||
|
||||
|
||||
/* compress fq[] into y[] */
|
||||
match prec {
|
||||
0 => {
|
||||
|
|
@ -437,7 +403,7 @@ pub(crate) fn rem_pio2_large(x : &[f64], y : &mut [f64], e0 : i32, prec : usize)
|
|||
fw += fq[i];
|
||||
}
|
||||
y[0] = if ih == 0 { fw } else { -fw };
|
||||
},
|
||||
}
|
||||
1 | 2 => {
|
||||
fw = 0f64;
|
||||
for i in (0..=jz).rev() {
|
||||
|
|
@ -446,38 +412,39 @@ pub(crate) fn rem_pio2_large(x : &[f64], y : &mut [f64], e0 : i32, prec : usize)
|
|||
// TODO: drop excess precision here once double_t is used
|
||||
fw = fw as f64;
|
||||
y[0] = if ih == 0 { fw } else { -fw };
|
||||
fw = fq[0]-fw;
|
||||
fw = fq[0] - fw;
|
||||
for i in 1..=jz {
|
||||
fw += fq[i];
|
||||
}
|
||||
y[1] = if ih == 0 { fw } else { -fw };
|
||||
},
|
||||
3 => { /* painful */
|
||||
}
|
||||
3 => {
|
||||
/* painful */
|
||||
for i in (1..=jz).rev() {
|
||||
fw = fq[i-1]+fq[i];
|
||||
fq[i] += fq[i-1]-fw;
|
||||
fq[i-1] = fw;
|
||||
fw = fq[i - 1] + fq[i];
|
||||
fq[i] += fq[i - 1] - fw;
|
||||
fq[i - 1] = fw;
|
||||
}
|
||||
for i in (2..=jz).rev() {
|
||||
fw = fq[i-1]+fq[i];
|
||||
fq[i] += fq[i-1]-fw;
|
||||
fq[i-1] = fw;
|
||||
fw = fq[i - 1] + fq[i];
|
||||
fq[i] += fq[i - 1] - fw;
|
||||
fq[i - 1] = fw;
|
||||
}
|
||||
fw = 0f64;
|
||||
for i in (2..=jz).rev() {
|
||||
fw += fq[i];
|
||||
}
|
||||
if ih==0 {
|
||||
y[0] = fq[0];
|
||||
y[1] = fq[1];
|
||||
y[2] = fw;
|
||||
if ih == 0 {
|
||||
y[0] = fq[0];
|
||||
y[1] = fq[1];
|
||||
y[2] = fw;
|
||||
} else {
|
||||
y[0] = -fq[0];
|
||||
y[1] = -fq[1];
|
||||
y[2] = -fw;
|
||||
}
|
||||
},
|
||||
_ => { unreachable!() }
|
||||
}
|
||||
_ => unreachable!(),
|
||||
}
|
||||
n & 7
|
||||
}
|
||||
|
|
|
|||
|
|
@ -2,40 +2,42 @@ use super::rem_pio2_large;
|
|||
|
||||
use core::f64;
|
||||
|
||||
const TOINT : f64 = 1.5 / f64::EPSILON;
|
||||
const TOINT: f64 = 1.5 / f64::EPSILON;
|
||||
|
||||
/// 53 bits of 2/pi
|
||||
const INV_PIO2 : f64 = 6.36619772367581382433e-01; /* 0x3FE45F30, 0x6DC9C883 */
|
||||
const INV_PIO2: f64 = 6.36619772367581382433e-01; /* 0x3FE45F30, 0x6DC9C883 */
|
||||
/// first 25 bits of pi/2
|
||||
const PIO2_1 : f64 = 1.57079631090164184570e+00; /* 0x3FF921FB, 0x50000000 */
|
||||
const PIO2_1: f64 = 1.57079631090164184570e+00; /* 0x3FF921FB, 0x50000000 */
|
||||
/// pi/2 - pio2_1
|
||||
const PIO2_1T : f64 = 1.58932547735281966916e-08; /* 0x3E5110b4, 0x611A6263 */
|
||||
const PIO2_1T: f64 = 1.58932547735281966916e-08; /* 0x3E5110b4, 0x611A6263 */
|
||||
|
||||
/// Return the remainder of x rem pi/2 in *y
|
||||
///
|
||||
/// use double precision for everything except passing x
|
||||
/// use __rem_pio2_large() for large x
|
||||
#[inline]
|
||||
pub(crate) fn rem_pio2f(x : f32) -> (i32, f64) {
|
||||
pub(crate) fn rem_pio2f(x: f32) -> (i32, f64) {
|
||||
let x64 = x as f64;
|
||||
|
||||
let mut tx : [f64; 1] = [0.,];
|
||||
let mut ty : [f64; 1] = [0.,];
|
||||
|
||||
let mut tx: [f64; 1] = [0.];
|
||||
let mut ty: [f64; 1] = [0.];
|
||||
|
||||
let ix = x.to_bits() & 0x7fffffff;
|
||||
/* 25+53 bit pi is good enough for medium size */
|
||||
if ix < 0x4dc90fdb { /* |x| ~< 2^28*(pi/2), medium size */
|
||||
if ix < 0x4dc90fdb {
|
||||
/* |x| ~< 2^28*(pi/2), medium size */
|
||||
/* Use a specialized rint() to get fn. Assume round-to-nearest. */
|
||||
let f_n = x64*INV_PIO2 + TOINT - TOINT;
|
||||
return (f_n as i32, x64 - f_n*PIO2_1 - f_n*PIO2_1T);
|
||||
let f_n = x64 * INV_PIO2 + TOINT - TOINT;
|
||||
return (f_n as i32, x64 - f_n * PIO2_1 - f_n * PIO2_1T);
|
||||
}
|
||||
if ix>=0x7f800000 { /* x is inf or NaN */
|
||||
return (0, x64-x64);
|
||||
if ix >= 0x7f800000 {
|
||||
/* x is inf or NaN */
|
||||
return (0, x64 - x64);
|
||||
}
|
||||
/* scale x into [2^23, 2^24-1] */
|
||||
let sign = (x.to_bits() >> 31) != 0;
|
||||
let e0 = ((ix>>23) - (0x7f+23)) as i32; /* e0 = ilogb(|x|)-23, positive */
|
||||
tx[0] = f32::from_bits(ix - (e0<<23) as u32) as f64;
|
||||
let e0 = ((ix >> 23) - (0x7f + 23)) as i32; /* e0 = ilogb(|x|)-23, positive */
|
||||
tx[0] = f32::from_bits(ix - (e0 << 23) as u32) as f64;
|
||||
let n = rem_pio2_large(&tx, &mut ty, e0, 0);
|
||||
if sign {
|
||||
return (-n, -ty[0]);
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue