math #

Description:

math provides commonly used mathematical functions for trigonometry, logarithms, etc.

fn abs[T](a T) T

abs returns the absolute value of a

fn acos(x f64) f64

acos returns the arccosine, in radians, of x.

special case is: acos(x) = nan if x < -1 or x > 1

fn acosh(x f64) f64

fn alike(a f64, b f64) bool

alike checks if a and b are equal

fn angle_diff(radian_a f64, radian_b f64) f64

angle_diff calculates the difference between angles in radians

fn aprox_cos(a f64) f64

aprox_cos returns an approximation of sin(a) made using lolremez

fn aprox_sin(a f64) f64

aprox_sin returns an approximation of sin(a) made using lolremez

fn asin(x_ f64) f64

asin returns the arcsine, in radians, of x.

special cases are: asin(±0) = ±0 asin(x) = nan if x < -1 or x > 1

fn asinh(x f64) f64

asinh returns the area hyperbolic sine of x

fn atan(x f64) f64

atan returns the arctangent, in radians, of x.

special cases are: atan(±0) = ±0 atan(±inf) = ±pi/2.0

fn atan2(y f64, x f64) f64

atan2 returns the arc tangent of y/x, using the signs of the two to determine the quadrant of the return value.

special cases are (in order): atan2(y, nan) = nan atan2(nan, x) = nan atan2(+0, x>=0) = +0 atan2(-0, x>=0) = -0 atan2(+0, x<=-0) = +pi atan2(-0, x<=-0) = -pi atan2(y>0, 0) = +pi/2.0 atan2(y<0, 0) = -pi/2.0 atan2(+inf, +inf) = +pi/4 atan2(-inf, +inf) = -pi/4 atan2(+inf, -inf) = 3pi/4 atan2(-inf, -inf) = -3pi/4 atan2(y, +inf) = 0 atan2(y>0, -inf) = +pi atan2(y<0, -inf) = -pi atan2(+inf, x) = +pi/2.0 atan2(-inf, x) = -pi/2.0

fn atanh(x f64) f64

atanh returns the area hyperbolic tangent of x

fn cbrt(a f64) f64

cbrt returns the cube root of a.

special cases are: cbrt(±0) = ±0 cbrt(±inf) = ±inf cbrt(nan) = nan

fn ceil(x f64) f64

ceil returns the least integer value greater than or equal to x.

special cases are: ceil(±0) = ±0 ceil(±inf) = ±inf ceil(nan) = nan

fn clamp(x f64, a f64, b f64) f64

clamp returns x constrained between a and b

fn close(a f64, b f64) bool

close checks if a and b are within 1e-14 of each other

fn copysign(x f64, y f64) f64

copysign returns a value with the magnitude of x and the sign of y

fn cos(x f64) f64

cos calculates the cosine of the angle in radians

fn cosf(a f32) f32

cosf calculates cosine in radians (float32)

fn cosh(x f64) f64

cosh returns the hyperbolic cosine of x in radians

special cases are: cosh(±0) = 1 cosh(±inf) = +inf cosh(nan) = nan

fn cot(a f64) f64

tan calculates cotangent of a number

fn count_digits(number i64) int

count_digits return the number of digits in the number passed.
Number argument accepts any integer type (i8|i16|int|isize|i64) and will be cast to i64

fn degrees(radians f64) f64

degrees converts from radians to degrees.

fn digits(num i64, params DigitParams) []int

You can also use it, with an explicit reverse: true parameter, (it will do a reverse of the result array internally => slower):

assert math.digits(12345, base: 10) == [5,4,3,2,1]

assert math.digits(12345, reverse: true) == [1,2,3,4,5]

fn egcd(a i64, b i64) (i64, i64, i64)

egcd returns (gcd(a, b), x, y) such that |ax + by| = gcd(a, b)

fn erf(a f64) f64

erf returns the error function of x.

special cases are: erf(+inf) = 1 erf(-inf) = -1 erf(nan) = nan

fn erfc(a f64) f64

erfc returns the complementary error function of x.

special cases are: erfc(+inf) = 0 erfc(-inf) = 2 erfc(nan) = nan

fn exp(x f64) f64

exp returns e**x, the base-e exponential of x.

special cases are: exp(+inf) = +inf exp(nan) = nan Very large values overflow to 0 or +inf.
Very small values underflow to 1.

fn exp2(x f64) f64

exp2 returns 2**x, the base-2 exponential of x.

special cases are the same as exp.

fn expm1(x f64) f64

expm1 calculates e**x - 1 special cases are: expm1(+inf) = +inf expm1(-inf) = -1 expm1(nan) = nan

fn f32_bits(f f32) u32

f32_bits returns the IEEE 754 binary representation of f, with the sign bit of f and the result in the same bit position.
f32_bits(f32_from_bits(x)) == x.

fn f32_from_bits(b u32) f32

f32_from_bits returns the floating-point number corresponding to the IEEE 754 binary representation b, with the sign bit of b and the result in the same bit position.
f32_from_bits(f32_bits(x)) == x.

fn f64_bits(f f64) u64

f64_bits returns the IEEE 754 binary representation of f, with the sign bit of f and the result in the same bit position, and f64_bits(f64_from_bits(x)) == x.

fn f64_from_bits(b u64) f64

f64_from_bits returns the floating-point number corresponding to the IEEE 754 binary representation b, with the sign bit of b and the result in the same bit position.
f64_from_bits(f64_bits(x)) == x.

fn fabs(x f64) f64

fn factorial(n f64) f64

factorial calculates the factorial of the provided value.

fn factoriali(n int) i64

factoriali returns 1 for n <= 0 and -1 if the result is too large for a 64 bit integer

fn floor(x f64) f64

floor returns the greatest integer value less than or equal to x.

special cases are: floor(±0) = ±0 floor(±inf) = ±inf floor(nan) = nan

fn fmod(x f64, y f64) f64

fmod returns the floating-point remainder of number / denom (rounded towards zero)

fn frexp(x f64) (f64, int)

frexp breaks f into a normalized fraction and an integral power of two.
It returns frac and exp satisfying f == frac × 2**exp, with the absolute value of frac in the interval [½, 1).

special cases are: frexp(±0) = ±0, 0 frexp(±inf) = ±inf, 0 frexp(nan) = nan, 0 pub fn frexp(f f64) (f64, int) { mut y := f64_bits(x) ee := int((y >> 52) & 0x7ff) // special cases if ee == 0 { if x != 0.0 { x1p64 := f64_from_bits(0x43f0000000000000) z,e_ := frexp(x * x1p64) return z,e_ - 64 } return x,0 } else if ee == 0x7ff { return x,0 } e_ := ee - 0x3fe y &= 0x800fffffffffffff y |= 0x3fe0000000000000 return f64_from_bits(y),e_

fn gamma(a f64) f64

gamma returns the gamma function of x.

special ifs are: gamma(+inf) = +inf gamma(+0) = +inf gamma(-0) = -inf gamma(x) = nan for integer x < 0 gamma(-inf) = nan gamma(nan) = nan

fn gcd(a_ i64, b_ i64) i64

gcd calculates greatest common (positive) divisor (or zero if a and b are both zero).

fn get_high_word(f f64) u32

get_high_word returns high part of the word of f.

fn hypot(x f64, y f64) f64

hypot returns the hypotenuse of the triangle give two sides

fn ilog_b(x f64) int

ilog_b returns the binary exponent of x as an integer.

special cases are: ilog_b(±inf) = max_i32 ilog_b(0) = min_i32 ilog_b(nan) = max_i32

fn inf(sign int) f64

inf returns positive infinity if sign >= 0, negative infinity if sign < 0.

fn is_finite(f f64) bool

fn is_inf(f f64, sign int) bool

is_inf reports whether f is an infinity, according to sign.
If sign > 0, is_inf reports whether f is positive infinity.
If sign < 0, is_inf reports whether f is negative infinity.
If sign == 0, is_inf reports whether f is either infinity.

fn is_nan(f f64) bool

is_nan reports whether f is an IEEE 754 ``not-a-number'' value.

fn lcm(a i64, b i64) i64

lcm calculates least common (non-negative) multiple.

fn ldexp(frac f64, exp int) f64

ldexp calculates frac*(2**exp)

fn log(a f64) f64

log returns the logarithm of x

Method : 1. Argument Reduction: find k and f such that x = 2^k * (1+f), where sqrt(2)/2 < 1+f < sqrt(2) .

2. Approximation of log(1+f).
   Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) = 2s + 2/3 s3 + 2/5 s5 + ....., = 2s + sR We use a special Remez algorithm on [0,0.1716] to generate a polynomial of degree 14 to approximate R The maximum error of this polynomial approximation is bounded by 2**-58.45. In other words, 2 4 6 8 10 12 14 R(z) ~ Lg1s +Lg2s +Lg3s +Lg4s +Lg5s +Lg6s +Lg7s (the values of Lg1 to Lg7 are listed in the program) and | 2 14 | -58.45 | Lg1s +...+Lg7s - R(z) | <= 2 | | Note that 2s = f - sf = f - hfsq + shfsq, where hfsq = ff/2.
   In order to guarantee error in log below 1ulp, we compute log by log(1+f) = f - s(f - R) (if f is not too large) log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy)

   3. Finally, log(x) = kln2 + log(1+f).
      = kln2_hi+(f-(hfsq-(s*(hfsq+R)+kln2_lo))) Here ln2 is split into two floating point number: ln2_hi + ln2_lo, where nln2_hi is always exact for |n| < 2000.

Special cases: log(x) is NaN with signal if x < 0 (including -inf) ; log(+inf) is +inf; log(0) is -inf with signal; log(NaN) is that NaN with no signal.

Accuracy: according to an error analysis, the error is always less than 1 ulp (unit in the last place).

fn log10(x f64) f64

log10 returns the decimal logarithm of x.
The special cases are the same as for log.

fn log1p(x f64) f64

log1p returns log(1+x)

fn log2(x f64) f64

log2 returns the binary logarithm of x.
The special cases are the same as for log.

fn log_b(x f64) f64

log_b returns the binary exponent of x.

special cases are: log_b(±inf) = +inf log_b(0) = -inf log_b(nan) = nan

fn log_factorial(n f64) f64

log_factorial calculates the log-factorial of the provided value.

fn log_gamma(x f64) f64

log_gamma returns the natural logarithm and sign (-1 or +1) of Gamma(x).

special ifs are: log_gamma(+inf) = +inf log_gamma(0) = +inf log_gamma(-integer) = +inf log_gamma(-inf) = -inf log_gamma(nan) = nan

fn log_gamma_sign(a f64) (f64, int)

fn log_n(x f64, b f64) f64

log_n returns log base b of x

fn max[T](a T, b T) T

max returns the maximum of a and b

fn maxof[T]() T

maxof returns the maximum value of the type T

fn min[T](a T, b T) T

min returns the minimum of a and b

fn minmax(a f64, b f64) (f64, f64)

minmax returns the minimum and maximum value of the two provided.

fn minof[T]() T

minof returns the minimum value of the type T

fn mod(x f64, y f64) f64

Floating-point mod function.
mod returns the floating-point remainder of x/y.
The magnitude of the result is less than y and its sign agrees with that of x.

special cases are: mod(±inf, y) = nan mod(nan, y) = nan mod(x, 0) = nan mod(x, ±inf) = x mod(x, nan) = nan

fn modf(f f64) (f64, f64)

modf returns integer and fractional floating-point numbers that sum to f. Both values have the same sign as f.

special cases are: modf(±inf) = ±inf, nan modf(nan) = nan, nan

fn nan() f64

nan returns an IEEE 754 ``not-a-number'' value.

fn nextafter(x f64, y f64) f64

nextafter returns the next representable f64 value after x towards y.

special cases are: nextafter(x, x) = x nextafter(nan, y) = nan nextafter(x, nan) = nan

fn nextafter32(x f32, y f32) f32

nextafter32 returns the next representable f32 value after x towards y.

special cases are: nextafter32(x, x) = x nextafter32(nan, y) = nan nextafter32(x, nan) = nan

fn normalize(x f64) (f64, int)

normalize returns a normal number y and exponent exp satisfying x == y × 2**exp. It assumes x is finite and non-zero.

fn pow(x f64, y f64) f64

pow returns base raised to the provided power.

todo(playXE): make this function work on JS backend, probably problem of JS codegen that it does not work.

fn pow10(n int) f64

pow10 returns 10**n, the base-10 exponential of n.

special cases are: pow10(n) = 0 for n < -323 pow10(n) = +inf for n > 308

fn powf(a f32, b f32) f32

powf returns base raised to the provided power. (float32)

fn powi(a i64, b i64) i64

powi returns base raised to power (a**b) as an integer (i64)

special case: powi(a, b) = -1 for a = 0 and b < 0

fn q_rsqrt(x f64) f64

fn radians(degrees f64) f64

radians converts from degrees to radians.

fn round(x f64) f64

round returns the nearest integer, rounding half away from zero.

special cases are: round(±0) = ±0 round(±inf) = ±inf round(nan) = nan

fn round_sig(x f64, sig_digits int) f64

Returns the rounded float, with sig_digits of precision.
i.e assert round_sig(4.3239437319748394,6) == 4.323944

fn round_to_even(x f64) f64

round_to_even returns the nearest integer, rounding ties to even.

special cases are: round_to_even(±0) = ±0 round_to_even(±inf) = ±inf round_to_even(nan) = nan

fn scalbn(x f64, n_ int) f64

scalbn scales x by FLT_RADIX raised to the power of n, returning the same as: scalbn(x,n) = x * FLT_RADIX ** n

fn sign(n f64) f64

sign returns the corresponding sign -1.0, 1.0 of the provided number.
if n is not a number, its sign is nan too.

fn signbit(x f64) bool

signbit returns a value with the boolean representation of the sign for x

fn signi(n f64) int

signi returns the corresponding sign -1.0, 1.0 of the provided number.

fn sin(x f64) f64

sin calculates the sine of the angle in radians

fn sincos(x f64) (f64, f64)

sincos calculates the sine and cosine of the angle in radians

fn sinf(a f32) f32

sinf calculates sine in radians (float32)

fn sinh(x_ f64) f64

sinh calculates hyperbolic sine.

fn sqrt(a f64) f64

special cases are: sqrt(+inf) = +inf sqrt(±0) = ±0 sqrt(x < 0) = nan sqrt(nan) = nan

fn sqrtf(a f32) f32

sqrtf calculates square-root of the provided value. (float32)

fn sqrti(a i64) i64

sqrti calculates the integer square-root of the provided value. (i64)

fn tan(a f64) f64

tan calculates tangent of a number

fn tanf(a f32) f32

tanf calculates tangent. (float32)

fn tanh(x f64) f64

tanh returns the hyperbolic tangent of x.

special cases are: tanh(±0) = ±0 tanh(±inf) = ±1 tanh(nan) = nan

fn tolerance(a f64, b f64, tol f64) bool

tolerance checks if a and b difference are less than or equal to the tolerance value

fn trunc(x f64) f64

trunc returns the integer value of x.

special cases are: trunc(±0) = ±0 trunc(±inf) = ±inf trunc(nan) = nan

fn veryclose(a f64, b f64) bool

veryclose checks if a and b are within 4e-16 of each other

fn with_set_high_word(f f64, hi u32) f64

with_set_high_word sets high word of f to lo

fn with_set_low_word(f f64, lo u32) f64

with_set_low_word sets low word of f to lo

struct DigitParams {
	base    int = 10
	reverse bool
}